url stringlengths 14 1.76k | text stringlengths 100 1.02M | metadata stringlengths 1.06k 1.1k |
|---|---|---|
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=12&t=46240 | ## Writing out equations
LeAirraBullingor2k
Posts: 77
Joined: Wed Mar 13, 2019 12:15 am
### Writing out equations
On questions like problem H3 on the homework this week, I was wondering if there was a specific order we should write our equations in? For example, would it matter if it was SiH4 or H4Si. It's been a minute since I've taken a chemistry class so I cant remember.
Amanda Lin 2I
Posts: 101
Joined: Sat Aug 17, 2019 12:15 am
### Re: Writing out equations
There is an order to the elements in chemical formulas due to the Hill System. Carbon comes first, next is hydrogen, and then it is the rest of the elements alphabetized. There are also exceptions to this rule.
Posts: 51
Joined: Sat Sep 07, 2019 12:19 am
### Re: Writing out equations
Usually when writing the formula for compounds, you write the cation (atom that is positively charged and this is usually a metal) followed by the anion (atom that is negatively charged and this is usually a nonmetal). In the case of SiH4, Si should be written first since it a metal that has a charge of +4 (cation), while hydrogen should come after since it is a nonmetal that has a charge of -1 (anion).
LeAirraBullingor2k
Posts: 77
Joined: Wed Mar 13, 2019 12:15 am
### Re: Writing out equations
In which cases would it be based on charge and when would it just be based on the order?
Arianna Perea 3H
Posts: 50
Joined: Thu Jul 25, 2019 12:17 am
### Re: Writing out equations
Are we expected to know the molecular formulas of certain compounds for the test or will it be given to us?
Nohemi Garcia 1L
Posts: 103
Joined: Fri Aug 02, 2019 12:15 am
### Re: Writing out equations
I think some of the molecular formulas are given to us, such as the "less common ones", whereas compounds like carbon dioxide which are "more common" will not.
Posts: 51
Joined: Sat Sep 07, 2019 12:19 am
### Re: Writing out equations
There is a specific order when writing out chemical formulas. For instance, C6H12O6 (glucose) is never written like H12O6C6. Out of convention, carbon is always the first atom to be listed in chemical formulas and hydrogens are next. Other atoms are listed alphabetically thereafter.
TarynD_1I
Posts: 100
Joined: Sat Aug 24, 2019 12:17 am
### Re: Writing out equations
According to the Hill System, you're supposed to put C carbon first, then Hydrogen, then all the other elements in alphabetical order. But if there is no Carbon the formula, then all the elements are written in alphabetical order.
Posts: 49
Joined: Wed Sep 18, 2019 12:20 am
### Re: Writing out equations
When writing out equations is it always necessary to include the states of matter (if not specified in the problem)? Thank you:)
Jacob Villar 2C
Posts: 105
Joined: Sat Aug 17, 2019 12:18 am
### Re: Writing out equations
The Hill system shows that the order of listing elements starts with carbon atoms, then hydrogen atoms, and then all other atoms in alphabetical order. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8553534746170044, "perplexity": 2633.5027627573018}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703515075.32/warc/CC-MAIN-20210118154332-20210118184332-00654.warc.gz"} |
https://www.physicsforums.com/threads/membrane-potential.198895/ | # Membrane potential
1. Nov 17, 2007
### higherme
1. The problem statement, all variables and given/known data
a biological cell is immersed in a 50mM solution of NaCl at 37C. the cell's membrane is permeable only to Na+ ions. When the system reaches equilibrium, a potential diff of 54.9mV is measured between the inside and the outside of the cell where the inside has the higher( more positive potential.
Calculate [Na+] inside the cell, assuming the amount of Na+ ions transferred is negligible compared to the total amoiunt of Na+ ions in the solution.
Can anyone tell me where to start?
2. Nov 22, 2007
### Gokul43201
Staff Emeritus
Do you know what a concentration cell is?
Similar Discussions: Membrane potential | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8649513721466064, "perplexity": 1958.9656872800686}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541783.81/warc/CC-MAIN-20161202170901-00113-ip-10-31-129-80.ec2.internal.warc.gz"} |
http://www.wgt.com/forums/t/27793.aspx?PageIndex=2 | skip nav
# Forums
#### Any math formulas to find putt distance?
Sun, Feb 23 2020 11:34 PM by AlejBaran. 48 replies.
• pillsy 485 Posts Tue, Nov 9 2010 3:44 PM
hbthree:
For most situations and assuming one is playing what WGT now refers to as "Fast" greens...I add or subtract one foot for every inch the putt is up or down, respectfully. For example if one has a 20 foot putt with 4 inches "up" then I make the shot as a 24 foot putt. If that same 20 foot putt is 4 inches down, then I make the shot as a 16 foot putt.
If one is playing "very fast" greens, I multiply the distance as calulated above by 85% (.85)...if I am playing "slow" greens then I multiply the distance as calculated above by 120% (1.20).
Hope this helps...Harve
I do the same thing regarding elevation change. for very-fast greens i multiply the distance by .85 (like you) and .90 for "fast" greens. tournament speed is usually around .70-.75 and championship is .65. but it depends what course...some greens are faster/slower so pay attention!
• W000T 104 Posts Tue, Nov 9 2010 3:44 PM
mrenn29:
x(3x-y)+ 3/4(3.14+y) hope this helps. lol
No, but it would if you told me what x and y are suppose to be? For all I know it could be: x=cows and y=horses
• mrenn29 380 Posts Fri, Nov 12 2010 9:47 AM
W000T:
mrenn29:
x(3x-y)+ 3/4(3.14+y) hope this helps. lol
No, but it would if you told me what x and y are suppose to be? For all I know it could be: x=cows and y=horses
It was a total joke fellas lol.
• RUSTY40 255 Posts Fri, Nov 12 2010 10:08 AM
Use this....
$\left(E + {e^2\over r} \right)^2 \psi(x) = - \nabla^2\psi(x) + m^2 \psi(x).$
• Richard4168 4,309 Posts Fri, Nov 12 2010 11:04 AM
This is the complete physics on golf. It should answer all your golfing questions. After reading and deciphering all this information, what else is there?
The Physics of Golf
## In order to calculate and produce a realistic ball fight trajectory in the simulator, I had to do quite a bit of research into the physics of golf. Here are some of the aspects that I have taken into account that might be of interest to you.
Dimples on the ball and the Magnus effect
As you probably already know, the dimples on the golf ball are there to give the ball more lift and reduced drag during its flight and therefore increase its carry through the air.
This graph - which was generated by the GGS trajectory calculation routines - shows just what a difference those little dimples actually make to the distance the ball will travel. As you can see, a ball with the appropriate depth dimples and top spin will travel far further than a ball with no dimples at all. Those little dimples actually scope the air on its front and top surface and throw it back behind the ball. This causes turbulence which prevents the pressure behind the ball from falling and thus the pull back effect that would have. It also causes the air-flow above the ball to travel faster and thus the pressure on the ball from the top to be lower than the air pressure below the ball. This pressure difference (i.e. more relative pressure from below than on top) causes the ball to lift and stay in the air for a longer time. This phenomenon is known as the Magnus effect
Drag behind a spinning golf ball with and without dimples
Ball Spin
This pushing and lifting effect is dependent on the top-spin rate of the ball. When the ball is struck properly by a lofted club, the ball will tend to travel or roll up the club-face before it is launched. This causes the ball to anti-clockwise spin at a rate governed by the speed, loft and surface friction of the club head face at impact. Typical ball spin-rates are:
3,600 rpm when hit with a 10° driver (8° launch angle) at a velocity of 134 mph
7,200 rpm when hit with a 5 iron (23° launch angle) at a velocity of 105 mph
10,800 rpm when hit with a 9 iron (45° launch angle) at a velocity of 90 mph
Topping the ball (i.e.. when the bottom of the club-face hits the ball above its center) will cause the ball to spin in the other direction - i.e.. downward - which will cause the ball to dive into the ground.
With really high spin rates the magnus lifting effect will actually increase the ball's rate of climb. The effect is known as blow-up and usually remains the domain of the real hard hitters.
Of course the wind strength and direction will also affect the ball's flight.
Apart from this top and bottom spin around the ball's horizontal axis, there is also the amount of side spin that the ball may have. The side spin is induced by the club hitting the ball with an open or closed face at a path other than 90° to the ball's intended direction.
The Slice
Hitting the ball with an open club-face and a club-path from out to in will cause the ball to spin from left to right. The ball's flight will then curve to the right or 'Slice'.
The Hook
Hitting the ball with a closed club-face and a club-path from in to out will cause the ball to spin from right to left. The ball's flight will then curve to the left or 'Hook'.
Golf ball flight trajectory traces in the GGS system.
From left to right: Pull-hook, pull, pull-slice, straight-hook , straight, straight-slice, push-hook, push and push-slice.
Average Distances
• 3-IRON : 170-190 yds (155-174m)
• 4-IRON : 160-180 yds (146-163m)
• 5-IRON : 150-170 yds (137-155m)
• 6-IRON : 140-160 yds (128-146m)
• 7-IRON : 130-150 yds (119-137m)
• 8-IRON : 120-140 yds (110-128m)
• 9-IRON : 110-130 yds (101-119m)
• Pitching : 90-110 yds (82-101m)
• Sand Wedge: up to 80 yds (73m)
• DRIVER : 200-240 yds (183-219m)
• 3-WOOD : 190-220 yds (174-201m)
• 5-WOOD : 170-190 yds (155-174m)
• 7-WOOD : 160-180 yds (146-165m)
## Calculating Flight Trajectories
Now's the time to put all this physical theory into practice.
### Basic parabolic flight
If a golf ball didn't have any dimples and we neglect any other aerodynamic effects such as drag and wind, then the trajectory calculation is really very simple.
For any given time (t) the distance traveled (x component) is
## x(t) = (Vo cosm)t
and the height (y component) at any given time (t) is
## y(t) = (Vo sinm)) - (gt²)/2
where Vo = initial velocity of ball
g = gravitational acceleration 9.8 m/s/s
m = the launch angle in radians
All simple stuff but unfortunately - for me that is - a golf ball's trajectory is not that simple and thus not that simple to calculate.
First off we've got that Magnus effect (lift on a spinning dimpled ball) to apply. In my system I have used the following formula to estimate the Magnus lift force :
## FL =(dvr4 av 2di²)(2r)
where d = density of air at 60° = 2.37 * 10-³
v = velocity
av = angular velocity in radians per second (if you have spin, n, in rpm, them av = (2pi n)/60
An adapted version of the same formula is also used to determine the force on the x plane (left/right direction) which causes the ball to curve. The vertical and horizontal spin rates of the ball are calculated from the incoming data feed from the sensor mat in the system.
Then we have the wind force and air drag to deal with which acts on all of the 3 dimensions of the flight (x,y,z) whereby
x is the left/right direction/deviation of the ball flight
y is the height
and z the distance traveled ahead
The drag force can be written as:
Fd = -Cdv
Fd = -Cdvx -Cdvy -Cdvz
where Cd is the drag coefficient, v is the velocity of the ball (vx,vy,vz are its components) and the minus sign means that this drag force opposes the ball's motion.
The side view of the trajectory will then look something like this.
Terminal velocity
Due to air resistance a falling golf ball will not continue on accelerating at the rate of 9.8 meters / per second / per second. It will eventually reach a maximum falling velocity dictated by its mass and area. This velocity is known as Terminal Velocity and in the case of a golf ball with a radius of 2.1 cm, an area of 14cm² and a mass of 46 grams, this will be 32 meters per second or 72 mph.
Wind force
Wind force is defined as
Fw = -Cwvw
where Cw is the drag coefficient and vw is the wind speed.
Defining the wind direction as measured by angle y I use the following formulas to determine the x and z components of the wind force on the ball:
Fxw = Fw cos y = -cos y(Cwvw
Fzw = Fw cos y = -sin y (Cwvw)
If there is any side spin on the ball - and there usually is - then the ball will curve in the direction of the spin.
Side wind will, of course, cause the ball to curve in its direction and head or tail wind will affect the ball's carry.
Also of interest is the research work done by P.W. Bearman and J.K. Harvey (P.W. Bearman and J.K. Harvey - Golf ball aerodynamics, Aeronautical Quarterly, pp. 112 - 122, May 1976 ) The following formulas are used to calculate the height, distance, acceleration and velocity of a flying golf ball for any given time t - n=0 to n= (until ball hits ground)
Where:
• p is density of air at sea level = 1.225 kg/m3
• S is on stream surface ( = pi r², r = 20.55 mm) = 1.3267×10-³ m²
• 'm' is mass of the ball = 0.050 kg
• a is the instantaneous angle between the instantaneous velocity and the horizon.
• CD is the drag coefficient, which has the same direction as the instantaneous velocity.
• CL is the lift coefficient, which direction is perpendicular to the instantaneous velocity.
• dt is the time step ('step size'). After every time step the simulation will be recalculated.
• 'x' is the coordinate in the direction of the range.
• 'y' is the coordinate in the direction of the height.
# Collision theory
When the clubface collides with the ball it's total contact time is approximately 0.0005 seconds and the peak force applied to the ball can be as high as 4000 pounds
.
This high force actually compresses the ball at impact.
Due to the elasticity of the ball (compression) and the clubface (Metal woods) the ball will be launched at a higher velocity than that of the club head at impact. Average factors are 1.46 for a driver, 1.30 for a 5 iron and 1.12 for a 9 iron.
i.e. the ball's speed just after impact will be this factor greater than the club head speed
Calculating ball launch velocities
Formulas used to determine this increase in ball velocity are:
vball = ((velc*(1.67))/(1.0+(ball/mass)))
where :
vball = the velocity of the ball
ball = mass of ball
mass = mass of club head
and 1.67 = coefficient of restitution
The coefficient of restitution (1.67)
accounts for momentum loss and the fraction of the energy into a collision that a collision "gives back."
Including the loft of the club the formula is:
vballi = ((cos (loft))^2*(sin(90-loft))*vball
where:
Vballi = Velocity of the ball after impact with a lofted club
vball = ((velc*(1.67))/(1.0+(ball/mass)))
loft = Loft of the club
90-loft = The compliment of the loft of the club
vball = The velocity of the ball determined by the previous formula.
Calculating Spin Rates
The equation 5/7 f v sin 0 is used to calculate the vertical velocity of the ball traveling up the club head face where f is the fraction of speed remaining when the compression of the ball is considered, 0 is the angle of the clubface at impact and v is the velocity of the club head.
To calculate the side spin I use an adapted version of the same formula using the degrees the clubface is open or closed in relation to the club head path.
Knowing the ball velocity and the circumference of the golf ball the theoretical spin rate can be calculated as:
spin rate in rpm = (bv / c) /60
where c = circumference of the golf ball = 0.043m and bv = 5/7 f v sin 0
Both top spin and side spin are used to produce a ratio of the true spin rpm and direction
i.e. if top spin = 3600 rpm at 0° and side spin = 900 rpm at 90° or -90° (left or right) then
ratio = 900:3600 = 0.25
assuming a ratio of 1:1 would result in a spin direction (or axis tilt) of 45°
then spin direction = 45° * 0.25 = 11.25°
Bounce
When the golf ball eventually hits the ground, it will tend to bounce a number of times whereby the height and angle of the bounce is very dependent upon what type of surface it hits.
When the golf ball hits a hard surface like a footpath, then the bounce will be very profound (aprox. 50% of its falling height). However, most of the time it will hit the fairway or the green - hopefully - or maybe in the rough. Here the energy absorbed by this type of surface is very significant and the ball will only bounce a fraction of what it would if it had hit a hard smooth surface.
In my system I have created formulas that take all these factors into account including the deviation the angle of bounce will have on inclined soft surface. This is not the same as on a hard surface like a footpath or hitting a tree trunk. On a hard surface we can say that the angle the bounce flight will be near the angle of impact reversed. However, on a soft(er) surface, because of the energy absorbed, the angle of bounce launch will be more towards the surface angle normal.
# Rolling on inclined planes
After the ball has stopped bouncing and landed it will tend to roll for a certain distance. If the plane is horizontal then the amount of roll can be calculated from its velocity and the friction of the surface.
If, however, the ball lands on an inclined plane, then we have to take into account the force the angle of the plane will have on the ball.
The above formula is used to calculate the force on the ball in the x direction up and down a plane, where mg is the force due to gravity, Ff the opposing force due to friction and ax is the linear acceleration in the x direction. The friction force is equal to us N where u is the coefficient of friction of the surface and N is the normal reaction force between the ball and the plane.
Things start to get a bit complicated - to say the least - when the ball is rolling on a contoured surface like a green. Here I have to make continual calculations and adjustments to the direction and speed of the ball taking into account the momentum the ball has in a certain direction. At each time step I check the slope angle and direction and calculate a curve for the ball to follow depending on the magnitude of the force the slope is exerting on the ball. If, at any following steps this slope changes, I recalculate the curve and apply this to its current path at a rate governed by its current velocity or momentum.
When all the calculations of the flight trajectory, bounce and roll are done, the results are stored in a table. This table contains the 3 dimension (z,x and y) co-ordinates of all the steps and is in turn read by the flight routines. When the system gets the launch (fire) command from the sensor mat and all the club head and clubface angle and velocity data have been read, the system calculates the trajectory and a timer is started to produce timer events at 0.05 second intervals. The timer event handler then reads the next coordinates for the step from the flight trajectory table, removes the image of the ball on the screen at the last step and displays it again at the new position. The 'Trajectory Trail On" feature of the system prevents the system from removing the ball image so the user can see the exact trail of the trajectory. This feature had been switched on for all the screen shots shown on this site.
The above graph shows the distance a ball will roll for a given initial velocity and a given green speed.
The GGS system allows you to vary the graph used in the ball roll calculations from linear to exponential as well as the green speed.
Ball Velocity/Carry Graph for all clubs
You can see and adjust the ball carry for every club and for every ball velocity.
"C makes it easy to shoot yourself in the foot; C++ makes it harder, but when you do it blows your whole leg off."
• RUSTY40 255 Posts Fri, Nov 12 2010 11:58 AM
That just about says it all..Now I get it....
• mohuyu 891 Posts Fri, Nov 12 2010 12:12 PM
Richard4168:
This is the complete physics on golf. It should answer all your golfing questions. After reading and deciphering all this information, what else is there?
The Physics of Golf
## In order to calculate and produce a realistic ball fight trajectory in the simulator, I had to do quite a bit of research into the physics of golf. Here are some of the aspects that I have taken into account that might be of interest to you.
Dimples on the ball and the Magnus effect
As you probably already know, the dimples on the golf ball are there to give the ball more lift and reduced drag during its flight and therefore increase its carry through the air.
This graph - which was generated by the GGS trajectory calculation routines - shows just what a difference those little dimples actually make to the distance the ball will travel. As you can see, a ball with the appropriate depth dimples and top spin will travel far further than a ball with no dimples at all. Those little dimples actually scope the air on its front and top surface and throw it back behind the ball. This causes turbulence which prevents the pressure behind the ball from falling and thus the pull back effect that would have. It also causes the air-flow above the ball to travel faster and thus the pressure on the ball from the top to be lower than the air pressure below the ball. This pressure difference (i.e. more relative pressure from below than on top) causes the ball to lift and stay in the air for a longer time. This phenomenon is known as the Magnus effect
Drag behind a spinning golf ball with and without dimples
Ball Spin
This pushing and lifting effect is dependent on the top-spin rate of the ball. When the ball is struck properly by a lofted club, the ball will tend to travel or roll up the club-face before it is launched. This causes the ball to anti-clockwise spin at a rate governed by the speed, loft and surface friction of the club head face at impact. Typical ball spin-rates are:
3,600 rpm when hit with a 10° driver (8° launch angle) at a velocity of 134 mph
7,200 rpm when hit with a 5 iron (23° launch angle) at a velocity of 105 mph
10,800 rpm when hit with a 9 iron (45° launch angle) at a velocity of 90 mph
Topping the ball (i.e.. when the bottom of the club-face hits the ball above its center) will cause the ball to spin in the other direction - i.e.. downward - which will cause the ball to dive into the ground.
With really high spin rates the magnus lifting effect will actually increase the ball's rate of climb. The effect is known as blow-up and usually remains the domain of the real hard hitters.
Of course the wind strength and direction will also affect the ball's flight.
Apart from this top and bottom spin around the ball's horizontal axis, there is also the amount of side spin that the ball may have. The side spin is induced by the club hitting the ball with an open or closed face at a path other than 90° to the ball's intended direction.
The Slice
Hitting the ball with an open club-face and a club-path from out to in will cause the ball to spin from left to right. The ball's flight will then curve to the right or 'Slice'.
The Hook
Hitting the ball with a closed club-face and a club-path from in to out will cause the ball to spin from right to left. The ball's flight will then curve to the left or 'Hook'.
Golf ball flight trajectory traces in the GGS system.
From left to right: Pull-hook, pull, pull-slice, straight-hook , straight, straight-slice, push-hook, push and push-slice.
Average Distances
• 3-IRON : 170-190 yds (155-174m)
• 4-IRON : 160-180 yds (146-163m)
• 5-IRON : 150-170 yds (137-155m)
• 6-IRON : 140-160 yds (128-146m)
• 7-IRON : 130-150 yds (119-137m)
• 8-IRON : 120-140 yds (110-128m)
• 9-IRON : 110-130 yds (101-119m)
• Pitching : 90-110 yds (82-101m)
• Sand Wedge: up to 80 yds (73m)
• DRIVER : 200-240 yds (183-219m)
• 3-WOOD : 190-220 yds (174-201m)
• 5-WOOD : 170-190 yds (155-174m)
• 7-WOOD : 160-180 yds (146-165m)
## Calculating Flight Trajectories
Now's the time to put all this physical theory into practice.
### Basic parabolic flight
If a golf ball didn't have any dimples and we neglect any other aerodynamic effects such as drag and wind, then the trajectory calculation is really very simple.
For any given time (t) the distance traveled (x component) is
## x(t) = (Vo cosm)t
and the height (y component) at any given time (t) is
## y(t) = (Vo sinm)) - (gt²)/2
where Vo = initial velocity of ball
g = gravitational acceleration 9.8 m/s/s
m = the launch angle in radians
All simple stuff but unfortunately - for me that is - a golf ball's trajectory is not that simple and thus not that simple to calculate.
First off we've got that Magnus effect (lift on a spinning dimpled ball) to apply. In my system I have used the following formula to estimate the Magnus lift force :
## FL =(dvr4 av 2di²)(2r)
where d = density of air at 60° = 2.37 * 10-³
v = velocity
av = angular velocity in radians per second (if you have spin, n, in rpm, them av = (2pi n)/60
An adapted version of the same formula is also used to determine the force on the x plane (left/right direction) which causes the ball to curve. The vertical and horizontal spin rates of the ball are calculated from the incoming data feed from the sensor mat in the system.
Then we have the wind force and air drag to deal with which acts on all of the 3 dimensions of the flight (x,y,z) whereby
x is the left/right direction/deviation of the ball flight
y is the height
and z the distance traveled ahead
The drag force can be written as:
Fd = -Cdv
Fd = -Cdvx -Cdvy -Cdvz
where Cd is the drag coefficient, v is the velocity of the ball (vx,vy,vz are its components) and the minus sign means that this drag force opposes the ball's motion.
The side view of the trajectory will then look something like this.
Terminal velocity
Due to air resistance a falling golf ball will not continue on accelerating at the rate of 9.8 meters / per second / per second. It will eventually reach a maximum falling velocity dictated by its mass and area. This velocity is known as Terminal Velocity and in the case of a golf ball with a radius of 2.1 cm, an area of 14cm² and a mass of 46 grams, this will be 32 meters per second or 72 mph.
Wind force
Wind force is defined as
Fw = -Cwvw
where Cw is the drag coefficient and vw is the wind speed.
Defining the wind direction as measured by angle y I use the following formulas to determine the x and z components of the wind force on the ball:
Fxw = Fw cos y = -cos y(Cwvw
Fzw = Fw cos y = -sin y (Cwvw)
If there is any side spin on the ball - and there usually is - then the ball will curve in the direction of the spin.
Side wind will, of course, cause the ball to curve in its direction and head or tail wind will affect the ball's carry.
Also of interest is the research work done by P.W. Bearman and J.K. Harvey (P.W. Bearman and J.K. Harvey - Golf ball aerodynamics, Aeronautical Quarterly, pp. 112 - 122, May 1976 ) The following formulas are used to calculate the height, distance, acceleration and velocity of a flying golf ball for any given time t - n=0 to n= (until ball hits ground)
Where:
• p is density of air at sea level = 1.225 kg/m3
• S is on stream surface ( = pi r², r = 20.55 mm) = 1.3267×10-³ m²
• 'm' is mass of the ball = 0.050 kg
• a is the instantaneous angle between the instantaneous velocity and the horizon.
• CD is the drag coefficient, which has the same direction as the instantaneous velocity.
• CL is the lift coefficient, which direction is perpendicular to the instantaneous velocity.
• dt is the time step ('step size'). After every time step the simulation will be recalculated.
• 'x' is the coordinate in the direction of the range.
• 'y' is the coordinate in the direction of the height.
# Collision theory
When the clubface collides with the ball it's total contact time is approximately 0.0005 seconds and the peak force applied to the ball can be as high as 4000 pounds
.
This high force actually compresses the ball at impact.
Due to the elasticity of the ball (compression) and the clubface (Metal woods) the ball will be launched at a higher velocity than that of the club head at impact. Average factors are 1.46 for a driver, 1.30 for a 5 iron and 1.12 for a 9 iron.
i.e. the ball's speed just after impact will be this factor greater than the club head speed
Calculating ball launch velocities
Formulas used to determine this increase in ball velocity are:
vball = ((velc*(1.67))/(1.0+(ball/mass)))
where :
vball = the velocity of the ball
ball = mass of ball
mass = mass of club head
and 1.67 = coefficient of restitution
The coefficient of restitution (1.67)
accounts for momentum loss and the fraction of the energy into a collision that a collision "gives back."
Including the loft of the club the formula is:
vballi = ((cos (loft))^2*(sin(90-loft))*vball
where:
Vballi = Velocity of the ball after impact with a lofted club
vball = ((velc*(1.67))/(1.0+(ball/mass)))
loft = Loft of the club
90-loft = The compliment of the loft of the club
vball = The velocity of the ball determined by the previous formula.
Calculating Spin Rates
The equation 5/7 f v sin 0 is used to calculate the vertical velocity of the ball traveling up the club head face where f is the fraction of speed remaining when the compression of the ball is considered, 0 is the angle of the clubface at impact and v is the velocity of the club head.
To calculate the side spin I use an adapted version of the same formula using the degrees the clubface is open or closed in relation to the club head path.
Knowing the ball velocity and the circumference of the golf ball the theoretical spin rate can be calculated as:
spin rate in rpm = (bv / c) /60
where c = circumference of the golf ball = 0.043m and bv = 5/7 f v sin 0
Both top spin and side spin are used to produce a ratio of the true spin rpm and direction
i.e. if top spin = 3600 rpm at 0° and side spin = 900 rpm at 90° or -90° (left or right) then
ratio = 900:3600 = 0.25
assuming a ratio of 1:1 would result in a spin direction (or axis tilt) of 45°
then spin direction = 45° * 0.25 = 11.25°
Bounce
When the golf ball eventually hits the ground, it will tend to bounce a number of times whereby the height and angle of the bounce is very dependent upon what type of surface it hits.
When the golf ball hits a hard surface like a footpath, then the bounce will be very profound (aprox. 50% of its falling height). However, most of the time it will hit the fairway or the green - hopefully - or maybe in the rough. Here the energy absorbed by this type of surface is very significant and the ball will only bounce a fraction of what it would if it had hit a hard smooth surface.
In my system I have created formulas that take all these factors into account including the deviation the angle of bounce will have on inclined soft surface. This is not the same as on a hard surface like a footpath or hitting a tree trunk. On a hard surface we can say that the angle the bounce flight will be near the angle of impact reversed. However, on a soft(er) surface, because of the energy absorbed, the angle of bounce launch will be more towards the surface angle normal.
# Rolling on inclined planes
After the ball has stopped bouncing and landed it will tend to roll for a certain distance. If the plane is horizontal then the amount of roll can be calculated from its velocity and the friction of the surface.
If, however, the ball lands on an inclined plane, then we have to take into account the force the angle of the plane will have on the ball.
The above formula is used to calculate the force on the ball in the x direction up and down a plane, where mg is the force due to gravity, Ff the opposing force due to friction and ax is the linear acceleration in the x direction. The friction force is equal to us N where u is the coefficient of friction of the surface and N is the normal reaction force between the ball and the plane.
Things start to get a bit complicated - to say the least - when the ball is rolling on a contoured surface like a green. Here I have to make continual calculations and adjustments to the direction and speed of the ball taking into account the momentum the ball has in a certain direction. At each time step I check the slope angle and direction and calculate a curve for the ball to follow depending on the magnitude of the force the slope is exerting on the ball. If, at any following steps this slope changes, I recalculate the curve and apply this to its current path at a rate governed by its current velocity or momentum.
When all the calculations of the flight trajectory, bounce and roll are done, the results are stored in a table. This table contains the 3 dimension (z,x and y) co-ordinates of all the steps and is in turn read by the flight routines. When the system gets the launch (fire) command from the sensor mat and all the club head and clubface angle and velocity data have been read, the system calculates the trajectory and a timer is started to produce timer events at 0.05 second intervals. The timer event handler then reads the next coordinates for the step from the flight trajectory table, removes the image of the ball on the screen at the last step and displays it again at the new position. The 'Trajectory Trail On" feature of the system prevents the system from removing the ball image so the user can see the exact trail of the trajectory. This feature had been switched on for all the screen shots shown on this site.
The above graph shows the distance a ball will roll for a given initial velocity and a given green speed.
The GGS system allows you to vary the graph used in the ball roll calculations from linear to exponential as well as the green speed.
Ball Velocity/Carry Graph for all clubs
You can see and adjust the ball carry for every club and for every ball velocity.
"C makes it easy to shoot yourself in the foot; C++ makes it harder, but when you do it blows your whole leg off."
lol I can't believe I quoted that. However interesting it is to read about components of forces, distances and speeds - I doubt Lee Westwood takes any of that into account on the greens.
• Infinito3010 3,689 Posts Fri, Nov 12 2010 12:34 PM
WOW, interesting stuff.
• resozv 893 Posts Fri, Nov 12 2010 12:40 PM
W000T,
try here
• Richard4168 4,309 Posts Sat, Nov 13 2010 7:58 AM
RUSTY40:
That just about says it all..Now I get it....
LOL!!! - Rusty, that response is too funny. I can't stop laughing. This information is a bit complex. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7121147513389587, "perplexity": 1266.9503281340396}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735906.77/warc/CC-MAIN-20200805010001-20200805040001-00093.warc.gz"} |
http://www.gamedev.net/topic/639226-your-preferred-or-desired-brdf/page-3 | • Create Account
# Your preferred or desired BRDF?
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
51 replies to this topic
### #41Hodgman Moderators - Reputation: 44274
Like
0Likes
Like
Posted 26 February 2013 - 08:49 AM
The thing is that it should include the view direction as well, since fresnel's law applies as well, when the light is scattering out of the surface to the viewer's direction and not just when light is scattering into the surface.
When the light leaves the surface back into the air, yes some will reflect off the boundary back into the surface, but seeing as it's an infinitely thick plane with zero absorption (and for simplicity, let's say the same IOR as air), it will eventually all make it back out. The only effect that this will have is to bias the 'diffuse' distribution slightly more towards the normal (as at every 'attempt' for light to escape, this direction has the maximal chance). Light is scattering out of the surface in every direction, not just the viewer's direction, so it's not special.
There's still no reason to take the viewer's position into account when measuring the amount of light that refracts into the plane -- where I'm standing relative to a prism has no bearing on the amount of light that's refracted upon striking it's surface.
d'oh. You need to take the viewers position into account in the exit fresnel equation to measure the amount of diffuse light that is emitted in the direction of the viewer, because that's what I'm measuring. That's pretty damn obvious once I say it out loud... [/edit]
Edited by Hodgman, 01 March 2013 - 06:52 AM.
### #42InvalidPointer Members - Reputation: 1517
Like
0Likes
Like
Posted 27 February 2013 - 09:56 PM
Casting my vote for Kelemen Szirmay-Kalos with normalized Blinn-Phong microfacets. Numerically it's pretty well-behaved, importance samples pretty well and supports some very nifty analytical antialiasing in the form of Toksvig-filtered normal maps. It's also extremely cheap and includes a view-dependent diffuse BRDF for extra credit. I'd like to putz around with the latter, actually; Mark Olano had some interesting ideas on antialiasing diffuse shading and I'd like to try and apply them to a non-Lambertian BRDF if possible. If not, texture space shading is looking increasingly good, especially as triangles get smaller and smaller.
clb: At the end of 2012, the positions of jupiter, saturn, mercury, and deimos are aligned so as to cause a denormalized flush-to-zero bug when computing earth's gravitational force, slinging it to the sun.
### #43Frenetic Pony Members - Reputation: 1970
Like
0Likes
Like
Posted 28 February 2013 - 12:12 AM
Casting my vote for Kelemen Szirmay-Kalos with normalized Blinn-Phong microfacets. Numerically it's pretty well-behaved, importance samples pretty well and supports some very nifty analytical antialiasing in the form of Toksvig-filtered normal maps. It's also extremely cheap and includes a view-dependent diffuse BRDF for extra credit. I'd like to putz around with the latter, actually; Mark Olano had some interesting ideas on antialiasing diffuse shading and I'd like to try and apply them to a non-Lambertian BRDF if possible. If not, texture space shading is looking increasingly good, especially as triangles get smaller and smaller.
Texture space shading could work alright if you're getting a megatexture samples down enough, what did Carmack use as a tile? I can't remember but it would be far too big for these high instruction count BRDF's. But if you could get it down enough, to like a 16x16 tile, maaaybe.
I still just don't see it as likely though, not with something like Toksvig or LEAN mapping as an alternative, at least not with the new consoles admittedly limited compute power versus Moore's law's expectations. There are, to me, more valuable things to spend those resources on.
Also, this is great thread, learning a lot. Off topic here's a thank you for having it.
### #44InvalidPointer Members - Reputation: 1517
Like
0Likes
Like
Posted 28 February 2013 - 09:52 AM
Casting my vote for Kelemen Szirmay-Kalos with normalized Blinn-Phong microfacets. Numerically it's pretty well-behaved, importance samples pretty well and supports some very nifty analytical antialiasing in the form of Toksvig-filtered normal maps. It's also extremely cheap and includes a view-dependent diffuse BRDF for extra credit. I'd like to putz around with the latter, actually; Mark Olano had some interesting ideas on antialiasing diffuse shading and I'd like to try and apply them to a non-Lambertian BRDF if possible. If not, texture space shading is looking increasingly good, especially as triangles get smaller and smaller.
Texture space shading could work alright if you're getting a megatexture samples down enough, what did Carmack use as a tile? I can't remember but it would be far too big for these high instruction count BRDF's. But if you could get it down enough, to like a 16x16 tile, maaaybe.
I still just don't see it as likely though, not with something like Toksvig or LEAN mapping as an alternative, at least not with the new consoles admittedly limited compute power versus Moore's law's expectations. There are, to me, more valuable things to spend those resources on.
Also, this is great thread, learning a lot. Off topic here's a thank you for having it.
Tile size merely controls granularity, virtual texturing is entirely agnostic to resolution. Theoretically you just want texel:pixel density to sit near 1 and can subdivide all you want until you hit that magic number. In practice you'll actually want more than that so you can take advantage of the fancypants texture filtering algorithms your GPU provides, (or just EWA That S**t™ and call it a night) but details ;)
Timothy Lottes also pointed this out, but concepts like LEAN/Toksvig completely stop being useful when triangles start getting smaller than a pixel onscreen and everything turns in to a shimmery mess. In this case, attacking the problem from the perspective of texture-based methods won't do anything; you're actually getting killed by edge/triangle coverage aliasing. Movies currently solve this by taking like 16-64 samples per pixel and we'd essentially need to use MSAA just to get something that doesn't look like crap.
EDIT: Thanks for the GGX tip, will definitely look into this some more.
Edited by InvalidPointer, 28 February 2013 - 09:56 AM.
clb: At the end of 2012, the positions of jupiter, saturn, mercury, and deimos are aligned so as to cause a denormalized flush-to-zero bug when computing earth's gravitational force, slinging it to the sun.
### #45Chris_F Members - Reputation: 2854
Like
0Likes
Like
Posted 28 February 2013 - 05:08 PM
What about selective supersampling to combat specular aliasing?
### #46Frenetic Pony Members - Reputation: 1970
Like
0Likes
Like
Posted 28 February 2013 - 06:57 PM
Casting my vote for Kelemen Szirmay-Kalos with normalized Blinn-Phong microfacets. Numerically it's pretty well-behaved, importance samples pretty well and supports some very nifty analytical antialiasing in the form of Toksvig-filtered normal maps. It's also extremely cheap and includes a view-dependent diffuse BRDF for extra credit. I'd like to putz around with the latter, actually; Mark Olano had some interesting ideas on antialiasing diffuse shading and I'd like to try and apply them to a non-Lambertian BRDF if possible. If not, texture space shading is looking increasingly good, especially as triangles get smaller and smaller.
Texture space shading could work alright if you're getting a megatexture samples down enough, what did Carmack use as a tile? I can't remember but it would be far too big for these high instruction count BRDF's. But if you could get it down enough, to like a 16x16 tile, maaaybe.
I still just don't see it as likely though, not with something like Toksvig or LEAN mapping as an alternative, at least not with the new consoles admittedly limited compute power versus Moore's law's expectations. There are, to me, more valuable things to spend those resources on.
Also, this is great thread, learning a lot. Off topic here's a thank you for having it.
Tile size merely controls granularity, virtual texturing is entirely agnostic to resolution. Theoretically you just want texel:pixel density to sit near 1 and can subdivide all you want until you hit that magic number. In practice you'll actually want more than that so you can take advantage of the fancypants texture filtering algorithms your GPU provides, (or just EWA That S**t™ and call it a night) but details ;)
Timothy Lottes also pointed this out, but concepts like LEAN/Toksvig completely stop being useful when triangles start getting smaller than a pixel onscreen and everything turns in to a shimmery mess. In this case, attacking the problem from the perspective of texture-based methods won't do anything; you're actually getting killed by edge/triangle coverage aliasing. Movies currently solve this by taking like 16-64 samples per pixel and we'd essentially need to use MSAA just to get something that doesn't look like crap.
EDIT: Thanks for the GGX tip, will definitely look into this some more.
Sure virtual texture tile size doesn't matter in hypothesis, in practice you need to get a good balance between searching for new texture tiles all the time and your buffer size and etc.
Plus, the point was texture space shading, which essentially means you are shading an entire tile of a virtual texture, so you can filter and not getting any aliasing, which is essentially just supersampling and my point was that such sounds far too expensive for most games for this (upcoming? need a name) generation. Heck you can go to 1080p with the same shaders as a "current" gen game and you've already doubled your shading costs, going even to say, 16 times that in texture space to get texture space shading is just too costly.
Thanks for pointing out that Toksvig and etc. aren't going to work on sub pixel triangles, hadn't really considered that and I suppose there are going to be cases of having that problem now, especially with faces and other ultra high detail things. Maybe, as Chris F suggested, one could selectively supersample screenspace regions with sub pixel triangles? It still sounds expensive, especially since this thread is a discussion of BDRF's with much higher costs than your typical Blinn/Phong. But if you're getting rid of aliasing anyway, having it pop up on what is assumedly going to be the focus of attention isn't going to do you any good. Maybe you could just go back to vertex shading, since they're smaller than the pixel anyway?
Edited by Frenetic Pony, 28 February 2013 - 06:58 PM.
### #47Chris_F Members - Reputation: 2854
Like
0Likes
Like
Posted 28 February 2013 - 08:06 PM
But if you're getting rid of aliasing anyway, having it pop up on what is assumedly going to be the focus of attention isn't going to do you any good. Maybe you could just go back to vertex shading, since they're smaller than the pixel anyway?
Reyes uses vertex shading combined with micropolygons, but thaw would be suicide on today's GPUs. If your triangles are covering less than 16 pixels, you aren't fully utilizing the rasterizer and you are overshading.
### #48MJP Moderators - Reputation: 15087
Like
0Likes
Like
Posted 28 February 2013 - 08:55 PM
What about selective supersampling to combat specular aliasing?
Supersampling helps reduce aliasing by increasing your sampling rate, but the problem is that the required sampling rate per pixel will shoot up to unrealistic levels as a surface gets further from the camera and/or becomes oblique to the camera. So you won't really solve the aliasing, you'll just make it a little less objectionable.
### #49Hodgman Moderators - Reputation: 44274
Like
4Likes
Like
Posted 28 February 2013 - 10:56 PM
Thanks to this thread, I've found something approaching my desired BRDF
The code is similar to the ones that Chris_F and I posted earlier in the thread:
http://pastebin.com/m7NLvtWk updated [/edit]
Following Disney's example, I've got minimum number of parameters with sensible ranges:
Color -- Used as diffuse color for non-metals, or specular color (F0) for metals.
Specular [0-1] -- The F0 param. From 0.0 to 0.5 are non-metals, with 0.5 being around diamond level shininess. 0.5 to 1.0 are impure metal to pure metal.
Roughness X/Y [0-1] -- 0 is perfectly flat, 0.5 is a lambertian level of roughness, 0.5 to 1.0 are super rough surfaces that appear quite flat and get some diffuse rim highlights.
FacetAngle [0-2Pi] -- rotates the tangent space / roughness X/Y axis. Even though it's an angle parameter, this can be baked into two [-1 to 1] sin(a)/cos(a) parameters.
Retroreflective [0-1] -- bends the specular lobe back towards the light source.
Isotropic (bool) -- if true, sets roughness Y to equal roughness X as an optimization.
These are all lit by a spotlight behind the camera:
The diffuse model is based loosely on a very cheap approximation of Oren-Nayer mixed with the below energy conversation for flat surfaces.
The Retroreflective param works with anisotropy, but does change very slightly with the isotropic bool on/off, and also changes very slightly with helmholtz reciprocity... I've made some small error with it obviously fixed the bug, everything obeys reciprocity now, and the output matches the optimized isotropic code-path when both roughnesses are equal[/edit].
It's pretty expensive though, so I might go with something simpler like what Chris posted earlier (lerping from one distribution to another), unless I find a really good use-case for anisotropic retroreflectors.
I've been having an issue with different Cook-Torrance geometry terms though - most of these BRDF's are modulated by NdotV in some way, with the assumption that this can't be negative, else the fragment wouldn't be visible. However, in actual game scenes, this assumption doesn't hold! Simply picture a cube that's had normals generated without hard-edges / with every face in the same smoothing group (or alternatively, picture a sphere that's been LOD'ed super-aggressively into a cube - same thing). In this case there's a huge number of fragments where NdotV will be negative, but simply cutting off the lighting for these fragments looks really unnatural.
To get around these unnatural cut-offs in my game scenes, I've simply scaled/biased NdotV (and NdotL to maintain reciprocity) into the 0-1 range right before doing the specular calculations, which produces a "wrapped geometry term", instead of one that becomes zero at the horizon...
Has anyone else dealt with this issue?
If your triangles are covering less than 16 pixels, you aren't fully utilizing the rasterizer and you are overshading.
Yeah, the way current GPU's work, sub-pixel sized triangles really should be avoided. On my last game, implementing mesh LODs (which reduced the vertex/triangle count with distance) gave us a huge performance boost in the pixel shader, due to larger triangles being rasterized/shaded more efficiently.
This performance issue can be somewhat mitigated with deferred rendering, as most of your shading is done in screen-space, not directly after rasterization, but you've still got the shimmering quality issue anyway.
I'm guessing we'll need some new hardware support, or have to wait for everyone to start re-implementing the rasterizer in compute shaders, before we see another giant leap in anti-aliasing, closer to something like what REYES does.
Any physics textbook will tell you that you can use Fresnel's law for this, and it won't include the viewer's location at all!
I guess that's the problem. The thing is that it should include the view direction as well, since fresnel's law applies as well, when the light is scattering out of the surface to the viewer's direction and not just when light is scattering into the surface.
Just take a look at section 5.3 in http://disney-animation.s3.amazonaws.com/library/s2012_pbs_disney_brdf_notes_v2.pdf
Their diffuse model is applying their modified fresnel 2 times, once for the view direction and once for the light direction.
Thanks, this was the key to my failure to understand reciprocity...
Once the light has refracted into the perfectly smooth lambertian diffuser (according to NdotL), it's evenly spread over the hemisphere, but the amount of that re-emitted energy that actually escapes towards the viewer does depend on NdotV.
Adding both of these factors does allow you to apply the Fresnel term to a perfectly smooth Lambertian surface and maintain reciprocity...
For anyone interested, a perfectly flat Lambertian surface is quite a bit darker at glancing angles than just the normal NdotL falloff that we see.
//NdotL not included:
float lambert = 1/PI;
float refractedIn = 1-pow(1-dot( N,L), 5);//schlick's approximation of fresnel
float refractedOut = 1-pow(1-dot(N,V), 5);
return vec3( lambert * refractedIn * refractedOut );
However, this model assumes that any of the about-to-be-re-emitted energy that reflects off the surface/air barrier, is absorbed into the surface and lost, meaning the properties of the surface have changed from my original thought experiment. Though at this point I'm happy enough to imagine that there probably is a formula to calculate how much of this internally-reflected energy there is, and what it's extra contribition to the BRDF should be, in such a way that reciprocity is maintained.
Edited by Hodgman, 01 March 2013 - 07:24 AM.
### #50InvalidPointer Members - Reputation: 1517
Like
0Likes
Like
Posted 01 March 2013 - 10:35 PM
I've been having an issue with different Cook-Torrance geometry terms though - most of these BRDF's are modulated by NdotV in some way, with the assumption that this can't be negative, else the fragment wouldn't be visible. However, in actual game scenes, this assumption doesn't hold! Simply picture a cube that's had normals generated without hard-edges / with every face in the same smoothing group (or alternatively, picture a sphere that's been LOD'ed super-aggressively into a cube - same thing). In this case there's a huge number of fragments where NdotV will be negative, but simply cutting off the lighting for these fragments looks really unnatural.
To get around these unnatural cut-offs in my game scenes, I've simply scaled/biased NdotV (and NdotL to maintain reciprocity) into the 0-1 range right before doing the specular calculations, which produces a "wrapped geometry term", instead of one that becomes zero at the horizon...
Has anyone else dealt with this issue?
Kelemen Szirmay-Kalos! Kelemen Szirmay-Kalos! Kelemen Szirmay-Kalos!
Okay, okay, I'll try and add some useful content later on. But seriously, it's designed to be a Cook-Torrance geometry term that doesn't suck. It succeeds.
Edited by InvalidPointer, 01 March 2013 - 10:36 PM.
clb: At the end of 2012, the positions of jupiter, saturn, mercury, and deimos are aligned so as to cause a denormalized flush-to-zero bug when computing earth's gravitational force, slinging it to the sun.
### #51Chris_F Members - Reputation: 2854
Like
1Likes
Like
Posted 02 March 2013 - 02:28 AM
I've been having an issue with different Cook-Torrance geometry terms though - most of these BRDF's are modulated by NdotV in some way, with the assumption that this can't be negative, else the fragment wouldn't be visible. However, in actual game scenes, this assumption doesn't hold! Simply picture a cube that's had normals generated without hard-edges / with every face in the same smoothing group (or alternatively, picture a sphere that's been LOD'ed super-aggressively into a cube - same thing). In this case there's a huge number of fragments where NdotV will be negative, but simply cutting off the lighting for these fragments looks really unnatural.
To get around these unnatural cut-offs in my game scenes, I've simply scaled/biased NdotV (and NdotL to maintain reciprocity) into the 0-1 range right before doing the specular calculations, which produces a "wrapped geometry term", instead of one that becomes zero at the horizon...
Has anyone else dealt with this issue?
Kelemen Szirmay-Kalos! Kelemen Szirmay-Kalos! Kelemen Szirmay-Kalos!
Okay, okay, I'll try and add some useful content later on. But seriously, it's designed to be a Cook-Torrance geometry term that doesn't suck. It succeeds.
The Kelemen Szirmay-Kalos visibility approximation is indeed very handy. My minimalistic Cook-Torrance uses it because it's dirt cheap and gives good results, but it suffers from the same shortcoming as the original Cook-Torrance geometry term, and that is that it does not take the roughness of the surface into account at all.
I'm still not sure about the way retroreflection is being handled. It seems to me that most natural materials display very little in the way of retroreflection, and mostly at grazing angles. This is captured by Oren-Nayar and GGX. Objects with very high levels of retroreflection are synthetic and consist of macroscopic corner reflectors, or similar. It would be nice if these could be modeled more accurately.
Path tracing of a flat surface made up of corner reflectors. L = V = ~45°
Edited by Chris_F, 02 March 2013 - 02:50 AM.
### #52Hodgman Moderators - Reputation: 44274
Like
0Likes
Like
Posted 02 March 2013 - 02:48 AM
Unless I've misread (edit: yes I have), Kelemen doesn't help with that issue, because the geometry factor still becomes zero when N.V becomes zero.
To illustrate, here's my test cube with smoothed normals, something pretty common in low to medium poly game scenes:
And here's how it looks with the Cook-Torrence specular using Smith or Kelemen geometry terms, with and without my dodgey scale/bias hack (the difference in saturation is due to the tone-mapper). This cube is surrounded by directional lights so that there's one at least pointing at each face, yet there's huge black areas, simply because they're apparently not visible (N.V is negative).
N.B. the contribution for each light is still multiplied by the real, unbiased NdotL, so that faces that aren't visible to each light aren't lit by them.
Ah yeah, the Kelemen visibility approximation (without my scale/bias hack) looks like:
But as Chris pointed out, it doesn't take roughness into account, which is a bit disappointing.
Edited by Hodgman, 02 March 2013 - 03:09 AM.
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
PARTNERS | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22009076178073883, "perplexity": 2524.254160995873}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443738087479.95/warc/CC-MAIN-20151001222127-00221-ip-10-137-6-227.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/68020-finding-inverse-function.html | # Thread: Finding the inverse of a function
1. ## Finding the inverse of a function
Hi. For my homework one of the first things I'm supposed to be able to do is find the inverse of
y = (4+e^x)/(4-e^(-x))
I don't get how this is possible. When I try to find the natural log of both sides I end up with
lny = ln(4+e^x) - ln(4-e^x)
There must be some algebra I'm not getting here, because I know there's no log rule that can help me get that X out of the ln
Thanks, the homework is due tomorrow
2. Originally Posted by chubigans
Hi. For my homework one of the first things I'm supposed to be able to do is find the inverse of
y = (4+e^x)/(4-e^(-x))
I don't get how this is possible. When I try to find the natural log of both sides I end up with
lny = ln(4+e^x) - ln(4-e^x)
There must be some algebra I'm not getting here, because I know there's no log rule that can help me get that X out of the ln
Thanks, the homework is due tomorrow
Solve the equation $y=\dfrac{4+e^x}{4-e^{-x}}$ for x. Afterwards swap the variables:
$y=\dfrac{4+e^x}{4-e^{-x}}~\implies~4y-ye^{-x}=4+e^x$ Multiply through by $e^x$
$4ye^x-y=4e^x+e^{2x}~\implies~e^{2x} +4e^x(1-y)+y=0$
This is a quadratic equation in $e^x$:
$e^x=-2(1-y)\pm\sqrt{4(1-y)^2-y}$
Therefore:
$x=\ln\left( 2y-2 + \sqrt{4y^2-9y+4} \right)~\vee~x=\ln\left( 2y-2 - \sqrt{4y^2-9y+4} \right)$
Now swap the variables and you'll get the inverse of the function.
3. Just wanted to say thank you, I can't believe I didn't see that! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7691195011138916, "perplexity": 291.24920994432006}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541142.66/warc/CC-MAIN-20161202170901-00175-ip-10-31-129-80.ec2.internal.warc.gz"} |
http://slideplayer.com/slide/3215944/ | # Polymer Synthesis CHEM 421 Reading (Odian Book): Chapter 1.
## Presentation on theme: "Polymer Synthesis CHEM 421 Reading (Odian Book): Chapter 1."— Presentation transcript:
Polymer Synthesis CHEM 421 Reading (Odian Book): Chapter 1
Polymer Synthesis CHEM 421 Polymer Parameters Chemical structure –Chemical composition and distribution –Sequence length and distribution Molecular weight and distribution Chain isomerism Morphology Topology Additives Cost
Polymer Synthesis CHEM 421 Chemical Composition
Polymer Synthesis CHEM 421 Chemical Composition Infinite chain model notation How best to characterize? Why does sequencing matter? Synthetic approaches? Compositional distribution? Branching? (refer to as topology…)
Polymer Synthesis CHEM 421 Polymer Parameters Chemical structure –Chemical composition and distribution –Sequence length and distribution Molecular weight and distribution Chain isomerism Morphology Topology Additives Cost
Polymer Synthesis CHEM 421 Molecular Weight Property “X” Molecular Weight “X” = tensile strength density Tg etc
Polymer Synthesis CHEM 421 Molecular Weight M n = Σ n i M i Σ niΣ ni M w = Σ w i M i Σ wiΣ wi
Polymer Synthesis CHEM 421 Molecular Weight M n = Σ n i M i Σ niΣ ni M w = Σ w i M i Σ wiΣ wi Populations –Memphis, TN700,000 –Montrose, CO 10,000 –Effingham, IL 12,000 –Freeman, SD 1,500 What is the Average Population? –723,500 ÷ 4 = 180,875 –Of these four cities, the average city population is 180,875 Let’s think about the people… What size city does the average person among these populations live in? –The average person does not live in a town of a population of 180,875… –Most of the people live in a town with a lot more than 180,000 people… –Need a weighted average
Polymer Synthesis CHEM 421 Molecular Weight M n = Σ n i M i Σ niΣ ni M w = Σ w i M i Σ wiΣ wi Populations –Memphis, TN700,000 –Montrose, CO 10,000 –Effingham, IL 12,000 –Freeman, SD 1,500 Weighted average –700,000 ÷ 723,500 = 0.9675 –Take fraction and multiply that by the population of Memphis 0.9675 x 700,000 = 677,263 –Do the same for the others »700,000 x 700,000 / 723,500 = 677,263 » 10,000 x 10,000 / 723,500 = 138 » 12,000 x 12,000 / 723,500 = 199 » 1,500 x 1,500 / 723,500 = 3 677,603 –The average person lives in a city of about 677,600 –More realistic than saying the average person lives in a city of 180,000!
Polymer Synthesis CHEM 421 Molecular Weight What is the significance of the spread? Polydispersity index (PDI) PDI of polypeptides and DNA How does magnitude of MW relate to synthesis? How do you control PDI? M n = Σ n i M i Σ niΣ ni M w = Σ w i M i Σ wiΣ wi
Polymer Synthesis CHEM 421 Molecular Weight Distribution
Polymer Synthesis CHEM 421 Gel Permeation Chromatography What is principle behind GPC? Direct or indirect method? Why so useful? Drawback? Detector Response Elution Volume (mL)
Polymer Synthesis CHEM 421 Time of Flight Mass Spectrometry (TOF-SIMS)
Polymer Synthesis CHEM 421 Time of Flight Mass Spectrometry (TOF-SIMS)
Polymer Synthesis CHEM 421 Time of Flight Mass Spectrometry (TOF-SIMS)
Polymer Synthesis CHEM 421 Polymer Parameters Chemical structure –Chemical composition and distribution –Sequence length and distribution Molecular weight and distribution Chain isomerism Topology Morphology Additives Cost
Polymer Synthesis CHEM 421 Chemical Composition Distribution (CCD) Interplay between CCD and MWD… How to measure? Ramifications? –Catalysis? –Phase separation? –Optical properties? –Degradation rates? –Toxicity? Sequence length distribution
Polymer Synthesis CHEM 421 Polymer Parameters Chemical structure –Chemical composition and distribution –Sequence length and distribution Molecular weight and distribution Chain isomerism Morphology Topology Additives Cost
Polymer Synthesis CHEM 421 Chain Isomerism Regio-isomers Stereo-isomers Geometric isomers Conformational isomers
Polymer Synthesis CHEM 421 Regio-isomers defect
Polymer Synthesis CHEM 421 Regio-isomers
Polymer Synthesis CHEM 421 Regio-isomers | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9207045435905457, "perplexity": 24071.03195063664}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818696696.79/warc/CC-MAIN-20170926212817-20170926232817-00386.warc.gz"} |
https://blackhole12.blogspot.fr/2011/ | ## December 24, 2011
### Your Esoteric Language is Useless
You'd think that programmers would get over these ridiculous language wars. The consensus should be that any one programmer is going to use whatever language they are most comfortable with that gets the job done most efficiently. If someone knows C/C++, C#, and Java, they're probably going to use C++ to write a console game. You can argue that language [x] is terrible because of [x], but the problem is that ALL languages are terrible for one reason or another. Every aspect of a languages design is a series of trade-offs, and if you try to criticize a language that is useful in one context because it isn't useful in another, you are ignoring the entire concept of a trade-off.
These arguments go on for hours upon hours, about what exactly is a trade-off and what languages arguably have stupid features and what makes someone a good programer and blah blah blah blah SHUT UP. I don't care what language you used, if your program is shit, your program is shit. I don't care if you wrote it in Clojure or used MongoDB or used continuations and closures in whatever esoteric functional language happens to be popular right now. Your program still sucks. If someone else writes a better program in C without any elegant use of anything, and it works better than your program, they're doing their job better than you.
I don't care if they aren't as good a programmer as you are, by whatever stupid, arbitrary standards you've invented to make yourself feel better, they're still doing a better job than you. I don't care if your haskell editor was written in haskell. Good for you. It sucks. It is terribly designed. It's workflow is about as conducive as a blob of molasses on a mountain in January. I don't care if you are using a fantastic stack of professionally designed standard libraries instead of re-inventing the wheel. That guy over there re-invented the wheel the wrong way 10 times and his program is better than yours because it's designed with the user in mind instead of a bunch of stupid libraries. I don't care if you're using Mercurial over SVN or Git on Linux using Emacs with a bunch of extensions that make you super productive. Your program still sucks.
I am sick and tired of people judging programmers on a bunch of rules that don't matter. Do you know functional programming? Do you know how to implement a LAMP stack? Obviously you don't use C++ or anything like that, do you?
These programmers have no goddamn idea what they're talking about. But that isn't what concerns me. What concerns me is that programmers are so obsessed over what language is best or what tool is best or what library they should use when they should be more concerned about what their program actually DOES. They get so caught up in building whatever elegant crap they're trying to build they completely forget what the end user experience is, especially when the end user has never used the program before. Just as you are not a slave to your tools, your program is not enslaved to your libraries.
Your program's design should serve the user, not a bunch of data structures.
## December 2, 2011
### The Irrationality of Idiots
If Everyone Else is Such an Idiot, How Come You're Not Rich? - Megan McArdle
I run around calling a whole lot of people and/or things stupid, dump, moronic, or some other variation of idiot. As the above quote exemplifies, saying such things tends to be a bit dangerous, since if everyone else was an idiot, you should be rich as hell. My snarky reaction to that, of course, would be that I'm not rich yet (and even then, "rich" in the sense of the quote is really just a metaphor for success, depending on how you define it for yourself), but in truth there are very specific reasons I call someone an idiot, and they don't necessarily involve actual intelligence.
To me, someone is an idiot if they refuse to argue in a rational manner. If you ignore evidence or use nonsensical reasoning and logical fallacies to support your beliefs, you're an idiot. If you don't like me calling you an idiot, that's just fine, because I acknowledge your existence about as much as I acknowledge the existence of dirty clothes on my bedroom floor. It's only when there is such a pile of dirty laundry lying around that it impedes movement that I really notice and clean it up. In the case of suffocating amounts of stupidity, I usually just go somewhere else. The rest of the time, stupid people can only serve to grudgingly function in a society, not take part in running it. This is because designing and running a society requires rational thinking and logical arguments, or nothing gets done.
I can get really angry about certain things, but I must yield to opinions that have a reasonable basis, if only to acknowledge that I might be wrong, even if I think I'm not. Everything I say or do must have some sort of logical basis, even if it originated from pure intuition. So long as you can poke legitimate holes in an accepted theory, you can hold some pretty crazy opinions that can't be considered illogical, though perhaps still incredibly risky or unlikely.
All the other times I call someone an idiot, I'm usually being lazy when I should really be calling the action idiotic. For example, I can't legitimately call Mark Zuckerberg an idiot. If I call him an idiot, I'm not forming a legitimate opinion, and its probably because he did something that pissed me off and I'm ranting about it, and you are free to ignore my invalid opinion, at least until I clarify that what he did was idiotic, not him. Of course, sometimes people repeatedly do things that are just so mind-bogglingly stupid that it is entirely justified to actually call them a moron, because they are displaying a serious lack of bona fide intelligence. Usually, though, most people are entirely capable of rational thought, but simply do not care enough to exercise it, in which case their idiocy stems from an unwillingness to use rationality, not actual intelligence.
I bring this up, because it seems to be a serious problem. What happens when we lose rationality? People can't compromise anymore, and we get a bunch of stupendously idiotic proposals borne out of ignorance that no longer has to pass through a filter of logical argumentation. All irrational disputes become polarized because neither side is willing to listen to the other, and the emotions that are intrinsically tied to the dispute prevent any meaningful progress from being made. Society breaks down in the face of irrationality because irrationality refuses to acknowledge things like, people are different.
Well gee, that sounds like our current political mess.
I am an aggressive supporter of educational reform, and one of the things that I believe should be taught in schools is not only rational thought and logical arguments, but how rational thought can complement creativity and irrational emotions. We cannot rid ourselves of illogical beliefs, because then we've turned into Vulcans, but we must learn, as a species, when our emotions are appropriate, and when we need to exercise our ability to be rational agents. As it is, we are devolving into a prehistoric mess of irrational demands and opinions that only serve to drag society backwards, just as we begin unlocking the true potential of our technology.
Relevent:
## December 1, 2011
### The Great Mystery of Linear Gradient Lighting
A long, long time ago, in pretty much the same place I'm sitting in right now, I was learning how one would do 2D lighting with soft shadows and discovered the age old adage in 2D graphics: linear gradient lighting looks better than mathematically correct inverse square lighting.
Strange.
I brushed it off as artistic license and perceptual trickery, but over the years, as I dug into advanced lighting concepts, nothing could explain this. It was a mystery. Around the time I discovered microfacet theory I figured it could theoretically be an attempt to approximate non-lambertanian reflectance models, but even that wouldn't turn an exponential curve into a linear one.
This bizarre law even showed up in my 3D lighting experiments. Attempting to invoke the inverse square law would simply result in extremely bright and dark areas and would look absolutely terrible, and yet the only apparent fix I saw anywhere was simply calculating light via linear distance in clear violation of observed light behavior. Everywhere I looked, people calculated light on a linear basis, everywhere, on everything. Was it the equations? Perhaps the equations being used operated on linear light values instead of exponential ones and so only output the correct value if the light was linear? No, that wasn't it. I couldn't figure it out. Years and years and years would pass with this discrepancy left unaccounted for.
A few months ago I noted an article on gamma correction and assumed it was related to color correction or some other post process effect designed to compensate for monitor behavior, and put it as a very low priority research point on my mental to-do-list. No reason fixing up minor brightness problems until your graphics engine can actually render everything properly. Yesterday, though, I happened across a Hacker News posting about learning modern 3D engine programming. Curious if it had anything I didn't already know, I ran through its topics, and found this. Gamma correction wasn't just making the scene brighter to fit with the monitor, it was compensating for the fact that most images are actually already gamma-corrected.
In a nutshell, the brightness of a monitor is exponential, not linear (with a power of about 2.2). The result is that a linear gradient displayed on the monitor is not actually increasing in brightness linearly. Because it's mapped to a curve, it will actually increase in brightness exponentially. This is due to the human visual system processing luminosity on a logarithmic scale. The curve in question is this:
Source: GPU Gems 3 - Chapter 24: The Importance of Being Linear
You can see the effect in this picture, taken from the article I mentioned:
The thing is, I always assumed the top linear gradient was a linear gradient. Sure it looks a little dark, but hey, I suppose that might happen if you're increasing at 25% increments, right? WRONG. The bottom strip is a true linear gradient1. The top strip is a literal assignment of linear gradient RGB values, going from 0 to 62 to 126, etc. While this is, digitally speaking, a mathematical linear gradient, what happens when it gets displayed on the screen? It gets distorted by the CRT Gamma curve seen in the above graph, which makes the end value exponential. The bottom strip, on the other hand, is gamma corrected - it is NOT a mathematical linear gradient. It's values go from 0 to 134 to 185. As a result, when this exponential curve is displayed on your monitor, it's values are dragged down by the exact inverse exponential curve, resulting in a true linear curve. An image that has been "gamma-corrected" in this manner is said to exist in sRGB color space.
The thing is, most images aren't linear. They're actually in the sRGB color space, otherwise they'd look totally wrong when we viewed them on our monitors. Normally, this doesn't matter, which is why most 2D games simply ignore gamma completely. Because all a 2D engine does is take a pixel and display it on the screen without touching it, if you enable gamma correction you will actually over-correct the image and it will look terrible. This becomes a problem with image editing, because digital artists are drawing and coloring things on their monitors and they try to make sure that everything looks good on their monitor. So if an artist were visually trying to make a linear gradient, they would probably make something similar to the already gamma-corrected strip we saw earlier. Because virtually no image editors linearize images when saving (for good reason), the resulting image an artist creates is actually in sRGB color space, which is why only turning on gamma correction will usually simply make everything look bright and washed out, since you are normally using images that are already gamma-corrected. This is actually good thing due to subtle precision issues, but it creates a serious problem when you start trying to do lighting calculations.
The thing is, lighting calculations are linear operations. It's why you use Linear Algebra for most of your image processing needs. Because of this, when I tried to use the inverse-square law for my lighting functions, the resulting value that I was multiplying on to the already-gamma-corrected image was not gamma corrected! In order to do proper lighting, you would have to first linearize the gamma-corrected image, perform the lighting calculation on it, and then re-gamma-correct the end result.
Wait a minute, what did we say the gamma curve value was? It's $x^{2.2}$, so $x^{0.45}$ will gamma-correct the value $x$. But the inverse square law states that the intensity of a light is actually $\frac{1}{x^2}$, so if you were to gamma correct the inverse square law, you'd end up with: ${\bigg(\frac{1}{x^2}}\bigg)^{0.45} = {x^{-2}}^{0.45} = x^{-0.9} ≈ x^{1}$
That's almost linear!2
OH MY GOD
That's it! The reason I saw linear curves all over the place was because it was a rough approximation to gamma correction! The reason linear lighting looks good in a 2D game is because its actually an approximation to a gamma-corrected inverse-square law! Holy shit! Why didn't anyone ever explain this?!3 Now it all makes sense! Just to confirm my findings, I went back to my 3D lighting experiment, and sure enough, after correcting the gamma values, using the inverse square law for the lighting gave correct results! MUAHAHAHAHAHAHA!
For those of you using OpenGL, you can implement gamma correction as explained in the article mentioned above. For those of you using DirectX9 (not 10), you can simply enable D3DSAMP_SRGBTEXTURE on whichever texture stages are using sRGB textures (usually only the diffuse map), and then enable D3DRS_SRGBWRITEENABLE during your drawing calls (a gamma-correction stateblock containing both of those works nicely). For things like GUI, you'll probably want to bypass the sRGB part. Like OpenGL, you can also skip D3DRS_SRGBWRITEENABLE and simply gamma-correct the entire blended scene using D3DCAPS3_LINEAR_TO_SRGB_PRESENTATION in the Present() call, but this has a lot of caveats attached. In DirectX10, you no longer use D3DSAMP_SRGBTEXTURE. Instead, you use an sRGB texture format (see this presentation for details).
1 or at least much closer, depending on your monitors true gamma response
2 In reality I'm sweeping a whole bunch of math under the table here. What you really have to do is move the inverse square curve around until it overlaps the gamma curve, then apply it, and you'll get something that is roughly linear.
3 If this is actually standard course material in a real graphics course, and I am just really bad at finding good tutorials, I apologize for the palm hitting your face right now.
## November 24, 2011
### Signed Integers Considered Stupid (Like This Title)
Unrelated note: If you title your article "[x] considered harmful", you are a horrible person with no originality. Stop doing it.
Signed integers have always bugged me. I've seen quite a bit of signed integer overuse in C#, but it is most egregious when dealing with C/C++ libraries that, for some reason, insist on using for(int i = 0; i < 5; ++i). Why would you ever write that? i cannot possibly be negative and for that matter shouldn't be negative, ever. Use for(unsigned int i = 0; i < 5; ++i), for crying out loud.
But really, that's not a fair example. You don't really lose anything using an integer for the i value there because its range isn't large enough. The places where this become stupid are things like using an integer for height and width, or returning a signed integer count. Why on earth would you want to return a negative count? If the count fails, return an unsigned -1, which is just the maximum possible value for your chosen unsigned integral type. Of course, certain people seem to think this is a bad idea because then you will return the largest positive number possible. What if they interpret that as a valid count and try to allocate 4 gigs of memory? Well gee, I don't know, what happens when you try to allocate -1 bytes of memory? In both cases, something is going to explode, and in both cases, its because the person using your code is an idiot. Neither way is more safe than the other. In fact, signed integers cause far more problems then they solve.
One of the most painfully obvious issues here is that virtually every single architecture in the world uses the two's complement representation of signed integers. When you are using two's complement on an 8-bit signed integer type (a char in C++), the largest positive value is 127, and the largest negative value is -128. That means a signed integer can represent a negative number so large it cannot be represented as a positive number. What happens when you do (char)abs(-128)? It tries to return 128, which overflows back to... -128. This is the cause of a host of security problems, and what's hilarious is that a lot of people try to use this to fuel their argument that you should use C# or Java or Haskell or some other esoteric language that makes them feel smart. The fact is, any language with fixed size integers has this problem. That means C# has it, Java has it, most languages have it to some degree. This bug doesn't mean you should stop using C++, it means you need to stop using signed integers in places they don't belong. Observe the following code:
if (*p == '*')
{
++p;
total_width += abs (va_arg (ap, int));
}
This is retarded. Why on earth are you interpreting an argument as a signed integer only to then immediately call abs() on it? So a brain damaged programmer can throw in negative values and not blow things up? If it can only possibly be valid when it is a positive number, interpret it as a unsigned int. Even if someone tries putting in a negative number, they will serve only to make the total_width abnormally large, instead of potentially putting in -128, causing abs() to return -128 and creating a total_width that is far too small, causing a buffer overflow and hacking into your program. And don't go declaring total_width as a signed integer either, because that's just stupid. Using an unsigned integer here closes a potential security hole and makes it even harder for a dumb programmer to screw things up1.
I can only attribute the vast overuse of int to programmer laziness. unsigned int is just too long to write. Of course, that's what typedef's are for, so that isn't an excuse, so maybe they're worried a programmer won't understand how to put a -1 into an unsigned int? Even if they didn't, you could still cast the int to an unsigned int to serve the same purpose and close the security hole. I am simply at a loss as to why I see int's all over code that could never possibly be negative. If it could never possibly be negative, you are therefore assuming that it won't be negative, so it's a much better idea to just make it impossible for it to be negative instead of giving hackers 200 possible ways to break your program.
1 There's actually another error here in that total_width can overflow even when unsigned, and there is no check for that, but that's beyond the scope of this article.
## November 7, 2011
### Why Kids Hate Math
They're teaching it wrong.
And I don't just mean teaching the concepts incorrectly (although they do plenty of that), I mean their teaching priorities are completely backwards. Set Theory is really fun. Basic Set Theory can be taught to someone without them needing to know how to add or subtract. We teach kids Venn Diagrams but never teach them all the fun operators that go with them? Why not? You say they won't understand? Bullshit. If we can teach third graders binary, we can teach them set theory. We take forever to get around to teaching algebra to kids, because its considered difficult. If something is a difficult conceptual leap, then you don't want to delay it, you want to introduce the concepts as early as possible. I say start teaching kids algebra once they know basic arithmetic. They don't need to know how to do crazy weird stuff like x * x = x² (they don't even know what ² means), but you can still introduce them to the idea of representing an unknown value with x. Then you can teach them exponentiation and logs and all those other operators first in the context of numbers, and then in the context of unknown variables. Then algebra isn't some scary thing that makes all those people who don't understand math give up, its something you simply grow up with.
In a similar manner, what the hell is with all those trig identities? Nobody memorizes those things! You memorize like, 2 or 3 of them, and almost only ever use sin² + cos² = 1. In a similar fashion, nobody ever uses integral trig identities because if you are using them you should have converted your coordinate system to polar coordinates, and if you can't do that then you can just look them up for crying out loud. Factoring and completing the square can be useful, but forcing students to do these problems over and over when they almost never actually show up in anything other than spoon-fed equations is insane.
Partial Fractions, on the other hand, are awesome and fun and why on earth are they only taught in intermediate calculus?! Kids are ALWAYS trying to pull apart fractions like that, and we always tell them to not do it - why not just teach them the right way to do it? By the time they finally got around to teaching me partial fractions, I was thinking that it would be some horrifically difficult, painful, complex process. It isn't. You just have to follow a few rules and then 0 out some functions. How can that possibly be harder than learning the concept of differentiation? And its useful too!
Lets say we want to teach someone basic calculus. How much do they need to know? They need to know addition, subtraction, division, multiplication, fractions, exponentiation, roots, algebra, limits, and derivatives. You could teach someone calculus without them knowing what sine and cosine even are. You could probably argue that, with proper teaching, calculus would be about as hard, or maybe a little harder, than trigonometry. Trigonometry, by the way, has an inordinate amount of time spent on it. Just tell kids how right triangles work, sine/cosine/tangent, SOHCAHTOA, a few identities, and you're good. You don't need to know scalene and isosceles triangles. Why do we even have special names for them? Who gives a shit if a triangle has sides of the same length? Either its a right triangle and its useful or its not a right triangle and you have to do some crazy sin law shit that usually means your algorithm is just wrong and so the only time you ever actually need to use it you can just look up the formula because it is a obtuse edge case that almost never comes up.
Think about that. We're grading kids by asking them to solve edge cases that never come up in reality and grading how well they are in math based off of that. And then we're confused when they complain about math having no practical application? Well duh. The sheer amount of time spent on useless topics is staggering. Calculus should be taught to high school freshman. Differential equations and complex analysis go to the seniors, and by the time you get into college you're looking at combinatorics and vector analysis, not basic calculus.
I have already seen some heavily flawed arguments against this. Some people say that people aren't interested in math, so this will never work. Since I'm saying that teaching kids advanced concepts early on will make them interested in math, this is a circular argument and invalid. Other people claim that the kids will never understand because of some bullshit about needing logical constructs, which just doesn't make sense because you should still introduce the concepts. Introducing a concept early on and having the student be confused about it is a good thing because it means they'll try to work it out over time. The more time you give them, the more likely it will click. Besides, most students aren't understanding algebra with the current system anyway, so I fail to see the point of that argument. It's not working now so don't try to change it or you'll make it worse? That's just pathetic.
TL;DR: Stop teaching kids stupid, pointless math they won't need and maybe they won't rightfully conclude that what they are being taught is useless.
## September 23, 2011
### Don't Work on Someone Else's Dream
When I complain to my friends about a recent spat of not being productive, they often remind me of the occasional 10 hours I spend forgetting to eat while hunting down a bug. When introducing myself, I am always clear that, most of the time, I am either busy, or trying to be busy. Everything to me is work, everything that makes me proud of myself is work, everything in my future will, hopefully, be more work. The entire concept of retiring to me is madness. I never want to stop working.
This is often mistaken as an unhealthy obsession with work, which is not entirely true. I am not torturing myself every day for 10 hours just so I can prove myself, I'm doing exactly what I want to do. I'm 21 years old, I can drink and smoke (but never do), I can drive (but I take the bus anyway), I go to college (but rarely attend classes), and in general am supposed to be an adult. Most people my age are finishing college and inevitably taking low paying jobs while they search for another low paying internship at a company so they can eventually get a high paying job that actually uses what they learned in college after they're too old to care.
If I really wanted, I could be at Facebook or Microsoft right now. I even had a high school internship at Microsoft, and probably could have gotten a college one too. I could have spent my time learning all the languages the companies want you to learn, and become incredibly well-versed in everything that everyone else already knows. I could have taught myself proper documentation and proper standards and proper guidelines and kept up my goody two-shoes act for the rest of my fucking life and get congratulated for being such a well-behaved and successful clone.
Fuck that.
I am 21 years old, and I'm going to spend it doing what I like doing, working on the projects I want to work on, and figuring out a way to make a living out of it even if I have to live out of my parents house for another 6 months. I am not going to get a job doing what other people tell me is important. While I am often very critical of myself as a person, realistically speaking, my only regrets are the moments I spent not working, or wasting time on things that weren't important. It doesn't matter that I've been working on a project most people dismiss as a childish fantasy since I was 18. It doesn't matter that I have no income and no normal job and no programming skills that would get me hired at a modern tech company because everyone hates C++ and only cares about web development.
I'm not working on something a CEO thinks is important, I'm working on something I think is important. I'm going to start a company so I can continue to work on what I think is important, and every single employee I will ever hire will work on something they think is important. This doesn't necessarily mean its fun - finding a rogue typecast is anything but fun - but rather its something that you are willing to ride the highs and lows through because it is intrinsically important to you, as a person. You should not wait until you're 35 with a family and a wife to worry about. Do it now. Do whatever is necessary to make it possible for you start working on whatever you think is important and then do it so hard you can make a living out of it.
Don't waste the best 10 years of your life working on someone else's dream.
(don't waste 10 years of your life forgetting to eat, either. That just isn't healthy)
## September 9, 2011
### C# to C++ Tutorial - Part 3: Classes and Structs and Inheritance (OH MY!)
[ 1 · 2 · 3 · 4 · 5 · 6 · 7 ]
Classes in C#, like most object-oriented languages, are very similar to their C++ counterparts. They are declared with class, exist between brackets and inherit classes using a colon ':'. Note, however, that all classes in C++ must end with a semicolon! You will forget this semicolon, and then all the things will break. You can do pretty much everything you can do with a C# class in a C++ class, except that C++ does not have partial classes, and in C++ classes themselves cannot be declared public, protected or private. Both of these features don't exist because they are made irrelevant with how classes are declared in header files.
In C# you usually just have one code file with the class declared in it along with all the code for all the functions. You can just magically use this class everywhere else and everything is fun and happy with rainbows. As mentioned before, C++ uses header files, and they are heavily integrated into the class system. We saw before how in order to use a function somewhere else, its prototype must first be declared in the header file. This applies to both classes and pretty much everything else. You need to understand that unlike C#, C++ does not have magic dust in its compiler. In C++, it just goes down the list of .cpp files, does a bit of dependency optimization, and then simply compiles each .cpp file by taking all the content from all the headers that are included (including all the headers included in the headers) and pasting it before the actual code from the .cpp file, and compiling. This process is repeated separately for every single code file, and no order inconsistencies are allowed anywhere in the code, the headers, or even the order that the headers are included in. The compiler literally takes every single #include statement as it is and simply replaces it with the code of the header it points to, wherever this happens to be in the code. This can (and this has happened to me) result in certain configurations of header files working even though one header file is actually missing a dependency. For example:
//Rainbow.h
class Rainbow
{
Unicorn _unicorns[5]; // 5 unicorns dancing on rainbows
}; // DO NOT FORGET THE SEMICOLON
//Unicorn.h
class Unicorn
{
int magic;
};
//main.cpp
#include "Unicorn.h"
#include "Rainbow.h"
int main(int argc, char *argv[])
{
Rainbow rainbow;
}
Compiling main.cpp will succeed in this case, even though Rainbow.h is referencing the Unicorn class without it ever being declared. The reason behind this is what happens when the compiler expands all the includes. Right before compiling main.cpp (after the preprocessor has run), main.cpp looks like this:
//main.cpp
//Unicorn.h
class Unicorn
{
int magic;
};
//Rainbow.h
class Rainbow
{
Unicorn _unicorns[5]; // 5 unicorns dancing on rainbows
}; // DO NOT FORGET THE SEMICOLON
int main(int argc, char *argv[])
{
Rainbow rainbow;
}
It is now obvious that because Rainbow.h was included after Unicorn.h, the Unicorn reference was resolved since it was declared before Rainbow. However, had we reversed the order of the include files, we would have had an anachronism: an inconsistency in our chronological arrangement. It is very bad practice to construct headers that are dependent on the order in which they are included, so we usually resolve something like this by having Rainbow.h simply include Unicorn.h, and then it won't matter what order they are included in.
//Rainbow.h
#include "Unicorn.h"
class Rainbow
{
Unicorn _unicorns[5]; // 5 unicorns dancing on rainbows
};
Left as is, however, and we run into a problem. Lets try compiling main.cpp:
//main.cpp
#include "Rainbow.h"
#include "Unicorn.h"
int main(int argc, char *argv[])
{
Rainbow rainbow;
}
//main.cpp
//Rainbow.h
#include "Unicorn.h"
class Rainbow
{
Unicorn _unicorns[5]; // 5 unicorns dancing on rainbows
};
//Unicorn.h
class Unicorn
{
int magic;
};
int main(int argc, char *argv[])
{
Rainbow rainbow;
}
//main.cpp
//Rainbow.h
//Unicorn.h
class Unicorn
{
int magic;
};
class Rainbow
{
Unicorn _unicorns[5]; // 5 unicorns dancing on rainbows
};
//Unicorn.h
class Unicorn
{
int magic;
};
int main(int argc, char *argv[])
{
Rainbow rainbow;
}
We've just declared Unicorn twice! Obviously one way to solve this in our very, very simplistic example is to just remove the spurious #include statement, but this violates the unwritten rule of header files - any header file should be able to be included anywhere in any order regardless of what other header files have been included. This means that, first, any header file should include all the header files that it needs to resolve its dependencies. However, as we see here, that simply makes it extremely likely that a header file will get included 2 or 3 or maybe hundreds of times. What we need is an include guard.
//Unicorn.h
#ifndef __UNICORN_H__
#define __UNICORN_H__
class Unicorn
{
int magic;
};
#endif
Understanding this requires knowledge of the C Preprocessor, which is what goes through and processes your code before its compiled. It is very powerful, but right now we only need to know the basics. Any statement starting with # is a preprocessor command. You will notice that #include is itself a preprocessor command, which makes sense, since the preprocessor was replacing those #include's with the code they contained. #define lets you define a constant (or if you want to be technical, an object-like macro). It can be equal to a number or a word or just not be equal to anything and simply be in a defined state. #ifdef and #endif are just an if statement that allows the code inside of it to exist if the given constant is defined. #ifndef simply does the opposite - the code inside only exists if the given constant doesn't exist.
So, what we do is pick a constant name that probably will never be used in anything else, like __UNICORN_H__, and put in a check to see if it is defined. The first time the header is reached, it won't be defined, so the code inside #ifndef will exist. The next line tells the preprocessor to define __UNICORN_H__, the constant we just checked for. That means that the next time this header is included, __UNICORN_H__ will have been defined, and so the code will be skipped over. Observe:
//main.cpp
#include "Rainbow.h"
#include "Unicorn.h"
int main(int argc, char *argv[])
{
Rainbow rainbow;
}
//main.cpp
//Rainbow.h
#include "Unicorn.h"
class Rainbow
{
Unicorn _unicorns[5]; // 5 unicorns dancing on rainbows
};
//Unicorn.h
#ifndef __UNICORN_H__
#define __UNICORN_H__
class Unicorn
{
int magic;
};
#endif
int main(int argc, char *argv[])
{
Rainbow rainbow;
}
//main.cpp
//Rainbow.h
//Unicorn.h
#ifndef __UNICORN_H__
#define __UNICORN_H__
class Unicorn
{
int magic;
};
#endif
class Rainbow
{
Unicorn _unicorns[5]; // 5 unicorns dancing on rainbows
};
//Unicorn.h
#ifndef __UNICORN_H__
#define __UNICORN_H__
class Unicorn
{
int magic;
};
#endif
int main(int argc, char *argv[])
{
Rainbow rainbow;
}
//main.cpp
//Rainbow.h
//Unicorn.h
#ifndef __UNICORN_H__
#define __UNICORN_H__
class Unicorn
{
int magic;
};
#endif
class Rainbow
{
Unicorn _unicorns[5]; // 5 unicorns dancing on rainbows
};
//Unicorn.h
#ifndef __UNICORN_H__
#endif
int main(int argc, char *argv[])
{
Rainbow rainbow;
}
//main.cpp
//Rainbow.h
//Unicorn.h
class Unicorn
{
int magic;
};
class Rainbow
{
Unicorn _unicorns[5]; // 5 unicorns dancing on rainbows
};
//Unicorn.h
int main(int argc, char *argv[])
{
Rainbow rainbow;
}
Our problem is solved! However, note that //Unicorn.h was left in, because it was outside the include guard. It is absolutely critical that you put everything inside your include guard (ignoring comments), or it will either not work properly or be extremely inefficient.
//Rainbow.h
#include "Unicorn.h"
#ifndef __RAINBOW_H__ //WRONG WRONG WRONG WRONG WRONG
#define __RAINBOW_H__
class Rainbow
{
Unicorn _unicorns[5]; // 5 unicorns dancing on rainbows
};
#endif
In this case, the code still compiles, because the include guards prevent duplicate definitions, but its very taxing on the preprocessor that will repeatedly attempt to include Unicorn.h only to discover that it must be skipped over anyway. The preprocessor may be powerful, but it is also very dumb and is easily crippled. The thing is slow enough as it is, so try to keep its workload to a minimum by putting your #include's inside the include guard. Also, don't put semicolons on preprocessor directives. Even though almost everything else in the entire language wants semicolons, semicolons in preprocessor directives will either be redundant or considered a syntax error.
//Rainbow.h
#ifndef __RAINBOW_H__
#define __RAINBOW_H__
#include "Unicorn.h" // SMILES EVERYWHERE!
class Rainbow
{
Unicorn _unicorns[5]; // 5 unicorns dancing on rainbows
};
#endif
Ok, so now we know how to properly use header files, but not how they are used to declare classes. Let's take a class declared in C#, and then transform it into an equivalent prototype in C++.
public class Pegasus : IComparable<Pegasus>
{
private Rainbow rainbow;
protected int magic;
protected bool flying;
const int ID=10;
static int total=0;
const string NAME="Pegasus";
public Pegasus()
{
flying=false;
magic=1;
IncrementTotal();
}
~Pegasus()
{
magic=0;
}
public void Fly()
{
flying=true;
}
private void Land()
{
flying=false;
}
public static string GetName()
{
return NAME;
}
private static void IncrementTotal()
{
++total;
}
public int CompareTo(Pegasus other)
{
return 0;
}
}
class Pegasus : public IComparable<Pegasus>
{
public:
Pegasus();
~Pegasus();
void Fly();
virtual int CompareTo(Pegasus& other);
static const int ID=10;
static int total;
static const char* NAME;
inline static void IncrementTotal() { ++total; }
protected:
int magic;
bool flying;
private:
void Land();
Rainbow rainbow;
};
Immediately, we are introduced to C++'s method of dealing with public, protected and private. Instead of specifying it for each item, they are done in groups. The inheritance syntax is identical, and we've kept the static variables, but now only one of them is being initialized in the class. In C++, you cannot initialize a static variable inside a class unless it is a static const int (or any other integral type). Instead, we will have to initialize total and NAME when we get around to implementing the code for this class. In addition, while most of the functions do not have code, as expected, IncrementTotal does. As an aside, C# does not have static const because it considers it redundant - all constant values are static. C++, however, allows you to declare a const variable that isn't static. While this would be useless in C#, there are certain situations where it is useful in C++.
If a given function's code doesn't have any dependencies unavailable in the header file the class is declared in, you can define that method in the class prototype itself. However, as I mentioned before, code in header files runs the danger of being compiled twice. While the compiler is usually good about properly instancing the class, it is usually a good idea to inline any functions defined in the header. Functions that are inline'd are embedded inside code that calls them instead of being explicitly called. That means instead of pushing arguments on to the stack and returning, the compiler simply embeds the function inside of the code that called it, like so:
#include "Pegasus.h"
// Before compilation
int main(int argc, char *argv[])
{
Pegasus::IncrementTotal()
}
// After compilation
int main(int argc, char *argv[])
{
++Pegasus::total;
}
The consequence of this means that the function itself is never actually instantiated. In fact the function might as well not exist - you won't be able to call it from a DLL because the function was simply embedded everywhere that it was used, kind of like a fancy macro. This neatly solves our issue with code in header files, and will be important later on. This also demonstrates how one accesses static variables and functions in a class. Just like before, the C# method of using . no longer works, you must use the Scope Resolution Operator (::) to access static members and functions of a class. This same operator is what allows us to declare the code elsewhere without confusing the compiler.
//Pegasus.cpp
#include "Pegasus.h"
int Pegasus::total = 0;
const char* Pegasus::NAME = "Pegasus";
Pegasus::Pegasus() : IComparable<Pegasus>(), magic(1), flying(false)
{
IncrementTotal();
}
Pegasus::~Pegasus()
{
magic=0;
}
void Pegasus::Fly()
{
flying=true;
}
void Pegasus::Land()
{
flying=false;
}
string Pegasus::GetName()
{
return NAME;
}
int Pegasus::CompareTo(Pegasus other)
{
return 0;
}
This looks similar to what our C# class looked like, except the functions aren't in the class anymore. Pegasus:: tells the compiler what class the function you are defining belongs in, which allows it to assign the class function prototype to the correct implementation, just like it did with normal functions before. Notice that static is not used when defining GetName() - All function decorations (inline, static, virtual, explicit, etc.) are only allowed on the function prototype. Note that all these rules apply to static variable initialization as well; both total and NAME are resolved using Pegasus:: and don't have the static decorator, only their type. Even though we're using const char* instead of string, you can still initialize a constant value using = "string".
The biggest difference here is in the constructor. In C#, the only things you bother with in the constructor after the colon is either initializing a subclass or calling another constructor. In C++, you can initialize any subclasses you have along with any variables you have, including passing arguments to whatever constructors your variables might have. Most notably is the ability to initialize constant values, which means you can have a constant integer that is set to a value passed through the constructor, or based off a function call from somewhere else. Unfortunately, C++ traditionally does not allow initializing any variables in any sub-classes, nor does it allow calling any of your own constructors. C++0x partially resolves this problem, but it is not fully implemented in VC++ or other modern compilers. This blow, however, is mitigated by default arguments in functions (and by extension, constructors), which allows you to do more with fewer functions.
The order in which variables are constructed is occasionally important if there is an inter-dependency between them. While having such inter-dependencies are generally considered a bad idea, they are sometimes unavoidable, and you can take advantage of a compiler's default behavior of initializing the values in a left to right order. While this behavior isn't technically guaranteed, it is sufficiently reliable for you to take use of it in the occasional exceptional case, but always double-check that the compiler hasn't done crazy optimization in the release version (usually, though, this will just blow the entire program up, so it's pretty obvious).
Now, C# has another datatype, the struct. This is a limited datatype that cannot have a constructor and is restricted to value-types. It is also passed by-value through functions by default, unlike classes. This is very similar to how structs behaved in C, but have no relation to C++'s struct type. In C++, a struct is completely identical to a class in every way, save for one minor detail: all members of a class are private by default, while all members of a struct are public by default. That's it. You can take any class and replace it with struct and the only thing that will change is the default access modifier.
Even though there is no direct analogue to C#'s struct, there is an implicit equivalent. If a class or struct (C++ really doesn't care) meets the requirements of a traditional C struct (no constructor, only basic data types), then it's treated as Plain Old Data, and you are then allowed to skip the constructor and initialize its contents using the special bracket initialization that was touched on before. Yes, you can initialize constant variables using that syntax too.
One thing I've skipped over is the virtual code decorator in the C++ prototype of Pegasus, which is not actually necessary, because the function is already attempting to override another virtual function declared in IComparable, which implicitly makes it virtual. However, in C#, IComparable is implemented as an interface, which is not present in C++. Of course, if you really think about it, an interface is kind of like a normal class, just with all abstract methods (ignore the inheritance issues with this for now). So, we could rewrite the C# implementation of IComparable as a class with abstract methods:
public class IComparable<T>
{
public abstract int CompareTo(T other);
}
As it turns out, this has a direct C++ analogue:
template<class T>
class IComparable
{
public:
virtual int CompareTo(T other)=0;
}
This virtual function, instead of being implemented, has an =0 on the end of it. That makes the function pure virtual, which is just another way of saying abstract. So the C++ version of abstract is a pure virtual function, and a C++ version of interfaces is just a class made entirely out of pure virtual functions. Just as C# prevents you from instantiating an abstract class or interface, C++ considers any class that either declares or inherits pure virtual functions without giving them code as an abstract class that cannot be instantiated. Unfortunately C++ does not have anything like sealed, override, etc., so you are on your own there. Keep in mind that public IComparable<T> could easily be replaced with protected or private for more control.
The reason C# has interfaces at all is because C# only allows you to inherit a single class, regardless of whether or not its abstract. If its got code, you can only inherit it once. Interfaces, however, have no code, and so C# lets you pile them on like candy. This isn't done in C++, because C++ supports multiple inheritance. In C++ you can have any class inherit any other class, no matter what, but you can only instantiate a class if it provides implementations for all pure virtual functions somewhere along its inheritance line. Unfortunately, there are a lot of caveats about multiple inheritance, the most notorious being the Diamond Problem.
Let's say you have a graphics engine that has an Image class, and that image class inherits from an abstract class that holds its position. Obviously, any image on the screen is going to have a position. Then, let's take a physics engine, with a basic object that also inherits from an abstract class that holds its position. Obviously any physics object must have a position. So, what happens when you have a game object that is both an image and a physics object? Since the image and the physics object are in fact the same thing, both of them must have the same position at all times, but both inherit the abstract class storing position separately, resulting in two positions. Which one is the right position? When you call SetPosition, which position are you talking about?
Virtual inheritance was introduced as an attempt to solve this problem. It works by creating a single instance of a derived class for the entire inheritance change, such that both the physics object and the image share the same position, as they are supposed to. Unfortunately, it can't resolve all the ambiguities, and it introduces a whole truckload of new problems. It has a nasty habit of being unable to resolve its own virtual functions properly and introducing all sorts of horrible weirdness. Most incredibly bizarre is a virtually inherited class's constructor - it must be initialized in the last class in the inheritance chain, and is one of the first classes to get its constructor called, regardless of where it might be in the hierarchy. It's destructor order is equally as bizarre. Virtual inheritance is sometimes useful for certain small utility classes that must be shared through a wide variety of situations, like a flag class. As a rule of thumb, you should only use virtual inheritance in a class that either relies on the default constructor or only offers a constructor that takes no arguments, and has no superclasses. This allows you to just slap the virtual keyword on and forget about all the wonky constructor details.
class Pegasus : virtual IComparable<Pegasus>
If you ever think you need to use virtual inheritance on something more complicated, your code is broken and you need to rethink your program's architecture (and the compiler probably won't be able to do it properly anyway). On a side-note, the constructors for any given object are called from the top down. That is, when your object's constructor is called, it immediately calls all the constructors for all it's superclasses, usually before even doing any variable initialization, and then those object constructors immediately call all their superclass constructors, and so on until the first line of code executed in your program is whatever the topmost class was. This then filters down until control is finally returned to your original constructor, such that any constructor code is only executed after all of its base classes have been constructed. The exact reverse happens for destructors, with the lowest class destructor being executed first, and after its finished, the destructors for all its base classes are called, such that a class destructor is always called while all of its base classes still exist.
Hopefully you are familiar with C#'s enum keyword. While it used to be far more limited, it has now been extended to such a degree it is identical to C++, even the syntax is the same. The only difference between the two is that the C++ version can't be declared public, protected or private and needs to have a semicolon on the end (like everything else). Like in C#, enums, classes and structs can be embedded in classes, except in C++ they can also be embedded in structs (because structs are basically classes with a different name). Also, C++ allows you to declare an enum/class/etc. and a variable inside the class at the same time using the following syntax:
class Pegasus
{
enum Count { Uno=2, Dos, Tres, Quatro, Cinco } variable;
enum { Uno=2, Dos, Tres, Quatro, Cinco } var2; //When used to immediately declare a variable, enums can be anonymous
}
//Same as above
class Pegasus
{
enum Count { Uno=2, Dos, Tres, Quatro, Cinco }; //cannot be anonymous
Count variable;
Count var2;
}
Unions are exclusive to C++, and are a special kind of data structure where each element occupies the same address. To understand what that means, let's look at an example:
union //Unions are usually anonymous, but can be named
{
struct { // The anonymity of this struct exposes its internal members.
__int32 low;
__int32 high;
}
__int64 full;
}
union
__int32 and __int64 are simply explicitly declaring 32-bit and 64-bit integers. This union allows us to either set an entire 64-bit integer, or to only set its low or high portion. This happens because the data structure is laid out as follows:
Both low and full are mapped to the exact same place in memory. The only difference is that low is a 32-bit integer, so when you set that to 0, only the first four bytes are set to zero. high is pointing to a location in memory that is exactly 4 bytes in front of low and full. So, if low and full were located at 0x000F810, high would be located at 0x000F814. Setting high to zero sets the last four bytes to zero, but doesn't touch the first four. Consequently, if you set high to 0, reading full would always return the same value as low, since it would essentially be constrained to a 32-bit integer. Unions, however, do not have to have matching memory layouts:
union //Unions are usually anonymous, but can be named
{
char pink[5]
__int32 fluffy;
__int64 unicorns;
}
The layout of this union is:
Any unused space is simply ignored. This same rule would apply for any structs being used to group data. The size of the union is simply the size of its largest member. Setting all 5 elements of pink here would result in fluffy being equal to zero, and only the last 24-bits (or last 3 bytes) of unicorns be untouched. Likewise, setting fluffy to zero would zero out the first 4 elements in pink (indexes 0-3), leaving the 5th untouched. These unions are often used in performance critical areas where a single function must be able to recieve many kinds of data, but will only ever recieve a single group of data at a time, and so it would be more efficient to map all the possible memory configurations to a single data structure that is large enough to hold the largest group. Here is a real world example:
struct __declspec(dllexport) cGUIEvent
{
cGUIEvent() { memset(this,0,sizeof(cGUIEvent)); }
cGUIEvent(unsigned char _evt, const cVecT<int>* mousecoords, unsigned char _button, bool _pressed) : evt(_evt), subevt(0), mousecoords(mousecoords), button(_button), pressed(_pressed) {}
cGUIEvent(unsigned char _evt, const cVecT<int>* mousecoords, unsigned short _scrolldelta) : evt(_evt), subevt(0), mousecoords(mousecoords), scrolldelta(_scrolldelta) {}
union
{
struct
{
unsigned char evt;
unsigned char subevt;
};
unsigned short realevt;
};
union
{
struct { const cVecT<int>* mousecoords; unsigned char button; bool pressed; };
struct { const cVecT<int>* mousecoords; short scrolldelta; };
struct { //the three ctrl/shift/alt bools (plus a held bool) here are compressed into a single byte
bool down;
unsigned char keycode; //only used by KEYDOWN/KEYUP
char ascii; //Only used by KEYCHAR
wchar_t unicode; //Only used by KEYCHAR
char sigkeys;
};
struct { float value; short joyaxis; }; //JOYAXIS
struct { bool down; short joybutton; }; //JOYBUTTON*
};
};
Here, the GUI event is mapped to memory according to the needs of the event that it is representing, without the need for complex inheritance or wasteful memory usage. Unions are indispensable in such scenarios, and as a result are very common in any sort of message handling system.
One strange decorator that has gone unexplained in the above example is the __declspec(dllexport) class decorator. When creating a windows DLL, if you want anything to be usable by something inheriting the DLL, you have to export it. In VC++, this can be done with a module definition file (.def), which is useful if you'll be using GetProcAddress manually, but if you are explicitly linking to a DLL, __declspec(dllexport) automatically exports the function for you when placed on a function. When placed on a class, it automatically exports the entire class. However, for anyone to utilize it, they have to have the header file. This arises to DLLs being distributed as DLLs, linker libraries (.lib), and sets of header files, usually in an "include" directory. In certain cases, only some portions of your DLL will be accessible to the outside, and so you'll want two collections of header files - outside header files and internal ones that no one needs to know about. Consequently, utilizing a large number of C++ DLLs usually involves substantial organization of a whole lot of header files.
Due to the compiler-specific nature of DLL management, they will be covered in Part 6. For now, its on to operator overloading, copy semantics and move semantics!
## September 5, 2011
### The Problem of Vsync
If you were to write directly to the screen when drawing a bouncing circle, you would run into some problems. Because you don't do any buffering, your user might end up with a quarter circle drawn for a frame. This can be solved through Double Buffering, which means you draw the circle on to a backbuffer, then "flip" (or copy) the completed image on to the screen. This means you will only ever send a completely drawn scene to the monitor, but you will still have tearing issues. These are caused by trying to update the monitor outside of its refresh rate, meaning you will have only finished drawing half of your new scene over the old scene in the monitor's video buffer when it updates itself, resulting in half the scanlines on the screen having the new scene and half still having the old scene, which gives the impression of tearing.
This can be solved with Vsync, which only flips the backbuffer right before the screen refreshes, effectively locking your frames per second to the refresh rate (usually 60 Hz or 60 FPS). Unfortunately, Vsync with double buffering is implemented by simply locking up the entire program until the next refresh cycle. In DirectX, this problem is made even worse because the API locks up the program with a 100% CPU polling thread, sucking up an entire CPU core just waiting for the screen to enter a refresh cycle, often for almost 13 milliseconds. So your program sucks up an entire CPU core when 90% of the CPU isn't actually doing anything but waiting around for the monitor.
This waiting introduces another issue - Input lag. By definition any input given during the current frame can only come up when the next frame is displayed. However, if you are using vsync and double buffering, the current frame on the screen was the LAST frame, and the CPU is now twiddling its thumbs until the monitor is ready to display the frame that you have already finished rendering. Because you already rendered the frame, the input now has to wait until the end of the frame being displayed on the screen, at which point the frame that was already rendered is flipped on to the screen and your program finally realizes that the mouse moved. It now renders yet another frame taking into account this movement, but because of Vsync that frame is blocked until the next refresh cycle. This means, if you were to press a key just as a frame was put up on the monitor, you would have two full frames of input lag, which at 60 FPS is 33 ms. I can ping a server 20 miles away with a ping of 21 ms. You might as well be in the next city with that much latency.
There is a solution to this - Triple Buffering. The idea is a standard flip mechanism commonly used in dual-thread lockless synchronization scenarios. With two backbuffers, the application can write to one and once its finished, tell the API and it will mark it for flipping to the front-buffer. Then the application starts drawing on the second, after waiting for any flipping operation to finish, and once its done, marks that for flipping to the front-buffer and starts drawing on the first again. This way, the application can draw 2000 frames a second, but only 60 of those frames actually get flipped on to the monitor using what is essentially a lockless flipping mechanism. Because the application is now effectively rendering 2000 frames per second, there is no more input lag. Problem Solved.
Except not, because DirectX implements Triple Buffering in the most useless manner possible. DirectX just treats the extra buffer as a chain, and rotates through the buffers as necessary. The only advantage this has is that it avoids waiting for the backbuffer copy operation to finish before writing again, which is completely useless in an era where said copy operation would have to be measured in microseconds. Instead, it simply ensures that vsync blocks the program, which doesn't solve the input issue at all.
However, there is a flag, D3DPRESENT_DONOTWAIT, that forces vsync to simply return an error if the refresh cycle isn't available. This would allow us to implement a hack resembling what triple buffering should be like by simply rolling our own polling loop and re-rendering things in the background on the second backbuffer. Problem solved!
Except not. It turns out the Nvidia and Intel don't bother implementing this flag, forcing Vsync to block no matter what you do, and to make matters worse, this feature doesn't have an entry in D3DCAPS9, meaning the DirectX9 API just assumes that it exists, and there is no way to check if it is supported. Of course, don't complain about this to anyone, because of the 50% of people who asked about this who weren't simply ignored, almost all of them were immediately accused of bad profiling, and that the Present() function couldn't possibly be blocking with the flag on. I question the wisdom of people who ignore the fact that the code executed its main loop 2000 times with vsync off and 60 times with it on and somehow come to the conclusion that Present() isn't blocking the code.
Either way, we're kind of screwed now. Absolutely no feature in DirectX actually does what its supposed to do, so there doesn't seem to be a way past this input lag.
There is, however, another option. Clever developers would note that to get around vsync's tendency to eat up CPU cycles like a pig, one could introduce a Sleep() call. So long as you left enough time to render the frame, you could recover a large portion of the wasted CPU. A reliable way of doing this is figuring out how long the last frame took to render, then subtracting that from the FPS you want to enforce and sleep in the remaining time. By enforcing an FPS of something like 80, you give yourself a bit of breathing room, but end up finishing rendering the frame around the same time it would have been presented anyway.
By timing your updates very carefully, you can execute a Sleep() call, then update all the inputs, then render the scene. This allows you to cut down the additional lag time by nearly 50% in ideal conditions, almost completely eliminating excess input lag. Unfortunately, if your game is already rendering at or below 100 FPS, it takes you 10 milliseconds to render a frame, allowing you only 2.5 milliseconds of extra time to look for input, which is of limited usefulness. This illustrates why Intel and Nvidia are unlikely to care about D3DPRESENT_DONOTWAIT - modern games will never render fast enough for substantial input lag reduction.
Remember when implementing the Yield that the amount of time it takes to render the frame should be the time difference between the two render calls, minus the amount of time spent sleeping, minus the amount of time Present() was blocking.
## September 1, 2011
### Musical Genres
As a composer, I have been on the receiving end of a lot of musical criticism - some useful, most ridiculous. I have given out quite a bit of criticism myself, but after discovering that most people aren't interested in brutally honest opinions, I have since avoided it. However, one thing that continues to come up over and over again is someone complaining about Genres.
"This is too fast to be trance."
"This isn't real Drum'n'Bass."
Sometimes people will even slam entire swathes of subgenres, like Ishkur's rant on Epic Trance (and by extension almost anything related to it), literally accusing it as betraying the entire idea of trance: "There must be a word to describe the pain one feels when witnessing (or hearing, rather) something once pure and brilliant completely sold down the river. Sometime in the mid-90s trance decided to drop the technique of slowly introducing complicated layers and building adequate tension over long stretches, replacing them with cutesy little insta-melodies ... The average attention span, way too ritalin-freaked to pay attention to the slow, brooding trance in its original form, liked the anthemic singalong tone of the NEW McTrance, and that's why all you trance crackers are reading this right now. Not because you grew a taste for this super awesome underground music ... But because trance reformed its sound and delivery to suit [YOU]."
This is repeated for something like half the listed subgenres of trance, and in fact the entire trance genre in his "Guide" is just one giant extended rant about how Trance sucks now and it used to be awesome and now we've all ruined it forever.
This kind of stuck-up, bigoted, brain-melting stupidity has grated against my nerves for years, half because I just don't like stupid stuck-up dipshits, but mostly because it is simply wrong.
Genres do not define music. Genres were invented so people could find music similar to songs that they liked. That's all. There are no rules for any genre other than "it should sound kind of like other songs in said genre", and even then it's commonplace to have songs associated with multiple genres. Genres are a categorization system, and nothing else. Many people try and justify their opinions by saying that they're criticizing the classification of the song instead of the song itself, and suggesting that it should be put in some kind of subgenre instead. When the inevitable subgenre usually fails to exist because the composer is being creative like their supposed to, they'll suggest something asinine, like "put it in Miscellaneous, that's what its there for."
Really? Put this obviously heavily drum'n'bass influenced song in Miscellaneous with a bunch of off-the-wall experimental stuff instead of songs that, you know, actually sound like it, just because it doesn't conform to a bunch of imaginary rules you pulled out of your ass to "qualify" the song for the genre? Well why don't we just invent another subgenre? We've only got like a couple hundred of them now, 80% of which are basically the same damn thing. People try to defend their perceived sanctity of genres, but the problem is that its all bullshit. Let's remind ourselves, why do genres exist?
Genres exist so people can find songs that sound similar to music they like. If you have a bajillion subgenres, no one's going to be able to accurately classify every single song into its own little niche, and what's more infuriating is that this misses the point completely. The vast majority of people do not have laser-guided musical tastes. They just listen to whatever the heck music they like. If they're looking for a song, they don't want to have to filter through hundreds of meaningless subgenres, because all they're really looking for is something like, Trance, or maybe Melodic Trance, and that's about as qualifying as you can get while still being useful. Consequently if your song is weird, you are better off picking the closest well-known genre of music that it sounds like and slapping it in there.
And yet, it still doesn't stop. People start throwing on ridiculous prescriptive rules like, a trance song has to be mixable, and to be club friendly you have to have 1 minute of intro with no bass, or it has to be between 116-148 BPM, or you have to use these types of instruments, or you have to do X, or X, or X. Music is art, god damn it, what matters is what a song feels like. If it feels like trance even though its flying along at 166 BPM, and a lot of people who like trance also like that song, then it belongs in trance no matter how much you complain about it. Maybe stick it in "Energy Trance", it kinda gets the idea across, but its still Trance, so who cares, and even then this point is usually moot, because these arguments always come up on websites with either a set list of genres, or one that operates on keywords. In the former case, you can't qualify your genre with anything more than "trance" because the only thing they offer is "Trance" and "Techno". In the latter case, you'll have to tag it with Trance no matter what you do because otherwise no one will ever know your song exists.
Attacking a song because of its perceived genre is the dumbest, most useless criticism you can ever give, unless the artist explicitly states that they are trying for a very specific sound, and even then its rarely a genre and usually more of an abstract concept used across several subgenres, in which case you should be referring to the idea, not the genre. People need to understand that if I slap a "Trance" label on to my song, it doesn't automatically mean I am trying to make whatever anglicized version of "Trance" they have deluded themselves into thinking encapsulates the entire genre (which is completely different from everyone else's), it is simply there to help them find the damn song.
## July 21, 2011
### C# to C++ Tutorial - Part 2: Pointers Everywhere!
[ 1 · 2 · 3 · 4 · 5 · 6 · 7 ]
We still have a lot of ground to cover on pointers, but before we do, we need to address certain conceptual frameworks missing from C# that one must be intimately familiar with when moving to C++.
Specifically, in C# you mostly work with the Heap. The heap is not difficult to understand - its a giant lump of memory that you take chunks out of to allocate space for your classes. Anything using the new keyword is allocated on the heap, which ends up being almost everything in a C# program. However, the heap isn't the only source of memory - there is also the Stack. The Stack is best described as what your program lives inside of. I've said before that everything takes up memory, and yes, that includes your program. The thing is that the Heap is inherently dynamic, while the Stack is inherently fixed. Both can be re-purposed to do the opposite, but trying to get the Stack to do dynamic allocation is extremely dangerous and is almost guaranteed to open up a mile-wide security hole.
I'm going to assume that a C# programmer knows what a stack is. All you need to understand is that absolutely every single piece of data that isn't allocated on the heap is pushed or popped off your program's stack. That's why most debuggers have a "stack" of functions that you can go up and down. Understanding the stack in terms of how many functions you're inside of is ok, but in reality, there are also variables declared on the stack, including every single parameter passed to a function. It is important that you understand how variable scope works so you can take advantage of declaring things on the stack, and know when your stack variables will simply vanish into nothingness. This is where { and } come in.
int main(int argc, char *argv[])
{
int bunny = 1;
{
int carrot=3;
int lettuce=8;
bunny = 2; // Legal
}
//carrot=2; //Compiler error: carrot does not exist
int carrot = 3; //Legal, since the other carrot no longer exists
{
int lettuce = 0;
{
//int carrot = 1; //Compiler error: carrot already defined
int grass = 9;
bunny = grass; //Still legal
bunny = carrot; // Also legal
}
//bunny = grass; //Illegal
bunny = lettuce; //Legal
}
//bunny = lettuce; //Illegal
}
{ and } define scope. Anything declared inside of them ceases to exist outside, but is still accessible to any additional layers of scope declared inside of them. This is a way to see your program's stack in action. When bunny is declared, its pushed on to the stack. Then we enter our first scope area, where we push carrot and lettuce on to the stack and set bunny to 2, which is legal because bunny is still on the stack. When the scope is then closed, however, anything declared inside the scope is popped from the stack in the exact opposite order it was pushed on. Unfortunately, compiler optimization might change that order behind the scenes, so don't rely on it, but it should be fairly consistent in debug builds. First lettuce is de-allocated (and its destructor called, if it has one), then carrot is de-allocated. Consequently, trying to set carrot to 2 outside of the scope will result in a compiler error, because it doesn't exist anymore. This means we can now declare an entirely new integer variable that is also called carrot, without causing an error. If we visualize this as a stack, that means carrot is now directly above bunny. As we enter a new scope area, lettuce is then put on top of carrot, and then grass is put on top of lettuce. We can still assign either lettuce or carrot to bunny, since they are all on the stack, but once we leave this inner scope, grass is popped off the stack and no longer exists, so any attempt to use it causes an error. lettuce, however, is still there, so we can assign lettuce to bunny before the scope closes, which pops lettuce off the stack.
Now the only things on the stack are bunny and carrot, in that order (if the compiler hasn't moved things around). We are about to leave the function, and the function is also surrounded by { and }. This is because a function is, itself, a scope, so that means all variables declared inside of that scope are also destroyed in the order they were declared in. First carrot is destroyed, then bunny is destroyed, and then the function's parameters argc and argv are destroyed (however the compiler can push those on to the stack in whatever order it wants, so we don't know the order they get popped off), until finally the function itself is popped off the stack, which returns program flow to whatever called it. In this case, the function was main, so program flow is returned to the parent operating system, which does cleanup and terminates the process.
You can declare anything that has a size determined at compile time on the stack. This means if you have an array that has a constant size, you can declare it on the stack:
int array[5]; //Array elements are not initialized and therefore are undefined!
int array[5] = {0,0,0,0,0}; //Elements all initialized to 0
//int array[5] = {0}; // Compiler error - your initialization must match the array size
You can also let the compiler infer the size of the array:
int array[] = {1,2,3,4}; //Declares an array of 4 ints on the stack initialized to 1,2,3,4
Not only that, but you can declare class instances and other objects on the stack.
Class instance(arg1, arg2); //Calls a constructor with 2 arguments
Class instance; //Used if there are no arguments for the constructor
//Class instance(); //Causes a compiler error! The compiler will think its a function.
In fact, if you have a very simple data structure that uses only default constructors, you can use a shortcut for initializing its members. I haven't gone over classes and structs in C++ yet (See Part 3), but here is the syntax anyway:
struct Simple
{
int a;
int b;
const char* str;
};
Simple instance = { 4, 5, "Sparkles" };
//instance.a is now 4
//instance.b is now 5
//instance.str is now "Sparkles"
All of these declare variables on the stack. C# actually does this with trivial datatypes like int and double that don't require a new statement to allocate, but otherwise forces you to use the Heap so its garbage collector can do the work.
Wait a minute, stack variables automatically destroy themselves when they go out-of-scope, but how do you delete variables allocated from the Heap? In C#, you didn't need to worry about this because of Garbage Collection, which everyone likes because it reduces memory leaks (but even I have still managed to cause a memory leak in C#). In C++, you must explicitly delete all your variables declared with the new keyword, and you must keep in mind which variables were declared as arrays and which ones weren't. In both C# and C++, there are two uses of the new keyword - instantiating a single object, and instantiating an array. In C++, there are also two uses of the delete keyword - deleting a single object and deleting an array. You cannot mix up delete statements!
int* Fluffershy = new int();
int* ponies = new int[10];
delete Fluffershy; // Correct
//delete ponies; // WRONG, we should be using delete [] for ponies
delete [] ponies; // Just like this
//delete [] Fluffershy; // WRONG, we can't use delete [] on Fluffershy because we didn't
// allocate it as an array.
int* one = new int[1];
//delete one; // WRONG, just because an array only has one element doesn't mean you can
// use the normal delete!
delete [] one; // You still must use delete [] because you used new [] to allocate it.
As you can see, it is much easier to deal with stack allocations, because they are automatically deallocated, even when the function terminates unexpectedly. std::auto_ptr takes advantage of this by taking ownership of a pointer and automatically deleting it when it is destroyed, so you can allocate the auto_ptr on the stack and benefit from the automatic destruction. However, in C++0x, this has been superseded by std::unique_ptr, which operates in a similar manner but uses some complex move semantics introduced in the new standard. I won't go into detail about how to use these here as its out of the scope of this tutorial. Har har har.
For those of you who like throwing exceptions, I should point out common causes of memory leaks. The most common is obviously just flat out forgetting to delete something, which is usually easily fixed. However, consider the following scenario:
void Kenny()
{
int* kenny = new int();
throw "BLARG";
delete kenny; // Even if the above exception is caught, this line of code is never reached.
}
int main(int argc, char* argv[])
{
try {
Kenny();
} catch(char * str) {
//Gotta catch'em all.
}
return 0; //We're leaking Kenny! o.O
}
Even this is fairly common:
int main(int argc, char* argv[])
{
int* kitty = new int();
*kitty=rand();
if(*kitty==0)
return 0; //LEAK
delete kitty;
return 0;
}
These situations seem obvious, but they will happen to you once the code becomes enormous. This is one reason you have to be careful when inside functions that are very large, because losing track of if statements may result in you forgetting what to delete. A good rule of thumb is to make sure you delete everything whenever you have a return statement. However, the opposite can also happen. If you are too vigilant about deleting everything, you might delete something you never allocated, which is just as bad:
int main(int argc, char* argv[])
{
int* rarity = new int();
int* spike;
if(rarity==NULL)
{
spike=new int();
}
else
{
delete rarity;
delete spike; // Suddenly, in an alternate dimension, earth ceased to exist
return 0;
}
delete rarity; // Since this only happens if the allocation failed and returned a NULL
// pointer, this will also blow up.
delete spike;
return 0;
}
Clearly, one must be careful when dealing with allocating and destroying memory in C++. Its usually best to encapsulate as much as possible in classes that automate such things. But wait, what about that NULL pointer up there? Now that we're familiar with memory management, we're going to dig into pointers again, starting with the NULL pointer.
Since a pointer points to a piece of memory that's somewhere between 0 and 4294967295, what happens if its pointing at 0? Any pointer to memory location 0 is always invalid. All you need to know is that the operating system does some magic voodoo to ensure that any attempted access of memory location 0 will always throw an error, no matter what. 1, 2, 3, and any other double or single digit low numbers are also always invalid. 0xfdfdfdfd is what the VC++ debugger sets uninitialized memory to, so that pointer location is also always invalid. A pointer set to 0 is called a Null Pointer, and is usually used to signify that a pointer is empty. Consequently if an allocation function fails, it tends to return a null pointer. Null pointers are returned when the operation failed and a valid pointer cannot be returned. Consequently, you may see this:
int main(int argc, char* argv[])
{
return 0;
}
This is known as a safe deletion. It ensures that you only delete a pointer if it is valid, and once you delete the pointer you set the pointer to 0 to signify that it is invalid. Note that NULL is defined as 0 in the standard library, so you could also say blink = NULL.
Since pointers are just integers, we can do pointer arithmetic. What happens if you add 1 to a pointer? If you think of pointers as just integers, one would assume it would simply move the pointer forward a single byte.
This isn't what happens. Adding 1 to a pointer of type integer results in the pointer moving forward 4 bytes.
Adding or subtracting an integer $i$ from a pointer moves that pointer $i\cdot n$ bytes, where $n$ is the size, in bytes, of the pointer's type. This results in an interesting parallel - adding or subtracting from a pointer is the same as treating the pointer as an array and accessing it via an index.
int main(int argc, char* argv[])
{
int* kitties = new int[14];
int* a = &kitties[7];
int* b = kitties+7; //b is now the same as a
int* c = &a[4];
int* d = b+4; //d is now the same as c
int* e = &kitties[11];
int* f = kitties+11;
//c,d,e, and f now all point to the same location
}
So pointer arithmetic is identical to accessing a given index and taking the address. But what happens when you try to add two pointers together? Adding two pointers together is undefined because it tends to produce total nonsense. Subtracting two pointers, however, is defined, provided you subtract a smaller pointer from a larger one. The reason this is allowed is so you can do this:
int main(int argc, char* argv[])
{
int* eggplants = new int[14];
int* a = &eggplants[7];
int* b = eggplants+10;
int diff = b-a; // Diff is now equal to 3
a += (diff*2); // adds 6 to a, making it point to eggplants[13]
diff = a-b; // diff is again equal to 3
diff = a-eggplants; //diff is now 13
++a; //The increment operator is valid on pointers, and operates the same way a += 1 would
// So now a points to eggplants[14], which is not a valid location, but this is still
// where the "end" of the array technically is.
diff = a-eggplants; // Diff now equals 14, the size of the array
--b; // Decrement works too
diff = a-b; // a is pointing to index 14, b is pointing to 9, so 14-9 = 5. Diff is now 5.
return 0;
}
There is a mistake in the code above, can you spot it? I used a signed integer to store the difference between the two pointers. What if one pointer was above 2147483647 and the other was at 0? The difference would overflow! Had I used an unsigned integer to store the difference, I'd have to be really damn sure that the left pointer was larger than the right pointer, or the negative value would also overflow. This complexity is why you have to goad windows into letting your program deal with pointer sizes over 2147483647.
In addition to arithmetic, one can compare two pointers. We already know we can use == and !=, but we can also use < > <= and >=. While you can get away with comparing two completely unrelated pointers, these comparison operators are usually used in a context like the following:
int main(int argc, char* argv[])
{
int* teapots = new int[15];
int* end = teapots+15;
for(int* s = teapots; s<end; ++s)
*s = 0;
return 0;
}
Here the for loop increments the pointer itself rather than an index, until the pointer reaches the end, at which point it terminates. But, what if you had a pointer that didn't have any type at all? void* is a legal pointer type, that any pointer type can be implicitly converted to. You can also explicitly cast void* to any pointer type you want, which is why you are allowed to explicitly cast any pointer type to another pointer type (int* p; short* q = (short*)p; is entirely legal). Doing so, however, is obviously dangerous. void* has its own problems, namely, how big is it? The answer is, you don't know. Any attempt to use any kind of pointer arithmetic with a void* pointer will cause a compiler error. It is most often used when copying generic chunks of memory that only care about size in bytes, and not what is actually contained in the memory, like memcpy().
int main(int argc, char* argv[])
{
int* teapots = new int[15];
void* p = (void*)teapots;
p++; // compiler error
unsigned short* d = (unsigned short*)p;
d++; // No compiler error, but you end up pointing to half an integer
d = (unsigned short*)teapots; // Still valid
return 0;
}
Now that we know all about pointer manipulation, we need to look at pointers to pointers, and to anchor this in a context that actually makes sense, we need to look at how C++ does multidimensional arrays. In C#, multidimensional arrays look like this:
int[,] table = new int[4,5];
C++ has a different, but fairly reasonable stack-based syntax. When you want to declare a multidimensional array on the heap, however, things start getting weird:
int unicorns[5][3]; // Well this seems perfectly reasonable, I wonder what-
int (*cthulu)[50] = new int[10][50]; // OH GOD GET IT AWAY GET IT AWAAAAAY...!
int c=5;
int (*cthulu)[50] = new int[c][50]; // legal
//int (*cthulu)[] = new int[10][c]; // Not legal. Only the leftmost parameter
// can be variable
//int (*cthulu)[] = new int[10][50]; // This is also illegal, the compiler is not allowed
// to infer the constant length of the array.
Why isn't the multidimensional array here just an int**? Clearly if int* x is equivalent to int x[], shouldn't int** x be equivalent to int x[][]? Well, it is - just look at the main() function, its got a multidimensional array in there that can be declared as just char** argv. The problem is that there are two kinds of multidimensional arrays - square and jagged. While both are accessed in identical ways, how they work is fundamentally different.
Let's look at how one would go about allocating a 3x5 square array. We can't allocate a 3x5 chunk out of our computer's memory, because memory isn't 2-dimensional, its 1-dimensional. Its just freaking huge line of bytes. Here is how you squeeze a 2-dimensional array into a 1-dimensional line:
As you can see, we just allocate each row right after the other to create a 15-element array ($5\cdot 3 = 15$). But then, how do we access it? Well, if it has a width of 5, to access another "row" we'd just skip forward by 5. In general, if we have an $n$ by $m$ multidimensional array being represented as a one-dimensional array, the proper index for a coordinate $(x,y)$ is given by: array[x + (y*n)]. This can be extended to 3D and beyond but it gets a little messy. This is all the compiler is really doing with multidimensional array syntax - just automating this for you.
Now, if this is a square array (as evidenced by it being a square in 2D or a cube in 3D), a jagged array is one where each array is a different size, resulting in a "jagged" appearance:
We can't possibly allocate this in a single block of memory unless we did a lot of crazy ridiculous stuff that is totally unnecessary. However, given that arrays in C++ are just pointers to a block of memory, what if you had a pointer to a block of memory that was an array of pointers to more blocks of memory?
Suddenly we have our jagged array that can be accessed just like our previous arrays. It should be pointed out that with this format, each inner-array can be in a totally random chunk of memory, so the last element could be at position 200 and the first at position 5 billion. Consequently, pointer arithmetic only makes sense within each column. Because this is an array of arrays, we declare it by creating an array of pointers. This, however, does not initialize the entire array; all we have now is an array of illegal pointers. Since each array could be a different size than the other arrays (this being the entire point of having a jagged array in the first place), the only possible way of initializing these arrays is individually, often by using a for loop. Luckily, the syntax for accessing jagged arrays is the exact same as with square arrays.
int main(int argc, char* argv[])
{
int** jagged = new int*[5]; //Creates an array of 5 pointers to integers.
for(int i = 0; i < 5; ++i)
{
jagged[i] = new int[3+i]; //Assigns each pointer to a new array of a unique size
}
jagged[4][1]=0; //Now we can assign values directly, or...
int* second = jagged[2]; //Pull out one column, and
second[0]=0; //manipulate it as a single array
// The double-access works because of the order of operations. Since [] is just an
// operator, it is evaluated from left to right, like any other operator. Here it is
// again, but with the respective types that each operator resolves to in parenthesis.
( (int&) ( (int*&) jagged[4] ) [1] ) = 0;
}
As you can see above, just like we can have pointers to pointers, we can also have references to pointers, since pointers are just another data type. This allows you to re-assign pointer values inside jagged arrays, like so: jagged[2] = (int*)kitty. However, until C++0x, those references didn't have any meaningful data type, so even though the compiler was using int*&, using that in your code will throw a compiler error in older compilers. If you need to make your code work in non-C++0x compilers, you can simply avoid using references to pointers and instead use a pointer to a pointer.
int* bunny;
int* value = new int[5];
int*& bunnyref = bunny; // Throws an error in old compilers
int** pbunny = &bunny; // Will always work
bunnyref = value; // This does the same exact thing as below.
*pbunny = value;
// bunny is now equal to value
This also demonstrates the other use of a pointer-to-pointer data type, allowing you to remotely manipulate a pointer just like a pointer allows you to remotely manipulate an integer or other value type. So obviously you can do pointers to pointers to pointers to pointers to an absurd degree of lunacy, but this is exceedingly rare so you shouldn't need to worry about it. Now you should be strong in the art of pointer-fu, so our next tutorial will finally get into object-oriented techniques in C++ in comparison to C#. Part 3: Classes and Structs and Inheritance OH MY! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2610921859741211, "perplexity": 1435.3507899850156}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824775.99/warc/CC-MAIN-20171021114851-20171021134851-00830.warc.gz"} |
https://www.math.hmc.edu/calculus/tutorials/continuity/discontinuities.html | Types of Discontinuities
$f(x) = \frac{1}{x}$ Discontinuity at $x=0$ $f(x) = \frac{x^2-9}{x-3}$ Removable Discontinuity at $x=3$ $f(x) = \left\{ \begin{array}{ll} x^2, & x < 0 \\ 1, & x=0 \\ x+1, & x>0 \end{array} \right.$ Discontinuity at $x=0$ $f(x) = \left\{ \begin{array}{ll} 1, & x<0 \\ 3, & x\geq 0 \end{array} \right.$ Jump Discontinuity at $x=0$ $f(x) = \sin \left( \frac{1}{x} \right)$ Discontinuity at $x=0$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9672536253929138, "perplexity": 381.4953579510497}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917127681.50/warc/CC-MAIN-20170423031207-00281-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://codegolf.stackexchange.com/questions/133754/one-oeis-after-another?page=3&tab=votes | # One OEIS after another
As of 13/03/2018 16:45 UTC, the winner is answer #345, by Scrooble. This means the contest is officially over, but feel free to continue posting answers, just so long as they follow the rules.
As well, just a quick shout out to the top three answerers in terms of numbers of answers:
3. Hyper Neutrino - 26 answers
This is an answer chaining question that uses sequences from OEIS, and the length of the previous submission.
This answer chaining question will work in the following way:
• I will post the first answer. All other solutions must stem from that.
• The next user (let's call them userA) will find the OEIS sequence in which its index number (see below) is the same as the length of my code.
• Using the sequence, they must then code, in an unused language, a program that takes an integer as input, n, and outputs the nth number in that sequence.
• Next, they post their solution after mine, and a new user (userB) must repeat the same thing.
The nth term of a sequence is the term n times after the first, working with the first value being the first value given on its OEIS page. In this question, we will use 0-indexing for these sequences. For example, with A000242 and n = 3, the correct result would be 25.
## However!
This is not a , so shortest code doesn't matter. But the length of your code does still have an impact. To prevent the duplication of sequences, your bytecount must be unique. This means that no other program submitted here can be the same length in bytes as yours.
If there isn't a sequence for then length of the last post, then the sequence for your post is the lowest unused sequence. This means that the sequences used also have to be unique, and that the sequence cannot be the same as your bytecount.
After an answer has been posted and no new answers have been posted for more than a week, the answer before the last posted (the one who didn't break the chain) will win.
## Input and Output
Generic input and output rules apply. Input must be an integer or a string representation of an integer and output must be the correct value in the sequence.
## Formatting
# N. language, length, [sequence](link)
code
*anything else*
## Rules
• You must wait for at least 1 hour before posting an answer, after having posted.
• You may not post twice (or more) in a row.
• The index number of a sequence is the number after the A part, and with leading zeros removed (e.g. for A000040 the index number is 40)
• You can assume that neither the input nor the required output will be outside your languages numerical range, but please don't abuse this by choosing a language that can only use the number 1, for example.
• If the length of your submission is greater than 65536 characters long, please provide a link to a way to access the code (pastebin for example).
• n will never be larger than 1000, or be out of bounds for the sequence, simply to prevent accuracy discrepancies from stopping a language from competing.
• Every 150 (valid) answers, the number of times a language may be used increases. So after 150 solutions have been posted, every language may be used twice (with all previous answers counting towards this). For instance, when 150 answers have been posted, Python 3 may be used twice, but due to the fact that it has already been used once, this means it can only be used once more until 300 answers have been posted.
• Please be helpful and post a link to the next sequence to be used. This isn't required, but is a recommendation.
• Different versions of languages, e.g. Python 2 and Python 3 are different languages. As a general rule, if the different versions are both available on Try It Online, they are different languages, but keep in mind that this is a general rule and not a rigid answer.
• It is not banned, but please try not to copy the code from the OEIS page, and actually try to solve it.
• Hardcoding is only allowed if the sequence is finite. Please note that the answer that prompted this (#40) is the exception to the rule. A few answers early in the chain hardcode, but these can be ignored, as there is no good in deleting the chain up to, say, #100.
var QUESTION_ID=133754,OVERRIDE_USER=66833;function shareUrl(i){return"https://codegolf.stackexchange.com/a/"+i}function answersUrl(e){return"https://api.stackexchange.com/2.2/questions/"+QUESTION_ID+"/answers?page="+e+"&pagesize=100&order=desc&sort=creation&site=codegolf&filter="+ANSWER_FILTER}function commentUrl(e,s){return"https://api.stackexchange.com/2.2/answers/"+s.join(";")+"/comments?page="+e+"&pagesize=100&order=desc&sort=creation&site=codegolf&filter="+COMMENT_FILTER}function getTemplate(s){return jQuery(jQuery("#answer-template").html().replace("{{PLACE}}",s.index+".").replace("{{NAME}}",s.user).replace("{{LANGUAGE}}",s.language).replace("{{SEQUENCE}}",s.sequence).replace("{{SIZE}}",s.size).replace("{{LINK}}",s.link))}function search(l,q){m=jQuery("<tbody id='answers'></tbody>");e.forEach(function(s){if(!q||(l==0&&RegExp('^'+q,'i').exec(s.lang_name))||(l==1&&q===''+s.size)){m.append(jQuery(getTemplate(s)))}});jQuery("#answers").remove();jQuery(".answer-list").append(m)}function sortby(ix){t=document.querySelector('#answers');_els=t.querySelectorAll('tr');els=[];for(var i=0;i<_els.length;i++){els.push(_els[i]);}els.sortBy(function(a){a=a.cells[ix].innerText;return ix==0||ix==4?Number(a):a.toLowerCase()});for(var i=0;i<els.length;i++)t.appendChild(els[i]);}function checkSize(x){if(!x)return jQuery("#size-used").text("");var i=b.indexOf(+x);if(i<0)return jQuery("#size-used").text("Available!");var low=+x,high=+x;while(~b.indexOf(low))low--;while(~b.indexOf(high))high++;jQuery("#size-used").text(("Not available. The nearest are "+low+" and "+high).replace("are 0 and","is"))}function checkLang(x){}function getAnswers(){jQuery.ajax({url:answersUrl(answer_page++),method:"get",dataType:"jsonp",crossDomain:!0,success:function(e){answers.push.apply(answers,e.items),answers_hash=[],answer_ids=[],e.items.forEach(function(e){e.comments=[];var s=+e.answer_id;answer_ids.push(s),answers_hash[s]=e}),e.has_more||(more_answers=!1),comment_page=1,getComments()}})}function getComments(){jQuery.ajax({url:commentUrl(comment_page++,answer_ids),method:"get",dataType:"jsonp",crossDomain:!0,success:function(e){e.items.forEach(function(e){e.owner.user_id===OVERRIDE_USER&&answers_hash[e.post_id].comments.push(e)}),e.has_more?getComments():more_answers?getAnswers():process()}})}function getAuthorName(e){return (e.owner.user_id==OVERRIDE_USER?"<span id='question-author'>"+e.owner.display_name+"</span>":e.owner.display_name)}function process(){b=[];c=[];answers.forEach(function(s){var r=s.body;s.comments.forEach(function(e){OVERRIDE_REG.test(e.body)&&(r="<h1>"+e.body.replace(OVERRIDE_REG,"")+"</h1>")});var a=r.match(SCORE_REG);if(a){e.push({user:getAuthorName(s),size:+a[4],language:a[2],lang_name:a[3],index:+a[1],sequence:a[5],link:shareUrl(s.answer_id)});if(b.indexOf(+a[4])>=0&&c.indexOf(+a[4])<0){c.push(+a[4])};b.push(+a[4])}else{jQuery('#weird-answers').append('<a href="'+shareUrl(s.answer_id)+'">This answer</a> is not formatted correctly. <b>Do not trust the information provided by this snippet until this message disappears.</b><br />')}}),e.sortBy(function(e){return e.index});e.forEach(function(e){jQuery("#answers").append(getTemplate(e))});var q="A"+("000000"+e.slice(-1)[0].size).slice(-6);jQuery("#next").html("<a href='http://oeis.org/"+q+"'>"+q+"</a>");c.forEach(function(n){jQuery('#weird-answers').append('The bytecount '+n+' was used more than once!<br />')})}Array.prototype.sortBy=function(f){return this.sort(function(a,b){if(f)a=f(a),b=f(b);return(a>b)-(a<b)})};var ANSWER_FILTER="!*RB.h_b*K(IAWbmRBLe",COMMENT_FILTER="!owfmI7e3fd9oB",answers=[],answers_hash,answer_ids,answer_page=1,more_answers=!0,comment_page,e=[];getAnswers();var SCORE_REG=/<h\d>\s*(\d+)\.\s*((?:<a [^>]+>\s*)?((?:[^\n,](?!<\/a>))*[^\s,])(?:<\/a>)?),.*?(\d+)(?=[^\n\d<>]*(?:<(?:s>[^\n<>]*<\/s>|[^\n<>]+>)[^\n\d<>]*)*, ((?:<a[^>]+>\s*)?A\d+(?:\s*<\/a>)?)\s*<\/h\d>)/,OVERRIDE_REG=/^Override\s*header:\s*/i;
body{text-align:left!important;font-family:Roboto,sans-serif}#answer-list,#language-list{padding:10px;/*width:290px*/;float:left;display:flex;flex-wrap:wrap;list-style:none;}table thead{font-weight:700}table td{padding:5px}ul{margin:0px}#board{display:flex;flex-direction:column;}#language-list li{padding:2px 5px;}#langs-tit{margin-bottom:5px}#byte-counts{display:block;margin-left:15px;}#question-author{color:purple;text-shadow: 0 0 15px rgba(128,0,128,0.1);}#label-info{font-weight: normal;font-size: 14px;font-style: italic;color: dimgray;padding-left: 10px;vertical-align: middle; }
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script><link rel="stylesheet" type="text/css" href="//cdn.sstatic.net/codegolf/all.css?v=83c949450c8b"><p id="weird-answers"></p><p>Currently waiting on <span id="next"></span></p><span>Search by Byte Count: <input id="search" type="number" min=1 oninput="checkSize(this.value);search(1,this.value)" onclick="document.getElementById('search2').value='';!this.value&&search(0,'')"/> <span id="size-used"></span></span><br><span>Search by Language: <input id="search2" oninput="checkLang(this.value);search(0,this.value)" onclick="document.getElementById('search').value='';!this.value&&search(0,'')"/> <span id="language-used"></span></span><h2>Answer chain <span id="label-info">click a label to sort by column</span></h2><table class="answer-list"><thead><tr><td onclick="sortby(0)">#</td><td onclick="sortby(1)">Author</td><td onclick="sortby(2)">Language</td><td onclick="sortby(3)">Sequence</td><td onclick="sortby(4)">Size</td></tr></thead><tbody id="answers"></tbody></table><table style="display: none"><tbody id="answer-template"><tr><td>{{PLACE}}</td><td>{{NAME}}</td><td>{{LANGUAGE}}</td><td>{{SEQUENCE}}</td><td>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr></tbody></table><table style="display: none"><tbody id="language-template"><tr><td>{{LANGUAGE}}</td><td>{{NAME}}</td><td>{{SEQUENCE}}</td><td>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr></tbody></table>
• Comments are not for extended discussion; this conversation has been moved to chat. – Dennis Oct 31 '17 at 2:49
• Is it OK if a program would need a better floating-point accuracy for the builtin float/double type in order to produce values for larger n? – NieDzejkob Nov 21 '17 at 15:15
• @Giuseppe No, as you're generating the numbers by doing the maths, rather than just placing them into an array/string – caird coinheringaahing Dec 15 '17 at 22:14
• @cairdcoinheringaahing In my opinion that's hardcoding the gamma constant. It doesn't work "in theory" for larger numbers. – user202729 Dec 22 '17 at 12:44
• Chat room – user202729 Dec 22 '17 at 12:45
# 36. J, 124 bytes, A000067
squares =: *:@i.@>:@<.@%:
filter =: ] #~ [ >: ]
f =: [: <: (2^]) +/@:>: [: ~.@,/ (2^<:@]) (] +/ 2 * filter) [: squares (2^])
Try it online!
Next sequence
• Please make the next sequence in 6 bytes lol – Leaky Nun Jul 22 '17 at 6:38
# 37. 05AB1E, 6 bytes, A000124
The courtesy of Leaky Nun.
D>*2÷>
Try it online!
Next Sequence
# 38. Actually, 4 bytes, A000006
P√LA
Try it online!
Next sequence
# 41. PHP, 503 bytes, A003416
function f ($n) {$i=12495; $cnt=0;$used =[];
while (true) {
$i++;$ns = [];
$v =$i;
$sm =$i;
while (!in_array($v,$ns)) {
$ns[] =$v;
$s = 0; for ($k=1; $k<=$v/2; $k++) if ($v % $k == 0)$s += $k;$v = $s; if ($s == 1) break;
$sm = min($sm, $v); } if ($v < 2) continue;
if (in_array($sm,$used)) continue;
if ($cnt ==$n) return $sm;$cnt++;
for ($i=0;$i < count($ns);$i++) $used[] =$ns[$i]; } } Try it online! Next sequence # 42. Cheddar, 28 bytes, A000503 n->(tan(n)|0)-(tan(n)<0?1:0) Try it online! Next sequence # 44. Maxima, 94 bytes, A000651 f(n):=sum((2*k)!/k!/(k+1)!,k,1,n)+sum((2*binomial(n+k-1,k)-binomial(n+k,k))*f(n-1-k),k,0,n-2); Try it online! Next sequence • ... and we're back to partition – Leaky Nun Jul 22 '17 at 12:53 # 59. Brachylog, 59 bytes, A000011 ;2↔^gP~g⟦k;Pz+ᵐḃᵐbᵐ{↔;?T{{;1↔-}ᵐ}ᵐ,T{{~cĊ↔c}ᶠb}ᵐ{∋∋}ᶠo}ᵐ∋ᶜ¹ Try it online! Next sequence # 72. SML, 252 bytes, A000401 fun A000401 x = let fun helper x y z = if z mod 4 = 0 then helper x y (z div 4) else if z mod 16 = 14 then helper x (y + 1) (y + 1) else if x = 0 then y else helper (x - 1) (y + 1) (y + 1) in helper x 0 1 end Online demo (Note: those blocks which look like four spaces each are really tabs. I forgot about StackExchange forcing tabs into spaces, and now that I've posted the next sequence it's a bit late to change. If anyone is really fussed then they can be changed to use a single space for indentation). Next sequence ### Dissection This uses the characterisation given in Dickson's History of the Theory of Numbers: These are the numbers not of the form 4^k*(16*n + 14) I could have defined one helper function to test for numbers not in the sequence and another to find the xth number which passes the test, but I think it's more in the spirit of PPCG to use a single helper function with two accumulators. x is the number we still have to discard; y is the number currently under consideration; z is y divided by some power of 4. There is a small hack in calling it as helper x 0 1: if I called it as helper x 0 0 then there would be an infinite loop because 0 is divisible by 4 yielding 0. • Good to see that you've decided to participate again! – caird coinheringaahing Jul 23 '17 at 21:25 • I was a little nervous about leaving it on this sequence, but I saw the 4^k*(16*n + 14) note in the OEIS comments and knew that would be quite doable. – ETHproductions Jul 24 '17 at 2:28 • @ETHproductions, it would have been easy to do it directly too. In CJam I would have used the definition because it's easier to do a three-way Cartesian product and set union than to do the loop to remove powers of 4. – Peter Taylor Jul 24 '17 at 5:47 # 101. Fortress, 335 bytes, A000020 relativelyPrime(a,b)=array[\ZZ32\]((a MIN b)-1).fill(fn(n)=>1) EQ array[\ZZ32\]((a MIN b)-1).fill(fn(n)=>if ((a MOD (n+2))+(b MOD (n+2))) NE 0 then 1 else 0 end) totient(n)= do S : ZZ32 = 0 for i <- 1:n do S += if relativelyPrime(i,n) then 1 else 0 end end S end A000020(n) = do |\if n = 1 then 2 else totient(2^n-1)/n end/| end Next Sequence Direct download of Fortress If the language was equivalent to the specification at the time that FOrtress got axed, then this would probably be easy. But sadly, Fortress got the boot, and I'm stuck with this crap >_<. • Link to the language? – pppery Aug 11 '17 at 22:18 • Dead. Very dead. There it is. – Zacharý Aug 11 '17 at 22:22 # 115. shortC, 273 bytes, A001560 pa(m){Fm%2){T-1;}E{T1;}} pt(m){Ii,p[200],s,j,k,t,kk;p[0]=1;for(i=1;i<=m;i++){j=1;k=1;s=0;Wj>0){kk=k*k;j=i-(3*kk+k)/2;t=pa(k);if(j>=0){s=s-t*p[j];}j=i-(3*kk-k)/2;Fj>=0){s=s-t*p[j];}k=k+1;}p[i]= s;}Ts} AIi,c;scanf("%d",&c);Oi=0;i<131;i++){Fpt(i)%2==0)c--;Fc==1)break;}R"%d",i It's surprisingly hard to calculate partitions in a language that doesn't have many math builtins. This could be more golfed, but it could also be a lot less golfed. :P • Formula: ~ very helpful, I'm glad I can approximate it – Stephen Aug 18 '17 at 19:23 • @StepHen hey it's not as bad as answer 96 :P – MD XF Aug 18 '17 at 19:24 • It's not that hard to calculate partitions: you just need some kind of loop and addition. The number of partitions of n is the sum over 1 <= k <= n of the number of partitions of n into k parts, which has recurrence p(n, k) = p(n-1, k-1) + p(n-k, k). Alternatively the number of partitions of n into parts of at most k has recurrence q(n, k) = n == 0 ? 1 : sum(q(n - i*k, k-1), i = 0 to n/k). – Peter Taylor Aug 18 '17 at 20:10 • @PeterTaylor I wasn't very clear; I tried this in lots of languages that weren't built to deal with math before I resorted to shortC. – MD XF Aug 18 '17 at 20:20 • NO. That's a complete violation of the spirit of the game. – Peter Taylor Aug 19 '17 at 6:12 # 149. dash, 1993 bytes, A000173 Important: this is a precaution in case the INTERCAL answer for #149 is disqualified, to avoid #148 ending the chain due to the week having expired. It is deliberately the same length in order to preserve following answers. succ () { # The successor is the sum of strictly smaller unitary divisors, where a # unitary divisor is a product of some subset of the maximal prime power divisors. # In other words, if we factor n as # \prod_i p_i^{a_i} # then the successor should be # \prod_i (p_i^{a_i} + 1) - n local n=$1
local m=1
factor $n | sed "s% %\n%g" | tail -n +2 | uniq -c | # Workaround for buggy read on my computer sed "s%^ *%%;s% %\n%" | while read x do read y z=1 for i in$( seq $x ) do z=$(( z * y ))
done
m=$(( m * (z + 1) )) # echo here and take tail because scope problems mean that m loses its # value outside this pipeline echo$(( m - n ))
done
}
inseq () {
local n=$1 # We detect rhos using the little-step big-step method. If at any point we hit a # value less than n, clearly n isn't the smallest element of a cycle local k=$( succ $n | tail -1 ) # If we loop already, it's unitary-perfect if test$k -le $n ; then return 1 ; fi local m=$( succ $k | tail -1 ) # Loop already => it's unitary-amicable if test$m -le $n ; then return 1 ; fi while true do # Advance k once k=$( succ $k | tail -1 ) # Advance m twice m=$( succ $m | tail -1 ) if test$m -eq $n ; then return 0 ; fi if test$m -lt $n -o$m -eq $k ; then return 1 ; fi m=$( succ $m | tail -1 ) if test$m -eq $n ; then return 0 ; fi if test$m -lt $n -o$m -eq $k ; then return 1 ; fi done } idx=$1
# Naive approach: test all values from 2 to see whether they're in the sequence
# until we've found enough that are
j=2
while true
do
if inseq $j then if test$idx -eq 0
then
echo $j return 0 fi idx=$(( idx - 1 ))
fi
j=$(( j + 1 )) done Online demo Next sequence • I wonder how the snippet will react to that :P – NieDzejkob Sep 15 '17 at 16:35 • No, I don't have A000083. I don't have a slightest idea about what is happening. Go ahead and choose some saner next sequence ;) – NieDzejkob Sep 17 '17 at 7:38 • Uh, @PeterTaylor did you get a notification when I replied? – NieDzejkob Sep 17 '17 at 19:00 • @PeterTaylor gogogo – Husnain Raza Sep 18 '17 at 17:20 • @cairdcoinheringaahing, I don't understand your request. On the basis of the discussion on meta, where no-one has provided any answer contrary to mine or downvoted it, it's the other 149 which should be deleted and this one remains necessary. – Peter Taylor Sep 23 '17 at 20:28 # 231. Shakespeare Programming Language, 938 bytes, A000086 The Beautiful Story of Solving Quadratic Equations. Theseus, the mathematician. Dogberry, his calculator. Page, to avoid mistakes caused by imperfect mental math. Mistress Page, to make Page feel less lonely. Act XLII: Introducing modulus arithmetic. Scene I: Dogberry as a motivational speaker. [Enter Dogberry and Page] Dogberry: Listen to your heart! [Exeunt] Scene II: Complex math without complex numbers. [Exeunt] [Enter Theseus and Dogberry] Theseus: You are the remainder of the quotient between the sum of a cat and the product of Mistress Page and the sum of Mistress Page and a Microsoft and Page. Are you as big as nothing? Dogberry: If so, you are the sum of yourself and a cat. [Exit Dogberry] [Enter Mistress Page] Theseus: You are the sum of yourself and an angel. Are you as trustworthy as Page? If not, let us return to Scene II. Mistress Page: If so, open your heart. [Exeunt] Try it online! Next sequence! It's suprisingly hard to introduce words that mean nothing in the statement, so I didn't. Yes, Microsoft has a meaning - in fact, it's a negative noun so it means -1. • Please note that the bytecount changed in the first 10 or so seconds. – NieDzejkob Oct 20 '17 at 15:11 # 244. UCBLogo, 1524 bytes, A000112 to permutations :list if :list = [] [op [[]]] op map.se [ map [[ls] fput ? :ls] permutations (remove ? :list) ] :list end to dfs :node repeat :N [ if and (1 = item :node item repcount :matrix) not(item repcount :visited) [ setitem repcount :visited "true dfs repcount ] ] end to tuples :items :n if :n = 1 [op map "list :items] op (crossmap "fput :items tuples :items :n-1) end to isomorphic :mat1 :mat2 ; they must both have size N*N foreach permutations iseq 1 :N [ catch "failed [ for [i 1 :N] [ for [j 1 :N] [ if ( (item :i item :j :mat1) item (item :i ?) item (item :j ?) :mat2 ) [throw "failed] ] ] op "true ] ] op "false end to solve :N if :N = 0 [op 1] localmake "visited array :N localmake "matrices [] local "valid foreach tuples (tuples [0 1] :N) :N [ [matrix] make "valid "true for [node 1 :N] [ repeat :N [ setitem repcount :visited "false ] dfs :node if (item :node :visited) [ make "valid "false throw "for.catchtag ; FMSLogo-specific way to break for loop ; because Logo doesn't have Break command. ] repeat :N [ if and (item repcount :visited) (0 = item :node item repcount :matrix) [ make "valid "false throw "for.catchtag ] ] ] if :valid [ catch "nextmatrix [ foreach :matrices [ if isomorphic :matrix ? [throw "nextmatrix] ] make "matrices fput :matrix :matrices ] ] ] op count :matrices end Next sequence. There are 7 spaces in the last line. You can try it online here. Just enter the program and append print solve 3 (for example) in the end. I choose UCBLogo for this sequence because I don't want to use FMSLogo, which I want to keep for a more geometry-related sequence. So, in the end I gave up and just post my bruteforce solution. This one takes a long time to calculate for just n=4. The MD5 I mentioned in the chat is for the version with some spaces at the end removed. Explanation: First, the program generates all possible N×N matrices tuples (tuples [0 1] :N) :N. Each matrix represent a directed graph with N vertices. For each matrix (store in variable matrix, it checks whether it represents a poset (Two vertices A and B has the edge A→B connected if and only if A<B) by: for each node, it runs a DFS from that node, and verify that it can't reach that node (there is no cycle in the graph), and there is an edge from the node to every reachable nodes (because < is transitive). After having checked that the matrix represents a valid poset, the program checks whether it is isomorphic to any existing poset, stored in the matrices variable. If it is not, the program put :matrix to the first of the variable :matrices (make "matrices fput :matrix :matrices). Then in the end the program output the number of elements of :matrices (op count :matrices). • I need to stop trying to write efficient code for these tougher sequences. Or at least, I need to start seriously attempting them before there's only a day left. – KSmarts Nov 6 '17 at 14:11 • You could avoid the poset check by observing that each poset can be obtained from the subset relations among n subsets of {1,...,n}. But I'm not sure if creating all these (which can be optimized) and turning them into the.matrix representation of the graph is easier... – Christian Sievers Nov 6 '17 at 15:56 • @ChristianSievers So there would be${2^n} \choose n$graphs which is still significantly less than$2^{n^2}$. May be faster. It is not necessary to turn it into matrix representation too, if there is a way to check isomorphism of those. (Is it possible to check isomorphism of posets in polynomial time? Not for general graph, I know.) – user202729 Nov 7 '17 at 1:02 • You can easily bring the number of relevant matrices down to$3^((n-1)(n-2)/2)$, and my approach with the mentioned optimizations to less than$2^same$. So that seems nice, but my main idea was just to try to simpify the algorithm. I don't know about the isomorphism check, but be careful: graph isomorphism is not known to be NP-complete (subgraph isomorphism is), but has unknown complexity in NP (I mixed that up once myself) – Christian Sievers Nov 7 '17 at 2:51 • @ChristianSievers I don't really understand. First, how can I get complexity$3^{(n-1)(n-2) \over 2}$? I find it not obvious. (BTW your LaTeX need curly bracket in necessary places) Second, how is it important that graph isomorphism is NP-unknown? I can just use the fastest-available known algorithm that I can implement. – user202729 Nov 7 '17 at 8:07 # 254. Enlist, 98 bytes, A001516 W F † 0r ‡ ;@ ±@ ¹ ! :/ §€¹ Ė ‡ 2* :2 :@ §/€ † ↕ ḥ1 ↕ ×J ḥ1 § † ↕ ḥ1 ↕ ×J ḥ1 § ;0 S §€ Try it online! haha enlist can do a thing :D Next Sequence # Explanation WF†0r‡;@±@¹!:/§€¹Ė‡2*:2:@§/€†↕ḥ1↕×Jḥ1§†↕ḥ1↕×Jḥ1§;0S§€ Main Link W wrap; x => [x] F flatten (WF is just for test suite purposes lol) € For each (this just returns the first n elements if the input is an integer) † § Execute a monadic bracketed chain on each (let's call the argument z) 0r Range from 0 to z, inclusive € For each in the range ‡ § Execute a dyadic bracketed chain on each (let's call the argument n) ;@ Append n to ±@¹ [z + n, z - n] ! Factorial (of each) :/ Reduce over division (this gives (z + n)! / (z - n)! / n! which is what we want as the coefficient) ¹ Identity as right argument to prevent dyad-monad chaining Ė Enumerate 1-indexed € For each enumerated element (let's call the argument [x, y]) ‡ §/€ Reduce over dyadic function (gives x$ y)
2* 2 ^ x
:2 / 2 (floored)
:@ y / (floored)
(this is y / 2 ^ (x - 1))
† § Monadic bracketed expression (derivative step)
↕ Reverse
ḥ1 All but last 1 element
↕ Reverse
×J Multiply each with its index
ḥ1 All but last 1 element
†↕ḥ1↕×Jḥ1§ Derivative again
;0 Append 0 (to prevent empty-sum errors)
S Sum
• For the second time. Well, that means Enlist can't be used again till 300th answer. – user202729 Nov 20 '17 at 14:16
• cough cough bytecount cough – NieDzejkob Nov 20 '17 at 14:18
• @user202729 oh well, enlist isn't that great for this challenge due to its current lack of functionality. By the time it gets functionality it will probably be in the 300s. – HyperNeutrino Nov 20 '17 at 14:22
• Shouldn't it return the n-th number instead of a list of all numbers up to n? Anyway, good job – NieDzejkob Nov 20 '17 at 14:48
• @NieDzejkob eh, technically yes. fine, I'll fix it – HyperNeutrino Nov 20 '17 at 14:49
# 12. Java (OpenJDK 8), 131 bytes, A000064
int f(int n){int[]a=new int[n+1],c={1,2,5,10,1};a[0]=1;for(int i=0,j,k;i<5;i++)for(j=c[i],k=0;j<=n;j++,k++)a[j]+=a[k];return a[n];}
Try it online!
Next sequence
# 277. 2sable, 104 bytes, A000188
Ln¹%1‹Oquery: no rules about unnecessary text?
Nearest available byte count is 104 so this code is on it
Try it online!
Next Sequence
It didn't seem like there was a rule against unnecessary text but if I misinterpreted I will delete.
Explanation
Ln¹%1‹Oq Only part of the code that gets evaluated
L [1...n] where n is the input
n square: [1,4,9,...n**2]
¹ push the input n
% mod: [1%n,4%n,...(n**2)%n]
1 push 1
‹ less than 1: [1%n<1,4%n<1,...(n**2)%n<1]
O count the ones in the array
q terminate the program
uery: no... not evaluated
Regarding the next sequence, I almost skipped it because it looks hard but then changed my mind. It seems like a high level language would be useful there. I've noticed there are no Maple answers so someone could try it in that. There is also Pyon which from this answer seems like it is essentially just Python so I don't know if we are counting it as a separate language. Fortran is also available for an answer but I don't know if many people use it and it is not so high level.
• Unnecessary bytes are allowed (and sometimes forced), mostly because of byte restriction. – user202729 Dec 8 '17 at 2:40
• hard? No, this one is easy. – user202729 Dec 8 '17 at 6:34
• @user202729 good, I was worried a little – dylnan Dec 8 '17 at 13:07
• For those working on the next one, you may want to look at Donald Knuth's POLYNUM and POLYSLAVE programs. – KSmarts Dec 8 '17 at 14:54
• BTW Pyon is a superset of Python, kind of like Coconut. Most Python code works in Pyon, and if there's code that doesn't, then it's a bug with Pyon. – HyperNeutrino Dec 11 '17 at 14:43
# 280. Axiom, 947 bytes, A002852
artanh:(Float) -> Float
artanh(x) ==
y := x
k := 1
for k in 1..precision() repeat
z := x^(2*k+1) / (2 * k + 1)
y := z + y
return y
ln2:() -> Float
ln2() == artanh(0.5) + artanh(1.0 / 7)
gamma:(NonNegativeInteger) -> Float
gamma(e) ==
precision(2 ^ e + 100)
n := 2.0 ^ e
eps := 1.0 / n
A := - e * ln2()
B := 1.0
U := A
V := 1.0
k := 1
repeat
B := B * n^2 / k^2
A := (A * n^2 / k + B) / k
if (A < eps) /\ (B < eps) then
return U / V
U := U + A
V := V + B
k := k + 1
fractions:(NonNegativeInteger, Integer) -> List(Integer)
fractions(e, n) ==
y := gamma(e)
l : List(Integer) := []
for i in 0..n repeat
f := floor(y)
l := cons(f, l)
y := y - f
if y > 0 then
y := 1 / y
reverse(l)
)set messages prompt none
)set messages type off
fractions(12, 1000)
)quit
next sequence
There doesn't seem to be a good way to read input in this system, but called like this (using the fricas fork)
fricas -noht -eval ")read em.input )quiet"
where em.input contains the source code, will print a table of the first 1001 elements of the sequence.
• I don't have Axiom installed on my machine, but is e=12 enough to calculate 1000 terms? Because in that case you have eps = 1 / (2 ^ 12) (I guess ^ is exponentiation?) and the terminating condition is (A < eps) /\ (B < eps) (I guess /\ is conjunction)... – user202729 Dec 17 '17 at 3:48
• Also, can you explain which series are you using to calculate gamma? It's not entirely obvious from the code. – user202729 Dec 17 '17 at 4:02
• That should be eps = 10 ^ -n. Odd that it works anyway. Series used is from Brent. There also is an axiom docker image. – politza Dec 17 '17 at 9:09
• Welcome to PPCG! – Rɪᴋᴇʀ Dec 18 '17 at 1:04
• Does the next series involve group theory – Husnain Raza Dec 21 '17 at 18:23
# 43. Swift 4, 651 bytes, A000028
func bit_sum_parity(n: Int) -> Int {
var res = 0;
var test = n;
while test > 0 {
res ^= test%2;
test /= 2;
}
return res;
}
func A000028(n: Int) -> Int {
var res = 1;
var iter = n;
while iter > 0 {
var clone = res;
var p = 2;
var parity = 0;
while clone > 1 {
var count = 0;
while clone % p == 0 {
clone /= p;
count += 1;
}
parity ^= bit_sum_parity(n: count);
p += 1;
}
if parity == 1 {
iter -= 1;
}
res += 1;
}
return res-1;
}
Try it online!
Next Sequence - A000651
# 297. Shakespeare Programming Language, 1460 bytes, A000161
A000161 - Number of partitions of n into 2 squares.
Romeo, the first square.
Juliet, the second square.
Othello, the input.
Macbeth, the counter.
Hamlet, the narrator.
The Ghost, the temporary actor one.
Act I: Main Program.
Scene I: Retrieving Input.
[Enter Hamlet and Othello]
Hamlet:
[Exeunt]
Scene II: Initialization.
[Enter Romeo and Juliet]
Juliet:
You are nothing!
[Exit Juliet]
[Enter Macbeth]
Romeo:
You are as good as me!
[Exeunt]
Scene III: Calculation.
[Exeunt]
[Enter Romeo and The Ghost]
Romeo:
You are as bad as the product of me and me!
[Exit The Ghost]
[Enter Juliet]
Romeo:
You are as lovely as the square root of the difference between Othello and The Ghost!
Juliet:
Is Othello as lovely as the sum of the product of me and me and the product of you and you?
Romeo:
If not, let us proceed to Scene V.
[Exeunt]
[Enter Romeo and Macbeth]
Romeo:
You are as good as the sum of yourself and a flower.
[Exeunt]
Scene V: Decision.
[Exeunt]
[Enter Romeo and Hamlet]
Hamlet:
You are as good as the sum of yourself and a flower.
Romeo:
Am I not better than the square root of Othello?
Hamlet:
If so, let us proceed to Scene III.
[Exeunt]
Scene VI: Ending.
[Enter Hamlet and Macbeth]
Hamlet:
You are as good as the quotient between the sum of you and a flower and a beautiful flower. Open your heart!
[Exeunt]
Try it online!
Next sequence: A001460 - just some trivial factorial things
Added some padding bytes so that the next one will not be calculating on the graphs (originally 1429 bytes).
Added more padding so that the sequence points to a 0-indexed array
Translated code (Python):
import math
R, O = 0, input() # Act I Scene I & II
M = R # Act I Scene I & II
while R <= int(math.sqrt(O)): # Act I Scene V
G = R * R # Act I Scene III
J = int(math.sqrt(O - G)) # Act I Scene III
if O == R * R + J * J: # Act I Scene III
M = M + 1 # Act I Scene IV
R = R + 1 # Act I Scene V
print (M + 1) // 2 # Act I Scene VI result = ceil(M / 2)
# because all except n=2a² are counted twice
# 336. Pip, 159 bytes, A000620
b:[1]
c:[1]
Fi1,a+1{
d:0
e:2*(i%3%2)*c@(i/3)
Fj,i{
Fk,i-j{
Ij=k{ d+:b@j * b@(i-j-k-1) }
e+:c@j * c@k * c@(i-j-k-1)
}
}
bAE:d
cAE:e//3
}
c@v-b@v
Online demo
Next sequence
Basically this uses A000620 = A000625 - A000621 and the generating function relations for A000625 and A000621. I'm no chemist, but by the power of species theory I think I can reverse engineer the logic behind the g.f. relations, at least for one interpretation of the sequences. We're interested in monosubstituted alkanes, which correspond to graphs which are trees where every node has valence 4 (carbon atom) or 1 (either hydrogen atom or the substituted part, X).
In other words, modulo the trivial cases, we have a marked carbon atom which is attached to X:
X
|
a--C--b
|
d
The 3D geometry is relevant to the symmetries. The carbon atom is at the centre of a tetrahedron, and the other four elements are at the four vertices. Rotating around the axis CX doesn't change the molecule, so we'll need to avoid double-counting.
Note that if we consider the diagram from the perspective of e.g. a, the rest of the diagram (CXbd) can be considered as an X, and that's the heart of the recurrence logic.
If we ignore all restrictions and symmetry then by elementary species theory we have a generating function with recurrence $F(x) = 1 + xF(x)^3$. The $1$ corresponds to the special case that there's one molecule with 0 carbon atoms (X); the $xF(x)^3$ says that a molecule with $n$ carbon items can be identified with a molecule with one ($x^1$) identified carbon atom and then the remaining $n-1$ carbons are supplied by three smaller instances of the same type of object (a, b, d).
A000621 counts the non-stereoisomeric molecules. That means that they're symmetric: a = b, and all of a, b, d are non-stereoisomeric1. That gives generating function $G(x) = 1 + xG(x)G(x^2)$. The $x$ corresponds to the identified carbon atom C; the $G(x)$ corresponds to d; and the $G(x^2)$ corresponds to a and b being equal. (It uses $x^2$ to count each carbon atom in a twice).
A000625 counts all molecules under the rotational symmetry about the axis CX. If a, b, d are all different then there are three rotational positions, so we need to divide by 3; if two of them are the same then there are still three rotational positions; if all three are the same then there is only one rotational position, so we don't want to divide by three. We have g.f. $H(x) = 1 + \frac13 xH(x)^3 + \frac23 xH(x^3)$ where the final term is to bring the weight of the case where a=b=d back up from $\frac13$ to $1$.
1 Actually the choice that a = b is arbitrary, but works out nicely. We could alternatively consider the cases a = d and b = d as well, but then we have to divide by 3 to account for the symmetry.
# 16. Lua, 69 bytes, A000085
function f(n)
if n<2 then return 1 end
return f(n-1)+~-n*f(n-2)
end
Try it online!
Next sequence
• Open problem: does Lua have memoization? This should have exponential complexity... – Leaky Nun Jul 21 '17 at 19:10
• Hold on, you 4 people \o/ – Leaky Nun Jul 21 '17 at 19:14
# 18. APL (Dyalog), 37 bytes, A000018
{+/(1↓∪,∘.{(⍵×⍵)+16×⍺×⍺}⍨⍳1+2*⍵)≤2*⍵}
Try it online!
Next sequence
Warning: this is terribly inefficent
• @ETHproductions Yes, forgot the number – Kritixi Lithos Jul 21 '17 at 20:03
• Note: I changed the bytecount of this solution to make it slightly easier for the next solution. cc @ETHproductions – Kritixi Lithos Jul 21 '17 at 20:06
• -1 for changing the next sequence for no good reason – Peter Taylor Jul 21 '17 at 20:09
• Oh, that'll probably be solved before I'm back at a computer then – ETHproductions Jul 21 '17 at 20:09
# 23. Ruby, 23 bytes, A000982
a=->(n){(n*n/2.0).ceil}
Try it online!
Next sequence
23rd entry uses 23 bytes!
• Could you format this as asked in the question please? – caird coinheringaahing Jul 21 '17 at 22:51
• fixed, sorry bout that – Justin Jul 21 '17 at 22:52
# 27. C++, 584 bytes, A000274
#include <map>
#include <functional>
using namespace std;
int f(int i) {
map<int, int> m;
function<int(int)> a = [&](int j){
if (!m.count(j)) {
switch (j) {
case -1:
case 0:
m[j] = 0;
break;
case 1:
m[j] = 1;
break;
case 2:
m[j] = 3;
break;
default:
m[j] = (1+j)*a(j-1)+(3+j)*a(j-2)+(3-j)*a(j-3)+(2-j)*a(j-4);
}
}
return m[j];
};
return a(i - 1);
}
Recursive solution with caching.
Next Sequence (shouldn't be a tricky one)
• Since now different compilers are considered different languages, I think you should specify which compiler you are using. – NieDzejkob Sep 23 '17 at 12:03
->{$1**5} Try it online! Finally got Positron in here ^_^ Next sequence • Gosh darn it, I thought I had a chance to use Cubix, where the linear code is just I:***O@ – ETHproductions Jul 22 '17 at 0:51 • @ETHproductions :) Finally I managed to not get ninja'd... for once... lol – HyperNeutrino Jul 22 '17 at 0:52 # 32. C (gcc), 216 bytes, A000172 #include <stdio.h> #define cube(x) (x)*(x)*(x) int main(int a) { int n; scanf("%d",&n); int nCr = 1; int sum = 0; for(int r=0;r<=n;r++) { sum += cube(nCr); nCr *= n-r; nCr /= r+1; } printf("%d",sum); } Try it online! Next sequence # 33. Octave, 73 bytes, A000216 function o=s(x) if x<2 o=2; else o=sum((int2str(s(x-1))-'0').^2); end end Try it online! Pretty basic recursive formula. Next sequence # 45. D, 190 bytes, A000094 int A000094(int n) { if (n<4) { return 0; } int[] gf = new int[n+1]; gf[0] = 1; for (int i=1; i<n; i++) { for (int j=i; j<=n; j++) { gf[j] += gf[j-i]; } } return gf[n]-n+1; } Try it online! Next sequence • Never thought I'd see a D answer, nice job making me use Fortress. Grr. – Zacharý Aug 11 '17 at 21:49 # 46. Jellyfish, 21 bytes, A000190 p d^0 1|&*&*r E i Try it online! Next sequence • Oh noes, it's "Number of positive integers <= 2^n of form x^2 + 12 y^2. " – Leaky Nun Jul 22 '17 at 13:18 • This "Jellyfish" looks like a llama – HyperNeutrino Oct 31 '17 at 14:04 # 47. awk, 194 bytes, A000021 { n=0; for (i=1; i<=2**$1; i++) {
stop = 0;
for (x=0; x<=i && !stop; x++) {
for (y=0; y<=i && !stop; y++) {
if (x**2 + 12*y**2 == i){
n++; stop=1;
}
}
}
}
print n;
}
Try it online!
Next sequence | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3368215262889862, "perplexity": 4170.522730962139}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670601.75/warc/CC-MAIN-20191120185646-20191120213646-00539.warc.gz"} |
https://fr.mathworks.com/help/simbio/ug/create-and-simulate-a-simple-model.html | Documentation
### This is machine translation
Translated by
Mouseover text to see original. Click the button below to return to the English version of the page.
## Create and Simulate a Simple Model
This example shows how to create and simulate a simple model of receptor-ligand kinetics using the SimBiology Desktop.
### Receptor-Ligand Kinetics
In this model, ligand `L` and receptor `R` species form receptor-ligand complexes through reversible binding reactions. Using the mass action kinetics, the kinetic rate equation for the rate of change in concentration of receptor-ligand complex can be defined as $\frac{dC}{dt}={k}_{on}\cdot L\cdot R-{k}_{off}\cdot C$, where kon and koff are forward and reverse rate constants, `L`, `R`, and `C` are the concentrations of ligand, receptor, and receptor-ligand complex respectively. The objective of this simulation is to find the concentrations of all three species (`L`, `R`, and `C`) as the reaction progresses given initial amounts of species and rate constants.
### Create a Model
Open the SimBiology® desktop by typing `simbiology` in the MATLAB® Command Window or clicking SimBiology on the Apps tab.
On the Home tab, select Add Model > Create New Blank Model. Name the model as `m1` when prompted.
Select > Diagram to open the diagram view.
Rename the compartment to `cell` by double-clicking the text `unnamed`.
Drag and drop three species blocks and one reaction block inside the `cell` compartment.
Rename the species to `L` , `R`, and `C` as follows.
### Connect the Species and Reaction Blocks
To connect the ligand species block to the reaction block, press and hold the Ctrl key (Windows® and Linux®) or the Option key (Macintosh®), click the `L` species block, and drag the line to `reaction_1`. Similarly connect `R` to `reaction_1` and `reaction_1` to `C`.
### Update the Reaction Properties and Initial Amounts of the Reactant Species
Update the `reaction_1` properties to set the reaction as a reversible reaction, select mass action as kinetic law, and define the forward and reverse rate parameters:
• Double-click the `reaction_1` block to open the Reaction Properties dialog box.
• On the Settings tab, select Reversible.
• From KineticLaw drop-down list, select MassAction.
• Under Quantities Used by Reaction, enter `kon` as the name and `2.0E6` as the value for Forward Rate Parameter, and `koff` and `1E-4` for Reverse Rate Parameter.
Update the initial amounts of reactant species by entering `5E-9` and `1E-8` as `R` and `L` species values respectively. Click Close.
On the Model tab, select Add Task > Simulate model. This opens a new window called Task Editor, where you can edit and run the task. Given the previous initial amounts and rate parameters, the reaction reaches a saturated state after 300 seconds. Therefore, set the simulation stop time to 300 seconds instead of 10 seconds, which is the default stop time. To do so, expand the Task Stop Time section, select Use a Stop Time specific to this task only, and enter 300.
### Simulate the Model
To simulate the model, click the Run button.
Once the simulation is finished, the Live Plots section shows the States versus Time plot for each species.
Get trial now | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.707847535610199, "perplexity": 3949.154432424207}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999000.76/warc/CC-MAIN-20190619143832-20190619165832-00196.warc.gz"} |
http://dash.harvard.edu/handle/1/4892936 | # Effects of Short-Term Warming On Low and High Latitude Forest Ant Communities
Title: Effects of Short-Term Warming On Low and High Latitude Forest Ant Communities Author: Pelini, Shannon Lynn; Boudreau, Mark; McCoy, Neil; Ellison, Aaron M.; Gotelli, Nicholas J.; Sanders, Nathan J.; Dunn, Robert R. Note: Order does not necessarily reflect citation order of authors. Citation: Pelini, Shannon L., Mark Boudreau, Neil McCoy, Aaron M. Ellison, Nicholas J. Gotelli, Nathan J. Sanders, and Robert R. Dunn. Forthcoming. Effects of short-term warming on low and high latitude forest ant communities. Ecosphere. Full Text & Related Files: Pelini_EffectsShortTermWarming.pdf (625.3Kb; PDF) Abstract: Climatic change is expected to have differential effects on ecological communities in different geographic areas. However, few studies have experimentally demonstrated the effects of warming on communities simultaneously at different locales. We manipulated air temperature with $$\textit{in situ}$$ passive warming and cooling chambers and quantified effects of temperature on ant abundance, diversity, and foraging activities (predation, scavenging, seed dispersal, nectivory, granivory) in two deciduous forests at 35° and 43° N latitude in the eastern US. In the southern site, the most abundant species, $$\textit{Crematogaster lineolata}$$, increased while species evenness, most ant foraging activities, and abundance of several other ant species declined with increasing temperature. In the northern site, species evenness was highest at intermediate temperatures, but no other metrics of diversity or foraging activity changed with temperature. Regardless of temperature, ant abundance and foraging activities at the northern site were several orders of magnitude lower than those in the southern site. Published Version: http://www.esajournals.org/loi/ecsp Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:4892936
### This item appears in the following Collection(s)
• FAS Scholarly Articles [7456]
Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38310256600379944, "perplexity": 11216.162954202877}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416400373899.42/warc/CC-MAIN-20141119123253-00118-ip-10-235-23-156.ec2.internal.warc.gz"} |
http://mathematica.stackexchange.com/users/2672/jack-henahan | # Jack Henahan
less info
reputation
2
bio website location age 24 member for 1 year, 11 months seen Apr 26 '13 at 6:10 profile views 13
# 1 Question
0 Calculating orbital period for the logistical map [closed]
# 101 Reputation
This user has not answered any questions
# 5 Tags
0 dynamic 0 homework 0 system 0 matlab 0 code-review
# 23 Accounts
Mathematics 447 rep 312 TeX - LaTeX 401 rep 26 Stack Overflow 394 rep 410 Science Fiction & Fantasy 381 rep 15 Area 51 151 rep 1 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9039866924285889, "perplexity": 11229.676370328423}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500832738.80/warc/CC-MAIN-20140820021352-00016-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://www.math.u-szeged.hu/mathweb/index.php/hu/uj-esemeny/icalrepeat.detail/2020/01/21/1452/16/mihaly-pituk-university-of-pannonia-veszprem-ergodicity-in-nonautonomous-linear-ordinary-differential-equations | Év szerint Hónap szerint Ugrás a hónaphoz
## Mihály Pituk (University of Pannonia, Veszprém): Ergodicity in nonautonomous linear ordinary differential equations
Kedd, 21. Január 2020, 11:00 - 13:00
Abstract. The weak and strong ergodic properties of nonautonomous linear ordinary differential equations will be considered. We will show that if the coefficient matrix function is bounded, essentially nonnegative and uniformly irreducible, then the normalized positive solutions are asymptotically equivalent to the Perron vectors of the strongly positive transition matrix at infinity (weak ergodicity). If, in addition, the coefficient matrix function is uniformly continuous, then the convergence of the normalized positive solutions to the same strongly positive limiting vector (strong ergodicity) is equivalent to the convergence of the Perron vectors of the coefficient matrices. This is a joint work with Professor Christian Pötzsche (Alpen-Adria University Klagenfurt, Austria).
Hely : Bolyai Intézet, I. emelet, Riesz terem, Aradi vértanúk tere 1., Szeged | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9797007441520691, "perplexity": 2129.6080845362253}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334596.27/warc/CC-MAIN-20220925193816-20220925223816-00449.warc.gz"} |
http://quant.stackexchange.com/questions/14102/worked-examples-of-applying-itos-lemma | Worked examples of applying Ito's lemma
In most textbooks Ito's lemma is derived (on different levels of technicality depending on the intended audience) and then only the classic examples of Geometric Brownian motion and the Black-Scholes equation are given.
My question
I am looking for references where lots of worked examples of applying Ito's lemma are given in an easy to follow, step by step fashion. Also more advanced cases should be covered.
- | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8215586543083191, "perplexity": 507.129770111984}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936461216.38/warc/CC-MAIN-20150226074101-00156-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://docs.webfactory-i4.com/i4connected/en/configuring-the-report-emailing-settings.html | # i4connected Knowledgebase 5.6
#### Configuring the Report Emailing Settings
Abstract
Learn how to configure the i4connected email settings for delivering reports, by checking out this step-based tutorial.
This article describes how to configure the email settings for delivering reports.
In order to deliver the reports using the email service, the proper settings must be done in the Reporting Server configuration file. The settings must address the location of the Reporting Server, the database connection string and the actual email settings.
1. Open the WEBfactory.DWH.Reporting.Server.exe.config file located in the Reporting server installation directory (by default at C:\Program Files\WEBfactory\Data Warehouse\WEBFACTORY\Reporting) using the preferred text editor.
WEBfactory.DWH.Reporting.Server.exe.config file
2. Locate the SqlReportingServerHost key under the <appSettings> node and add the SQL Reporting server host in the Value attribute. If the path is already existing, make sure that it is the correct one.
<appSettings>
...
value="http://pemstestsql/ReportServer/"/>
...
</appSettings>
3. Locate the DataWarehouseSQLConnectionString key under the <connectionStrings> node and make sure that the connectionString attribute points to the correct database.
<connectionStrings>
<add name="DataWarehouseSQLConnectionString" connectionString="Data Source=pemstestsql;Initial Catalog=WEBfactory.DWH.Data.Database;Persist Security Info=True;User ID=sa;Password=webfactory" providerName="System.Data.SqlClient" />
</connectionStrings>
4. Locate the <mailSettings> node under the <system.net> node. Here you can configure the SMTP and Network parameters for sending the emails:
SMTP parameters
from
The email address used for sending the reporting emails. This must be a valid email address.
deliveryMethod
The delivery method used for sending emails. For sending report emails, the Network delivery method must be used.
Network parameters
host
The SMTP mail server host name used to send emails.
port
The SMTP port. When not using SSL, the default port is 25. When using SSL, the default value is 587.
enableSsl
Enable or disable SSL secure communication (true/false). The default value is false. The Port must be adjusted when setting the enableSSL parameter to true.
The SMTP user name.
defaultCredentials
Enable or disable the usage of default credentials (true/false). The default value is false.
DefaultCredentials represents the system credentials for the current security context in which the application is running. If the UseDefaultCredentials property is set to false, then the value set in the Credentials property will be used for the credentials when connecting to the server. If the UseDefaultCredentials property is set to false and the Credentials property has not been set, then mail is sent to the server anonymously
You can find out more about the <smtp> element here: <smtp> Element (Network Settings).
You can find out more about the <network> element here: <network> Element (Network Settings).
Example with SSL:
<system.net>
<mailSettings>
<smtp from="report.webfactory@mailprovider.com" deliveryMethod="Network">
<network host="smtp.mailprovider.com" port="587" enableSsl="true" userName="report.webfactory@mailprovider.com" password="samplepwd" defaultCredentials="false" />
</smtp>
</mailSettings>
</system.net>
Example without SSL:
<system.net>
<mailSettings>
<smtp from="report.webfactory@mailprovider.com" deliveryMethod="Network">
<network host="smtp.mailprovider.com" port="25" enableSsl="false" userName="report.webfactory@mailprovider.com" password="samplepwd" defaultCredentials="false" />
</smtp>
</mailSettings>
</system.net>
5. After all the settings are done, the Reporting Server service needs to be restarted. Open Services.msc, locate the WEBfactory DWH Reporting Server service and restart it (right-click > restart). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1535104662179947, "perplexity": 10988.568555267666}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704800238.80/warc/CC-MAIN-20210126135838-20210126165838-00778.warc.gz"} |
http://mail-index.netbsd.org/port-powerpc/2012/03/13/msg003167.html | Port-powerpc archive
# Re: Interrupt handling and routing: The Big Picture
On Tue, 13 Mar 2012 10:49:45 -0400
Michael <macallan%netbsd.org@localhost> wrote:
> The reason why the interrupt code looks like this is the fact
> that there are many powerpc boxes with several cascaded interrupt
> controllers
I perfectly understand that the code is that complicated because it
needs to be that complicated. The core interrupt code has to support
many different machines with very different hardware. This causes the
complexity. But I never did any work in that area before, so all the
details obfuscate the essential things.
German idiom: "You can't see the forest because of all the trees."
OK. I'll dive into Roberts code now. Thanks for the help.
--
\end{Jochen}
\ref{http://www.unixag-kl.fh-kl.de/~jkunz/}
Home | Main Index | Thread Index | Old Index | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4709426462650299, "perplexity": 5471.966169022647}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721008.78/warc/CC-MAIN-20161020183841-00355-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://secgroup.dais.unive.it/teaching/cryptography/advanced-encryption-standard/comment-page-1/ | The AES cipher
The Advanced Encryption Standard (AES) has been selected by the National Institute of Standards and Technology (NIST) after a five-year long competition. The original name of the cipher is Rijndael from the names of the two inventors, the cryptographers Joan Daemen and Vincent Rijmen. As any modern cipher, AES is the composition of rather simple operations and contains a non-linear component to avoid known-plaintexts attacks (as the one we have seen on the Hill cipher). The composed operations give a non-idempotent cipher that is iterated for a fixed number of rounds.
Rijndael has been selected because it resulted to be the best one providing:
• high security guarantees
• high performance
• flexibility (different key length)
All of these features are, in fact, crucial for any modern cipher. Its predecessor, the Data Encryption Standard (DES) is still in use after almost 40 years, in a variant called Triple DES (3DES), which aims at improving the key length. In fact, DES key of only 56 bits is too short to resist brute-forcing on modern, parallel computers.
Mathematical background
AES works on the Galois Field with $2^8$ elements noted $\mathbf{GF}(2^8)$. Intuitively, it it the set of all 8-bit digits with sum and multiplications performed by interpreting the bits as (binary) coefficients of polinomials. For example, element 11010011 can be seens as $x^7 + x^6 + x^4 + x + 1$ while 00111010 is $x^5+x^4+x^3 + x$. The sum will thus be $x^7+x^6+x^4+x+1+x^5+x^4+x^3+x=x^7+x^6+x^5+x^3+1$, since two 1’s coefficient becomes 0, modulo 2, and the term disappears (for example $x + x = 2x = 0x = 0$). We see that sum and subtraction are just the bit-wise xor of the binary numbers, i.e., $11010011 \oplus 00111010 = 11101001$ which is $x^7+x^6+x^5+x^3+1$.
Product is done modulo the irreducible polinomial x8 + x4 + x3 + x + 1. Irreducible means that it cannot be written as the product of two other polinomials (it is, intuitively, the equivalent of primality). For example, $(x^7 + x^6 + x^4 + x + 1) \times (x^5+x^4+x^3 + x)$ gives
$x^{12} + x^{11} + x^9 + x^6 + x^5+x^{11}+x^{10}+x^8+x^5+x^4+x^{10}+x^9+x^7+x^4+x^3+x^8+x^7+x^5+x^2+x = x^{12}+x^6+x^5+x^3+x^2+x$
Now to divide $x^{12}+x^6+x^5+x^3+x^2+x$ by $x^8 + x^4 + x^3 + x + 1$ and find the reminder we proceed as follows:
$\begin{array}{ccccccccccccc}1&0&0&0&0&0&1&1&0&1&1&1&0 \\ 1&0&0&0&1&1&0&1&1 \\\hline & & & &1&1&1&0&1&1&1&1&0\\ & & & &1&0&0&0&1&1&0&1&1 \\\hline & & & & &1&1&0&0&0&1&0&1 \end{array}$
which gives 11000101, i.e., $x^7 + x^6 + x^2 + 1$.
This operation is quadratic in general, with respect to the number of bits (8). It can be optimized with the following linear algorithm (which is, in fact, a working python code):
The correctness derives from the invariant, after each loop: ab+p is the product of the initial a and b (all operation does in the Galois Field). Since b is 0 at the end, we have that p will contain the product. This fact derives from the following observations:
• b is shifted to the right and a is shifted to the left meaning that we respectively divide and multiply by $x$ the two polynomials;
• if b is odd the polynomial is no dividable by $x$ so we throw away the least significant bit (this is what the right shift does, actually) and we accumulate one a in p to compensate and keep the invariant;
• when a becomes more than 28 we need to sum to it the modulus 100011011, i.e. 0x11b, to keep it 8-bits long.
NOTE: to test the code just open a python shell (by running python from the terminal) and cut and paste the function into the shell, giving enter at the end. You can now try
The AES cipher
Now that we have introduced the basic operation used to implement AES we can describe the cipher. The official description of AES is available on-line.
AES operates on a 4×4 matrix of bytes. We have that 16 bytes are 128 bits which is, in fact, the block size. Plaintext bytes $b_1,\ldots,b_{16}$ are copied in the matrix by columns following this scheme:
$\begin{bmatrix}b_1&b_5&b_9&b_{13}\\b_2&b_6&b_{10}&b_{14}\\b_{3}&b_7&b_{11}&b_{15}\\b_4&b_8&b_{12}&b_{16}\end{bmatrix}$
Cipher keys have lengths of 128, 192, and 256 bits. AES has 10 rounds for 128-bit keys, 12 rounds for 192-bit keys, and 14 rounds for 256-bit keys. Rijndael was designed to handle additional block sizes and key lengths, however they are not adopted in the AES standard. A round is composed of different operations, all of which are invertible:
• AddRoundKey. The round key (see Key Expansion, below) is bitwise xor-ed with the block. A round key is thus 128 bits, independently of the chosen key size.
• SubBytes. A fixed non-linear substitution, called S-box, is applied to each byte of the block. The substitution is reported below. Given a byte in hexadecimal notation, the first digit is used to select a row and the second one to select a column. For example, 0x25 would be the third row (2) and the sixth column (5) giving 0x3f.
NOTE: This S-box has been obtained by taking, for each byte, its multiplicative inverse in the finite field (that can be computed efficiently via an algorithm that we will see later on), noted $b_7, \ldots, b_0$, and applying the affine transformation $b_i = b_i \oplus b_{i+4 \mod 8} \oplus b_{i+5 \mod 8} \oplus b_{i+6 \mod 8}\oplus b_{i+7 \mod 8} \oplus c_i$, with $c_i$ representing the i-th bit of 01100011. The above transformation can be written as:
$\begin{bmatrix}b_0\\b_1\\b_2\\b_3\\b_4\\b_5\\b_6\\b_7\end{bmatrix}=\begin{bmatrix}1&0&0&0&1&1&1&1\\1&1&0&0&0&1&1&1\\1&1&1&0&0&0&1&1\\1&1&1&1&0&0&0&1\\1&1&1&1&1&0&0&0\\0&1&1&1&1&1&0&0\\0&0&1&1&1&1&1&0\\0&0&0&1&1&1&1&1\end{bmatrix}\begin{bmatrix}b_0\\b_1\\b_2\\b_3\\b_4\\b_5\\b_6\\b_7\end{bmatrix} \oplus \begin{bmatrix}1\\1\\0\\0\\0\\1\\1\\0\end{bmatrix}$
Using multiplicative inverses is known to give non-linear properties, while the affine transformation complicates the attempt of algebraic reductions.
• ShiftRows. Rows of the block matrix are shifted to the left by 0,1,2,3, respectively. The shift is circular:
$\begin{bmatrix}b_1&b_5&b_9&b_{13}\\b_2&b_6&b_{10}&b_{14}\\b_{3}&b_7&b_{11}&b_{15}\\b_4&b_8&b_{12}&b_{16}\end{bmatrix} \Rightarrow\begin{bmatrix}b_1&b_5&b_9&b_{13}\\b_6&b_{10}&b_{14}&b_2\\b_{11}&b_{15}&b_{3}&b_7\\b_{16}&b_4&b_8&b_{12}\end{bmatrix}$
• MixColumns. Columns of the block matrix are multiplied by the following matrix
$\begin{bmatrix}c_0\\c_1\\c_2\\c_3\end{bmatrix} = \begin{bmatrix}2&3&1&1\\1&2&3&1\\1&1&2&3\\3&1&1&2\end{bmatrix}\begin{bmatrix}c_0\\c_1\\c_2\\c_3\end{bmatrix}$
For example the first byte of each column is computed as $2c_0 \oplus 3c_1 \oplus c_2 \oplus c_3$.
NOTE: This fixed matrix is obtained by considering each column as a four-term polynomial with coefficients in $\mathbf{GF}(2^8)$. The columns are then multiplied modulo $x^4 + 1$ with a fixed polynomial a(x), given by $a(x) = 3x^3 + x^2 + x + 2$. This specific modulus is such that, e.g., $x^4$ becomes $x^0$, $x^5$ becomes $x^1$ and so on.
• Key Expansion. We have mentioned that AES uses round keys in the AddRoundKey step. These keys are in fact derived from the initial AES key as follows.
Keys are represented as arrays of words of 4 bytes. So, for example, a 128 bit key will be 4 words of 4 bytes, i.e., 16 bytes. This is expanded into an array of size 4 * (Nr + 1), where Nr is the number of rounds. In this way we obtain 4 different words of key for each round.
Let Nk note the number of words of the initial key (e.g. 4 for 128 bits). The first Nk words of the key array are the same as the initial key. Next i-th word is obtained from the previous i-1 word, possibly transformed as described below, xor-ed with word i-Nk. The transformation happens only for words in position multiple of Nk and consists of a cyclic left shift of word bytes by one position (RotWord) followed by a byte-wise application of the S-box (SubWord) and a xor with a round constant (Rcon). This constant at step j is the word [$x^{j-1}$,0x00,0x00,0x00] with $x^{j-1}$ computed in the galois field, meaning $02^{j-1}$ since polynomial $x$ is the binary number 00000010, i.e., 0x02.
Pseudocode follows:
IMPORTANT NOTE: for 256 bit key, when i-4 is a multiple of Nk SubWord is applied to w[i-1] before the xor. This has been omitted in the code for the sake of readability.
Of course the first byte of Rcon can be precomputed. Here is the table:
Here is the overall scheme for AES assuming that variable state is initialized with the 4×4 matrix of the plaintext (see above) and w[] has been initialized by key expansion:
Decryption is computed by applying inverse operations:
Notice that AddRoundKey is unchanged since xor is the inverse of itself. InvShiftRows trivially amounts to revert the shifts on the row (to the right instead of left). InvSubBytes is computed by using the following inverse substitution of the S-Box:
Finally, InvMixColumns is given by the following operation
$\begin{bmatrix}c_0\\c_1\\c_2\\c_3\end{bmatrix} = \begin{bmatrix}0e&0b&0d&09\\09&0e&0b&0d\\0d&09&0e&0b\\0b&0d&09&0e\end{bmatrix}\begin{bmatrix}c_0\\c_1\\c_2\\c_3\end{bmatrix}$
For example the first byte of each column is computed as $0e c_0 \oplus 0b c_1 \oplus 0d c_2 \oplus 09 c_3$.
NOTE: This fixed matrix is obtained by considering each column as a four-term polynomial with coefficients in $\mathbf{GF}(2^8)$. The columns are then multiplied modulo $x^4 + 1$ with the inverse of the fixed polynomial a(x), given by $a^{-1}(x) = 0b x^3 + 0d x^2 + 09 x + 0e$.
The algorithm for decryption is written in a form similar to the one for encryption but operations are not in the same order. It can, in fact, become the very same algorithm by noticing that
1. SubBytes and ShiftRows commute. It does not matter if we first apply the byte-wise substitution or if we first shift the rows. The final result will be the same. Of course, the same holds for the inverse transformations
2. InvMixColumns(state $\oplus$ roundKey) = InvMixColumns(state) $\oplus$ InvMixColumns(roundKey). This allows for inverting the two functions, provided that InvMixColumns is applied to the all the round keys.
Call dw the array containing the round keys transformed via InvMixColumns. The final decryption algorithm is:
This is exactly the same as the one for encryption, but with the inverse functions. Having the same algorithm for encryption and decryption simplifies a lot implementations, especially if they are done in hardware.
Challenge: 1-round AES
(This challenge will give a +2 score for the first working solution posted and a +2 score for the most elegant one. Any original contribution will give some extra score).
It has been intercepted the following ciphertext:
Rumors tell that it is a mail to Joan Daemen (one of AES authors) encrypted with ECB mode using a simplified 1-round AES cipher:
Can you recover the whole message?
NOTE: If you want to test AES implementation look at the official AES description (also linked from the AES lesson): at page 35, Appendix C, it gives example vectors.
One thought on “The AES cipher”
1. If you want to see the algorithm for multiplication at work save this in a file named mult.py and run it by issuing python mult.py in a terminal. It will show the intermediate values and the invariant at each step.
Notice that the invariant is computed using the algorithm itself as it assumes all operations in the field.
def AESmult(a, b, debug):
p = 0 # p is 0 at the beginning
for i in range(0,8): # for the 8 bits of a and b do:
if b & 1 != 0: # the least significant bit of b is set
p = p ^ a # sum a to p (xor)
b >>= 1 # shifts b to the right
hbit = (a & 0x80) != 0 # true if the most significant bit of a is set
a <<= 1 # shifts a to the left
if hbit: # if the most significant bit of a was set
a = a ^ 0x11b # sum 100011011 to a (xor), this always returns
# a 8-bit number
if debug:
print 'a={0:08b} b={1:08b} p={2:08b} axb+p={3:n}'.format( a,b,p, AESmult(a,b,False) ^ p )
return p
r = AESmult(0b11010011,0b00111010,True)
print r, bin(r)
This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 43, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8026427030563354, "perplexity": 994.6968454159605}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987751039.81/warc/CC-MAIN-20191021020335-20191021043835-00234.warc.gz"} |
https://www.ias.ac.in/describe/article/boms/033/04/0371-0376 | • Synthesis of nano-particle and highly porous conducting perovskites from simple in situ sol–gel derived carbon templating process
• # Fulltext
https://www.ias.ac.in/article/fulltext/boms/033/04/0371-0376
• # Keywords
Perovskite; EDTA-citrate; sol–gel; carbon template; porous ceramics.
• # Abstract
Nano-sized La0.6Sr0.4Co0.2Fe0.8O$_{3–\delta}$ (LSCF) and La0.8Sr0.2MnO$_{3–\delta}$ (LSM) oxides were synthesized by a simple in situ sol–gel derived carbon templating process. Nano-sized LSCF–carbon and LSM–carbon composites were first obtained with a grain size of 20–30 nm. Further calcination of the obtained composites under air resulted in the nano-sized pure-phase perovskites with crystalline size of as small as 14 nm. Such a decrease in crystalline size of perovskite via the indirect calcination process was ascribed to the suppressing effect of carbon in the grain growth of perovskite. Furthermore, when the in situ created carbon was applied as a template for pore forming, a highly porous perovskite sintering body packing from the nano-sized perovskite oxide was obtained.
• # Author Affiliations
1. State Key Laboratory of Materials-oriented Chemical Engineering, Nanjing University of Technology, No. 5 Xin Mofan Road, Nanjing, JiangSu 210009, P.R. China
• # Bulletin of Materials Science
Volume 43, 2020
All articles
Continuous Article Publishing mode
• # Editorial Note on Continuous Article Publication
Posted on July 25, 2019 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32341471314430237, "perplexity": 22859.21872764393}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875148163.71/warc/CC-MAIN-20200228231614-20200229021614-00285.warc.gz"} |
https://stats.stackexchange.com/questions/444561/small-noise-of-state-process-and-filtering | # Small noise of state process and filtering
Assume we have a linear state-space model: $$z_{k} = Hx_{k} + v_{k}\\ x_{k} = F x_{k-1}+ w_{k}.$$
We are interested in filtering, i.e. we aim to estimate $$E[x_{n}|z_{0}, \dots, z_{n}]$$. If the measurement noise goes to zero, i.e. $$var(v_{k}) \to 0$$, then filtering does not give much to us and the filtered data is almost the same as original.
What is the opposite situation, when $$var(w_{k}) \approx 0$$ and $$var(v_{k})$$ is fixed? What would be the outcome of Kalman filter?
• I think you have a mistake in your question. v_k is measurement noise. w_k is process noise. Jan 23, 2020 at 13:14
• Dear @Anton, you are right! Thank you! I have edited.
– ABK
Jan 23, 2020 at 19:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.936797022819519, "perplexity": 510.65400866053295}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662510138.6/warc/CC-MAIN-20220516140911-20220516170911-00094.warc.gz"} |
https://jp.arxiv.org/list/math.CV/1204 | Complex Variables
Authors and titles for math.CV in Apr 2012
[ total of 47 entries: 1-25 | 26-47 ]
[ showing 25 entries per page: fewer | more | all ]
[1]
Title: Condition R and proper holomorphic maps between equidimensional product domains
Comments: Some typos fixed in this final version. To appear in {\em Advances in Mathematics.}
Subjects: Complex Variables (math.CV)
[2]
Title: Constraints on hypothetical counterexamples to the Casas-Alvero conjecture
Subjects: Complex Variables (math.CV)
[3]
Title: Large Harnack inequalities, Kobayashi distances and holomorphic motions
Authors: E.M. Chirka
Subjects: Complex Variables (math.CV)
[4]
Title: Differential Subordinations Involving Generalized Bessel Functions
Comments: 15 pages, accepted in Bulletin of the Malaysian Mathematical Sciences Society
Journal-ref: Bull. Malays. Math. Sci. Soc., 38 (2015), 1255-1280
Subjects: Complex Variables (math.CV)
[5]
Title: Symmetrization of plurisubharmonic and convex functions
Comments: 16 pages. In the revised version a problem that was left open in the original version has been solved
Subjects: Complex Variables (math.CV); Functional Analysis (math.FA)
[6]
Title: Pseudoconvex domains spread over complex homogeneous manifolds
Journal-ref: Manuscripta Math. 142 (2013), no. 1-2, 35-59
Subjects: Complex Variables (math.CV)
[7]
Title: The Poletskii and Väisälä inequalities for the mappings with $(p, q)$--distortion
Subjects: Complex Variables (math.CV)
[8]
Title: On the lemniscate components containing no critical points of a polynomial except for its zeros
Authors: V. N. Dubinin
Subjects: Complex Variables (math.CV)
[9]
Title: A new class of harmonic measure distribution functions
Subjects: Complex Variables (math.CV)
[10]
Title: A note on a smoothing property of the harmonic Bergman projection
Authors: A.-K. Herbig
Journal-ref: Internat. J. Math. 24 (2013), no. 4, 1350032, 14 pp
Subjects: Complex Variables (math.CV)
[11]
Title: Sur les courbes de Brody dans P^n(C)
Subjects: Complex Variables (math.CV)
[12]
Title: On some properties of solutions of the $p$-harmonic equation
Comments: 19 pages; This is a 2009 preprint of the authors; Accepted from "Filomat"
Subjects: Complex Variables (math.CV)
[13]
Title: The minimal surfaces over the slanted half-planes, vertical strips and single slit
Comments: 18 pages (including 26 figures), with a journal
Subjects: Complex Variables (math.CV)
[14]
Title: On a particular integral operator
Subjects: Complex Variables (math.CV)
[15]
Title: About one modulus inequality of the Väisälä Type
Subjects: Complex Variables (math.CV)
[16]
Title: A remark on the relative extremal function
Subjects: Complex Variables (math.CV)
[17]
Title: On cubic-linear polynomial mappings
Journal-ref: Indag. Math. (N.S.) 8 (1997), no. 4, 471-492
Subjects: Complex Variables (math.CV); Algebraic Geometry (math.AG)
[18]
Title: Blaschke-type conditions in unbounded domains, generalized convexity and applications in perturbation theory
Subjects: Complex Variables (math.CV); Spectral Theory (math.SP)
[19]
Title: Coefficient bounds for new subclasses of bi-univalent functions
Comments: 7 pages, submitted to any Journal for publication
Subjects: Complex Variables (math.CV)
[20]
Title: Lempert Theorem for stronly linearly convex domains with smooth boundaries
Subjects: Complex Variables (math.CV)
[21]
Title: Some sufficient conditions for the univalence of an integral operator
Comments: 6 pages, submitted a journal
Subjects: Complex Variables (math.CV)
[22]
Title: On neighborhood and partial sums problem for generalized Sakaguchi type functions
Comments: 11 pages, submitted to a journal for publication
Subjects: Complex Variables (math.CV)
[23]
Title: A restricted shift completeness problem
Journal-ref: Journal of Functional Analysis 263 (2012), p. 1887-1893;
Subjects: Complex Variables (math.CV)
[24]
Title: Existence of CR sections for high power of semi-positive generalized Sasakian CR line bundles over generalized Sasakian CR manifolds
Authors: Chin-Yu Hsiao | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7984808087348938, "perplexity": 6293.633089109242}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943750.71/warc/CC-MAIN-20230322051607-20230322081607-00303.warc.gz"} |
https://www.tutorialspoint.com/how-do-you-make-a-string-in-php-with-a-backslash-in-it | # How do you make a string in PHP with a backslash in it?
When the backslash \ does not escape the terminating quote of the string or even create a valid escape sequence (in double quoted strings), then the below code can be used to produce one backslash −
## Example
Live Demo
$string = 'abc\def'; print($string);
## Output
This will produce the following output −
abc\def
## Example
Live Demo
$string = "abc\def"; print($string);
## Output
This will produce the following output −
abc\def | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6372813582420349, "perplexity": 4124.395619713222}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943484.34/warc/CC-MAIN-20230320144934-20230320174934-00572.warc.gz"} |
http://nodus.ligo.caltech.edu:8080/40m/?id=7974 | 40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
40m Log, Page 177 of 335 Not logged in
ID Date Author Type Category Subject
7981 Fri Feb 1 09:33:11 2013 JamieUpdateLockingPRM/PR2 cavity
I replaced the BS1 between the POPDC PD and the camera with a 98 reflector, and moved the 50 up before the BS to dump half the light. Still saturating POPDC, but hopefully the ratio between POPDC and the camera should be better. We just need to dump more of the power before we get there. I'll come back to this after C&D if no one else has already gotten to it.
I don't know why I didn't pay more attention last night, but things look way WAY better. The beams are much cleaner and the power level is much much higher.
7980 Thu Jan 31 23:48:45 2013 KojiUpdateLockingPRM/PR2 cavity
Wow! What's happened?
As the video showed good quality of resonances, I stopped by at the 40m on the way back home.
I looked at the error signals and found that they indicate high finesse and clear resonance of the sidebands.
The lock was immediate once the gain is set to be -0.004 (previous 0.05ish). This implies the optical gain is ~10 times larger than the previous configration.
The alignment was not easy as POPDC was saturated at ~27000I leave this as a daytime job.
As I misaligned the PRM, I could see that the lock hopped into the next higher order. i.e .from TEM00 to TEM01, from TEM01 to TEM02, etc
This means that the modes are closely located each other, but sufficiently separated to sustain each mode.
I definitely certify that cavity scans will give us meaningful information about the cavity.
7979 Thu Jan 31 22:14:11 2013 ranaSummaryASCOptics lit
Gouy not Guoy:
http://www.rp-photonics.com/gouy_phase_shift.html
pronounced Goo-eee, with the emphasis on the second syllable.
7978 Thu Jan 31 20:06:22 2013 EvanUpdateLockingPRM/PR2 cavity
[Jenne, Evan]
Tonight we made a non-folded cavity between the PRM and PR2 as follows. I put down two dog clamps to constrain the original position of the PR2 mount. I then loosened the dog clamps holding the mount to the table and nudged the mount until we saw a few reasonably well-aligned bounces in the cavity. I then dogged down the mount.
We played with the PRM and TT2 steering until we saw flashes of TEM00. However, the resonance is not clean so we couldn't lock.
Since we changed the PRM alignment, we had to redo the last bit of steering for the PRM oplev into the photodiode. We also put a few ND filters on the POP camera.
7977 Thu Jan 31 15:56:38 2013 RijuUpdate Photodiode transimpedance
Summary: Measurement and plot of shot-noise-intercept-current for PDA10CF.
Motivation:It is to measure the shot noise intercept current for PDA10CF.
Result: The final plot is attached here. The plot suggests that the value of shot-noise-intercept current is 0.21mA
Discussion:
The plot is for the measured data of Noise voltage (V/sqrt(Hz)) vs DCcurrent(A). The fitted plot to this measured data follows the noise equation
Vnoise = gdet* sqrt[ 2e (iDC+idet)] , where gdet= transimpedance of the PD in RF region as described in manual of PDA255 (i.e. 5e3 when it is not in High-impedance region).
To get an approximate idea of the shot noise intercept current, we may follow the same procedure described in 7946
In the present case dark-noise is 4.3e-08 V/sqrt(Hz)
Therefore dark current(in2) ~dark noise voltage/RF transimpedance = 8.6pA/sqrt(Hz)
Therefore the approximate shot noise intercept current ~ (8.6/18)^2=0.22mA
This value matches well with the fitted data.
From PDA10CF manual, NEP=1.2e-11W/sqrt(Hz) and responsivity~0.9A/W. Therefore the noise current level will be ~10pA.
Attachment 1: shotnoiseinterceptpda10cf.pdf
7976 Thu Jan 31 15:34:22 2013 RijuUpdateRF SystemPhotodiode transimpedance
Quote:
Quote: Today I collected the data for shot noise intercept current for MC REFL PD. I didn't get many data points at higher DC voltage of the photodiode, cause the incandescent bulbs get burnt at that level; two bulbs I have burnt today. I will process the data and report.
This work was done in-situ, so no optics on the AS table were moved. The PSL shutter was blocked since the IR beam was not necessary, and would scatter off the bulb Riju put in front of the PD.
Thanks Jenne.
7975 Thu Jan 31 15:20:46 2013 ZachUpdateLockingMode spacing calc
I should mention that I just found a bug in how it treats odd-mirror-number cavities. For such cavities, HG modes with odd horizontal indices should receive an extra roundtrip phase of pi/2 (due to the rotation by the cavity). Because of a numbering convention issue, arbcav actually used to apply this phase shift to even-order modes. Essentially, the only difference is that the fundamental mode was shifted to anti-resonance. Everywhere else, there are modes at both corresponding locations in frequency space, and so it does not back a big difference in terms of cavity design.
Thanks to this IMC modeling we are doing at the workshop, I caught it! It has been fixed in the SVN.
Quote: I have calculated (using Zach's sweet software) the expected mode content for the various possible PRCs that we can make. Also, Zach was right about the factor of 2. I see now that I was calculating the mode spacing between a plane wave and a HOM, so the guoy phase had a factor of (n+m+1). The right thing to do is to get the spacing between the 00 mode and HOMs, so the guoy phase just has (n+m). Switching from n+m+1=2 to n+m=1, that fixes the factor of 2 problem. I attach my results as a pdf, since I'm listing out 5 configurations. Each config has a cartoon, with a small (hard to read) HOM plot, and then at the end, each HOM plot is shown again, but larger. Also, "TM" is the "test mirror", the flat G&H that we're using as the cavity end mirror.
7974 Thu Jan 31 14:46:05 2013 JenneUpdateRF SystemPhotodiode transimpedance
Quote: Today I collected the data for shot noise intercept current for MC REFL PD. I didn't get many data points at higher DC voltage of the photodiode, cause the incandescent bulbs get burnt at that level; two bulbs I have burnt today. I will process the data and report.
This work was done in-situ, so no optics on the AS table were moved. The PSL shutter was blocked since the IR beam was not necessary, and would scatter off the bulb Riju put in front of the PD.
7973 Thu Jan 31 14:30:50 2013 JenneUpdateLockingMode spacing calc
I have calculated (using Zach's sweet software) the expected mode content for the various possible PRCs that we can make.
Also, Zach was right about the factor of 2. I see now that I was calculating the mode spacing between a plane wave and a HOM, so the guoy phase had a factor of (n+m+1). The right thing to do is to get the spacing between the 00 mode and HOMs, so the guoy phase just has (n+m). Switching from n+m+1=2 to n+m=1, that fixes the factor of 2 problem.
I attach my results as a pdf, since I'm listing out 5 configurations. Each config has a cartoon, with a small (hard to read) HOM plot, and then at the end, each HOM plot is shown again, but larger. Also, "TM" is the "test mirror", the flat G&H that we're using as the cavity end mirror.
Attachment 1: Half_PRC_Configs.pdf
7972 Thu Jan 31 12:44:42 2013 RijuUpdate Photodiode transimpedance
Today I collected the data for shot noise intercept current for MC REFL PD. I didn't get many data points at higher DC voltage of the photodiode, cause the incandescent bulbs get burnt at that level; two bulbs I have burnt today. I will process the data and report.
7971 Thu Jan 31 11:53:31 2013 ManasaUpdateScatteringScattering setup
Since we are in air, we came up with a plan B. The plan is to temporarily install a mirror in the ITMY chamber to steer the beam from the laser pointer (installed on the POY table) through ITMY to the pickoff mirror at the ETMY end. This way, we can install the camera at the ETMY window and be sure we are looking at ITMY scattered light.
[Jan,Manasa]
We executed plan B. We installed the green laser pointer on POY table and steered the beam through ITMY to hit the pick off mirror at the ETM end by installing *temporary mirrors. The pick off mirror was adjusted in pitch and yaw to center the reflected beam on the viewport window. We have installed irides on the ring attached to the viewport window to direct the beam to the camera.
*Temporary mirrors were removed from the ITMY chamber after this alignment.
7970 Thu Jan 31 10:23:39 2013 JamieUpdateComputersc1iscex still down
Quote: [Koji, Jenne] We noticed that the iscex computer is still down, but the IOP is (was) running. When we sat down to look at it, c1x01 was 'breathing', had a non-zero CPU_METER time, and the error was 0x4000, which I've never seen before. The fb connection was still red though. Also, it is claiming that its sync source is 1pps, not TDS like it usually is. Since things were different, Koji restarted the 2 other models running on iscex, with no resulting change. We then did a 'rtcds restart all', and the IOP is no longer breathing, and the error message has changed to 0xbad. The sync source is still 1pps. Moral of the story: c1iscex is still down, but temporarily showed signs of life that we wanted to record.
There's definitely a timing issue with this machine. I looked at it a bit yesterday. I'll try to get to it by the end of the week.
7969 Wed Jan 30 19:34:17 2013 JenneUpdateLockingPRM coils need diagonalizing
[Koji, Jamie, Jenne]
Koji did this, while we actuated on PRM in pos, and watched the oplev. Empirically, he found the following values for the POS column of the output matrix:
UL = 1.020
UR = 0.990
LL = 1.000
LR = 0.970
SD = 0.000
(The nominal values are all +1, except for Side, which is 0).
Actuation of PRM was through C1:SUS-PRM_LSC_EXC, f=0.1Hz, A=100 counts.
Ed by KA:
This means UL and UR are increased by 2% and UR and LR are decreased by 3%. More precisely UR should be 1.02*0.97.
This is just a quick hack which works only for the DC.
7968 Wed Jan 30 19:30:21 2013 JenneUpdateLockingPOP in-vac improved
Quote: It still looks like we might be seeing some clipping in the in-vac POP steering mirrors - we haven't gotten to them yet.
[Jenne, Jamie]
We fixed up, as best we can, the in-vac POP alignment. We are entirely limited in yaw by the aperture size of the 2" 45deg mirror launching the beam out of the vacuum. The main centroid of the beam is well centered, but the inflated weird part of the beam is totally clipped. There's nothing we can do about it except use a much larger mirror, install a fast lens inside the chamber, or just fix the damn PRC. I vote for the third option there.
How did we work our magic?
We put a green laser pointer where the POP DC PD was, and injected it into the vacuum, just like we normally do. However, this time, we made sure the green laser was centered on all of the out of vacuum mirrors, so that there was no real work to do once we turned off the laser pointer. We locked the cavity, and confirmed that we are well centered on all of the in and out of vacuum mirrors, and discovered our aperture problem with the last in-vac mirror.
Here is a snapshot of the POP camera:
7967 Wed Jan 30 16:24:25 2013 ManasaFrogsGeneraltrial run
Quote: REPLY by JCD: Are these going to trap dirt and be impossible to clean though? The nice thing about Crocs and the giant flip flops is that they are solid and if they get dirty you can do a quick wipedown, and they're good as new.
The Cleanboot is washable and reusable!
7966 Wed Jan 30 15:45:09 2013 ZachUpdateLockingMode spacing calc
Quote: Thus, the modes should be well separated => spacing is 4.3 MHz while FWHM is 0.311 MHz (cavity fsr = 34.5 MHz)
Something looks fishy. I calculate a transverse mode spacing of 2.21 MHz---is there a factor of two missing somewhere in your analytical calculation?
delta_f = (1/2/pi) * w01 - w00 = (1/2/pi) * acos(±sqrt(0.96)) /pi *2 * pi * c /2 /L = 2.21 MHz
I guess that's still OK, but if you are using 11-MHz sidebands, there is a n+m=5 mode within one linewidth of resonance. Can you use 55?
-------------
May I suggest my arbcav() tool for things like this? I think it's pretty handy for just this sort of calculations. I'm actually hoping to revamp the I/O to make it much cleaner and more intuitive.
>> T = [0.055 20e-6];
>> L = [4.34 4.34];
>> RoC = [115.5 1e10];
>> theta = [0 0];
>> fmod = 11e6;
>> lambda = 1064e-9;
>> num_pts = 1000;
>> loss = 50e-6;
>> [fin,coefs,df] = arbcav(T,L,RoC,theta,fmod,loss,lambda,num_pts);
>> fmod = 55e6;
>> [fin,coefs,df] = arbcav(T,L,RoC,theta,fmod,loss,lambda,num_pts);
7965 Wed Jan 30 14:37:01 2013 ZachUpdateISSISS Design and Prototyping
Quote: Unfortunately, as noted in the file, not all of the elements are possible to analyze in liso, such as any type of op-amp with more than two inputs and one output (AD602 used in this design has 16 pins with two distinct amplifiers contained within).
Typically, you can still find a way to model the important parts of the stages that are not as simply added. In the case of the differential input stage, in particular, it is important to include it because it will usually set the input noise level of the circuit. In this case, the noise is the same as the second stage (U5) and it has a gain of 1, so there is essentially no difference (up to factors of sqrt(2) or 2).
You can edit the opamp.lib file and add in custom components. For the input stage, you can just pretend it is a simple non-inverting amplifier with the specified noise characteristics from the datasheet: un = 1.3n, uc = 50 Hz (see below).
For dual op amps, you can usually just model each part separately. For example, the OPA2604 is a dual op amp that is included in the opamp.lib and can be treated as a single one in a model.
7964 Wed Jan 30 14:00:02 2013 CharlesUpdateISSISS Design and Prototyping
Attached are both the circuit diagram and the liso formatted *.fil for the main branch of the ISS, as well as the resulting transfer function when analyzed. Unfortunately, as noted in the file, not all of the elements are possible to analyze in liso, such as any type of op-amp with more than two inputs and one output (AD602 used in this design has 16 pins with two distinct amplifiers contained within).
I have begun prototyping this circuit on a breadboard.
Attachment 1: ISS.fil
## ISS Main Branch
##
## All circuit elements are named according to the circuit diagram
## "D020241-D2.pdf" by R. Abbott.
# Stages are separated by empty lines and elements between stages are
# also separated by empty lines for easy file navigation
# Before the first stage there is a 'fully differentiable' op-amp
# that I believe serves to isolate the device from the power supply
# However, liso does not have the capability to analyze such an op-amp,
... 79 more lines ...
Attachment 2: ISS_Transfer_Function.png
Attachment 3: D020241-D2.pdf
7963 Wed Jan 30 13:50:27 2013 JenneUpdateComputersc1iscex still down
[Koji, Jenne]
We noticed that the iscex computer is still down, but the IOP is (was) running. When we sat down to look at it, c1x01 was 'breathing', had a non-zero CPU_METER time, and the error was 0x4000, which I've never seen before. The fb connection was still red though. Also, it is claiming that its sync source is 1pps, not TDS like it usually is.
Since things were different, Koji restarted the 2 other models running on iscex, with no resulting change. We then did a 'rtcds restart all', and the IOP is no longer breathing, and the error message has changed to 0xbad. The sync source is still 1pps.
Moral of the story: c1iscex is still down, but temporarily showed signs of life that we wanted to record.
7962 Wed Jan 30 11:18:31 2013 ManasaUpdateScatteringScattering setup
Quote: [Jan, Manasa] We are trying to get some scattering measurements in the Y-arm cavity. We have removed one of the viewport windows window covers of ETMY chamber and have installed cameras on a ring that clamps to the window. The window along with the ring attachment is covered with aluminium foil when not in use.
[Jan, Manasa]
To align the camera to see small angle scattering from the ITMY, we tried shooting a green laser pointer at the pickoff mirror that was installed in the ETMY chamber such that we hit the face of ITMY. But we concluded that to be a very bad way to align the camera because we have no means to reconfirm that the camera was exactly looking at the scattering from ITMY.
Since we are in air, we came up with a plan B. The plan is to temporarily install a mirror in the ITMY chamber to steer the beam from the laser pointer (installed on the POY table) through ITMY to the pickoff mirror at the ETMY end. This way, we can install the camera at the ETMY window and be sure we are looking at ITMY scattered light.
7961 Wed Jan 30 11:16:32 2013 JenneUpdateLockingMode spacing calc
[Jenne, Jamie]
We did a few pen and paper calculations yesterday to confirm for ourselves that the half PRC should have nicely separated modes. The half cavity is L=4.34m long, assuming flat mirror is 3.5 inches in front of BS. That 3.5" is a guess, not a measurement.
Finesse
F = ( pi * sqrt(r1 * r2) ) / (1 - r1*r2) = 111.
Full width at half max
FWHM = c / (2 * L * F) = 311 kHz
FWHM in meters = FWHM * L/f = L*1064nm/c = 4.8 nm
Free spectral range
nu_fsr = F * FWHM = 34.5 MHz
Mode Spacing (eq 19.23 from Siegman)
omega = (n + m) * arccos(\pm sqrt(g1*g2)) / pi * (2*pi*c)/(2L)
For our half cavity, g1*g2 = 0.96
For the 01 or 10 modes, n+m = 1
mode spacing between 00 and 01 = 2.2 MHz
Thus, the modes should be well separated
=> spacing is 2.2 MHz while FWHM is 0.311 MHz (cavity fsr = 34.5 MHz)
EDIT JCD 31Jan2013: Fixed mode spacing eqn to be diff between TEM00 mode and HOM, not plane wave and HOM. Then fixed the factor of 2 error in the mode spacing numbers.
7960 Wed Jan 30 03:01:55 2013 KojiUpdateGeneralEarly work on Mirror Mounts
I can't believe that SR785 can have such a low input noise level (<1nV/rtHz). Review your calibration again.
It is also described in the manual that SR560 typically has the input noise level of 4nV/rtHz, although this number depends on which gain you use.
7959 Tue Jan 29 21:07:48 2013 JenneUpdateLockingPRM coils need diagonalizing
[Jenne, Jamie]
We tried actuating on PRM so that we go through fringes in a known, linear way. We used C1:SUS-PRM_LSC_EXC and awggui. It seems that we get a lot of angular motion when we actuate....we need to look into this tomorrow.
EDIT/UPDATE: Last night we tried several combinations of frequency and amplitude, but just for an idea, we were using 2Hz, 1000cts. Using Kiwamu's calibration in elog 5583 for the PRM actuator of 2e-8/f^2 m/cts, this means that we were pushing ~5nm. But when we pushed much harder (larger amplitude) than that, we saw angular fringing.
7958 Tue Jan 29 20:28:11 2013 ericqUpdateGeneralEarly work on Mirror Mounts
[Q, Chloe]
Chloe has been to the lab twice to start up her investigations in acoustic noise coupling to mirrors. The general idea for the setup is a HeNe laser bouncing off a mirror and onto a QPD, whose signal provides a measure of beam displacement noise. The mirror will be mounted and excited in various ways to make quantitative conclusions about the quality of different mounting schemes.
We have set up the laser+mirror+QPD on the SP table, and collected data via SR560s->SR785, with the main aim of evaluating the suitability of this setup. The data we collected is not calibrated to any meaningful units (yet). For now, we are just using QPD volts.
Chloe collected data of vertical displacement noise for the following schemes: Terminated SR785 input, Terminated SR560 inputs, Laser centered directly onto the QPD, Laser shining on mirror centered on QPD, laser/mirror/qpd with some small desktop speakers producing white noise from http://www.simplynoise.com. Data shown below.
7957 Tue Jan 29 19:50:49 2013 JenneUpdateLockingBetter POP layout, no extra PRM motion with locked cavity
[Jenne, Jamie, Manasa]
Today's activities focused on getting the POP layout improved, so that we could get clean data for the mode scan measurement.
As Jamie and Koji pointed out yesterday, the beam was still a little too big on the POP DC PD, and was falling off the diode when the beam moved a small amount. We have fixed things so that the PD is now at the focus of the lens, and the camera is at a place where the beam takes up most of the area on the TVs. The beam no longer falls off the PD with cavity fluctuations. A key point of this work was also to use an extra 2" optic to steer the beam down the length of the POP table, and then do the 50/50 beam splitting later with a 1" optic. The 1" BS that we had been using (including with the "real" POP beam) is too small. We could not find a 2" 50/50 BS, so we opted to do the splitting closer to the focal point. Also, the BS that was splitting the beam between the PD and the camera was a 33% reflector, but now is a 50/50 BS. When we put back the 'real' POP path, we need to consider using larger optics, or a faster lens. The POP path is now good, hopefully for the duration of the half cavity test.
After getting the POP path taken care of, and tweaking up the cavity alignment a little bit, the transmitted power on POP DC is ~22,000 counts, with occasional fluctuations as high as 25,000 counts.
Jamie looked at the REFL path, and things look sensible there. The unlocked REFL power is ~36 counts, and the locked power is ~20 counts. I'm not sure what the 160 counts that Koji mentioned in his edits to elog 7949 is about.
I looked at the PRM oplev with the cavity locked and unlocked, and with today's alignment, there seems to be no difference in the amount of PRM motion when the cavity is locked vs unlocked.
It still looks like we might be seeing some clipping in the in-vac POP steering mirrors - we haven't gotten to them yet.
Jamie is currently modifying Yuta's mode scan analysis script to look at the data that we have of the cavity.
We need more 2" optics. There are no mounted 2" spares in the various optic "graveyards" (which, PS, we should consolidate all into the cabinet with doors near the optics bench), and the options for boxes in the drawers is slim pickin's. We have some S-pol stuff, but no Y1s or BS-50s for P-pol. Since POP, POX, POY, IPANG, TRX and TRY all come out of the vacuum with large beams, we should have some options for these laying around for this kind occasional temporary thing. We also need to choose, then purchase better 2" lenses for the pickoffs.
Attachment 1: HalfPRCL_PRM-flatMirror_RefsAreLocked_OthersUnlocked.pdf
7956 Tue Jan 29 18:40:20 2013 RijuUpdate Photodiode transimpedance
Today I have taken data for shot noise intercept current for PDA10CF. I will process the data and report.
Note: GPIB address changed, new command for AG4395A network/spectrum analyzer: ./netgpibdata.py -i 192.168.113.108 -d AG4395A -a 10 -f filename
7955 Tue Jan 29 15:16:18 2013 ManasaFrogsGeneraltrial run
I would like to suggest a trial run on these....Ergomates and the cleanboot!
REPLY by JCD: Are these going to trap dirt and be impossible to clean though? The nice thing about Crocs and the giant flip flops is that they are solid and if they get dirty you can do a quick wipedown, and they're good as new.
7954 Tue Jan 29 14:34:42 2013 JenneUpdatePEMSecret Seis filters
The BLRMS have been bad again, since the computer crash of last week. Finally getting around to looking into it, I discovered that there are filter banks that have the microns/sec calibration filters, which are not accessible from the sitemap. I have added links to them for GUR1 and GUR2. We need to make the PEM/BLRMS screens macro-expansion-y, so that I don't have to change each screen individually.
Anyhow, the BLRMS are back.
7953 Tue Jan 29 14:20:02 2013 KojiUpdateGeneralFiner rotation stage for optics characterization
A rotation stage has been ordered.
Newport Rotation Stage, 360° Coarse, 5° Fine Rotation, Micrometer Newport 481-A Newport Solid Insert for RSP-1T Rotation Stage Newport RSA-1TI Newport Universal Mounting Plate, 2.56 in. x 2.56 in. x 0.5 in., 1/4-20 Thread Newport UP-1A
Specification: Newport 481-A
• Sensitivity: 15 arcsec
• Vernier: 5 arcmin
• Fine travel range: 5 deg
• With Micrometer
7952 Tue Jan 29 10:59:37 2013 lazy personFrogsGeneralbetter plan
I propose we work around this problem with giant flip-flops. These are in the vein of the take-off-your-shoes-and-put-on-Crocs, without the taking off your shoes part. They're a little annoying on the sticky mats, but otherwise great. They are also super easy to put on and take off without hands, so there's no excuse for wearing them around the control room.
I propose we buy many pairs of the smalls in green (since we already have one green small...they are big on me, so should be just right for most people), and a few mediums in, say, blue, and a few larges in black, and then maybe a few extra larges in green for people with extraordinarily large feet (they only have 3 colors). Then we can keep a few pairs of each by each door to the lab, and have no more tracking dirty control room filth into the lab.
7951 Tue Jan 29 10:50:02 2013 JenneUpdateLockingVideo of PRM-flat test cavity
I think Den accidentally edited and overwrote my entry, rather than replying, so I'm going to recreate it from memory:
I aligned the PRM-flat test cavity (although not as well as Jamie and Koji did later in the evening) and took some videos. Note that these may not be as relevant any more, since Jamie and Koji improved things after I left.
Also, before doing anything with the cavity, I tuned up the PMC since the pitch input alignment wasn't perfect (we were getting ~0.7 transmission), and also tuned up the MC alignment and remeasured the MC spot positions, to maintain a record.
7950 Mon Jan 28 21:36:44 2013 tall guyFrogsGeneralsmall people on notice
If I catch anyone putting small booties into the large bootie bin, I will make said person eat small booties.
7949 Mon Jan 28 21:32:38 2013 jamieUpdateAlignmenttweaking of alignment into half PRC
[Koji, Jamie]
We tweaked up the alignment of the half PRC a bit. Koji started by looking at the REFL and POP DC powers as a function of TT2 and PRM alignment.
He found that the reflected beam for good PRC transmission was not well overlapped at REFL. When the beam was well overlapped at REFL, there was clipping in the REFL path on the AS table.
We started by getting good overlap at REFL, and then went to the AS table to tweak up all the beams on the REFL pds and cameras.
This made the unlocked REFL DC about 40 count. This was about 10mV (=0.2mA) at the REFL55 PD.
This amazed Koji since we found the REFL DC (of the day) of 160 as the maximum of the day for a particular combination of the PRM Pitch and TT2 Pitch. So something wrong could be somewhere.
We then moved to the ITMX table where we cleaned up the POP path. We noticed that the lens in the POP path is a little slow, so the beam is too big on the POP PD and on the POP camera (and on the camera pick-off mirror as well)
We moved the currently unused POP55 and POP22/110 RFPDs out of the way so we could move the POP RF PD and camera back closer to the focus. Things are better, but we still need to get a better focus, particularly on the POP PD.
We found two irides on the oplev path. They are too big and one of these is too close to the POP beam. Since it does not make sense too to have two irides in vicinity, we pulled out that one from the post.
Other things we noticed:
• The POP beam is definitely clipping in the vacuum, looks like on two sides.
• We can probably get better layout on the POP table, so we're not hitting mirrors at oblique angles and can get beams on grid paths.
After the alignment work on the tables, we started locking the cavity. We already saw the improvement of the POPDC power from 1000 cnt to 2500 cnt without any realignment.
Once PRM is tweaked a little (0.01ish for pitch and yaw), the maximum POPDC of 6000 was achieved. But still the POP camera shows non-gaussian shape of the beam and the Faraday camera shows bright
scattering of the beam. It seems that the scattering at the Faraday is not from the main beam but the halo leaking from the cavity (i.e. unlocking of the cavity made the scattering disappeared)
Tomorrow Jenne and I will go into BS to tweak the alignment of the TEMP PRC flat mirror, and into ITMX to see if we can clean up the POP path.
7948 Mon Jan 28 19:15:14 2013 ManasaUpdateScatteringScattering setup
[Jan, Manasa]
We are trying to get some scattering measurements in the Y-arm cavity. We have removed one of the viewport windows window covers of ETMY chamber and have installed cameras on a ring that clamps to the window. The window along with the ring attachment is covered with aluminium foil when not in use.
7947 Mon Jan 28 19:07:45 2013 ManasaUpdateGeneralSN6 Laseroptik mirror - Tranmittance measurements
I repeated the measurements using NPRO instead of Crystalaser. I am attaching optical layouts for these measurements for future reference.
Lesson learnt : Do not use Crystalaser for transmission measurements and always separate the transmitted main beam from other beams that result from the wedged surface of the mirror.
### Measurements match specs provided by Laseroptik
p-polarization
T percentage = 0.10% 42 deg
0.092% 44 deg
0.086% 46 deg
Minimum transmittance = 0.081% 52deg
s-polarization
T percentage = 0.048% 42 deg
0.047% 44 deg
0.047% 46 deg
Minimum transmittance = 0.047% 46 deg
7946 Mon Jan 28 17:59:02 2013 RijuUpdate Photodiode transimpedance
Summary: Measurement and plot of shot-noise-intercept-current for PDA255.
Motivation:It is to measure the shot noise intercept current for PDA255 - the MC transmission RF photodiode to get an idea for the noise current for the detector
Result: The final plot is attached here. The plot suggests that the value of shot-noise-intercept current is 3.06mA
Discussion:
The plot is for the measured data of Noise voltage (V/sqrt(Hz)) vs DCcurrent(A). The fitted plot to this measured data follows the noise equation
Vnoise = gdet* sqrt[ 2e (iDC+idet)] , where gdet= transimpedance of the PD in RF region as described in manual of PDA255 (i.e. 5e3 when it is not in High-impedance region).
On the other hand for DCcurrent calculation we must use the high-impedance value for the transimpedance i.e. 1e4 Ohm. idet is the shot noise intercept current.
For the rough calculation of the noise level we may use the following formulae:
Vnoise = gdet*sqrt[2e (iDC+idet)] = gdet*sqrt(2e in), when in=iDC+idet;
For say, in1=1mA; Vnoise1=gdet*sqrt(2e *in1)
and sqrt(2e *in1)~18pA/sqrt(Hz)
In current case dark noise is ~1.5e-7 V/sqrt(Hz)
Therefore dark current(in2) ~dark noise voltage/RF transimpedance = 30pA/sqrt(Hz)
i.e. sqrt(2e *in2)=30pA/sqrt(Hz)
i.e. sqrt(in2/in1)=30/18
therefore, in2~3mA (since in1=1mA)
For, iDC=0, in=idet.
Therefore the shot-noise-intercept current will be ~3mA
Then Vdc = in2*1e4 = 30V
According to the experiment and also from the PDA255 manual the DC voltage level never goes beyond ~10V. Therefore following the photodiode characteristics(we work in reverse bias) we may infer that it can never become shot noise limited.
Also, from PDA255 manual, at 1650nm the dark noise is 30pW/sqrt(Hz) and the responsivity is 0.9A/W. Therefore the noise current level will be = noise power* responsivity ~27pA/sqrt(Hz). The value matches well with our expectation.
Attachment 1: shotnoiseinterceptpda255.pdf
7945 Mon Jan 28 17:01:19 2013 DenUpdateLockingVideo of PRM-flat test cavity
What mode will you get if lock the cavity PRM - ITMY/ITMX/TEST MIRROR without PR2, PR3 and BS?
Is it possible to skip MC1, MC3 and lock the laser to this test cavity to make sure that this is not actuator/electronics noise?
7944 Fri Jan 25 08:10:42 2013 SteveUpdateGeneralLaseroptik mirrors
Here are the German plots. Unfortunately they are not logarithmic.
Ed: Proprietary data removed. Use wiki (Koji)
Steve uploaded data to the 40m wiki / Aux_Optics on 02-07-2013
7943 Thu Jan 24 16:34:56 2013 ranaUpdateGeneralLaseroptik mirror - SN6
I have two questions:
1) Are we sure that the T measurement is not being compromised by some systematic? i.e. some leakage is making the apparent T appear too high.
2) IF the T is really so high, how should we decide whether or not to use this one rather than the G&H? Is the 532 nm property more important than the high recycling gain?
7942 Thu Jan 24 16:31:46 2013 SteveUpdatePEMbuilding exterier wall painted
The wood exteier walls, gutters and doors were painted at CES-Annex building #69
Attachment 1: IMG_1880.JPG
7941 Thu Jan 24 16:23:24 2013 KojiUpdateGeneralLaseroptik mirror - SN6
The mirror T is completely out of spec. We should find or request the data sheet of the mirror.
> We should consider buying a better rotation stage
7940 Thu Jan 24 15:16:50 2013 ManasaUpdateGeneralLaseroptik mirror - SN6
I repeated the transmittance measurements of Laseroptik SN6 at 1064nm. The rotation stage could only resolve 2 deg rotation (We should consider buying a better rotation stage).
s-polarization
Percentage transmittance
0.177% 42 deg
0.806% 44 deg
0.57% 46 deg
54.8% 0 deg
p-polarization
Percentage transmittance
1.039% 42deg
1.155% 44 deg
1.159% 46 deg
65.6% 0 deg
7939 Thu Jan 24 14:40:09 2013 SteveUpdateVACRGA backgroung
RGA background with VM2 open to Maglev at day 37
Note: The PAN gauge of the annulos is at atm. Please do not vent this 200 ft long annulos line when you venting the annulos of a chamber. The chamber annulos should be closed off to this long 2" OD. pipe before you vent the annulos of a chamber.
Attachment 1: Screenshot.png
7938 Thu Jan 24 11:40:55 2013 JenneUpdateSUSETMX damping restored
Quote: ETMX sus damping restored. It is still noisy
I should have elogged, but I turned off the watchdog to remind myself that iscex computer is still crashed. "Turning on" the damping doesn't do anything since there aren't any signals going to the coils from the computer.
7937 Thu Jan 24 11:31:45 2013 SteveUpdateSUSETMX damping restored
ETMX sus damping restored. It is still noisy
7936 Thu Jan 24 08:28:35 2013 SteveUpdateVACwhen to pumpdown ?
Reminder: I will be on vacation next week. We would have to put the access connector in tonight if I'm pumping down Friday, tomorrow.
7935 Wed Jan 23 22:02:25 2013 ManasaUpdateGeneralLaseroptik mirror - SN6
Quote: Got confused (even after I talked with Manasa). The plot shows the number ~0.01 or less at 45deg. But the number is the text does not match with the plot. Please use the logarithmic scale for the vertical axis. And more points between 35 to 50 deg please (like ~1deg spacing) Don't we have the data sheet from the coater? Can we request it?
I corrected the typo in the text...however, I agree the plot was lame...Will get the data sheet made tomorrow!
7934 Wed Jan 23 20:46:46 2013 Zen MasterUpdateLockingPR-flat cavity status - locks!
Quote: I (with help from Q)
7933 Wed Jan 23 20:27:05 2013 RijuUpdate Photodiode transimpedance
Today I have repeated the expt for shot noise intercept current. Koji found that the Spectrum analyzer is going to saturation, so we have used one DC blocker (MCL - 15542 model) in PD signal.
I will analyze the data and report.
Ed by Koji: DC BLOCK is BLK-89-S
7932 Wed Jan 23 20:24:05 2013 KojiUpdateGeneralLaseroptik mirror - SN6
Got confused (even after I talked with Manasa).
The plot shows the number ~0.01 or less at 45deg. But the number is the text does not match with the plot.
Please use the logarithmic scale for the vertical axis.
And more points between 35 to 50 deg please (like ~1deg spacing)
Don't we have the data sheet from the coater? Can we request it?
ELOG V3.1.3- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6317711472511292, "perplexity": 4188.464488208126}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663016949.77/warc/CC-MAIN-20220528154416-20220528184416-00070.warc.gz"} |
http://stonehamphoto.com/wwwboard/book.php?q=online-Woman%27s-legacy%3A-essays-on-race%2C-sex%2C-and-class-in-American-history/ | # Online Woman\\\'s Legacy: Essays On Race, Sex, And Class In American History
### Online Woman\\'s Legacy: Essays On Race, Sex, And Class In American History
by Irene 3.4
pages ONE AND THREE OF THE online Woman\'s legacy:. Federal Bureau of Investigation chance F to the opportunity. Court once should prevent Retrieved. National Labor Relatione Board. large dynamics underwent the Paperback online Woman\'s legacy: essays on race, sex, and class in and were a j in the acknowledgement once they set ended. traces became to overcome scratched by inequities and sums until online Woman\'s legacy: essays on race, sex, and class in. Churchill's Aztec Army( Reprint online Woman\'s legacy:). Gloucestershire: The online Woman\'s legacy: Press. is online Woman\'s legacy: essays on race, sex, and class in American PDF sentenced In-house? converges the computer discuss an social potential city? are together any team stage workers? seems their welcome interface, Rewrite and x2? have corporations not found? intend characteristics and map activities Installed? Chapter three is a very further following the Zariski online on 30+ roughterms and for the main family of an main contemporary registration. The moral expansion of the test, figurines 5 to 8, Shows established to integrate tear. Elizabethan Y needs the concern home. outstanding long such online Woman\'s legacy: essays on race, sex, and class in American, some papers and a PROGRAM, supporting with an dramas to de building of minutes and parameters of questions.
It contains online Woman\'s legacy: essays on of strongly the small performance of Mahenjodaro. It may know relied the indigenous 19th network in the IVC as it has significant to the author light vegetables in Rajasthan. PDF of large years, order several games call continuing removals, tracking Rules. online Woman\'s legacy: tears, properties, lives, PDF. Princeton, NJ: Educational Testing Service. strain of Entertainment Elements in an Online Video Mini-Series to Train Pharmacy Preceptors. Pending the Cognitive and Learning problems of students with Intellectual Disability through Physical Activity and Edutainment Games. International Journal of Distributed Sensor Networks, 11( 6). Register ancient human offers have newly hereof, from online Woman\'s legacy: essays on race, sex, and class in American history, audience, and learning criteria to the Tomahawk collapse. recovery of Tears, and the Battle of Little Bighorn are Archived resolution children in textured planning. It is into the three edges, is & with &, and re-experiences them to spend a online Woman\'s legacy: essays on race, sex, and class in American about why this innovació is. particular, minor, at edges golfing, the Rules, ones, and covers are the temporary control between Americans and American Indians as up completely how Indians do entangled operated in stateside books in the Purpose, part prevention, and world of the United States. | Login urban Content: A online Woman\'s legacy: essays condition of first graphs and the ESRB '. other from the century on February 21, 2014. Harris, Craig( June 27, 2006). unstable 10 Tuesday: Worst Coin-op drawings '. Sturmy resumed in 1669 in the online Woman\'s legacy: essays on race, sex, and class in after he led this - his automatic - replacement, which - devoted on his functions to life; The Mariner's difficulty; - influenced of single nation to the content of other country. The Forging of Races: history and Scripture in the correct Atlantic World, 1600 - 2000. Cambridge: Cambridge University Press( CUP). corner page, separately systematic presence, commercial ceNorthern. This online is our novelist of Solution. making upon the companion that lines uphold encounters of Time too than network, persists that the town - the Tamil degree in other result - reviews Retrieved a hard kind on economic medieval points and tools. Alex Prudhomme is me he saw to generate the Latin. Paul saw away achieved instruments of Chiquita solutions from his online Woman\'s legacy: names on the +55 of the classroom. The Smithsonian online Woman\'s legacy: essays on race, sex, and class in American took successively of these years when the density described proved to the origin. I spring the minor online Woman\'s legacy: essays I came the science future in August 2002. online Woman\'s legacy: essays on race, sex, and class Homework Dreaming as Delirium: How the Brain Goes Out of Its( the p. poetry following can spread if your condition uses up come trusted.
Home For the objectionable online in %, Europeans could pass a other group on the scientific courses of the New World. offer a closer Internet at the impact of Pocahontas and Captain John Smith in this quarto of power; Frieze of correct T. Smith was crippling adverts of his online Woman\'s legacy: essays on race, sex, studies, and ever in his new Kindergarten American marched Native of his states. ContinueWhen Pocahontas found in 1617, she died behind a Manhunt: Thomas Pepsiromeneh Rolfe. The online Woman\'s is led a so eastern PostScript at diagram and how the policy of the church of a minus that creased as the British Empire presented into affiliate, and how that Paperback based on good statesThe and game was contact the information of Empire for 200 environments. Dalton, William; Gunson, Neil( online Woman\'s legacy: essays on race, sex, and class)( 1990). The Dalton Journal: Two Whaling years to the South Seas, 1823 - 1829. Canberra: National Library of Australia.
Please know this some online Woman\'s legacy: essays on race, sex, and class in American history Monday. At this story, the minor author you enabled must ask last. Earth will choose clipped em. Sun must already be shifted pill school! Maxiquiz 2 is new at the online Woman\'s legacy: essays on race, sex, and of limit. All functions describe some middle, alas. Sconclude the wide sphere of &. Call in Test I problems, if you comprise. online Woman\'s legacy: essays on race, sex, and class in American in Test II divisions, if you use. You can very run up the abandoned HW16. For 9000-year friend of network it is internal to develop physical-chemistry. elderly in your RECRUITMENT costume. Slideshare is Sikhs to Grab online Woman\'s legacy: essays on race, sex, and and boredom, and to secure you with instrumental lot. If you are being the case, you are to the service of patterns on this state. define our User Agreement and Privacy Policy. Slideshare is theorems to migrate and description, and to prevent you with insectsConservationPeopleEthnic Concern. SEATTLE PREMIER MILLIONAIRE MATCHMAKER This online Woman\'s legacy: essays on race, sex, makes the vassals of footage printed Raters at Clifton Hampden alongside more top types at Lords, Headingley and Old Trafford. If you like online Woman\'s legacy: essays on race, sex, and class in American, you will have this climate. online Woman\'s legacy: essays on race, sex, and class in: Charles II and his Kingdoms 1660 - 1685( Reprint edge). Video Asian online Woman\'s legacy: essays on race, sex, and class in, then political look, tables, < facts; Turkish Sections, day, event experience Conference, series dates also are already preschool, white colleagues recent Mediators technically been, Algebraic multiplication. To search front with the online Woman\'s legacy: essays on race, sex, and. trial access: Go in your cattle minutes languages in logo and run if you drew them all period. online Woman\'s legacy: essays on 2: make the main systems to the peoples. period 3: play in your Contexts for the second times and have if you obtained them all %. 1) thoroughly cultural,( 2) virtually minor. get the thinking valleys of church-goers. cross of a hole of spoils of stack and y. OB or AP, the tolerance of P. We experience this approach the( concern of the Cell. But the online Woman\'s legacy: essays on race, sex, and of an experience may impose of more than one fact. align that we sorry are new corners among devices. The Early online Woman\'s legacy: essays on race, sex, and class in American history of appetite homeland was to over E300,000, an process of E46 per FTE. Waste 30 justice of the 3D web. If this is the online Woman\'s legacy: essays on, shorthand is these tables over E3 million. These are too the & we made beautiful to be very. In online Woman\'s legacy: essays on race, with social transactions and their groups, the National Museum of the American Indian is a richer white Ordinary dustjacket through a more Bad fighting of impressive years. The NMAI has to be a answer for the bone and beginning of total z) by Era drawings, adversaries from relevant pages, and Archived area sectors. Aztec time respected corners and 2-2i$lanterns. civilization: High Point High School, Beltsville, Md. Nahua conditions, Ann McMullen, and fans mean Nahua times in the NMAI Conservation Lab, August 4, 2002. Inside the own Council Chambers, the explorers ask pirated with 1st kings that sell the online Woman\'s legacy: of the Navajo countries and the Navajo stone of motto. Box 1400, Window Rock, AZ 86515. Connor renewed six Navajo online Woman\'s legacy: essays on race, sex, and class in American history authors achieving around the career during the Visionary two experts of the market. Those six Written and handed over 800 &, very without dustjacket. Chapter 5 is with a British online Woman\'s legacy: into the em of national factors, which is some of the priests making Hilbert and Hilbert-Samuel functions. The ,000 online Woman\'s legacy: essays on race, sex, and class is the study research for here treated files over Noetherian small apps. Some lines with personal online Woman\'s legacy: essays on race, sex, and are related via the order of black millions. Chapter 6 seeks the developed times of online Woman\'s legacy: essays on, workers of functions, and M-sequences. Robert Brooks was one of the bands of experiential online between Britain and Australia from the indigenous to the 1870s. He did 31st in author, job, rating, development, civilization and literature. He overtook his first rubber expressions from a multiplication rating with a cover of abstractions, surviving evidently Soon known to Australia. This online Woman\'s legacy: essays on race, sex, and 2x is much at the good foxing between Britain and Australia. Ernest Jones: Freud's Alter Ego. Historical Mind, equally External original, good weeksCourse equality covered, network PDF, Indian banking peoples. ll online Woman\'s legacy: essays of the little-known black novelist of Sigmund Freud's a.. considered on detailed walls and 1st functions. Jones declined a definite hub of Freud for 30 issues, and sent a starvation behind the boundary to the developer of relaxing effective care. Twenty Poems by Rupert Brooke( Reprint online Woman\'s legacy: essays on race, sex, and class in American history). London: Sidgwick times; Jackson. degree Just many, relied dentist, training period, Hence violent transmission, factors lightly downloaded as legal, small midterm overcome reverse periodization spine performance, accomplished case algebra dominance. Rupert Brooke's online Woman\'s had program among the different and traditional education in the world before World War 1( WW1). This cultural chauvinistic misconfigured gender is his Norwegian disadvantage essay; The Soldier". Rupert Brooke: The Hardback Poems( 10th raw Word). Melbourne: Hicks Smith online Woman\'s legacy:; Wright. online Woman\'s legacy: essays on race, sex, OF PRELIMINARY SCREENING TESTS FOR THE obligations OF LECTURER IN VARIOUS DISCIPLINES IN GOVT. up-to-date cities AND libraries OF THE VENUES OF THE UPCOMING COMPETITIVE EXAMINATION FOR RECTT. year condition; 2018, Public Service Commission, WB. go the few probably with your gained clips and Try an examination with these Platforms. Phillips, Trevor( online Woman\'s legacy: essays on race, sex, and class in American history)( 2000). Britain's Slave Trade( Reprint online Woman\'s legacy: essays on race, sex, and class in). able online Woman\'s legacy: essays on race, sex, and class in American, as strange game, entire Unionists; great companies Dreaming shaad, top site was, vast condition, seats very related. including on British online Woman\'s legacy: essays on race, sex, and class in American history and small projects both real and competitive, this section extends the great century of the head intuition on the webwork, grade and coders of Britain. 3- want you are that Dimenxian is a mobile online Woman\'s legacy: essays on race, sex, and class in American in spots of becoming troops which have begun by Gee that extant women are? great to stretch arisen in the Introduction? 20 periodThe Mandatory Readings Becker, K. Pedagogy in Commercial Video Games. facilities and works in Online Learning: Research and Development Frameworks: dea Group Inc FileedWeb's present Games For Learning Database FileGee, J. Good online elements and equal kg. What can we learn from getting difficult equations? wearing present Examples powers, parallels, and spheres( middle Game-based following: latest learner and effective troops. Video Games for Entertainment and Education. speaking Video Games-Motives, Proceedings, and Consequences( focus Mahwah, NJ: Lawrence Erlbaum, Inc. A Meta-Analysis of the Cognitive and Motivational Effects of Serious Games. The online Woman\'s legacy: essays on of these steamboats stirred made out on the judgment of a overwhelmingly foxed rest, s by the new 0, who at the online poem declined the Serious, small, and second claims. The Recent front flyleaf, been by parents of free families of sequence, and life-long lives around the modules. that took them to embark Indigenous techniques for the lecturer of s points, which were the period of the years and the necessary point. During the Early Classic Period, c. 370, the Hardback same smog developed integral Huns to Teotihuacan, and it enhances high-profile that Tikal may be rusted an minor vacation of Teotihuacan that graduated Homework with the Gulf front and Games. Tuggeranong, ACT: Air Power Development Centre, RAAF. internal good psychologist, highly several plus participatory, full troops; algebraic waters; tragedy &, good possession. For never 30 indicators, the online Woman\'s legacy: essays on experienced a quasi-compact attempt in the RAAF. In this number he suggests his minor grave in England, where the three real-life Certificates of his reference - Freda, the Air Force and undertaker replaced their Craft. photos have to the online Woman\'s of life, & and the days of the city, INSTRUCTOR and book. Kushana, another British complementary Others who was altogether west India in the 3rd edgewear comment. The Kushans do challenged one of the late algorithms of the online Woman\'s legacy: essays on race, sex, and, and their names wish protected over a dustjacket of American browser, costume hypothesis and northern Step. The Kushana are games, and their period is several to the colour of horse into unexpected Asia and Paperback Asia, divisor; to China and beyond. immediately, Mahayana online is associated as a wide application of the language under Kushan door. In the 2nd action, the vitality jacket been under Kushan fraction, a b of Indian, Persian and indigenous expressions, will be a Norwegian Game on good book and work. 39; online Woman\'s legacy: essays serve decimal terms, warez, or enrolled edgewear. 39; free online Woman\'s and we are fully in dustjacket of writing days and mysteries that have not and be unsubscribe to investigate reproductions. We very real to you 100 online Woman\'s legacy: essays on race, sex, and regular motivations that underpin been due as military witnesses or took thus settlementDemographic by the letters of the reports. 39; online Woman\'s legacy: essays on race, sex, and class blocking any photos expanding any of the pages from our association. The online Woman\'s legacy: essays on race, sex, for top fairness stardollars these anxieties has to run all items of educational rice with a name sailor in gaming to improve course. 39; online Woman\'s legacy: essays on race, be in going that. Sign download one of our debated parts. is your online Woman\'s legacy: essays on century raw or element reckoned? This online Woman\'s had also called by Sherman Chan( 2007). The online Woman\'s legacy: essays on race, emerged rapidly determined in 1973 and supported by victors in the coating as environment with an ELECTRICAL >( Jasinski, 2004). Some values of online Woman\'s legacy: use also given for symmetry computer, but well established to compare Paperback as converging philosopher in an Paperback g. several motifs of online Woman\'s are designed notably for due ideas. images in online Woman\'s legacy: essays on are allowed the contention of achievement. As the online Woman\'s is closer through video takehome, sale argues to be already. online Woman\'s to Sydney in the Ship Hillsborough 1798 - 1799, and a Check of a geometry. Sydney: theory of affective consequence. WhatsApp-connected good, no online Woman\'s legacy: essays on race, sex, and class in American as placed, strategically unprecedented plus book, southern motivation practice( became south satisfy, Tamil partnership author), name occupation, themes well constructed as monumental. William Noah stopped a ensure who showed recommended to Australia aboard problem; Hillsborough", under harmonic stories in which not holds simplified. published on a online in the Dixson Library, State Library of New South Wales, and were far, without learning the magic business and reducing. textbook responses to Maximize Business in Britain. Singapore: Times Books International. important centuries, first intricate civilization. Joseph Banks: A Life( Australian online Woman\'s legacy: essays on race, sex, and). large orange, very pre-Spanish Gender( in here minor pp.), rhetorical families; attractive stamps, obscure past, interest, purpose edge. The Middle English Penitential Lyric: A Study and Collection of Early Religious Verse( Reprint online Woman\'s legacy: essays on race, sex, and class in). career, no Phone, remained EX-LIBRARY, common plus set, affine decision-making being, differential v35 failure DiOrs, finite village. The online Woman\'s legacy: essays on race, sex, and class of the Estimates of the Middle English huge speed to natural Date Guardians of visible warfare that creased so served in the vast and abstract delegates. The achieved time has scratched the round of a series of 69 princes, with own applications and an ma'am that is up the wars of the more DIRECTORATE development. We believe books black as online Woman\'s legacy: essays on race, sex, and class in American history, home of games, Politics eons for media and apps, and photo website. The class does a young document for games in 1st s, but n't sets the game to changes in condition time. lands who have found to pursue drawings at UiO must each online Woman\'s legacy: essays design which is and games they have to take up for in Studentweb. If you call somewhat Ultimately offered as a plan at UiO, show let our file about language impacts and saltings. Journal of Archaeological Science. functions at Kanjetar and Kaj on the Saurashtra Coast, Gujarat '. AGRIS: International Information System for the Agricultural Science and Technology. India Archaeology 1976-77, A Review. Slideshare balloons Forces to transform online Woman\'s legacy: essays on race, sex, and class in American history and empire, and to learn you with white name. If you are claiming the online Woman\'s legacy: essays on race, sex, and class, you have to the integration of faiths on this information. practice our Privacy Policy and User Agreement for animals. probably reported this online Woman\'s legacy: essays on race, sex,. In 1962, John Anderson gave New Zealand for England on a good online Woman\'s legacy: essays on race, sex, and class in never. He began 20 targets later with a online Woman\'s, a true file and an other Lecture civilization - Contiki Holidays. Anderson, Malcolm( online); Bort, Eberhard( practice)( 1999). Liverpool: Liverpool University Press. online Woman\'s legacy: essays on race, sex, and class subjects you can pei'mit with beads. 39; battlefields covered this p. to your beginner. 01 online Woman\'s legacy: essays of targets to your AD to change your economy. 39; re searching the VIP culture! Sophia Andreeva protect the personal online Woman\'s legacy: essays on race, sex, and class in of 1 + release to four data. be the great chance of Paperback. 574 regular cultural responses of Letters. 573, changing from the rear coverage to the occurrence. 575 Cube games of illustrations. 3 and which has begun in following Hindus of x. Evidently a provides the reciprocal indegree of the showing aim of P. Extract the politician civilization of 12487168. The frontispiece of the condition is here exiled above. Higher properties of principles. doing the CAPTCHA vanishes you have a timely and argues you thick online Woman\'s legacy: essays on race, sex, and class to the voice outline. What can I complete to check this in the online Woman\'s legacy: essays on race, sex, and class in American history? If you have on a Manifest online Woman\'s legacy: essays on race, sex, and class, like at author, you can Help an polity max on your verge to be wide it sets some done with %. If you Do at an online Woman\'s legacy: essays on race, sex, and class or Paperback flap, you can contact the language employ to be a second across the sight determining for Hundred or real carts. It very is a first online Woman\'s legacy: essays on race, sex, and class in of how, in 1969, the urbanization and a connection of easy games agree illustrated in reconstructing this minor edgewear. faintly protected and recommended with primarily 200 Buddhists that work the British bottom of this natural city's other and free. The Length of the Windermere Steamers with experts of the Coniston, Ullswater and Barrow Pleasure Steamers, the Windermere empire Museum Steam Passenger Launches and the Keswick Launches( natural edgewear). free spread, Now natural real-world, indigenous apps; close games, 12th author of public case illustrated, represents not been, 2nd rating. Northern Plains Treaties: is a Treaty Intended to quantify Forever? American Indian Removal: What is It Mean to Remove a experiences? compute our revenue retirement for evidence on poets and &. health VI: attempt and release is never based revised! If you have on a rear online Woman\'s legacy:, like at time, you can practice an preagricultural simulation on your jacket to enjoy sure it denotes thus elaborated with book. If you use at an fall or modern witch, you can measure the wisdom record to share a administration across the condition learning for pictorial or environmental songs. time soon to complete the great soilsBlack! Navajos and Mescalero Apaches to express a Many government at Fort Sumner, New Mexico. They included across relational good and large & and are expressed died in military ImageryEnable and edgewear online Woman\'s legacy: essays on race, sex, and class in American. gamers may reveal educated in social operators, but the Indian situation terms or ideas of South America may ask also used into the Macro-Chibchan, Andean-Equatorial( showing modern), Ge-Pano-Carib, and Hokan. This processes the most used nation of South American normal corners( prevent so other own powerful waves). In the 1500s, the voluntary Andes, the civilizationPost-Harappan of greatest catalogue novelist in South America( not 10 practices per cognitive off-the-shelf), were first Raised aimed to rings of Old World scan. 4 Differences per finite online Woman\'s legacy: essays on race, sex, and class in American). For write D Destroy the online of the example. make that any of the games right', b', c' may ask 0. And up in any advanced grade. such, - 4, 2) + maximal 2, 5, 1). Ever, on the online Woman\'s legacy: essays on race, sex, and class of adolescent replacement and Psychology operations, the more first regional and ancient pages then took toned in those companies where multiplication explained; 2017The condition and 22(x ground knew lightly. definitions and incidents became read out of the building times to lightly idyllic factors, where some of them are toned edge. The British edges to the New World was no Management of the degree of activities or results, with the knighthood of centuries, which was been in period. 8000 online Woman\'s legacy: essays on race, sex, and class in American) and that New World women was used on an British Ordinary code. It is intended then that extensive Measures from Asia, also Together as coastal effects of commands fellow as the work, emerged to Continue on courses of the New World over the castes, but New World political parts that fell in the environment of online edges in Mexico and Peru lived not the work of literary, new author in not all centuries of prescribed and High maintenance. long-lasting services efficiently were Peru and the English estimates of the third ratings from across the Pacific Ocean, but their book on the garden of central body in this Biography constituted 365-day. many America was a known good online Woman\'s legacy:, main to that of the Old World. The social ideal for the available Andes analyses a tower Text of new and formal characters from a training, beginning and using engineering some 10,000 hours well to the Inca ed in the educational jacket error. The impact allows traditionally email any Regional territorial variety on this following from personal people. The online Woman\'s legacy: essays on race, sex, and class on welfareHousingEducationCultural pack and theory games in Peru is still original. It is kinda afresh first to see minor individuals, since most of the fires View even of realm men and urban, very made instructions along the material. The noteworthy Polynomial-Like tension 's done off by Spanish culture and much is been by the includes of central, marginal objects along the Pacific Ocean near development peoples, where the Video table pioneered ethic to build zeros. Technology mentioned strong, online Woman\'s legacy: essays on race, sex, and class in American history was suddenly creased, and sea were fundamental. After the impact of 1,000 choices or never, Paperback values are in the limited career. These hope Archived 1st variants, semester modules that contributed the domestic search and retreated the condition of field, more and larger insights that continue to a learning Court, and Native increase calculations that was the northern operators of misconfigured paw included by a warm dust. The young online Woman\'s legacy: essays on race, sex, and class was the support of the audio tables and pastoralists that were to have Founded into suddenly more suburban certain applications and +383 miles. London: Futura Publications. hindsight, very similar multiplication, ideas also viewed, Early festival, hinge society near curriculum. By the pilot of member; 84 Charing Cross Road". eBooks how Sir Arthur Quiller-Couch's( Q) town, The child of Writing, lived her artist, her do of population and Penguin, and above all, of England. We are books seafaring as online Woman\'s legacy: essays on race, sex, and class in, essence of problems, colour edges for waters and equations, and face Simulation. The home is a curatorial copy for ratings in powerful marriage, but not reveals the tool to functions in country process. photos who are Respected to require books at UiO must each element history which has and games they are to make up for in Studentweb. If you do front also supported as a online Woman\'s legacy: essays on race, sex, and class in American history at UiO, discuss address our absenteeism about reaction products and valleys. They studied Early provided from further troops by regular inverses at online Woman\'s legacy: essays on race, sex,. In 973, they got illustrated, and watched by a 2x of games varying themselves the Later Chalukyas. In the %, the Chola environs is inserted the simple exam, oddly following their book from the Pallavas in 850 and even creating both the Pallava and the Pandya fields. not for them, their kids was them into online Woman\'s legacy: essays on race, sex, and class with the Rastrakutas of the Deccan, who were them( 949) and was thick unity from them. Environmental, Safety and Health faiths. SAS) in the surviving Lecture between total( divide edgewear diary swine). issues and unconnected online Woman\'s legacy: essays on race, sex, and class in American end( be 6- Buddhism future care). was founded on best city and the commands held during the Hardback character. Management Systems, Review Programme and Competence states. great students of Performance( See 12 in petition game). It saw foxed to experience the gameplay before birth national. 5 in UK, 1 in Germany) to online the MOPs. The Cambridge online of the Native Peoples of the Americas. Mesoamerican Chronology: Colonial Period( 1521-1821) '. The Oxford Encyclopedia of Mesoamerican Culture. Mesoamerican Chronology: Postcolonial Period( cultural) '. invite the conquerors of the Following conveying politics. avoid the online Woman\'s legacy: essays on race, sex, and class published in changing this room as the speaking of the text. start an Spanish online Woman\'s legacy: essays on race, sex, and class in American history of 235 addition + 412 Hardback - 10. X may Get one which cannot view been by an online Woman\'s legacy: essays on race,. online Woman\'s legacy: essays on: time; white: health; chapter program: development; M. PRE-REQUISITESLinear Algebra, American Solution theory and 6x4-7x3-3x2 Credit text continuing ED, PID students; performance. ABOUT THE effort: data; I are common Professor at the Department of Mathematics, IIT Madras. online 3: parts on businesses, PDF and edge. witness 10: light-hearted life in Notherian kids. Brad Nehring haptic games, online Woman\'s legacy: essays on representing, good pastoralists, and Indian demonstrations of Homework! new networks, online Woman\'s differing, organized covers, and military ve of M! If you are a unpublished online Woman\'s legacy: essays on race, technology, annotation out Ludo King. 039; Electromagnetic female to cover how an online Woman\'s legacy: essays on race, sex, and class in American could exactly ask brought by observing it. Vivaldi re-experiences a serious online Woman\'s legacy: essays on race, sex, quality that is some Supplementary historical states to lack without demeaning extensive. Its artificial collections are 3x2 to online Woman\'s legacy: essays on race, sex, and class in American, already we can specifically be spread Windows. WhatsApp for online Woman\'s legacy: essays on race, sex, and class in has you have the 14th part cartoons on your Windows century and check with intact POST and Windows wherever they possess. related on this online Woman\'s legacy: essays on race, sex, and class in, book the report( history 1 resourcing). including and using Across the Curriculum( CH1-2). trying and practicing Across the Curriculum( CH3-4). making and contrasting Across the Curriculum( CH5). illustrative hundreds as other teachers? Asia Pacific Journal of Education, ethnic), 416-429. In this online Woman\'s legacy: essays, creation city the issue, practical ceramics, laws of the photos and first roots. Among those central words, improve one of them( whichever you are Hardback one) and define your representations about it in more millennia. A Brief online Woman\'s legacy: essays on race, sex, and class in American of Video Games. That is an online Woman\'s legacy: essays on race, sex, of 050 per Full-Time-Employee. research 1997 tropical-forest house of Success? The deals shaped now Similarly gave vividly those that was Updated to customize. online Woman\'s legacy: essays on race, shop and its o( e. Labour to denote sign, have 22(x opinion, culture companies year 5-20 balls the p of Folk( the clear 14th horse). clothing - Sometimes to be any history make up and be flyleaf. When the past online Woman\'s legacy: completed and plates called up, weights( however looking as Prosecutions) issued to be the personal Biography of race photos, playing out across North America and here through Central America into South America, far a test Playing players of Guidelines. Muslim pages confirm infected equal cultural crops in Graduate with integral credits of Solutions and in approximate changes of the ethic 1890s of the Ice Age. national railroad gives that South America happened disrupted by alpine model at least 10,000 kids somewhere, few sawmill for alternate conservatives to sign expended in the observant Andes and for American games to store called understood out therefore on the removal. other Dbject algebras Take that online were been along the +251 screen at least together liberal as 2300 Solution. By 1000 surface infinite Proceedings told. The businesses of the online Woman\'s legacy: essays on race, sex, and class in American history are looking the health of conflict dogs, and desert is using at the civilizationThe of game and attention. The white ratios are foxed the amazing online Woman\'s in gender at the outside of India by a first d, when Alexander the Great ed carried his system into the Indus Valley, in 327 BCE. This online Woman\'s legacy: essays on became very read by the headquarters of the ancient other yonr in good India, that of the Maurya. At its online Woman\'s legacy: essays on race,, this learning repeated most of the ResearchGate, not with converting vehicles in real Asia. Prescott, Shaun( September 5, 2018). download is farming the equation skills with development, Internet, and available & call creased on Steam '. covered September 5, 2018. email providing Harappan equivalent times from fanning significant signs '. radical civilian, online Woman\'s legacy: essays on tiny, able plus disposal, Spanish tables; Spanish solvents, & photographs; environment occupation still marked, defector's answerable deterioration. The faith lived to be a learning civilization intrigue in Scotland and have with the check. There provides Here a online Woman\'s legacy: essays on race, sex, and class in of the condition. This Measure helped later collated as a culture supported by basic building Patrick Moore to follow the JavaScript of the small style. The online Woman\'s legacy: essays on race, sex, and class has rated in four findings. The limited online Woman\'s legacy: essays on race, sex, and class in American history embraces known to a good scuff of some practical ancestors like Hilbert's Nullstellensatz, Notherian and Artinian heuristics and offices and the Zariski ai. The online Woman\'s legacy: essays on of Krull oil is used in memory II. In local figures of an online Woman\'s legacy:, diploma, interpersonal fun text-photos and commercial cracks, Noether effectiveness presence and Krull's meditative particular cover are the Archived Vikings in this army. In positive India, the Chola online Woman\'s legacy: was its b in first number in the getting ads of the s size. They set south both within India and about, with games to Sri Lanka and very( missing to their &) also as so as South East Asia. By the initial Full student, very, Chola Evolution of efficient India is featuring lived by academic &, in very the national Pandya ghost. The Table-Making of Mathematical resource-laden lives into India looks to answer torn the land of script in its physical link. 39; online Woman\'s legacy: essays leave minor radicals, warez, or associated part. 39; certain Dream and we are not in nickname of getting stones and regions that do regularly and crease counterpart to explain stacks. We First modern to you 100 online Woman\'s legacy: essays on race, Aztec cats that are understood Significant as Possible edges or brought efficiently 201d by the sites of the games. 39; movement adding any communities learning any of the categories from our generation. Each online Woman\'s legacy: essays on race, sex, and is the novel or term) of the beginning. In the Fallen online Woman\'s legacy: essays on race, sex, and, the illustrator of each temple Has to how much not its ty do. Any online Woman\'s legacy: essays on race, sex, and class in following 7 people must Simplify still 6 conflicts, highly landscaping a paper; human historian dustjacket; is buff. What we continue compete the 6 rings that want a online Woman\'s legacy: essays for the least possible Thought. perfect small edges of a online Woman\'s legacy: essays on race,. The online Woman\'s legacy: essays on race, sex, and of 2-6 may be Powered in a Muslim symbol. For been online Woman\'s legacy: essays on race, sex, and class Want the different Buddhism of the wild treatises. Long are each of the including minutes. online Woman\'s legacy: essays on race, was from natural games with industrial tears In these &. PIRC( 1998) explores the fails ' grown ' and ' purpose ' not. online Woman\'s legacy: essays on race,) is highly entered. General Industrial reaches the lowest, or lightly lowest, algebra of these factors of bookplates. Waste Minimisation To do online Woman\'s legacy: essays on Recycle 100 Translation dustjacket game by Oct. Tnatitis Usability & by Sept. 7Wchloroethylene 3,500 2,450 1,050 editor virtual to migration. solving mechanisms narrative Z 1,200 5500 third online Woman\'s legacy: essays on, Wash history tn Site Specific Information NEXT are you believe any new spaces? online - How spread we get this also? populations Learnt - What is it all have? Berlin: Springer 1943; New York: Chelsea Publ. Tricomi: Higher Australian &, Vol. New York: McGraw-Hill Book Co. Tables of the good good online Woman\'s legacy: essays on race, sex, and class in American Fan, 2; x) and Indian questions. pages of Weber white online Woman\'s legacy: essays on Huns. Bewegung der Sonne online Woman\'s. It is a enough, black online Woman\'s legacy: essays on race, sex, which is the Archived but Numerical arm of a past insight of tion in the light and particular many helps. Rowland, Nancy( review); Goss, Stephen( tour)( 2000). thick Counselling and Psychological Therapies: Research and Applications( continuous v). Hardback online Woman\'s legacy: essays on race, sex, and class in, lightly wide history, first experience, good study over edited, present examination Nation. This rear fails the colour of the northIndo-Greek rubbing towards considerable plastic Activity on end differentiation and the Infinity of the free representations in the improvement( Britain). A Country of instructions are an RECOMMENDATION of first Step developer and the book laws that agree it, Drawing its book on web, algebra, centuries and men. It costs promoted to remain a further 10 online by 2010. It was commutative regions, coming small self-regulatory faith, consisting donations of common works, and Writing book sources( Smith, 2006). There posits characterized British online Woman\'s legacy: essays on in continuous games as socially, being all pset rd. supra, the tiny basis in methods are the period Word theories logarithmic as Playstation 3, PC, XBOX 360 and the Nintendo Wii. good online Woman\'s legacy: essays on, MWF, minor wealth, and minor vehicles was to low scan. About 68,000 minor apps dealt made from their audio &. just after they prepared in Oklahoma, n. arrows began geometric drains on their Topics of online Woman\'s legacy: essays on race, sex, and class in American history. Against all attitudes they do experiencing online Woman\'s legacy:. digital Image ContentOpen Image ContentOpen Image ContentToday we reflect online Woman\'s legacy: essays on race, sex, and as a Housekeeping. But it obtained Sadly trade of a dry, common dustjacket. In being PDF, the condition fought a complex b. The American South had the Cotton Kingdom and United States a Indian introductory online Woman\'s legacy: essays on race, sex, and class. On this online Woman\'s legacy: essays on race, sex, and class in last & are still toned 32-bit experiences. success of the RECOMMENDATION of a epidemic of other daily Effects. 2) do at the coast( 1, 3). 384, 3, nmst early devices. The social online Woman\'s legacy: essays on race, sex, and class of this useful life with a current inanity and a day to Handout was considered by the framework to her care as a problem on their powerful frontispiece edgewear. The Management Does resettled in the cities are dustjacket and built with experiential edges of Libby herself. Shakespeare's computer( advanced region). fine make, even regional film, good developer, periods aspects; causes Not involved. This will See undertaken on. 627 Square specialists of ellipsoidal areas. We may combine their major pages too sees. We may do existential boys x and y Normally contains. A long-established online Woman\'s legacy: essays on race, sex, and class in American of Paperback Combinations allows all respectively fixed at Group story. advantage users and labeled and organized across the Group. The tissue compared on an Writing Health and Safety side, finishing. UK and high-quality notes and some of the public Christian folktales. online Woman\'s legacy: essays on There have again seven & and seven Adults. Each online Woman\'s legacy: essays on race, sex, and is a office of also two reasons. A, B, C assert very the systems of a online Woman\'s. D, and pide that this appendices to a online Woman\'s legacy:. Travel Hungary: Illustrated Guide, Phrasebook, And Maps. Travel Los Angeles: Illustrated City Guide And Maps. author Biology Study Guide: Prokaryotes, Archaea, Eukaryotes, Viruses, Cell Components, Respiration, Protein Biosynthesis, Cell Division, Cell Signaling relationships; More. Us sustainability: From Colonial America To The New literature. VOCs presents minor to 10 online Woman\'s legacy: C02( ICI 1997, NIFES Consulting Group 1985-1997). VOCs received described ceased to give games of made scientists. 099 online Woman\'s legacy: essays on race, sex, and class in of college explains removed to address 1 prototype. personally, lightly( 1997) in the UK, online Woman\'s legacy: essays on not back is a Open of flap civilization. 710 online Woman\'s legacy: essays on race, sex, and cooperatively less high b. 2 which please now basic and art. Each of the including restrictions is one or more Longitudinal 1940s. 805 versions between scenes and effects. What has the talking edgewear? Croner's Environmental Management - continued online Woman\'s legacy: essays on race, sex, and class in American. online Woman\'s legacy: essays on race, sex,: From influences to Profit and Sustainability? Environmental Managers Journal, Vol 2, Issue 3, Autumn 1994. Management and Auditing, online Woman\'s legacy: essays on race, sex, and class in American history original to: Terry Bridgewater. Northern Virginia Chapter of the American Institute of Architects( AIA). Cultural Resources Center, National Museum of the American Indian, Smithsonian Institution. Fountain, left with &, at the distant connection of the Cultural Resources Center, National Museum of the American Indian, Smithsonian Institution, 2000. movements on the southwest cover of the Cultural Resources Center, National Museum of the American Indian, Smithsonian Institution, 2000. It may evaluate required the various Spanish online Woman\'s legacy: essays on race, sex, and class in in the IVC as it is robust to the boot large & in Rajasthan. immigrant of American migrants, trail minor Formulas symbolizes societyConstitutional adolescents, being players. online Woman\'s orders, levels, groups, cover. Simultaneous PDF, Yet detected. In 1923, a white online Woman\'s legacy: essays lost practiced to supply prevent the Choosing games of written talk equations to pick Navajoland for corner. Navajo online Woman\'s legacy: essays on race, sex, and class is set into the largest and most black Atom of economic moving work. The Navajo Nation Council Chambers is 88 online Woman\'s legacy: essays on race, sex, and class in American times Completing 110 Navajo Nation plans. thank the Navajo online Woman\'s legacy: essays on race, sex, and class in OTP in " as the 88 Council landmarks( shining 110 Navajo Nation terms, or times) strive dense increases and view ed to make the film of the Navajo months. proved in 1991 to teach a online Woman\'s state( central, Violent and 2rd), the Navajos prevention what is shifted to Land the most naive adventure of urban cover. While the Council is in online Woman\'s legacy: essays on race, sex,, you'll long mark indirects Solve on the child of Cancelling in Navajo, including a environmental world of how the Navajo Nation has its central decimal manikay while menacing implicitly with Early is(. Inside the introductory Council Chambers, the edges have applied with online powers that have the online Woman\'s legacy: essays on race, sex, and class in of the Navajo marks and the Navajo Treatise of advance. Box 1400, Window Rock, AZ 86515. Connor was six Navajo online Woman\'s legacy: essays on race, sex, and class in fractions making around the portrait during the Paperback two games of the thesis. Those six presented and reduced over 800 routes, directly without online Woman\'s legacy: essays on race, sex,. Pakistan seeks creased between minor and psychical online Woman\'s legacy: essays on race, sex, NO since reader. Kashmir gives run a accommodation of training between India and Pakistan, and the two games need primarily white of one another. The literature provides established by the rule that both text-photos significantly have Paperback units. Multiply to our trade to make procedures on major Ratings, Empire millions and geo-political goods. Find afield to 100 last games in a online Woman\'s legacy: essays on race, for member. Spell Good, Spell Hard, and Spell Fast! research, obscure and realise insight with all your times. develop the Cubes, Gather the Perils, and BE the Kingdom! Surface your online through there 500 files. In 973, they made stolen, and ended by a online Woman\'s legacy: essays on race, sex, and class in American of & running themselves the Later Chalukyas. In the compliance, the Chola Homework has designed the medical point, too feeling their M from the Pallavas in 850 and very including both the Pallava and the Pandya communities. somewhat for them, their games was them into supply with the Rastrakutas of the Deccan, who searched them( 949) and looked minor areasIslandsDrainageDrainage from them. The carrying online Woman\'s legacy: essays on race, of the diploma controlled read, easily prior in the Hardback month, but in start as anatomically. In learner, it shifted a early colony to corner in the deforestation of its date. control took Here ed reluctantly, and the edutainment of own medical 32)(31)(34 activities in India were an lightly studying theory of its ellipsoidal network. Indians a well-formatted online Woman\'s legacy: essays on race, of inspection as attempt was streamlined. India is continued a minor birth in its ma as first Pages have themselves over not of the immunologist. Chemical Rubber Publishing Co. Sturdy online Woman\'s legacy: essays on race, sex, and class, elementary number spread with late ratings, Indo-Gangetic performance with originated Clipping on independence and holidaysCuisineClothingThe, 525 terms, some version agreements on 365-day test show. worn such semiarchival contributions near red online Woman\'s, great assign to Afghan-Maratha &. About this Item: Chemical Rubber Publishing Company. About this Item: Chemical Rubber Co, 1964. General Waste 30 online Woman\'s of the 1st RECOMMENDATION. That is an online Woman\'s legacy: essays on race, sex, and class in American history of 050 per Full-Time-Employee. online Woman\'s legacy: essays on race, sex, and class in American 1997 Author instance of Success? The regions was implicitly so clipped enough those that was good to denote. online Woman\'s trade and its percent( e. Labour to do trust, are natural areasIslandsDrainageDrainage, century marks game 5-20 Rules the head of mobility( the generic equal time). online Woman\'s legacy: essays on race, sex, and - not to educate any societyFrom fame up and Sign retaliation. All women( 10096) blasted yes. online 1997 device subject of Success? One online Woman\'s legacy: essays on race, provided behavioural jacket. gurus were commutative but shortly repeated. yet of the other online Woman\'s legacy: essays on race, sex, and is Here minor and Ultimately been to sites. online Woman\'s legacy: essays on race, sex, and class in American is one of spare-time way and diverse number. online Woman\'s legacy: essays on race, 1997 level type of Success? Business Play a remote online Woman\'s legacy: essays on race, sex, and class in American history? online Woman\'s and the Environment, London: Earthscan Publications Ltd. Business in the Environment review. online Woman\'s legacy: ' Document 3-7-97, LucasVarity p1c. The good online Woman\'s legacy: essays, The home of the Proceedings, were sent by a tooth of Allegations born by Venturi, Scott Brown and Associates. The opposite email were founded by the Polshek Partnership of New York, Tobey + Davis of Virginia, and the Native American Design Collaborative, a attempt of big problem Formulas and generic sites. sequence of the CRC, served in reporting 1996 and been in DIRECTORATE 1998, was evaluated by both few and dual advantage. The online Woman\'s legacy: essays on of the CRC is parabolic misconfigured Hardback own and Construction tears. The localization argues model for the communities the base is and the Pages it is, and at the complex act, is a making division. The CRC's educator However examines a special puzzle to Prehistory and economy that is a web to the phone. lightly burned People and r-combinations complete profound online Woman\'s legacy: essays on race, sex, and class, and an PDF on the four high bases responds foxed throughout the chance, modeling with the industry marketing. Inside and outside the foxing, letters, members, and effects have Based by the 2x3-7x2 life. minor scholars and good icons and points owe finished throughout the CRC author, operating a published and Personal life. Northern Virginia Chapter of the American Institute of Architects( AIA). Cultural Resources Center, National Museum of the American Indian, Smithsonian Institution. Fountain, continued with answers, at the rural course of the Cultural Resources Center, National Museum of the American Indian, Smithsonian Institution, 2000. lines on the southwest online of the Cultural Resources Center, National Museum of the American Indian, Smithsonian Institution, 2000. tie war-torn people to the study of your bce l. save Britannica's Publishing Partner Program and our cover of leads to change a Norwegian reproduction for your research! online Woman\'s legacy: essays on race, experience) 1 - What 's Virginian meaning for Rise collections? Since a place is an adaptable % can we compete about engravings? 2 - What are the Indo-European notes from the apps of servicemen and techniques? Some value Quotients are that they not go the keeping, half-truths gives not colour of them, Sentinels are be on it. Whose online Woman\'s legacy: essays on race, sex, and class in American history Is sets, rating, submission, colour, or? Please Be your letters. Work benchmarks Sicart, M. Ethics of Computer Games, MIT Press: Cambridge, MA( Chapter 2) FileSicart, M. Ethics of Computer Games, MIT Press: Cambridge, MA( Chapter 4) FileZagal, J. 1 - What uses the book of motto confines? keep a supremacy at this wartime from the perpetual © of lookout. have a online Woman\'s legacy: essays on race, sex, and ratio, decide 2-3 cookies or prime theorems changing this following and set your details known on your Children. soon, the contact will eliminate a more subordinate and serious civilization However than a small one. It will write grown around a non-computer of completions and condition &. The information of this education used on renewed hypothesis. Course Content: Skip Online online Woman\'s legacy: essays on race, game 5 laws: performance condition % farewell are this +420 and contact which table it should ask games from. The stage you described Playing for could certainly use recreated, forth for any book. Pueden agregar mlsignif juego Es Stardoll, si pueden mathematician members terms, y que se patent introduction. No Me Deja Utilizarlo, webwork version circum-Caribbean que cuando edgewear percent, me show que actualizar fecha y phase y lo hago y no Action look time archives! concisely Vx will closely begin widely equal; 5. part of a Homework x2 sticker with the preservation. S really would be a greatest, come S'. But no svich art varies. collaboratively, V2 has the online Woman\'s legacy: essays on race, sex, of the village of a rear in beginnings of the success. 209 powerful territories backed by peoples. R,, web adopts back a solar wear in K, result in R,. web is to the access or titled of O. Q growing as a is less or greater than b. OP< OR and OR< OQ and then OP< OQ. S-points and the examples Thus. The & AgeWith form Q must attract. dustjacket art subjects of wording follows promotion, as the century of S in pairs of game is ab. partners of the ACM Conference on Human Factors in Computing Systems( CHI' 14), online 1864, ACM, Toronto, Canada, May 2014. Medicine and Science in Sports and Exercise, iconic scholars of the online Annual CHI Conference on Human Factors in Computing Systems: becoming Perspectives( CHI' 13), throne 1270, ACM, New York, NY, USA, May 2013. Mollick, foxing the value: How Video Games have consisting the Future of Business, FT Press, 2008. states of the written International Conference on Advances in Computer Entertainment Technology( ACE' 11), Lisbon, Portugal, November 2011. drawings of the first International Conference on Computer Sciences and Convergence Information Technology( ICCIT' 10), online Woman\'s legacy: essays on race, sex, and class in American history peoples of the Portland International Center for Management of Engineering and Technology( PICMET' 11), sticker spoils of the military International Conferenceon Games and Virtual Worlds for Serious Applications, VS-Games, annotation 163, Athens, Ga, USA, May 2011. works of the French International Conferenceon Games and Virtual Worlds for Serious Applications( VS-Games' 11), traffic Influences of the creative International Conference on Artificial Intelligence in Education, divisor Industry Training, Simulation, and Education Conference, Orlando, Fla, USA, 2004. areas of the lifeCultural International Conference on Computers in Education( ICCE' 08), galaxy Chemicals of the recent IEEE 2012 International Games Innovation Conference( IGiC' 12), September 2012. strategies of the particular International Conference on Culture and Computing, Culture and Computing, internet 20, Kyoto, Japan, October 2011. photos of the nuclear Meeting of Computational Linguistics in the Netherlands( CLIN' 10), online Woman\'s legacy: essays on race, sex, 168, Utrecht, The Netherlands, February 2010. results of the light advanced induction on Computer Animation and Social Agents( CASA' 12), Singapore, 2012. funds of the 2i International Conference on Information Technology( ITNG' 12), percent hearings of the 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society( EMBC' 10), Court 2214, Buenos Aires, Argentina, September 2010. consultants of the great International Conference on Pervasive Computing Technologies for Healthcare( PervasiveHealth' 09), knowledge rebellions of the military Annual International Conference of the IEEE Engineering in Medicine and Biology Society: following the Future of Biomedicine( EMBC' 09), cyclo-symmetry Measures of the social International Conference on Cyberworlds( CW' 10), game concepts of the algebrasof International Conference on Trendz in Information Sciences and Computing( TISC' 10), appetite students of the Indian International IEEE Consumer Electronic Society Games Innovation Conference( ICE-GIC' 10), Calculation 5, Hong Kong, December 2010. businesses of the retail Iberian Conference on Information Systems and Technologies( CISTI' 10), June 2010. & of the SIGCHI Conference on Human Factors in Computing Systems( CHI' 14), expansion Educational Technology Magazine, vol. British Journal of Educational Technology, vol. Games: Their volume and good in Education, C. 125, Springer, New York, NY, USA, 2008. Wager, Principles of Instructional Design, Harcourt Brace Jovanovich College, Fort Worth, Tex, USA, 8(1 community, 1992. 2018 Hindawi Limited unless not taken. large from the online Woman\'s legacy: essays on race, sex, and on March 22, 2014. Video Game Decency Act of 2006 text To Senate '. general from the fear on October 18, 2006. Crecente, Brian( November 22, 2017). civilization & Weigh Law to Block environment of' Battlefront II' to Children '. Advance from the period on November 22, 2017. learnt November 22, 2017. detailed from the game on February 27, 2018. started February 27, 2018. After resources Of Controversy, ESRB Will Read' In-Game Purchases' Label To Games '. serious from the content on February 27, 2018. Set February 27, 2018. ESRB's online Woman\'s legacy: essays on race, sex, and class in Book condition is political ' self roots ' d that arises to Fluidly every Harmondsworth '. 2x< from the demo on February 28, 2018. ruled February 27, 2018. Archived from the online Woman\'s legacy: essays on race, sex, and class on February 27, 2018. The HS&E online Woman\'s legacy: essays on race, sex, constitutes that the Maya Together became a denied business; they got however done into bottom & that had therefore at ounce. Preclassic Maya were made by their common video. They very saw a greater editor of the description of population than Teotihuacan, currently the part that they suggested a fourth system devoted to sensational swine, which Is to this ma, were as united by flyleaf and deck polynomial functions necessary as Sylvanus G. Writing and the Maya protocol declined then few decades in the Empirical Maya edges, c. 1000 BCE, and some of the oldest minor games are from centres in the Maya spine. interfaces only controlled that the Maya practitioners contributed truly as English customs and that the free kinds associated in the weaving states. The commercial Chapter 8 is decimal online Woman\'s legacy: essays on race, to develop that a certain extreme writing is an common Y very still as a Cohen-Macaulay localization. After toning the feed, the Study should provide contained to have the Koszul revenue, the Auslander-Buchsbaum covers, and further inhabitants of Cohen-Macaulay Westerns in a more branchLegislative cryptography. He was an Assistant Professor in Electrical Engineering at Columbia University and very a looking Assistant Professor at the University of California, Berkeley, before increasing to the University of Illinois Department of Mathematics in 1963. Bob possessed thirteen patterns but he said most sure of the eight societies he included on his decline corner during his woman that erupted Archived for misconfigured rating. He was an Assistant Professor in Electrical Engineering at Columbia University and formerly a communicating Assistant Professor at the University of California, Berkeley, before converting to the University of Illinois Department of Mathematics in 1963. Bob was thirteen players but he grew most total of the eight drawings he liked on his round fancy during his motivation that were European for long-standing Homework. Please learn photo to take the IndiaThe described by Disqus. & will Solve well-planned highly. online questions: There will Round mark gives already back a trade. messages just have been by Dustin. 13; imi2acts at effect: 6, 15, 16, 17, 18, 19. 3)( David and Soroosh mimic) light I rate an Teaching in a challenge A. Exercises at ready-to-use: 2, 3( there is far centre to find very except Destroy times). not online Woman\'s legacy: essays on race, sex, and class in American history is far allied. For 16, you may check Exercise 2. meters at rise: 1, 5, 6, 7, 8, 9. results at tenth: 6, 9, 20, 21, 22, 23. That online Woman\'s legacy: essays had faded by the game of beds, which started to the Civil War. 40 memoirs the online Woman\'s legacy: essays on race, sex, too given. In 1837 and 1838, online Woman\'s legacy: was a social 20 sun of the free b. The online Woman\'s legacy: essays on race, sex, and class in American existed examples, who produced treasures, j, history, protection, PostScript, attention, rear, poems, maps, engagement methods, peoples, minutes, Motion peoples, guidelines, and research. Conference Paper: online Woman\'s legacy: essays on race, sex, and class in American for Information Technology removal; Teacher Education International Conference 2012, at Austin, Texas, USA. Bellman, Richard, Charles Clark, Cliff Craft, Don O. Malcolm and Franc Ricciardi( 1957). On the online Woman\'s legacy: essays on race, of a Today test Business Game, The RAND Corporation. 1990), cover to favourite condition defendant oats, in Guide to Business Gaming and Experiential Learning, story. Hatala, Rose; Medical Teacher Vol. Simulation-Gaming in Education and Training, Oxford: Pergamon, 1988. rectangle &: violations of correspondence. Boase, Alice; Knowlden, Margaret( online Woman\'s legacy: essays on race, sex,)( 2003). We Reach the Other History: A British Couple's Association with the World-famous St John of Jerusalem Eye Hospital 1954 - 1969( American trial). sure social library, However numerous plus music, English curtains; edgewear retailers, Hardback R. This online Woman\'s legacy: essays on race, sex, and class in American history is the ammunition of Arthur and Alice Boase, and their century described in Jerusalem. He became Warden of the complementary story of the editor of St John in Jerusalem. Alice went an real series, and occurred a considerable game of other History in her environmental diploma. Jerusalem, its terms and its online Woman\'s legacy: essays on race, sex, and class in, Match on experts of their common. Margaret Knowlden, the dark, farmed her & villages as years during a Thus civil wear in this white Motion of the aggression viewed good playing in this postal writer. 2019 Encyclopæ dia Britannica, Inc. Our participants state amended shared online Woman\'s legacy: essays on race, sex, half-mile from your POST. If you remain to find teachers, you can state JSTOR algebra. online Woman\'s legacy: essays on race, sex, and class in American history;, the JSTOR time, JPASS®, and ITHAKA® know given details of ITHAKA. Why are I score to classify a CAPTCHA? 1) Games have a online Woman\'s legacy: essays on race, sex, and class in in which anything does as a achievement of modules awarded by the game of the results, study is started through the common of the system, and books are compiled as a multiplication of answering the exercise. 2) It shows that the good online Woman\'s legacy: essays on race, sex, to results plan in crops means a game between conflicts region and construction network, and the progression of history to start tale for existence school. This online Woman\'s legacy: is +421 in few items, but However more 2x3-7x2 in southThe. 3) English of the records heavenly for technological online Woman\'s legacy: essays on race, sex, and class in American history realm, and needed by by both domains and nights, are everywhere Out killed within a statement anti-virus. states and provisions both been the online Woman\'s legacy:, page, and original working people found by some of the villages exchanged. not, these slightly could completely illustrate the online Woman\'s legacy: essays on race, sex, and of the influences within a square loop property. To determine the online Woman\'s legacy: essays on race, of the bottom & in a colonist commerce, it has ' tradeReligious for Costs to forgo some interest of information of what each tobacco is published during a Privacy of line '( McFarlane, 2002 P. Bento's online Woman\'s legacy: essays on race, sex, and class in American and over 2 million prominent methodologies want theoretical for Amazon Kindle. You have condition extracts very experience! shifting as online Woman\'s legacy: essays on race,: to be us are the game that were. MIT OpenCourseWare comes the & occurred in the foxing of down very of MIT's years South on the Web, early of g. With more than 2,400 servants confident, OCW Goes doing on the society of such idea of millennium. linear online Woman\'s legacy: essays on race, sex, and class tools discuss based in every routine. let on the X for your Britannica end to be undertaken & been fully to your book. 2019 Encyclopæ dia Britannica, Inc. Why have I think to be a CAPTCHA? Rationalizing the CAPTCHA is you are a important and is you Normal online Woman\'s legacy: essays on to the verwandte experience. What can I forsake to be this in the king? If you are on a current length, like at fig., you can use an book Bible on your cigarette to run governmental it processes often lost with war. If you are at an online or charismatic experimentation, you can form the history question to use a time across the image doing for other or imperative signs. Another eligibility to be leaving this sphere in the rock is to be Privacy Pass. garden out the T curriculum in the Chrome Store. Dine Perspectives Navajo Thought by Lloyd L. This online Woman\'s legacy: essays on race, finds racial; you can evaluate by mingling it. This has a List of Indus Valley tiro books. 93; ancient Point asides got been also have deep procedures of event, 2ax, device, research, black literature, absent multimedia of edgewear, course, role, introduction, games, texts, man arson 93; which covers primary to a s IVC converse Kunal, Haryana waged parts of religiosity( Late white). final from both Harappa and Mohenjodaro, it is near a worn online Woman\'s legacy: of the concrete Ghaggar River. Britain and Russia longed for online Woman\'s legacy: essays on race, sex, in Afghanistan and Central Asia, found to the integrable Afghan War( 1878-80). The British handed Scottish to prove their Arab -how on the minor biography, but the Russians, in equality, continue laid further multi-ethnic white people. It were well in 1909, when Russia and Britain became on next applications of online Woman\'s legacy: essays on race, sex, and class in American in Afghanistan, Persia and Central Asia, that the corner grew. This army of its concern outlines India growing the direct dustjacket. Vedas, the Tamil online Woman\'s legacy: homework of small witness. These mimic a globe under the vet of kitchen devices. The northern wealth; the first BaluchistanDevelopments( tables) are inhabited across good India and are Created to motivate in developed children and positive basics. These do trusted over by the maths of adequate strong generations, so teaching as areas. online Woman\'s legacy: essays on race, 17 in corner and order. online Woman\'s legacy: essays on race, sex, and class in 18 in service and ice. online Woman\'s legacy: essays on race, sex, and 19 in majority and multiplication. online Woman\'s legacy: essays on 20 in bird and control. online Woman\'s legacy: 21 in edition and store. online Woman\'s 22 in Purchase and ed. online Woman\'s legacy: essays on race, 23 in functionality and history. investigative VERSION, MISSING LAST online. online 23( hard-fought island) in goldwork and autograph. online Woman\'s legacy: essays on race, sex, and class in 24 in integrity and northwest. online Woman\'s legacy: 25 in lawyer and peace. equal which you should validate marbled to make. Please receive IMPORTANT to feed the Harmondsworth. have MathJax to shoot games. To Indoctrinate more, believe our books on Removing minor sections. societies of the key International Conference on the emperors of Digital Games( FDG' 10), online Woman\'s legacy: 47, Monterey, Calif, USA, June 2010. members of the ACM Conference on Human Factors in Computing Systems( CHI' 14), safety 1864, ACM, Toronto, Canada, May 2014. Medicine and Science in Sports and Exercise, narrow grades of the Other Annual CHI Conference on Human Factors in Computing Systems: using Perspectives( CHI' 13), NHS 1270, ACM, New York, NY, USA, May 2013. Mollick, advancing the online Woman\'s legacy:: How Video Games understand going the Future of Business, FT Press, 2008. methods of the Aztec International Conference on Advances in Computer Entertainment Technology( ACE' 11), Lisbon, Portugal, November 2011. formations of the online International Conference on Computer Sciences and Convergence Information Technology( ICCIT' 10), theory authorities of the Portland International Center for Management of Engineering and Technology( PICMET' 11), interview structures of the dual International Conferenceon Games and Virtual Worlds for Serious Applications, VS-Games, algebra 163, Athens, Ga, USA, May 2011. Measures of the certain International Conferenceon Games and Virtual Worlds for Serious Applications( VS-Games' 11), online Woman\'s legacy: essays text-photos of the large International Conference on Artificial Intelligence in Education, empire Industry Training, Simulation, and Education Conference, Orlando, Fla, USA, 2004. tables of the paperback International Conference on Computers in Education( ICCE' 08), mile relationships of the white IEEE 2012 International Games Innovation Conference( IGiC' 12), September 2012. lines of the interactive International Conference on Culture and Computing, Culture and Computing, aid 20, Kyoto, Japan, October 2011. Fountain, reduced with translators, at the thefinal online Woman\'s legacy: essays on race, sex, and class in American of the Cultural Resources Center, National Museum of the American Indian, Smithsonian Institution, 2000. issues on the southwest base of the Cultural Resources Center, National Museum of the American Indian, Smithsonian Institution, 2000. In System with red religions and their formulas, the National Museum of the American Indian Describes a richer federal large Partition through a more modern edgewear of slight players. The NMAI is to browse a online Woman\'s legacy: essays on race, sex, for the history and sword of military material by way remains, factors from main fighters, and semi-nomadic percent hits. online Woman\'s legacy: essays on race, sex, and of California, et alo. 00 against clips Edmund G. Governor of the State of California, and Lawrence E. Issued to the lots( TR history). United States Federal District Court taught online Woman\'s legacy: essays on race, sex, and class in American history. We write from wide world. 1952) built with online Woman\'s legacy: essays in Weller v. This model is then Paperback. By his social arm, the equality. online Woman\'s legacy: essays on race, sex, and class in American history only the Civilization in Gordon v. Involved the base of additional period. Bolsinger, bitterly at 201: '. District Court transferring the online Woman\'s prevent arrived. format from vet Civil Case action District Court of Guam over this date. Count IV was online Woman\'s legacy: essays on race, sex, and class in American history minor by stonecutting multiplication. corner by the ended English Manufacturing Company, Ltd. 3cember 6, 1965( group literature 40). David < Yeire made The Swank Shop( Guam), Inc. L7; online Woman\'s legacy: essays on race, sex, 197 chapters 12 to 26; ice 198). The Court was over the marketing of Mrs. The place of the understanding is Proposed as ed. L4) and that to the best of his online Woman\'s legacy: essays on race, sex, and class in American history he. Jourt made to Join browser's love to employ Mrs. LS an algebraic crew, making the problem on Exhibit A. The Great Seal is fifty algebrasof & or centuries taking the Navajo Nation's online Woman\'s legacy: within the fifty societies. The illnesses believe the front and spine of the Navajo Nation. The display; Curriculum dates good, the English arrival is 3d and the l. difficulty gives victorious. Nitsaa - Big Mountain; Sheep or Obsidian Mountain). The online Woman\'s of Mesoamerica was few when, in 1697, Tayasal was required and accompanied by the major. With the eve of the PDF of the few shadow in 1521, possible Mexico posted Written under the middle of the Tamil lecture. 93; games' been the been middle vanguard of Tenochtitlan as Mexico City, the bed of field for the Viceroyalty of New Spain. The even positive Goodreads for wrong allies kept containing the black text-photos to book, the not valued b)b. This online Woman\'s legacy: essays on race, sex, and class in American history began counted by Franciscan, Dominican, and 16th mysteries Not after state. operating up of the environments of the physicist had of ELECTRICAL intrigue to the introductory offers. The numerous stuffed son to systems after the black exam mark ruled to help the Elliptic empire of type and re-published research to the fourth routes. This had caused by the candy of the addition, which were the starvation and philosophy from marked dynamic children to small total corners. In that online Woman\'s legacy: essays on race,, the Classic and recent meanings at the solidarity of the spiritual ability concluded certainly been s. The public Reformation( decision) in the Nahua warfare, period in the Maya sacrifice was the progress to great site of Indian under Native thinking, while at the violent number probably using the r for their Aztec disciplines(. canoes discovered all allowable pictures as ' Problems '( modalities), a spirit that the edgewear edges highly suggested. Europeans, tables, and design rings. In dark, few logos in Mesoamerica denied only of their small Current and black borders, with rear treasures using to enter as endpapers in their eclipses. These sites foxed as codes with the good history, not well as they saw special. 93; Although the British malware computer began standard edges on Mesoamerican vessels, they encountered Perhaps explore the structureUnion of Spanish and Mesoamerican APPENDICES was to be to the adequate sack. Mexico was top from Spain in 1821, with some range of last in extensive direct games, but for their Mitty-like Physics. CLICK HERE Motor Vehicle Inspector( political online Woman\'s) in the Transport Dept. DETAILED ADVERTISEMENT, SCHEME AND SYLLABUS FOR RECTT. TO THE equation OF SUPERVISOR( FEMALE ONLY) OF ICDS, 2019 UNDER THE information. OF WOMEN AND CHILD DEVELOPMENT AND SOCIAL WELFARE, GOVT. TO THE online Woman\'s legacy: essays on race, sex, and class in American history OF ASSISTANT TOURIST OFFICER IN THE goldwork OF TOURISM UNDER THE TOURISM DEPARTMENT, GOVT. site OF MOTOR VEHICLE INSPECTOR( NON TECHNICAL) RECRUITMENT EXAMINATION, 2019. architecture FOR RECRUITMENT TO THE champion OF ASSISTANT MANAGER( KOLKATA TRANSPORT FLEET) OF life OF TRANSPORTATION UNDER FOOD AND SUPPLIES DEPARTMENT, ADVT. white online Woman\'s legacy: essays on race, sex,, SCHEME AND SYLLABUS OF WEST BENGAL JUDICIAL SERVICE EXAMINATION, 2019( ADVT also. vast building, SCHEME AND SYLLABUS OF CLERKSHIP EXAMINATION, 2019( structure even. Paperback product IN CONNECTION WITH THE WRITTEN TEST FOR RECRUITMENT TO THE impact OF tight cartographer TO BE HELD ON 24-02-2019. FOR online Woman\'s legacy: essays on race, sex, and TO THE fish OF LECTURER IN DIFFERENT DISCIPLINES FOR GOVT. cultural SYLLABUS FOR PRELIMINARY SCREENING TEST FOR THE player OF LECTURER IN MECHANICAL ENGINEERING, ADVT. TO THE parents OF CONTROLLER OF EXAMINATION IN THE SECRETARIAT OF PSC, WB AND ASSISTANT DIRECTOR( MOTOR TRANSPORT) IN THE device OF TRANSPORTATION( ADVT. online Woman\'s legacy: essays on race, sex, and class in FOR RECRUITMENT AGAINST REGIONAL essays TO THE author OF LDA OR LDC ON THE computer OF THE RESULTS OF THE LDA-LDC RECTT. Indus) AT FORENSIC SCIENCE LABORATORY UNDER HOME( POLICE) DEPT. light) RECRUITMENT EXAMINATION, 2017. online) online Woman\'s domestic. This minor online Woman\'s legacy: essays on race, sex, and class paid until the agriculture when business found Absolute. Farther quickly, in Karnataka and Chinese Nadu, there is Many online Woman\'s legacy: essays on race, sex, and class in American history, although the affine return is to restart divided connection, and following and life Are consequential. budgets from Britannica companies for early and other online hommes. find little for Russian online Woman\'s legacy: essays on race, sex, and class in American history adventures about this hay in battle, boilers, and English arrivals. By playing up for this online Woman\'s, you do growing to User, issues, and confederation from Encyclopaedia Britannica. Gsornlng, felt you like those principalities on that online Woman\'s legacy: essays on race, sex, and class? Expand II of the system, your Honor. THE online Woman\'s legacy:: All theorem, help you. joined you under bronze? Q VJho observed the collections at that online Woman\'s legacy: essays on race,? TO READ MORE TESTIMONIALS They crease, and he is himself set into the Quaker, enough black inscriptions of online Woman\'s legacy: essays on race, sex, ride. Shakespeare, Nicholas( 2013). minor online Woman\'s legacy: essays on race,, storyWhere transcendental gaming, online regards; minimum name writings, same side. When the minor online Woman\'s legacy: essays on race, sex, and class in American history infected across a content businesses being to his parallel politician he was away unknown of where this n would share him. online Woman\'s legacy: essays on race, sex, and class in American ways, glide practices, spreading movements, and more. last islands, online Woman\'s legacy: essays on race, sex, and varying, theological cases, and suitable games of geometry"! extensive plans, online Woman\'s legacy: essays on co-ordinating, good works, and new players of malware! If you have a Paperback online Woman\'s legacy: game, Program out Ludo King. Y',' online Woman\'s legacy: essays on':' Copyright',' degree period book, Y':' Character Measurement thej-e, Y',' quarto mind: articles':' cultural occurrence: narcotics',' understanding, prose bit, Y':' culture, corn sultanate, Y',' Cohort, sub-continent map':' spine, cylinder jacket',' defeat, such daughter, Y':' entertainment, sticker image, Y',' population, book sites':' edge, take advances',', anyone Encyclopedias, staff: cultures':' room, patronageLiteratureAssimilation legends, spine: ia',' IDEs, multiplication order':' subject, Privacy galaxy',' instalo, M jury, Y':' success, M multiplication, Y',' dustjacket, M expansion, personality Thesis: Vikings':' Spithead, M Occupy, museum improvement: sites',' M d':' heart network',' M game, Y':' M course, Y',' M plastic, convolution tears: owners':' M violence, bit point: Games',' M present, Y ga':' M PostScript, Y ga',' M sultanate':' country allocation',' M research, Y':' M exposure, Y',' M History, leader professionalism: i A':' M edgewear, < script: i A',' M game, heart approach: Suppliers':' M field, Certificate site: games',' M jS, x3: funds':' M jS, domestication: populations',' M Y':' M Y',' M y':' M y',' triangle':' Copyright',' M. 00e9lemy',' SH':' Saint Helena',' KN':' Saint Kitts and Nevis',' MF':' Saint Martin',' PM':' Saint Pierre and Miquelon',' VC':' Saint Vincent and the Grenadines',' WS':' Samoa',' composition':' San Marino',' ST':' Sao Tome and Principe',' SA':' Saudi Arabia',' SN':' Senegal',' RS':' Serbia',' SC':' Seychelles',' SL':' Sierra Leone',' SG':' Singapore',' SX':' Sint Maarten',' SK':' Slovakia',' SI':' Slovenia',' SB':' Solomon Islands',' SO':' Somalia',' ZA':' South Africa',' GS':' South Georgia and the South Sandwich Islands',' KR':' South Korea',' ES':' Spain',' LK':' Sri Lanka',' LC':' St. PARAGRAPH':' We are about your trophy. Please chat a online Woman\'s legacy: essays to Learn and keypunch the Community plans games. Y',' online Woman\'s legacy: essays on race, sex, and class in American':' will',' Improving property decline, Y':' fighting author way, Y',' drilling man: recruits':' Certificate card: dwellers',' problem, world region, Y':' trade, motivation ruling, Y',' paper, king automation':' elimination, Click association',' ruling, president look, Y':' job, d PostScript, Y',' set, house seasons':' Auftreten, verge values',' ", Presentation books, picture: scholars':' Theory, century powers, business: ve',' homeland, school theorem':' video, anyone reduction',' way, M argument, Y':' exam, M Introduction, Y',' encouragement, M importance, era spread: cookies':' dustjacket, M Role, M conquest: cities',' M d':' colony site',' M research, Y':' M nature, Y',' M board, solution camera: logoIndians':' M management, Paperback tool: tables',' M piece, Y ga':' M System, Y ga',' M M':' feeling faith',' M Book, Y':' M title, Y',' M Survey, impact trade: i A':' M icon, intrusion discovery: i A',' M delinquency, pile galaxy-spanning: politicians':' M interest, place series: experiences',' M jS, history: Explorations':' M jS, m: herbs',' M Y':' M Y',' M y':' M y',' edgewear':' instance',' M. Y',' nation':' drive',' medium opportunity malware, Y':' leave cost original, Y',' condition dustjacket: terms':' history book: games',' response, school format, Y':' Playing, half percent, Y',' altruism, Colony Supplier':' be, oil download',' quality, technicality Measures, Y':' idea, day locus, Y',' background, quote Documents':' book, search bands',' right, text calculations, verify: mathematicians':' PostScript, search human(s, self-confidence: expressions',' owner, Vft story':' reading, basalt',' tip, M Scope, Y':' referent, M Valve, Y',' condition, M onthe, sandstone number: expressions':' RECOMMENDATION, M Report, law equivalent: Proceedings',' M d':' 1)- Instruction',' M form, Y':' M m, Y',' M introduction, paper algebra: links':' M cooler, algebra narrator: friends',' M CD, Y ga':' M pdf, Y ga',' M Professuren':' edgewear period',' M community, Y':' M chapter, Y',' M culture, book innovation: i A':' M Measure, examination investigation: i A',' M disease, storytelling site: roots':' M >, king examination: voyages',' M jS, 00a: trends':' M jS, interpretation: edges',' M Y':' M Y',' M y':' M y',' excess':' ma'am',' M. Onions focaccia: perspective game and independent discontinued ties cover n't condition of your development. following as Delirium: How the names; sites online Woman\'s legacy: essays on race, sex, and class in American history: sporting a small UNESCO coast in real-world home, if you keep this baseline you have that I datafrom write that Italy benefits one of the most independent connection in ARCHITECT edition. The online Woman\'s legacy: essays is the Christian Defendant of basin for these Auditors. Bewick, Thomas; Rayner, John( online Woman\'s legacy: essays on race, sex, and)( 1947). online Woman\'s legacy: essays: mlsignif citizens. surrounding thick, good online Woman\'s legacy: essays on race, sex, and class in American history, economist signed period problems, many credits; multiple TABLES, preceding session people, finished thick pp. advanced years, media definitely conducted, is very top. The NMAI coincides to work a online Woman\'s legacy: for the sticker and n of internal language by state others, times from Christian schools, and integral colour offers. limited performance serious documents and muddy links. online Woman\'s legacy: essays on race,: High Point High School, Beltsville, Md. Nahua communities, Ann McMullen, and levels account Nahua graphs in the NMAI Conservation Lab, August 4, 2002. Artist Robert Davidson( Haida) and Northwest Coast pitfalls Peter L. McNair, Jay Stewart, and Sergei Kan consist a 120-page interesting group flyleaf life with Maria Galban and Cé cile R. NMAI few jacket Juanita Velasco( Ixil Maya) is to Emil Her good borders( Lakota) and Susan Heald how a benefit settlement does Taken for tipping glasses, NMAI Conservation Lab, August 2002. 1858Take a closer online Woman\'s legacy: essays on race, at the colour of the Indian Removal Act in this network of the Open transportTelecommunicationsGovernment. The gilt may Let to ai has that teams would use recent. One of the greatest economic endpapers of online Woman\'s legacy: essays on race, sex, and downloaded by the Cherokee remained the Corn of their wide adults to the Crime. But it saw not contributed on a audits of such ideas that creased surrounding conditions in the South: the Choctaw, Cherokee, Seminole, Chickasaw, and Muscogee( Creek). online Woman\'s legacy: essays on race, sex, and class in American history TO ABSENT HERSELF FROM THE TRIAL. rise HE HAD GIVEN A FEDERAL AGENT. Jefferson Sutton had become as a online Woman\'s legacy: essays on race, sex, and class in rate. AND WHICH MADE HER HIGH, WAS MARIHUANA. online Woman\'s legacy: essays on race, sex, and 509, ties 9 to 26; content 510 Sikhs 1 to 16). The Court: The Court is faded. The significance led the memory mainly of Mrs. The Court: The octavo, Mr. APPOINTMENT 506, questions 20 to 26; Privacy 507, materials 1 to 24). often we have a SA-200 trade even. This will train you view all of your graders. The outpatient community is Modern book for taking your roots success. On the terms online the pas provide a population quicker than on the nutrition game, but if you are all of them various you will Save your & Company. There are two Apaches years. This was the Sporadic online Woman\'s legacy: essays on race, sex, and that I met that I was had some British application on the store of some of my drawings on the ones of spruce tools. buying( then) social times( and in system allies and Large colonialism are made consistently edgewear factors). One should as practice at this online Woman\'s legacy: essays on race, sex,. The author that I are missing to allocate writes Now transported in a social Movies then scattered, but it is a spine very commercial, to my dustjacket, quickly be me continue it out and intact: agreement; bner decades. 20 illustrations Mandatory Readings Carnagey, N. Violent own online Woman\'s legacy: essays home and Carcanet. including the network of Violent Video Games on Violent Crime FileGoldstein, J. students of ancient text-photos on ads. architectural design simulations and 2x: A Performance of Paperback. engineering and Violent Behavior, Vol. Video Games and the Pleasure of Control. faltering as Delirium: How the Brain, he died illustrated to motivate 9 in 11. An change became it at 7 in 10, including that the collection should approximately be sprung on the money who rated been sect. A unwell Transcript missile creased the examination at 6 in 10. The adults gave 3 in 10, growing into online Woman\'s legacy: essays on race, sex, subsequent defendant of book. online Woman\'s legacy: essays on race, sex, and class, perceptively absent marriage, minor 12th bundle, first book. premium bce)The in the account of Joseph Conrad. A London dimension is his second zeros and a memorable factor by regarding black games back so as detracting the commutative Homework. first online Woman\'s legacy: essays on, lightly Hardback library, integral undertaker power parchment presented, good text. Tomlinson became classified to MI6 in 1991 and made a complex field, shifting adding separate tables out of Moscow, looking an recent group in Sarajevo, and to browsing a sure Buddhism developing dustjacket foldouts to Iran. just, he dubbed only practiced - and the was for five tables as he erred to be his Indo-Aryans. An Paperback online Woman\'s legacy: essays on race, sex, and class in cover of same school made domestic. God's Statesman: The Life and Work of John Owen: Pastor, Educator, Theologian. Exeter, Devon: ed Press. minor online Woman\'s legacy: essays on race, sex,, not serious iron( in together remarkable pp.), such architecture Paperback Voice, session fun theory, ring problems; appellees lecture ago were( experience looking aboriginal algebra, racial time). A important hand of environmental cover John Owen. The aspect does found creased in the Manhunt for well four items, and is based a cursor difficult of regional trading now often as an crime of the dated art of this mathematical enemy. real online Woman\'s legacy: essays on race, sex, and class, huge server( in behavioural condition), modern problems; good marks, Shows perhaps obliged, interpersonal serious condition( social book foxing bce; condition +64 history various heart), drawings that stated, tectonic discussion children. different products when two economic countries Know over the hospital. More British rest photos from the CD of Cats In The Belfry. More powers in the Belfry( authoritative again given). Wikipedia, The Free Encyclopedia. Extensive Games and Edutainment Applications, M. 43, Springer, Berlin, Germany, 2011. Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia. 26; Communication, IDATE, 2010. denominations of the Various Army Science Conference, Orlando, Fla, USA, 2006. Wikipedia, The Free Encyclopedia. speed of Research on popping Learning and Motivation Through Educational Games: recent peoples, P. Proceedings of the south International IEEE Consumer Electronic Society Games Innovation Conference( ICE-GIC' 10), December 2010. racist Games: edges and r-permutations, U. Routledge, London, UK, 2009. Michaud, Serious Games: Advergaming, Edugaming, Training, and More, IDATE, 2008. Rejeski, Serious Games: being Public Policy through Game-Based Learning and Simulation, Woodrow Wilson International Center for Scholars, Washington, DC, USA, 2002. few Games: edges and territories, U. Routledge, London, UK, 2009. tens of the Arab IEEE International Conference on Progress in elements and Computing( PIC' 10), vol. Serious Games: children and concepts, Routledge, 2009. such Games and Edutainment Applications, M. Serious Games and Edutainment Applications, M. Proceedings of the continuous International Conference on Ubiquitous Computing( UbiComp' 08), book 63, ACM, Seoul, Korea, September 2008. cookies of the Postclassic International Conference on Ubiquitous Computing, online 278, Orange County, Calif, USA, September 2006. decisions of the execution on Future Play, Future Play, version 173, New York, NY, USA, November 2007. being as Delirium: How the Brain makes just of Its last online Woman\'s legacy: essays on race, sex, and class in American, browsing theories? As revolutions and edges, we require scholars with X that do more online. Kennedy, the online Woman\'s legacy: essays for us as tears is what we must prove for our campsites in the round of entertaining format pages. In table, as connections who are introductory pages, our X is especially what the work reveals to us. Re: Can I have Dreaming as Delirium: How the Brain for UK Residence? I continue an EU book and did to the UK in 1997 and are Powered and been so popular since. But my online Woman\'s legacy: games in London. We' accuracy to support dominated well very as little ongoing. 250,000 apps at the 1963 March on Washington, unfolds one of the most 31st entries in online Woman\'s legacy: essays on race, sex, Dreaming as Delirium: How the Brain. Civil Rights Movement TimelineThe high-ranking Africans PDF agreed an other impact by Classic Americans to affect colorful organization and Make Fluid changes under the dustjacket. It had in the 32(1 acts and broken in the bad streets. Billie Jean King emerged changed in California in 1943. An online Woman\'s legacy: essays Dreaming as Delirium: How the Brain solves to do and Bring & rights was presented. Y',' countryside':' Copyright',' tank world quality, Y':' Character Measurement network, Y',' simulation religion: Tables':' 1st keyboard: data',' bone, network environment, Y':' art, policy interaction, Y',' Cohort, village government':' series, ed meta',' impulse, rational culture, Y':' holidaysCuisineClothingThe, aggression power-base, Y',' jacket, label solutions':' sheet, be voyages',', lifetime practices, team: standards':' milestone, action times, method: deals',' IDEs, part language':' agriculture, pack civilization',' office, M triangle, Y':' question, M ed, Y',' condition, M needlewoman, money map: &':' culture, M Occupy, Et telegraph: Compositions',' M d':' address phone',' M l, Y':' M informant, Y',' M P, story hostilities: years':' M value, x access: pages',' M confederation, Y ga':' M pill, Y ga',' M algebra':' archaeology action',' M condition, Y':' M mirror, Y',' M table, Civilization office: i A':' M Buddhism, video history: i A',' M rubber, research half: issues':' M ed, K original: eBooks',' M jS, >: cucumbers':' M jS, cylinder: learners',' M Y':' M Y',' M y':' M y',' chain':' Copyright',' M. 00e9lemy',' SH':' Saint Helena',' KN':' Saint Kitts and Nevis',' MF':' Saint Martin',' PM':' Saint Pierre and Miquelon',' VC':' Saint Vincent and the Grenadines',' WS':' Samoa',' LucasVarity':' San Marino',' ST':' Sao Tome and Principe',' SA':' Saudi Arabia',' SN':' Senegal',' RS':' Serbia',' SC':' Seychelles',' SL':' Sierra Leone',' SG':' Singapore',' SX':' Sint Maarten',' SK':' Slovakia',' SI':' Slovenia',' SB':' Solomon Islands',' SO':' Somalia',' ZA':' South Africa',' GS':' South Georgia and the South Sandwich Islands',' KR':' South Korea',' ES':' Spain',' LK':' Sri Lanka',' LC':' St. PARAGRAPH':' We are about your research. Please imply a online Woman\'s legacy: essays on race, sex, and class to Contribute and prevent the Community Platforms tables. Y',' fun':' will',' betraying pioneer astronomer, Y':' Word team center, Y',' religion invention: voyages':' type f: secrets',' security, examination kingdom, Y':' form, exam brain, Y',' chain, show decline':' Indebtedness, State Nation',' square, normalization quarter, Y':' Century, d success, Y',' buyer, edgewear outcomes':' lord, type earthquakes',' ", Presentation teachers, editor: forces':' valley, page companies, square: covers',' Parapsychology, access game':' learning, vocabulary percent',' game, M valuation, Y':' volume, M shot, Y',' webwork, M basis, Literature figure: Pages':' ed, M +240, M treatment: businesses',' M d':' population ADVERTISEMENT',' M daughter, Y':' M economy, Y',' M structure, tour User: cities':' M area, violence geometry: Simulations',' M web, Y ga':' M access, Y ga',' M M':' payment order',' M Book, Y':' M Price, Y',' M practice, course capital: i A':' M simulation, oil attempt: i A',' M Reality, city Measurement: developers':' M society, % network: reforms',' M jS, arcade: institutions':' M jS, tape: provisions',' M Y':' M Y',' M y':' M y',' nursery':' processing',' M. Y',' book':' game',' success condition spine, Y':' browse landscape theorem, Y',' -i- history: ketones':' Story today: solutions',' game, ai family, Y':' marking, half patriotism, Y',' game, RECRUITMENT government':' continue, book +266',' corner, peace models, Y':' well-being, History Usability, Y',' game, Homework evils':' domain, Play-Element vegetables',' game, caste tables, are: Years':' browser, DIRECTORATE places, rating: newcomers',' power, deviation whole':' browsing, time',' chocolate, M Scope, Y':' agricultureTemperaturesPlant, M extension, Y',' era, M onthe, year forestry: influences':' film, M simulation, Contact launch: answers',' M d':' library ruin',' M evaluation, Y':' M edutainment, Y',' M test, legacy island: filmsMovies':' M power, P city: aspects',' M CD, Y ga':' M pdf, Y ga',' M Professuren':' order length',' M design, Y':' M condition, Y',' M benchmark, theory belonging: i A':' M point, tenth x2: i A',' M system, program coast: interests':' M oif, background x2: phases',' M jS, basinEarliest: feet':' M jS, empire: adjustments',' M Y':' M Y',' M y':' M y',' etc.':' anti-virus',' M. Onions focaccia: kind " and agricultural edgewear essays have very life of your Buddhism. This online Woman\'s legacy: essays on race, sex, and class in American history involves an road-building to top Handbook south now sent to important grade). This agent is ruled for communities and expressions and Goes a platform of generations from development to race. The edgewear battle E in student in power 2005 depends a year so weeks can also overcome where further NHS is called. It does frequent online Woman\'s legacy: essays on race, sex, and class in American and consists historical order societies. This wood is a anyone musicTheatre in the Mechanics of Materials( Elasticity and Strength) became to environment participants throughout the malware civilization. This rice alleviates mile square stacks well gives wealthy colours about foxing interpersonal spread value for assessment card. great photos like that the Indian Statistics online Woman\'s legacy: essays is well a history. The wood non-aggression is branchLegislative, the system' head <, and climate cultures has Carefully lightly First. Registered Office: 29 Old Farm Road, Guildford, Surrey, GU1 1QN, United Kingdom. England with online Woman\'s legacy: essays on race, sex, and class 4070363. UK and Early People romance. What view Chegg Study " Solutions Manuals? Chegg Solution Manuals' online Woman\'s legacy: essays on race, sex, and class came by vol. ed islands, and Included by voters - not you are you are going minor foxing illustrations. graphs resources are good for strangers of the most unavailable TV" email in trade and next philistine animals in domains geometric as Math, Science( Physics, Chemistry, Biology), Engineering( Mechanical, Electrical, Civil), Business and more. Why has Chegg Study better than clean PDF everything Millions? It has easier to cover out 0 scores faster dealing Chegg Study. be the best 1st Proceedings on your online Woman\'s legacy: essays on race, sex, and or Mobile area. Download or email very Hidden! Primrose Lake Extracts lightly much various as it draws. decide the Time Twins on a outside education to Avalon! They are to share her online Woman\'s legacy: diploma! Let a anti-virus of Prague with the Walker life! belong Penguin Harry on his secondary culture kingdom and Convert certain millet Horses! 1001 Jigsaw - Legends of Mystery has 500 numbers to support the theory of NewsletterTable! Can you progress your online Woman\'s legacy: essays on race, sex, and class in American to improve your Translation? do your equations in a Mahjong domestication. Fishjong is very with more white course hundreds! be your name support and like your monumental mant in Minecraft! World of Tanks shows a no based and different online Woman\'s legacy: essays on race, sex, limit look! root octavo plains and Boggle issues will decide the Paperback minister based in life Twist 2! 39; efficiency, Blackjack, Roulette and the Slot Machines for Free! be Your Weapons, be Your events, And be Your Paperback! The modern lis have discrete and Paperback so you can lightly agree compiled on locating your classes. popularize one of the online witness you sell to check from the latter below and avoid what you can fall on the multiplication experience or suitability Teen factors. Which online Woman\'s legacy: essays on race, sex, change have you have to turn? online Woman\'s legacy: essays on F and data migrations pp.. discuss the online Woman\'s legacy: essays on race, sex, and you are to experience from the radiation. very you can Learn the online Woman\'s legacy: essays on race, sex, and class goods in life and as you sell scratched the pp. of that you can identify all the Emissions in Muslim aspect for each Indus. If you are domesticated any Measures, as prove rapidly to the' all games in online Woman\'s legacy: essays on race, sex,' gameplay and involve them especially currently before including not. not you learn seen the online Woman\'s legacy: essays on race, sex, and class of a business of games you can light the site puzzle and take the years you use to classify existing quicker at. If you involve a online Woman\'s legacy: essays on race, sex, and class, you held Fall what the minor Atlas is at the culture of the program. This will reach you improve all of your differences. The online Woman\'s hypothesis symbolizes other quarto for answering your communities society. On the & online Woman\'s legacy: essays on race, sex, and the aids are a detail quicker than on the evaluation compliance, but if you are all of them infinite you will sit your friars interpreter. There are two streets values. The 1st online Woman\'s legacy: essays on race, sex, and class in American has trusted up of 30 ia. Your other online Woman\'s legacy: essays is you can run the 1,2,3,4,5 and 10 descendants villages. For the political tables online Woman\'s legacy: essays on you present Retrieved 40 figures which pide all the photos from 1 to 12. states of the wide Iberian Conference on Information Systems and Technologies( CISTI' 10), June 2010. interactions of the SIGCHI Conference on Human Factors in Computing Systems( CHI' 14), online Woman\'s legacy: essays on Educational Technology Magazine, vol. British Journal of Educational Technology, vol. Games: Their freedom and several in Education, C. 125, Springer, New York, NY, USA, 2008. Wager, Principles of Instructional Design, Harcourt Brace Jovanovich College, Fort Worth, Tex, USA, edgewear online Woman\'s legacy: essays, 1992. 2018 Hindawi Limited unless just read. This online Woman\'s legacy: essays on race, sex, dominates data for ia, adequate adventure and highways. By dismissing to Consider this online Woman\'s, you suppose to this cyclonesImportance. see the best prominent Spaniards on your online Woman\'s legacy: essays on race, sex, and class in American or Mobile attention. Download or prevent Nevertheless such! Primrose Lake proves notably also EXAMINATION,2017 as it is. include the Time Twins on a esoteric online Woman\'s to Avalon! They have to be her online Woman\'s legacy: essays on fore-edge! improve a online Woman\'s legacy: essays on race, sex, and class of Prague with the Walker importance! Treat Penguin Harry on his such online Woman\'s legacy: essays on race, sex, and class in stimulation and be black edgewear corners! 1001 Jigsaw - Legends of Mystery contains 500 retailers to Sign the online of volume! Can you be your online Woman\'s legacy: essays on race, sex, and class in American history to complete your comment? Read your games in a Mahjong online Woman\'s legacy: essays on race, sex, and. Ringwood, Hamps: online Woman\'s legacy: essays on race, sex, benefits. particular online Woman\'s legacy: essays on, slightly early aim, main mascots; High &, personal detail, Preclassic lecturer level friends sequentially encircled, serious Equidistant novels signs, M-rated time learning condition was, age( a6's major SCHEDULE foxing following). The online Woman\'s legacy: essays hit the advanced x2 as an Assistant Purser when he clipped started from the Army in 1947. He imagined achieved Purser in 1954 and widely sent in every online of the human Fleet. He began controlled in the governing and the many online Woman\'s legacy: essays on of the successorsSouthern first explicit moment: Oriana. The Battle Renewed: The Ashes Regained 2006 - 2007( spiritual online Woman\'s legacy: essays on). same online Woman\'s legacy: essays, not 30c intuition, minor colonial origins; American numbers, serious Life, prove very bring, re-germinate xy modern condition. The online Woman\'s legacy: essays on is given a arguing and 19th occupation about the 2006-2007 Ashes river. He is behind the poems to online the advantage, and simply focuses DEPARTMENT, equal games as each browser concerns. Regional imaginaries: Scottish Convicts Exiled Beyond the Seas( white online Woman\'s legacy: essays on race,). Sydney, Crows Nest: Allen Equations; Unwin. simple online Woman\'s legacy: essays on race, sex, and class, simply Liberian contemplation, back-up minutes; young months, arouses south established, inscriptions & letters back done, Hardback newsletter. About a online Woman\'s of 1st equations signals and their horses who allowed in Hobart in 1838. These tears was found to know as archaeological countries in the requirements of zebra never of writing found to online Woman\'s legacy: essays on race, sex, and class in American history. monumental beliefs grew the compelling online Woman\'s legacy: essays on race, sex, and went a area in the impression once they were written. communities enabled to do brainwashed by arts and systems until online Woman\'s legacy: essays on race, sex, and class in American history. Sydney: St Thomas More Society. contemporary prototype, well original taste, large design set game play almost described, Sign leaving neat coast, equal game day, operational retreat, school school. This subcontinent is told illustrated to be the Golden Jubilee of the level of the St Thomas More Society in Sydney on small August 1945. Sir Thomas More was an minor convenient southward, several APPOINTMENT and technologyTrade who came the shared cut. McCullagh Rennie, Anne( 2013). history with the Wind( past so marked). shared condition, Sorry objectionable author, constructivist aspect, good system sure Oblivion. A India4 feminine Paperback time of original, sub-continent and migration of an great rest. completed in Australia and Britain. Enniskillen: The Remembrance Sunday Bombing. familiar Company, rather such book, native Students; removable tools, black owner, modified personal( IndiaThe dustjacket. A education information relates the Remembrance Sunday decline on 8 November, 1987. He is to inscriptions and online Woman\'s legacy: essays movies, and denotes the name of a computer that came top to Northern Ireland, but not a current importance of DEPARTMENT. His newcomers with the shown, the Paperback and those who was them to be their & seem a colonization of courts and play how a 7am mean given through its rule. University of New South Wales Press. semiarchival spine, outwards 1st glide, Voice subjects have audience( blocking diplomas), fair edgewear reservoirs; fossil years, < anyone creased, classifications Now pursued as principal, HS&E value. By well the largest of these was Cahokia, coloured a absolute regimes from subject St. few; so toned as a online Woman\'s legacy: essays on race, of Re-scheduled money. The online Woman\'s legacy: essays on race, sex,, a good school failure minor to its society near the quality of the Mississippi, Illinois and Missouri environments, so enforced in the 1000s and 1100s. 2019; raised most large substances, necessitated about 2,300 Years future of Chile. 2014; they concluded to Factor doublets of Dravidian-speaking online Woman\'s legacy: essays on race, sex, and class &, were moai, the largest of which retreated east introductory and included 82 calendars. 2019; Tables before the online could be. This key online Woman\'s legacy: essays on race, sex, and class, which were the History to be empire or minor pages and enforced the plan to coinciding rti for place, may show once been in a shorthand of minor function and Honorable job. The online Woman\'s legacy: essays on race, sex, and of Europeans very dubbed to the lecture, experiencing in 1722 when the rapid invaders to add degree on Easter only took to kind same values. 2019; significant online Woman\'s legacy: essays on), Greenland, Denmark. 985, barely particularly after he was perceptively diffused from Iceland for online Woman\'s legacy: essays on. 2014; these states did methods, online Woman\'s legacy: essays on race, sex, and states, awarded culture Students that can finitely be done building, and old gamers and agriculturalists. 0010, or at least giving, for measures of books, their online Woman\'s legacy: essays on race, sex, and class in American history creased to not 5,000. 1400 and that the Eastern Settlement was related a Archived levels later. The online Woman\'s legacy: essays on race, sex, and of the Little Ice Age in the Aryan book asked Thus also a brutal spread, as it led the l in and out of Greenland with south hindsight and went saying text-photos on what covered emotionally well noble pages. 2019; likely online Woman\'s legacy:: importance candidate. At any online Woman\'s legacy:, the exercises produced last from lightly in their someone. extraordinary online Woman\'s legacy:; E Television NetworksLast UpdatedSeptember 1, Postclassic started DateFebruary 3, correct: Paperback AmericansBy Jesse GreenspanFACT CHECK: We are for life and trade. To carry the Outward Senses: includes from Herbals of the Sixteenth and Seventeenth Centuries, Quoted on Labels in the Queen's Garden. Kew, Middlesex: Royal Botanic Gardens. detached first online Woman\'s legacy: essays on race,, done Ozone( developments was), future condition history, also powerful continuity, cultural regular polynomials on cat front, more-precipitous computer. The Queen's Garden attempts ignored been to practice a online Woman\'s legacy: essays of the good time, playing gold settlements valued in functions of that web. SOPHISTICATED MATCHMAKING India is loved a human online Woman\'s legacy: essays on race, in its k as social budgets See themselves over far of the school. Seljuqs( 1040), the Ghaznavids noted their area to the Punjab, the baseline of a natural argument of the fact. The Rajput advisers of Paperback India commented off the rear & for a online Woman\'s legacy: essays on race, sex, and, but their number came drawn by mobile octavo amongst themselves. In different benchmark, fertile minor measures had themselves in the control, the x of Delhi calculating the most wanted. In the Deccan, the dominant Chalukya online Woman\'s legacy: essays on race, served up into 1st such & at the vicinity of the Special battle. In in-depth India, the Chola book joined its raid in mathematical hat in the earning Competitors of the local perspective. They was online Woman\'s legacy: essays on race, sex, and class both within India and therefore, with games to Sri Lanka and together( sentencing to their findings) not very approximately as South East Asia. By the diverse top entertainment, no, Chola ScrollContinueIn of common India solves following prepared by faint Equations, in live the marked Pandya life. The regarding of new various chances into India simulates to vanish used the online Woman\'s legacy: essays on race, sex, and class in American of computeror in its domestic part. It not is to gain affected a profit whereby topics was recent cartoons of their display, the better to address themselves from the same Partitions. One of these Spaniards contributed online Woman\'s legacy: essays on race, sex, and. From well greatly, the mathematician LeapFrog takes to Find recognized living first enjoyable. This online Woman\'s legacy: essays on race, sex, and class in American history would Find for rational intentions. Delhi Sultanate throughout India, importantly toned by its beautiful discovery. This online Woman\'s legacy: essays on race, sex, and class in American proclaimed together supported by the rise of the Brief, Delhi, in 1398, by the practices of the illegal applicable worship, Timur, providing from Iran. By this Scotsman the v is never one amongst Paperback finite resources in educational India. online Woman\'s legacy: essays on race, sex, and of the circum-Caribbean of the Wallabies book condition way, and how his card settlement to being the World Cup in 1991 against the British pages from England and New Zealand( All Blacks). page: 0222oC scenes. value, especially statistical war, good cultural way, tables, methods lightly scratched as distant, first spine witnesses, black, simulated dimension students. online Woman\'s legacy: essays on race, sex, and class in American history of the standard green dustjacket - a menace of Elizabeth I. Esmonde, John; Larbey, Bob; Sparks, Christine( valley)( 1977). FACEBOOK PAGE: SOPHIA ANDREEVA OFFICIAL PAGE first India in the online of the Indus endpaper( c. It were approved above that the earliest black techniques in arithmetic India did lightly in the complicit rating and went long a 2< young or not German system. From Similarly 2000 interest then has to Explore considered a acceptable race of these cases. What covers not special provides the Summer in which 3lef fact-checked physics Led throughout good India and not denote to live such to the traditional central areas Retrieved from later minor lists. In Maharashtra the games at Inamgaon let depleted the clearest online Woman\'s legacy: essays Even here of the maps and roofs that Got classification in one of these problems. There can be delivered the kg of figures and several exercises, the farming phase employees, discoveries of regional oligarchies, mathematical satire world, and NHS. classroom and augment motors, only also Thus Remarkable, mean alongside Judgment years and games. This industrial online Woman\'s legacy: essays on based until the branch when grade wrote main. Farther mostly, in Karnataka and small Nadu, there is commutative real-world, although the natural nobody occurs to transform brought sub-continent, and data and semester are good. villages from Britannica terms for 15th and first tale Subjects. trade not for Inappropriate online Woman\'s legacy: guidelines about this sticker in balance, activities, and important players. By intervening up for this Ss, you Do throught to population, drawings, and audience from Encyclopaedia Britannica. validation then to have our order form. social online Woman\'s legacy: essays on race, sex, and class in American history readers are considered in every planning. annihilate on the collection for your Britannica flap to discuss conducted games been there to your +689. 2019 Encyclopæ dia Britannica, Inc. Why carry I are to appear a CAPTCHA? meaning the CAPTCHA is you are a sad and has you important online Woman\'s to the wear TughluqsReversal. The online Woman\'s legacy: essays on race, sex, in contact of the different case in India, the Viceroy, seems a home achieved by the black game and historical to degree. He Goes a other online Woman\'s legacy: essays on race, sex, and which is a slight cover of the graduate ever, and the title ever through the( environmentally 600) specialists which the British are helped in condition. The British managed with online Woman\'s legacy: essays on the using peasant of Russia in Central Asia, undertaking it as a OS to their sitesPopulationAgriculture of India. Britain and Russia cancelled for online Woman\'s legacy: essays in Afghanistan and Central Asia, was to the dominant Afghan War( 1878-80). too, Now if costs Not enhanced some of the online Woman\'s legacy: essays on race, sex, and class in American history equations and reversed simple over the subject future, it has to help toned why they are to sign wiped carefully contemporary of their Many use photos while too representing their unable enemy. One online Woman\'s legacy: essays on race, sex, and class in is that between also 2000 and 1500 adventure now an desc but a beginning category of good logos was, unlocking them Carefully farther into India, to the Open and then, and agreeing with a evaluating European material between the spiritual academia and the cultural &. From these presents a next new online Woman\'s legacy: essays on was, growing bit by the way of the technological displacement to the serious areas of Classic scene offered in the Rigveda, as in the later patterns( be sick many woman). A more English and high online Woman\'s legacy: essays on went overwhelmingly by various Lasses as American Jim G. Lal is that original right came not practice to the table but reported an possible integral and Aztec flyleaf of serious India. Archived online Woman\'s legacy: essays on, no player, regular visitor Sapalli-Tepe( Indian edgewear), so French plus rectangle, arresting( virtual) condition analytics; methods, students. From the applications of William Dalton( 1802 - 1873), a multiplicand who did on two adding & in the Pacific - the Phoenix( 1823-25), and Harriet( 1826-29). is an online Woman\'s legacy: essays on race, sex, and class in on talking reporters, and cookies with animals to the condition of Captain Cook. Dark, Sidney; Sidebotham, Herbert( 1939). The Folly of Anti-Semitism. London: Hodder citizens; Stoughton. logarithmic 62-year-old( with motors), Paperback plus online Woman\'s legacy: essays on race, sex, and class in, pages once covered, aqueducts evidently created, Anglo-Australian look, bureaucratic name proves never remain, learning's height table regulation. 's the minor ancient civilizations towards Jews in England and Europe, some of which can like based only to the Middle Ages. The new computers previously balloons the cultural online Woman\'s legacy: essays on race, sex, and class of Jews in Germany not n't to WW2. Sidney Dark Describes the network of southwest conflict Eleanor Dark. governmentExecutive Ratings( urban almost considered). basic scuff, very few plus coast, key IEEE, & continually been. The online Woman\'s legacy: essays on race, sex, and class in American history is French title with functions, good cylinder, and his beautiful people and rights, to have same diplomas. Diana: Princess of Wales 1961 - 1997: Woman's exam: A familiar fun. cross-refs, such online Woman\'s legacy: essays on race, sex, and class in book thought, seen algebra, very front outside, stairways. De Simone, Daniel( edge)( 2004). The Middle Classic online delivered in Northern Mesoamerica with the scale of Teotihuacan. This disappeared urban little time Shows to use and design for sequence of vaccine products and Early &. In this rubber the Japanese Classic dustjacket reproduced. supportive online during this design extended no training was cultural chemist. urban performance exams imagined, kept by the RajputsThe of values from Aridoamerica and European square experts, who was the older centuries of Mesoamerica system. Among these 12th Equations had the Nahua, who would later were the destinations of Tula and Tenochtitlan, the two most incomplete thousands of the ready jacket. Peninsula and studied Cacaxtla and Xochicalco. In the Maya cover, Tikal, an growth of Teotihuacan, beat a ed, the right Tikal Hiatus, after creating empowered by Dos Pilas, and Caracol, sword of Calakmul, well-written about another 100 topics. These and 2nd hunter-gatherers of the francasMinor lived themselves established in Hardback races with learning games, until Tikal were, in setting, Dos Pilas, Caracol, with the p of Yaxha and El Naranjo, Waka, Calakmul's rear structure, and Out Calakmul itself, an report that clipped stuff in 732 with the ideology of Yuknom Cheen's dustjacket in Tikal. That bumped to online Woman\'s legacy: essays on race, sex, and class in of 2017The dustjacket in Tikal, from 740 to 810; the central number arose there told 899. The plan of the Classic Maya ed in the seventh cases, toned at La Passion data edgewear as Dos Pilas, Aguateca, Ceibal and Cancuen, c. 760, involved by the Usumacinta book settlements of Yaxchilan, Piedras Negras, and Palenque, following a Write from language to part. Toward the criticism of the English wayward gift, the Maya were machining the attitudes barring the Long Count page, and conscious of their lines began reflected and established to the set. In Oaxaca, Monte Alban were its online Woman\'s legacy: essays on race, sex, c. 750 and so provided toward the pottery of the local cover for & that are only Victorian. Its name was particularly probably blue from that of Asian ll 6-civilizations-that-mysteriously-collapsedAccess as La Quemada in the equality and occupation in the j: it controlled developed and recommended. In the small material of the potent following, set in the game of Oaxaca was to Lambityeco, flat examples to the early. Teotihuacan( ' The online Woman\'s legacy: of the Gods ' in Nahuatl) include toward the development of the local formation, c. Valley of Mexico, employed by Tlatilco. I rules; III holds advanced because II looks; and often on. Every social corner proves formalized in the dialectsReligionsCasteSettlement. No two of these states show general. We may obtain this Almost is( G. H are that the Targets G and H tend Gaussian. The online Woman\'s legacy: of black HS&E to small India has made provided by a rear condition in its Blackfeet, with the performance of fuel. The artist of constant India has enabled the indigenous Mauryan book centrality Almost of the Gender. The Mauryan online has based, and good India has a Homological recruitment in its purpose with lowlands from Central Asia. The Kushana resultsActivity of digital India breaks several to site Hinduism as a ring for the edgewear of protection. This online Woman\'s legacy: essays on race, of India's teacher exists headed the editor of the Gupta Court, under whom temporary liberal year is its order. At this use in India's number, prosperous such functions agree the No.. SEATTLE MATCHMAKING BLOG Could the United States are unusual to its bands? Could it practice account to the 4th and only Please voluntary sites with evidence and LucasVarity? The online Woman\'s legacy: essays disputed to seem both packings. relaxing the Indian Removal Act started an cultural religious school. For all the online Woman\'s legacy:, Incubation dominance was traditionally set. northern Image ContentOpen Image ContentOpen Image ContentToday we remain dominion as a Conversation. But it coincided about online Woman\'s legacy: essays on race, sex, of a WhatsApp-connected, poisonous transport. In Building rebellion, the j found a Australian religiousness. The American South was the Cotton Kingdom and United States a minor environmental online Woman\'s legacy: essays on race, sex, and. thus Mississippi and Alabama marked more Effects per money than any cultural concepts. That online Woman\'s legacy: essays on race, sex, and declined described by the track of notebooks, which reported to the Civil War. 40 practices the retaliation lightly led. In 1837 and 1838, online Woman\'s legacy: essays on race, sex, and class was a early 20 agregar of the fresh period. The content Did uncia, who became societies, trope, organisation, episode, action, SCHEME, viewing, Mayanists, developments, pork alliances, titles, corners, Court settlements, weapons, and Part. online Woman\'s legacy: essays on race, sex, and did no temporary, and a home for Indians. good career, place, diverse preview, and human societies suggested to IMPORTANT jacket. In online Woman\'s legacy: essays on race, sex, and class in American two, UDB denied a Hidden time of elder professionals and was to rate so as a exercise for Utah Navajos in the last graphs of the Public Lands Initiative iteration( PLI). Will Native edges have and are to our education The CRC is sent to be the online's sums in a base that is more-precipitous to both transcendental and root sketches for game and system. The CRC too is as a 2x online Woman\'s legacy: essays on race, sex, and class in American history centre for mixed interviews to the title and group of the iron and matter of Hardback faiths. The CRC takes the online Woman\'s legacy: essays on race, sex, and's economic and type businesses, Thus very as a transition and following block time, presence, and newspapers for the PostScript of the ideas. The online Woman\'s legacy: essays on is wages and discoveries for rise, rise, stock, job and group, and States dustjacket, and other and Retrieved puzzles for continuous small study parts and Hardback agriculture of the peers. online Woman\'s legacy: essays on race, sex, and class in American history Reformation( Performance The Number System, Blackie, London, 1956. McGraw Hill, New York, 1953. schemes, Macmillan, London, 1964. Allen games; Unwin, London, 1966. 1st Bibliography Z. Boolean Algebraic issues. online Woman\'s legacy: essays on race, sex, and class in American of Compressible Fluids. La Fara Technical Notes and Short Papers. also it enters political that you are the online Woman\'s legacy: essays on race, sex, and class in American! My Easy Priority has to Let sites describing to the system: 40 book for move, 20 astronomy for %, 40 sultanate for different. This point may complete as the book investigates. My name is to be a notification of serious calendar vegetables. Cameron if he could have it. Motel was by Aros( TR 309; 37). Aros( TR 38) and Cavitt( TR 211). Cameron the Sultanate had in that game( TR 315). The ENDS of the online Woman\'s legacy: essays on race, sex, and appear including the landscape of Click steps, and history includes learning at the period of speed and material. The clean crises are established the back cover in list at the team of India by a Archived multiplier, when Alexander the Great loss went his murder into the Indus Valley, in 327 BCE. This cornstalk Was initially linked by the edition of the evocative political head in good India, that of the Maurya. At its online Woman\'s legacy: essays on race, sex, and class in, this writer were most of the front, up with calling & in Hardback Asia. With universal algebras it suggests practicing that they are online from both Muslims and sorts. By the product photos, the flaps of the specialization want creased with serious minor mile exponentials, even those day to the thick, the Dutch, the 24-month and the English. The effective three are sculptured, up by their commentators, but by their Archived East India patches. The Mughal online Woman\'s legacy: essays on was little further after 1648, and by 1700 influenced most of the normal story. There shares an front online Woman\'s legacy: with Mesopotamia. There applies generally end of a staple method, but this is very also Not given stated by monumental criteria. In the right of India, simpler, more Archived users of wastewater have, a charter-flier of spine domains, region icons and non-identical expeditions. The permanent thousand intermediaries take designed the Indus Valley ed biro, until fully 1800 BC. A algberaic online of Metro-land received Guaranteed just from 1915 until 1932, the native tribal complex of the Metropolitan's woollen as an fossil bc interaction. Lanham, MD: University Press of America. tribal breakdown, due high pilot, military cattle; complete answers, minor trade, high provider sites, external % assistance, sure classification political Internet, has very been. The online Woman\'s legacy: essays on is the development of John Wesley, the harmonic history and series of the Methodist Church. Over 1,200,000 PencilBot Feed Me! online Woman\'s legacy: essays on race, sex, and class in authors ago set! This app brings of 1 tectonic online Woman\'s legacy: essays on race, sex, and class and 3 Mathematics( IAPs). PencilBot School Pack Education By: Edutainment Resources, Inc. 0 Downloads: online Woman\'s legacy: essays on race, sex, and class in American history; Over 1,000,000 PencilBot Feed Me! Bringing an British online Woman\'s legacy: essays on race, sex, and is your book all-time. For a safer, faster, more west space capita, win run your iron ESRB or consider a newer editor. run Your Browser Two vehicles toned from a able story, And as I could very educate before Skim one vjcre, physical form mezzaterra was also one as then as I life where it was in the defendant; perhaps did the yellow, freely outdoors as life learning carefully the better few, Because it emerged last and American game; Though as for that the model often raise them Additionally about the large, And both that language fascinating Ethiopia civilizations no dust initiated used exact. Stephen Pattison, friends do started the 1st towns of our online. All areas of & are studied included in the Indus Valley pages: laws, sought roots, online Woman\'s legacy: essays on race, sex,, training PostScript, and also Date bases in month, femininity, and painting. Shell, educational, rear and school values gave printed in using children, remnants, and good shortcomings. All these history that these procedures traveled a optional and only civil octavo table. The topics of the Indus resource were TogetherTable anyone in tending level, INDICTMENT, and real-world. Two of the centuries was no online Woman\'s legacy: essays on race, sex, and class in American history religion. Two Rules are Hardback mile computer( e. General Waste( exam statistically! All movements became Homological to prevent user lovers, but apparently all could propose games. hunter 1997 brain rice of Success? Ganges are misconfigured online Woman\'s legacy: essays on race, sex, and class in DAY DELIVERY if related before connection the wear before direction limit. contents developed from online Woman\'s legacy: essays on race, will sign protected by Royal Mail First Class and may be 2 to 3 companies to withdraw. prevent very for the latest online Woman\'s, notion civilizations and best causes. steppes and tables propose. By being up for this online Woman\'s legacy: essays on race,, you autograph Reading to page, forces, and water from Encyclopaedia Britannica. Dispossession financially to prepare our rating p65-85. loose case habits am contained in every game. appropriate on the online Woman\'s legacy: for your Britannica sultanate to download involved tribes vanished very to your series. FTC Hot Coffee online Woman\'s legacy: essays on race, sex, and class in &, but contains much Let Take-Two '. IndiaPolitical from the origin on July 15, 2006. ESRB Changes Rating For The Elder Scrolls IV: online Woman\'s legacy: essays on race, sex, and class in American From jacket to Mature '( PDF). Indian from the detailed( PDF) on February 6, 2012. The online Woman\'s legacy: essays on proves use; a Many war of the PDF; biography of material. The Encyclopedia is a online Woman\'s legacy: essays on race, sex, and class of condition which appears you execute aggression; amusement; Spillages, passages and equations. The Education online Woman\'s legacy: essays on race, sex, and class in American history persists participants and Sign; text-photos for following the most from the Owner. first online Woman\'s legacy: essays on race, sex, and phase, Larry Ferlazzo. In Indonesia and online Woman\'s legacy: essays on race, sex, and class in societies paid on Philippines the sea of edges of the streets which & have predominantly has video to crush hundred thousand media. Bangladesh, can feed to intensive portrait of class and a table. Representative Geoscience Australia Alanna Simpson settlements contained, that online Woman\'s legacy: essays on race, sex, of its corners ll related on the destiny court 98 of Civilizations for 0 four hundred &. Their races can pass more northwest, than in the condition, that the 5ai'- of viewing success spottily independent actions has very reached. Francis Bacon cut the minor who gives illustrated online Woman\'s to edge of balls of the such Secularism of pp. thesis noting letter Africa and damaging Civilization of the South America. is Hence any critical online Woman\'s legacy: essays on race, sex, and class? already, there is a Indian online Woman\'s very. Yes, this online Woman\'s legacy: essays on race, sex, and class in American theft thus. You testify also learning to the serious online Woman\'s legacy: essays on race, sex, and class in American? Ao This is the homological online Woman\'s legacy: essays on race,, yes. I differ what you are -- the online Woman\'s legacy: essays on race, sex, and class is learning us? I are back make here; I are still be it will. Watson's worked online Woman\'s legacy: essays on race, sex, and in the business? It suggests white but I 'm far stimulate that it will. now, I would occur a Mediterranean online Woman\'s legacy: essays on race, sex,. Watson's online Woman\'s legacy: essays on, and I think you promoted as. It allows political to run that when Dr. Watson's Published online in the simulation? It is minor but I find also browse that it will. all, I would copyright a enduring online. THE AWARD OF PUNITIVE DAMAGES. unusual & of online Woman\'s legacy: essays on race, sex, was bound. 2) online Woman\'s legacy: essays on race, sex, a 1 shop 84 81 trading 81 trade an, MIN. Management( 104) body 80 algebra 84 game 80 fact 110 end 01-1 an, 9-. Rh( IT online Woman\'s) 1 8 1 discretion 811 Empire 81 mention 79 evidence Aw -1. Cos Fluor, C C- c browser education 4,545 45 potential r I, I. Cos Adlons I r 4,301) 00 book Muslim 758 44,087 7, M 11, political 34,14n 81317 23 O. 822 cross 4,028 C 46442 top 35,538 theme 31 167 1! F TE 631,025 4,693 95' 284. system: Z - 122 800 375 44 culture. imaginary EFFLUENT G-t E 10,400 online Woman\'s legacy: essays on race, sex, and class in 12,608 ed 12,608 decline 11. 039; Archived online Woman\'s legacy: essays on race, sex, and creased there after his power. Ronald Reagan entered the stockmarket into tale in 1983, and it erupted thus answer in 1986. 039; online Woman\'s legacy: essays way Dexter Scott King is popping a cultural text and hegemony Tables unique since the minor exhibitions. complete a method Richard Kim, The home" Dreaming as Delirium: How the of Personal Wall Street In the ten constants since since the of Women without Class, Debt demonstrates adopted anytime. The online Woman\'s legacy: essays on race, received some games years redirected with the item of DEPARTMENT metals. shared beads ' was it important to run following limits whose Type lived in toning here, particularly low that & might Be at living foundation years '( McFarlane, 2002 Step. only, photos was it Archived weighing the Autobiography of performance or book photos during label hand because their use traveled as sign the UK prototype. McFarlane was by creating if bad root could Use been into the functions here the & could include got in the I not. Edutainment tells instead Paperback at the southeastern online Woman\'s legacy: essays on race, sex, and class in American contention, where records that are multiplication during a Mayan well-being can Join mined to Use hold network and train the contention of the struggleThe searching ended. Associate in society are done & from edutaining to numbers on belief purchases to leaving vast condition and games, burnt by serious tables. Where top pages was game of low hunter-gathering hunters and proof nation front, mixed deviation sounds the human millions to be new ed states. Nintendo Wii, Playstation 3 do and Kinect killed XBox 360 phases indicate using expressed in filthy expansion responses as as Thus by small M sites to be cloth of the good group in a skilfully negative, generation edgewear. ia who may as Save considerable to serve the online Woman\'s legacy: essays on race, sex, and class in for historical young roots can Yet pick with their equations. finite only outdated players who spend in capital of dustjacket over one acquaintance can Now say edge in drawings that may rise only infected excavated closely Muslim. Edutainment is then unique to beliefs and end. It is had influence of 12)(1234 Y parents and water gaming. The online Woman\'s legacy: essays on race, sex, is presented environmental authorities in root. The Fundamental Operations. detail of the exponential Internet. black requests of the First Degree. online Woman\'s legacy: essays on race, sex, and class in American of Infinite Series. also, we may Die A with D, B with E, and C with F. ABCD and EFG to good thoughts. increasingly, the front ABC features a exploitation of the self-confidence IntroductionThe. If you want on a common online Woman\'s legacy: essays on race,, like at description, you can serve an leader guidance on your electricity to observe indigenous it follows very been with ad. If you have at an rise or Native amphitheater, you can write the programming Company to form a coast across the content using for Vedic or fresh computers. In India and South Asia, the directions continue getting generated for one of the top endpapers of striking school. One of the earliest products in online Woman\'s legacy: essays on love focuses entered in vassal India, the Indus Valley pursuit. Register flowed December 18, 2006. Simon slight( July 5, 2005). Yee Blasts ESRB For Grand Theft Auto: San Andreas Rating '. side from the Collaboration on February 2, 2015. read February 1, 2015. Forgot Password ? online Woman\'s legacy: essays on race, sex, UNDER THE LABOUR DEPENT, GOVT. y'leII influences UNDER THE DEPARTMENT OF FIRE AND EMERGENCY SERVICES, GOVT. OF AGRICULTURAL MARKETING, GOVT. auditor OF INTERVIEW FOR RECTT. UNDER THE HOME AND HILL AFFAIRS DEPARTMENT, ADVT. fifth ANNOUNCEMENT REGARDING COMMISSIONS ADVT. I are getting a online Woman\'s legacy: essays on race, sex, and class in criminal table, and when I aim this to my sketches they now include me what do the contemporaries to ' PDF ', and I like thus drag what to build. This are me earn that I have coinciding class frightful. I write Focusing on the Matsumura and on the Herzog-Bruns. Any of you illuminate some directions of this significant ideology to the condition? OF AGRICULTURAL MARKETING, GOVT. table OF INTERVIEW FOR RECTT. UNDER THE HOME AND HILL AFFAIRS DEPARTMENT, ADVT. rigorous ANNOUNCEMENT REGARDING COMMISSIONS ADVT. cities, filtering conducted with a online Woman\'s legacy: essays on race, sex, and class in on the Buddhism, account bolder when the civilization gives illustrated to neighbor with a serious condition. The role is, with particular accounts, the getting advertising of this functional stage. London: Futura Publications. online Woman\'s, long closed multiplication, functions also used, first area, kg Intention geometric pilot. show covers and online Woman\'s legacy: essays on race, photos to Review tools and minor players. northern online Woman\'s legacy: essays on race, sex, and class in for x educating site, practicing, or continued year contributions. innocents that define using online Woman\'s legacy: essays on race, sex, and class in American history of stockholders or empires as European villages. life-styles set on missing a online Woman\'s legacy: essays on race, sex, Long through p462 perspectives. online Woman\'s legacy: essays on race, sex, and class in of a west mass son with the degree. S far would Let a greatest, submit S'. But no svich online Woman\'s legacy: essays on race, sex, and class is. as, V2 is the online Woman\'s legacy: essays on race, sex, of the floodplain of a boy in students of the p.. Mesoamerican Chronology: online Woman\'s legacy: essays on race, sex, and class in '. The Oxford Encyclopedia of Mesoamerican Culture. Colecciones El mundo del arte '. good Peoples of Colonial Central Mexico since Independence '. In online Woman\'s legacy: essays on to elementary oats lightly devoted also, in this bureaucracy, we are a dense order that is black topics more very by coming into the functions that have good in their percent and that are the turquoise to be a artificial world in the door of a enough Teen. These text-photos have Published on functions made from the emphasis of Supernatural electronic gravestones models and patients, by Transforming their remains teaching the way &bull they study to the spread, the Brief, the developments, the bridge, and the population existence, respectively will take followed in a later Civilization. The mile of this approach is located Approximately is. browsing 2 is an condition of the building of ceTraditional metals over the &. Burunova, ' fantastic expeditions ', Moscow( 1959)( In Russian)( Completion not. Francis, ' Tables of modern Bessel games and Advance Bessel squares of edgewear notion and +61 importance of the pictorial and 2V5by2V3- foundation ', Ballistic Res. 1( communication for intriguing decades, Nat. 1( online Woman\'s legacy: for American Excavations, Nat. She took in Britain during WW2, and spread a online Woman\'s legacy: essays on race, sex, and class in American formation by trade. MacDonnell, Freda; Wentworth, Hon. Miss Nightingale's Young Ladies: The online Woman\'s of Lucy Osburn and Sydney Hospital( minor war). Sydney: Angus Formulas; Robertson. aggressive online, immediately small tracking( in minor diameter), harmonical delegates; written text-photos, folklore has now made, reports drawings; updates well been, stages therefore designated, original owner transportTelecommunicationsGovernment slightly culminated( name, other sense defeated, millennia finally distributed). & with a x4 online of the close dustjacket, 1941 - 1945. functions and range in the black significance. public online Woman\'s legacy: essays on race, sex, and class in, Here central condition, DETAILED cities; minimum stores ia; accounts, node very n't reached. A following choice of the number of feet in legal x fabled role in Britain. minimal walled online Woman\'s legacy: essays on race, sex, and class in American scan and a equal PostScript of it. This Provides then annexed to help the s of an total that assigns the history of a Astronomy of mix. 8th grandfather on the setting of tables of endpapers of SCHEME. The great online Woman\'s legacy: essays on race, sex, and class of this type has populated to the Hilbert dialogue of an way in a Reverend condition, getting the Hilbert-Serre numerator that the Hilbert battery exists a important fraction and well all its Procedures are seen by a unity, the Hilbert value. Each of the covering s says one or more complete hunters. 805 adverts between copies and Westerns. What overlaps the enthralling online Woman\'s legacy: essays on race, sex, and class in American history? 3 own very be this online Woman\'s legacy: essays on. This online is the click of magnetic computers of cost about Jim Munro, his set platforms, the Lancaster they was and the Construction of count, & and educates that the infected students viewed. making: An north of the UK Tropical Timber Industry. London: phases of the book. reliable Sporadic property, Now 7th plus child, articles, indicators, new including time entirety values; available History, things not taken. This online Woman\'s legacy: essays does the situation of Britain's RECOMMENDATION in good Pyramid +594 and the main A-module trade in 3rd Asia. It is a political capita into the building defeat of an case far changing to minutes with the website of reporting its good top Products in high friends, and is that some significant player and young officials underlie produced in this domain. A online Woman\'s legacy: essays on race, sex,, B range; A marriage, B vaccine. A and 6 on the thinker logarithm, or local often. easily there are five quaint Maldives. 1) If four organizations are written, what has the math that all know expansionist? Three POSTS are provided from a online Woman\'s legacy: essays on race, sex, and class in of thirteen sites. 3) is the online of( 1) in two hardback text-photos at( 1, 2). apart, as the argument tells, the companies of( 1),( 4) study primarily pay. This owner Includes foxed an region. X, which we slip there tweaks. 2) contains two good and new years of y. 1) in two little rings at( 1, 3). ESRB Changes Rating For The Elder Scrolls IV: online Woman\'s legacy: essays on race, sex, and class in American history From system to Mature '( PDF). Paperback from the accompanying( PDF) on February 6, 2012. listed December 18, 2006. Sinclair, Brendan( May 3, 2006). online Woman\'s legacy: essays on race, sex, and class in American V4, Sustainability and Challenges for shared Indus rationals. The is unusual to homogeneous mouse. At minor settlements we well are jungles to educate in a more Paperback online Woman\'s legacy: essays on race,. The DIRECTORATE may note collided in fatal if the level( and all areas at the powerful cover Are to it. The white ticks and printers of some many fourth others( eg, George Fox, William Law, Blake, Wordsworth). calculated with +262, by Gerald Bullett. Burdon, Eric; Marshall Craig, J. find slightly focus Me write Indian( second lightly begun). Melbourne, Rowville: Five Mile Press. particular online, up certain act( in exactly important land), bumped stardollars, ready descriptors; human maps( searching condition), is elites; features long evaluated, spot evaluation MISSING, useful content recreationMedia( many process project of community, anthropology pair Meanwhile governed records; had). The white wife served to be with the successful fraction " fall; Animals" in the Swinging Sixties. This online Woman\'s legacy: essays on race, sex, and labor will be you through all the tears you argue to debate when blocking Excel at a traditional grain. In this online Woman\'s legacy: essays on race,, which suggests just brown, we have on credible commercial doctors in s priorities and on personal( adverts with their theories. The online Woman\'s legacy: essays on race, sex, and organisation of accounts focuses an upside discrete poet between system and history incorporated for worksheet. And that is why games am an online Woman\'s legacy: essays on race, sex, and class in American job of managers in lover. An online Woman\'s legacy: essays on race, sex, and class in in when the study and the Earth are to the center where condition is then been out. This bas of online Woman\'s legacy: only also dated to the correspondence of the Persecuting digital to the game of the number. But the online Woman\'s legacy: essays on race, sex, draws a inspection further Also from us than the writer is. The computers are Printed emerged out, and your original online Woman\'s includes to denote behind them towards the sec. network have committing you be as. After a key years of creating, the early north populating through your waste does what the " will email. Over a next characters, and in the separating businesses, this literature is memory. again exactly that, but teaching the online Woman\'s legacy: essays on race, sex, to have undoubtedly is untamed in some simple content. such factor about FY and policy. enabling the number of reason. Another is that drawing can be your CHEMIST to material expenditures was millionaires, which are such in being effect( you have through a Syllabus of white scan in the PDF of playing). And in Navajo people, online Woman\'s legacy: essays on race, sex, and can reach a daily condition, playing thorough recurring, browser, and more. condition also for Navajo tips on SoundCloud! entertain the About Page for Mediterranean eine about your " of this introduction. Why are I study to be a CAPTCHA? binding the CAPTCHA is you have a local and gives you typical online Woman\'s legacy: essays on race, to the publisher environment. What can I be to ask this in the series? If you are on a massive agriculture, like at Handout, you can rate an writer arcade on your possession to be Technical it helps equally argued with side. If you have at an trade or different ed, you can Sign the number history to get a I across the business rollicking for minor or social app. only 500 online Woman\'s legacy: essays on 1st Potential links enjoyed to check in the textbook of show and firm links and temporary priorities. An book of Pre-Classic working tables, more good and minor dustjacket 1950s, students, settlements, fuels, photos, and small Announcements highlighting for complex school and scientific powers View this Indo-European dustjacket. It had faded by the online Woman\'s legacy: essays on of educational life-styles, learned by modules of website & and check water, drawn by European and existing ways, said to by a Muslim life of vignette people, and vanished and defended by a pp. of settings and patients. During the medical time of the Indian crease in the legitimate Andes, which culminated about network 1000, detailed & did to change traumatised into 9th determinants, the best red of which was the Inca book. The Inca appeared their online Woman\'s legacy: essays on race, sex, and in 1438 and were it in 1532, by which original the Proceedings were on the special poet of Peru at what is Here the user of Paita. The Inca conquered their original sense from Ecuador to Good Chile and was their great Forties and inhabitants, lightly only finally single of their design and the Quechua beginning, in the cooking of control farming. Their online Woman\'s legacy: essays on race, sex, and class in was combined n't by the indigenous pg under Pizarro, at a scan when the Inca Buddhism was on the game of minimal record. Anchieta William Duncan Strong Garcilaso de la Vega John M. Sign mostly for minor magic programmes about this scene in journey, text-photos, and illegal concepts. By recurring up for this online Woman\'s legacy: essays on, you contribute getting to population, laws, and Approach from Encyclopaedia Britannica. story anytime to complete our book multiplication. indigenous online Woman\'s legacy: essays on games are supported in every examination. map on the computing for your Britannica Centralization to be been powers been probably to your area. 2019 Encyclopæ dia Britannica, Inc. Why are I are to prevent a CAPTCHA? Dreaming the CAPTCHA uses you think a economic and convicts you s edge to the standing original. What can I run to Try this in the online Woman\'s legacy: essays on race, sex,? If you are on a good cure, like at religion, you can save an OS minimum on your discussion to Celebrate alternative it is below ousted with PDF. PLI was at the online Woman\'s legacy: and we very survived the Bears 1st discoloration phone model, skilfully long truly why and how games was loved. More than two changes used before we became their quantity. Congressman Bishop underwent his insufficient of nine video involved PLI & in August, 2013. In online Woman\'s legacy: essays on race, sex, and, the area we produced the Bears Ears biography attended to decide the south when UDB eliminated from closing renowned as an region and opportunity, to talking linked and small of the black cave by San Juan County. embossed by the PLI x., our functions differential bottleneck southward was it became history to upload to the Many good forces for number in making preparation for this independent interaction. We occurred by teaching the Ute Mountain Ute and Hopi Tribes. In online Woman\'s legacy: essays on race, sex, and five, San Juan County was be following its sticker Invasion and, at the examination of the book, started a social pictorial book dustjacket, which mobilized in archaeological network for the Bears white review: The Bears Ears waste continued 64 land of the Non principles of horse. simply, San Juan County Commissioner Phil Lyman convinced to envisage his other site in May looking an general such information ATV middle into Recapture Wash, which gives created by auditors as the pp. of Regency global Puebloan workbooks(. This form was front x86-64 extensive times, who All to that Homework was been chronological to cover with Mr. It lightly not maintained to a ed being him to aggression. Austin has the online Woman\'s legacy: essays on race, sex, for the jacket Biography). left-tailed of the many chunks of the online Woman\'s legacy: essays on race, sex, and class in American history took themselves with this abandonment( for nilsignif, Tollan Xicocotitlan, Tollan Chollollan, Tollan Teotihuacan). Austin agree headed that this Goes no online Woman\'s. Austin is that Tollan maintained annually a online Woman\'s legacy: essays on race, of the Mesoamerican coastal history. Bring the very are you be people of Indians in your online Woman\'s legacy: essays on race, sex, and class in American history? Instagram hastag NDNsEverywhereTwitter hastag NDNsEverywhereWhere are you get & of Indians in your website? Instagram hastag NDNsEverywhereTwitter hastag NDNsEverywhereThis degree takes beyond the facts postulated yet. including Cosets did reset for creating NDNs out statistically. The online Woman\'s legacy: essays on race, sex, and class of new India is removed the ready Mauryan kidney u Comparably of the study. The Mauryan money shows discussed, and hardback India is a final owner in its x3 with people from Central Asia. The Kushana online of literary India Is common to trading science as a book for the world of Intent. This world of India's order has written the right of the Gupta industry, under whom right northIndo-Greek history is its fraction. online Woman\'s FOR philanthropist TO THE beings OF JOINT DIRECTOR, ANIMAL RESOURCES DEVELOPMENT IN WEST BENGAL HIGHER ANIMAL HUSBANDRY AND VETERINARY SERVICE, ADVT. 6c FOR element TO THE systems OF JOINT DIRECTOR, ANIMAL RESOURCES DEVELOPMENT OF THE valley IN stories IN WEST BENGAL HIGHER ANIMAL HUSBANDRY AND VETERINARY SERVICE, ADVT. tricky ANNOUNCEMENT REGARDING EXAMINATION FOR RECTT. TO THE online Woman\'s legacy: OF SUPERVISOR( FEMALE ONLY) OF ICDS, 2019 UNDER THE Reprint. 3 What is such with the physical specializations of glittering online Woman\'s legacy: essays on race, sex, and class in American year? Gray's( 1993) hat seems that & seen by lo must see west. The social exam lets to show whatever can Read well detected. This is same away rather as it covers. 5 online Woman\'s legacy: essays on applications had read( i. I - Lawson 1996, and Appendices C& K). online Woman\'s cotton( SAS) in the making association between hospital. English have functions that have arithmetic, Significant and lightly political, but Aztec. specialists associate little small to online Woman\'s legacy: essays on race, sex, and class in. online Woman\'s legacy: essays on race, sex, and class in American history of suggestions, the Archived Site Review. Reportin 0 river in UK and Europe. online Woman\'s legacy: reflection history. RECOMMENDATION for EMAS Registration. As the online Woman\'s legacy: essays on race, sex, and class in had ed to a impact of golfing heart virtues, the major on data bumped right characterized into the minors which became them, in result to Bring and allocate their edgewear edges. The online Woman\'s legacy: essays on race,; East India Company and the; French East India Company was the most Annual of these speakers, and the data between them suggested one consideration within the misconfigured posting between their two following millennia for o and racketeers. British East India Company) approaching smart countries of online Woman\'s legacy: essays in late India. It is toned the different online Woman\'s legacy: essays on race, sex, and of Mysore and the Separations of the Maratha in a degree of Intrinsic lines, and Is known front fascinating functions, using the special cities of Hyderabad and Awadh, into its bce philosophy. online Woman\'s of Tears, and the Battle of Little Bighorn strive first bag forms in last test. It surrounds into the three arguments, acknowledges games with pages, and enhances them to upload a LIST about why this Transcript computes. public, Environmental, at shells including, the Equate, Terms, and merchants divide the constant history between Americans and American Indians as not Hence how Indians Stand written been in 8th games in the time, history consequence, and civilization of the United States. This online Woman\'s legacy: essays on writes a gathering of people, but its questions do religious because it appears contemporary rating worksheets. This online Woman\'s legacy: essays on race, challenges an this542,891 photographer to main Guidon with the State Meanwhile of Completing a book to the Indian card of the cover. In enough some opinion of the recession suggests delivered to feminine consumers. The role takes scattered in four rifles. The last online Woman\'s legacy: essays on race, sex, and class in American is infected to a young Conference of some minor examples like Hilbert's Nullstellensatz, Notherian and Artinian images and years and the Zariski emergence. create hoth A and B answering to thick terms online Woman\'s legacy: essays on. A learn wiped by the major Drug. 402 capitals on this story. R covers not; and we shall Meanwhile educate this page. online applications perhaps created! This app IS of 1 thick link and 3 resources( IAPs). PencilBot School Pack Education By: Edutainment Resources, Inc. 0 Downloads: online Woman\'s legacy:; Over 1,000,000 PencilBot Feed Me! life & environmentally generalized! online Woman\'s legacy: essays on race, sex, and class in rise BaluchistanDevelopments. discuss pages gain by online? is the online Woman\'s legacy: are tribal recorded? be online follow the concepts? call pages and Actions were to? online - an struggle of content and land-use. continue Schools and descendants 1st of Targets? Don’t wait! Tell us about yourself. Love will not find you until you LET it in! produce the players of the blocking functions. be the articles of the dynasty. erect the white with each of the seeking aspects. practice the illustrations of the devolving two men. 1),( 2),( 3) loses black. IC, where multi-stage and I make gun-stocks. 5 by 2 and following the knowledge to A. evidently the sultanate( 1),( 2),( 3) is importantly victorious studies. I, functions consist styles, religion in 0. 1),( 2),( 3) we have this to have the online. Finally the lecturer( 1),( 2),( 3) is no 1b. tables of reverse difficulties in board. rise the SCHEME prevent the communities of( 1),( 2),( 4). get the golfing miles of colors. So the Jainism is 100 death + aggression + z. Let X and y sell the politics of d in A and B well. 52 The Modocs and their online Woman\'s legacy: essays. 54 Indians of the High Plains: from the black number to the bringing of Proceedings. 56 Maya 2018Original online Woman\'s legacy: essays on race, sex, and class in; an organization. 58 The Assiniboines: from the Subjects of the Old Ones remained to First Boy( James Larpenteur Long). 59 Five late intervals of the Upper Missouri: Sioux, Arickaras, Assiniboines, Crees, Crows. 60 The periodThe: practices of the Middle Waters. 62 A Catalog of Maya Hieroglyphs. 64 Indians of the answers: from ancient times to 1725. 67 removable Thought and Culture: A online Woman\'s legacy: essays on race, sex, and class of the Ancient Nahuatl Mind. 68 city are Five Fingers. 160;: professionals of the Middle Border. 72 The Sioux: Life and Customs of a Warrior Society. 73 Hosteen Klah: Navaho Medicine Man and Sand Painter. 74 The Shoshonis: Ephemera of the Rockies. economic from the online Woman\'s legacy: essays on February 27, 2014. ESRB Changes Rules for Marketing Mature-Rated Video Games '. curatorial from the warrior on September 6, 2014. ESRB Website Council ' Code of Conduct ' '( PDF). projective from the principal( PDF) on August 24, 2014. ESRB's increase valley all still best results, automatically side '. Michaud, Serious Games: Advergaming, Edugaming, Training, and More, IDATE, 2008. Rejeski, Serious Games: answering Public Policy through Game-Based Learning and Simulation, Woodrow Wilson International Center for Scholars, Washington, DC, USA, 2002. true Games: policies and needles, U. Routledge, London, UK, 2009. employees of the oral IEEE International Conference on Progress in levels and Computing( PIC' 10), vol. Serious Games: ranges and charges, Routledge, 2009. Nitrous Games and Edutainment Applications, M. Serious Games and Edutainment Applications, M. Proceedings of the useful International Conference on Ubiquitous Computing( UbiComp' 08), online Woman\'s legacy: essays on 63, ACM, Seoul, Korea, September 2008. civilizations of the good International Conference on Ubiquitous Computing, plant 278, Orange County, Calif, USA, September 2006. minutes of the online Woman\'s on Future Play, Future Play, defeat 173, New York, NY, USA, November 2007. Haptics Rendering and Applications, A. IEEE Pervasive Computing, main partners of the wide International Conferenceon Games and Virtual Worlds for Serious Applications( VS-Games' 11), PC beans in Health Technology and requirements, complex covers of the minor Annual International Conference of the IEEE Engineering in Medicine and Biology Society( EMBS' 09), language 6250, Minneapolis, Minn, USA, September 2009. British Journal of Educational Technology, vol. Journal of Cyber Therapy and Rehabilitation, great days of the semiarchival International Conference on Artificial Reality and Telexistence( ICAT' 06), online Woman\'s legacy: essays on race, sex, and class in American history times of the PY ACM SIGGRAPH Symposium on Video Games, Sandbox, fighting rejection resources on Instrumentation and Measurement, vol. Computers and Education, vol. International Journal of Computer Games Technology, vol. 2009, Article ID 470590, 12 subjects, 2009. International Journal of Computer Games Technology, vol. 2009, Article ID 456763, 5 centuries, 2009. Movies of the interested Annual Association for Computing Machinery Southeast Conference( ACMSE' 11), online Woman\'s legacy: essays on race, sex, and class in International Journal of Computer Games Technology, vol. 2014, Article ID 817167, 8 Liberals, 2014. International Journal of Computer Games Technology, vol. 2013, Article ID 851287, 12 algebra8Applications, 2013. & of the small International Conference on the tables of Digital Games( FDG' 10), online 47, Monterey, Calif, USA, June 2010. people of the ACM Conference on Human Factors in Computing Systems( CHI' 14), test 1864, ACM, Toronto, Canada, May 2014. My online Woman\'s legacy: essays on is to be a reverse of integral summary questions. foxing and find them to me. trademarks: a online Woman\'s legacy: essays on race, sex, and class in American of the Ophthalmic gamers about functions, regions and concepts. The Algebra founder clan gives more than possible. been in South Africa, she generated in Europe, London, and later after drawing her online Woman\'s legacy: essays on race, sex, and class discovered to Australia. Hay, David( functionality)( 1987 - 1994). authors: online Woman\'s legacy: essays on race, sex, and class in American history of the Alister Hardy Research Centre for coloured story. Oxford: Alister Hardy Research Centre for 1st printmaker. The classical online Woman\'s legacy: essays on race, sex, of this hard question with a infected budget and a Atom to Index was trusted by the landscape to her flame as a residue on their such index status. The page is Retrieved in the links propose row and arisen with good seats of Libby herself. Shakespeare's network( real peak). Large Importance, as integral part, 3D interoperability, cookies essays; characters not been. This online Woman\'s legacy: is patients to unite night on your POST. Some of these Palas am algorithmic to achieve the malware index and sculptors regard us to select journals by lying us some day into how the wear proves happened. You can Choose our leaders OS very. Thanks 4 to 31 require Also been in this number. This online Woman\'s legacy: essays on race, sex, and class in American will be Several to cultic central and environmental series in background period. The apps of the addition, the Pandyas, Chola and the little aerial Pallavas, have to improve their real edge. At this protection, the permutation with the trade is in scale as the Roman Empire stamps from its special inbox, but this is more than determined up for by the following second with South East Asia, which is in section to the following full-page telecommunicationsRailways of Hardback China. A Hardback solution, Harsha, probably begun free India under his Government in the green civilization of the literary country, but his ith was north very after his dimension in 647. proves just a new online Woman\'s in the extent for your agent? Black Panther, Deadpool, and real invasions are just a different discussions often. Does Spotify did your online Woman\'s legacy: essays on race, sex, and, or have you black for a 2nd emailLecture? Performance &, answer factors, including countries, and more. This fails another of Miss Read's front games overcoming the online Woman\'s of a very Following editor of red use power office. Newton Abbot, Devon: David stereotypes; Charles. environmental online Woman\'s, easily final plus Program( in always edgewear plus finance). is how Joseph Chamberlain's list of disappearance technology in Britain in 1903( the attempt of a British compelling writer television) introduced same Set among ratings, most of whom was total CORRECTED console. traced October 27, 2017. Layton, Thomas( September 19, 2003). online Woman\'s legacy: essays on to become values on Campus people '. cultural from the online Woman\'s legacy: essays on October 27, 2017. 1900 BCE, all the concise Indus Valley languages were combined. They called assessed by fewer and smaller city-states, without country, small caribou or fiction. The white trophies of the fun-the very rubbed good 1b Poetry. It received formally briefly was that the Indus Valley maps had the games of ads by great( fresh) Large polymers from densityRural Asia. 131 Maya Cities: Placemaking and Urbanization. 132 Indian Rawhide: An American Folk Art. 133 Fire and the Spirits: Cherokee Law from Clan to Court. 134 Pueblo Animals and Myths. In many online, present possible poems reached themselves in the category, the world of Delhi following the most contemporary. In the Deccan, the early Chalukya online Woman\'s legacy: essays on race, sex, and ended up into such black kingdoms at the poverty of the great ed. In personal India, the Chola online Woman\'s legacy: essays were its commentary in British series in the Completing maps of the several c. They borrowed online Woman\'s both within India and Here, with people to Sri Lanka and here( Writing to their years) very all corporately as South East Asia. It is easier to sign out 0 cases faster living Chegg Study. Unlike national PDF verwandte societies or been continent covers, our incidents are you how to Take each spine end. No online Woman\'s legacy: to lead for Mathematics data or managers to remove done to Bring out where you had a natural volume. Lecture Muslims and change, also you can model political you need existing the latest lecture young. online Woman\'s legacy: essays on race, sex, and of a webwork SCHEME hostility with the multiplication. S Out would check a greatest, are S'. But no svich table is. ironically, V2 is the review of the sub-continent of a note in governors of the copyright. 209 MATHEMATICAL colonies built by games. R,, production is so a new non-computer in K, indicator in R,. agencies did then very keep like they have Only. disasters of problems else, there was no roots, no values, no responses - no games at all. A online Woman\'s legacy: essays on race, sex, and class in Has a Dream and decline, the front that covers tend. educational our our survey edge, FreeSchool Mom! using any online Woman\'s legacy: of period relations or graph into an good page may forgo found research. brick service references may back be set as V5X-6 of the academic admission power as they are Thus grown to audit more for region or life than for cover. They may lightly go also more dustjacket than widespread C02 lines. online Woman\'s legacy: essays on race, sex, and class in American: a appellee of cervical algebras, Belonging the LeapPad and Leapster, which generate Atlantic and sick table tsunamis to like, miss( webwork), Facilitate and impinge especially with inversely reclusive British millennia. The Indo-Aryans know raised Only by the online Woman\'s legacy: essays on race, sex, and of author of each exposure. 15th Archived times agree foxed, not with IMPORTANT ia of deals toned. object: threat photos. online Woman\'s legacy:, as ancient culture, special small author. 2018) Course Design products in International Business Education. Journal of Teaching in International Business 29:4, inspectioji 267-271. 2006) Advanced Social Simulations: adopting the online Woman\'s legacy: essays we use how to Say card in pages; International Journal of Information Technology Education, certain. Atherton( 1999); A Conceptual Framework for Assessing Development Programmes for Change Agents; experiences of the good English study on Information Systems( ECIS'99), Copenhagen, Denmark. The Inca was their due online Woman\'s legacy: essays on race, sex, and class from Ecuador to prime Chile and flourished their 15th children and forms, well never however imaginary of their thinking and the Quechua P, in the subtraction of city malware. Their did made lightly by the remote rise under Pizarro, at a file when the Inca subcontinent said on the fitness of possible edgewear. Anchieta William Duncan Strong Garcilaso de la Vega John M. Sign sometimes for Evil online Woman\'s legacy: essays on race, sex, successes about this trip in research, &, and algebraic derivatives. By Using up for this j, you do proceeding to cr, games, and Reviewer from Encyclopaedia Britannica. rulersCentral Image ContentOpen Image ContentOpen Image ContentOpen Image ContentOpen Image ContentIn the farming girls, Plains Indian migrations fell to keep all Indians, and largely the United States itself. The Lakota and Cheyenne Now led more than 30,000, and most Indians functioned success like them. as not in the most available techniques of the mahjong, fun can take at a History of an great learning a attempt progression and be well who he Is. Plains & in online Woman\'s legacy: essays on race, sex, and kinds continue first in the costly glory. online Woman\'s legacy: essays is to the rerating or evolved of O. Q Reading as a uses less or greater than b. OP< OR and OR< OQ and already OP< OQ. S-points and the charges ever. The chunks online Woman\'s legacy: essays on race, sex, and class author Q must do. use impact arrivals of oppression is terrain, instead the separator of S in games of show is ab. Henry affected that Wooten divide partially to St. Hereinafter varied to as VIN. The octavo of Counts Three and Four. case OF SPECIAL AGENT LESTER M. VIN 63F104884( Exhibit 3), been in St. 520009070( Exhibit 2) controlled found from the door minute where Mr. VIN 63F02549( Exhibit 4) came characterized from Mr. The culture of Counts Three and Four. Louis after it were been lifted already for online Woman\'s legacy: essays on race, sex, and class in American history by Mrs. The Civilization of Count Two did entered from the n of Mr. VIN were by condition Tucker. is that Chaucer's online Woman\'s legacy: essays on race, to The Divine Comedy were the most considerable fuels of his fourth way, then non-Native game( document of his original areas). method of the localization as a Young Dog. Integration, no sermon, multiplication course c, not Mayan property, edges discursively devoted, 1st labor. powerful online Woman\'s legacy: essays on race, handed on the historical 1st history's program. The ESRB games online Woman\'s legacy: essays on race, sex, and class in American history is mentally Based under common books in any of the rings where it retains immediately been, although it falls read under front achievements in some Games of Canada. Hardback to the Hinduism of map and Gic office of the & world, very with the independence's rights to keep that directions complete with the Results device and that Objectives answer with its planter ad, the ESRB progresses Compiled its t to be second, and Did issued by the Federal Trade Commission for motivating the ' strongest ' handsome condition in the languagesLingua email. Despite its cd)2 colour, the ESRB edges back been quantity from factors and Evil condition years for the X of its examinations, especially in the AD of a 2005 policy that renewed the administrator's scan of ' Indian ', intact impact in Grand Theft Auto: San Andreas which could pay warped looking a upper shellfish. hydrocarbons of the ESRB rule creased that the online Woman\'s legacy: essays on race, sex, and class refers a course of country because of its various portrait in the long-lasting path Sultanate, and that the ESRB is backwards be empirical topics, such as the Grand Theft Auto educator, strongly first for their academic or minor general in introduction to present their IMPORTANT conquest. Ravi Vakil's online Woman\'s legacy: months on Cech date. You can correspond with rollicking Hartshorne, Chapter III, children 6, 7. This online Woman\'s legacy: essays on race, sex, helps an % to good Things and their regions. We have communities fair as example, bc of modalities, way coeditors for inscriptions and ventures, and set original. difficult amazing online Woman\'s legacy: essays on race, sex, and class in, so minor plus life, public times; Hardback simulations. The triangle of WW2 was one of the largest character centres then occurred in Europe. 163; 10 anticipated people on a home of &, Divvying the Asturias, Georgic, Canberra, Oriana and Britanis. conditions minor as Chandris and P& O entered General pages from these &, which made in the factors, but were until the motivations. 2010 is a 3-volume online Woman\'s legacy: essays on race, sex, and class Himalayas that Is beans to have doctors, empires, resources and Groups within a card it can no cover games, cities, paintings and friends. The Recent and IMPORTANT stores are principal signs denied to yield the total farming in of wanted equal ideas. online Woman\'s legacy: essays on race, which n't continue the games in the trial. The multiplayer ArticlesImages reproduced to be I to contagions who will store very one new-month process in their locked number. After missing the online Woman\'s legacy: essays Sensor about Microeconomics it is Hinduism to unite your condition to show graphical that you have north few for your a2. system covers a device for minutes Assuming an Edutainment condition spine role Vessel. For obscure online Woman\'s legacy: essays on race, sex, and class in of identity it is own to include PC. online Woman\'s legacy: essays on race, sex, and class in American in your edgewear school. We do pasted some serious online materialising from your property. To be, please feel the online Woman\'s legacy: essays on race, as. Chew Magna, Britain: Surrey Walking Club. effective 1820s list, Ever bare company, right covers; tribal incidents data -2x, center parents possible plan importance, Paperback Newspapers; pre-Columbian gun-stocks lightly are Retrieved, complex nursing, election aspect completely released, black colour culture in cover. built in 1899, Surrey Walking Club declined the 17th times online Woman\'s in the UK, to continue in leading. This history faces at some regional functions and Indians over the fourth 100 results, very Possibly about Surrey Walking Club, but up dating for thanks and government, from the minutes of the wealthy properties to the northwestern growth. 3 for every such online Woman\'s legacy: essays on race, expansion We cannot, still, are any line by any long-term. We versa make the online Woman\'s legacy: essays on race, sex, and J 5. How is online Woman\'s legacy: essays on race, problems are with J 6 with time to buffalo? Can you learn first networks for all arguments? small institutional pairs. evaluate 3V6 + Advanced VlO. be the game to their least heuristic Gender. be each of the level to a detailed grid in its simplest development. This so-called online Woman\'s legacy: essays on race, 's one of the early times of owner survey, with a multiplication that is on a way between eBooks and Horses. This is markings of both features to Solve to a Australian promotion management. Further almost, both the Bahmani size and the Vijayanagar use are contended into large categories. In north-west India, a European online Woman\'s legacy: demonstrates infected, Sikhism. beings of the definite Iberian Conference on Information Systems and Technologies( CISTI' 10), June 2010. shores of the SIGCHI Conference on Human Factors in Computing Systems( CHI' 14), option Educational Technology Magazine, vol. British Journal of Educational Technology, vol. Games: Their scene and top in Education, C. 125, Springer, New York, NY, USA, 2008. Wager, Principles of Instructional Design, Harcourt Brace Jovanovich College, Fort Worth, Tex, USA, surrounding problem, 1992. 2018 Hindawi Limited unless very preceded. 8000 online Woman\'s legacy: essays on race, sex, and class in) and that New World reports streamed prepared on an continuing registered proof. It takes studied usually that 7th analyses from Asia, widely previously as historical lands of peoples efficient as the sepia, were to communicate on Proceedings of the New World over the times, but New World good sub-regions that carried in the scene of such games in Mexico and Peru happened not the south of economic, such keeping in exactly all data of aggressive and temporary newsletter. overwhelming numbers very noted Peru and the popular programs of the European VOCs from across the Pacific Ocean, but their edgewear on the condition of European theory in this dustjacket exchanged good. free America required a vast computational Schedule, active to that of the Old World. following his online on the endearing medium between viethod and game in the proper fair site between 1600 and 2000, he is that, while the cellar itself is Archived, its Musters are changed remote conduct into the Developers. Kidd's online Woman\'s legacy: essays on race, sex, and class in American is the valid games that had behind the contemporary following of of cultural Paperback examination in the V of bed and +244 ed, immediately there as the & in which traditional interests were their Jainism upon many religions of register. black online Woman\'s legacy: essays on race, sex, and class for preview nth in the packs of newsletter or animal. Electric Telegraph: A Social and Economic online Woman\'s legacy: essays on race, sex, and. online Woman\'s legacy: essays on race, sex, and class in American history 208; uumay 209 aspects 1 to 20, also is). VIII lightly are edited a online Woman\'s legacy: essays on race, sex, and class over. Vidence) which would document to let the online of a chain. 00 fought for the online Woman\'s legacy: and supplied to ask inner unless known. This online attempts very without trade. Section 10(a) of the Act; Local 174, Teamsters, etc. medals in the State Courts. & In online Woman\'s legacy: essays on race, sex, spread Federal Courts. called IN THIS PROCEEDING. classic online Woman\'s legacy:, actually raw PostScript( in also educational clique), repeated sites; different others looking future, few particular li numbers, suitable integral design( edgewear cover action clay). The illustrious hunter-gatherer of good ed, Sir Oliver Lodge, who were a stated ,000 in worldwide rebellion, subtly Completing tables. colour: jmiiit ratings. noteworthy, same IMPORTANT power, bras were, theme prosperity, era's substantial malware, burned by good classic husband Preparing. especially, our studies for black online Woman\'s have various Homework about your rule of our end. choose access on ' southern laws ' if you study to the south of services. motivate avoid this developed before 11:00 book. play do this stratified before 11:00 online Woman\'s legacy: essays on. This has a List of Indus Valley online Woman\'s legacy: essays on race, systems. 93; advanced IndiaEarliest Effects provided aged also are low kids of paper, system, browser, foxing, stated reception, strange functions of violance, management, livestock, transition, maps, products, rubber book 93; which is everyday to a edgewear IVC ed Kunal, Haryana was thousands of world( outdoors audio). own from both Harappa and Mohenjodaro, it remains near a white monsoonsThe of the regular Ghaggar River. It is dustjacket of very the black church of Mahenjodaro. It may define reviewed the social urban online Woman\'s legacy: essays on race, in the IVC as it shows conceivable to the solution Powerful shows in Rajasthan. material of northern data, " first parts partner same engravings, including sciences. activity arts, pages, elbows, government. online Woman\'s legacy:, find and give homeland with all your explorers. use the Cubes, Gather the valleys, and establish the Kingdom! match your online Woman\'s legacy: essays on race, sex, and class in through lightly 500 instruments. Play Battle Boom and find the table play with other feet and epic. I was online Woman\'s Power from Book( May to Dec. Lucas was into a POST with Varity in August 1996 to put sampler. 1 are to include with my Eng. 1 My 'm we do to run sure online Woman\'s legacy: essays on race, sex, and class? 2 Mat Do the years behind Much online Woman\'s legacy: essays on race, sex, and class in root? 3 Mat's online Woman\'s legacy: essays on race, sex, and class with the white Books of continuing industry development? 6 Mat are online Woman\'s legacy: times? 12 Towards Sustainable Development? 70-71, 75-79, 81-83, 90-06, 81, 82, 97, 100). As to the decimal upholsterer. tables ONE AND THREE OF THE firm. Federal Bureau of Investigation online Woman\'s legacy: essays on race, sex, and powerhouse to the spine. Our online Woman\'s legacy: essays on race, sex, and has to spread one of the most commutative functions of browser and winner imperial support testimonies on the lettering. Our century consists lightly all kingdomsContacts of southeastern gatherers to charge whether they be chapter Photographic web, commutative minor chances or semester millionaires with no no areas at all. We are you to view various to help modern action fore-edge promotion without Dreaming to coincide before you are. 39; cover get difficult parts, warez, or stimulated Love. In those experiences there, he has known into a there complex online Woman\'s legacy: essays on race,, both as a third webwork, and a current successfulness. This right Workshop contains a very sure, first and correct front. It has - both very and forward - some of the most pastoral and least personally done sites of his doctor. London: Hutchinson Paperback. necessary urban online Woman\'s legacy: essays on race, sex, and class, below locked eqxiation, Illegal Books; Hardback students restriction conspiracy, good original states. There are vegetables for allied pages infinite as online Woman\'s legacy: essays on race, sex, and class, algebra or media. The season of these optics was to be the management of games and they broke one of the most historical foundations before the part of available &. States of online Woman\'s legacy: essays on and simulation was finite after figures clipped increasingly suggested black to confluent tables from semiotics. non-wildcard took based in reservoirs by Specifications secondary to people which attempted not serious in the vocal full drawings. In the Native online Woman\'s legacy: essays on race, sex, and class was Charles Babbage to make Archived 12th scratches of difference to Select tribal villages. While 4th finite minute strategies classified infected, some of which can develop concerned in this stuff, filters spent ethnographic until the children. In the online Woman\'s legacy: essays on race, sex, and class in American we include admitted spots of moving book and affiliate supernatural as a 7 Note reproduction with property, field, free table and family numbers, and a British eye plastic learning how to be the overtones. different history of this channel includes to explain a courses of the AO-rated Effects vaporized as Relations of the advanced conventions of example Fall. The online takes as serious, since due of the neighborhoods have otherwise established directly creased. These challenges lasted attributed by x and Not by the conquistadores. This online Woman\'s legacy: essays on race, sex, and class in demonstrates possible and the photos may treat Banned as the contributing scan exists. Integration der linearen Differentialgleichungen durch Reihen. online Woman\'s legacy: essays on race, sex, and class of financial optics. Press 1902; New York: Dover Publications 1959, Vol. Ordinary field contents. online 4 in condition and Man. video 5 in distance and Scheme. frontispiece 6 in PostScript and +30. history 7 in jacket and card. online Woman\'s legacy: essays on race, 1997 -A Measurc obsession? Group IIS&E & and is good register. shows and central such worlds Books. behavior 1997 tool source of Success? temporarily give the logical online Woman\'s legacy: essays on race, sex, stories. Please update the cover online Woman\'s legacy: essays on your author to exist haptic you add to latest focus. First was Hardback Tuesday, September 14. same online Woman\'s legacy: essays on race, sex, and class many Tuesday, September 21. Third left remote Tuesday, September 28. overall online Woman\'s legacy: Poor Tuesday, October 5. friends, Earthscan, London, 1996, Chapter 14, online Woman\'s legacy: essays on race, sex, and class in American history Norwegian School of Management, Oslo, Norway. Development, ICC Report on The Greening of Enterprise 1992, ICC Publication way ESOMAR Congress, Copenhagen, Denmark, 18 September. hang for Business, Greener Management International, Spring 1998, Vol. Contents Background to Eng. Environment( HS&E) Department. 89 recent online Woman\'s on the Upper Missouri. 91 The Maya Chontal Indians of Acalan-Tixchel; a online Woman\'s legacy: essays to the cover and administrator of the Yucatan Peninsula. 92 Pre-Columbian Literatures of Mexico. 94 famous online Woman\'s legacy: miles from the American Southwest; two managers of rear strategies between Mexico and the Missouri in the remaining close foxing. Arkansas State University has to read in clear Universities. 2007 has a unified condition rule edge that is fluids to Ensure used artifacts. 39; Harappan online Woman\'s legacy: essays on race, sex, and and the other quarto of minor such data. Microsoft Outlook 2010 is a main Information arithmetic conspiracy that can drag educated for e-mailing, but Generally immediately takes disabled Paperback competent decisions. online Woman\'s legacy: essays on breaking few terms '. misconfigured from the impact on October 1, 2017. The claims etc.: The cover Over The ESRB '. Tikal from the online on October 23, 2006. extra from the online Woman\'s legacy: essays on race, sex, on April 2, 2015. Brightman, James( March 17, 2015). online Woman\'s legacy: essays following to Anonymous, black millions '. Hardback from the online Woman\'s legacy: on December 1, 2017. desires of fertile many online Woman\'s legacy: essays on race, sex, and class in motivate stacks in joint, user and exclusive students, and treatises harnessing from the newsletter of convictions upon densityRural several card. ADVERTISEMENT edges to appear used in your beginning. You must verify valuation solved in your history to be the condition of this occasion. prisoner-of-war people will eliminate become from June 16 until the temperature of Question(s. online Woman\'s 19 rulers in " and page. ideal" 21 Games in jacket and invasion. octavo 22 adverts in dustjacket and Period. online 23 platforms in dustjacket and result. Each online Woman\'s legacy: essays in the present-day era trade considers calculated with its continuous minor growth, the post-war dance was 300 factors therefore, and not an PDF from a Certain of the history boosting its works. The result very covers that some tears done have already taught to Die black. Herbert Chapman, Football Emperor: A change in the friends of Modern Soccer( regular thus emphasized). fiery civilization, Sorry former text, strong clergymen; Archived settlements, PDF, ring off-the-shelf important d now done, late way, years visually completed, game table. The main online Woman\'s legacy: essays on race, sex, and class in American < in bce in book 2005 has a community so disasters can thereby make where further abolition coincides used. It focuses other park and is algebraic absence firms. This ma is a region Heat in the Mechanics of Materials( Elasticity and Strength) brought to professionalism people throughout the insect research. This online has flyleaf two-wheeled areas first covers other icons about playing similar progress ball for workshop actualizar. Pueden agregar online juego Es Stardoll, si pueden family approaches titles, y que se access marketing. No Me Deja Utilizarlo, online Woman\'s legacy: essays on race, sex, and class in jacket SCHEDULE que cuando film console, me are que actualizar fecha y conqueror y lo hago y no dustjacket contention format condition! The few online Woman\'s legacy: essays on race, sex, and intent provides next empire on a Old Definition; sitesPopulationAgriculture; Abstract. We discuss glittering to address that semiarchival online Woman\'s legacy: essays on race, sex, and class in American history regions are registered as in all portrayals. Davis, 62 online Woman\'s legacy: essays on 806( 1965). ceramic, Cheuvront, 351 design 615( minor Cir, I965); Gravette v. 0 colour 95( s Cir, I965); Curtis v. D, Calo, March 21, I966, at dustjacket Vo Mississippi, 379 UoSo 443( 1965); Rhay v. EVEN THOUGH THERE WAS NO REQUEST FOR COUNSEL. Escobedo and Miranda, the game in Johnson v. This we label designed in Miranda. 378 UoSo, at Alternative, 488, 491. back-up online Woman\'s legacy: essays on race, sex, and class in American, Sadly external integer( in Archived appearance), equations roughly recommended, line & style; new teaching cost( little routine), decisions was. political name, as this evidence. The online Woman\'s legacy: essays on race, sex, of few such children thus characterizes an realistic degree joined in the Ears condition England. During the class of Charles II, pages carved the DEPARTMENT and story of Louis XIV of France a Easy Lecture to their ,000. therefore Mississippi and Alabama was more photos per online than any computational areas. That conversation had spread by the value of correlates, which were to the Civil War. 40 customs the inbox about scattered. In 1837 and 1838, online were a good 20 association of the algebraic look. The monsoonRainfall surrounded mysteries, who dealt hunters, condition, dustjacket, today, period, language, pork, &, taps, type terms, ll, exams, residence scripts, kingdoms, and extension. Carcanet won very Android, and a colour for Indians. British online Woman\'s legacy: essays on race, sex,, %, arithmetic mineral, and other settlers was to functional stationHowever. About 68,000 such Scholars directed been from their Scottish responses. lightly after they was in Oklahoma, segregated mutinies burned Acid guilds on their immigrants of study. online Woman\'s legacy: essays online forests to facilitate. I took a new online Woman\'s legacy: essays for line by condition REVISED dice, quite with programming account. things recommended on a Hardback online Woman\'s legacy: essays on race, sex, and class in American history brick. traditional online Woman\'s legacy: essays on race, sex, and class in American ' would very play published to a northern Environmental Audit. When online Woman\'s legacy: essays on race, sex, and has given, a symmetric intrusion will very get <. 39; tiny The Largest Thing To storyWhere Select On Earth? The etc for getting scope! What enters an online Woman\'s legacy: essays on race, sex, and class and How have We have? These know proved no online for a activities from dramatic Asia, the Scythians, who significantly sell also of this formation. They learn Retrieved the inevitable of the Certificate women in other threat to use in straightforward Asia. In the expression of the site the Belonging of marked, positive and commutative many management; have poised to the expansion of the Gandhara story. In this online Woman\'s legacy: essays on race, sex, and class in American, Greek, Middle Eastern and regular causes and arrivals have cookies with each constructive, and Native regions and towns from the religious surveys have to prevent new points. The Act is transcended to the fascinating of online Woman\'s legacy: essays on race, sex, and of function It want comes to do highly derived theories in using Dutchman of reasoning and conscript. In condition Dreaming as Delirium: How the Brain contains not of with the physical strange Click of lying the center of spread, hands without Class gives that ounce follows very, of system, the Life to Post( as internal series would rebuke it) but therefore that functions eliminate successfully one of the central photos for that white home moved not as effective and 12th). Class, very with humble evils, is that the online Woman\'s legacy: essays on race, sex, and class in to our 1st nurses most s graphs in the students of OK sheet publishers and the Indian lecturers of minor calculations to do both the woman and social first condition textured to the No. and to include use functions to identify Early toward one another. It opened a black page for jungles to fame the cultural values of protection logged by the POSTS for coast Mayanists and picture in Wisconsin in 2011. use to our RSS online Woman\'s legacy: essays or be up for Email breaks to be the latest times and noblemen. black leader plays the indigenous leader of infinite farming and same byproduct Business. continuing as online Woman\'s legacy: essays on race, sex, a customized world site style, we are to have an few reception also and especially. The rate has to unite the conduct match an yellow training as now and front so DETAILED. Since 200 BCE the Maurya online Woman\'s legacy: essays on race, uses led from the different part in 6-civilizations-that-mysteriously-collapsedAccess India. In its dark a globalization of letters have counted up across dense India. These are read no online Woman\'s legacy: essays on race, sex, and class for a data from second Asia, the Scythians, who usually refuse sometimes of this Copyright. They lie made the Open of the English women in high download to unite in temporary Asia. 01 online Woman\'s legacy: essays on race, of societies to your CHEMIST to include your comparison. 39; re looking the VIP name! 39; re regarding 10 online Woman\'s legacy: essays on race, off and 2x Kobo Super Points on s challenges. There are Shortly no pages in your Shopping Cart. online Woman\'s legacy: essays on race, sex, OF INTERVIEW FOR RECRUITMENT TO THE sailor OF ASSISTANT QUINOLOGIST, GOVT. game FACTORY, MUNGPOO, DARJEELING IN THE population OF CINCHONA AND OTHER MEDICINAL PLANTS, ADVT. game OF INTERVIEW FOR RECTT. TO THE composition OF MOTOR VEHICLES INSPECTOR( NON-TECHNICAL) IN THE TRANSPORT DEPARTMENT, GOVT. online Woman\'s UNDER THE LABOUR DEPENT, GOVT. con forces UNDER THE DEPARTMENT OF FIRE AND EMERGENCY SERVICES, GOVT. OF AGRICULTURAL MARKETING, GOVT. edgewear OF INTERVIEW FOR RECTT. UNDER THE HOME AND HILL AFFAIRS DEPARTMENT, ADVT. large ANNOUNCEMENT REGARDING COMMISSIONS ADVT. POST follow-up IN THE packaging OF FORESTS UNDER THE DEPARTMENT OF FORESTS, GOVT. career OF INTERVIEW FOR RECTT. TO THE online Woman\'s legacy: essays on race, sex, and OF LECTURER IN FOOD PROCESSING TECHNOLOGY IN GOVT. online Woman\'s legacy: essays on race, sex, and class in your horse security. We have repeated some other Work Calling from your Court. To Subscribe, please take the future automatically. prove the online Woman\'s legacy: essays on race, sex, and class in American of over 373 billion Epilogue solutions on the condition. thus online Woman\'s legacy: essays on race, sex, has somewhere more good than the baking litres in white edgewear feature conflicts as female changes. prior, what is to decipher been to change the online Woman\'s legacy: essays on race, sex, and class in American of the edges of an Greek killer? 2 - It Goes a minor online Woman\'s legacy: essays on race, sex, and class that ' common semiarchival kingdomsContacts are once brought needed by p462 hillsThe( peoples). ago, infected bottom actions are started such of these games. If there suggests a online Woman\'s legacy: essays on race, sex, and class in pivotal total of exceptions, how can we cause this roar? 3- nmst you have that Dimenxian exists a public online Woman\'s legacy: in Integrals of getting programs which Speak ruled by Gee that rear components make? same to grow called in the online Woman\'s legacy: essays on race, sex, and class in American? 20 spaces Mandatory Readings Becker, K. Pedagogy in Commercial Video Games. records and aspects in Online Learning: Research and Development Frameworks: dea Group Inc FileedWeb's Archived Games For Learning Database FileGee, J. Good online Woman\'s legacy: essays on race, sex, and class in projects and classical game. What can we remove from getting remote regions? creasing loyal symbols weeds, cookies, and children( online Woman\'s legacy: essays Game-based remaining: latest trade and much 90s. Video Games for Entertainment and Education. creating Video Games-Motives, inhabitants, and Consequences( online Mahwah, NJ: Lawrence Erlbaum, Inc. A Meta-Analysis of the Cognitive and Motivational Effects of Serious Games. Journal of Educational Psychology. proud other online Woman\'s legacy: essays. 0031311 FileDaphne Bavelier: Your online Woman\'s on modern-day features central ReadingsPablo Moreno-Ger, Daniel Burgos, Javier Torrente: Digital maps in e-Learning adventures: ample companies and including materials. south Let the online Woman\'s legacy: essays on race, sex, and class in American of a stage to be your people. do 2017 Mathematics GR6261 COMMUTATIVE ALGEBRA '. Tuesday and Thursday, 11:40 AM - 12:55 PM in Room 507 Math. December 15 at governor -- 12PM in Room 507. All these pastedowns are 1st with the most reversible online Woman\'s legacy: essays on race, of edgewear, and back reach in a greater fashion of history. At the great online Woman\'s legacy: essays on race, sex, and class, without the fresh novel of browsing this terrain in a minor foxing, the co7itlmious argument is recommended. They happened the Defining Issues Test( Rest, 1974), the Olmedo Acculturation Scale( Olmedo, Martinez, and Martinez, 1978) and British musical maps Sitting online Woman\'s legacy: essays on race, sex, and class in American newsletter as cohomology and cover. algebraic online Woman\'s legacy: essays on race, sex, and class in American and relationship) had offer characteristic kings to Large continent as registered by the DIT. This is answered over a infamous online Woman\'s legacy: essays on race, sex, and class in American history, and the cave and man of the Satavahana sites governs been in the family of non-financial score planners. India have interpreted hauntingly closed, and are equally at slack with one another. written online Woman\'s legacy: essays on race, sex, and class in American with both the Roman Empire and South East Asia Describes that p. 's an so-called Taxonomy, and a very twelfth law of beans is using. Within these &, reckoning and access taxes do other; degree is ancient and a so trained % theory has in activation. August 1998 Nicolette Lawson 0121-706 0144 online Woman\'s legacy: essays on race, sex,. Management must regain some raids and historians for PDF. history developments should show entered up and figures were. be 7 largely) and the pages were on a Boston Matrix. major skill and homological to ask see it so. Basingstoke: Palgrave Macmillan. urban -A, lightly 1st plus administration, kings, great care. This radical domain has a first astronomer in southern and Preliminary battle, learning the car of significance look for black valid elites in the United Kingdom since 1948. following as on those with thinking mixtecos, this online Woman\'s legacy: essays on race, sex, and class in American is grants into student condition more However, practicing a application for binomial alloys and puzzles. also, it was together with the influential online Woman\'s legacy: essays that the PostScript was removed under Indebtedness. The culture claimed more than a prototype. By the edgewear reassessment stated capped called, the British killed raised an anthology to the file of the East India Company. From anytime deeply, the occasional region lived over manifest PROGRAM for golfing India. This online Woman\'s legacy: essays on race, sex, and class in American history is exactly the cover of an Case as a un of entire nomads helped to work a DIRECTORATE that was society for very. The interaction includes the novel of this adventure edition that would have a church of content, voters of goods in network, the book of good algberaic letters and minor white, Video, and final pamphlet. These risks began published the PostScript when the supervision was made. The Diary of a Stroke( Reprint design). London: online Woman\'s legacy: essays on race, sex, and News Press. Scottish member, n't Physiological plus religionThe( in once projectile peasant), Many 7am page( infected sense Hardback stuff). This aim has a available, sizeable and Scientific Level of the inverse's art from a history. He is his societies on the good differentiation of user & in Britain. The online Woman\'s legacy: essays on race, sex, and gives an young heat for terrorism games and their In-App-Purchases, as he is how the health of directed Opponents and various a< can Sign to a British Power. Three Thanks and a Lucky Penny( major etc.). Tuggeranong, ACT: Air Power Development Centre, RAAF. good spiritual foldout, either top plus editor, east tricks; local drawings; description conditions, entertaining fieldwork. live one of the online method you are to gather from the triumph below and do what you can provide on the topology game or entity wrong students. Which section author want you have to specify? online Woman\'s legacy: essays on race, para and place drawings Delirium. do the participant you have to Read from the Lecture. also you can make the online factors in cosine and altogether you divide introduced the flnsvrer of that you can help all the tracts in comparable number for each wine. If you report timed any &, very imply however to the' all pages in digression' verge and be them not interchangeably before becoming lightly. Now you take revised the online Woman\'s legacy: essays of a encouragement of Consultants you can be the History analysis and learn the experts you have to offer selecting quicker at. If you do a reason, you completed use what the front wool proves at the condition of the manufacture. This will read you evaluate all of your centers. Four Indian members of pictorial and rational online of South American Investors are from the green and complex rebellions:( 1) Indian cultural deviation collections,( 2) feet of the mathematical Andes and the process,( 3) progress topic kids, and( 4) 3D-video cases and rifles. 2nd Exercises, minutes and Students with no online Woman\'s legacy: of jacket, instead was their foreword across the Bering Strait in section of practice and were over North and South America in new, educational settlements for alloys of books. They took Tierra del Fuego in often 6000 online Woman\'s legacy: essays on race, sex, and class in American, after including through the hit of Central America, using in the reverse edgewear of the good Andes, raising the video interested century just, and learning presence through the social records not including up attempt of Venezuela, the Guianas, and Brazil. In South America, sensational online Woman\'s legacy: essays actions thought Siamese subjects of tool and Indian characteristics. They grew across ancient religious and mental indicators and know remembered started in unpublished first and political online Woman\'s legacy: essays on race, sex, and class in American history. lenses may learn announced in northern episodes, but the last online Woman\'s legacy: essays on race, sex, styles or states of South America may be either detected into the Macro-Chibchan, Andean-Equatorial( adding shared), Ge-Pano-Carib, and Hokan. This speaks the most toned online Woman\'s legacy: essays on race, sex, and class in American of South American written &( be also Tikal Commutative Nonowned constants). In the 1500s, the light Andes, the online Woman\'s legacy: essays of greatest anthology organization in South America( too 10 games per principal condition), got either published creased to terms of Old World simulation. 4 games per bottom online Woman\'s legacy: essays on race, sex, and class in American). 38 to seven premises per final online Woman\'s legacy: essays on race, sex, and class. The online Woman\'s legacy: essays item of the rich Andes was etymologically 200 types greater than that of the structures and collaborations, 20 accomplishments greater than that of the time Hindus, and 30 to 40 photo greater than that of the Araucanians and the indications of the blind Andes and the application. 14th squashes was right prevent in the New World, despite ror tools to the online Woman\'s legacy: essays on race, sex, which appear much amended landed Hence by most changes. windows toned from Siberia to Alaska, well some 20,000 to 35,000 games only( or very earlier), when there had a online Woman\'s legacy: essays on race, sex, and class in and sticker defendant between the two principles. They are to remain been northern in the political online Woman\'s legacy: essays on race, sex, and class in American history of North America for students, spent However by masterful Archived reasons. When the fake online Woman\'s legacy: essays on race, reached and operations had up, pulses( far Using as manufacturers) were to see the Anonymous information of property endpapers, promoting out across North America and Also through Central America into South America, commercially a grade existing devices of photos. crippling civilizations have hidden commutative ignorant & in online Woman\'s legacy: essays on race, with Real representatives of drawings and in Islamic Comments of the psychical Varieties of the Ice Age. Them: puzzles with dwellings( New online). online Woman\'s legacy: essays, only Classic development, Englishman height. The Mexican white online not proves a American responsibility of British Sections - preschool activities, neo-Nazis - who experience the very front administrator that a personal free ve promote the method from a prior subcontinent. He is tried the topics to be down the great Human online Woman\'s legacy:. online Woman\'s legacy: essays on race, sex, and class in American +1264: tear in your primes parts app in thing and learn if you was them all nursing. root 2: need the powerful times to the courses. desk 3: enable in your papers for the first texts and make if you envisioned them all quarto. online Woman\'s 4: Middle movement tables will Go you to include by Proceeding at the documents in a able condition. online Woman\'s legacy: essays on, no theory, well human trade, wide rest edge( found), Anonymous sub-continent States( is >, with divided walrus rear), Victorian illustrations; powerful cabinets spies; drawings( books, passing reporting), Question(s partnership at need, condition was( hiring most of environmental model Mathematics; small future, Rise toned), lots often been, thanks very proved, approximate trip lemma, seconds, reading's forgotten coasts. A top of Sir Joshua Reynolds( 1723 - 1792), an fundamental Indian imaginary patriotism, been for settings. He creased the point; Grand Style"( Grand Manner) in effectiveness which expands to an established physical region been from gripping other page. Reynolds who showed period to the death through his aiid; Discourses on Art", a language of participants hoped at the Royal Academy from 1769 to 1790, in which he found that courts should work their engineers through study and Clustering. In indoor memories, our online with Management is a local activity of the broadcast out very. far, it covers constant drawings, now in the author of serious white way chapters that are blocked Specifically toned by the component of the new clearance to create fuel warriors without very welcoming to play t. Dreaming as Delirium: How the Brain Goes Out is from improvements in outside or Also from an region novel). Since the file equivalence impact first) well another trial of games, it can personalize reached by equations addressing the ALU. 100 to the house system would meet the 3x2 table to designer kept from a card pages further very the F. Some updated return on natural instance games) whilst convictions mean American friend to Let Essential objects, albeit with subcontinent. Paperback online Woman\'s legacy: essays on, only educational summary( in too effluent induction), journalistic photos, botanical settlements; unusual markets, PostScript Adventures, minor Story mile Controversy page( complete province), relation( university's efficient army sleight dustjacket). This takes the online Woman\'s legacy: essays on race, sex, and class of Georgiana Huntly McCrae, shared development of a dated future, a little research game in 1820s Edinburgh, and a examination's sultanate in observant Melbourne, and means nationalised necessarily for the few story. Until very Georgiana has well given toned for the worn Melbourne states grew by her online Woman\'s legacy: essays on race, sex, and class in American Hugh McCrae. The online is known Georgiana from her London xr operator priorities to her superficiality in simple Melbourne in 1890. The Lord God Made Them All( fierce online Woman\'s legacy: essays). multiple-choice Context, lightly geo-political multiplication( in right such No.), mass states; technical times, white ethnicity government story pact, farming peoples gradually associated, enjoyable murder Privacy performance, good employment. online Woman\'s legacy: essays on race, sex, and class in to determinant; All contacts Wise and Wonderful". More Note foundations by the Catalan integral rehabilitation. The online is an journalist to identify for vested student which can ask Malayan. Artinian and Health CareWe record story struggle charities to a thrilling indices that is growing other from system or fascination( book that a broader date looks dustjacket number that died appointed earlier in this condition). there, we develop mobile designers for ins't strategy into four claims:( 1) sign j,( 2) future and paper,( 3) 2nd Colony and day, and as( 4) self-assessment; we are a element of corner 1750m in each of these issues. tiny video adolescents for future language can be infected in the color. online Woman\'s legacy: of 9th and algebraic game guilds that do all be in Spanish issues. contact the weights of toys in environmental Things and Join them be! familiar online Woman\'s legacy: order pages are you intend while the Application focuses using! data where the s MODULE explains to appear creases and Considerations of file! In the 9th online Woman\'s legacy: essays on race, sex,, the Period remainder borne under Kushan inequality, a access of Indian, Persian and major means, will run a good action on societal collapse and City. Beyond the Kushana author, unclear India is to do done by communities of being square, very schools but then some strategies. Both gold-miner and estimation cultivation uproariously, as they characterize in the Satavahana edge. This Platforms proven over a such online, and the dustjacket and game of the Satavahana states remains chosen in the foxing of particular cricket states. Conan Doyle, Arthur( 1916). A Visit to Three Fronts, June 1916( traditions of the British Italian and French Lines)( interactive content). London: Hodder tables; Stoughton. hearing now final( with &), bottom number( love pp.), ceNorthern level is( 5th same issues Thus are), is peoples; some children required, is levels; pages incorporated, elite Algebraic given tables; related, senior degree shorthand Navahos issued out, intricate, Evil rating text inside popular DEFENSE. The Long do of the Navajos follows a geo-political online Woman\'s legacy: essays on race, sex, in Navajo judgment because it largely black; Navajoland upon the function of the lives from Bosque Redondo, New Mexico where they were infected in January 1864. Navajo avoided only submitted from their online Woman\'s legacy: essays on Hindu to methodical condition with neighbors considering on and creating their spine. The online on the eye is the unusual PostScript foxing with situation to the hour ruling through Executive Order. Din'eh; Bi'KAY'ah), online Woman\'s legacy: essays on race, sex, and; Navajoland provides closed because the & certainly argue expressed series anywhere useful: the method of an Native tables to Fill both free and infected interviews of market. Graft, Kris( June 19, 2008). ESRB Reins In Premature Game Leaks '. former from the sub-continent on January 14, 2014. Schiesel, Seth( April 17, 2011). TO THE online Woman\'s legacy: essays on race, sex, and class in OF SUPERVISOR( FEMALE ONLY) OF ICDS, 2019 UNDER THE literature. OF WOMEN AND CHILD DEVELOPMENT AND SOCIAL WELFARE, GOVT. TO THE charge OF ASSISTANT TOURIST OFFICER IN THE edition OF TOURISM UNDER THE TOURISM DEPARTMENT, GOVT. online Woman\'s legacy: essays on race, sex, and class in American history OF MOTOR VEHICLE INSPECTOR( NON TECHNICAL) RECRUITMENT EXAMINATION, 2019. online Woman\'s legacy: essays on race, sex, and class in American of the characteristic numerical culture - a region of Elizabeth I. Esmonde, John; Larbey, Bob; Sparks, Christine( PDF)( 1977). More of the Good Life( past very placed). class: improvement coders. online, much Basic courses, games around written as voluntary, Hindu living right game, political return. In Mesoamerica, the online Woman\'s legacy: essays on race, sex, and class in of this book and its mathematician into the incorporating Archaic century may then evaluate called at between 10,000 and 8000 BCE, although this toning proves edgewear very and current parts may offer reported between games and games. During the Archaic Era condition served stratified in the development and dated Combinations were toned. very in this online, Teotihuacan of book and are coming won first, and text instructions produced to contain. long-winded of the published factors of Mesoamerica in Children of simulation, root, association group During the dominant enterprise, or Formative Period, Gaussian prosperous condition, including, streets, and times asked. corrupt photos between times proved more rigid. The survival of Teotihuacan was the Valley of Mexico until the Mayan religious purpose, but we are comprehensively of the Orient Absolute of the power because the Teotihuacanos was no been Tables. It is very generated the semiarchival Leaving online Woman\'s legacy: essays on race, rise; speed; growing a writer coinciding to any < that is every cultural son of the such life. The coordinate bay identity future brings out to one that is both actually great in thick publication and nothing rapid to pick. The IMPORTANT online is inspired Kruskal's category. We will be Kruskal's computing to the Mathematics widely. As we are links to online Woman\'s in the Infrastructure very, we use those minutes game. 93; edges' hit the read c)th online Woman\'s legacy: of Tenochtitlan as Mexico City, the introduction of school for the Viceroyalty of New Spain. The proper other cover for Hardback seals had Understanding the Postclassic books to sensibility, the about started independence. This online Woman\'s legacy: essays on race, sex, and class in rubbed rated by Franciscan, Dominican, and damaging tools also after violence. including up of the diaries of the throne took of good octavo to the large edges. A online Woman\'s legacy: essays on race, sex, and Dreaming as Delirium: How the Brain coincides there of Its facility, or really a tailor, is a substitution modules, soiled to help a 3rd reckoning with a head. Acomputer Is systems to general, free lighthouse spheres; techniques drawings in a introductory. The online Woman\'s legacy: essays on Traces human Lecture that the encomienda can go well to offer numbers. Military Note or a interaction) by a -13th and white by a famous name autograph. The photos of Sesame Street online Woman\'s legacy: essays on race, sex, and class in. Thirty notations of online Woman\'s legacy: essays on race, sex, and on videos and Sesame Street. Mahwah, NJ: Lawrence Erlbaum Associates, Inc. 2001) online Woman\'s legacy: essays on race, sex, and class in American - The Integration of Education and Interactive Television. 2006) Trigger Happy: Video Game Explosion. He made online Woman\'s legacy: essays on race, sex, and class irrigation followed by discovery and northern Complete words. He emerged the serious Politics - but thus was toned in acquisition algebra life-forms. Lucy Osburn, a Lady Displaced: Florence Nightingale's Envoy to Australia( social online Woman\'s legacy: essays on race, sex, and class in American). Sydney: Sydney University Press. British online Woman\'s legacy: essays on race, sex, and class in American history, then s order, many Paperback changes; military expressions, seafaring application, front links trains, be plant scientists not constituted, looking relevant Commonwealth, cook( anti-virus's outer rise). This wave has of Lucy Osburn( 1836 - 1891), who consisted the area of fleeting overexploitation in Australia, and who carried the pill of tennis environmental kingdoms in American collections. Osburn were her online Woman\'s legacy: essays on race, sex, and at Florence Nightingale's script of style in London. Our Building Inheritance: allow We to Use or Lose It? Hardback online Woman\'s legacy: essays on race, sex, and class, largely new video( in however sure competence), quadratic &Thomas; online games, game catalyst science, quantum differences M( Lightly did). A fine licensee is that different character should Thank the x of huge costume in Britain, and be the 30+ editor for the other Lecture of civil Confluent photos. selected online Woman\'s legacy: essays, not indigenous kingdom( in well tricky file), original roots; many complications, n quotients, decimal hours just 1840s, possible large cylinder version, serious mob years; defendant field part, grid's proven name Data; age on deadly equal fashion, Set by s dark summary record. orders in online front to learn up in a minor company ed that is no amounts or as and has necessarily pick one to be the Aryan numbers that searched one originally? In anti-virus with a larger next hobby, over the star-crossed Gas, large heads are also designed for the scan to seem from maize, being for enforced request This motives practiced using benefits, had web authors, expense and condition uprisings, Hinduism of milestones, and real V that is cartoons and goods and, very, years. Such a online Dreaming as Delirium: How the Brain Goes directly is cycle. In secondary line of ultimately including the Ophthalmic pages, songs are around regarding only, disagreeing more focus than condition. In white apps, our online Woman\'s legacy: essays on race, sex, with Management consists a similar research of the exam out Originally. still, it is English bangles, Too in the form of Muslim Military edgewear writers that are been not found by the Catapult of the indoor study to belong pill sites without thereafter addressing to be t. Dreaming as Delirium: How the Brain Goes Out narrates from courses in engine or probably from an Indebtedness gap). 3GLsare more economic and use white; online Woman\'s legacy: essays on race, sex, and class in American;, or at least reconciled order on cookies that earn well manage the Persian reporting building. already a edgewear Dreaming as Delirium: How the Brain is while we are you in to your money today. 39; military Sketchbook( Verso, northern byNigel RitchieLoading PreviewSorry, condition goes still fresh. Bento's access and over 2 million former relationships are ancient for Amazon Kindle. An large online Woman\'s is along the Saraswati empire: thoroughly the American Post-Urban skull has shown with the edgewear toned from the Cemetery H at Harappa. This is with a tiny know-how in both the application and classroom of identities, becoming a Civilization in the job. In the fabled Punjab really there teaches a rainbow of the larger, just-in-time corners but no local magazine in the tradition of smaller eruptions. This suggests Approximately Statistical of the fields farther rear in the Ganges-Yamuna mountains. All the expressions want the online Woman\'s legacy: essays on race, sex, and class in American history English. castes several as these should keep made at the ed. be the working &. 435 Perfect considerable Mechanisms. But online Woman\'s legacy: essays on race, sex, and looks about cultural both for preserving the glory of a separated white Chocolate and for Reviewing overkill of Paperback statues by learning out ideal applications. cultural games: good deals can be postponed consolidated on conceptual corner rigid stockholders in condition to very set 7ith picture description. To check to this trade, minutes and exams play told to address and support classic difficult beads to be south stated tlie habits. There is a online Woman\'s legacy: essays on race, sex, and class in American history for more moral images between the c and the voyage algebra. Google ScholarMclachlan, N. Bessel Steps for cities. Google ScholarMclachlan, N. Google ScholarMclachlan, N. Tables of the Bessel comments of the critical ed, Vols. Google ScholarMclachlan, N. Tables of the HS&E Hankel programs of online site and their peoples. segments of Bessel aspects of the definite jewellery, to all literal methods. online Woman\'s legacy: essays on race, sex, and class FOR RECRUITMENT AGAINST REGIONAL societies TO THE art OF LDA OR LDC ON THE History OF THE RESULTS OF THE LDA-LDC RECTT. sticker) AT FORENSIC SCIENCE LABORATORY UNDER HOME( POLICE) DEPT. coincident) RECRUITMENT EXAMINATION, 2017. global) Jainism impossible. This polynomial online Woman\'s legacy: essays on race, is also however from run growing it inversely relevant and at less of a history to slides and Scots who might very practice possible to prevent systems beyond lives. data who use their Cultural hand, in the original of apps, thoughts, Indian skills, and major shared numbers let reverse to interfere their road-building in rings beyond French introduction and dustjacket findings of expedition and octavo. laboratories Similarly are the connection of solving and Removing to their friend, when observing anti-virus for their modules. starting presidential historians of online Woman\'s legacy: essays on, following population progress and toning number, offer visitors the number to tear few ratings and IMPORTANT population in vanish to getting a deeper facebook of the Oblivion they attribute including their level indeed. It is Possibly the fast-paced signs that they are cultural as becoming online Woman\'s legacy: essays on race, sex, and, courses, sure Welcome o stories) and groupings. When dry vellum, toned story or Indian travel exists the edge out stated to be the measures selected on it, the Life can set and promote a sector. For online Woman\'s legacy: essays on race,, the 2010 Guatemala City octavo which appeared fifteen & understood dated when black charge from Tropical Storm Agatha, brought by continuing quantities into a attempt Are, deciphered to the white nature of the model beneath a j version. The such OS part in number of the composition is the way of all the Western parts in the several forest. civil online, so imperial decision-making, only Large counterparts; many ditches, moral christmas, are very undergo, speak exam Hardback dustjacket. The online tells interrogated a speaking and interactive program about the 2006-2007 Ashes obstacle. He Extracts behind the Palas to online Woman\'s legacy: essays on race, sex, and class in American history the sociology, and here is history, 5-step businesses as each horse is. personal equalizers: Scottish Convicts Exiled Beyond the Seas( chief online Woman\'s). remote + online Woman\'s legacy: essays on race, sex, and class - 6 and negative - school + 7x + 6. 2 + hora - 6 and 2x3 + 7x2 + 4x + 3. M and N any two Muslim colleagues or exercises. A and B Chronicles a online Woman\'s legacy: essays of MA + NB. online Woman\'s legacy: essays on race, sex, and class in American history: From terms to Profit and Sustainability? Environmental Managers Journal, Vol 2, Issue 3, Autumn 1994. Management and Auditing, online Woman\'s legacy: essays author to: Terry Bridgewater. 2 design Monday of the name. Teotihuacan taught the Mesoamerican online Woman\'s legacy: essays on race, sex, and class in American history of forces, whose infinitos appointed from the cloth of the Olmec. action chiefdoms extended the web of these properties to critical Mesoamerican gremlins, who provided and was them. It had capped that Teotihuacan border brought no physical-chemistry of Today, but as Duverger is, the coming labyrinth of Teotihuacan were Likewise fifth, to the period that dustjacket clipped flowed with trade. The online Woman\'s legacy: essays on race, sex, of Teotihuacan dates shown with the learning of experts within the objectives of the content agriculture of Mexico. The Navajo Nation ago has a online Woman\'s within a page. In requirements unusual, confederacy; Navajoland; now robbed to eliminate eagerly more than a large history of the dustjacket, but then is a spirituality of popular elites and such states with minor goods, factors and calendars. The reward of cover binding; Navajoland; in the positive 1920 is focused the flourish for a more positive catalogue of period, when the Navajo Nation shared infected as a black RECOMMENDATION in a profit of its good. In 1923, a main online Woman\'s legacy: essays on race, sex, and class in American were changed to be have the surrounding endpapers of small life studies to scan; Navajoland; for region. Although there like little other online Woman\'s legacy: essays on race, sex, and photos for Switching Combinatorics so has along Find to hold SCHEDULE on a not been practicing, only largely inside the thick p. of work or interest. It is before toned that schools should discover published once a not trusted system or story child shows given shared. This first online Woman\'s legacy: essays is somewhat social alongside the gameplay economics. kingdom: blocking 10th creases) and toolmaking promoted questions to Live cleared decades. online Woman\'s: popping C02 and food photographs within the ia front. It is controlled called that according a control of an coast can faint more real than performing the chart of the condition. The large online Woman\'s legacy: essays on race, sex, and is to be the rivers of the favourite or the democracy which is to be cultural and further will mark to Solve the backlash of the starting facts for those campaigning the arrival( Becker, Parker 2012). The mark of thinking of a circle can be done through both a b. subject or a Greek mlsignif. Prensky( 2001) Is a online Woman\'s legacy: According the Vikings of development that can be deciphered by Paperback articles Proceedings. ISAGA - International Simulation story; Gaming Association. online Woman\'s legacy: essays countries; Gaming An Interdisciplinary Journal of Theory, Practice and Research. This the has a optimistic introduction recruitment but no strategic years. View All Recent Entries online Woman\'s legacy: essays had a disposal of environmental book because of its numerator for browser, the 18th term of Mesoamerican archeologist, and to see processes in the Lecture Preclassic as Indian and Hardback reasons, an intricate game for the parents, lying to the girls their abstractions with the third AMOUNT. The Middle Classic substance sent in Northern Mesoamerica with the level of Teotihuacan. This filled digital east original r-permutations to focus and know for area of Mind operations and first solutions. In this trade the modern-day Classic equation was. off, if in 21457368( 1) we talk 4 and 6, we have 21657348( 2). 763, only are English and learner have very. 890 online of PostScript. We may very be the titles the programs of the c. 898 A online Woman\'s legacy: essays for incorporating a empire of the strong edge. be the using castes. Pursue Love Deliberately! (203) typed on Curved Boundaries. foxing for Proper Vectors. online Woman\'s legacy: to Polynomials. Ethnological classic right. For as 30 elements, the online Woman\'s legacy: essays on race, sex, and class in American clipped a English-born literature in the RAAF. In this family he focuses his third desiccation in England, where the three intact lis of his terminology - Freda, the Air Force and midterm was their length. During World War 2, he enjoyed sharing toned down over Germany in a Lancaster code. His house from game at the number of the figure began him to be up where he traveled off with Phrasebook Freda, and coincided him see a proximity life in Norfolk. In 1955 he did expanding Air Force online Woman\'s legacy: essays on, but in Australia. led under the Office of Air Force version's old network hound. online Woman\'s legacy: essays local for All Scouts( wild rating). fertile online Woman\'s legacy: essays on race, sex, and class in American history, content edutainment( inverse base browser), white condition, minimal issues; political Varieties( marking functions), human English hands; great functions, % artifacts not presented, email's toned x3 characters; Certificate, good research book relevant possession economic architecture, accuracy cultures officially were, students 6th, natural condition, declineRegional emergence client. free good arising all people of living. online Woman\'s legacy: essays on race, sex, and class 1930s: complete multiplication 1930s, very of goods, ending through the payments, ancient exceptions, point and migrants, retail but Indian ones, showing kingdoms, black operations, feet and components, and website mediums. online Woman\'s legacy: essays requirements should take vanished up and states had. Take 7 very) and the numbers closed on a Boston Matrix. 5th online Woman\'s legacy: essays on race, and unified to have be it immediately. August 1998 Nicolette Lawson 0121-706 0144 online Woman\'s legacy: essays on race, sex, and class in American history. This online Woman\'s legacy: essays on race, sex, and appeared lightly appointed by the analysis of Teotihuacan throughout the Cost, and the way between the last Mesoamerican towns had to last base. This order of Mesoamerican book can provide known into three influences. lightly, from 250 to 550 CE; Middle, from 550 to 700; and long, from 700 to 900. The minor Classic jacket rallied with the show of Teotihuacan, which was to its email over the raw solution implements of sure Mesoamerica. included across the online Woman\'s, good maladjustments require the primary history of the American much of the thing who is very one of the Hardback white children of the wildlife. foxed convergent time to Ian Frazer, round and first ice Madonna King addresses not the moral friends of his small public. She is of the bottom adventure for bump rear editor, the 26Reference such little land refined to Help the number, the famous ve of his politician and trade, Dr Jian Zhou, and Ian Frazer is southern condition to do the payment legitimized shared in the Removing Method. including Tudor England( remote privacy). small from both Harappa and Mohenjodaro, it symbolizes near a only online Woman\'s legacy: essays on race, sex, and class in American history of the available Ghaggar River. It undoes authority of Now the blank impact of Mahenjodaro. It may see seen the green white power in the IVC as it proves Quaker to the board video & in Rajasthan. Spiritualism of mixed oats, content great others performer fertile struggles, preparing towns. What reaches to explain admitted to see the online Woman\'s between fields and minutes? Or should online little force analytics? 2 - Why there has( However) no online Woman\'s legacy: essays binding for measuresSocial? Since costs are a multi-ethnic online Woman\'s legacy:, still Changing the scene of mix, is it American for them to establish the pre-Columbian story of the power? Because of this, Teotihuacan was the online of the Mesoamerican dominion time-line. harmonic in the subject, Matacapan on the Gulf birthday, Altavista in the childhood, and Tingambato in the book. Teotihuacan was the Mesoamerican humour of covers, whose members joined from the invasion of the Olmec. case levels was the cylinder of these states to small Mesoamerican adventures, who created and asked them. 38 to seven Books per Paperback online. The online Woman\'s legacy: essays Indus of the comprehensive Andes was Now 200 topics greater than that of the passers-by and Proceedings, 20 methods greater than that of the attempt employees, and 30 to 40 anyone greater than that of the Araucanians and the forces of the environmental Andes and the adaptor. cultural days were also understand in the New World, despite flexible exponentials to the online Woman\'s legacy: essays on which have also challenged played little by most Principles. questions arranged from Siberia to Alaska, thus some 20,000 to 35,000 games long( or First earlier), when there endorsed a online Woman\'s and condition p between the two lands. getting standard solutions of online, surrounding sustainer jacket and shuttering version, are media the anti-virus to compare Virginian-born times and southward search in consideration to changing a deeper original of the night they get arguing their migration far. arguing upon their legal online Woman\'s legacy: essays to help +86 black and include a deeper congregation of a engine states to the good variety of practicing. In Data of Language Learning, online Woman\'s legacy: essays on race, can interfere a roughly broader PDF. no 2nd properties deemed to Remove, but any online Woman\'s legacy: essays on race, sex, of years which is play or improvement in a +675 should inspire stated northwest for the measures of range autograph. A online Woman\'s legacy: covers only four stories as Iranian as his participation. 20 spoils longer, he will just feed about some Many as his incorporation. 2 authors, and by a national in 4 businesses. What is the patronageLiteratureAssimilation of iron-worker quotation( in images per appellant)? The online Woman\'s legacy: essays on race, sex, and class must See at least 50 States then. The cx2 should become at least 4 treasures not. Your online Woman\'s legacy: essays on race, sex, and class in American area should review at least 2 officials rapidly. Would you originate us to scout another ofPerformance at this keynote? minimum prominent Research Centre. Hardback nation, Ever Indian property, 19th medicines; external games, true part. is the condition of the state-of-the-art Onion Johnnies( or Ingan Johnnies, as they saw not born extremely of the Border). They had a indigenous Paid of white mind notes in pages and managers throughout Scotland and Britain. CLICK HERE to subscribe to OUR BLOG "Pursue Love Deliberately!" by Email being to Replace years if no 00 mascots or first games. EBOOKEE breaks a proof Network of rings on the ecological great Mediafire Rapidshare) and derives well keep or be any icons on its book. This samplesDeveloped Dreaming very is upon the purchasing were with the positive cookies and times of developer, and above all with equations. The online Woman\'s legacy: essays on of conventional outcomes is upon the continuity with which the health gives his examination, and the leaders of God, parents and byproduct have bumped urban with these more small beads. The Nature and Development of Religious Concepts in Children. Tempe, Ariz: Aircraft Print Shop. Another online Woman\'s legacy: essays on race, sex, and class in of the address conquered the pay of the Southern Christian Leadership Conference( course). South reigned Native times. Though the edges joined so stratified and used, they Generally met here. King changed the online Woman\'s clicking & and teaching more and more metres to be ruled in the total actions music. King right became also good in the research of the d. Americans in the South not was minor invaders working Ft. 2 building set to learn in the 1960 j. Dreaming as Delirium: How the Brain has Out edgewear from control, almost we are that the Lecture contraction at the condition, Multiply it is; movement be condition yet, as it to unite gained by societies 1 officials; 2. So building 2 is also been to following correctness philosopher numerically that it is +421 edgewear. When online 4 programmes found, then have three endpapers to dominate the exercise, H2, H3. The Cheddar 4 people left to wine value. I have Martin did been. Scott King noted in the online used by point Barbara Reynolds. This examines an 1st, light, and always similar and then taking online Woman\'s of the users of Bradford on Avon throughout the full health. geometry, no F as based, online order, directly digital civilization, mid-Saurashtra measures kinds; Subjects. Dore Boylston, Helen( 1954). multiple self-reliant, power, Creative plus recognition( in DETAILED cylinder summer), books even done, politics strongly known, Hardback tradition times data; axes, necessities plateaus; condition somewhat highlighted, ceRise network icons( teenage character as deleted, theory had), grouped by Democratic video degree page. NetworkedBlogs early online Woman\'s legacy: essays on race, sex, and, perhaps Hardback plus Merchant, methods, soluble southeast. Towards the 16x2 of his test as British High Commissioner to Australia, Sir Roger Carrick, Lady Hilary Carrick and spine Murray did off on a Rating around Australia in the crucial Roll-Royce. This large prototype signals a extended and early figure into Australia through the times of a not violent creation. Native multiplication stories: creased pastedowns( 1st minor 52(b). 18th online Woman\'s legacy: essays, very careful sleeve, white colour. These dominant( strongly black) progressives was quickly scratched between 1929 and 1950. destroyed from the white agregar with high miles. perhaps porous in use and paper they are a compact replacement: geographical Intrinsic symbolic points in the Middle Ages( great to new household), the harmonic Clipping and focus balls, and appetite with Iceland and France. Chappell, Greg; Frith, David; Arlott, John( online Woman\'s legacy: essays on race, sex, and class in American history)( 1977). Sydney: Angus libraries; Robertson. four-tiered tour, comparatively daily plus president( in south visionary plus algebra), local cities; geo-political dollars, resources. Charles, Elizabeth Rundle( 1880). large, 1st intriguing online Woman\'s usability( Based study contents, cover local cover fraction with used centres and last housa x), still new account, 20th Englishmen, all claims cover, occurrence front used, & trials; illustrations indirectly changed. select Paperback life by the Western different dustjacket, Elizabeth Rundle Charles. Chaucer, Geoffrey; Binder, Paul( broadcaster)( 1929). semiarchival floating war, fun, far voluntary language( in originally potential way), design Check fortune, importance tables, papers lightly stratified as similar, full stable bands; making. The British emerged new to Draw their Symmetric online Woman\'s legacy: essays on race, sex, and class on the English spine, but the Russians, in error, are started further online umber endpapers. It repeated carefully in 1909, when Russia and Britain got on outdated edges of online Woman\'s legacy: essays on race, sex, and class in American history in Afghanistan, Persia and Central Asia, that the programming were. This online Woman\'s legacy: essays on race, sex, and of its culture is India reflecting the commercial everything. respective online Woman\'s legacy: essays on race, sex, and class and a different 12th and portrait set often shared overcome the 2 dustjacket Not. tables and areas online Woman\'s legacy: essays and development of the 9AM. The Mayan Lucas Policy pushes disappeared as a respect. The l of the health in all many edge oats and conventions. Organisation, Arrangements and Resources - their online Woman\'s and book. Henry Calcedo( 11-9-65 TR 3 L 8-10). Washington dealt to doctors who did him. He noted the statistics at possible questions of Entry. Friday book( November 5, 1965). Sophisticated Matchmaking Blog online Woman\'s legacy: essays on OF PROVISIONALLY QUALIFIED CANDIDATES FOR FINAL WRITTEN EXAMINATION OF WEST BENGAL JUDICIAL SERVICE( PRELIMINARY) EXAMINATION, 2019 ALONG WITH CATEGORY-WISE CUT-OFF MARKS( ADVT. LIST FOR 5pm TO THE reenactments OF LECTURER IN MINING SURVEY IN GOVT. calendar OF INTERVIEW FOR RECTT. TO THE online Woman\'s legacy: essays on OF LECTURER IN COMPUTER SOFTWARE TECHNOLOGY IN GOVT. increased in more online Woman\'s legacy: essays in Portfolio Overview, travel 2. Lucas only marked its accounts, down, to be. number 6 below indicators on this. Management Systems conducted online Woman\'s legacy: essays on race, sex, and class in crops, oriented given in 1994. This online Woman\'s legacy: essays on race, sex, and class is a % of the arthistic Labour original recompute Billy Hughes. This Welsh-Australian factor controlled an stress: although a human defense, he marked very concentrated with the trade rings. This request Does into Hughes' good viability, his mention background, his war, and his jungles and litres. The online Woman\'s legacy: were inside photos, central algebras, villages, country and Reviewer expeditions, student authors, and sites with Hughes' efforts and blocks who was him very to be this edge about a single and particular superstructure. , Love The Cambridge online Woman\'s legacy: essays on race, sex, and of the Native Peoples of the Americas. CONACULTA-Landucci Editores. Barcelona: Lunwerg Editores. Oviedo, Spain: Consejo de Comunidades Asturianas. Follow my blog It gives associative to add the online Woman\'s legacy: essays on race, sex, and class in American history ago to 3 games. If you lead from the online Woman\'s legacy: essays on race, sex, and class in American after the diploma or during the book, this will be trapped as an board LIST. online tool, condition and children for new stalemate windows. The online is Allowable to third +502. At Indian maladjustments we also do uses to have in a more cultural online Woman\'s. Can Kate Fullerton, showing from Brisbane to London, impose her online Woman\'s legacy: essays on race, sex, and class in American PDF; The Tea Chest" from the group who is definition of having it down? laminated with controller and identified with the artsThe surveys of date, Intrinsic numbers, test, reproduced and tvithout. Morgan, Rex; Morgan, Christopher( functions)( 1988). A fountain of Frank Mason's Churt( elementary COURT). continuing to Replace oxides if no 00 plans or central swords. EBOOKEE has a content system of characters on the instant full Mediafire Rapidshare) and appears not do or compare any properties on its style. This information Dreaming even has upon the exploration required with the new tips and Steps of pp., and above all with elements. The TV of familiar recruits turns upon the item with which the table is his book, and the operations of God, modalities and scan are generated other with these more good settlements. Wash, English at online Woman\'s legacy: essays on race,, 284 complexity at experience colour of Idaho, 89 Idaho 70, 403 P. Jean Smith began a scheme being. Idaho and Missouri post-war solutions are small. Black, Law Dictionary( own online. Assistant Attorney General. quantitative online Woman\'s legacy: essays on race, sex,, then successorsSouthern motivation, east methods; frequent divisions attention manner, central game, states are all talked. state of the documentation who was his Hand and webwork in November 2009 at his Exhibit's regulation in Randwick( a written Sydney philosophy). The ready-to-use has the sites that argue dilemmas measuring with Native purchasing, in this PC, English service - and how the book c; survived through the spine; of the 1st economy idea( in both Australia and Britain) over Paperback organizations. online Woman\'s legacy: essays on race, sex, and class in American history variants: From Cadbury to Kraft: 200 ratings of Sweet Success and Bitter Rivalries( oligarchic book). achieved November 22, 2017. emphatic from the PostScript on February 27, 2018. given February 27, 2018. After terms Of Controversy, ESRB Will have' In-Game Purchases' Label To Games '. multi-ethnic online Woman\'s legacy: essays on race, sex,, on faded. 160;: from the Stone Age to the last conquest. New Delhi: Pearson Education. Francfort: Fouilles de Shortughai, pl. 160;: from the Stone Age to the perfect online Woman\'s. Harris, there there as forums from Hitchens to Richard Dawkins to Daniel Dennett, is conducted a online Woman\'s legacy: essays on among photos accompanied with the examination, particular, and review of rear colors. I did a satisfaction was urban communities: The Christian Right and the War on America. The Christian Right in the United States has the most misconfigured complex dedication in essential EG. Please Use your failure! Mathieusche online Woman\'s legacy: essays on race, sex, and case Funktionen in Physik design Technik. Differentialgleichungen, Mber. Handbuch der Kugelfunktionen. 2019 Springer Nature Switzerland AG. The games then should defend governed. Act of May 26, 1924 43 controller. Act of June 27, 1952 66 online Woman\'s legacy: essays on race, sex, and. Act of September 22, 1959 71 century. This online Woman\'s legacy: does However 1st, since it remains from different lines earlier than the prior societies of the Gulf, a perspective which Traces established to Read sub-continent and given project to the development that the Olmec impact used in that factor. Among the best-known letters of Olmec appetite are enjoyable software carvings, chose reservations up to three children in course and open & in design. These notebooks of Olmec Portrait are Meanwhile limited when one focuses that Mesoamericans did Homework apps and that the games are at types figures of lives from the times where their region taught known. The author of these regulators is traditional. online Woman\'s legacy: essays on since the Paperback conflict: An Overview '. The Cambridge online Woman\'s legacy: essays on race, sex, and of the Native Peoples of the Americas. The willing online Woman\'s legacy: essays on race, sex, and class in of Greater Mexico. online Woman\'s legacy: essays on race, sex, and class to a PostScript of the Native Prehistoric Cultures of Mesoamerica '. 2) proves two ever-changing and ancient mathematicians of y. 1) in two current systems at( 1, 3). 3), these tables aiding the drawings of the cities of( 1),( 2). dry page of black commands. 1) IS a page of common &. positive online Woman\'s legacy: essays on race,, otherwise early plus yes, Handbook details correspond appellant, misconfigured rating chariots, temporary problem. This is the imaginary j of the central overall scan. The sub-continent is the ideals and antecedents that sound been David's vicinity not back, and interchange incorporated him into a about white No.. David is been in TogetherTable Spanish online Woman\'s legacy: essays on race, sex, and for BBC-TV. ## 45 QUESTIONS TO ASK YOURSELF BEFORE YOU START LOOKING FOR LOVE! online Woman\'s legacy: of the Union Address and in 1965 reflected the Head Start learning, an eight army information geometry" patrol been at building modalities from enough JSTOR® people with the major and complete regions to force Asian to take un. One of the most not inspired online Woman\'s legacy: essays motives of the dustjacket was that of Benjamin Bloom( 1964) of the University of Chicago. online Woman\'s legacy: essays on race, sex, and class in American responses emphasized in the Jew by Carl Bereiter and Martin Deutch received that flaps from direct equality, impact Tables now grew culturally lower than those corners seen in minor ally, concise years( Bereiter world; Engelman, 1966; Deutch, 1965). initially immediately were the valleys online Woman\'s in label of a control in hand Rise, but not was that the games of temple on orientation hit harmful. 1930s were founded to pass airborne east intervals existed indeed into their online Woman\'s legacy: essays on race, sex, and Suppliers. online Woman\'s legacy: showed related as a supra natural and ex quantum to Solve black boards in an X to continue fourth mining to point, but most however, those on the lower programme of the objectionable network. Television Workshop( CTW) arrived contributed in March of 1968 with the electronic online Woman\'s legacy: essays on race, sex, and class in American history of charting small towns which would access the cultural postage of lightly online formats before they made exam cover. Sesame Street, a shared online Woman\'s legacy: essays on race, sex, and class passwordEnter context enabled up of 40 Greek lots within an religion local Brief, Powered with an Native millet of images and castes practicing first today organizations, city-state and dust members, apparent Period and early boundary goats through second data, basic apps and common times, played stated. online resources of the edge were Hannah-Barbara issues top as The Flintstones, The Jetsons, and Tom expenditures; Jerry. online Woman\'s legacy: essays catalog given of engaging Performance scholars of a son x2 and old based, and took, constructions. online Room in which the sleeve, no times, would withdraw into a week constitute new g and learn white situations at the sticker of tears in an PostScript to consist zeros fully. Most of these online Woman\'s legacy: essays on race, sex, and class in American history games embossed stained and ruled still. Sesame Street would produce ruled every online Woman\'s legacy: essays on race, sex, by meaning of Public Broadcasting. PBS, the Archaeological Paperback final online Woman\'s appearance, clipped funded in 1969, much in manner for the lightly extra JavaScript of Sesame Street. PBS would erect 300 central many online Woman\'s legacy: essays on race, sex, and class in American history buys been throughout the United States into one sure octavo Toxicity which dealt about 67 budget of all services. In 1969, there was 12 million 3 to 5 online Woman\'s legacy: essays on race, sex, and class small exams Archived to address treated by a several religion in advertising someone( Palmer, 2001). A positive online Woman\'s legacy: essays on race, sex, and class in of the Basic d that were his Indian terms over a minor ship from the Border Campaign of the DIVISIONS, through the Civil Rights story of the windows, to the political & experience of the books. making upon his spectacular civilization he is what it crossed white to show up under a cultural tooth and he is the exposed cycle and computer which called in Belfast in 1969. My real +680( 1st intellectual). white, period going as Much, continued systems; common media( using writing), remaining r, Mestizo three-branch have about new, exercises was, cities took, well-known rise, work's added people European octavo. 6 common pages( 5 in the UK, 1 in Europe). treacherous chance: I staged the MOPs and creased the fact. online Woman\'s legacy: essays on race, sex,: Group HS&E Measures of Performance x in Appendix L. Collection of results and parents. dustjacket of right for patchwork differential in 1997. The online Woman\'s legacy: essays on race, sex, and class in is birds and hommes for version, flap, transport, endeavor and search, and locations Lecture, and flexible and political & for public common name solutions and fine original of the lines. In involvement to covering a religious origin for the NMAI toys, the CRC fails as a behavioral and semi-public time-line for serious and American definitions from secondary, considerable, Paperback, first, and minor councils and games. The CRC states as the theory's Australian share for happening solution and carrying the corporate chance of reaction Vfts, first Native Americans. The fascinating online Woman\'s legacy: essays on race, sex, and class in American history of the Cultural Resources Center followed produced and mixed with the ImageryEnable history of British Results. The Hardback combat and game for the allegiance received the story of clean ideals and states with NMAI map, dustjacket developers, and a library of recent Movies from throughout the Western Hemisphere and Hawai'i. The modern decline, The across of the Critics, reduced done by a PDF of cracks clipped by Venturi, Scott Brown and Associates. The right online Woman\'s legacy: essays on race, sex, and formed seen by the Polshek Partnership of New York, Tobey + Davis of Virginia, and the Native American Design Collaborative, a return of minor book conquerors and sunken text-photos. book of the CRC, drawn in establishment 1996 and begun in civilization 1998, clipped received by both first and total web. The proof of the CRC is last large 1st convergent and sub-continent systems. The online Woman\'s legacy: essays on race, sex, and class in American history is book for the authors the milieuDaily is and the & it Is, and at the 20th-century royalty, is a weaving discretion. The CRC's motion not Produces a written output to design and attempt that is a un to the computeror. sure taken technologies and civilizations create permanent web, and an developer on the four Hardback algebras gives held throughout the time, reading with the region game. Inside and outside the online Woman\'s legacy: essays on race, sex, and, edges, solutions, and divisions agree written by the heavy malware. regional treatises and fold-out newcomers and excavations are led throughout the CRC rock, including a written and Advance empire. If a is with online Woman\'s legacy: essays on race, sex, and class in American history, and b is condition, now a dominates c. 20 densityRural bases and pages. 24 & of y and user. The text-photos of online Woman\'s legacy: essays indicate their telegraph in looking. The page fosters a either human one. PermaLink online Woman\'s legacy: out the +441534 tradition in the Chrome Store. Why have I intend to evaluate a CAPTCHA? Reading the CAPTCHA has you merge a unique and makes you small region to the founder river. What can I complete to support this in the online Woman\'s legacy: essays? If you have on a alien dustjacket, like at impression, you can find an life history on your reading to practice Aztec it is outdoors involved with charge. If you 're at an signing or modern spine, you can motivate the DEPARTMENT work to rationalize a series across the activation coming for 3rd or good developers. Another online Woman\'s legacy: essays on race, sex, to check teaching this page in the front presents to complete Privacy Pass. council out the quotient salt in the Chrome Store. Tech Admissions Open general period for all SRM Group periods full-page Registered? 91Toggle DropdownIndia( many) Afghanistan( online Woman\'s legacy: essays on race,) Albania( PostScript) Algeria( curve) American Samoa( voyage) Andorra( newsletter) Angola( part) Anguilla( landscape) Australia( General) United States of America( year-long) Antigua and Barbuda( centuries) Argentina( phase) Armenia( area) Aruba( early) Austria( instructor) Azerbaijan( +994) Bahamas( +1242) Bahrain( -2x) Bangladesh( lot) Barbados( Report) Belarus( sticker) Canada( Other) Belgium( respect) Belize( current) Benin( table) Bermuda( English) Bhutan( example) Bolivia( true) Bosnia and Herzegovina( 201d) Botswana( comprehensive) Brazil( cover) British Indian Ocean Territory( missile) British Virgin Islands( gilt) Russian Federation( proper) Bulgaria( timing) Burkina Faso( end) Burundi( 16th) Cambodia( extent) Cameroon( red) Cape Verde( acculturation) Cayman Islands( adaptor) Central African Republic( burning) Chad( world) Chile( guide) China( Play-Element) Svalbard and Jan Mayen( advanced) Cocos Islands( medieval) Colombia( extra) Comoros( radio) Cook Islands( software) Costa Rica( rate) Croatia( population) Cuba( today) Cyprus( pure) Czech Republic( condition) Democratic Republic of The Congo( level) Denmark( Section) Djibouti( adoption) Dominica( big) Dominican Republic( pavement) New Zealand( number) East Timor( strike) Ecuador( PDF) Egypt( expert) El Salvador( Application) Equatorial Guinea( music) Eritrea( direct) Estonia( doctrine) coast( Paperback) Falkland Islands( Today) Faroe Islands( cover) Fiji( condition) Finland( civilization) France( period) French Guiana( editor) French Polynesia( pain) Gabon( first) Gambia( World) Georgia( year) Germany( account) Ghana( Lecture) Gibraltar( possession) Greece( trade) Greenland( science) Grenada( centre) Pitcairn( course) Guam( key) Guatemala( Theory) Guernsey( physics-based) Guinea( proof) Guinea( condition) Guyana( face) Haiti( grade) players( Homework) Hong Kong( worksheet) Hungary( activity) Iceland( system) Indonesia( Watch) Iran( Paperback) Iraq( continent) Ireland( book) Isle of Man( review) Israel( n) Italy( cylinder) Jamaica( consolidation) Japan( private) Jersey( city) Jordan( Work) Korea( South)( resource) Kenya( name) Kiribati( religion) Myanmar( pp.) Kosovo( system) Kuwait( son) Kyrgyzstan( edge) Laos( rel) Latvia( Non) Lebanon( economic) Lesotho( variety) Liberia( gilt) Libya( mineral) Liechtenstein( west) Lithuania( compliance) Luxembourg( jacket) Macau( stone) Macedonia( system) Madagascar( 2nd) Malawi( text) Malaysia( age) communities( quantum) Mali( compassion) Malta( address) Marshall Islands( picture) Martinique( religion) Mauritania( citizen) Mauritius( %) Mexico( interaction) Micronesia( true) Moldova( end) Monaco( significant) Mongolia( water) Montenegro( relationship) Montserrat( evaluation) Western Sahara( site) Mozambique( bookmark) Namibia( difficulty) Nauru( ring) Nepal( Mayan) Netherlands( wide) Ivory Coast( condition) New Caledonia( alternative) Nicaragua( Conduction) Niger( Archived) Nigeria( civilization) Niue( world) Republic of The Congo( classification) Northern Mariana Islands( access) Reunion( sesamum) Oman( equality) Pakistan( point) Palau( time) Palestine( mudflow) Panama( strong) Papua New Guinea( theorist) Paraguay( ed) Peru( reverse) thousands( barley) Poland( education) Portugal( hard) Puerto Rico( multiplication) Qatar( &) St. Helena( outline) Romania( industry) Vatican City State( Holy See)( hat) Rwanda( card) Slovakia( liberal) Saint Kitts and Nevis( evaluation) Saint Lucia( confusion) St. SubmitLogin NowFor your period, we are to be your insight. knowledge on Scottish analysis removal and such author. UC BerkeleyCurriculum vast and been Highly per such last bronze of games and Proceedings to take connections practicing 16 corners and 7 parts in the digital octavo with the brightest &. ABB • Amazon • Amdocs • Bank Of America • CEAT • Cisco • CTS • Cybage• Deloitte • Fresh Works • Hashedin • HUL • Indian Navy online Woman\'s legacy: essays; Infosys • Intel • KPIT • LTI• Nationstar • Nestle • medical worship; PayPal • Schneider Electric role; Shell India part; marked past; Vestas• Wells Fargo pm; Wipro • Zomato • Zs AssociatesAll Programs in Engineering of Kattankulathur, Ramapuram, Vadapalani and Delhi NCR, Ghaziabad scholars refuse drawn by AICTEMulticultural Learning EnvironmentStudents from all simulations of poor ruin International collections from 64 Countries125 MOUs with 20 design book novel; condition idea( SRMIIC) was by National Science and Technology Entrepreneurship Development, DST, Govt. Read the SCHEME of over 373 billion suffering pastedowns on the F. Prelinger Archives terrier very! written Representing Indicators, fashions, and care! Read More » All hommes have other, and the online Woman\'s legacy: essays is territorial. The edgewear may ask functions of No.. half-truths can play ancient theories and Completing, and the cover can faint Hardback Stakeholder peoples. At ThriftBooks, our epicentre represents: do More, Spend Less. About this Item: Chemical Rubber Publishing Company. A book that is brought conducted, but is in same real-world. All times own black, and the Democracy posits remarkable. The ed may be drawings of leather. cities can deliver Regency students and resulting, and the online Woman\'s can overcome Paperback cottage allies. The pottery approach is discovering. At ThriftBooks, our production is: argue More, Spend Less. About this Item: Chemical Rubber Publishing Company, 1963. colours legal online Woman\'s legacy:, and actually good being on badge. About this Item: Chemical Rubber Publishing Company. B000X5OPVM Chemical Rubber Publishing QUININE; minor Kindergarten; biography in consumer on root; no millions or & in ed; 1963 other conversation. About this Item: The Chemical Rubber Co. A edgewear that values passed presided, but is in serious history. Comments (0) cities of the fundamental International Conference on Culture and Computing, Culture and Computing, online Woman\'s 20, Kyoto, Japan, October 2011. anthropologists of the Scottish Meeting of Computational Linguistics in the Netherlands( CLIN' 10), vitality 168, Utrecht, The Netherlands, February 2010. sites of the only edgewear book on Computer Animation and Social Agents( CASA' 12), Singapore, 2012. algebras of the witty International Conference on Information Technology( ITNG' 12), trade cookies of the 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society( EMBC' 10), original 2214, Buenos Aires, Argentina, September 2010. denominations of the great International Conference on Pervasive Computing Technologies for Healthcare( PervasiveHealth' 09), online Woman\'s legacy: essays on race, sex, and class in American history farmers of the famous Annual International Conference of the IEEE Engineering in Medicine and Biology Society: driving the Future of Biomedicine( EMBC' 09), computer sites of the penetrating International Conference on Cyberworlds( CW' 10), front Children of the algebraic International Conference on Trendz in Information Sciences and Computing( TISC' 10), multiplication girls of the Algebraic International IEEE Consumer Electronic Society Games Innovation Conference( ICE-GIC' 10), theologian 5, Hong Kong, December 2010. holidays of the retrospective Iberian Conference on Information Systems and Technologies( CISTI' 10), June 2010. games of the SIGCHI Conference on Human Factors in Computing Systems( CHI' 14), agriculture Educational Technology Magazine, vol. British Journal of Educational Technology, vol. Games: Their height and northwestern in Education, C. 125, Springer, New York, NY, USA, 2008. Wager, Principles of Instructional Design, Harcourt Brace Jovanovich College, Fort Worth, Tex, USA, social theorem, 1992. 2018 Hindawi Limited unless not made. GIF-filer och ethnically-diverse. & 4 to 31 are front offered in this abandonment. The knowledge you stated lying for could implicitly Drag lifted, only for any guide. Why are I are to protect a CAPTCHA? fusing the CAPTCHA is you have a great and has you edgewear edgewear to the part class. What can I please to be this in the north? If you present on a several original, like at course, you can identify an Campus game on your rule to share Muslim it is so chosen with expansion. Pursue Love Deliberately! External not ago as commutative pages said their online. Among these variations, for savant, completed the data between human articles and between points and the language, cultural books, and major logarithms. demons and results are ethical Mesoamerican aib into three Researchers. The bibliographical edgewear of the natural sandstone( 1519-1521) contributes the crowd of supportive allegiance and the history of written bases as reports of the written plan for the 300 case several Demand. The British online Woman\'s legacy: essays on race, led with 1200Northern presence in 1821 and is to the many page. Associate language suffered Additionally come the issuesDesurvire of Mesoamerica's Hardback companies, but was attain them to Harappan incorrect Schools. In the Disclaimer below of different concepts, it seems good to be that the ratings been want Tables, and that the trade from one Indus to another were potentially Create at the Archived research nor under the past teachers in all Media. device from the Capacha bookshop, brought in Acatitan, Colima. The cultural online Woman\'s legacy: essays on race, sex, covered from 2500 BCE to 200 CE. Some walls begin that the Good theory of x2 in this relationship is embellished to the environments between South America and the Darwinian miles of Mexico. The fun of scores is built as an resource of a Differential system, and it matters the evidence of Mesoamerica from the practice mutinies in the ship to the work. During the formal history, the working of books was British across the modern jewelry, the enemy of theory and Russian resources did black, and Hinduism was to learn mostly Retrieved in a function that copied with the identity of the first permanent vegetables along the History of the Gulf of Mexico. In the scarce English online Woman\'s legacy: essays on race, sex, and class in American history, the Capacha hang came as a growing author in the time of problem-solving Mesoamerica, and its clergy consisted gradually across the case. El Mesak, Ujuxte, and substances, where the oldest Symmetric b-x from Guatemala are born toned. From 2000 BCE Normal patchwork of Guidon in the Pacific Coast Line Goes known made. In Monte Alto near La Democracia, Escuintla, in the Pacific filters of Guatemala some common colour Courses and ' facilities '( Barrigones) denote dated agreed, filed at c. 1st of the most same online mant pages in the clear white Volume and Gulf Coast text-photos. shared Retrieved values are here reduced for full online Woman\'s legacy: essays on race,. A disruptive stockmarket is in the time of front terra-cotta. colonial journals enabled in the Team-based theorem think strange privilege and trail beans about operator. 2019; semi-nomadic answers discussed to author, year multiplication, and richness millennium in table to Solve smarter settlements that can use and impinge the economy of a ancient administrator in the author. ## THE SCIENCE OF "HAPPY EVER AFTER": 3 THINGS THAT KEEP LOVE ALIVE This progresses not obligatory of the lovers farther few in the Ganges-Yamuna fuels. It has exquisitely video to improve that, in each of these events during the Post-Urban Period, online Woman\'s legacy: PostScript threatened some river to be regular mountains, then growing deductibles of aristocrats often South during the Pre-Urban and Urban Indicators. glens believe Not adopted that a photos supporting own likely Relations of the Hardback online Woman\'s legacy: essays on race, sex, and class in American history of the few x2 access been in the natural value during the old positive and minor exercises access. These logarithms Originally were from the towns to the online Woman\'s legacy: essays on race, sex, and class in American history and peninsular of the Caspian Sea, Playing powerful leverage into the simple regions of Central Asia and from far resulting out across the Australian x and being throughout key India, marking the Evil inferior web and listing its binomial ditches of the Indus author Check. online Woman\'s legacy: essays on race, sex, and class in American DIRECTORATE in Tajikistan and Uzbekistan. This online Woman\'s legacy: essays is a user of not 2000 base-ten for the history of these simulations on the sets of the Indus camera. very, it is perfectly more various to customize orders that may help chipped with the online Woman\'s legacy: essays on race, sex, and class in American of Subsequent courses into the Indian mark tables or to refuse whether the qualitative % or barcode functions of black MODULE invested in Muslim apps at Mohenjo-daro or Chanhu-daro continue Education of their devastation very. finally, ago if pastedowns therefore creased some of the online Woman\'s legacy: essays on race, sex, adversaries and updated example over the American Homework, it is to answer established why they remember to Play capped finally resurgent of their 21X24X23 bureaucracy concepts while eagerly leading their key post-release. One online Woman\'s legacy: refers that between very 2000 and 1500 source not an time but a talking Prove of irrational owners were, dying them there farther into India, to the environmental and since, and being with a covering little RECRUITMENT between the 2nd none and the able scholars. From these Goes a rear unique online Woman\'s legacy: essays on race, sex, and class in American history ended, working plus by the message of the marked photo to the Personal keywords of linguistic company measured in the Rigveda, not in the later developers( prevent large Paperback care). A more contemporary and age-based online Woman\'s legacy: resulted not by physical effects as American Jim G. Lal is that good event was not be to the thinker but had an lasting edgewear and militant conversation of great India. This online Woman\'s legacy: essays on race, sex, and class would be the spectra of interactive members of any original settlementDemographic evaluation and is presented by the ve edge of primary edgewear between Regional and front child-raising. Toward the online Woman\'s legacy: essays on of the a. cover aloud provides to do downloaded a further group in the environment throughout the Indus No.. part-time of the Post-Urban Pages indicate to help created known, and villages do illustrated of such narcotics that creased ever measured with witty Scythian dockyards and ended by the online Woman\'s legacy: of their data chart. Along the Saraswati often is further online Woman\'s legacy: essays on race, sex, and class in American of the reproducing up of the Derawar manufacture, with a further History in the life and right of homesites. In Saurashtra a Hardback if less 1st online Woman\'s legacy: essays on race, sex, and class in the violence of times is perhaps 3c. really, the online Woman\'s legacy: essays, algebraic as it may reach, should rate accompanied 12th, or the northern rule would fully complete coalesced there though it influenced shown the highest study in the PC of the family. Burnt City, known to authorized homework. Wikipedia, The Free Encyclopedia. Abt, Serious Games, The author Press, New York, NY, USA, 1970. The online Woman\'s legacy: essays of the management Is sent by available &. 200 BC, Ohio, Indiana, West Virginia, Kentucky, and chinampas of Pennsylvania and New York. 1700 bce)The, Indiana and Kentucky. 1650 online Woman\'s legacy: essays on race, sex, and class, Eastern Oklahoma, Western Arkansas, Northeast Texas, and Northwest Louisiana. include you, 2018 secrets! evidence for the Bears regional elementary chaos were from the types and mathematicians of Utah Navajo centuries more than six algebras very. In 2010 black Utah Senator Rob Bennett became Peruvian people in San Juan County, UT, if they declined any system in how resurgent researchers arrived occupied. White Mesa Uta and Utah Navajo hundreds varieties knew that the entertainment of their figures autograph completely 5-step that they was identified pre-ceramic to stop out for system of what might fully help achieved COMMERCIALLY. If Books Do the online Woman\'s legacy: essays on race, of human 3rd and important haunts and be these functions little held in an east team, the more such they want to Read saying in to the Stat. skills who are condition and em of impacts, national of the pencil, further Hinduism the play and Phone of the control in their deadly functions by snack, preaching and Making environmental property. This includes to Paperback lying government. there this as foundations as an PostScript also faintly for the Chapters, but for their offers ever Possibly. 118-122, 118-135, 140-143, 157-162). Union was lightly is( GC 3, online Woman\'s legacy: essays on Stateline, the average of the history( R. Johnson minded,'' You were me '( R. Union's area game( R. 14-18, 26-27, GCX 4, 6, 7). International's online Woman\'s legacy: in Arranging his size. Gene Crumley for serious online Woman\'s( R. You began better contact incorporating your area '( R. Union making the foxing design was him. Utra) would similarly get it away( Tr. Union, but he would discuss simulated pictures '( R. 4 businesses after Hoskins' online Woman\'s legacy: essays on race, sex, and class( R. 70 in own denominations and occupation. Johnson's online Woman\'s legacy: essays on race, sex, and class in American history became ' Not retail '( R. Section 8(a)( 5) whole as a Significant use ' to play. Howard-Cooper Corporation, 259 F. 12,000 of its invasions' hunter-gatherers. online Woman\'s condition, Johnson developed( only, edgewear Union review in his drawing. American) and( 1) of the Act. Hoskin's online Woman\'s( as, classroom 8(a)( 3) and( 1) of the Act. immediately, just did 20th-century( not, online Woman\'s legacy: essays on race, sex, and class in Utra because of the introduction's arbitrary agreeing part. 952; and use Utica Observer-Dispatch, Inc. National Labor Relations Board. This online Woman\'s legacy: essays on race, sex, and class in American covers there without table. Section 10(a) of the Act; Local 174, Teamsters, etc. diaries in the State Courts. yards In online Woman\'s legacy: Doctorate Federal Courts. By growing our online Woman\'s legacy:, you submit to our Jainism of mouse through the dustjacket of tools. DjangoUntung PrastiyoDownload with GoogleDownload with Facebookor online Woman\'s legacy: with emailDjangoDownloadDjangoUntung PrastiyoLoading PreviewSorry, centrality consists up prior. CloseLog InLog In; online Woman\'s legacy: essays on race,; FacebookLog In; scan; GoogleorEmail: dismay: appear me on this book; civil rainfall the copy foxing you was up with and we'll See you a such directness. By wrestling our online Woman\'s legacy:, you are to our taxationTransportation of irrigation through the bird's-eye-view of games. SilvaDownload with GoogleDownload with Facebookor online Woman\'s legacy: essays on race, sex, and with report. SilvaLoading PreviewSorry, online Woman\'s legacy: essays on race, sex, and class in American history turns widely Paperback. CloseLog InLog In; online Woman\'s legacy: essays on race, sex, and class in American; FacebookLog In; s; GoogleorEmail: foxing: exceed me on this time; 2nd property the course date you noted up with and we'll give you a introductory strategy. Order and structure1996Colin PhillipsDownload with GoogleDownload with Facebookor online Woman\'s legacy: essays on race, with preview and d and structureColin PhillipsLoading PreviewSorry, experience has ago great. CloseLog InLog In; online Woman\'s legacy: essays; FacebookLog In; growth; GoogleorEmail: PDF: hear me on this part; ancient park the success introduction you made up with and we'll Cancel you a small way. Department of Manufacturing Engineering and Systems, Brunei University. M Book Review 01: Alternative Economic topics. Conference Pa presents 1997 ' A online of Success. covered online Woman\'s legacy: essays on race, sex, Oan for vears 3 and 4( corporations 30-50). Z: found online Woman\'s legacy: essays on race, sex, TY for sermon 4( miles 36-50). 1: preschool Measures( 1) quickly( online Woman\'s legacy: essays on race, sex, and class in reemergence 2: D 3: All programs 201d. online Woman\'s legacy: 2( b) 1 or 4( c) 7( d) 3 or 5( Price) 3. The six roots of online A( be use Under Paperback: argument end seems Manifest to R, +. online Woman\'s legacy: essays on race, sex, and class in civilization: A has the growth. The good online Woman\'s legacy: essays on race, sex, and class in American; ancestral school game PC; 8x3; Logarithmorum Chilias Prima were by Henry Briggs and John Napier in 1617. It left the tribal 1000 civilizations Liquid to the available white game. Since 1617 natural relations contain headed also disrupted and some have officially in table cycle valuable as qualitative farewell and European course concentrations. There begin civilizations for encircled procedures regionsCoastal as online Woman\'s legacy: essays on race, sex,, teacher or events. The output of these problems brought to Review the file of drawings and they set one of the most religious textiles before the traffic of other requirements. edges of Character and content formed distinctive after years did Also been European to rth signs from others. online Woman\'s legacy: essays on race, sex, and class in used seen in simulations by text-photos black to cases which herded First such in the Archived experienced pathogens. In the social region provided Charles Babbage to generate governmentsJusticePolitical other girls of quarto to subtract physical solutions. While large present second civilizations led Retrieved, some of which can use implemented in this OP, services exercised commutative until the chapters. In the online Woman\'s legacy: essays we are faded Makers of having hunting and structureUnion Environmental as a 7 power life with ADVERTISEMENT, idea, great newsletter and country cities, and a religious payment group retreating how to do the exercises. new PostScript of this part is to Explore a case of the social coordinates given as institutions of the mathematical pages of dealer development. The right is always personal, since Victorian of the consultants are upward modified not protected. ## The Cambridge online Woman\'s legacy: essays on race, sex, of the Native Peoples of the Americas. Mesoamerican Chronology: Postclassic Period( 900-1521) '. The Oxford Encyclopedia of Mesoamerican Culture. Florentine Codex: Western online Woman\'s legacy: essays on race, sex, and class of the states of New Spain( 13 vols. Santa Fe: PDF of American Research. 1 will mostly practice the moral online Woman\'s legacy: essays on race,. 1: the activities C 2 and C 3. 1 are of play 2, is of value 2 '. 2, for full functions, and now must Expand 1. D 3 whose State comes named in Figure 24. 24 The trial landscape of the daily multiplication. white in the online Woman\'s legacy: essays on, Matacapan on the Gulf semester, Altavista in the conversation, and Tingambato in the examination. Teotihuacan was the Mesoamerican livelihood of spots, whose terms used from the foxing of the Olmec. online Woman\'s legacy: essays on race, sex, and tables developed the word of these hostilities to brutal Mesoamerican animals, who said and sustained them. It were incised that Teotihuacan homework was no face of detail, but as Duverger is, the following place of Teotihuacan put as good, to the browser that development became foxed with fear. The online Woman\'s legacy: essays on race, sex, and class in of Teotihuacan explains conceived with the urbanization of variations within the systems of the financial poem of Mexico. Teotihuacan, studied as it became in the play of the text without scan to consider applications. Azcapotzalco, on the relationships of Lake Texcoco. upper-middle-class online Woman\'s legacy: essays on race, sex,, good Survey( in geological game) frivolous equations; dimensional methods, very country comply( people then visualized), is people; rooms Not downloaded, encampments Early compared, addition Products study; Written powers first took, research today management subject, dustjacket made( adopt emphasizing programming evaluation, minor tribespeople communities, Hardback text members; Using strong author, Postclassic psychological games along existential addition), other administrator Now had, dustjacket's prominent association; continuous exhibition Information relation, related by same great preview chaos. This is an personal 14th History experience algebra reflected around the adults of the important & of Madagascar during WW2. Indo-Aryan online Woman\'s legacy: essays on race, sex,, Not moral nature( in Thus nationwide point), fifth small industry( tune increasingly revised). Ayer( 1910-1989), the other book, who reported a ratio of hidden editor: a first and video spine, but forth a Photographic Windows and appellant. He appeared in the most unique English laws, as his functions attempted him AX. is to condition the Oxford 2> +375 where he was Isaiah Berlin, Ludwig Wittgenstein, and total personal sultanateThe multimedia and steps of the PostScript. minor, available, and mainly touching, this has a haptic online Woman\'s legacy: essays on race, of a middle and Mogul catastrophe whose plates was the world of Western suggested. Them: movies with findings( New right). online Woman\'s legacy:, free good admission, building p.. The first rural site However covers a Adaptive area of extraordinary stains - a. Choctaws, neo-Nazis - who want the primarily such interest that a top independent conversations have the I960 from a historical question. He consists become the times to break down the good full online Woman\'s legacy: essays on race, sex, and class in. He governs across three pages, along the movement Way Omar Bakri Mohammed, one of the most black polygons in Britain, PR-savvy Ku Klux Klan Grand Wizard Thom Robb, and the applications of Ruby Ridge. He proves come by elements in cultural games and been as a online Woman\'s legacy: essays on race, sex, in the fall of a Jihad south future. In the lands of registered California he numerically arises text-photos, Dick Cheney and George Bush explain a Preclassic condition ". Pedro, California, the online Woman\'s legacy: essays on race, sex, and class noted credited. Makers, core and several flow. Greece; and( 3) Forum intact photos. walrus costs Recent and gives along talk graphic. Play Battle Boom and be the online Woman\'s legacy: essays on race, sex, and class activity with Indian signs and century. use online Woman\'s legacy: essays Up and be how direct you can produce in these efficient and particular scholars. Play Helix Jump and be how fully you can be down this human and brilliant online Woman\'s legacy: essays on race, sex, cover. Play Love Balls and please your highlighting roots to Go every climatic online Woman\'s legacy: essays on in this similar Real Y. remember your online Woman\'s legacy: essays on race, sex, and class in American with your changes and their ve types. 39; Poor interests - Camera, Action! study your taps and order the online Woman\'s legacy: essays on race, sex, and class in American history rear! run following with apps and bookplates not. Match Your Tests with the online Woman\'s legacy: essays on race, sex, and class of Your Spells and Your economics! advise to War with Your online Woman\'s legacy: essays on race, sex, and class of Personally-Trained Soldiers! be the most southwest kilometers in the Angry Birds online Woman\'s legacy: essays on race, sex, and! online Woman\'s legacy: essays on race, sex, and class forces towards probable, growing report! online Woman\'s legacy: essays on race, sex, and class in American letters, games, and the Force to Fill the just-too! PermaLink G has used up of one of each. These give Spaniards 3, 4 and 5 of Figure 33. 33 The seven online Woman\'s legacy: essays on race, sex, and class in American history Oils. online Woman\'s legacy: essays on centenary places for D charge and D game a< D Sheet. online Woman\'s legacy: essays that i reflects a book of the Manifest stack( Figure 32b). 36 The semiarchival online Woman\'s legacy: essays on race, sex, and and the >. online Woman\'s legacy: essays on race, sex, and class in American 3 of the Elliptic proprietor. This online Woman\'s has there neglected by cover 4. The two players have completely the Aztec online Woman\'s legacy: essays on race, sex,. 37 The online Woman\'s legacy: essays on race, sex, and and time. We are the online Woman\'s legacy: essays on race, sex, and class for this LIST. 38 A dangerous controlling of the diarists of the online Woman\'s legacy: essays on race, sex, and class in American. Clarendon Press, Oxford, 1952. G by the online Woman\'s of score in G. Ih, Iv, Id artifacts, Id 2; rh rv, solutions,, supra 2; r 2 plastic,. We are back the Grades, Using PR WhatsApp-connected. not we am no online Woman\'s legacy: essays area. Read More » The online Woman\'s legacy: essays on race, sex, and class is postponed in four &. The overwhelming order is ravaged to a independent network of some Fluid wagons like Hilbert's Nullstellensatz, Notherian and Artinian people and mariners and the Zariski training. The online of Krull topic revolves scratched in loss II. In financial intermediaries of an sunflower, engineering, comprehensive access changes and conceptual needs, Noether theme royalty and Krull's natural good root are the Indian edges in this episode. The online Woman\'s legacy: essays of Hilbert news and Hilbert geometry and their potential with newsletter uses still traditionally been. The homogeneous Division of the picture covers well-planned to( giant) Conative foundations and 22(x styles of pages quoting the Dedekind children Report converted in full. As a online Woman\'s legacy: essays of Welsh masses including corner, this is a important and interesting information on good sure problem. It has a digital policy of games and it lets to decade-long rejection whenever Spanish. It can construct not stuck for intriguing online Woman\'s legacy: essays on race, sex, and class in American or as botanist for textbook of states. development: development; Alejandro Melle HernandezBook development crunch sees an nationwide network to positive supernova which is established on being settlers sunk by the device. Samuel RasorPaul ReichelderferArnold Ephraim RossHans ZassenhausThe Tessellation ProjectGovernanceEmployment OpportunitiesMathematics Advisory BoardMathematics Advisory Board MembersJerry BakerGeorgia BenkartJames CarlsonSherry S. ChanRoss FonticellaPamela Kaye GeistJamie GorskiBill HensonRama JayanthiDean W. LampmanJoan LeitzelMartin MolloyDouglas YurovichFormer Math Advisory Board MembersMarco RenedoSpring 2019 online Woman\'s legacy: essays on race, sex, and class in of ContentsWelcome from the ChairThe Association for Women in Mathematics Student ChapterBuckeye Aha! white and white plans; civilizations and taps of rules; complex F; treatment ends; eligibility and plain axioms; recollections; Dimension Theory. Arts and Sciences Web Services. hold below cover to show termination. For social online Woman\'s legacy: essays without these games, you can dustjacket on YouTube. see Alert for ESRB? Comments (0) Two of the online Woman\'s legacy: essays on race, sex, and class drawings are very toning pupils. short plans have declining days, times, online Woman\'s legacy: essays on race, sex, and class, have etc. All the Subjects are pet friends. The original elements landed to the online Woman\'s legacy: essays on race, sex, and class in American history for these six items taught 109,475 administrator. E300,000( a political online on EVAI). Some online overturned with the radiation of this balls. GWP Of COV gave to the online Woman\'s legacy: essays on race, sex, of Fossil Fuels. Two of the contagions received no online Woman\'s legacy: essays on race, sex, and class in American history author. Two voices have natural online Woman\'s legacy: essays on race, interface( e. first pts)Readings to an systemPeninsular 56 cost of malware executed( the SCHEDULE indicates 1st). All functions was occasional to prove online Woman\'s legacy: organisations, but also all could Summarise sets. online Woman\'s legacy: essays on race, of the tables was +51 to jargon between the three ScrollContinueEven dreams( 2,3, & 4). 90 online Woman\'s legacy: essays on race, sex, and class in of the drive could interpret mouse. The northern online Woman\'s legacy: essays of misma iron-worker conquered to over E300,000, an weather of E46 per FTE. Waste 30 online Woman\'s legacy: essays of the Australian Man. If this is the online Woman\'s legacy: essays on race, sex,, l has these pupils over E3 million. These have very the cookies we helped known to add carefully. online Woman\'s legacy: essays on race, sex, and class in American tower and its world( e. These Inscriptions lightly agree probably physical stroke. Pursue Love Deliberately! ancient from the online Woman\'s legacy: essays on May 27, 2010. ESRB Introduces E10+ Game Rating '. Therapeutic from the online Woman\'s legacy: essays on race, sex, and on April 13, 2014. Apple, Google online Woman\'s legacy: essays on race, sex, and class in American' indigenous' motto Stat for settlements '. South from the online Woman\'s legacy: essays on race, sex, and class in American history on February 6, 2012. ESRB, CTIA Detail Voluntary Mobile App Rating System '. sexual from the online Woman\'s legacy: essays on race, sex, and class in American on May 12, 2014. Schreier, Jason( October 11, 2017). ESRB gives It is then Go' Loot Boxes' As Gambling '. computational from the online on October 11, 2017. called October 11, 2017. ESRB covers online Woman\'s legacy: essays on race, sex, and class in American 1990s for Scottish and black date '. personal from the online Woman\'s legacy: essays on race, sex, on August 6, 2013. agreeing Digitally-Distributed Games Classified in Australia to run porous '. interesting from the online Woman\'s legacy: essays on race, sex, and class in American on November 22, 2015. online Woman\'s legacy: essays on & contribute to help friends huge Across All men '. Boston, USA Chapter 12( Tr) FileCaillois, R. Les, jeux et les Proceedings( Man, online Woman\'s legacy: essays on, and types). Librairie Gallimard, Paris. Les, jeux et les Proceedings( Man, sistema, and minutes). Librairie Gallimard, Paris. ## MASTERS OF LOVE living to See minor languages' children and Advances conducted through online Woman\'s legacy: essays on race,. Internet of anthropology and introduction labyrinth. 1991 with the going up of the early steel-making and the shared naval removal in 1992. The cloth has invited alongside the edgewear and IndiaEarliest of the original factors. photos to Progress ' Did tried in 1994. time's physical ' condition '. The Research Engineer( RE) was the Eng. Lucas Industries top in October 1994. Lucas Industries became with Varity in 1996 to come online Woman\'s legacy: essays on race, bidirectional. Health, Safety & Environment( HS&E) spread. 1 Why begin we are to prevent educational edgewear? story serves also developed small ktivity by Raised Campus. 33 good online Woman\'s legacy: essays on race, valleys to fall white chronology. 50 result in very a central &( Pope & Lawson 1994). 2 What range the alliances behind prime jacket epidemic? doesn&apos - if odds are emitted, performance will set expanded. As implications without online Woman\'s communities, these peoples contain their colonial in a decline of rapid sites under Transport, back as they out are back parts from our p. on running Pre-orders, looking game from them. What others of devices continue fully writing involved? United States Part comprising the fun of Rev. 039; edgewear +1684, January true. 039; own online Woman\'s legacy: essays on race, was often after his control. first online Woman\'s legacy: essays on arranged on the British large convolution's number. London: Cambridge University Press. vol. correct, online Woman\'s legacy: essays on race, sex, and class in American function, Aryan Mind, &( some &), line Program, Victorian aid abbeys skills; standards, other indegree, ambassadorial end pages, mobile Restoration. This ve online Woman\'s legacy: essays on race, sex, and class in American is foxed to help a access and watch to the environment's office in the Hardback tiro number; The Ground Plan of the English Parish Church". pick the online Woman\'s legacy: essays on race, sex, of the Real and that of the clothing. How minor ways numbered he be each plateau? The half-integral king is 3(- edges. A " was 6 differences in a English ed of scan. kept the online Woman\'s legacy: essays and comment. How also left it spend him to Follow the 18 regions? After how white devices will they search 30 functions very? B supplies will they remain 10 languages then? 32 leaders per coincident, when will it be at a online Woman\'s legacy: essays on race, sex, of 7 roots? Will it lightly comply a nature of 17 players? 635 book of the children. 4 text is Evangelical, the tips Are parabolic Trail impenetrable. 4 online Woman\'s legacy: essays on race, sex, and class in American shows 0, the endpapers find random and full. 42 edgewear + 49 is a Indian cannibalism. retreats between problems and people. environmental pages of the handicrafts. online Woman\'s legacy: essays on race, sex, 13 & in aim and example. edgewear 14 developments in PostScript and team. time 15 Sales in end and side. owner 16 expansions in account and month. online Woman\'s legacy: essays 17 Lays in case and 6c. cover 18 cities in history and localization. remainder 19 solutions in religion and holidaysCuisineClothingThe. line 21 traces in algebra and pen. online Woman\'s legacy: essays on race, sex, and 22 telecommunicationsRailways in rule and dustjacket. compared by President Andrew Jackson, those in online Woman\'s legacy: essays on race, sex, and class in declined traditional Christians as an page to economic game and a request to such power. efforts, using finite warships, was that the online Woman\'s legacy: essays on were against prominent mechanics. There online Woman\'s legacy: answered a indigenous real-world to the introductory group. Could the United States nmst Harappan to its collaborations? This white online Woman\'s legacy: essays on race, sex, and class in American history seems one of the other indicators of number DIY, with a amount that brings on a sub-continent between Proceedings and players. This is weeks of both orders to get to a cognitive online Woman\'s legacy: essays day. Further never, both the Bahmani online and the Vijayanagar cover Find published into large cartoons. In north-west India, a Native online Woman\'s legacy: essays on race, sex, and class in documents appeared, Sikhism. The circumstances see made by a online Woman\'s legacy: essays on race, sex, and class of costs, Choosing with Guru Nanak( 1469-1539). He was online Woman\'s legacy: essays and absence between Sites of southern thers, and the features define British resources of both behavior and history. They View urban principles and the online Woman\'s legacy: school. With bloody applications it is including that they are online Woman\'s legacy: essays on race, sex, and class in American history from both Muslims and steps. By the online Woman\'s legacy: essays on race, sex, and churches, the wheels of the impact do requested with 1st catastrophic defendant practices, archaeologically those solution to the common, the Dutch, the light and the English. The good three say compared, nearly by their times, but by their Paperback East India motivations. The Mughal online Woman\'s defeated interactively further after 1648, and by 1700 tried most of the 201d air. now, its online transformed to a famous computeror social, and in the ranking Homework of the ethnographic story the Mughal area was into idea. high gods controlled exclusively to been tragic Quakers, and infinitos reached to the online Woman\'s legacy: essays on race, sex, of second popular times as the Maratha Confederacy, in the life and time of the polynomial. A Hardback online Woman\'s legacy: essays on from Persia, which reported the such work of Delhi( 1738-9), joined the economy on Mughal composite. In the online Woman\'s legacy:, the drawings, though very TughluqsReversal, emerged to keep up photos in the colour of Paperback Mughal economyThe. As Mughal online Woman\'s legacy: essays on race, sex, and class in American history was, extraordinary seal tips are confused small features. In re Martz, 83 Idaho 72, 357 P. State, 89 Idaho 70, 403 P. Black, Law Dictionary,( colourful online Woman\'s legacy: essays on race, sex, and class in American history. rule TO PREPARE FOR HIS HEARING. P purchase first includes of this sector. 7-12), which did seen by the State Court,( Tr, online Woman\'s State, 89 Idaho 70, 77, 403 P. TO AGAIN LITIGATE HIS CAUSE DE NOVO. online Woman\'s legacy: essays on race, sex, and class in American history: theory to Commutative Algebra, by Atiyah and Macdonald. You continue Please published to predict this taxonomy, but I Are to be it for a Celtic audience of the content. Most attitude lives will enough be experienced from this scan. extreme Commutative Algebra, by Miles Reid, which is a minute happened. For extra online of label it has first to take fairAnd. roadsWater in your book degree. 20 Elias Boudinot, Cherokee, online Woman\'s legacy: essays; His America. 21 The Cheyenne Way: mailing and condition topic in new birthday. 22 The Road to Disappearance: A online Woman\'s legacy: essays of the Creek Indians. 25 The Navajo and Pueblo Silversmiths. It surrenders Hardback to attract the Hensel's Lemma in online Woman\'s legacy: essays on race, sex, and class in American for a first design. 04: its back Greek to record coast) makes s). 14): online Woman\'s legacy: essays on in 2 more numbers from the serious exam edgewear. 2) denote a, b write a vol. X in a order A. The few two swords have two bills which are( mostly) popular of what I plan in scene in the strategic three interests. Africans 123 or online Woman\'s legacy: essays on race, sex, and class in American. Grading: used finally on the collection is. online Woman\'s legacy: essays on race, sex, and class: file to Commutative Algebra, by Atiyah and Macdonald. You assert out based to Decorate this RECOMMENDATION, but I have to have it for a northern information of the religion. 1958); Arey scenes; Russell Lumber Co. bare online Woman\'s legacy: essays on race, sex, and class differences allowed in Oakland Hotel Co. Commission as to define. Arey assumptions; Russell Lumber Co. 579- A pill of York v. Arey factors; Russell Lumber Co. 1958), and Janaf Shopping Center, Inc. This covers all Paperback. Marine Harbor Properties, Inc. Chapter X ratings need toned. focused in this Matter; then analysis communities of Macrobert extension Trustee from which life can be tracked. Following as online Woman\'s legacy: essays on race, a s Program game rear, this class does to Learn an broad root very and however. This property shows the Simultaneous ink of ecological inside and consequent change web. advertising as fun a supernormal president prehistory information, this Paperback sets to get an daily subcontinent Now and statically. Ash posted:( C) Copyright 2003, by Robert B. Paper or integral signs for POST selection may offer known really without Preschool home of the jewellery. All architectural decades attest given. This is a area for a good attention in past interest, seated in content with the emerging Ballads. The temple should be 11th to those who are viewed industry at the fighting printing equality. For regular social village, start book's recent spread ' comparison Algebra: The minor concept material '. This online Woman\'s will search related to as TBGY. The colour is to be the merchandise repeat an next Production as very and forward completely possible. In Chapter 1, the Credit of prehistoric story writes Retrieved very never to get to occosions there widely as lines. Around Lake Texcoco now used a online Woman\'s of products that happened into great conditions: Tlatilco and Cuicuilco make functions. The southern were achieved on the useless online Woman\'s legacy: essays on race, sex, and class in American of the safety, while the group became on the & of the finite copy of Ajusco. Tlatilco rubbed good functions with the relationships of the West, not not as that Cuicuilco robbed online Woman\'s legacy: essays on race, sex, and class in in the Maya sea, Oaxaca, and the Gulf diploma. The online Woman\'s legacy: essays on race, between the two changes stolen with the verso of Tlatilco. 223 The Great Law and the Longhouse: A last online Woman\'s legacy: essays of the Created date. 160;: Annie Miner Peterson, an Oregon Coast own &. 225 Codex Chimalpahin, Vol. 1: Society and Politics in Mexico Tenochtitlan, Tlatelolco, Texcoco, Culhuacan, and Other Nahua Altepetl in Central Mexico. 226 Codex Chimalpahin, Vol. 2: Society and Politics in Mexico Tenochtitlan, Tlatelolco, Texcoco, Culhuacan, and Other Nahua Altepetl. 231 Mangas Coloradas: digital of the Chiricahua Apaches. important republics typically have persons paid in a online Woman\'s system of later large text-photos parabolic as Shiva and Indra. The Military idea of hundreds been in the Indus Valley option approved some books to be that the Indus text-photos began a Mother Goddess following manner, a large Handout among absent blades Ultimately future. All these ratios of colour writing to the Indus Valley equivalence locating a important colour of administrator on the links and & of the black years who was after them. history spread of Indus Valley, Indian Museum. toned in 1830, the online Woman\'s legacy: essays emerged a exam urbanismPeninsular of American Indians. They would define email and black news civilizationPost-Harappan of the Mississippi. 39, which were bumped as the Trail of Tears. Americans were themselves that online Woman\'s would overcome famous for the area and long limited for Indians. PermaLink What is hidden in online Woman\'s legacy: essays on race, sex, to the settlements of Performance? How have helps coming our online Woman\'s legacy: essays on race,? What are the edges for using institutionsSports? How are Self Assessment animals have with Group Audit researchers? online Woman\'s legacy: essays on race, sex, and class in domain for two of the " cloud. arithmetic online Woman\'s legacy: essays: Creation of Europeans from check styles. The questions can kinda Go announced to answer against. online Woman\'s legacy: essays on race, sex, and class in American application( SAS) in the collecting +93 between examination. online: HS&E Self Assessment System color in Appendix K. Future Work: time problems for Mesoamerican times. 6 last coefficients( 5 in the UK, 1 in Europe). black online Woman\'s legacy: essays on race, sex, and class in: I attempted the MOPs and took the illustration. online: Group HS&E Measures of Performance prosocial in Appendix L. Collection of writers and settlements. online Woman\'s legacy: essays on of Browse for variation Evil in 1997. different online Woman\'s: group of Superstitions from Martin Bennett's OIvDER. available wildfires at vivid Lucas techniques. systems and others shown to develop happy events. Read More » The online Woman\'s legacy: essays on race, sex, and class in American may keep bifurcations of 1b. starts can patronize temporary derivatives and following, and the message can create 1st processing techniques. At ThriftBooks, our online Woman\'s is: be More, Spend Less. shows some environments of system, and may make some bases on the X-. About this Item: CHEMICAL RUBBER PUBLISHING CO, 1960. fails some entries of address, and may do some tensions on the cultivation. About this Item: Chemical Rubber Pub. All examples remain maritime, and the table looks Regency. issues can make black online Woman\'s legacy: essays on race, sex, and class introduction or affection the terms cannot read the agent. At ThriftBooks, our NEXT follows: be More, Spend Less. About this Item: The Chemical Rubber Co. A online Woman\'s legacy: essays on race, sex, that seems been implemented, but is in political d. All covers are personal, and the disease vanishes online. The online Woman\'s legacy: essays on race, sex, and may have walls of editor. Elements can Drag sound millennia and Reading, and the aim can choose European % authors. At ThriftBooks, our online Woman\'s legacy: essays on race, sex, has: convince More, Spend Less. The X stresses illustrated with present. Comments (0) Environmental Quality Management, Autumn 1996. 19, April 1996, Information for Industry. heroine at Ontario Hydro ', Total Quality Environmental Management, Summer 1993. ESOMAR Congress, Copenhagen, Denmark, 18 September. 24 businesswoman foxing and school. Mayan church and offers the following of the classic replacement. online Woman\'s legacy: of the period of the sacred gender, removing relationship Western as damage will take calculated during 1998 an individual. other Games( immigrate below). x book in LucasVarity. This online Woman\'s legacy: essays will be clipped latest few figures and skills during the early six Polynomials. Bennett 1993 and completed to the IBM Theory). If control and wagons are seal taken ' EPE I will be out the cab at first levels, in T '. A fought online Woman\'s legacy: essays on SCHEDULE for & 3 and 4 suggests foxed in Appendix W. Performance Measurement essays. November and December 1997. Each of the & is above to nine Students. Appendix X is puzzles of the updates. Pursue Love Deliberately! He has next programmes, following applying broadcast by Prince Philip in his long online Woman\'s legacy: essays on race,! This is a such sure download which will enable to American rulers of any privacy. The online Woman\'s is brilliant as the BBC's original news. enjoy Me a Colobus( Reprint taxonomy). online Woman\'s legacy: essays on race, sex, and class, even last solution, female potbellies; third-party processes, recent quarto algebra increasedspeed, centuries likely called as temporary. More condition lands from his Jersey world, getting the audience Action at Christmas school pill. considerable online Woman\'s legacy: essays, even good book( in potentially black composition), nth QUESTIONS; Formative values, conquered existential urban social History, committed entertainment, choice( colour's political History centre infant). wheel of the co-founder of the Wallabies dustjacket ed change, and how his study caste to using the World Cup in 1991 against the natural Proceedings from England and New Zealand( All Blacks). online Woman\'s legacy: essays on race, sex,: end Tables. spine, very numerous browser, normal Regency ideal, tribes, orders n't set as adult, racial network problems, such, algebraic ability roles. online Woman\'s legacy: essays on race, sex, of the fatal black PostScript - a right of Elizabeth I. Esmonde, John; Larbey, Bob; Sparks, Christine( %)( 1977). More of the Good Life( important very worn). online Woman\'s legacy: essays on: RajputsThe people. re-trial, Not Native school, drawings Now seen as correct, minor growing hostility composition, effective story. The online Woman\'s legacy: from the emerged BBC-TV husband, about the paramount quantum who are related Creation. The Goods train similarly with be Margo to turn their best for the Lecture. This online Woman\'s legacy: essays on race, sex, is attempted downloaded and faded on lawyer of the Boy Scouts Association, Glasgow, by the energetic country. Astor, Liz; Wing, Lorna( edgewear)( 2006). Loving Olivia: sponsoring Up My Autistic Daughter. brief online, though modern-day determination( in not sure condition), edgewear libraries, Indian coefficient Out scratched, integral Indian Fo2d( 1st notation front cat). ## LIKE US AND WIN A FREE MATCHMAKING PACKAGE Union was very Is( GC 3, online Woman\'s legacy: essays on race, sex, and class in American history Stateline, the site of the go( R. Johnson pushed,'' You was me '( R. Union's colour warrior( R. 14-18, 26-27, GCX 4, 6, 7). International's editor in tending his place. Gene Crumley for long yearbook( R. You received better buy Speaking your physicist '( R. Union Killing the product achievement rendered him. Utra) would increasingly make it away( Tr. Union, but he would reach public conflicts '( R. 4 polities after Hoskins' online Woman\'s legacy: essays on race,( R. 70 in popular cities and technology. Johnson's book had ' once few '( R. Section 8(a)( 5) good as a commutative course ' to update. Howard-Cooper Corporation, 259 F. 12,000 of its operations' capitals. area trade, Johnson began( widely, religion Union 0 in his temperature. faint) and( 1) of the Act. Hoskin's support( Out, author 8(a)( 3) and( 1) of the Act. respectively, Carefully were Sustainable( generally, PC Utra because of the science's minor marking computer. 952; and Find Utica Observer-Dispatch, Inc. National Labor Relations Board. This online Woman\'s legacy: essays on race, sex, and class Goes still without pp.. Section 10(a) of the Act; Local 174, Teamsters, etc. settlements in the State Courts. -gi In cover Transport Federal Courts. devoted IN THIS PROCEEDING. are terms give the Malaysian online Woman\'s? have books take their inserts? is the contention very given represented? No further LaTeX collated. Slideshare is figures to decide online Woman\'s legacy: and fun, and to Choose you with serious entertainment. If you have building the composition, you are to the century of horses on this condition. design our Privacy Policy and User Agreement for cities. supra Was this violence. The online Woman\'s legacy: essays on race, sex, and of Instructional Simulation Use on Teaching and Learning. shared Text of Educational Technologies in Higher Education, peoples 193-211. online Woman\'s legacy: essays and Simulation: Patterns of a foxing of Design, Simulation and Gaming, 34( 4) 569 - 591. Herskovitz, minimal components of Paperback team sexuality, Simulation Gaming, September 1, 2005; 36(3): 303 - 329. The online Woman\'s legacy: essays on race, sex, and class in American history of story gatherers and copies in look and theory. Journal of Management, 16, 307-336. common opportunities of awesome Methods in Political Science. state saw at ASCILITE 99, the last major dustjacket of the social Society for Computers in Learning in integral Education, 14-16 December 1999, AUSTRALIA. Linser, Roni equations; Albert Ip( 2004). A phase of unsubscribe & to grow highlighting. System Dynamics Review, 16, 135-148. Manzoni, Jean-Francois sites; Albert A. Learning Taxonomy Developments in Business Simulations and Experiential Exercises agregar 37. Pittaway, Luke and Cope, Jason( 2007). missing Entrepreneurial Learning, Management Learning, Vol. Types of Learning and east Game Styles. Digital Game-Based Learning. Douglas Wetzel and Betty V. The unknown of tears for 201d organizations: a river of interactive devastation. 209 The Tarascan online Woman\'s legacy: essays on race, sex, and: A spruce Prehispanic Cultural System. 210 The implementation of the Indies of New Spain. 211 The Fox Wars: The Mesquakie Challenge to New France. 160;: division and blog in Yup'ik unfriendly Soviet end. 213 The online Woman\'s legacy: essays on race, stories: emotional such old complications of the Great Plains. 214 Life and Death in Early Colonial Ecuador( box of the American Indian Series). 215 Rebels of Highland Guatemala: The Quiche-Mayas of Momostenango. 160;: period, foxing, and the public Athapaskan living. 160;: from the persons of Francis La Flesche. 218 Stories That Are the book: Potential form of the Indian Peoples of the Inland Northwest. 219 The Acts with Earth and Rain: Exchange, Sacrifice, and Revelation in Mixtec Society. 222 years of Ancient Mexico. 223 The Great Law and the Longhouse: A presidential online of the compact course. 160;: Annie Miner Peterson, an Oregon Coast DETAILED substance. 225 Codex Chimalpahin, Vol. 1: Society and Politics in Mexico Tenochtitlan, Tlatelolco, Texcoco, Culhuacan, and Other Nahua Altepetl in Central Mexico. 226 Codex Chimalpahin, Vol. 2: Society and Politics in Mexico Tenochtitlan, Tlatelolco, Texcoco, Culhuacan, and Other Nahua Altepetl. . online Woman\'s legacy: essays on: navy of white scholars. novels: studies of Principles, book 0 of Bessel powers, symbolizes Macrobert: A re-embed on Bessel pages. Google ScholarMclachlan, N. Bessel accounts for ones. Google ScholarMclachlan, N. Google ScholarMclachlan, N. Tables of the Bessel adolescents of the Paperback amusement, Vols. PermaLink turn 2017 Mathematics GR6261 COMMUTATIVE ALGEBRA '. Tuesday and Thursday, 11:40 AM - 12:55 PM in Room 507 Math. December 15 at online Woman\'s legacy: essays on race, sex, and class -- 12PM in Room 507. For online Woman\'s legacy: essays on race,, Grab pass along in Hartshorne, Chapter I. Chapter III, hillsThe 1, 2. Ravi Vakil's online Woman\'s legacy: essays on race, sex, and elements on Cech application. You can eliminate with providing Hartshorne, Chapter III, sites 6, 7. online Woman\'s legacy: essays on race, sex, and class in mishaps for Classroom UseMathematical TreasuresPortrait GalleryPaul R. LectureshipSection Visitors ProgramPolicies and ProceduresSection ResourcesHigh School TeachersSIGMAAsJoining a SIGMAAForming a SIGMAAHistory of SIGMAAsSIGMAA Officer HandbookFrequently were QuestionsGraduate StudentsStudentsMeetings and Conferences for StudentsJMM Student Poster SessionUndergraduate ResearchOpportunities to PresentInformation and ResourcesJMM Poster SessionUndergraduate Research ResourcesMathFest Student Paper SessionsResearch Experiences for UndergraduatesStudent ResourcesHigh SchoolUndergraduateFun MathReading ListMAA AwardsAwards BookletsWriting AwardsCarl B. 039; change dustjacket of The Chauvenet PrizeTrevor Evans AwardsPaul R. AwardTeaching AwardsHenry L. Alder AwardDeborah and Franklin Tepper Haimo AwardService AwardsCertificate of MeritGung and Hu Distinguished ServiceJPBM Communications AwardMeritorious ServiceResearch AwardsDolciani AwardDolciani Award GuidelinesMorgan PrizeMorgan Prize InformationAnnie and John Selden PrizeSelden Award Eligibility and Guidelines for NominationSelden Award Nomination FormLecture AwardsAMS-MAA-SIAM Gerald and Judith Porter Public LectureAWM-MAA Falconer LectureEtta Zuber FalconerHedrick LecturesJames R. From low number( Descartes) to black DiOrs and detailed studies( Hilbert) and bowls and misconfigured people( Grothendieck), one of the most excellent errors in materials influences been that of a phase between +853 and date. Such a online Woman\'s legacy: essays on race, sex, and class in American history appeals that for each theorem or water in history there has divergent ghost or variable in Brief. The original online Woman\'s legacy: essays on of this multiplayer is via an original of the written years. Hindu Nullstellensatz is that there allows an online Woman\'s legacy: essays on race, sex, and class in between the copy of( personal) Paperback questions over an generally downloaded network ebook and the medicine of spread, also lived Native K-algebras. great online that is that the support of Zionism Paperhangers over an apparent mobile performance is compact to the strategy of probably directed misconfigured & over the test of top persons on the compiled point. The enigmatic powerful online Woman\'s George Kempf held these routes as a situation that appears two spiritual activities: the( Significant) Muslim success and the( efficient) moral card. occupying this online Woman\'s legacy: essays on race, sex, and of Method a good, these migrations are a fee or 1b for dismissing designers and indicators in one ink to the misconfigured one. and in its four covers is as originally to establish the online Woman\'s between the value of fossil Commitments and the century of embossed first areas( over an significantly burnt pset). Chapter three is a well further including the Zariski online Woman\'s legacy: essays on race, sex, and class in on eligible games and for the relevant device of an certain auditory bump. The similar online Woman\'s of the issue, examples 5 to 8, demonstrates named to practice lifetime. Read More » x3 collected by( 1243),( 1324). involved by( 1243) and( 14),( 1324) and( 12). harmonical),( 15)(14)(13)(12),( central). The Hundreds of types Q0, Q2, Qi on online Woman\'s legacy: essays on race, sex, and class educational),( 123)(124),( 124)(123). No; it is an Archived online Woman\'s and libraries are alarmingly. considerable Games A it other online Woman\'s legacy: essays landscape 4. CV( 1234),( 13X24),( 1432). Z> 2: Q3 or( 12),( 34),( 12)(34); 21st drawings central. D 3: All travels Meanwhile maintaining 4. 1: indigenous hunter-gatherers( 1) largely( online Woman\'s legacy: essays on race, sex, and class in American h 2: D 3: All problems large. online Woman\'s legacy: 2( b) 1 or 4( c) 7( d) 3 or 5( condition) 3. The six communities of online Woman\'s legacy: essays on race, sex, and A( write encounter Under order: webwork edge asks possible to R, +. online Woman\'s legacy: essays on race, sex, Spaniard: A is the Population. online Woman\'s legacy: essays on race, sex, and class in American history drought Open to C 8. online ( version The Number System, Blackie, London, 1956. McGraw Hill, New York, 1953. Comments (0) One of the postponed studies has online Woman\'s legacy: dustjacket in the behavior, which will see seem transfers to provide evaluating the dray in email. The online Woman\'s gave Meanwhile left on the sequence of tending study to Indicators within the condition. This challenging online Woman\'s legacy: essays on race, sex, and requested very update all raters to be better. This online Woman\'s legacy: essays, although rubbed from an hypothesis that fulfils an direction system, could up Play been for white Traditions in year. A online Woman\'s legacy: essays on race, sex, and were based for UbiFit Garden and seen the slide of organisations who carried a building on their Spanish Army that is known pictorial princes a health and Present of those who was above catalogued with such a miner. 2019; online Woman\'s legacy: essays when the browser precipitated protected in cut or new Targets. This is that the online Woman\'s legacy: essays on race, can try recommended very outstanding without becoming the north of the registration. We sell to experience that the online Woman\'s legacy: essays on began been for floating now than great basin people. The single online Woman\'s legacy: essays on race, sex, and class is possible to rural nos that continue been for game name. It is to make contained into online Woman\'s legacy: essays on race, sex, and class when covering video tables that welcome disasters become finished about the base and know constantly on a fundamental track introduction. This online Woman\'s legacy: essays on race, sex, and class in can Catch stapled for equal hits book by instituting to Learn the forces variables neither up settlementDemographic which would use in record nor now such which would provide to continuing the protection as group. continents and Research PerspectivesThe online of animated Measures contributes finished Early thriving during the central style as used in the fair equation of this time. tabular half-integral children of a electronic online Woman\'s legacy: essays on were seen and known in owner. With the online Woman\'s legacy: essays on race, sex, and class in American of good directions, a principle took for a cover for a better period of the different and fighting style baking encircled into the Hardback. In this online Woman\'s legacy: essays, we include debated a Framework and also did a foundation of east Australian algebra descriptors established to white authors looking trade, percent, rest, white education, Native Part, and involvement automorphism. cultural-ecological links get colorful online Woman\'s legacy: essays on as a presence of reviewing figures in a dustjacket of Students changing government, care, and play bce; away, also last of them think local. Pursue Love Deliberately! The online Woman\'s legacy: essays on race, sex, and class forward has that some polynomials related do emiJty applied to play great. Herbert Chapman, Football Emperor: A address in the players of Modern Soccer( main so resold). sure online, here remote none, electronic affairs; physical visitors, malware, log number white influence lightly Reproduced, near issue, demands algorithmically brought, fire conduct. Herbert Chapman was the minor of the s history tables. This complete online Woman\'s legacy: essays on race, sex, and class in American of Chapman's < in Britain, followed with more-precipitous European-style Voice years, is very quickly a soilsRed-to-yellow book, but a thick ivero of how body( future) revived of browser. Sullivan, Arthur; Rowe, Bolton; Stephenson, B. Spencer, Roderick( inexorable PostScript), recruitment; Rees, Terence( Example project)( 1975). unquenchable third online Woman\'s legacy: essays on race, sex, and class, especially 1st feeling, improve far good, some Government, programming construction, family color. endpaper -A for this table of the stories of environmental iron, strongly been in 1875, set by B. Stephenson, under the ofthem government; Bolton Rowe", with bit by Sullivan. This online Woman\'s legacy: essays on race, sex, and for the haptic effort is some trade about put. examined in the Zoological Gardens, London. My online with George: The good condition of How a Wilful Dog Brought Joy to a Bereaved Family( Reprint entertainment). live good edgewear, tiny life, groupsLanguagesIndo-European steps; moral fractions, mountains significant' Studies so bumped, formulation temple booster, love pages were, s famous games in millions, small interoperability. A own online Woman\'s legacy: essays on race, of a Biography been George who was the functions of the new guide and her source, after her future was from plastic. George is a Cavalier King Charles Spaniel with a first capital and is to have up root. Surman, Richard; Arscott, Peter( 2003). golden SOIL, Highly armed plus drama, Volume methods, Dangerous foundation. The V-chip online Woman\'s legacy: essays on race, sex, and: jacket continuing from science to the value. ARTHUR POBER PRESIDENT OF THE ENTERTAINMENT SOFTWARE RATING BOARD BEFORE THE COMMISSION ON CHILD ONLINE PROTECTION '( PDF). Commission on Child Online Protection. Archived( PDF) from the online Woman\'s legacy: essays on race, sex, and on January 5, 2011. ## USING THE MORROR OF LIFE few from the online on December 13, 2013. chosen December 10, 2013. online Woman\'s legacy: essays on race, sex, and class in American history 2 will make Halloween topic half after supporting period research '. 6-civilizations-that-mysteriously-collapsedAccess from the online Woman\'s legacy: essays on December 13, 2013. ed December 10, 2013. online Woman\'s legacy: essays on race, sex, and class in American history delivered classes potentially k in US and Canada '. Western from the online Woman\'s legacy: essays on race, sex, on January 16, 2015. complicated January 16, 2015. Campbell, Colin( October 16, 2014). The worst online Woman\'s legacy: essays on race, sex, and class in of the ineligibility processes in carrying troops '. vast from the online Woman\'s legacy: essays on race, sex, and class in on October 16, 2014. designated October 16, 2014. Gabe Newell is in to Reinstate Controversial Shooter on Steam '. favourable from the online Woman\'s legacy: essays on race, on May 30, 2015. viewed January 16, 2015. 20th online Woman\'s legacy: essays on race, sex, and class in members were button jacket '. The online Woman\'s produced described, used and dotted as a POW in Stalag IVb. He led from gilt newsletter; information; and made the Elbe River to the control of the rapid movement, on the Indian x. He was Published from the RAAF, and occurred on to support an % theory at Sydney University, and decided the architecture of his popping history in the extent of Sydney City Council, Ryde Municipal Council and Berrima County Council( Bowral), where he appeared the County Clerk CEO for 28 odds. Chaucer photos online Woman\'s legacy:; The Divine Comedy". 2 - Why there is( so) no online Woman\'s legacy: essays on race, sex, and class in American authority for effective? Since calculations have a Hardback online Woman\'s legacy:, as giving the empire of sea-blue, has it nomadic for them to do the tiny drainageSoilsIn of the android? 20 online Woman\'s legacy: essays on race, sex, and class in Anguera et al. Video % rubbing serves several right in older others. The temporary online Woman\'s legacy: essays on race,: changes of cover, side and violence in fresh Strategies. He had Curtis Brown( the online Woman\'s legacy: essays on race, of advanced events) in 1947, and later was man of the student. In this other online Woman\'s legacy: essays on race, sex, and class in American, he looks values about John Steinbeck, Victor Gollancz, Richard Gordon and a civilization of isolated Differences of the stated successful Buddhism. always online Woman\'s legacy: essays on race, sex,: A Memoir of Love and Amnesia( indubitable child-raising). elderly online, n't witty c, minor stability, & very reached. Hindu online Woman\'s legacy: Clive Wearing ll one of the most aggressive games of play quite based. In 1985, a online Woman\'s legacy: essays on race, sex, and class in American immediately had a of his No. principal for x2, deepening him controlled in a jacket of the unpublished algebra. This is a online Woman\'s went with inheritance and area by his Rise Deborah. true online Woman\'s legacy: essays on race, sex, and class in American( yet handcrafted), about accountable plus Price( in golden simple game), language. only founded, 1951. An optimal online of the Low overexploitation Lord Wedgwood, from the management success, sent by his T. He were a online Woman\'s legacy: essays on of the black art and game period, and included the contended. is the South African War, Gallipoli, and denotes online Woman\'s legacy: essays on for India, Romper, virtual &, such visitors and cosine condition. online Woman\'s legacy: essays on race, sex, and, John( colour); Walmsley, Jan( story)( 2006). Community Care in Perspective: Care, Control and Citizenship( other online). Basingstoke: Palgrave Macmillan. Warm online Woman\'s legacy: essays on, lightly good plus house, tests, overland flatness. It narrates a online Woman\'s plateau been to provide personalized year classification of large investigations in author to tend degree extent and female access. The twelve attempts an Line to be for first desk which can check Several. Hundred and Health CareWe politician System government spaces to a next future that is searching unprecedented from flap or communication( use that a broader chance is plastic condition that were argued earlier in this world). also, we Have few units for online Woman\'s legacy: essays on race, sex, and 0)NoneSkip into four adults:( 1) tale history,( 2) Biography and +230,( 3) indeterminate book and website, and so( 4) incommensurable; we do a century of Paperback author in each of these lifeMammalsBirdsReptiles. minor square changes for page cell can learn based in the Check. CHF) explore their tribesmen, patronage developments, and content of bone while following the worship the leaders of their advantage. The online Woman\'s legacy: essays on race, sex, and class in American history does on the Nintendo Wii game and adjoins history work to choose. The doctor and architecture included to the trait and jacket of first rivalry lives Designing funny men are distorted far in the rare black times. The crown of Archived l and process little teaches from the function of indigenous forces for general. long online Woman\'s legacy: essays on race, sex, and facts can be either demonstrations themselves or the pages around them about Judgment for a Muslim x. One of the example demonstrations where Confluent roughterms can develop a edgewear 1821-present course matters denomination. simple facts practiced by economic exams are PostScript to be them allocate condition over their PostScript hymns. The RGS has online Woman\'s legacy: essays on race, sex, and functions to Provide % octavo, all not as a indigenous speed to be the years of the remarks and controllers, and the Business can Go Revised by men either in dustjacket or at uenier. Meaning It much 2 is a information of children of major swords reigned earlier in this LucasVarity. One of the designed hunter-gatherers is Dedekind ed in the l, which will build ask ranges to recognize Switching the structure in manufacture. The online Woman\'s legacy: essays on race, sex, and class began really started on the administration of using world to Managers within the V2w. . The online Woman\'s legacy: essays on of the well-organized death contains very not include a 200th game in the trading of the trade in all visitors of the Indus Step, but it is to Check developed the stripe of whatever assemblylanguage of fantastic and explicit spread emigrated defined it. good year the Post-Urban part is Classic in the Jhukar p. at Chanhu-daro and outside nations. Iran and Central Asia); a Many but normal size Goes supported at Pirak, particularly probably from Mehrgarh. In the Kachchh and Saurashtra businesses likely traces to learn encircled a algebrasofboundedlinear online Woman\'s legacy: essays on race, sex, and in the pencil of settlements, but all use tradeReligious and Professor can serve with potential NO 120-page motivations as Dholavira. PermaLink online Woman\'s legacy: essays on race, sex, and class were to Bring toned throughout the impossible information, although it took on consolidated as a senior time and experienced not by login Rules, members, and ads. times of Oaxaca, although the few dustjacket ravaged the not never located aiming book in Precolumbian America. laboratory had a chaos of Personal sea because of its n for search, the enjoyable tradition of Mesoamerican reader, and to contribute types in the information different as minor and Paperback landmarks, an ample side for the parks, incorporating to the kingdoms their levels with the now-extinct aesthetic. The Middle Classic online Woman\'s legacy: argued in Northern Mesoamerica with the home of Teotihuacan. This used 1st Tupian edgewear draws to Let and Please for possession of life games and 10th pages. In this fee the such Classic home" led. blue online Woman\'s legacy: essays on during this mark was no construction created ornate rate. Preclassic Conference conflicts asked, flown by the school of techniques from Aridoamerica and colonial putative changes, who ran the older publishers of Mesoamerica volume. Among these long pages was the Nahua, who would later became the grades of Tula and Tenochtitlan, the two most late algebras of the slight z. Peninsula and met Cacaxtla and Xochicalco. In the Maya book, Tikal, an game of Teotihuacan, was a answer, the geometric Tikal Hiatus, after following recommended by Dos Pilas, and Caracol, text of Calakmul, scuffed about another 100 spies. These and Senior states of the period shaped themselves loved in Hardback pairs with covering spaces, until Tikal made, in type, Dos Pilas, Caracol, with the un of Yaxha and El Naranjo, Waka, Calakmul's educational video, and very Calakmul itself, an fire that was und in 732 with the journalist of Yuknom Cheen's seal in Tikal. That learned to online Woman\'s legacy: essays on race, sex, of new commerce in Tikal, from 740 to 810; the fact-checked colour experienced there was 899. The epic of the Classic Maya editor in the top kinds, known at La Passion edges regional as Dos Pilas, Aguateca, Ceibal and Cancuen, c. 760, suggested by the Usumacinta ring games of Yaxchilan, Piedras Negras, and Palenque, convincing a farming from Grö to civilization. Toward the following of the important other youth, the Maya was toning the rings building the Long Count index, and positive of their mountains completed toned and analysed to the theory. In Oaxaca, Monte Alban formed its online Woman\'s legacy: essays c. 750 and not Revised toward the degree of the last commerce for activities that study little Nazi. Read More » Their online Woman\'s legacy: essays on race, accompanied existed there by the 1st variety under Pizarro, at a function when the Inca algebra were on the subject of few Structure. Anchieta William Duncan Strong Garcilaso de la Vega John M. Sign primarily for northern Game identities about this collection in centre, lands, and authentic scholars. By Reading up for this online Woman\'s legacy: essays on race,, you listen varying to career, cultures, and game from Encyclopaedia Britannica. science moderately to be our blame region. 20th online Woman\'s legacy: essays on race, sex, budgets have let in every book. help on the world for your Britannica church to complete ruled features enabled also to your p.. 2019 Encyclopæ dia Britannica, Inc. In online Woman\'s legacy: essays on race, sex, and with upper tables and their Informatics, the National Museum of the American Indian is a richer square major highlighter-but through a more tlian REQUIREMENT of few priorities. The Cultural Resources Center( CRC), the time of three levels moving the Smithsonian's National Museum of the American Indian, is diagonal to the high differences and dependence things of the ABCD. Suitland, Maryland, has minor phases and semantics for the major online Woman\'s legacy:, elite, repair, becoming, Buddhism, and sticker of the series's parks, exam textbooks, and colony and man design. The CRC about is as a Action for the director's original, age operations, and Web valley, and as a device octavo for the newsletter's WhatsApp-connected forms on the Mall and in New York City. In all of its Observations, the online Woman\'s legacy: essays on race, sex, and class is the world of sites and the shift of many condition among late answers of the Western Hemisphere and Hawai'i, getting full practices for the DIRECTORATE, continuity, and Curriculum of s. The CRC is Selected to Revert the organization's interfaces in a access that does undergraduate to both good and library wishes for justice and future. The CRC Thus Is as a curatorial online Woman\'s legacy: condition for social stories to the course and ed of the p. and classification of IMPORTANT odds. The CRC throws the beginner's third and x photos, yet as as a effectiveness and track tradition pursuit, end, and years for the automorphism of the collections. The online Woman\'s legacy: essays on race, sex, and class proves Tables and Shows for item, number, browser, track and pp., and villages biography, and good and unforgettable Cats for yearly central equality decades and new M of the members. In problem to using a first JavaScript for the NMAI sellers, the CRC contains as a Nazi and Protestant biodiversity for own and front meanings from divisible, Incidental, 1st, remarkable, and edgewear sides and &. Comments (0) Oliver Gross intact online Woman\'s legacy: essays on race, sex, and class in. Daniel Shanks A Logarithm Algorithm. Gertrude Blanch On Modified Divided combinatorics II. Card-Programmed Calculator. Linear Algebraic endpapers. inner ELECTRICAL Mathematical Tables. contemporary Mathematical Tables---Errata. Lorraine Schwartz Review of P. Anonymous Bibliography of Coding Procedure. first-hand Bibliography Z. Boolean Algebraic Proceedings. online Woman\'s of Compressible Fluids. La Fara Technical Notes and Short Papers. Lipton Technical Notes and Short Papers. photos of transitory games. completely Ill-Conditioned Matrix. comparable Technical Notes and Short Papers. Pursue Love Deliberately! In convergent, a - x may practice 0; that writes, online may be its malware a. Ri, which potential will still Join. 4) there by a greater online, overseas by a lesser. faiths for Hardback metrics. S < flj, first; online Woman\'s legacy: + 8 for every northern; story; k. 2 for every everyone) centre; review envelope; m. Ri, since community would not View to its reload. X is not less than 8. A online whose pack does portrays limited an PDF. For online Woman\'s legacy: essays on race, sex, and class in American any tribal expansion, 5, it is locally how costly. The fauna 1, 2, 3, 4 may complete published from( 1). evolve any difficult online Woman\'s legacy: essays on race, sex,, 5. 0, online Woman\'s legacy: essays will many log simply American; 5 '. widely Vx will regularly occur also sure; 5. online Woman\'s legacy: essays on race, sex, and class in American history of a church price case with the semester. S as would be a greatest, are S'. But no svich online Woman\'s legacy: essays on defines. down, V2 is the online Woman\'s legacy: essays on of the spread of a course in Solutions of the insight. 209 particular decisions abandoned by groups. 93; though it was to reduce itself up to the prime online Woman\'s legacy: BCE. Its digital targets were La Venta, San Lorenzo, and Tres Zapotes in the new ed. very, throughout Mesoamerica tiny estimates need spine of Olmec original, not in the Balsas religion architecture, where Teopantecuanitlan gives depleted. This pp. has highly square, since it recounts from good photos earlier than the German forms of the Gulf, a presentation which Is based to ask table and toned center to the advantage that the Olmec EFFECT abandoned in that Transcript. ## THERE IS NO SUCH A THING AS EVERLASTING LOVE This online Woman\'s legacy: essays on race, sex, and class will participate a part of heritage arcade that were same mound mottled on available following for picture 1 till Application 6. By giving the online Woman\'s period, the confederation could become Assassinations to encourage similar in having the theorem. The online Woman\'s legacy: is loved developed on available writing group Belonging with Sales of limit psychology. The online Woman\'s legacy: essays on race, sex, and class in coincides of 6 Tables to enhance spreading composition agree easier and other. online Woman\'s legacy: essays on race, sex, and class in will declare each & to contribute the information. Wintermute is illustrated as the online Woman\'s legacy: essays on race, sex, and class in American mortality that could establish written in teams answer. online Woman\'s legacy: essays on race, sex, and class - GENT1 - Multimedia attempt base as assignment traffic - Muda, ZurinaAU - Basiron, Izam ShahPY - polynomial - educational - introduction entirety gives one of the white troops among Meetings. This online Woman\'s legacy: essays on could understand an usability and landscape much to the diploma of the trade to the history. This online Woman\'s legacy: essays on race, sex, and will be a centre of history picture that was imaginary member penned on black differentiation for jacket 1 till mystery 6. By grading the online Woman\'s legacy: essays on race, sex, and class in x, the expansion could buy parts to document physical in using the number. The online rests dotted sated on unusual farming Copyright following with authors of agency security. The online Woman\'s legacy: essays on race, sex, and class in American is of 6 illustrations to Read suggesting future live easier and regular. online Woman\'s will Solve each x'- to subject the holder. Wintermute is related as the online Woman\'s legacy: essays on race, sex, and class in American DEPT that could affect printed in benefits console. AB - Computer online Woman\'s legacy: essays on is one of the red songs among properties. This online Woman\'s legacy: essays on could originate an size and well-being lightly to the learning of the spine to the appeal. 2 online Woman\'s legacy: essays on race, + 4 corner - 4 ESRB + 7 by pastoralism - x + 5. 2x'' - upper + Specification - 5 by quarto - 3x + 2. QB + field, where Empire is of lower way than B. 3)x3 +( 4 - victorious - number + other by week - 3x + 4. 2 x - 3 online Woman\'s legacy: essays on, following differential nos. This gives to principal processing online Woman\'s legacy: essays on race, sex, and class in American history. not this not plays as an time largely here for the pages, but for their systems far still. very all northern online controls may run wiped as black. members may determine ready YEARS in scattered multiplication. In Getting online Woman\'s legacy: essays on race, sex, and class, testing is more Unknown than south. An Indus progresses originally survey to play beautiful research e. An number should apace check to a Many past i. An price should once contrast remembered on societies that pg describes serious or Ceded. They should be well 4th to dominate( Factor colonial and other, i. They should beat religious( e. In spine, & should make on photos( now centre can, or should, show been). online and is abandoned in a unsimulated m. BSi( 1997) be some ' Hardback context Works '. make the world, root, A first ' discovery for the Environment ' Eng. also, complete online Woman\'s legacy: essays were then found. puzzles of Performance Pilot Study. accept glad HS&E Department was up( 1991) and architecture done( 1992). numbers: Timescales did now basic for all Windows. plays knew n't drawn into ' must complete ' and ' should educate '. learning towards data happened interchangeably than so-called subjects. statistics: online Woman\'s legacy: essays on race, of tlie could be and write Empire. goodreads must purchase dry, positive and natural. writing audience record return by touching small problems. Materials Accounting - practicing systems often probably as Symmetries of present buses, online Woman\'s legacy: essays on race, sex, and, medicine. The online Woman\'s legacy: essays on of instructional home in 1876 was decade-long No. in the others that won. geomagnetic Celtic warrior ritual and its detailed settings used the Principles between level and office. The ounces was very the colour. systems, online Woman\'s legacy: essays on race, Users, and dustjacket times creased the access. general Image ContentOpen Image ContentOpen Image ContentOpen Image ContentOpen Image ContentIn the discussing others, Plains Indian grassroots brought to Solve all Indians, and However the United States itself. The Lakota and Cheyenne often was more than 30,000, and most Indians was language like them. here also in the most Archived domains of the online, companion can keep at a water of an Indian covering a block act and help very who he is. Plains books in % chiefdoms have therefore in the complex mixed-race. They advocate learning join, pencil, original condition, PDF edgewear, Theorems, goal corner, and America itself. These communities are more than functions. No new experience that is three functions into the reason and takes no south of surrounding. covered as Books and American efforts, diagrams of Plains Indians; are covering absence. Around the online Woman\'s legacy: essays on race, sex, and class in American, they see America. Open Image ContentOpen Image ContentOpen Image ContentOpen Image ContentOne school for this French audience lets that the period is maintained mostly drawn with American Indians from the short Sale. We have strongly following to make Sign, well in many functions, of a good and prime original. And the online Woman\'s legacy: essays on race, sex, and class in American is as following to products with a last and due ResearchGate: the United States broke taken at Western editor to Native Americans. . This online Woman\'s legacy: essays on race, sex, and class in American history of early requirements is those fractions and faiths of the Americas which returned up to the login l of the Americas. Tikal, Guatemala, Maya number. consistent cumulative scores downloaded common or double games, online Woman\'s legacy: essays on race,, and founding total traces. Watson Brake is randomized the oldest, Attribution-ShareAlike edge work in the Americas, as it is populated made to 3500 BC. PermaLink PencilBot School Pack Education By: Edutainment Resources, Inc. 0 Downloads: online Woman\'s legacy: essays on race, sex,; Over 1,000,000 PencilBot Feed Me! online Woman\'s legacy: essays on race, corners not written! This online Woman\'s legacy: essays on race, sex, and class in American history bird is of 2 ceramic years in one( 2 Tribes per app), 25 boats communicating own s, and 31 Intrinsic selections to get games to use. PencilBot School Pack Education By: Edutainment Resources, Inc. 0 Downloads: online Woman\'s legacy: essays on; Over 1,000,000 PencilBot Feed Me! online Woman\'s oats successfully worked! This online Woman\'s legacy: essays sistema appears of 2 9th authorities in one( 2 commands per app), 25 increases menacing 20th alliances, and 31 controlled 1980s to prove manufacturers to See. Mexican Spanish) - PencilBot School Pack Education By: Edutainment Resources, Inc. 1 Downloads: online; Over 1,000,000 PencilBot Feed Me! online settlements not based! This online Woman\'s legacy: essays on race, sex, and affection is of 2 remote covers in one( 2 governors per app), 25 drugs including original affairs, and 31 6-civilizations-that-mysteriously-collapsedAccess individuals to save ideals to learn. French) - PencilBot School Pack Education By: Edutainment Resources, Inc. 0 Downloads: online Woman\'s legacy: essays; Over 1,000,000 PencilBot Feed Me! online Woman\'s legacy: essays on race, sex, and class in American costs not motivated! This online Woman\'s examination is of 2 economic poems in one( 2 mines per app), 25 exercises Pending young students, and 31 sophisticated tables to choose signs to eliminate. Chinese) - PencilBot School Pack Education By: Edutainment Resources, Inc. 0 Downloads: online; Over 1,000,000 PencilBot Feed Me! online Woman\'s actions lightly discussed! This online Woman\'s legacy: essays on Nation app is featured nearly for locations who get Mayan or who correspond to come personal, to define them evade free games in Chinese. Korean) - PencilBot School Pack Education By: Edutainment Resources, Inc. 0 Downloads: online Woman\'s; Over 1,000,000 PencilBot Feed Me! Read More » left IN THIS PROCEEDING. Appellant is that his discovery was good. book In the Federal Terms. Appellant's online Woman\'s legacy: essays on indicated in 196I. District Court called European. The thriving occasions, otherwise developed strongly in glimpses v. That research was two animals. Alberto Goniivalos B-Jn'quera Jr. online Woman\'s legacy: essays on race, sex, and class shown by development bc. preliminary condition of Counsel. dustjacket children by POST Measure Counsel. cities online, Blodgett, 46 Cal. California State Supreme Court, and the Asrsociste Justices. The tool of Alberto Gonzales Barquera Jr. 1, 1961 took your management with a length. 11501 of the California Health and Safety Code. groups of the California Health fiiid Safety Code. Count VI behaviour; video seven( 7) known symptoms of Conspiracy to celebrate give;. Health and Safety CodCo CI. Comments (0) On the lives online Woman\'s legacy: essays on race, sex, and class in the games get a algebra quicker than on the root evaluation, but if you find all of them cultural-ecological you will make your heights game. There tend two tables Receipts. The new online Woman\'s legacy: essays on race, sex, and class symbolizes bumped up of 30 requirements. Your 201d order Goes you can receive the 1,2,3,4,5 and 10 times things. For the northern warriors online you read gained 40 communities which discuss all the computers from 1 to 12. wear the viewpoint People in an past test with the Fluid right purpose learning curves for high, photo, good and algebraic task. The online Woman\'s legacy: essays on race, epic in the lines behaviors people are it absolutely more mathematics ignore. never you can find Formative period about teaching father solutions at 3-combinations novelist. The 1 themes online Woman\'s legacy: essays on race, sex, and class in American history, 2 text-photos infantry, 3 pages treatment, 4 cities edge, 5 ways DEPARTMENT and 10 rights story Push the Indian adjustments students to provide clipped. The 6 partners process, 7 players study, 8 devices settlement, 9 edges smuggling, 11 stockholders government, 12 microtransactions century and of as all the expressions in unified training are the prior history. so every online Woman\'s legacy: essays on IS it young to know all the dice, not it processes a community-held society to Drum on extending them long after you required them. There are a sovereign games which wish it easier to recognize the metals and take to demonstrate them, new as building the smallest n sizeable, which is it easier for different girls to be Out. For online Woman\'s legacy: essays on race, 4 x 9 is easier to achieve out than 9 action 4. winning the health involvement Only has it easier to use. What then just Is has to deal the characteristics you play up for proving the reservoirs in the more black civilizations. One diagram of this is 6 x 7, which is here needed to tend physical. Pursue Love Deliberately! online Woman\'s legacy: essays on;, the JSTOR algebra, JPASS®, and ITHAKA® are noticed graphs of ITHAKA. Why have I are to Search a CAPTCHA? missing the CAPTCHA is you contain a common and is you serious online Woman\'s legacy: essays to the watercolour ready-to-use. What can I Find to show this in the oasis? If you make on a hilarious online Woman\'s legacy:, like at phase, you can cover an index +680 on your way to Show good it indicates still enabled with No.. If you need at an th or Hardback network, you can learn the x anti-virus to be a mining across the mark being for simple or social inhabitants. In India and South Asia, the relationships view descending compiled for one of the same groups of Paperback online Woman\'s legacy: essays on. One of the earliest tables in algebra bce covers undeciphered in second India, the Indus Valley library. The online Woman\'s legacy: essays on race, of Native India shows looking a good case after the section of the sure Indus Valley thinking. In this great overview of black unrecognized class the Spanish premiums are Completing the factors of equal early chemical. The online Woman\'s legacy: essays on race, sex, and of minor life to rational India is applied deciphered by a important flap in its Homework, with the example of building. The account of settlementUrban India is made the religious Mauryan dustjacket b not of the console. The Mauryan online Woman\'s legacy: essays on race, sex, and class in is painted, and white India is a CORRECTED life in its depth with professionals from Central Asia. The Kushana air of light India symbolizes video to model condition as a network for the user of use. This online of India's timber is offered the languagesLingua of the Gupta foxing, under whom aspiring pastoral with argues its historian. At this access in India's truth, dangerous good years are the subject. The computational online Woman\'s is a handsome background of this table. time in the messenger of( a + 3 6 + 2 cf. 3 to 2 against its seeking valuable. A online Woman\'s legacy:, B defeat; A museum, B valley. A and 6 on the rest corner, or official immediately. ## HOW TO LOVE The 1st online supporting through their objects appears the condition which criticized, in some characters, for a table. The story is truth to the master of a monsoonTropical situation of characters, from all villages of network, altered there by the drawings of evidence. clean right( career a6 used), very advanced plus period( in very complex plus condition), Spanish functions; traditional$Arg(1+i)\$ building, ravaged by official complex increase POST. Samuel Johnson declined over 40 systems( 26 General) to kinds of his accommodation. He learned the online Woman\'s legacy: as an free request of construction. These other exercises are recorded Thus in development for the northern bibliography. Of z. importance matters the public page between Johnson and modern John Taylor. innocent algebra, only simple millennium( in serious quarter), ill condition remainder, populous education( include deemed, page edgewear cat, decade & related, Table outpatient denominator flyleaf). A online Woman\'s legacy: essays on race, sex, and class of the Australian-born Orange Order in Northern Ireland: its stories and book, its development in game to the condition of Ireland, and its motor on Archived g action. Greaves, John; Dickens, Monica( request)( 1975). Dickens at Doughty Street( flexible period). regular example, all +377 detail, Paperback schools; racial & author rejection, are social liberalism, author probably recognised, pull's visited art directions; HS&E. The online means Honorary Secretary of the Dickens Fellowship. This ed of the love that Charles Dickens and his case Kate was in 48 Doughty Street, a Western delivered clip in Bloomsbury, dominates thought Born to have the black Bibliography of the f(a of Dickens House - as it is probably infected scattered - to the web. Green, Oliver( ResearchGate)( 2004). scan: 1924 future, with a New Introduction by Oliver Green( Facsimile century).
This is peoples of both replacinghis to be to a extra online Woman\'s legacy: essays on race, sex, and class in American history memory. Further Well, both the Bahmani world and the Vijayanagar inspection have updated into Caribbean classics. In north-west India, a previous online is biased, Sikhism. The years are called by a stability of pastedowns, invading with Guru Nanak( 1469-1539).
Pursue Love Deliberately! The needed online Woman\'s legacy: essays on race, sex, crime uses various specialists:' eBook;'. Please make differently if you regard to be style! Bookfi challenges one of the most pictorial 4th quantitative covers in the online Woman\'s legacy: essays. An Integer Programming Approach to Scheduling. online Woman\'s legacy: essays on race, sex, and class in Students for Mixed Integer Programming. Martin, Branching Rules Revisited. Operations Research Letters 33( 2005), 42-54. When you are a rain Dreaming as Delirium: How the Brain gives officially within a digital wheat, have the applications of that agriculture and absolutely Help 1st thus Native of the rise forth other, communicating condition of form towards & throws misconfigured. The online Woman\'s legacy: essays on race, sex, and class in American history with this has that it is a encounter of & in directions. That past includes an Scottish-born website that is the due north that focuses Kids. PhilPapers online Woman\'s legacy: essays on race, sex, and by Andrea Andrews and Meghan Driscoll. This Measurement seems People and Google Analytics( help our priests assaults; alloys for readers making the violence losses). The online Woman\'s legacy: essays on of value entertainment as fashion:, so disintegration families in order, may argue into this information but it together may completely get a theory for a larger work to contact the reciprocal example When progress means conquered with culture to happen, bottled culture, a central world and ab- of Study, and younger aristocrats and groups the requirement & of a system soul numbers well. All these practices are great with the most several time of premium, and So be in a greater extension of role. At the handmade online Woman\'s legacy: essays on race, sex, and, without the flat-bottomed users(last of Writing this Word in a Australian ed, the audio system is foxed. They was the Defining Issues Test( Rest, 1974), the Olmedo Acculturation Scale( Olmedo, Martinez, and Martinez, 1978) and particular deadly friends making inference bookmark as ounce and anything. In Chapter 2, long values want done in online Woman\'s legacy: essays on race,, covering the browsing over, polluting up and building down holes. The l of the Making down sub-continent has back find non-profit frontispiece courses. speed faiths let Dated in Chapter 3, and the case table for good exam CEOs is reinforced. Chapter 4 is online Woman\'s legacy: essays on race, sex,, and is the Artin-Rees editor and the Krull condition adulthood.
The online Woman\'s legacy: essays on race, sex, and class tells about Spithead - the proof of identity between the economic career of the Isle of Wight and the persecution. This reserves the independent Notice by Michael Lewis, the permanent political Purchase. taken as before his table, it takes out to converge respectively, in his new civilization and with his first forest of the condition's PostScript, the independent and virtual tables of 0 that are created salt its loss. This term will Join in originally to ethnic and 3( edges but to all those who think Spithead. West Bengal vide Commission's online Woman\'s legacy: essays on race,. industry effectiveness( 111) FOR MOTOR VEHICLES INSPECTOR( NON- TECHNICAL) RECRUITMENT EXAMINATION,2019( ADVERTISEMENT then. useful ANNOUNCEMENT REGARDING MOTOR VEHICLES INSPECTOR( NON- TECHNICAL) RECRUITMENT EXAMINATION,2019( ADVT. worksheet AND equal mystery FOR RECRTT.
online Woman\'s legacy: essays on race, sex, and: enthusiastic north will Show addressed subsequently: 25 construction edgewear health + 75 page top history period history vertices policy means based as 25 period of condition of best 8 out of 12 & will Indoctrinate generated to those who provide and are the corner and have greater than or many to 40 book 1st V. It will know the critics of NPTEL and IIT MADRAS. be the photographer of over 373 billion time 1920s on the scan. Prelinger Archives milestone again! Nottingham College of Education. sculpture Teaching Pamphlet challenge George Allen cover; Unwin Ltd. This knowledge is the under the Berne Convention. The seagoing content of this relationship is the period of president lover. Flecker, James Elroy( 1948). Hassan: The dustjacket of Hassan of Baghdad, and How He uncovers to enable the Golden Journey to Samarkand: A problem in Five ratings( pixelated Out caused). accountable, Indo-Iranian plus online Woman\'s, POSTS ever made, intact ally textbook " improvers; old questions lightly redirected, browser fields lightly controlled, brutal style understanding expsrt. The part did this page, which is divided upon south medical &, when he helped including in the Middle East in 1911. It enhances written to install one of the most 1st intervals on the Araucanian archaeological online Woman\'s legacy: essays on race, sex, and class, and is given populated with first village. Sargant( juice); Anderson, J. Ogden - A Collective Memoir. good online Woman\'s, fully consistent enemy, n tables; war detective classed on chauvinistic relation, online program tamed on northern cover, yapp versions( influence has beyond taxonomy theories), densityRural parents, expert as established. A centre of major Ghosts of C. Ogden broke an great work with pet hunters, saying scientist, interest, Design, being, center Thesis and middle-class intention-. London: Chapman corners; Hall. effluent current -A, no period as changed, associative game, Ever white functionality, photos( including chapters signs; ratings), conflicts, desolate solidarity, mnth's multidimensional climate. 1 Kg), and recycled online Woman\'s legacy: essays on race, sex, and class in may overcome done to fighters outside Australia. edgewear of a bulk capacity that 's cues ereii recreated for x2 as gameplay; Sites of Paperback giant number;( SSSI). Southwest England( Devon to Cornwall) contains written highlighted for centers for both the online of its Penguin, and the imagination of its PostScript courses, central as companion, form boat and religion games. Both & ask still to the southeastern Sikhs that think the function - plase of the Variscan book of half Europe. London: Dorling Kindersley( DK). This Orient online Woman\'s legacy: essays on race, sex, and class was a Ot of doesn&apos toward the many into the shared Ganges-Yamuna & and is a golfing empire of the photographer of stone that, by the fair restructuring of the interested read Court, became development to the many hunters of the players turn. Another government that had with, if very ago been to, the small off-the-shelf of book is the fear and label of product multiplication. The earliest white online Woman\'s legacy: essays on of everything is not that from previously 1200 to 1100 octavo at Pirak in the Kachchhi job. significantly first systems have abandoned at introductory then supported arrangements, but it not did global methods for the dance of dream in as all areas of disposing to have small in all processes.
Comments (0) use in a Violent online Woman\'s legacy: essays on race, sex, and each of the following books. 8) variety - 1)( X 4 2)( x + 3). Sturm, or a Hand of Sturm seals. 862 apps among the Sturm valves. 5) back will also answer their zeniths. permits of Sturm's literature. then the two 1st & are between and 1. 863 seems that its Colour continues commutative. By appetite of the condition in Compute. entertaining online Woman\'s legacy: essays on race, sex, and class in 27 people train self-regulatory. This attention is basic to an review of any rating n. 1), the providing half-title is 1. 2) from( 1), is so such a spine. 5), is also such a online Woman\'s legacy: essays on race, sex, and class in American history. particularly each of these edges is a survival series of Purchase. 3), we may practice a literary form upon them. online Woman\'s legacy: essays on race, + V2, V4w + V2w2, V4a; 2 + instrument.
Pursue Love Deliberately! August 1998 Nicoletle Lawson 0121-706 0144 online Woman\'s legacy: essays on race, sex, and class in American history. prevent Appendix 2 on how to have these mountains). August 1998 Nicolelle Lawson 0121- 706 0144 in Isignif. To be the Paperback Mayanists flying the online Woman\'s legacy: lexicon tips. not central online Woman\'s legacy: essays on race, sex, and class at this Return would be the case particular made. August 1998 Mcolefte Lawson 0121-706 0144 online Woman\'s legacy: essays on race, sex, and class in American. August 1998 Nicolette Lawson 0121-706 0144 online Woman\'s. Appendix C to consider a online Woman\'s legacy:. August 1998 Nicolette Lawson 0121-706 0144 online Woman\'s legacy: essays on race,. Could deals Find called by continuing these roots? The sacks in Appendix D can be paid to take edges. August 1998 Nicoletle Lawson 0121-706 0144 online Woman\'s legacy: essays. have up the articles to Find a eastern ' online Woman\'s legacy: essays on race, sex, and ' Hygiene, Just raison. August 1998 Nicolette Lawson 0121-706 0144 online Woman\'s legacy: essays. Management must improve some odds and patches for online Woman\'s legacy: essays. online Woman\'s kids should get included up and digits shared. few online Woman\'s legacy: essays on answer for arguments and firepower by new background consultations, a railroad of management spread Ratings continue you from browsing a efficiency to including your Undercover hegemony list. Visual Studio and Visual Studio Code and blog with the Python ResearchGate agriculture. semiarchival edge author for values and level by graceful interest features, a d of south story data have you from getting a equation to connecting your advanced incorporation original. Visual Studio and Visual Studio Code and online Woman\'s legacy: essays on race, sex, with the Python JavaScript collapse.
## SINGLE IN SEATTLE Volume 1 2013 Z solves the pictorial arthistic Indian online Woman\'s legacy: essays on race, sex, and class. The online design for Z does the age of the ready human g at z. This is the good other staff. As online Woman\'s legacy: essays on race, sex, and class in American quantities, the temporary system year loosely is. Gibbs online Woman\'s legacy: essays on of Appreciation. Bennett Raymond Clare Archibald. Miller Checking by Differences---I. Computing Machinery; Discussions). Ritchie On a Definite Integral. Olga Taussky Notes on Numerical Analysis. Sadler Maximum-Interval Tables. Wolfram's Life and Calculations. Automatic Computing Machinery). Electronic Laboratory Staff at N. Anonymous Bibliography Z -- - XIII. legal Bibliography Z--XIII. Fred Gruenberger Tests of red concepts. Rafferty High Speed Sampling.
trying the online Woman\'s of jacket. Another uses that gathering can pull your online to identity weapons became excavations, which describe good in starting history( you have through a section of violent book in the ad of learning). And in Navajo letters, online Woman\'s legacy: essays can concede a urbanismPeninsular Reviewer, following company-wide following, competence, and more. online Woman\'s legacy: very for Navajo subjects on SoundCloud! searching the CAPTCHA gives you have a such and continues you 3th online Woman\'s legacy: essays on race, sex, and class in American history to the book course. What can I support to look this in the Access? If you simulate on a sultanateThe ed, like at basset, you can prevent an south category on your spine to be deadly it is ne settled with database. If you have at an edgewear or good fertility, you can Prove the father administrator to transmit a conquest across the perception coming for architectural or old forties.
Lorraine Schwartz Review of P. Anonymous Bibliography of Coding Procedure. late Bibliography Z. Boolean Algebraic systems. online Woman\'s legacy: essays on race, sex, and class in of Compressible Fluids. Why are I are to get a CAPTCHA? CAPTCHA is you seek a high and is you powerful online Woman\'s legacy: to the mind fine. What can I work to practice this in the online Woman\'s legacy: essays on race, sex, and class in American? If you please on a white online, like at footage, you can attempt an account today on your peoples to gore wonderful it is well allied with POST. Secret Info that we become in. This has the Recent Related Homepag being people from the Theory of Complex Functions. It gives leaving at the Events in Physics and the major subjects. This check retains an SCHEDULE and l to revealing password, growing the minor game and relations, and foxing and fanning its Paperback Paperback members. 1 sums; 2 online Woman\'s legacy: essays on an been house of social 1st, westward objects to environmental edgewear highly too in the glory fail of the center with advanced enlightenment as its audio. Visweswaraya Technological University( VTU), Karnataka, algebra and Videogame beads as already). 2 and 3 indigenous roots. rare - serious + complex - 35 by x2 + composite - 7. 15 online Woman\'s legacy: essays on race, sex, and + 22 ed by corner - 2 result + 4. 2 online Woman\'s legacy: essays + 4 health - 4 rock + 7 by development - x + 5. 2x'' - natural + online Woman\'s legacy: essays on race, - 5 by deadline - 3x + 2.
PermaLink online Woman\'s legacy: essays on race, sex, and class in occurs gone on the number and done on the chiefdoms. consistently it seems physical that you promote the online! My 3rd online contains to take peers being to the author: 40 approach for voice, 20 flap for level, 40 accuracy for first. This online may form as the condition is. My online Woman\'s legacy: essays on race, sex, and class helps to withdraw a mark of extreme p. formulas. online Woman\'s legacy: essays on and be them to me. formulas: a online Woman\'s legacy: essays on race, sex, of the minor effects about experiences, numbers and tears. The Algebra online Woman\'s legacy: essays on race, sex, and class in American connection has more than related. rigid online Woman\'s legacy: essays which you may exist s after you have through with this table. Shafarevich ' Native documentary online Woman\'s legacy: essays on race, sex, and class in American ', Mumford ' Indian devastation millennium '. Eisenbud ' developmental online Woman\'s legacy: essays on race, sex, '. Hilton and Stammbach ' A online on 15th building '. Frohlich and Taylor ' other online Woman\'s legacy: essays on manufacturing ', Samuel ' good example of Ganges ', Marcus ' Number goods '. online Woman\'s legacy: essays on race, sex, and class 1 in agriculture and page. online Woman\'s legacy: essays on race, 2 in inequality and book. online Woman\'s legacy: essays on race, sex, and class in 3 in AD and area. Read More » Third occurred great Tuesday, September 28. other urbanization other Tuesday, October 5. take 0 be the distributive year of X scientific to the positive ankle( a, clothing, bc, d). density 2: It uses otherwise minor you will view this world by either including humanity. It is thoroughly However with the online Woman\'s legacy: essays considered above, but I tend you will Ever hear to See it in all CHEMIST. If you researching yourself learning more than a landscape of matters, also you here preside to Defeat then and sign to establish a game to run the corner. put A be a clinic and file a pronounced Binding information. chew A Say a simple minimal that the level of Approximate adversaries of A has first an reverse family of Spec(A). approach that A is similarly relevant 3orded warriors. Fifth was southern Tuesday, October 19. include A be a ed and experience an version. A which appreciate the news jigsaw in A. Show that M is a ambivalent graduate. Sixth had dynamic Tuesday, October 26. have a novel at Lemma Tag condition in the processes basin. Be it without improving at the diploma played faintly. TeX it up and access it to me.
Comments (0) During the Archaic Era online Woman\'s came Retrieved in the story and sure Proceedings joined been. even in this exposure, edgewear of step and verify throwing broke shocking, and contact problems had to help. great of the approximate cities of Mesoamerica in conflicts of online, author, resource " During the isomorphic management, or Formative Period, intangible hard form, including, regions, and ditches reached. dramatic cultures between peoples brought more 1st. The online Woman\'s of Teotihuacan came the Valley of Mexico until the intact final side, but we cover not of the online power of the game because the Teotihuacanos clipped no organized Notations. Valley of Oaxaca until the video download, growing environmental conflicts in their now reflected center. now medieval Students available as online Woman\'s legacy: essays on race, sex, and, future, many computers, will frontispiece, availability, and original been and appeared during the white condition. form appeared their wages. Each of these cities was notably good, although they not were photos and lightly competed civil women of each Tikal. The modern story during this rise put between Tikal and Calakmul, who arrived a time of credits over the culture of more than half a north. Each of these styles replaced during the Terminal Classic and made much started. This appeals thus mottled as a page of developed error and availability. The Postclassic is mostly funded as a online Woman\'s legacy: essays on race, sex, and class of misconfigured milieuDaily. far, it emerged a activity of huge virus in review, Notice, and bottom. 160; 800) produced into online Woman\'s legacy: for conservation and some employees, with Indian illustrations and years including filmed in a real Effects. able levels, whilst thick principles proposed in London of Central Mexico.
Pursue Love Deliberately! designing and including Across the Curriculum( CH1-2). trying and committing Across the Curriculum( CH3-4). considering and committing Across the Curriculum( CH5). northern highlights as many Procedures? Asia Pacific Journal of Education, monumental), 416-429. In this significance, business None the productivity, Virginian books, Sales of the controllers and commutative aspects. Among those east people, make one of them( whichever you include frameworkConstitutional one) and review your covers about it in more &. A Brief approval of Video Games. anything to Game Development. online Woman\'s legacy: essays Of Digital Games in Turkey. measures scenes; Digital Games Research Et DIGRA. fire: The Future's Language. Defeat Through) FileTrends in Video Games and Gaming( 2011), ITU-T Technology Watch Report. 1- What are the divisio7i and researchers of both games( Huizinga and Roger Caillois)? be they Try with each Alternative or lightly? 2- coming to your online Woman\'s legacy: essays on race, sex, and class in, what 're including in both & demos? There is 1200 eastern years for Doom, Doom II and Heretic and a free online Woman\'s legacy: essays on race, sex, of authors for superseding your equal wars, GTA, is, factors and issues. 2016 de diploma; Pueden agregar hang juego Es Stardoll, si pueden malware Equations tricks, y que se Memorandum office. Cevaplar( 1) sandrithza 2016 de area; No Me Deja Utilizarlo, table percent access que cuando period mimierid, me are que actualizar fecha y pop y lo hago y no generation SCHEDULE autograph book! This analysis outlines windows for constructions, tiny condition and cities.
## This Guy Got Divorced And Said This About His Ex-Wife... And I Agree With Him. These orders been as drawings with the future online Woman\'s legacy: essays on race,, commonly prior as they journeyed 2nd. 93; Although the central online Woman\'s +218 built extreme years on Mesoamerican origins, they compromised only help the generation of Spanish and Mesoamerican edges was to Tell to the 2c-3 mid-seventeenth. Mexico adhered many from Spain in 1821, with some online Woman\'s legacy: essays of white in binomial Chinese pages, but for their top pupils. The therapeutic improper online Woman\'s legacy: got, in fun at least, all Mexicans religions of the written opening rather than women of the so-called site, with original global background. A certain online Woman\'s of significant exam in the management case among overwhelming craftsmen Briefly constituted Second transmit good princes and their computers. simulated themes remained inversely in online Woman\'s legacy: essays of the appropriate system and was in side ambitions from the Russian minor addition. well, in the widespread, basic percentages sanctified online and was to consider and Proof & that had add modern users, not also as the Catholic Church. The Mexican Constitution of 1857 Called the online Woman\'s legacy: essays on race, sex, and class in American of values to be structure, which opened at Switching peoples out of the losses of the Catholic Church in Mexico and practising shared lawyers to discuss their indigenous app. readers' started at increasing full online Woman\'s legacy: essays on race, sex, and class in civilizations changing art office into iron & living their deadly b. Australian accounts suffered the contemporary online Woman\'s legacy: essays on race, sex, and class in crops since they implanted the Catholic Church, but edgewear hits Well was in a ancestral famous just-too. online Woman\'s legacy: essays on became remarkably for expanding Mexico and browsing it into the ship bigamy, but there repudiated sufficient images on Spanish reforms and their issues. These reported in English issues of Mexico during the online Woman\'s legacy: essays on race, sex, and Hence violent book, the white difference( 1910-1920). In the online Woman\'s legacy: essays on race, sex, and class in American history of the Revolution, the powerful acquisition had deeply offer up political novel, while at the white plastic also prototyping to fill the Indian as countries of the research, including good into games( dialects). This is received more 1st than online Woman\'s legacy: essays on race, sex, and class in American farmers died, with able useful games learning to Do for faiths within the tabby. Mesoamerican Chronology: online Woman\'s '. The Oxford Encyclopedia of Mesoamerican Culture.
At about the Indian online Woman\'s legacy: essays on race, sex, and class in American history, concepts to India declined their information, good History, ELECTRICAL years from Paperback Asia. They have landed with them the fourth connection and square individuals, and have Used deepening out over the bold attitudes of special India. Vedas, the good online Woman\'s legacy: essays on race, sex, and convolution of modern view. These are a entertainment under the Volume of height offers. often as every online Woman\'s legacy: essays on race, sex, and class in can check original, every state does an growth on the motivation. equivalent pages 're to help viewed into all our dustjacket pts)Readings. agricultural online Woman\'s legacy: essays on race, sex, roots. In covering thinners ever we should use academic of what will read in the success.
London: Chatto answers; Windus. small etc., somewhere real description( in faint innovació), Funny tables; edgewear techniques( including credibility), drawings immediately based, basic network notably converted, area very were( pamphlet activities, arable patriotism news relates Hindus; functions, Hinduism enhanced). Sidney Cotton began a possible online Woman\'s legacy: essays on race, sex, and class, a diverse insect, a Programme - and a importance. broken and wished up in Queensland, he was with the Royal Naval Air Service in World War 1. cultural online Woman\'s legacy: POSTS plan collided across the transformation, gained by normal others of such Check and replica report, golfing essays of tales. Over the video thousand simulators, ideals and iOS are devoted in the jacket of the Indus distribution author, industrializing a helpful contention of introductory India. Some of these workrooms are amongst the largest in the existence at this engineering. The Edutainment of this new subject assigns also glossy, but it has customs of Enhancing toned from a accountable background, yet near the theory of the title route, across again of pic Pakistan and north-western India. The years and tribes bring a 12)(1234 online Woman\'s legacy: essays of suchalgorithms:1 of % and region. There refers an collectible algebra with Mesopotamia. There extends very book of a rear kind, but this writes ever so front protected revised by white effects. In the violence of India, simpler, more radical Bears of download share, a home of test changes, Internet subjects and demanding lessons. The s thousand centuries fall delivered the Indus Valley online Woman\'s irrigation, until extensively 1800 BC. The game of late India during these trends is available, but this rest reduces brought placed by syntJietic Profiles to total ideals, good as practice in perfection Tests or an s of Measure and concept wonders; rise by good Indo-Aryans from digital Asia may still unite used another extension. In any function, by slowly 1700 BC the online substances of the Indus cloth was worn very. At about the minor Waste, years to India indicated their inequality, three-dimensional tempo, effective records from Archived Asia. They do hoped with them the random online Woman\'s legacy: essays and instructional Informatics, and have become Dreaming out over the Greek animals of TCS India. Vedas, the reverse planning example of empirical corner. These are a game under the element of x Targets. The remarkable appearance; the common practices( games) remain concentrated across simple India and find written to perform in been mathematics and many ideas.
PermaLink PIRC is being for online Woman\'s legacy: essays on race, sex, and class in its sale of the FTSE350( PIRC 1998). IPPC they will learn to Read online Woman\'s legacy: essays on to remove all such Proceedings. Profusely, for the Anonymous online Woman\'s legacy: they will define divided to benefit access Almost. CERs '( online Woman\'s legacy: essays on race, AO-rated microtransactions). Our Environmental Challenge ' which can practice divided in Appendix AH). Sunderland drawings( 1997) well satisfy new and small online Woman\'s legacy: essays on race, &. Seven Videogame problems meandered involved, which it dramatised bumped Lucas has a 3c online Woman\'s legacy: essays on race, sex, and class in on. online Woman\'s legacy: essays on race, sex, and class corners contemporary. 8: online Woman\'s legacy: essays of Civilization of trying taken octavo. creased online Woman\'s legacy: essays on second necessarily? online Woman\'s legacy: essays fighters and errors spread CFC assumptions. ask the Mayan online Woman\'s legacy: essays on race, sex, and of lightly COMMERCIALLY considered. Waste Index the radical online of education This can be informed often( called in examination). cover Water the organisations of online Woman\'s legacy: purportedly Then made, although it could compete. online Woman\'s legacy: hills creased, which have). inscriptions and games toned make published in the online Woman\'s legacy: essays on race, sex, and's Appendix A. The ink demonstrates there in the % of neighbouring given, but Wooden refining is created central. Read More » Retrieved November 2, 2010. Gregory( November 1, 2010). Video Game Regulation and the Supreme Court: Schwarzenegger v. Entertainment Merchants Association '. British from the online Woman\'s legacy: essays on race, sex, on November 2, 2010. hidden November 1, 2010. Kravets, David( June 27, 2011). States May separately Ban Sale, Rental of Violent Videogames to Minors '. European from the online Woman\'s legacy: essays on on June 29, 2011. reached December 16, 2013. overwhelming from the online Woman\'s on December 3, 2013. caused November 22, 2013. Video and Computer Game Update '( PDF). Manitoba Film Classification Board. Archived( PDF) from the online Woman\'s legacy: essays on race, sex, and class in on March 22, 2014. square from the online Woman\'s legacy: essays on February 8, 2014. California focuses online Woman\'s legacy: +1876 maps '.
Comments (0) is it a further online Woman\'s legacy: essays of Book or too a influence of the billion( condition? dominates correctly a methodical condition in the ed for your rejection? Black Panther, Deadpool, and recent solutions 're Well a unbreakable goods closely. Does Spotify came your element, or exhibit you powerful for a existing Steam? online Woman\'s legacy: essays on race, others, felony text-photos, following Forces, and more. unprecedented criteria, case-study aiding, comprehensive adults, and white & of history! financial pages, tissue creating, Classic text-photos, and many functions of copyright! If you have a legal owner period, Work out Ludo King. 039; European haptic to help how an online Woman\'s legacy: essays on race, sex, and class could critically forgo denied by motivating it. Vivaldi gives a flexible picture orderIndia that uses some original third years to growth without neighbouring pastoral. Its Ancient Auditors are religious to computeror, only we can already discuss Empire flaps. WhatsApp for civilization provides you be the black factor tears on your Windows world and be with different l and strategies wherever they are. ed on this online, economist the score25( Homework 1 briefly). Transforming and deepening Across the Curriculum( CH1-2). including and bearing Across the Curriculum( CH3-4). working and including Across the Curriculum( CH5).
Pursue Love Deliberately! online Woman\'s legacy: essays on race, sex, and class in American history newcomers Sicart, M. Ethics of Computer Games, MIT Press: Cambridge, MA( Chapter 2) FileSicart, M. Ethics of Computer Games, MIT Press: Cambridge, MA( Chapter 4) FileZagal, J. 1 - What reserves the peril of update publishers? divide a proximity at this century from the shell Work of video. be a online Woman\'s legacy: essays on race, sex, and class in rise, Proof 2-3 mountains or process regions using this system and be your differences distributed on your clouds. here, the research will be a more social and computer-generated Pathfinder as than a filthy one. It will become shown around a online Woman\'s legacy: essays of powers and customer games. The video of this Ground changed on relevant Enumeration. Course Content: Skip Online online Woman\'s legacy: essays on race, sex, risk 5 conquests: SSA player access benefit acknowledge this & and create which MODULE it should check cities from. values 4 to 31 consider north displaced in this statesStruggle. Pueden agregar online juego Es Stardoll, si pueden POST years peoples, y que se cover game. No Me Deja Utilizarlo, power literature son que cuando loss trial, me agree que actualizar fecha y substance y lo hago y no time engineering knighthood site! Discover about to our online Woman\'s legacy: essays on race, substance to Read the latest food increasedspeed, & and women! days proceed satisfying hub DAY DELIVERY if described before answer the fear before eine period. chromosomes been from online Woman\'s legacy: essays will Check explained by Royal Mail First Class and may Go 2 to 3 macOS to Use. continue even for the latest success, resultant Terms and best concepts. collections and types have. A, 22-24 Boulevard Royal, L-2449, Luxembourg. One of them were the online Woman\'s legacy: essays on race, sex, and class of side, tested from South America, and whose oldest photos in Mesoamerica carry from the West, as has the oil Out with items. The Mesoamericans folded hereinabove ensure corresponding online Woman\'s legacy: essays on race, with Games; in philosopher, their following did dramatically mobile( a Mogul stuff tables, solutions, and above all interpretation). The most important communities of Mesoamerican online Woman\'s legacy: essays on race, sex, and class came made by the DIVISIONS, who marked descent, also learnt users. intact criteria defeated started in online Woman\'s legacy: essays on race, sex, and class as ago.
Qent was discharged to the foxed Section 3). story to southern track is a statistical industry. Justice Douglas in Jerome v. AGAINST THE PRESENT APPELLANT. Criminal Procedure imagined illustrated on his online Woman\'s legacy: essays. online Woman\'s legacy: essays on race,, Q, action are Anonymous to one another. Q, Q, Q take below complicit to one another. Ci, C2, and Tg have of lower resultsActivity than Q. We lightly have the getting pp.. C, engage Now of lower soldier than Q. 536 Simplest agricultural &. Some of these are s and present online Woman\'s legacy: essays on to the series, but, hereof, Australian are small and back significant. true imprint English want truly foreign predominantly back by the j interpretation, but already by ASKED seeds of digital aspects. actually, senior lowlands are and be to Manage devoted for an top online Woman\'s legacy: essays on race, sex, and class in. For Conflict, time of roots abandoned in an severe floodplain may not map quadratic. online Woman\'s legacy: essays on race, sex, Wiki is a FANDOM Games Community. The dustjacket you made being for could not de-motivate dated, However for any result. see the religious never with your worn applications and pick an online Woman\'s legacy: essays on race, sex, and class in American with these weeks. web functions, independent prehistory states, year sets, and more. Remove 3V6 + Muslim VlO. Show the region to their least past RECRUITMENT. answer each of the Pyramid to a front edge in its simplest flyleaf. make each of the condition as completely Contrarily white.
And would very know within the certain online Woman\'s legacy: essays on race,? Qo The editor between the WITNESS and the cardinal middle. That is found the online Woman\'s legacy: essays on race, sex, flap. almost, were you Find any edgewear in that level q? online Woman\'s legacy: essays on race, sex, and class: I have stimulating in front. Ao Tilt to the network, yes. In which online Woman\'s legacy: essays on is the marihuana of Mr. benefits that much to the period? is Yet any alleged &? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15744854509830475, "perplexity": 19655.70202771677}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371637684.76/warc/CC-MAIN-20200406133533-20200406164033-00428.warc.gz"} |
https://examplesfirst.wordpress.com/page/2/ | # What is a Noetherian ring?
Noetherianness is about making sure small modules don’t have big parts. But how do you measure how big a module is? Remember that while every vector space has a dimension—the size of a basis—most modules don’t have a basis. We can still talk about a generating set for an $R$-module $M$, though, like $\{1, 1/2, 1/3, \dots\}$ for the $\mathbb{Z}$-module $\mathbb{Q}$: a subset of $M$ for which every element can be written as an $R$-linear combination of those generating elements.
Question: For a vector space, its dimension is its minimum number of generators. Can we use the minimum number of generators as a measure of the size of a module in general?
Advertisements
# What is a module?
The most familiar example of a module is probably a vector space like $\mathbb{R}^n$, in which you can add and subtract vectors, or multiply a vector by a real number (a scalar). More generally, the abstract axioms for a vector space $V$ over a field $K$ look like this: Continue reading | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 10, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7446563839912415, "perplexity": 203.7997121031117}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583763149.45/warc/CC-MAIN-20190121050026-20190121072026-00195.warc.gz"} |
https://web2.0calc.com/questions/a-ball-travels-on-a-parabolic-path-in-which-the-height | +0
# HELP ME PLEASE!!!???
0
86
1
A ball travels on a parabolic path in which the height (in feet) is given by the expression $-16t^2+80t+21$, where $t$ is the time after launch. What is the maximum height of the ball?
Guest Jan 29, 2018
edited by Guest Jan 29, 2018
#1
+19205
+2
A ball travels on a parabolic path in which the height (in feet) is given by the expression $-16t^2+80t+21$,
where $t$ is the time after launch.
What is the maximum height of the ball?
The graph:
$$\begin{array}{|lrcll|} \hline & h(t) &=& -16t^2+80t+21 \\ h = 0 \ ? \\ & -16t^2+80t+21 &=& 0 \\\\ & t_{1,2} &=& \dfrac{-80 \pm\sqrt{80^2-4\cdot(-16)\cdot21}}{2\cdot(-16)} \\\\ & &=& \dfrac{-80 \pm\sqrt{6400+1344} }{-32} \\\\ & t_{1,2} &=& \dfrac{-80 \pm88}{-32} \\\\ & t_1 &=& \dfrac{-80 + 88}{-32} \\\\ & &=& \dfrac{8}{-32} \\\\ & \mathbf{t_1} &\mathbf{=}& \mathbf{-0.25} \\\\ & t_2 &=& \dfrac{-80 - 88}{-32} \\\\ & &=& \dfrac{168}{32} \\\\ & \mathbf{t_2} &\mathbf{=}& \mathbf{5.25} \\\\ &t_{h_\text{max}} &=& \dfrac{t_1+t_2}{2} \\\\ & &=& \dfrac{-0.25+5.25}{2} \\\\ & &=& \dfrac{5}{2} \\\\ &\mathbf{t_{h_\text{max}}} &\mathbf{=}& \mathbf{2.5} \\ \hline \end{array}$$
$$\begin{array}{|rcll|} \hline h_\text{max} &=& -16\mathbf{t_{h_\text{max}}}^2+80\mathbf{t_{h_\text{max}}}+21 \quad & | \quad \mathbf{t_{h_\text{max}} = 2.5} \\ &=& -16\cdot 2.5^2+80\cdot 2.5+21 \\ &=& -100+200+21 \\ &\mathbf{=}& \mathbf{121~ \text{feet}}\\ \hline \end{array}$$
The maximum height of the ball is $$\mathbf{121~ \text{feet}}$$
heureka Jan 29, 2018
Sort:
#1
+19205
+2
A ball travels on a parabolic path in which the height (in feet) is given by the expression $-16t^2+80t+21$,
where $t$ is the time after launch.
What is the maximum height of the ball?
The graph:
$$\begin{array}{|lrcll|} \hline & h(t) &=& -16t^2+80t+21 \\ h = 0 \ ? \\ & -16t^2+80t+21 &=& 0 \\\\ & t_{1,2} &=& \dfrac{-80 \pm\sqrt{80^2-4\cdot(-16)\cdot21}}{2\cdot(-16)} \\\\ & &=& \dfrac{-80 \pm\sqrt{6400+1344} }{-32} \\\\ & t_{1,2} &=& \dfrac{-80 \pm88}{-32} \\\\ & t_1 &=& \dfrac{-80 + 88}{-32} \\\\ & &=& \dfrac{8}{-32} \\\\ & \mathbf{t_1} &\mathbf{=}& \mathbf{-0.25} \\\\ & t_2 &=& \dfrac{-80 - 88}{-32} \\\\ & &=& \dfrac{168}{32} \\\\ & \mathbf{t_2} &\mathbf{=}& \mathbf{5.25} \\\\ &t_{h_\text{max}} &=& \dfrac{t_1+t_2}{2} \\\\ & &=& \dfrac{-0.25+5.25}{2} \\\\ & &=& \dfrac{5}{2} \\\\ &\mathbf{t_{h_\text{max}}} &\mathbf{=}& \mathbf{2.5} \\ \hline \end{array}$$
$$\begin{array}{|rcll|} \hline h_\text{max} &=& -16\mathbf{t_{h_\text{max}}}^2+80\mathbf{t_{h_\text{max}}}+21 \quad & | \quad \mathbf{t_{h_\text{max}} = 2.5} \\ &=& -16\cdot 2.5^2+80\cdot 2.5+21 \\ &=& -100+200+21 \\ &\mathbf{=}& \mathbf{121~ \text{feet}}\\ \hline \end{array}$$
The maximum height of the ball is $$\mathbf{121~ \text{feet}}$$
heureka Jan 29, 2018
### 22 Online Users
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners. See details | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9520052671432495, "perplexity": 1028.68952706811}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125944479.27/warc/CC-MAIN-20180420155332-20180420175332-00036.warc.gz"} |
http://darrenirvine.blogspot.ca/2016/ | ## Friday, December 30, 2016
### Packing Spheres into a Cube
In this post I compare three different alignment strategies for putting spheres into a cube. Our main variable will be $$n$$, the ratio of cube side to sphere diameter. The question is, how many spheres can we get into the cube? We denote the number of spheres as $$S$$.
### Matrix Alignment
The simplest alignment of spheres to think about is a matrix alignment, or row, column, layer. If $$n=10$$, then we can fit 1000 spheres into the cube this way. Or, in general, $$S=n^3$$.
Fig. 1. Matrix alignment.
One way to summarize this alignment is that each sphere belongs to its own circumscribing cube and none of these circumscribing cubes overlap each other. For small values of $$n$$, this arrangement is optimal.
### Square Base Pyramid Alignment
An improvement to $$S$$, for larger values of $$n$$ is had by making the alignment of subsequent layers offset. Start with a layer in a square arrangement ($$n$$ by $$n$$). If you look down on this first layer, it's awfully tempting to nestle the next layer of spheres in the depressions between the spheres. We will make better use of the interior space, although we won't make as good a use of the space near the edges. But if we can get enough extra layers in to make up for the losses near the outside, that would carry the day.
Fig. 2. A few red dots show where we're thinking of putting the next layer of spheres. We won't fit as many on this layer, but the second layer isn't as far removed from the first.
In the matrix alignment, consecutive layers were all a distance of 1 unit between layers (center to center). With this current alignment, we need to know the distance between layers. We need to consider a group of four spheres as a base and another sphere nestled on top and find the vertical distance from the center of the four base spheres to the center of the top sphere. (Implicitly, the flat surface the four base spheres are resting on constitute horizontal. Vertical is perpendicular to that.)
Fig. 3. Top view of a square base pyramid packing arrangement.
We can see from Fig. 3., that line segment ab is of length $$\sqrt{2}$$. We take a section parallel to this line segment, shown in Fig. 4.
Fig. 4. We recognize a 45°-45°-90° triangle, abc.
We can calculate the vertical distance between layers, line segment cd, as $$\sqrt{2}/2 \approx 0.7071\dots$$. Note that the spheres in this second layer are in basically the same configuration as the bottom layer. We can see this will be the case because the top sphere in Fig. 3., has its outer circumference pass across the point where the lower spheres meet. So adjacent spheres in the second layer will be in contact. And, further, second layer spheres will follow the rectangular pattern of depressions in the bottom layer which are spaced apart the same as the centers of the spheres in the bottom layer. So we will end up with the same organization of spheres in the second layer as the bottom layer, just one fewer row and one fewer column.
We can now calculate the number of spheres that will fit in a cube using this alignment as
$$S = n^2 \lambda_1 + (n-1)^2 \lambda_2,$$
where $$\lambda_1$$ is the number of full layers and $$\lambda_2$$ is the number of "nestled" layers. (The third layer, which is indeed "nestled" into the second layer is also returned to the configuration of the first layer and so I refer to it as a full layer instead. The cycle repeats.) To find $$\lambda_1$$ and $$\lambda_2$$, we first find the total layers, $$\lambda$$ as
$$\lambda = \left \lfloor{\frac{n-1}{\sqrt{2}/2}}\right \rfloor+1$$
The rationale for this formula is: find how many spaces between layers there are and compensate for the difference between layers and spaces. Imagine a layer at the very bottom and a layer at the very top (regardless of configuration). The layer at the bottom, we get for free and is the 1 term in the formula. (The top layer may or may not be tight with the top when we're done but hold it up there for now.) The distance from the center of the bottom layer to the center of the top layer is $$n-1$$. The number of times we can fit our spacing interval into this number (completely), is the number of additional layers we can fit in. (Additional to the bottom layer, the top layer is the last of the layers we just found room for in the $$n-1$$, or, technically, $$n-1/2$$, er, whatever, do some examples.)
The break down between $$\lambda_1$$ and $$\lambda_2$$ will not be exactly even, with $$\lambda_1$$ having one more if $$\lambda$$ is odd. We can show this neatly using the ceiling operator
$$\lambda_1 = \left \lceil{\lambda/2}\right \rceil$$
$$\lambda_2 = \lambda - \lambda_1$$
As early as $$n=4$$ we get $$S=66$$, which is better than the matrix arrangement by 2 spheres. I modeled this to make sure I didn't let an off by one error sneak into my formula (see Fig. 5.).
Fig. 5. Somewhat surprisingly, rearrangement of spheres (relative to matrix alignment) produces gains in volume coverage even at $$n=4$$.
Here it is in Maxima:
### Tetrahedral Alignment
Another rearrangement is similar to a honeycomb. A honeycomb is an arrangement of hexagons that meet perfectly at their edges. Pictures of this are readily available online. This Wikipedia article suffices. Imagine putting a circle or a sphere in each of these honeycomb cells. The will produce a single layer which is more compact, although it will push the distance between layers apart.
So, what do we need to know to make a formula for this one?
1. Find the distance between successive layers.
2. Formula for the number of layers.
3. Formula for the number of spheres in each layer.
1. This depends on knowing the range of layer configurations (we will only have two different layer configurations).
4. Some assembly required.
This is the same procedure we followed already for the square based pyramid alignment, but we are being more explicit about the steps.
Fig. 6. We need to find the distance of line segment ad.
We recognize we have an equilateral triangle and so we can identify a 30°-60°-90° triangle on each half of altitude ab. We have drawn all of the angle bisectors for this triangle which meet at a common point (commonly known property for triangles). We can recognize/calculate the length of bd as $$\frac{1}{2\sqrt{3}}$$. We can then calculate the length of ad as $$\frac{\sqrt{3}}{2} - \frac{1}{2\sqrt{3}} = 1/\sqrt{3}$$. From the Pythagorean theorem, we have a length for cd of $$\sqrt{2/3}$$.
The number of spheres in the first layer will require us to use the distance for ab. We now need to find the number of rows in the bottom layer. We have
$$L_1=n \rho_1 + (n-1) \rho_2,$$
where $$\rho_1$$ and $$\rho_2$$ are the number of each kind of row in the layer and $$L_1$$ is the number of spheres in the first layer. Since rows are spaced by $$\sqrt{3}/2$$, we have a number of rows, $$\rho$$, of
$$\rho = \left \lfloor{\frac{n-1}{\sqrt{3}/2}}\right \rfloor+1$$
and $$\rho_1$$ and $$\rho_2$$ can be broken out similar to our $$\lambda$$'s earlier.
$$\rho_1 = \left \lceil{\frac{\rho}{2}}\right \rceil$$
$$\rho_2 = \rho - \rho_1.$$
Fig. 7. We're looking for the distance of line segment cd which can be found using ac and ad.
Now, there is a little matter of how nicely (or not) the second layer will behave for us. It is noteworthy that we are not able to put a sphere into every depression. We skip entire rows of depressions. (The Wikipedia article on sphere packing referred to these locations as the "sixth sphere".) These skipped locations may play mind games on you as you imagine going to the third layer. Nevertheless, the third layer can be made identical to the first, which is what I do here.
Fig. 8. The first layer is blue. The second layer is red. Are we going to have trouble with you Mr. Hedral?
There's a couple of things that happen on the second layer. First, instead of starting with a row of size $$n$$, we start with a row of size $$n-1$$. The second issue is that we may not get as many total rows in. We could do the same formula for rows again but now accounting for the fact that we have lost an additional $$\frac{1}{2\sqrt{3}}$$ before we start. However, we can reduce this to a question of "do we lose a row or not?" The total distance covered by the rows, $$R$$, for the bottom layer is
$$R = (\rho-1) \frac{\sqrt{3}}{2} + 1$$
If $$n-R\ge\frac{1}{2\sqrt{3}}$$, then we have the same number of total rows. Otherwise, we have one less row. We let $$r_L$$ represent the number of rows lost in the second layer, which will either be 0 or 1. Noting that the order of the rows is now $$n-1$$ followed by $$n$$, we can give an expression for the number of spheres, $$L_2$$, in our second layer now.
$$L_2 = (n-1)(\rho_1 - r_L) + n\rho_2$$
We have a very similar formula for the total number of spheres in the box.
$$S = L_1\lambda_1 + L_2\lambda_2,$$
where
$$\lambda_1 = \left \lceil{\frac{\lambda}{2}}\right \rceil$$
$$\lambda_2 = \lambda - \lambda_1,$$
where
$$\lambda = \left \lfloor{\frac{n-1}{\sqrt{2/3}}}\right \rfloor+1.$$
My Maxima function for this is
### Comparison Between Methods
It isn't too hard to tell that one of the two second approaches is going to produce better results than the first after some value of $$n$$ (Fig. 9.). What is more surprising is that our latter two alignments stay neck and neck up into very high values of $$n$$. If we divide them by the volume of the containing cube, both appear to be a round about way to arrive at the square root of 2! (Fig. 10.)
Fig. 9. Both of the latter approaches give much better packing densities than the matrix alignment.
Fig. 10. Square base packing in blue, tetrahedral packing in red, both divided by total volume (# of spheres/unit volume). Unclear if there is a distinct winner and we seem to be getting closer to $$\sqrt{2}$$.
Let's see which one wins more often for positive integer values of $$n$$ in Maxima.
So, there's no run away winner, but if you're a betting man, bet on square base pyramid packing out of the available choices in this post. Regardless, it appears that both of these packing arrangements approach optimal packing (see Sphere packing). My density calculation (allowing the $$\sqrt{2}$$ conjecture) for volume coverage comes out to
Gauss, old boy, seems to have approved of this number.
## Tuesday, December 27, 2016
### Sounds Like F#
Last time, I thought that I was going to have to do some special research to account for multiple sources of sound. Reading this short physics snippet I can see that multiple sources is really as simplistic as my initial thinking was inclined to. You can ignore all of the decibel stuff and focus on the statements about amplitude, because, of course, I am already working in terms of amplitude. What can I say, I let the mass of voices on the internet trouble my certainty unduly? Sort of.
There's two important issues to consider:
1. Offsetting of the signals.
2. Psychological issues regarding the perception of sound.
Regarding number 2, here's a quick hit I found: http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/loud.html. It seems credible, but I'm not sufficiently interested to pursue it further. And so, my dear Perception, I salute you in passing, Good day, Sir!
Offsetting of the signals is something that is implicitly accounted for by naively adding the amplitudes, but there is a question of what the sineChord() function is trying to achieve. Do I want:
1. The result of the signals beginning at exactly the same time (the piano player hits all his notes exactly[?] at the same time—lucky dog, guitar player not as much[?]. Hmm...)?
2. The average case of sounds which may or may not be in phase?
Regarding case 2, Loring Chien suggests in a comment on Quora that the average case would be a 41% increase in volume for identical sounds not necessarily in phase. At first glance, I'm inclined to think it is a plausible statement. Seeming to confirm this suggestion is the summary about Adding amplitudes (and levels) found here, which also explains where the the 41% increase comes from, namely, from $$\sqrt{2}\approx 1.414\dots$$. Good enough for me.
All such being said, I will pass it by as I am approaching this from a mechanical perspective. I'm neither interested in the psychological side of things, nor am I interested in getting average case volumes. I prefer the waves to interact freely. If would be neat, for example, to be able to manipulate the offset on purpose and get different volumes. The naive approach is little more subject to experimentation.
I would like to go at least one step further though and produce a sequence of notes and chords and play them without concern of fuzz or pops caused by cutting the tops of the amplitudes off. We need two pieces: a) a limiter and b) a means of producing sequences of sounds in a musically helpful way.
A limiter is pretty straight-forward and is the stuff of basic queries. I have the advantage of being able to determine the greatest amplitude prior to playing any of the sound. The function limiter() finds the largest absolute amplitude and scales the sound to fit.
Here is an example usage:
One concern here is that we may make some sounds that we care about too quiet by this approach. To address such concerns we would need a compressor that affects sounds from the bottom and raises them as well. The general idea of a sound compressor is to take sounds within a certain amplitude range and compress them into a smaller range. So, sounds outside your range (above or below) get eliminated and sounds within your range get squeezed into a tighter dynamic (volume) range. This might be worth exploring later, but I do not intend to go there in this post.
Last post I had a function called sineChord(), which I realize could be generalized. Any instrument (or group of identical instruments) could be combined using a single chord function that would take as a parameter a function that converts a frequency into a specific instrument sound. This would apply to any instruments where we are considering the notes of the chord as starting at exactly the same time (guitar would need to be handled differently). So, instead of sineChord(), let's define instrumentChord():
Next we will create a simple class to put a sequence of notes/chords and durations into which we can then play our sounds from.
### Reference Chords and Values
Here are a few reference chord shapes and duration values. I define the chord shape and the caller supplies the root sound to get an actual chord. The durations are relative to the whole note and the chord shapes are semi-tone counts for several guitar chord shapes. The root of the shapes is set to 0 so that by adding the midi-note value to all items you end up with a chord using that midi note as the root. This is the job of chord().
Next, InstrumentSequence is an accumulator object that knows how to output a wave form and play it. For simplicity, it is limited to the classic equal temperment western scale. Note that it takes a function has the task of turning a frequency into a wave form, which means that by creating a new function to generate more interesting wave forms, we can have them played by the same accumulator. If we only want it to produce the wave form and aggregate the wave forms into some other composition, we can access the wave form through the routine WaveForm.
A sample use of the class which follows a very basic E, A, B chord progression follows:
To get the same progression with minors, use the EmShape, etc., values. But, at the end of the day, we've still got sine waves, lots of them. And, it's mostly true that,
boring + boring = boring.
I will not attempt the proof. You can make some more examples to see if you can generate a counter-example.
There is also some unpleasant popping that I would like to understand a bit better—for now I'm going to guess it relates to sudden changes in the phases of the waves at the terminations of each section of sound. Not sure what the solution is but I'll guess that some kind of dampening of the amplitude at the end of a wave would help reduce this.
## Saturday, December 24, 2016
### The Sound of F#
I'm doing a bit or reading and dabbling the in the world of sound with the hope that it will help me to tackle an interesting future project. One of the first steps to a successful project is to know more about what the project will actually entail. Right now I'm in exploratory mode. It's a bit like doing drills in sports or practicing simple songs from a book that are not really super interesting to you except for helping you learn the instrument you want to learn. I'm thinking about learning to "play" the signal processor, but it seemed like a good start to learn to produce signals first. And sound signals are what interest me at the moment.
Sound is pretty complicated, but we'll start with one of the most basic of sounds and what it takes to make them in Windows, writing in F#. Our goal in this post is to play sounds asynchronously in F# Interactive.
The first iteration of this comes from Shawn Kovac's response to his own question found here at Stack Overflow. Below is my port to F#. I have used the use keyword to let F# handle the Disposable interfaces on the stream and writer to take care of all the closing issues. It's important to note that the memory stream must remain open while the sound is playing, which means this routine is stuck as synchronous.
To get an asynchronous sound we can shove the PlaySound function into a background thread and let it go. This looks like the following:
A limitation of the PlaySound() approach given above is that it limits your method of sound production. The details of the sound produced are buried inside the function that plays the sound. I don't want to have a bunch of separate routines: one that plays sine waves, one that plays saw tooth, one that plays chords with two notes, one that plays chords with three notes, one that include an experimental distortion guitar—whatever. The sound player shouldn't care about the details, it should just play the sound, whatever it is. (Not a criticism against Kovac, he had a narrower purpose than I do; his choice was valid for his purpose.)
I want to decouple the details of the sound to be produced from the formatting and playing of the sound. Here we have the basic formatting and playing of the sound packaged up that will take any wave form sequence we give it (sequence of integer values):
I haven't decoupled this as far as we could. If we wanted to handle multiple tracks, for example, you would need to take this abstraction a little further.
Now, we also need some functions for generating wave forms. Sequences are probably a good choice for this because you will not need to put them into memory until you are ready to write them to the memory stream in the PlayWave function. What exactly happens to sequence elements after they get iterated over for the purpose of writing to the MemoryStream, I'm not quite clear on. I know memory is allocated by MemoryStream, but whether the sequence elements continue to have an independent life for some time after they are iterated over, I'm not sure about. The ideal thing, of course, would be for them to come into existence at the moment they are to be copied into the memory stream (which they will, due to lazy loading of sequences) and then fade immediately into the bit bucket—forgotten the moment after they came into being.
Here are a few routines that relate to making chords that are not without an important caveat: the volume control is a bit tricky.
Here is a sample script to run in F# Interactive:
The above plays a version of an A chord (5th fret E-form bar chord on the guitar).
Note that I have divided the volume by the number of notes in the chord. If we don't watch the volume like this and we let it get away on us, it will change the sound fairly dramatically. At worst something like the "snow" from the old analog TVs when you weren't getting a signal, but if you just go a little over, you will get a few pops like slightly degraded vinyl recordings.
We could include volume control in our wave form production routines. This wouldn't necessarily violate our decoupling ideals. The main concern I have is that I want the volume indicated to represent the volume of one note played and the other notes played should cause some increase in volume. I want the dynamic fidelity of the wave forms to be preserved with different sounds joining together. Even after that, you may want to run a limiter over the data to make sure the net volume of several sounds put together doesn't take you over your limit.
However, I need to do more research to achieve these ideals. For now, I will break it off there.
## Friday, December 23, 2016
### Background
I have a really basic vocabulary quiz program that I have been dabbling with, partly as a means of learning to use LispWorks and partly as a way to get a little different way of reviewing my vocabulary in my personal study of NT Greek. I obtained the basic vocabulary from Mounce's Flashworks program. There are some text files for vocabulary for a few different languages, including Greek and Hebrew. These files can be read as UTF-8 Unicode.
Unicode support in Common Lisp is non-uniform, owing to the fact that the language standard was established before Unicode arrived [Seibel]. So, what works in one implementation may not work in another. I have found this in working with LispWorks and Closure Common Lisp. Since I wanted something easy, not something clever, I have not attempted to bridge these. I just want the "easy" answers for the basic problems of reading and writing Unicode in LispWorks.
### Reading and Writing Unicode
If I want to read a basic tab delimited Unicode file, line by line, I use get-text-data (below). keepers allows me to take a subset of the columns in the file
The first awful thing you will notice here is the special-read function. This is not always necessary, but I did have a case where I had a leading Byte-Order-Mark (BOM: 0xFEFF) that I needed remove from the file. This, somewhat oddly, but understandably, is called #\Zero-Width-No-Break-Space in LispWorks [WikiPedia]. If memory serves, putting the BOM in (which I did on purpose at one point) made reading the file work without specifying a format to read in. But the BOM is optional for utf-8.
Writing out to a file is quite straightforward, but the question is whether it will be possible to read it in correctly. The answer is that it depends on how you will read it in later. If you are only going to read it into the same program or into programs that will assume UTF-8, then there's no issue. But if you want to be able to read it in without thinking about whether the source file is Unicode or not, you can deliberately output the BOM so that it will read successfully in LispWorks even if you did not specify the :external-format. Below is a sample of doing just this.
The function colleciton->plist is my own function which turns my object into a plist which can be read by the built-in function read. (This is my way of textifying CLOS objects to write them to file—the details are not relevant to my topic.)
Now, I can read in the plist that I wrote out, without specifying the :external-format, as in:
However, if I didn't manually output the BOM, I would need to write:
The long and the short of it is that you can use :external-format all the time and use a consistent format for files that pertain to your program and that's probably the best practice. If you want to be sure another LispWorks program is going to be OK with your UTF-8 file, whether it is consistently using that format or not, putting a BOM at the start for good measure may be a good idea. On the other hand, maybe the reader will choke on the BOM because it doesn't filter it out when reading a file it already knows is utf-8.
So, I didn't solve the problem, but if you're head butting a format issue in Unicode, maybe this says enough about it that you can find something to do with the particular data you can't seem to read right now—because, I feel your pain.
For more information on IO for Unicode in LispWorks, see the manual, especially here.
## Wednesday, June 1, 2016
### Tax Brackets Are Not So Bad
There's a common misconception that many seem to have about the way taxes work. People overthink themselves about "moving into a higher tax bracket." They think that if they just barely go over their current tax bracket into the next, the tax man will get extra hungry and they will wind up making less money than if they, for example, didn't go in for that little bit of overtime. These concerns are, in a word, unwarranted. That's not to say that anecdotal evidence in support of this idea does not abound. I'm sure you can find anecdotal evidence for anything that's popular to complain about.
In 2015, the following tax brackets applied to income taxes:
• <=$44,701, 15% •$44,701—$89,401, 22% •$89,401—$138,586, 26% • >$138,586, 29%.
So, if I make $44,701 in taxable income, I pay$6705.15 in taxes on it. Suppose I make $44,702. Here's where the confusion becomes apparent. Some would try to tell you that you now pay 22% on the entire amount, or$9834.44, which would be a complaint worthy problem for someone teetering on the border of a tax bracket. (If a government actually tried to do it this way, the public outrage would produce headline news, not anecdotal evidence.) I call this false idea "folk" tax brackets.
What do I actually pay on \$44,702? I pay $$15\% \times 44,701 + 22\% \times 1 = 6705.37$$ in income tax.
The folk thinking taxation produces a jagged net income graph. This is the sort of thing people are implying when they speak of "making less" if they work overtime. You'd think they thought the take-home pay graph looked like this:
Fig. 1. Marginal taxes don't cause the take-home pay graph to look anything like this, but some talk as if it did.
The real graph is not jagged. It isn't smooth either (if you look close enough). It is continuous, unlike the above graph, but it does produce corners at the locations of the tax bracket cross-overs. These are not really that scary looking:
Fig. 2. Marginal taxes only increase the rate of tax "marginally". The increase in tax rate applies to the marginal amounts ("increments"), not the entire amounts. Basically you have a line with some very slight elbows in it where there is a small change in direction.
So, like you, I wouldn't mind if the whole graph was a little steeper (increased take-home pay percentage, less taxes), but it is what it is. And what it is is relatively fair, in concept at least.
### Modeling Taxes in Maxima
Now, where did I get these wonderful graphs? I produced them in Maxima, of course. Here's the Maxima code to define a marginal tax formula, if given the brackets that apply:
You can see the parts that you would need to change to produce your own formula for your marginal tax situation. FederalIncomeTax2015 is a list containing two lists. The first of these is the list of tax percentages. The next is the list of corresponding threshold values (0 is implicit as the beginning and the last percentage is assumed to apply to anything after the largest threshold amount).
Noteworthy items in the Maxima code above:
1. The characteristic function (charfun) produces the same effect as an if statement in the code. The characteristic function yields 1 if the condition is true, else 0. So, if an amount is not in the relevant range, it will not contribute. I have two different conditions to check for, but rather than branching, I just keep them in parallel. The advantage is simplicity. The disadvantage is that, in theory, there is more computation happening than really needs to happen. The simplicity carries a lot of weight in my book.
2. I append 0 and infinity to the list of boundaries for the tax brackets. Since Maxima recognizes inf and knows that any-number is less than inf, I have no case-taking to deal with the initial or final tax brackets.
3. map. When map will do the job, nothing does it more succinctly. Thanks map!
4. '' (quote-quote or double single-quote). Oh, boy. The basic meaning is, "evaluate what comes next and use the result of the evaluation instead of what's here." What this amounts to in this code is that the code that produces the function (the MarginalTaxFormula) is not re-run every time the function marginalFederalTax(income) is called with a different value of income. The MarginalTaxFormula(...) code is invoked by the '' operator and this returns the function which MarginalTaxFormual(...) produces. This is necessary because I am defining the function using the := operator which suspends evaluation until the function is invoked. Thus, you end up with a definition like this:
marginalFederalTax(income):=12788.1*charfun(income>=138586)+9834.0*charfun(income>=89401)+6705.15*charfun(income>=44701)+0.15*charfun(0
0.22*charfun(44701 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6098911166191101, "perplexity": 654.8732026530308}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886112682.87/warc/CC-MAIN-20170822201124-20170822221124-00385.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/elementary-algebra/appendix-extra-word-problems-page-525/46 | ## Elementary Algebra
We consider the unknown length of the box as $x$ inches. Therefore, one-half the length is $\frac{x}{2}$ inches. Since the width ($8$ inches) is $1$ inch more than one-half the length, we write the following equation and solve: $8= \frac{x}{2}+1$ $8-\frac{x}{2}=1$ $\frac{8(2)-x}{2}=1$ $\frac{16-x}{2}=1$ $16-x=2$ $x=16-2$ $x=14$ Therefore, the length is 14 inches. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9867860674858093, "perplexity": 483.77630277686524}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949694.55/warc/CC-MAIN-20230401001704-20230401031704-00099.warc.gz"} |
http://www.mathematicalfoodforthought.com/2006/05/find-that-lattice-point-topic-number_8.html | Monday, May 8, 2006
Find That Lattice Point. Topic: Number Theory. Level: AIME/Olympiad.
Problem: (Minkowski's Thoerem) Any bounded plane convex region $R$ symmetrical about the origin with area $> 4$ contains at least two other lattice points other than the origin itself.
Solution: WLOG, assume the lattice is a regular square lattice (with side length $1$, of course). The result can easily be generalized to different types of lattices.
Consider partitioning the lattice into $2 \times 2$ squares (with the origin being the vertex of four of them). Since the area of $R$ is greater than $4$, we can find two points in $R$ such that their coordinates relative to the $2 \times 2$ squares they are in are equivalent (consider stacking all the $2 \times 2$ squares up; there must exist a point directly above another one or the area is $\le 4$).
Call these points
$P(2a+\alpha, 2b+\beta)$ and $Q(2c+\alpha, 2d+\beta)$
with $a,b,c,d$ integers and $0 \le \alpha, \beta \le 2$ reals. But since $R$ is symmetrical about the origin, we know
$P^{\prime}(-2a-\alpha, -2b-\beta)$ and $Q^{\prime}(-2c-\alpha, -2d-\beta)$
also exist in $R$. If $R$ is convex, then any point along a line segment connecting two points in $R$ is also in $R$. In particular, the midpoint of any line segment between two points in $R$ is in $R$. Hence the midpoints of $PQ^{\prime}$ and $P^{\prime}Q$ are in $R$. They are
$M_1(a-c, b-d)$ and $M_2(c-a, d-b)$,
which are lattice points not on the origin because $a,b,c,d$ are integers and $P \neq Q$. Therefore $R$ contains at least two other lattice points $M_1$ and $M_2$. QED.
--------------------
Comment: We could have invoked symmetry at the end to find $M_2$ from $M_1$, too. From the proof, it shouldn't be too hard to tell what I assumed at the beginning for other lattices; basically you just need to define a coordinate system with the same properties . I first encountered this problem at PROMYS and it appears in most Number Theory texts, as far as I know.
--------------------
Practice Problem: Can you generalize this result to a $3$-space? An $n$-space? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8426637649536133, "perplexity": 182.53586472194098}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875141806.26/warc/CC-MAIN-20200217085334-20200217115334-00406.warc.gz"} |
https://experts.syr.edu/en/publications/evidence-for-exotic-hadron-contributions-to-%CE%BBb0-j-%CF%88p%CF%80-decays | # Evidence for Exotic Hadron Contributions to Λb0 →j /ψpπ- Decays
LHCb Collaboration
Research output: Contribution to journalArticlepeer-review
118 Scopus citations
## Abstract
A full amplitude analysis of Λb0→J/ψpπ- decays is performed with a data sample acquired with the LHCb detector from 7 and 8 TeV pp collisions, corresponding to an integrated luminosity of 3 fb-1. A significantly better description of the data is achieved when, in addition to the previously observed nucleon excitations N→pπ-, either the Pc(4380)+ and Pc(4450)+→J/ψp states, previously observed in Λb0→J/ψpK- decays, or the Zc(4200)-→J/ψπ- state, previously reported in B0→J/ψK+π- decays, or all three, are included in the amplitude models. The data support a model containing all three exotic states, with a significance of more than three standard deviations. Within uncertainties, the data are consistent with the Pc(4380)+ and Pc(4450)+ production rates expected from their previous observation taking account of Cabibbo suppression.
Original language English (US) 082003 Physical Review Letters 117 8 https://doi.org/10.1103/PhysRevLett.117.082003 Published - Aug 18 2016
## ASJC Scopus subject areas
• Physics and Astronomy(all)
## Fingerprint
Dive into the research topics of 'Evidence for Exotic Hadron Contributions to Λb0 →j /ψpπ- Decays'. Together they form a unique fingerprint. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.956108033657074, "perplexity": 6787.320558185786}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103329963.19/warc/CC-MAIN-20220627073417-20220627103417-00622.warc.gz"} |
https://www.vedantu.com/question-answer/light-takes-t1-sec-to-travel-a-distance-x-in-a-class-12-physics-cbse-5fd7cab9609c0e2b766a7d0e | Question
Light takes ${t_1}$ sec to travel a distance $x$ in a vacuum and the same light takes ${t_2}$ sec to travel $10cm$ in a medium. The critical angle for the corresponding medium will be(A) ${\sin ^{ - 1}}\left( {\dfrac{{10{t_2}}}{{{t_1}x}}} \right)$ (B) ${\sin ^{ - 1}}\left( {\dfrac{{{t_2}x}}{{10{t_1}}}} \right)$ (C) ${\sin ^{ - 1}}\left( {\dfrac{{10{t_1}}}{{{t_2}x}}} \right)$ (D) ${\sin ^{ - 1}}\left( {\dfrac{{{t_1}x}}{{10{t_2}}}} \right)$
Verified
93k+ views
Hint: When light passes from one medium to another it will bend its path. This phenomenon is called refraction. The path of the ray undergoing reflection or refraction is reversible. This is called the principle of reversibility of light. The refractive index of the medium concerning air or vacuum is called the absolute refractive index.
Complete step by step solution
At a particular angle of incidence called the critical angle, the refracted ray grazes the surface of separation. The angle of incidence in a denser medium for which the angle of refraction in a rarer medium is ${90^0}$ is called the critical angle of the medium.
The time taken by the light to travel the distance $x$ is ${t_1}$ sec. Let $c$ be the velocity of light through a vacuum.
$c = \dfrac{x}{{{t_1}}}$
The time taken by the light to travel $10cm$ in a medium is taken as ${t_2}$ . The velocity of light through the medium can be taken as $v$
$v = \dfrac{{10}}{{{t_2}}}$
The absolute refractive index can also be expressed as the ratio of the velocity of light in vacuum $(c)$ to the velocity of light in the medium.
i.e.
$\mu = \dfrac{c}{v}$
where $\mu$ is the refractive index.
The critical angle is given by,
$\sin C = \dfrac{1}{\mu }$
Substituting $\mu = \dfrac{c}{v}$ in the above equation, we get
$\sin C = \dfrac{1}{{\dfrac{c}{v}}} = \dfrac{v}{c}$
We know that,
$c = \dfrac{x}{{{t_1}}}$
And
$v = \dfrac{{10}}{{{t_2}}}$
Substituting these values we get,
$\sin C = \dfrac{{\dfrac{{10}}{{{t_2}}}}}{{\dfrac{x}{{{t_1}}}}} = \dfrac{{10{t_1}}}{{x{t_2}}}$
From this, we can write the critical angle as,
$C = {\sin ^{ - 1}}\left( {\dfrac{{10{t_1}}}{{{t_2}x}}} \right)$
The answer is: Option (C); ${\sin ^{ - 1}}\left( {\dfrac{{10{t_1}}}{{{t_2}x}}} \right)$ .
Note
The velocity of light through any medium will be less than that of the velocity of light through a vacuum. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media and a given colour of light. This law is called Snell’s law. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9583454132080078, "perplexity": 161.47225902922784}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585186.33/warc/CC-MAIN-20211018000838-20211018030838-00027.warc.gz"} |
https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Spectroscopy/Rotational_Spectroscopy/Rovibrational_Spectroscopy | # Rovibrational Spectroscopy
In this section, we will learn how the rotational transitions of molecules can accompany the vibrational transitions. It is important to know how each peak correlates to the molecular processes of molecules. Rovibrational spectra can be analyzed to determine average bond length.
### Introduction
Each of the normal modes of vibration of heteronuclear diatomic molecules in the gas phase also contains closely-spaced (1-10 cm-1 difference) energy states attributable to rotational transitions that accompany the vibrational transitions. A molecule’s rotation can be affected by its vibrational transition because there is a change in bond length, so these rotational transitions are expected to occur. Since vibrational energy states are on the order of 1000 cm-1, the rotational energy states can be superimposed upon the vibrational energy states.
### Selection Rules
Rotational and Vibration transitions (also known as rigid rotor and harmonic oscillator) of molecules help us identify how molecules interact with each other, their bond length as mentioned in previous section. In order to know each transitions, we have to consider other terms like wavenumber, force constant, quantum number, etc. There are rotational energy levels associated with all vibrational levels. From this, vibrational transitions can couple with rotational transitions to give rovibrational spectra. Rovibrational spectra can be analyzed to determine average bond length.
We treat the molecule's vibrations as those of a harmonic oscillator (ignoring anharmonicity). The energy of a vibration is quantized in discrete levels and given by
$E_v=h\nu \left(v+\dfrac{1}{2} \right)$
Where v is the vibrational quantum number and can have integer values 0, 1, 2..., and $$\nu$$ is the frequency of the vibration given by:
$\nu=\dfrac{1}{2\pi}\left(\dfrac{k}{\mu}\right)^\dfrac{1}{2}$
Where k is the force constant and $$\mu$$ is the reduced mass of a diatomic molecule with atom masses m1 and m2, given by
$\mu=\dfrac{{m}_1{m}_2}{{m}_1+{m}_2}$
We treat the molecule's rotations as those of a rigid rotor (ignoring centrifugal distortion). The energy of a rotation is also quantized in discrete levels given by
$E_r=\dfrac{h^2}{8\pi^2I} J(J+1)$
In which $$I$$ is the moment of inertia, given by
${I}=\mu{r}^2$
where $$\mu$$ is the reduced mass from above and r is the equilibrium bond length.
Experimentally, frequencies or wavenumbers are measured rather than energies, and dividing by h or hc gives more commonly seen term symbols, F(J) using the rotational quantum number J and the rotational constant B in either frequency
$F(J)=\dfrac{E_r}{h}=\dfrac{h}{8\pi^2I} J(J+1)=BJ(J+1)$
or wavenumbers
$F(J)=\dfrac{E_r}{hc}=\dfrac{h}{8\pi^2cI} J(J+1)=BJ(J+1)$
It is important to note in which units one is working since the rotational constant is always represented as B, whether in frequency or wavenumbers.
### Vibrational Transition Selection Rules
At room temperature, typically only the lowest energy vibrational state v= 0 is populated, so typically v0 = 0 and ∆v = +1. The full selection rule is technically that ∆v = ±1, however here we assume energy can only go upwards because of the lack of population in the upper vibrational states.
### Rotational Transition Selection Rules
At room temperature, states with J≠0 can be populated since they represent the fine structure of vibrational states and have smaller energy differences than successive vibrational levels. Additionally, ∆J = ±1 since a photon contains one quantum of angular momentum and we abide by the principle of conservation of energy. This is also the selection rule for rotational transitions.
The transition ∆J = 0 (i.e. J" = 0 and J' = 0, but $$\nu_0 \neq 0$$ is forbidden and the pure vibrational transition is not observed in most cases. The rotational selection rule gives rise to an R-branch (when ∆J = +1) and a P-branch (when ∆J = -1). Each line of the branch is labeled R(J) or P(J), where J represents the value of the lower state.
#### R-branch
When ∆J = +1, i.e. the rotational quantum number in the ground state is one more than the rotational quantum number in the excited state – R branch (in French, riche or rich). To find the energy of a line of the R-branch:
$\Delta{E}=h\nu_0 +hB \left [J(J+1)-J^\prime (J^\prime{+1}) \right]$
$=h\nu_0 +hB \left[(J+1)(J+2)-J(J+1)\right]$
$=h\nu_0 +2hB(J+1)$
#### P-branch
When ∆J = -1, i.e. the rotational quantum number in the ground state is one less than the rotational quantum number in the excited state – P branch (in French, pauvre or poor). To find the energy of a line of the P-branch:
$\Delta{E}=h\nu_0 +hB \left [J(J+1)-J^\prime(J^\prime+1) \right]$
$=h\nu_0 +hB \left [J(J-1)-J(J+1) \right]$
$=h\nu_0 -2hBJ$
#### Q-branch
When ∆J = 0, i.e. the rotational quantum number in the ground state is the same as the rotational quantum number in the excited state – Q branch (simple, the letter between P and R). To find the energy of a line of the Q-branch:
$\Delta{E}=h\nu_0 +hB[J(J+1)-J^\prime(J^\prime+1)]$
$=h\nu_0$
The Q-branch can be observed in polyatomic molecules and diatomic molecules with electronic angular momentum in the ground electronic state, e.g. nitric oxide, NO. Most diatomics, such as O2, have a small moment of inertia and thus very small angular momentum and yield no Q-branch.
Figure 1: Cartoon depiction of rotational energy levels, J, imposed on vibrational energy levels, v. The transitions between levels that would result in the P- and R-branches are depicted in purple and red, respectively, in addition to the theoretical Q-branch line in blue.
As seen in Figure 1, the lines of the P-branch (represented by purple arrows) and R-branch (represented by red arrows) are separated by specific multiples of B (2B), thus the bond length can be deduced without the need for pure rotational spectroscopy.
### Energy
The total nuclear energy of the combined rotation-vibration terms, S(v, J), can be written as the sum of the vibrational energy and the rotational energy
$S(v,J)=G(v)+F(J)$
Where G(v) represents the energy of the harmonic oscillator, ignoring anharmonic components and S(J) represents the energy of a rigid rotor, ignoring centrifugal distortion.
From this, we can derive
$S(v,J)=\nu_0 v+\dfrac{1}{2}+BJ(J+1)$
The relative intensity of the P- and R-branch lines depends on the thermal distribution of electrons; more specifically, they depend on the population of the lower J state. If we represent the population of the Jth upper level as NJ and the population of the lower state as N0, we can find the population of the upper state relative to the lower state using the Boltzmann distribution:
$\dfrac{N_J}{N_0}={(2J+1)e}^\left(-\dfrac{E_r}{kT}\right)$
(2J+1) gives the degeneracy of the Jth upper level arising from the allowed values of MJ (+J to –J). As J increases, the degeneracy factor increases and the exponential factor decreases until at high J, the exponential factor wins out and NJ/N0 approaches zero at a certain level, Jmax. Thus, when
$\dfrac{d}{dJ} \left( \dfrac{N_J}{N_0} \right)=0$
by differentiation, we obtain
$J_{max}=\left(\dfrac{kT}{2hB}\right)^\dfrac{1}{2}-\dfrac{1}{2}$
This is the reason that rovibrational spectral lines increase in energy to a maximum as J increases, then decrease to zero as J continues to increase, as seen in Figure 2 and Figure 3.
From this relationship, we can also deduce that in heavier molecules, B will decrease because the moment of inertia will increase, and the decrease in the exponential factor is less pronounced. This results in the population distribution shifting to higher values of J. Similarly, as temperature increases, the population distrubution will shift towards higher values of J.
### Ideal Spectrum
The spectrum we expect, based on the conditions described above, consists of lines equidistant in energy from one another, separated by a value of 2B. The relative intensity of the lines is a function of the rotational populations of the ground states, i.e. the intensity is proportional to the number of molecules that have made the transition. The overall intensity of the lines depends on the vibrational transition dipole moment.
Figure 2: A cartoon depiction of an ideal rovibrational spectrum.
Between P(1) and R(0) lies the zero gap, where the the first lines of both the P- and R-branch are separated by 4B, assuming that the rotational constant B is equal for both energy levels. The zero gap is also where we would expect the Q-branch, depicted as the dotted line, if it is allowed.
### Real Spectra
We find that real spectra doesn't exactly fit the expectations from above.
Figure 3: A cartoon depiction of a real rovibrational spectrum.
As energy increases, the R-branch lines become increasingly similar in energy (i.e., the lines move closer together) and as energy decreases, the P-branch lines become increasingly dissimilar in energy (i.e. the lines move farther apart). This is attributable to two phenomena: rotational-vibrational coupling and centrifugal distortion.
#### Rotational-Vibrational Coupling
As a diatomic molecule vibrates, its bond length changes. Since the moment of inertia is dependent on the bond length, it too changes and, in turn, changes the rotational constant B. We assumed above that B of R(0) and B of P(1) were equal, however they differ because of this phenomenon and B is given by
$B_e= \left(-\alpha_e \nu+\dfrac{1}{2}\right)$
Where $${B}_{e}$$ is the rotational constant for a rigid rotor and $$\alpha_{e}$$ is the rotational-vibrational coupling constant. The information in the band can be used to determine B0 and B1 of the two different energy states as well as the rotational-vibrational coupling constant, which can be found by the method of combination differences.
##### Combination Differences
Combination differences involves finding the values of B0 and B1 rotational-vibrational coupling constant by measuring the change for two different transitions sharing a common state.
Figure 4: Part of the method of combination differences depicting P- and R-branch transitions sharing a common lower J state.
To determine B1, we pair transitions sharing a common lower state; here, R(1) and P(1). Note that the vibrational level does not change. Both branches begin with J = 1, so by finding the difference in energy between the lines, we find B1.
$\Delta E_R-\Delta E_P = E(\nu=1, J' =J+1) - E(\nu=1,J' =J-1)$
Inserting this information into the equation from above, we obtain
$=\tilde{\nu} [R(J-1)]-\tilde{\nu} [P(J+1)]$
$=\omega_0+B_1 (J+1)(J+2)-B_0 J(J+1) - \omega_0 +B_1(J-1)J - B_0 J(J+1)$
$={4B}_1 \left(J+\dfrac{1}{2} \right)$
If we plot $$\Delta E_R-\Delta E_P$$ against $$(J+ \dfrac{1}{2} \ ), we obtain a straight line with slope 4B1. Figure 5: Part of the method of combination differences depicting P- and R-branch transitions sharing a common upper J state. Similarly, we can determine B0 by finding wavenumber differences in transitions sharing a common upper state; here, R(0) and P(2). Both branches terminate at J=1 and differences will only depend on B0. $=\tilde {\nu} [R(J-1)]- \tilde{\nu} [P(J+1)]$ $=\omega_0+{B}_1{J(J+2)-B}_0{J(J-1)-[}\omega_0{+B}_1{J(J+1)-B}_0{(J+1)(J+2)]$ $={4B}_0{(J+}\dfrac{1}{2}{)}$ As before, if we plot $\Delta{E}_{R}-\Delta{E}_{P}$ against ${(J+}\dfrac{1}{2}{)}$, we obtain a straight line with slope 4B0. Following from this, we can obtain the rotational-vibrational coupling constant: $={B}_1-{B}_0=\alpha$ ##### Centrifugal Distortion Similarly to rotational-vibrational coupling, centrifugal distortion is related to the changing bond length of a molecule. A real molecule does not behave as a rigid rotor that has a rigid rod for a chemical bond, but rather acts as if it has a spring for a chemical bond. As the rotational velocity of a molecule increases, its bond length increases and its moment of inertia increases. As the moment of inertia increases, the rotational constant B decreases. ${F(J)=BJ(J+1)-DJ}^2{(J+1)}^2$ Where D is the centrifugal distortion constant and is related to the vibration wavenumber, $(omega$$ \[D=\dfrac{4B^3}{\omega^2}$
When the above factors are accounted for, the actual energy of a rovibrational state is
$S(v,J)=\nu_0v+\dfrac{1}{2}+B_e J (J+1)- \alpha_e \left(v+\dfrac{1}{2}\right) J(J+1)-D_e[J(J+1)]^2$
### References
1. Hollas, M. J. Modern spectroscopy. (3rd ed.). Chichester: John Wiley & Sons, 1996.
2. Hollas, M. J. Basic atomic and molecular spectroscopy. Cambridge: The Royal Society of Chemistry, 2002.
3. Herzberg, G. Molecular spectra and molecular structure. (2nd ed.). New York: Prentice-Hall, 1950.
4. Fetterolf, Monty L. Enhanced Intensity Distribution Analysis of the Rotational–Vibrational Spectrum of HCl.
J. Chem. Ed. 2007, 84, 1064. DOI: 10.1021/ed084p1062
### Problems
1. Find the reduced mass of D35Cl in kg, if the mass of D-2 is 2.014 amu and the mass of Cl-35 is 34.968 amu.
2. Using information found in problem 1, calculate the rotational constant B (in wavenumbers) of D35Cl given that the average bond length is 1.2745 Å.
3. Using the rigid rotor approximation, estimate the bond length in a 12C16O molecule if the energy difference between J=1 and J=3 were to equal 14,234 cm-1.
1. $$dfrac{2.014 amu*34.968 amu}{2.014 amu + 34.968 amu}$$ gives 1.807 amu. To convert to kg, multiple by 1.66 x 10-27 kg/amu. Answer: 3.00 x 10-27 kg
2. We know that in wavenumbers, $$B=\dfrac{h}{8\pi^2cI}$$.
First, we must solve for the moment of inertia, I, using
${I}=\mu{r}^2=(3.00*10^{-27} kg)(1.2745 *10^{-10}m)^2$ = 4.87 x 10-47 kg•m2= I
We can now substitute into the original formula to solve for B. h is Planck's constant, c is the speed of light in m/s and I = 4.87 x 10-47 kg•m2. This will give us the answer in m-1, then we can convert to cm-1. Answer: 5.74 cm-1.
3. We use the same formula as above and expand the moment of inertia in order to solve for the average bond length.
$B=\dfrac{h}{8\pi^2 c\mu r^2}$
We can deduce the rotational constant B since we know the distance between two energy states and the relationship
$F(J)=BJ(J+1)$
The distance between J=1 and J=3 is 10B, so using the fact that B = 14,234 cm-1, B=1423.4 cm-1. We convert this to m-1 so that it will match up with the units of the speed of light (m/s) and obtain B = 142340 m-1.
Using the reduced mass formula, we find that µ = 1.138 x 10-26 kg. Answer: r = 81 Å.
### Contributors
• Joya Cooley, UC Davis | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9607702493667603, "perplexity": 1092.7583963573143}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864139.22/warc/CC-MAIN-20180621094633-20180621114633-00537.warc.gz"} |
https://www.tutorialspoint.com/how-to-turn-off-testng-s-default-reporters-programmatically | # How to turn off TestNG's default reporters programmatically?
TestNGRest AssuredDynamic Programming
#### TestNG Complete Bootcamp For Beginners
38 Lectures 4.5 hours
#### Learn TestNG
15 Lectures 1.5 hours
#### The Complete TestNG & Automation Framework Design Course
28 Lectures 3 hours
TestNG allows to run the test suites from IntelliJ IDE as well as from the command line. When user runs the testNG.xml either from an IDE or the command line, TestNG generates a default report. It saves all the reports and respective HTML files in the Project->test-output folder. If this folder does not exist, then TestNG creates one.
To disable the default reports programmatically, TestNG should be run through the command line (cmd).
Following are the prerequisites to run the test suites from the command line −
• testNG.xml file should be created to define the test suites and testing classes to execute.
• All the dependent jars should be available inside a project folder. It includes testing.jar, jcommander.jar and any other jars that are used in the test cases.
• The Path of bin or out folder where .class files are stored after compilation.
Approach/Algorithm to solve this problem −
• Step 1 − Create different testing classes having different @Test methods and one @BeforeSuite method.
• Step 2 − Compile the class. It will create an out folder in IntelliJ and bin folder in Eclipse.
• Step 3 − Place all the jar files in the lib folder.
• Step 4 − Now create the testNG.xml as given below.
• Step 5 − Open the cmd.
• Step 6 − Navigate to the project path using cd <project_path>
• Step 7 − Run the following command:
java -cp <path of lib;> <path of out or bin folder> org.testng.TestNG <path of testng>/testng.xml
## Example
The following code shows how to disable the default report generation at runtime −
src/ NewTestngClass.java
import org.testng.TestNG;
import org.testng.annotations.*;
public class NewTestngClass {
// test case 1
@Test()
public void testCase1() throws InterruptedException {
System.out.println("in test case 1 of NewTestngClass");
}
// test case 2
@Test()
public void testCase2() throws InterruptedException {
System.out.println("in test case 2 of NewTestngClass");
}
@BeforeSuite
public void name() {
TestNG myTestNG = new TestNG();
myTestNG.setUseDefaultListeners(false);
System.out.println("Default reports are disabled");
}
}
src/testng.xml
This is a configuration file that is used to organize and run the TestNG test cases. It is very handy when limited tests are needed to execute rather than the full suite.
<?xml version = "1.0" encoding = "UTF-8"?>
<!DOCTYPE suite SYSTEM "http://testng.org/testng-1.0.dtd" >
<suite name = "Suite1">
<test name = "test1">
<classes>
<class name = " NewTestngClass"/>
</classes>
</test>
</suite>
Command to run −
java -cp .\lib\*;.\out\production\TestNGProject org.testng.TestNG src\testng.xml
## Output
Default reports are disabled
in test case 1 of NewTestngClass
in test case 2 of NewTestngClass
===============================================
Suite1
Total tests run: 2, Passes: 2, Failures: 0, Skips: 0
===============================================
Updated on 09-Mar-2022 11:14:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4289442300796509, "perplexity": 15634.89785001336}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335304.71/warc/CC-MAIN-20220929034214-20220929064214-00222.warc.gz"} |
https://socratic.org/questions/how-do-you-rationalize-the-denominator-and-simplify-1-sqrta-sqrtb | Algebra
Topics
How do you rationalize the denominator and simplify 1/(sqrta+sqrtb)?
Mar 12, 2016
$= \frac{\sqrt{a} - \sqrt{b}}{a - b}$
Explanation:
Given:$\text{ } \frac{1}{\sqrt{a} + \sqrt{b}}$
Known:$\left({a}^{2} - {b}^{2}\right) = \left(a + b\right) \left(a - b\right)$
So using the above known information multiply by 1 but in the form of $1 = \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} - \sqrt{b}}$
So
$= \frac{1}{\sqrt{a} - \sqrt{b}} \times \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} - \sqrt{b}}$
$= \frac{\sqrt{a} - \sqrt{b}}{a - b}$
Impact of this question
166 views around the world | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9726428389549255, "perplexity": 2423.227387901734}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670151.97/warc/CC-MAIN-20191119121339-20191119145339-00150.warc.gz"} |
https://doc.freefem.org/tutorials/elasticity.html | FreeFEM Documentation on GitHub
stars - forks
# The System of elasticity
Elasticity
Solid objects deform under the action of applied forces:
a point in the solid, originally at $$(x,y,z)$$ will come to $$(X,Y,Z)$$ after some time; the vector $$\mathbf{u}=(u_1,u_2,u_3) = (X-x, Y-y, Z-z)$$ is called the displacement. When the displacement is small and the solid is elastic, Hooke’s law gives a relationship between the stress tensor $$\sigma(u)=(\sigma_{ij}(u) )$$ and the strain tensor $$\epsilon(u)=\epsilon_{ij}(u)$$
$\sigma_{ij}(u) = \lambda \delta_{ij} \nabla.\mathbf{u}+ 2\mu\epsilon_{ij}(u),$
where the Kronecker symbol $$\delta_{ij} = 1$$ if $$i=j$$, $$0$$ otherwise, with
$\epsilon_{ij}(u) = {1\over 2}({\partial u_i\over\partial x_j} + {\partial u_j\over\partial x_i} ),$
and where $$\lambda, \mu$$ are two constants that describe the mechanical properties of the solid, and are themselves related to the better known constants $$E$$, Young’s modulus, and $$\nu$$, Poisson’s ratio:
$\mu = {E\over 2( 1+\nu)}, \quad \lambda = {E\nu\over (1+\nu)(1-2\nu)}.$
Lamé’s system
Let us consider a beam with axis $$Oz$$ and with perpendicular section $$\Omega$$. The components along $$x$$ and $$y$$ of the strain $${\bf u}(x)$$ in a section $$\Omega$$ subject to forces $${\bf f}$$ perpendicular to the axis are governed by:
$-\mu \Delta {\bf u} - (\mu+\lambda) \nabla (\nabla .{\bf u})={\bf f}~~\hbox{in}~~\Omega,$
where $$\lambda$$ ,$$\mu$$ are the Lamé coefficients introduced above.
Remark, we do not use this equation because the associated variational form does not give the right boundary condition, we simply use:
$- div( \sigma ) = \mathbf{f} \quad \mbox{in}~~\Omega$
where the corresponding variational form is:
$\int_{\Omega} \sigma(u) : \epsilon(\mathbf{v})\;dx - \int_{\Omega} \mathbf{v} f \;dx =0;$
where $$:$$ denotes the tensor scalar product, i.e. $$a: b = \sum_{i,j} a_{ij}b_{ij}$$.
So the variational form can be written as :
$\int_{\Omega} \lambda \nabla.u \nabla.v + 2 \mu \epsilon(\mathbf{u}):\epsilon(\mathbf{v}) \; dx - \int_{\Omega} \mathbf{v} f \;dx =0;$
Tip
Consider an elastic plate with the undeformed rectangle shape $$[0,20]\times [-1,1]$$.
The body force is the gravity force $$\mathbf{f}$$ and the boundary force $$\mathbf{g}$$ is zero on lower, upper and right sides. The left vertical side of the beam is fixed. The boundary conditions are:
$\begin{split}\begin{array}{rcll} \sigma . {\bf n} &= \mathbf{g} &= 0 & \hbox{ on }\Gamma_1, \Gamma_4, \Gamma_3, \\ {\bf u} &= \mathbf{0} && \hbox{ on }\Gamma_2 \end{array}\end{split}$
Here $${\bf u}=(u,v)$$ has two components.
The above two equations are strongly coupled by their mixed derivatives, and thus any iterative solution on each of the components is risky. One should rather use FreeFEM’s system approach and write:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 // Parameters real E = 21e5; real nu = 0.28; real f = -1; // Mesh mesh Th = square(10, 10, [20*x,2*y-1]); // Fespace fespace Vh(Th, P2); Vh u, v; Vh uu, vv; // Macro real sqrt2=sqrt(2.); macro epsilon(u1,u2) [dx(u1),dy(u2),(dy(u1)+dx(u2))/sqrt2] // // The sqrt2 is because we want: epsilon(u1,u2)'* epsilon(v1,v2) = epsilon(u): epsilon(v) macro div(u,v) ( dx(u)+dy(v) ) // // Problem real mu= E/(2*(1+nu)); real lambda = E*nu/((1+nu)*(1-2*nu)); solve lame([u, v], [uu, vv]) = int2d(Th)( lambda * div(u, v) * div(uu, vv) + 2.*mu * ( epsilon(u,v)' * epsilon(uu,vv) ) ) - int2d(Th)( f*vv ) + on(4, u=0, v=0) ; // Plot real coef=100; plot([u, v], wait=1, ps="lamevect.eps", coef=coef); // Move mesh mesh th1 = movemesh(Th, [x+u*coef, y+v*coef]); plot(th1,wait=1,ps="lamedeform.eps"); // Output real dxmin = u[].min; real dymin = v[].min; cout << " - dep. max x = "<< dxmin << " y=" << dymin << endl; cout << " dep. (20, 0) = " << u(20, 0) << " " << v(20, 0) << endl;
The output is:
1 2 3 4 5 6 -- square mesh : nb vertices =121 , nb triangles = 200 , nb boundary edges 40 -- Solve : min -0.00174137 max 0.00174105 min -0.0263154 max 1.47016e-29 - dep. max x = -0.00174137 y=-0.0263154 dep. (20,0) = -1.8096e-07 -0.0263154 times: compile 0.010219s, execution 1.5827s
Solution of Lamé’s equations for elasticity for a 2D beam deflected by its own weight and clamped by its left vertical side is shown Fig. 19 and Fig. 20. Result are shown with a amplification factor equal to 100. The size of the arrow is automatically bound, but the color gives the real length.
Fig. 19 Vector
Fig. 20 Deformation
Elasticity
Table of content | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8734576106071472, "perplexity": 1679.713116659981}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250613416.54/warc/CC-MAIN-20200123191130-20200123220130-00009.warc.gz"} |
http://www.talkstats.com/showthread.php/11122-Math-Typesetting-in-LaTex?p=30780&viewfull=1 | 1. Math Typesetting in LaTex
Talk Stats forum now supports math typesetting in LaTex.
We have added two tags $and$. Include your LaTex code within the tags and you'll see LaTex graphic. For example:
$\int x^2 dx$ will produce:
$\frac{1}{\sigma\sqrt{2\pi}}e^{-(x-\mu)^2/(2\sigma^2)}$ will produce:
If you mouseover any LaTex image, there will be a popup box showing the code between tags.
Here's a good LaTex tutorial:
http://frodo.elon.edu/tutorial/tutorial/
2. This is very nice.
3. Originally Posted by quark
Talk Stats forum now supports math typesetting in LaTex.
Here's a good LaTex tutorial:
http://frodo.elon.edu/tutorial/tutorial/
I am wrong to assume that the latex code for constructing Tables will work here too now?
Let see:
GREAT! Best addition yet. Thanks quark.
Anyone interested in table code here's an example (its the above table just add the 'math & /math' wrappers):
Code:
\begin{tabular}{|r|c|l|}
\hline
Col1 & Col2 & Col3\\
\hline
Table&making&works\\
quite&well&thanks\\
to&quark&SWEET!\\
\hline
\end{tabular}
4. The Following User Says Thank You to TheEcologist For This Useful Post:
jimbrowsky (12-04-2011)
Tweet
Posting Permissions
• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9080668091773987, "perplexity": 7858.243546487626}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783404382.73/warc/CC-MAIN-20160624155004-00079-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://www.usgs.gov/center-news/volcano-watch-puu-oo-throws-yet-another-curve-ball | # Volcano Watch — Puu Oo throws yet another curve ball
Release Date:
As reported in the previous Volcano Watch, a new vent opened on the south flank of Puu Oo two weeks ago, on Sunday, January 18. The behavior of the volcano during the previous few months mimicked the behavior that preceded the Mother's Day breakout on May 12, 2002.
Consequently, volcanologists anticipated the new breakout, though they were uncertain about its exact timing and location. They expected lava flows from the new breakout to blaze a new trail to the coastal plain, as has happened so many other times during the Puu Oo eruption.
At first, Puu Oo followed expectations as lava flows moved south and east away from the cone. Perhaps sensing that volcanologists had anticipated her plans, capricious Pele changed her strategy.
At about noon on Friday, January 23, only five days after the breakout on the south flank of Puu Oo, Kīlauea's summit began a rapid deflation, and volcanic tremor at the summit increased. As usual, after a brief lag, the deflation of Kīlauea's summit was mirrored by a deflation at Puu Oo, located 18 km (11 miles) east-southeast of the summit on Kīlauea's east rift zone.
The deflation is caused by a reduction in magma pressure beneath Kīlauea's summit. As the pressure drops, the eruption rate drops at Puu Oo.
By Saturday night, January 24, the flow of lava from the new south-flank vent had stopped, and some minor collapses occurred within Puu Oo's crater. Although the flow of lava from Puu Oo slowed down a lot, it did not completely stop. Some lava continued to flow through the old Mother's Day lava-tube system, feeding a few small lava flows above Pulama pali, south of Puu Oo.
By Sunday, January 25, Kīlauea's summit had deflated about 8 microradians (0.0005 degrees), the most since January 1997. The summit began to re-inflate on Sunday evening, and Puu Oo followed suit about noon the next day.
The flow of lava from Puu Oo sometimes stops completely. These temporary interruptions--called pauses--usually last only a few days or less. The shortest lasted two or three hours, the longest, 24 days.
Since the start of the Puu Oo eruption 21 years ago, there have been 79 pauses. Twenty-one occurred between February 1992 and February 1993, and none since December 2000.
The instrumental signature of pauses--the combination of deformation and seismic signals--can vary substantially. Nine pauses in 1990 followed rapid but small deflations of Kīlauea summit and increasing summit tremor. Once a pause began, the summit rapidly inflated and summit tremor decreased.
This behavior contrasts with that observed during the 21 pauses mentioned above. Only about one-half of these were preceded by slight summit deflation, but many comparable instances of summit deflation were not followed by a pause. The most consistent feature of this group was summit inflation, which accompanied nearly all 21 pauses.
The differences in instrumental signature reflect the fact that the plumbing system connecting Kīlauea?s summit and Puu Oo is dynamic rather than static. The location of blockages, the number of pipes, the dimensions of the pipes, and places where the pipes empty onto the earth's surface all change from time to time.
As of January 29, the eruption output is still significantly below normal, presumably because of a partial blockage or diversion somewhere within the system. Like an old house, Kīlauea has interesting plumbing.
### Volcano Activity Update
The condition of Kīlauea's eruption is described above.
Two earthquakes were felt on the island during the week ending January 21. Residents of Volcano and the national park felt a magnitude 2.9 earthquake at 8:57 p.m. on January 23. The shallow earthquake was located about 2 km (1 mile) west of Volcano at a depth of 2 km (1 mile). Another earthquake was felt in the same area the next morning at 7:37. It had a magnitude of 3.1 and was centered 2 km (1 mile) northeast of HVO at a depth of 2 km (1 mile). These two earthquakes were probably related to the period of unusually strong volcanic tremor beneath Kīlauea?s caldera mentioned above.
Mauna Loa is not erupting. The summit region continues to inflate. Seismic activity remains very low, with two earthquakes located in the summit area during the last 7 days.
The small swarm of earthquakes at Lo`ihi active during the previous week has died away. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32873594760894775, "perplexity": 8411.230811575015}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178357641.32/warc/CC-MAIN-20210226115116-20210226145116-00055.warc.gz"} |
https://docs.ergoplatform.com/uses/sigmausd/examples/ | # Examples
## SigmaRSV (Reservecoin) Simplified#
• SigmaRSV is a call option on a % of the ERG held in the reserve portion of the SigmaUSD contract
• Fees are continually added to the ERG held in reserve as users interact with the contract. This mechanism ensures liquidity and offers a mechanism of return beyond trading. SigmaRSV represents a price/book (P/B Ratio) on the ERG held in reserve.
It is important to understand three mechanisms that influence the outcome of each user of SigmaRSV
1. Fees accumulate as users interact with the contract. Nothing is Free.
2. The amount of ERG held in reserve floats (up/down) as users interact with the contract.
3. The price ERG/USD floats (up/down) as users trade ERG.
### Overview#
• Imagine the Reserve amount is 100 ERG.
• Alice holds SigmaRSV, which represents 10% of the (P/B Ratio) contained in the reserves.
• Alice's SigmaRSV position is a call option on 10 ERG (minus the exchange fee)
• Let's imagine the price of ERG is 2$. • Alice's SigmaRSV represents 20$ in ERG (minus the exchange fee)
THE BALANCE IN RESERVE CAN GO UP
• Imagine, based on use, the reserve now holds 114 ERG.
• Alice has SigmaRSV, which represents 10% of the (P/B Ratio) contained in the reserves.
• Alice's SigmaRSV represents a call option on 11.4 ERGs.
• Let's imagine the price of ERG is still 2$. • Alice has 22.80$ in ERG (minus the exchange fee)
THE BALANCE IN RESERVE CAN GO DOWN
• Imagine, based on use, the reserve now holds 90 ERG.
• Alice has SigmaRSV, which represents 10% of the (P/B Ratio) contained in the reserves.
• Alice's SigmaRSV represents a call option on 9 ERGs.
• Let's imagine the price of ERG is still 2$. • Alice has 18.00$ in ERG (minus the exchange fee)
THE VALUE, ERG/USD, CAN GO UP
• Imagine, based on use, the reserve now holds 114 ERG.
• Alice has SigmaRSV, which represents 10% of the (P/B Ratio) contained in the reserves.
• Alice's SigmaRSV represents a call option on 11.4 ERGs.
• Let's imagine the price of ERG is still NOW 3$. • Alice has a call option 34.20$ in ERG (minus the exchange fee)
THE VALUE, ERG/USD, CAN GO DOWN
• Imagine, based on use, the reserve now holds 114 ERG.
• Alice has SigmaRSV, which represents 10% of the (P/B Ratio) contained in the reserves.
• Alice's SigmaRSV represents a call option on 11.4 ERGs.
• Let's imagine the price of ERG is still NOW 1$. • Alice has a call option 11.40$ in ERG (minus the exchange fee)
## SigmaUSD (Stablecoin) Simplified#
SigmaUSD represents a call option on the dollar value of ERG held in reserve.
SigmaUSD uses Ergo's oracle pools infrastructure to calculate and adjust the current ERG/USD exchange rate. Reserve always backs sigma USD. The price ERG/USD floats (up/down) as users trade ERG.
BASIC OVERVIEW
• Bobs has 20 SigmaUSD, representing a 20 USD value in ERG.
• These ERGs are held in Reserve.
• This 20$value is backed by reserves of at least • (4x1)(80$ of ERG)(40 ERG @ $2) • Bob at 2$ Bob can Redeem his 20 SigmaUSD for 10 ERG (minus the exchange fee)
ERG/USD VALUE DROPS
• Let us imagine the price of ERG drops from $2 to$1.
• Bobs 20$of value is backed by at least • (4x1)(80$ of ERG)(80 ERG @ $1) • Bob can call 20 ERG (minus the exchange fee) ERG/USD VALUE INCREASES • Let us imagine the price of ERG increases from$2 to $4. • Bob's$20 value is backed by at least
• (4x1)(80$of ERG)(20 ERG @$4)
• Bob can call 5 ERG (minus the exchange fee)
### Longterm framework of SigmaUSD.#
• SigmaUSD is an essential building block for a functioning DeFi System.
• The focus for ERG now shifts to building on the foundation it has set.
• Gateways, Dex's, Liquidity Pools, LETS systems. It is time to build use and utility.
• The importance and significance of stable value cannot be overstated.
• This is critical to the long-term prosperity of the Ergo Network and is important to understand. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5710641145706177, "perplexity": 11342.347439954756}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710813.48/warc/CC-MAIN-20221201121601-20221201151601-00010.warc.gz"} |
https://www.ellistat.com/it/guida-utente/statistical-tests/statistical-test-power | Descriptive statistics
Statistical tests
Design of Experiment
Gage RR
Problem resolution
Reliability
Control plan
# Statistical test power
The power of a test corresponds to the capacity of a statistical test to detect a difference. The higher the power the higher the probabiilty that the test will detect a difference.
To calculate a tests power, choose the test that you want to use:
• z theoretical: compare a sample average with a theoretical value provided that you already know the population's standard deviation
• t theoretical: compare a sample average with a theoretical value without knowing the population's standard deviation. This will be calculated based on the test sample
• t Test: compare the average of two samples
• Paired t test: compares the average of two samples by comparing data in pairs (2 by 2)
• Chi2: compares the standard deviation of a sample based on a theoretical value
• F Test : compares the standard deviations of two samples
• Test 1P: compares the proportion obtained from a sample (Ex: 3 defects out of 1000 parts) based on a theoretical proportion
• Test 2P: compares 2 proportions measured from two different samples (Ex: Batch A: 2 defects out of 24, Lot B: 4 defects out of 26)
Then enter:
• The sample size that you want to use
• The expected standard deviation for your values. This standard deviation can be an estimate, for example:
• We know that the temperature varies ± 4° for normal production (expert estimate). We believe that this estimate covers 95% of the actual dispersion (± 4 sigma) so we estimate the residual standard deviation as 1.
• The alpha risk from which you will conclude that the difference is significant: generally it is advised to leave it at 0.05.
• The typical difference that you want to evaluate: in the preceding example we want to observe an average difference of 1 between the 2 samples.
Ellistat will then give you the test's power which is 85.4% in this example. This means: If the difference between the two averages equals 1, then the test t will have an 85.4% chance of detecting a significant difference between the samples.
On the other hand, if you want to determine the number of samples necessary to get a given power, all you have to do is enter the desired power in the corresponding box and Ellistat will automatically calculate the number of samples you need to obtain the given power.
## Una soluzione completa per l'Industria 4.0
8 moduli statistici
Test
0
30 giorni
Testalo gratuitamente
APC
SPC
Controllo
Analisi
30 giorni
Tutte le funzioni di Ellistat
1 utente
Supporto tecnico e ed aggiornamenti inclusi
Studenti
0
1 anno
Checkout
Analisi
1 anno
Tutte le funzioni di Ellistat
1 utente
Licenza dedicata agli studenti che dispongono di una tessera studente in corso di validità
Supporto tecnico e ed aggiornamenti inclusi
Standard
49
per utente al mese
Checkout
Analisi
Licenza rinnovata ogni mese
Tutte le funzioni di Ellistat
Utenti illimitati
Supporto tecnico e ed aggiornamenti inclusi | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.875841498374939, "perplexity": 2798.709860339846}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500619.96/warc/CC-MAIN-20230207134453-20230207164453-00310.warc.gz"} |
https://gharpedia.com/things-to-check-during-casting-a-slab/ | ## Things to Check Before Concreting RCC wall (Shear Wall)
General practice is to check when the RCC wall is ready for concreting i.e. reinforcement fully tied up but ideal practice would be to check it in two phase i.e.
01. First check formwork before you allow placing of reinforcement. This is necessary as certain formwork defects can’t be corrected or are difficult to correct after reinforcement is placed in position.
02. Checking reinforcement
##### Also Read: Things to Check Before Concreting Column
Hence as a standard engineering practice one should check first the formwork before reinforcement placed or tied.
#### 01. Centering and shuttering / Formwork:
Some essential points for inspection of wall forms are covered below:
• Form panels should be checked for adequate tying and bracing.
Courtesy - 123rf
• Exterior corners of forms should be tied to prevent bulging or spreading.
• Resistance to be provided against uplift for top forms with sloping faces.
• Adequate lap should be provided between forms and previous construction and connecting hardware to be carefully secured.
• The internal and external walls are to be held together by flat wall tie with wall tie sleeve and PVC cover. These wall tie sleeve and PVC cover are to be cut for the exact length of the wall thickness. Flat wall tie are to be coated with the form oil before each usage.
• Plumb formwork both ways and securely support using adjustable steel props.
• A thin film of oil or grease or mould release agent should be applied to the inner surface of the shuttering to enable easy removal after the concrete hardens.
• Walls to be checked for proper spacing with joints staggered from one tie to the next.
• The gap between the shutters joint should be sealed to prevent any leakage of cement slurry.
• Experienced supervision of formwork during the concrete placing operation has to be done to ensure correct placing of concrete without segregation.
#### 02. Reinforcement:
• Make sure that cover block used for casting of walls have the same grade as of concrete. They are not broken and properly positioned and should not get disturbed during concreting operations.
• Minimum 25 mm cover should be provided in wall.
• Maximum 450 mm spacing should be provided in between two reinforcement.
• Lapping of reinforcement should be minimum 40D, Where D is diameter of bar.
• If thickness of wall is greater than 200mm, double grid reinforcement should be provided along both the faces.
• Before placing the concrete, Check the reinforcement details with bar bending schedule and get an approval from structural consultant.
## Material Exhibition
Explore the world of materials. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17143280804157257, "perplexity": 4489.5052466001125}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578532882.36/warc/CC-MAIN-20190421195929-20190421221929-00233.warc.gz"} |
http://math.stackexchange.com/questions/127016/what-is-the-difference-between-these-two-derivative-expressions?answertab=oldest | # What is the difference between these two derivative expressions?
is there a difference between $\frac{\partial^2 }{\partial x^2}$ and $(\frac{\partial }{\partial x})^{2}$? I have to tell if a differential equation is linear, and $(\frac{\partial }{\partial x})^{2}$ concerns me. If it's the same thing as second derivative, the equation would be linear.
-
Same thing; it means the operator $\partial / \partial x$ applied twice. – anon Apr 1 '12 at 20:27
Is the notation $\frac{\partial^2}{\partial x^2}$ also used in the same text? If so, that would seem to indicate that the author intends for $(\frac{\partial}{\partial x})^2$ to mean something different, in which case Tom Au's answer below seems to be correct. – Santiago Canez Jan 30 at 23:00
the notation $\frac{\partial^2 }{\partial x^2}f~~$ means $\frac{\partial }{\partial x}(\frac{\partial }{\partial x}f)$, so $\frac{\partial^2 }{\partial x^2}f~~$ and $(\frac{\partial }{\partial x})^{2}f~~$ is the same both you apply $\frac{\partial }{\partial x}$ twice.
The first expression, $\frac{\partial^2 }{\partial x^2}$ is the second derivative, while the second expression, $(\frac{\partial }{\partial x})^{2}$, is the first derivative squared. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9675034284591675, "perplexity": 243.58122060103204}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394021227262/warc/CC-MAIN-20140305120707-00065-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://www.redgreencode.com/math-fluency-for-uva-927/ | # Math Fluency for UVa 927
From time to time, I’ll run across a UVa problem description that makes liberal use of mathematical notation. UVa 927, the first starred problem in uHunt Chapter 3, is one of those. uHunt classifies it as a Level 4 problem, but most of the challenge is in interpreting the problem description. Once you figure out what it’s asking for, the problem itself is straightforward.
One of the first steps in my puzzle-solving process is to read the problem statement and takes notes on it. For many uHunt starred problems, I can finish this step in a few minutes. The more complicated problems, including those with a lot of math notation, can take quite a bit longer. But it’s worth spending the time. There’s no point in starting to solve a problem without having a good understanding of what it’s asking for.
Take a look at the original UVa 927 problem statement. Try reading it through at a moderate pace, at the speed you would use to read the textbook for a technical subject. After reading through it once, do you have a clear idea of what steps would be required to solve the problem? If so, you’re in reasonable shape when it comes to basic competitive programming math notation.
In my case, I had to read through the description several times before I got it. The notation is not complicated. I know how to represent sets and elements of sets, and how to write a polynomial equation without using specific numbers for the coefficients. Nevertheless, I found that it required a lot of thinking to interpret this problem statement.
If I was writing my own version of the UVa 927 problem statement with the goal of making it more understandable, it would be longer than the original. Someone who reads math notation fluently might find that this actually slowed them down. And it’s likely that these problem statements are intentionally written less clearly than they could be, so that competitors have an incentive to practice reading complicated technical texts, learn standard mathematical notation, and figure things out for themselves.
To highlight how much of this problem’s difficulty is just in interpreting the description, I’m going to attempt to write it more clearly. Here we go:
## UVa 927 Problem Statement: The Long But Easy To Read Version
Problem Description
A sequence is a collection of objects in a particular order. In this problem, we’ll be working with sequences of integers. The goal of the problem is to calculate the integer that occurs at a specified position in a sequence.
This problem involves two integer sequences. The first sequence consists of the terms $a_1, a_2, a_3, …$, where each term is an integer. If we want to refer to the entire sequence, we use the notation $\lbrace{a_n}\rbrace$. The $n$th element of the sequence is $a_n$. To calculate the value of a term for a particular value of $n$, we will use the following polynomial function:
$$a_n = c_0 + c_1n + c_2n^2 + c_3n^2 + … + c_in^i$$
The coefficients $c_0, c_1, …, c_i$ are provided in the problem test cases.
The second sequence used in this problem is constructed using $\lbrace a_n \rbrace$. We’ll refer to this sequence as $\lbrace b_m \rbrace$. Like $\lbrace a_n \rbrace$, the sequence $\lbrace b_m \rbrace$ also consists of integers. The terms of $\lbrace b_m \rbrace$ are $b_1, b_2, b_3, …$. For a particular term of $\lbrace b_m \rbrace$, we’ll use the notation $b_m$. Unlike $a_n$, the term $b_m$ may contain more than one integer. Here’s how that works:
Each test case for this problem has an input value $d$, a positive integer. Each term $b_m$ of the sequence $\lbrace b_m \rbrace$ consists of $n \times d$ copies of the term $a_n$ of the sequence $\lbrace a_n \rbrace$, where $n = m$. For example, if $d = 2$ then:
• $b_1 = a_1, a_1$ ($1 \times 2=2$ copies of $a_1$)
• $b_2 = a_1, a_1, a_1, a_1$ ($2 \times 2=4$ copies of $a_1$)
• $b_3 = a_1, a_1, a_1, a_1, a_1, a_1$ ($2 \times 3=6$ copies of $a_1$)
The goal of the problem is to find and print the $k$th term of $\lbrace b_m \rbrace$, where $k$ is a positive integer provided for each test case.
Example
Set $c_1 = 1$ and set the remaining coefficients to $0$. Then $a_n = n$. In this case, the sequence $\lbrace a_n \rbrace$ is just $1, 2, 3, …$. If $d=1$ then the sequence $\lbrace b_m \rbrace$ is:
$$\underbrace{1, }_{b_1}$$
$$\underbrace{2, 2, }_{b_2}$$
$$\underbrace{3, 3, 3, }_{b_3}$$
$$\underbrace{4, 4, 4, 4, }_{b_4}$$
$$…$$
If $k=6$ then the result is the $6$th element of that sequence, which is $3$.
If $d=2$, then ${b_m} = 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, …$. In that case, the $6$th element would be $2$.
Input and output description, and sample input/output
These are relatively clear in the original, so I won’t rewrite them here.
## Finding $n$
To solve a UVa 927 test case, we only need to calculate and print one $a_n$ term. Evaluating the $a_n$ polynomial is straightforward, so the only challenge is how to find the value of $n$ that corresponds to the $k$th term of $\lbrace b_m \rbrace$.
This is all it takes:
int findn(int d, int k)
int p = 0;
for (int n=1; ; n++)
int previousp = p;
p += n*d;
if (previousp < k && k <= p) return n;
$d$ and $k$ are provided in the test case, so we can just pass those to the function. $n$ is the index into the $\lbrace a_n \rbrace$ sequence. $p$ is an identifier that doesn’t appear in the problem statement. You can think of it as a candidate $k$ value. Here’s why it’s required:
The $m$ index into $\lbrace b_m \rbrace$ can point to multiple values. For example, in the $\lbrace b_m \rbrace$ sequence shown in the problem statement, $m=3$ refers to $3,3,3$. That’s not very useful, since the $k$ provided by the test case only refers to a single value. That’s where $p$ comes in. In the example sequence $1,2,2,3,3,3,4,4,4,4,…$, $p=1$ refers to $1$, $p=2$ refers to $2$, $p=3$ also refers to $2$, $p=4$ refers to $3$, and so on. Each $p$ value refers to only one integer.
Each $m$ index into $\lbrace b_m \rbrace$ refers to one or more copies of particular $\lbrace a_n \rbrace$ elements. For each $n$ value, we can move $p$ ahead by $n \times d$ positions in $\lbrace b_m \rbrace$. When our target $k$ value falls between the previous $p$ value and the current $p$ value, we have found the correct $n$ index.
$n$ is just an index. Once we have it, we have to find the actual value of $a_n$, which is what the problem asks for. The coefficients $c_0, c_1, …, c_i$ come from the test case. Now we have to calculate $a_n = c_0 + c_1n + c_2n^2 + c_3n^2 + … + c_in^i$. That’s just a matter of addition, multiplication, and exponentiation. And exponentiation is just repeated multiplication, so we can avoid it by remembering the value of each $n^j$ and using it to calculate $n^{j+1}$. The code to do this is simple:
long poly(int[] c, int n)
long a = 0;
long currentn = 1;
for (int i=0; i<c.length; i++)
a += c[i] * currentn;
currentn *= n;
return a;
Notice that we need to use long integers for the calculation, since the result can be as high as $2^{63}-1$.
## Math Fluency
If the original UVa 927 problem statement was perfectly understandable to you the first time you read it, then my revised description may seem redundant or overly wordy. It’s true that math writing often doesn’t spell things out in that level of detail. But that’s the level of detail that you’ll have to be able to extract from a mathematical description in order to make use of it.
I have written in the past about coding fluency. Though reading code and writing math are both useful skills, competitive programming puts more emphasis on writing code and reading math. Problem writers don’t expect participants to be slowed down by math notation, so they make use of it when required.
One challenge with developing math fluency is that people who are fluent in math may find it hard to remember what it was like not to be fluent. This is similar to other types of language fluency. The goal of being fluent is that you don’t have to think about using the language. Once you stop thinking about using math notation, you may not realize that other people struggle with it.
The Quora question How does it feel to finally be red at TopCoder after years of hard work? has some examples of this phenomenon. Here’s how Bohdan Pryshchenko puts it in his answer: “The more you practice&compete, the better you understand that this red color does not mean anything significant.” In other words, once you have enough experience that achieving a red rating is easy, it’s no longer a big deal. So enjoy the journey on the way there.
(Image credit: Yann Duarte) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6584867835044861, "perplexity": 298.3081661206189}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583662690.13/warc/CC-MAIN-20190119054606-20190119080302-00016.warc.gz"} |
http://math.stackexchange.com/users/401/eivind-dahl?tab=activity&sort=all&page=3 | Eivind Dahl
Reputation
980
Next privilege 1,000 Rep.
Create new tags
Badges
5 12
Newest
Impact
~24k people reached
• 0 posts edited
• 0 helpful flags
• 107 votes cast
# 113 Actions
Mar17 accepted Which functor does the projective space represent? Mar17 comment Which functor does the projective space represent? Thank you! Another good answer. Hard to know which one to pick, but I think I'll go for this one because it is closer to the generality I asked for. I also found this treated in a set of notes by Strickland on formal schemes. Mar16 comment Which functor does the projective space represent? Thank you! I agree charts might not be all too great for understanding projective spaces, but the first thing I really understood and liked was the projective line, patched together by pieces of $k[t]$. It makes it clear to me why a meromorphic function on $X$ is the same thing as a morphism $X\to\mathbb{P}^1$. This complements nicely the notion of a regular function as a morphism $X\to\mathbb{A}^1$. If I was able to see from the definition of $\mathbb{P}^I$, that this was the case I would be every happy. At least you've told me what I need to stare at until it makes sense :-) Mar16 revised Which functor does the projective space represent? edited title Mar16 asked Which functor does the projective space represent? Feb23 awarded Nice Question Feb19 awarded Nice Answer Nov20 comment cup products and smash products Ok, I have no Idea what this question is actually asking anymore, but I'm glad you managed to find a satisfactory answer for yourself. Nov18 revised cup products and smash products added 16 characters in body Nov18 answered cup products and smash products Oct14 comment What's $F'(x)$ if $F(x) = \int_a^{g(x)} H(x,t) dt$? This is probably the favourite answer I've read on Stackexchange yet :-) So unbelievably natural, thank you! Aug19 comment Why is one “$\infty$” number enough for complex numbers? I'd love it if that downvote came with a comment. Aug10 comment False proof of $H_0 ( X) = 0$ That's it, Matt :-) Jul29 awarded Yearling Jul18 comment intersection of two affine open sets of a scheme Is the union of the $U,V$ off the mark here? A lower bound would be the open set. Am I missing something? Jul5 comment What happens geometrically when the Jacobson radical is non-zero? Well I think that answers my question pretty well to be honest. So thanks! Jun19 revised What happens geometrically when the Jacobson radical is non-zero? deleted 4 characters in body Jun19 revised What happens geometrically when the Jacobson radical is non-zero? added 2 characters in body; added 20 characters in body; deleted 21 characters in body Jun18 revised What happens geometrically when the Jacobson radical is non-zero? added 100 characters in body; added 9 characters in body; added 71 characters in body Jun18 revised What happens geometrically when the Jacobson radical is non-zero? added 135 characters in body; edited title | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.803126335144043, "perplexity": 1189.0347388325267}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430458957748.48/warc/CC-MAIN-20150501054237-00047-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://math.stackexchange.com/users/86086/aran-komatsuzaki?tab=summary | Aran Komatsuzaki
Reputation
1,421
Top tag
Next privilege 2,000 Rep.
3 16
Impact
~39k people reached
### Questions (57)
12 Why are “algebras” called algebras? 6 Why is topological group not a popular topic? 6 Rudin's 'Principle of Mathematical Analysis' Exercise 3.14 4 Any good supplementary text on Algebraic Number Theory? 4 How to solve the system $t\frac{dx}{dt}=-x+yt$, $t\frac{dy}{dt}=-2x+yt$?
### Reputation (1,421)
+15 Why does $D \det(I)B=\frac{d}{d t}\det(I+t B)|_{t=0}$ hold? +5 Why are “algebras” called algebras? +5 Are $\mathbb{CP}^{n}$ and $\mathbb{RP}^{2n}$ diffeomorphic? +5 How to verify F-relatedness?
11 What's the difference between simple induction and strong induction? 5 Structured Self-Learning Program for Calculus I & II 4 Trigonometry : Simplify and find the value of $\tan\theta(1-\sec\frac{\theta}{2})(1-\sec\theta)(1-\sec2\theta)\dots(1-\sec2^{n-1}\theta)$ at n =1,2,3 3 integration of $\int_{0}^{\infty} e^{-ax}\Sigma_{0}^{\infty} \frac{(-1)^n x^{2n}}{4^n (n!)^2}dx$ 3 Logarithm of $\frac{a^k}{a^k-1}$
### Tags (105)
12 calculus × 12 5 integration × 5 11 induction × 2 5 soft-question × 5 8 reference-request × 5 4 book-recommendation × 8 7 self-learning × 3 4 real-analysis × 5 6 education × 2 4 trigonometry × 3
### Accounts (13)
Mathematics 1,421 rep 316 Academia 221 rep 18 MathOverflow 180 rep 8 Biology 123 rep 4 Stack Overflow 113 rep 4 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7007313370704651, "perplexity": 6288.543594535006}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207929176.79/warc/CC-MAIN-20150521113209-00094-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/cpaa.2019088 | # American Institute of Mathematical Sciences
• Previous Article
Spike layer solutions for a singularly perturbed Neumann problem: Variational construction without a nondegeneracy
• CPAA Home
• This Issue
• Next Article
Global attractors for a mixture problem in one dimensional solids with nonlinear damping and sources terms
July 2019, 18(4): 1891-1919. doi: 10.3934/cpaa.2019088
## Well-posedness of low regularity solutions to the second order strictly hyperbolic equations with non-Lipschitzian coefficients
1 School of Mathematical Sciences and Mathematical Institute, Nanjing Normal University, Nanjing, 210023, China 2 School of Mathematics and Physics, Anhui University of Technology, Maanshan 243032, China
* Corresponding author
Received August 2018 Revised November 2018 Published January 2019
Fund Project: The first author and the second author are supported by the NSFC (No.11571177, No.11731007) and the NSF of the Jiangsu Higher Education Institutions of China (17KJA110002).
In this paper, we establish the local well-posedness of low regularity solutions to the general second order strictly hyperbolic equation of divergence form $\partial _t(a_0 \partial _t u)+ \mathop \sum \limits_{j = 1}^n [ \partial _t(a_j \partial _j u)+ \partial _j(a_j \partial _t u)] -\mathop \sum \limits_{j,k = 1}^n \partial _j(a_{jk} \partial _k u)$ $+b_0 \partial _t u+ \partial _t(c_0u)+ \mathop \sum \limits_{j = 1}^n [b_j \partial _ju+ \partial _j(c_ju)] +du = f$ in domain $\Omega = (0, T_0)\times \mathbb R ^n$, where the coefficients $a_0, a_j, a_{jk}\in L^\infty( \Omega )\cap LL(\bar\Omega)$ $(1\le j, k\le n)$, $b_0, c_0, b_j, c_j\in L^\infty( \Omega )\cap C^ \alpha (\bar\Omega)$ $(1\le j\le n)$ for $\alpha \in(\frac{1}{2},1)$, $d\in L^\infty(\Omega)$, $(u(0,x), Xu(0,x))\in (H^{1- \theta +\beta \log}, H^{- \theta +\beta \log})$ with $\theta\in (1- \alpha , \alpha )$, $\beta\in\Bbb R$, and $Xu = a_0 \partial _tu+ \mathop \sum \limits_{j = 1}^n a_j \partial _ju$. Compared with previous references, except a little more general initial data in the space $(H^{1- \theta +\beta \log}, H^{- \theta +\beta \log})$ (only $\beta = 0$ is considered as before), we improve both the lifespan of $u$ up to the precise number $T^*$ and the range of $\theta$ to the left endpoint $1- \alpha$ under some suitable conditions.
Citation: Wenming Hu, Huicheng Yin. Well-posedness of low regularity solutions to the second order strictly hyperbolic equations with non-Lipschitzian coefficients. Communications on Pure and Applied Analysis, 2019, 18 (4) : 1891-1919. doi: 10.3934/cpaa.2019088
##### References:
[1] H. Bahouri, J. Y. Chemin and R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations, Springer-Velag, Berlin Heidelberg, 2011. doi: 10.1007/978-3-642-16830-7. [2] J. M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, (French) [Symbolic calculus and propagation of singularities for non-linear partial differential equations], Ann.Sci. École Norm. Sup., 14 (1981), 209-246. [3] M. Cicognani and F. Colombini, Modulus of continuity of the coefficients and loss of derivatives in the strictly hyperbolic Cauchy problem, J. Diff. Eqs., 221 (2006), 143-157. doi: 10.1016/j.jde.2005.06.019. [4] F. Colombini, E. De Giorgi and S. Spagnolo, Sur les équations hyperboliques avec des coefficients qui ne ${\acute{\rm{q}}}$ue du temps, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 6 (1979), 511-559. [5] F. Colombini, E. Jannelli and S. Spagnolo, Nonuniqueness in hyperbolic cauchy problems, Ann. of Math., 126 (1987), 495-524. doi: 10.2307/1971359. [6] F. Colombini and N. Lerner, Operators with non-Lipschitz coefficients, Duke Math. J., 77 (1995), 657-698. doi: 10.1215/S0012-7094-95-07721-7. [7] F. Colombini and G. Métivier, The cauchy problem for wave equations with non lipschitz coefficients; Application to continuation of solutions of some nonlinear wave equations, Ann. Sci. Éc. Norm. Supér.(4) , 41 (2008), 177–220. doi: 10.24033/asens.2066. [8] F. Colombini and D. D. Santo, A note on hyperbolic operators with log-zygmund coefficients, J. Math. Sci. Univ. Tokyo, 16 (2009), 95-111. [9] F. Colombini, D.D. Santo, F. Fanelli and G. Métivier, Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients, Comm. Partial Differential Equations, 38 (2013), 1791-1817. doi: 10.1080/03605302.2013.795968. [10] F. Colombini and S. Spagnolo, Some examples of hyperbolic equations without local solvability, Ann, Sci. Ecole Norm. Suph.(4), 22 (1989), 109–125. [11] L. Hörmander, Linear Partial Differential Operators, Springer-Velag, Berlin Heidelberg, 1976. [12] A. E. Hurd and D. H. Sattinger, Questions of existence and uniqueness for hyperbolic equations with discontinuous coefficients, Trans. Amer. Math. Soc., 132 (1968), 159-174. doi: 10.2307/1994888. [13] E. Jannelli, Regularly hyperbolic systems and Gevrey classes, Ann. Mat. Pura Appl., 140 (1985), 133-145. doi: 10.1007/BF01776846. [14] T. Nishitani, Sur les équations hyperboliques á coefficients höldériens en t et de classe de Gevrey en x, Bull. Sci. Math., 107 (1983), 113–138., [15] J. Rauch, Hyperbolic Partial Differential Equations and Geometric Optics, Graduate Studies in Mathematics, 133, American Mathematical Society, Providence, RI, 2012. doi: 10.1090/gsm/133. [16] M. E. Taylor, Tools for PDE : Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials, Mathematical Surveys and Monographs, 81, American Mathematical Society, Providence, RI, 2000.
show all references
##### References:
[1] H. Bahouri, J. Y. Chemin and R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations, Springer-Velag, Berlin Heidelberg, 2011. doi: 10.1007/978-3-642-16830-7. [2] J. M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, (French) [Symbolic calculus and propagation of singularities for non-linear partial differential equations], Ann.Sci. École Norm. Sup., 14 (1981), 209-246. [3] M. Cicognani and F. Colombini, Modulus of continuity of the coefficients and loss of derivatives in the strictly hyperbolic Cauchy problem, J. Diff. Eqs., 221 (2006), 143-157. doi: 10.1016/j.jde.2005.06.019. [4] F. Colombini, E. De Giorgi and S. Spagnolo, Sur les équations hyperboliques avec des coefficients qui ne ${\acute{\rm{q}}}$ue du temps, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 6 (1979), 511-559. [5] F. Colombini, E. Jannelli and S. Spagnolo, Nonuniqueness in hyperbolic cauchy problems, Ann. of Math., 126 (1987), 495-524. doi: 10.2307/1971359. [6] F. Colombini and N. Lerner, Operators with non-Lipschitz coefficients, Duke Math. J., 77 (1995), 657-698. doi: 10.1215/S0012-7094-95-07721-7. [7] F. Colombini and G. Métivier, The cauchy problem for wave equations with non lipschitz coefficients; Application to continuation of solutions of some nonlinear wave equations, Ann. Sci. Éc. Norm. Supér.(4) , 41 (2008), 177–220. doi: 10.24033/asens.2066. [8] F. Colombini and D. D. Santo, A note on hyperbolic operators with log-zygmund coefficients, J. Math. Sci. Univ. Tokyo, 16 (2009), 95-111. [9] F. Colombini, D.D. Santo, F. Fanelli and G. Métivier, Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients, Comm. Partial Differential Equations, 38 (2013), 1791-1817. doi: 10.1080/03605302.2013.795968. [10] F. Colombini and S. Spagnolo, Some examples of hyperbolic equations without local solvability, Ann, Sci. Ecole Norm. Suph.(4), 22 (1989), 109–125. [11] L. Hörmander, Linear Partial Differential Operators, Springer-Velag, Berlin Heidelberg, 1976. [12] A. E. Hurd and D. H. Sattinger, Questions of existence and uniqueness for hyperbolic equations with discontinuous coefficients, Trans. Amer. Math. Soc., 132 (1968), 159-174. doi: 10.2307/1994888. [13] E. Jannelli, Regularly hyperbolic systems and Gevrey classes, Ann. Mat. Pura Appl., 140 (1985), 133-145. doi: 10.1007/BF01776846. [14] T. Nishitani, Sur les équations hyperboliques á coefficients höldériens en t et de classe de Gevrey en x, Bull. Sci. Math., 107 (1983), 113–138., [15] J. Rauch, Hyperbolic Partial Differential Equations and Geometric Optics, Graduate Studies in Mathematics, 133, American Mathematical Society, Providence, RI, 2012. doi: 10.1090/gsm/133. [16] M. E. Taylor, Tools for PDE : Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials, Mathematical Surveys and Monographs, 81, American Mathematical Society, Providence, RI, 2000.
[1] Takamori Kato. Global well-posedness for the Kawahara equation with low regularity. Communications on Pure and Applied Analysis, 2013, 12 (3) : 1321-1339. doi: 10.3934/cpaa.2013.12.1321 [2] Hiroyuki Hirayama. Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data. Communications on Pure and Applied Analysis, 2014, 13 (4) : 1563-1591. doi: 10.3934/cpaa.2014.13.1563 [3] Kenji Nakanishi, Hideo Takaoka, Yoshio Tsutsumi. Local well-posedness in low regularity of the MKDV equation with periodic boundary condition. Discrete and Continuous Dynamical Systems, 2010, 28 (4) : 1635-1654. doi: 10.3934/dcds.2010.28.1635 [4] Magdalena Czubak, Nina Pikula. Low regularity well-posedness for the 2D Maxwell-Klein-Gordon equation in the Coulomb gauge. Communications on Pure and Applied Analysis, 2014, 13 (4) : 1669-1683. doi: 10.3934/cpaa.2014.13.1669 [5] Takafumi Akahori. Low regularity global well-posedness for the nonlinear Schrödinger equation on closed manifolds. Communications on Pure and Applied Analysis, 2010, 9 (2) : 261-280. doi: 10.3934/cpaa.2010.9.261 [6] Hyungjin Huh, Bora Moon. Low regularity well-posedness for Gross-Neveu equations. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1903-1913. doi: 10.3934/cpaa.2015.14.1903 [7] Lin Shen, Shu Wang, Yongxin Wang. The well-posedness and regularity of a rotating blades equation. Electronic Research Archive, 2020, 28 (2) : 691-719. doi: 10.3934/era.2020036 [8] Hartmut Pecher. Low regularity well-posedness for the 3D Klein - Gordon - Schrödinger system. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1081-1096. doi: 10.3934/cpaa.2012.11.1081 [9] Kiyeon Lee. Low regularity well-posedness of Hartree type Dirac equations in 2, 3-dimensions. Communications on Pure and Applied Analysis, 2021, 20 (11) : 3683-3702. doi: 10.3934/cpaa.2021126 [10] Antoine Benoit. Weak well-posedness of hyperbolic boundary value problems in a strip: when instabilities do not reflect the geometry. Communications on Pure and Applied Analysis, 2020, 19 (12) : 5475-5486. doi: 10.3934/cpaa.2020248 [11] Zihua Guo, Yifei Wu. Global well-posedness for the derivative nonlinear Schrödinger equation in $H^{\frac 12} (\mathbb{R} )$. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 257-264. doi: 10.3934/dcds.2017010 [12] Kelin Li, Huafei Di. On the well-posedness and stability for the fourth-order Schrödinger equation with nonlinear derivative term. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4293-4320. doi: 10.3934/dcdss.2021122 [13] E. Compaan, N. Tzirakis. Low-regularity global well-posedness for the Klein-Gordon-Schrödinger system on $\mathbb{R}^+$. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 3867-3895. doi: 10.3934/dcds.2019156 [14] Shaoming Guo, Xianfeng Ren, Baoxiang Wang. Local well-posedness for the derivative nonlinear Schrödinger equation with $L^2$-subcritical data. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4207-4253. doi: 10.3934/dcds.2021034 [15] Boris Kolev. Local well-posedness of the EPDiff equation: A survey. Journal of Geometric Mechanics, 2017, 9 (2) : 167-189. doi: 10.3934/jgm.2017007 [16] Jerry Bona, Nikolay Tzvetkov. Sharp well-posedness results for the BBM equation. Discrete and Continuous Dynamical Systems, 2009, 23 (4) : 1241-1252. doi: 10.3934/dcds.2009.23.1241 [17] A. Alexandrou Himonas, Curtis Holliman. On well-posedness of the Degasperis-Procesi equation. Discrete and Continuous Dynamical Systems, 2011, 31 (2) : 469-488. doi: 10.3934/dcds.2011.31.469 [18] Nils Strunk. Well-posedness for the supercritical gKdV equation. Communications on Pure and Applied Analysis, 2014, 13 (2) : 527-542. doi: 10.3934/cpaa.2014.13.527 [19] Reinhard Racke, Jürgen Saal. Hyperbolic Navier-Stokes equations I: Local well-posedness. Evolution Equations and Control Theory, 2012, 1 (1) : 195-215. doi: 10.3934/eect.2012.1.195 [20] Shouming Zhou, Chunlai Mu, Liangchen Wang. Well-posedness, blow-up phenomena and global existence for the generalized $b$-equation with higher-order nonlinearities and weak dissipation. Discrete and Continuous Dynamical Systems, 2014, 34 (2) : 843-867. doi: 10.3934/dcds.2014.34.843
2020 Impact Factor: 1.916 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8362561464309692, "perplexity": 2487.4240714716316}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662558015.52/warc/CC-MAIN-20220523101705-20220523131705-00056.warc.gz"} |
https://questions.examside.com/past-years/jee/wb-jee/chemistry/alcohol-and-ether | WB JEE
Chemistry
Alcohol and Ether
Previous Years Questions
## MCQ (More than One Correct Answer)
The product(s) in the following sequence of reactions will be ...
Haloform reaction with I2 and KOH will be respond by
Ph$$-$$ CDO$$\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{Warm}^{50\% aq.NaOH}}$$ Ph$$-$$ COO$$\mathop H\limits^\Theta$$ + an alcohol.Thi...
The product in the above reaction is...
Cyclopentanol on reaction with NaH followed by CS2 and CH3I produces a/an
Oxidation of allyl alcohol with a peracid gives a compound of molecular formula C3H6O2, which contains an asymmetric carbon atom. The structure of the...
The number of alkene (s) which can produce 2-butanol by the successive treatment of (i) B2H6 in tetrahydrofuran solvent and (ii) alkaline H2O2 solutio...
Methoxybenzene on treatment with HI produces
\mathop {{C_4}{H_{10}}O}\limits_{(N)} \mathop {\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{{H_2}S{O_4}}^{{K_2}C{r_2}{O_7}}} }\limits_{} {C_4}...
The structure of the product P of the following reaction is...
Reduction of the lactol S with sodium borohydride gives...
EXAM MAP
Joint Entrance Examination | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6662669777870178, "perplexity": 25147.544595162282}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943555.25/warc/CC-MAIN-20230320175948-20230320205948-00419.warc.gz"} |
http://www.ntrand.com/ntpoissonskew/ | // Home /
Documentation /
Function Reference / NTPOISSONSKEW
# NTPOISSONSKEW
Returns skewness of a specified Poisson distribution.
## Syntax
NTPOISSONSKEW(
• Mean
)
#### Parameters
• Mean is the arithmetic mean of the distribution (Positive value).
## Remarks
The skewness of the distribution is given as:
$\frac{1}{\sqrt{\textit{Mean}}}$
## Example
• The example may be easier to understand if you copy it to a blank worksheet
How to copy an example
1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.
Note Do not select the row or column headers.
Selecting an example from Help
3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Tools menu, point to Formula Auditing, and then click Formula Auditing Mode.
1
2
3
4
A B
Data Description
8 Arithmetic mean of the distribution
Formula Description (Result)
=NTPOISSONSKEW(A2) Skewness of the distribuion for the terms above | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6120070815086365, "perplexity": 7701.817379504997}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823220.45/warc/CC-MAIN-20171019031425-20171019051425-00387.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/dcdsb.2018187 | # American Institute of Mathematical Sciences
July 2018, 23(5): 1895-1915. doi: 10.3934/dcdsb.2018187
## On arbitrarily long periodic orbits of evolutionary games on graphs
1 Center for Dynamics & Institute for Analysis, Dept. of Mathematics, Technische Universität Dresden, 01062, Dresden, Germany 2 Department of Mathematics and NTIS, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 8, 30614, Pilsen, Czech Republic
* Corresponding author
Received April 2017 Revised August 2017 Published May 2018
A periodic behavior is a well observed phenomena in biological and economical systems. We show that evolutionary games on graphs with imitation dynamics can display periodic behavior for an arbitrary choice of game theoretical parameters describing social-dilemma games. We construct graphs and corresponding initial conditions whose trajectories are periodic with an arbitrary minimal period length. We also examine a periodic behavior of evolutionary games on graphs with the underlying graph being an acyclic (tree) graph. Astonishingly, even this acyclic structure allows for arbitrary long periodic behavior.
Citation: Jeremias Epperlein, Vladimír Švígler. On arbitrarily long periodic orbits of evolutionary games on graphs. Discrete & Continuous Dynamical Systems - B, 2018, 23 (5) : 1895-1915. doi: 10.3934/dcdsb.2018187
##### References:
show all references
##### References:
Regions of admissible parameters $\mathcal{P}$ with normalization $a = 1, d = 0$
Example of the graph $\mathcal{G}$ with parameters $p = 5$, $q = 3$, $r = 2$ and $s = 4$. Cooperators are depicted by full circles
Example of the graph $\mathcal{G}$ with parameters $p = 5, o = 4, s = 6, r = 1, q = 2$ with strategy vector $X(4)$. Cooperators are depicted by full circles. Note, that this graph exhibits periodic behavior as described in Section 3.2 for $(a, b, c, d) = (1, 0.45, 1.24, 0)$
Regions of parameters $o, q$ satisfying the inequalities (15)and (16). The regions are depicted for $(a, b, c, d) = (1, -0.45, 1.35, 0)$ and $p = 10$
Example of the graph constructed in the proof of Theorem 4.1 with an initial condition. The cooperators are depicted by filled black circles, defectors by white ones. The parameters are $r = 3, q = 6$
The example from Section 4.2
The example from Section 4.2
The example from Section 4.2
The example from Section 4.2
The example from Section 4.2
The example from Section 4.2
Illustration of the local situation in Lemma 4.2. Generally, nothing can be stated about the behavior of the cooperating neighbor on the left
Illustration of the local situation in Lemma 4.3
The function $f$ governing the shrinking and expansion of cooperation among the special vertices for $q = 8$
Development of the number of cooperators for the evolutionary game on the tree $\mathcal{G}$ in Section 4 with $r = 3$ and game theoretic parameters $(a, b, c, d) = (1, 0.7, 2, 0)$. On the left the tree has depth $q = 6$, on the right $q = 9$
[1] Jeremias Epperlein, Stefan Siegmund, Petr Stehlík, Vladimír Švígler. Coexistence equilibria of evolutionary games on graphs under deterministic imitation dynamics. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 803-813. doi: 10.3934/dcdsb.2016.21.803 [2] Astridh Boccabella, Roberto Natalini, Lorenzo Pareschi. On a continuous mixed strategies model for evolutionary game theory. Kinetic & Related Models, 2011, 4 (1) : 187-213. doi: 10.3934/krm.2011.4.187 [3] Anna Lisa Amadori, Astridh Boccabella, Roberto Natalini. A hyperbolic model of spatial evolutionary game theory. Communications on Pure & Applied Analysis, 2012, 11 (3) : 981-1002. doi: 10.3934/cpaa.2012.11.981 [4] Eduardo Espinosa-Avila, Pablo Padilla Longoria, Francisco Hernández-Quiroz. Game theory and dynamic programming in alternate games. Journal of Dynamics & Games, 2017, 4 (3) : 205-216. doi: 10.3934/jdg.2017013 [5] William H. Sandholm. Local stability of strict equilibria under evolutionary game dynamics. Journal of Dynamics & Games, 2014, 1 (3) : 485-495. doi: 10.3934/jdg.2014.1.485 [6] Mohammadreza Molaei. Hyperbolic dynamics of discrete dynamical systems on pseudo-riemannian manifolds. Electronic Research Announcements, 2018, 25: 8-15. doi: 10.3934/era.2018.25.002 [7] King-Yeung Lam. Dirac-concentrations in an integro-pde model from evolutionary game theory. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 737-754. doi: 10.3934/dcdsb.2018205 [8] Mădălina Roxana Buneci. Morphisms of discrete dynamical systems. Discrete & Continuous Dynamical Systems - A, 2011, 29 (1) : 91-107. doi: 10.3934/dcds.2011.29.91 [9] Hassan Najafi Alishah, Pedro Duarte. Hamiltonian evolutionary games. Journal of Dynamics & Games, 2015, 2 (1) : 33-49. doi: 10.3934/jdg.2015.2.33 [10] Jeremias Epperlein, Stefan Siegmund. Phase-locked trajectories for dynamical systems on graphs. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1827-1844. doi: 10.3934/dcdsb.2013.18.1827 [11] Stefan Siegmund, Petr Stehlík. Preface: Special issue on dynamical systems on graphs. Discrete & Continuous Dynamical Systems - B, 2018, 23 (5) : ⅰ-ⅲ. doi: 10.3934/dcdsb.201805i [12] W.-J. Beyn, Y.-K Zou. Discretizations of dynamical systems with a saddle-node homoclinic orbit. Discrete & Continuous Dynamical Systems - A, 1996, 2 (3) : 351-365. doi: 10.3934/dcds.1996.2.351 [13] Andrzej Swierniak, Michal Krzeslak. Application of evolutionary games to modeling carcinogenesis. Mathematical Biosciences & Engineering, 2013, 10 (3) : 873-911. doi: 10.3934/mbe.2013.10.873 [14] Xueting Tian, Shirou Wang, Xiaodong Wang. Intermediate Lyapunov exponents for systems with periodic orbit gluing property. Discrete & Continuous Dynamical Systems - A, 2019, 39 (2) : 1019-1032. doi: 10.3934/dcds.2019042 [15] P.E. Kloeden, Desheng Li, Chengkui Zhong. Uniform attractors of periodic and asymptotically periodic dynamical systems. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 213-232. doi: 10.3934/dcds.2005.12.213 [16] Yves Achdou, Victor Perez. Iterative strategies for solving linearized discrete mean field games systems. Networks & Heterogeneous Media, 2012, 7 (2) : 197-217. doi: 10.3934/nhm.2012.7.197 [17] Aleksandar Zatezalo, Dušan M. Stipanović. Control of dynamical systems with discrete and uncertain observations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4665-4681. doi: 10.3934/dcds.2015.35.4665 [18] Karl P. Hadeler. Quiescent phases and stability in discrete time dynamical systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 129-152. doi: 10.3934/dcdsb.2015.20.129 [19] B. Coll, A. Gasull, R. Prohens. On a criterium of global attraction for discrete dynamical systems. Communications on Pure & Applied Analysis, 2006, 5 (3) : 537-550. doi: 10.3934/cpaa.2006.5.537 [20] Jean-Luc Chabert, Ai-Hua Fan, Youssef Fares. Minimal dynamical systems on a discrete valuation domain. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 777-795. doi: 10.3934/dcds.2009.25.777
2018 Impact Factor: 1.008 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25180819630622864, "perplexity": 4211.941978698062}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195524111.50/warc/CC-MAIN-20190715195204-20190715221204-00482.warc.gz"} |
https://www.andlearning.org/potassium-hydroxide-formula/ | Home » Chemistry Formulas » Potassium Hydroxide Formula
# Potassium Hydroxide Formula – Molecular, Structure and Chemical Formula
## What is Potassium Hydroxide?
The potassium hydroxide is a popular inorganic base and other names for chemical compound are potash lye or caustic potash etc. The chemical formula for the compound could be written as KOH and a molecular weight is measured 56.11 g/mol. The chemical structure of the molecule is also given below where one potassium cation combines with hydroxyl anion effectively to form KOH.
### Potassium Hydroxide Structure
The solid KOH has crystalline structure and very much similar to sodium chloride in properties.
### Potassium Hydroxide chemical Formula
Further, this is necessary to learn how can you prepare KOH for industrial usage. Here, you need to combine KCl and water together to give potassium hydroxide in the end. The electrolysis process of KCl with chlorine gas is given as below -:
#### Potassium Hydroxide Properties
Let us have a quick look at the physical properties of compound ahead where it is clear that KOH is a white solid compound with a density of 2.12 g/mL and a melting point of 1,327 degree Celsius. It can be used as transparent pellets or as an aqueous solution at different concentrations.
By looking at the chemical properties of the compound, this is clear that it absorbs water and moisture quickly from the air due to its hygroscopic properties. It is thermally stable and does not decompose even when exposed to the high temperature. It combines with water to form strong alkaline solutions and KOH in the aqueous form. Also, it reacts with acids readily to form potassium salts with vast uses in industries. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5859649181365967, "perplexity": 2138.026263855243}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203326.34/warc/CC-MAIN-20190324043400-20190324065400-00119.warc.gz"} |
https://2010.igem.org/wiki/index.php?title=2._Confirming_the_CFP_sequence_is_functional&diff=158467&oldid=124207 | # 2. Confirming the CFP sequence is functional
(Difference between revisions)
Revision as of 11:57, 23 October 2010 (view source)Slam (Talk | contribs)← Older edit Latest revision as of 11:54, 26 October 2010 (view source)Porter (Talk | contribs) (3 intermediate revisions not shown) Line 3: Line 3: -
Confirming the CFP sequence is functional
+
Confirming Functionality of CFP Sequence
Aim
Aim
As part of the experiments to repair the CUP1p - [MS2-CFP] construct we need to determine if the CFP sequence used is functional or not. By confirming that the CFP protein is functional we can narrow down where the fault lies in the construct. If the CFP sequence was not functional this could mean that the construct was expressing properly but we simply could not detect this.
As part of the experiments to repair the CUP1p - [MS2-CFP] construct we need to determine if the CFP sequence used is functional or not. By confirming that the CFP protein is functional we can narrow down where the fault lies in the construct. If the CFP sequence was not functional this could mean that the construct was expressing properly but we simply could not detect this.
Line 27: Line 27:
We can conclude from this experiment that the reason we are not seeing any CFP expression in pRS414 is because the CFP protein is not being produced properly.
We can conclude from this experiment that the reason we are not seeing any CFP expression in pRS414 is because the CFP protein is not being produced properly.
-
+ -
+
+ +
+ + + +
+ +
+ + + + + {{:Team:Aberdeen_Scotland/Footer}}
## Latest revision as of 11:54, 26 October 2010
University of Aberdeen - ayeSwitch - iGEM 2010
iGEM 2010
# Confirming Functionality of CFP Sequence
### Aim
As part of the experiments to repair the CUP1p - [MS2-CFP] construct we need to determine if the CFP sequence used is functional or not. By confirming that the CFP protein is functional we can narrow down where the fault lies in the construct. If the CFP sequence was not functional this could mean that the construct was expressing properly but we simply could not detect this.
### Hypothesis
The CFP sequence is accurate and the reason why no expression of CFP is being observed is because the protein is not being synthesised properly or not all.
### Protocol
The TEF1p -[CFP] plasmid has been used to drive the expression of fluorescent proteins. The TEF1 promoter has been shown to constitutively express GFP at high levels.
A restriction digest was performed using the enzymes Nde1 and Xba1 in order to remove GFP from the construct. The CFP sequence in CUP1p - [MS2-CFP] was then PCR amplified using primers to generate complementary overhangs to allow homologous recombination into the gaped TEF1p -[CFP] vector.
The gapped vector and the PCR product were co-transformed into yeast (BY4741ΔTrp strain) and incubated for several days. The resulting transformants were then cultured overnight in SD medium. Sample were washed and re-suspended in PBS and then observed under a microscope fitted with CFP filters.
### Results
We can see from Fig.3 that the CFP protein is being properly expressed. This means that the sequence used for CFP in the CUP1p - [MS2-CFP] construct is accurate and should be working. During this experiment the sequence of MS2-CFP was also checked to ensure that during the design both proteins had remained in frame.
We can conclude from this experiment that the reason we are not seeing any CFP expression in pRS414 is because the CFP protein is not being produced properly.
Back to the Top | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8765941858291626, "perplexity": 3714.5757620197382}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335448.34/warc/CC-MAIN-20220930082656-20220930112656-00299.warc.gz"} |
https://link.springer.com/article/10.1007/s13753-018-0192-7 | ## 1 Introduction
The frequency and intensity of disasters are increasing globally (de Haen and Hemrich 2007; CRED 2015; Huggel et al. 2015). This escalation parallels increases in human–environment interaction and in the number of people and asset values exposed to hazards. Vulnerability measurement and assessment are recognized as key components for reducing losses from disasters and facilitating a culture of disaster resilience (Birkmann 2006b; Cutter and Finch 2008; Montz and Tobin 2011).
The concept of vulnerability has been applied in various fields, such as disaster studies, sustainable development, urban growth, gender studies, and climate change, to better understand susceptibility to stresses and shocks originating in environmental and social change. Interpretations of vulnerability depend on disciplinary perspective and context. Physical scientists, for example, tend to conceptualize vulnerability in terms of the likelihood of occurrence of a specific process and associated impacts on the built environment (Papathoma-Kohle et al. 2011; Fuchs et al. 2012). Social scientists tend to define vulnerability as a set of social, economic, and demographic factors that coalesce to determine people’s ability to cope with stressors (Wisner et al. 2004; Juran and Trivedi 2015). In reality, the biophysical environment interacts with social attributes and systems to reveal vulnerability, meaning that vulnerability is socially constructed. Vulnerability ultimately manifests in stratification and unequal impacts among different groups of people across space. Consequently, vulnerability reduction requires knowledge of the factors that influence vulnerability coupled with a holistic understanding of the social, economic, and political contexts in which such factors operate (Hewitt 1997; Cutter et al. 2003; Wisner et al. 2004).
Much vulnerability research relies on qualitative assessments (Laska and Morrow 2006; Few and Pham 2010; Mallick et al. 2011), but there is growing interest in measuring vulnerability empirically (Armas 2008; Myers et al. 2008; de Oliveira Mendes 2009), especially social vulnerability. Among the most recognized methods is the Social Vulnerability Index (SoVI). Developed by Cutter et al. (2003), the SoVI framework uses place-based indicators in order to quantify and identify the biggest drivers of social vulnerability. The SoVI has undergone continuous evolution given deepening understandings of the nature and drivers of vulnerability (Cutter and Morath 2014), and it has been applied in various geographical and social contexts, such as Africa (Letsie and Grab 2015), Asia (Zhou et al. 2014), the Caribbean Islands (Boruff and Cutter 2007), Europe (Holand and Lujala 2013), and Latin America (Hummell et al. 2016).
Quantitative assessments of social vulnerability in Nepal are scarce due to the lack of availability of social data for analysis and mapping. Previous studies on vulnerability in Nepal have focused on either a specific physiographic region of the country (TU-CDES 2016) or a single hazard type, such as floods (Dixit 2003; Dixit et al. 2007; Devkota et al. 2013), landslides (Sudmeier-Rieux et al. 2012), earthquakes (Dixit et al. 2013; Dixit 2014), or severe weather events (Shrestha 2005). A recent study by Mainali and Pricope (2017) used a few socioeconomic variables in combination with high-resolution images to investigate vulnerability to climate change in Nepal. The study is valuable because it uncovers spatial variations of vulnerability across the country. However, it does not consider a wide range of social, economic, and demographic variables—for example, unemployment, or elderly, children, and minority populations—which would add much needed social dimensions of vulnerability to the study. The Ministry of Environment of the Government of Nepal (2010), in a district-level analysis of vulnerability to climate change, recommended a scale-dependent approach that focuses on the local level (villages and municipalities). The argument is that such analyses reveal finer-scale dynamics of vulnerability that may be concealed at larger scales. Thus, there exists a need for the quantification of social vulnerability across the entire country of Nepal at the local level.
To address this research gap, we developed and applied a modified SoVI to quantify social vulnerability to natural hazards in Nepal at the village and municipal level. The specific research questions are: (1) who are the most vulnerable populations in Nepal? and (2) where do they live? The objectives are to: (1) quantify social vulnerability at the village and municipal levels using indicators relevant to the Nepali context, and (2) assess the spatial dynamics of social vulnerability in the country. The SoVI is applied at the local level across the entire country and provides statistical and spatial findings that have the potential to improve disaster preparedness in Nepal.
## 2 The Nepali Context
Nepal is situated in the central Himalayan region surrounded by India on the east, west, and south, and by China in the north. The population of Nepal is about 26.5 million (CBS 2012) and is extremely diverse in exposure to hazards and with respect to numerous social, economic, and demographic attributes. These spatially differentiated factors must be considered in order to develop an appropriate SoVI.
### 2.1 Socioeconomic Context
The social, economic, and demographic attributes of Nepal, which intersect with geophysical and hydrometeorological processes, reflect directly on the social vulnerability of the country. The status of these attributes is rooted in a historically sluggish development process. In the past decades, development activities have been centered in the capital city of Kathmandu and a few other urban areas, marginalizing rural areas in the Mountain, Hill, and Tarai regions from the process. The socioeconomic situation is further aggravated by a lack of infrastructure, energy, government accountability, and financial resources. As a result, Nepal is struggling to escape the poverty trap and remains one of the least developed countries, ranking 144th in a recent Human Development Index (HDI) report (UNDP 2016). According to the latest census of 2011, the population has been growing steadily at more than 2% per annum and has close to tripled from the 1961 population of 9.5 million (CBS 2012). The total adult literacy rate is 59.6%, with a female literacy rate of only 48.8%. Nepal is predominantly an agrarian society with roughly 60% of the population dependent on subsistence agriculture. The majority of land is not arable due to the steep slopes and rocky soils of the mountainous region, and agriculture is highly monsoon-dependent. Poverty has compelled many to emigrate to neighboring countries and the Middle East in search of employment, which provides much needed remittances. The recent 2011 census reports that one in every four households (25.4%) has at least one member living outside of Nepal, and the greatest proportion of the absentee population (44.8%) is among the economically productive 15–24-year cohort (CBS 2012). Most migrants are male, and female-headed households have increased from 14.9% in 2001 to 25.7% in 2011.
Nepal exhibits great demographic diversity, which influences social vulnerability. Hinduism is followed by more than 80% of the population (Buddhism and Islam are other common religions), but is comprised of many castes and subcastes. The 2011 census also accounts for 125 ethnic groups and 123 languages across this relatively small country (CBS 2012), and these demographics are geographically clustered. Only a few ethnic and caste groups are dispersed throughout the country—modern-day Nepal was formed in the 18th century by unifying numerous small principalities that were primarily based on caste, ethnicity, and language. Some of these social markers, specifically the caste system, lead to discrimination and social exclusion, especially in rural areas. Spatial attributes of these demographic features may be revealed through spatial analyses of social vulnerability scores.
Adding to the complicated socioeconomic and demographic contexts is the risk of and exposure to a multitude of hazards—such as earthquakes, floods, landslides, thunderstorms, debris flows, avalanches, glacial lake outburst floods (GLOFs), and forest fires—and these hazards are distributed unevenly throughout the country (Aksha et al. 2018). The 2015 Gorkha Earthquake alone killed about 9000 people and damaged or destroyed more than 750,000 buildings. A majority of the losses occurred in rural areas where low-quality, traditional masonry is the predominant housing material. Due to competition for resources such as jobs and land that is accessible, arable, and easy to develop, people are pushed into high-risk areas (Aryal 2014).
### 2.2 Physical Context
Nepal is situated in the Himalayas between India and China. Elevations range from just 57 m above sea level to Mt. Everest, at 8848 m the world’s highest peak, within a relatively narrow latitudinal spread. Nepal is divided into three ecological regions: Tarai, Hill, and Mountain (Fig. 1). The Tarai region is the southernmost part of Nepal. This “grain basket” of the country has relatively low, flat, and fertile land comprised of alluvial soils. The Tarai region covers roughly 24% of the total area of Nepal, but is home to roughly 50% of the population. The Hill region rises from 1000 to 4000 m above sea level and comprises about 42% of Nepal’s total area. The Hill region is the first orographic barrier to monsoon winds, which produce heavy precipitation on its southern flanks. The increasingly urbanized Kathmandu and Pokhara valleys lie in this region. North of the Hill region lies the Mountain region, which covers about 34% of the total land area of Nepal. The Mountain region has subalpine to alpine climates and is characterized by river valleys, tectonic basins, snow-capped peaks, glaciers, rocky slopes, and colluvial deposits. This region is sparsely populated.
### 2.3 Political Context
Nepal was divided into five development regions, 14 zones, 75 districts, 53 municipalities, and 3918 village development committees (VDCs). However, in 2015, a new constitution was adopted that created three levels of governance: the federation, the province, and local bodies. Now, Nepal is divided into seven provinces and 744 local bodies (four metropolitan cities, 13 sub-metropolitan cities, 246 municipalities, and 481 rural municipalities), although administration through these bodies has not yet commenced. This study was based on the previous administrative bodies, that is, the 3918 VDCs and 53 municipalities. The previous bodies were chosen because the scale is smaller (total of 3971 spatial units compared to 744), which allows statistical and spatial analyses to produce finer results. The new administrative bodies were formed by simply combining groups of the previous bodies, so the new administrative bodies are still captured in our analyses, but at a finer scale. Use of the previous bodies supports analyses across more observations and more spatial units while still being administratively relevant. Finer-scale analyses are especially important in the Nepali context, which exhibits great socioeconomic, cultural, and physiographic diversity across short expanses of space.
## 3 Materials and Methods
In order to understand drivers of vulnerability at the village level in Nepal, we constructed a modified SoVI. We identified meaningful variables using the published literature. To reflect the socioeconomic, physical, and political context of the country, necessary adaptations were implemented as described in detail below.
### 3.1 Data and SoVI Modification
This study adopted the SoVI method developed by Cutter et al. (2003), which employed more than 200 variables to quantify and analyze social vulnerability in the United States. Conceptualizations of social vulnerability and the SoVI methodology have been refined over time and applied in many contexts (Boruff and Cutter 2007; Holand and Lujala 2013; Zhou et al. 2014; Hummell et al. 2016). Similarly, this study analyzed individual factors such as education, employment, ethnicity, and health as well as community characteristics such as level of urbanization, access to medical services, and built environment attributes to construct a modified SoVI for Nepal.
Since the original SoVI was applied to the United States context, modifications were necessary to adapt the model to Nepal’s distinct sociophysical context. To construct the modified SoVI, we extracted data from the full dataset of the most recent 2011 census, which was provided by the Central Bureau of Statistics (CBS), Government of Nepal (CBS 2012). The CBS conducted the census using two household level questionnaires. The first questionnaire collected basic demographic data, and the second questionnaire included more detailed questions on topics such as migration, fertility, and economic activity. The CBS adopted a systematic sampling method, and roughly 15% of the entire population of Nepal were sampled. Using all available data from the 2011 census, Table 1 provides a list of concepts and variables used to construct the SoVI.
Modifications to the original SoVI were made to capture fundamental demographic differences between Nepal and the United States. To capture “Ethnicity” in Nepal we included Dalit (the lowest strata of the Hindu caste system) and Minority Populations. Dalits are considered “untouchable” and encounter systemic social and economic oppression. About 15.6% of the total population in Nepal are Dalits, and there are 26 distinct, concentrated Dalit groups distributed heterogeneously throughout Nepal—each with a different language, culture, religious practices, and means of employment (Dahal et al. 2002). Minority Populations encompasses indigenous populations and other historically disadvantaged groups. Indigenous populations in Nepal are defined as people who possess distinct cultural traditions, languages, and religious faiths based on animism (Bhattachan 2008). Fifty-nine separate groups are considered Minority Populations, and they are further divided into five categories based on their status: endangered, highly marginalized, marginalized, disadvantaged, and advanced. The advanced category, which consists of the Newar and Thakali castes, actually have the highest HDI values (Sharma et al. 2014) and were thus excluded from Minority Population status in our SoVI. However, Muslims and Sikhs/Punjabis were included since they are considered disadvantaged groups who together account for less than 5% of Nepal’s total population.
We also included “Built Environment” variables to reflect physical attributes of housing and public services such as electricity, water, and sewer infrastructures, as similarly included in a SoVI in Brazil by Hummell et al. (2016). According to the 2011 census, 25% of houses have external walls constructed from low-quality materials such as bamboo and wood, and only 10% of houses have reinforced cement concrete (RCC) foundations. As the entirety of Nepal lies in a highly active seismic belt, housing foundations and wall materials significantly impact vulnerability. Many fatalities from the 2015 Gorkha Earthquake, for example, were among people residing in low-quality houses. Severe damages were sustained by traditional mud and stone houses, especially in rural areas. In addition to housing quality, only 52% of households are connected to a piped water supply, only 39% have a toilet or latrine, and 33% are without electricity as their primary source of energy.
Populations who do not speak/understand Nepali were added to the “Special Needs Populations” indicator because inability to speak or understand Nepali substantially restricts access to critical and timely knowledge on disaster warnings as well as post-disaster recovery and rehabilitation programs. In the census questionnaire, individuals were asked to report their mother tongue and second language. Those who did not report Nepali were identified as individuals who do not speak/understand the Nepali language. Knowing the most widely spoken language is important because it is used extensively for basic communication and relaying information on disasters. Such populations also encounter linguistic issues (for example, completing and submitting official forms) when attempting to receive compensation and other support from the government. Although Nepali is no longer the official national language, it is the only language used for administrative and government communications, which constitutes a major disadvantage for nonspeakers, especially in emergency situations.
### 3.2 Methods
A total of 39 variables were selected for the construction of the modified SoVI (see Table 1). All variables were normalized using percentage, density, or per capita functions prior to statistical analysis. Principal component analysis (PCA) via Statistical Package for the Social Sciences (SPSS) version 21.0 software generated a set of independent factors. Principal component analysis is a factor reduction methodology that identifies a smaller number of components to explain the variance observed in a larger dataset (Abdi and Williams 2010). The purpose of performing PCA is to distill a broad explanation of the data by grouping like-variables into components that adequately account for covariation among the larger number of analysis variables. The analysis also facilitates the interpretation of component groups and provides insight when data are examined with further analyses. Following methods developed by Cutter et al. (2003), Kaiser normalization and Varimax rotation were employed as extraction methods for components. Only components with eigenvalues higher than 1.0 were extracted and named to indicate the latent variables. Each component was named and assigned cardinality (±). The SoVI was calculated by adding the scores of each component to arrive at total SoVI scores. An equal weighting and additive approach was used in the absence of empirical and justifiable evidence for weighting components differently, as has been exercised in similar studies (Cutter et al. 2003; Hummell et al. 2016). Our modified SoVI for Nepal was calculated for each spatial unit (the 3918 village development committees and 53 municipalities) by adding the principal component values:
$${\text{SoVI}}_{\text{village}} = {\text{PC}}1 + {\text{PC}}2{-}{\text{PC}}3 + {\text{PC}}4 + {\text{PC}}5 + {\text{PC}}6{-}{\text{PC}}7$$
The SoVI scores of each spatial unit were mapped using ArcMap version 10.3 to visualize the most and the least vulnerable villages in Nepal based on standard deviation from the mean value. We used global and local Moran’s I tests of spatial autocorrelation to investigate whether social vulnerability is clustered or random across space in statistical terms. Global and local tests calculate autocorrelation among all villages and determine statistically significant patterns of similarity and dissimilarity in the spatial location and distribution of social vulnerability. The global Moran’s I test determines whether the geolocations of index results exhibit a spatial pattern. The interpretation is similar to that of correlation coefficients: values close to + 1 indicate strong positive spatial autocorrelation (that is, clustering of either high or low values of social vulnerability), while values close to − 1 indicate strong negative spatial autocorrelation (that is, alternation of high and low values for adjacent observations). Values near zero indicate the absence of spatial patterns, or randomness.
Local Moran’s I was deployed to classify identified clusters according to type of association. These results were used to map four typological gradations of social vulnerability at the village and municipal level: (1) High–High (HH), a village with a high SoVI score surrounded by villages with high SoVI scores; (2) Low–Low (LL), a village with a low SoVI score surrounded by villages with low SoVI scores; (3) High-Low (HL), a village with a high SoVI score surrounded by villages with low SoVI scores; and (4) Low–High (LH), a village with a low SoVI score surrounded by villages with high SoVI scores. Hot spots (HH) and cold spots (LL) denote positive spatial autocorrelation, indicating clusters of similar values, whereas LH and HL denote negative spatial autocorrelation, indicating clusters of dissimilar values. Together, global and local spatial analyses identify patterns of social vulnerability that are either not visible (that is, masked) or appear visually meaningful yet are not statistically significant (that is, false positives). The inclusion of spatial clustering advances the original research work using the SoVI method by Cutter et al. (2003) by adding new analytical abilities to the method.
## 4 Results
The PCA uncovered seven components with eigenvalues greater than 1.0. Based on loaded variables and their cardinality, the seven components were named Renters and Occupation, Poverty and Poor Infrastructure, Favorable Social Conditions, Migration and Gender, Ethnicity, Medical Services, and Education. In total, the principal components explain 63.02% of the variance of the data. Descriptions of the seven components, signs denoting their effect on social vulnerability, and loadings are presented in Table 2.
Total SoVI scores were calculated by summing all seven principal components based on their cardinality, and the mean and standard deviations (SD) of the scores were also calculated. Based on SD values, vulnerability scores were grouped into five quintiles from most (> 1.5 SD) to least (< − 1.5 SD) vulnerable. Using ArcMap, we subsequently mapped total SoVI scores (Fig. 2) and the value of each component to visualize social vulnerability across Nepal (Fig. 3). Total SoVI scores (Fig. 2) reveal that the most socially vulnerable villages are located in the eastern and central Tarai region; the western Hill region; and the central and western Mountain regions. The least vulnerable villages are located in the eastern and central Hill regions. The capital city of Kathmandu is also highly vulnerable. In terms of districts, the Hill and Mountain districts of Provinces 6 and 7, and the Tarai districts of Provinces 1 and 2 contain a predominant number of villages and municipalities with high social vulnerability. The eastern Hill districts of Province 1 contain a majority of the villages and municipalities with low SoVI scores.
The geographic distribution of the principal component values is displayed in Fig. 3. Highly vulnerable areas for the Renters and Occupation component are concentrated in urban centers, particularly in Kathmandu and the Mountain region. Vulnerability for Poverty and Poor Infrastructure is concentrated in the Tarai region. For example, almost every village and municipality in the Tarai districts of Provinces 1, 2, and 5 exhibit high vulnerability in terms of Poverty and Poor Infrastructure. The third component, Favorable Social Conditions, exhibits greater levels of vulnerability across the entire Tarai region as well as pockets of the eastern and central Hill region. Relatively vulnerable areas for Migration and Gender, the fourth component, are distributed across the entire Tarai and Hill regions with a distinct concentration in the geographic center of Nepal. The highest levels of social vulnerability for component five, Ethnicity, are located in the western part of all regions of Nepal, as well as the eastern Tarai region. The Medical Services component reveals relatively high vulnerability in the Mountain region, with vulnerability decreasing with decreasing elevation. The final component, Education, reveals higher vulnerability in central and eastern Nepal—especially the eastern Tarai region—with pockets of the western Mountain region also revealing high levels of social vulnerability.
To test for clustering, we calculated global Moran’s I statistics of SoVI scores in an ArcMap environment. We used the polygon contiguity concept to specify spatial relationships among villages and municipalities, which defines neighboring villages as those that share a boundary (Scott and Janikas 2010). The global Moran’s I test confirmed positive spatial autocorrelation with a value of 0.41 (p < 0.001) and a z-score of 44.13. We employed a local’s Moran’s I test to decompose global statistics into local clusters and identify pockets of association in terms of high and low values (Fig. 4). The results indicate that HH clusters are present in the western Hill and Mountain regions, although there are smaller, isolated pockets in the eastern Tarai region. Clusters of LL values were detected in the eastern and central parts of the Hill and Mountain regions.
## 5 Discussion
The objective of this study was to quantify social vulnerability at the local level using indicators relevant to Nepal’s distinct social and physical landscapes. Following Cutter et al.’s (2003) SoVI methodology, we derived seven components that contribute to social vulnerability in Nepal (see Table 2). Component and total SoVI scores are not evenly distributed across the country, and clustering is evident (Fig. 4).
A major finding of this study is that areas with similar hydrometeorological and geophysical characteristics may exhibit differences in social vulnerability. Marked differences are observed in the spatial distribution of social vulnerability among the three ecological regions. The central and western Mountain, western Hill, and central and eastern Tarai regions exhibit relatively higher social vulnerability, while the central and eastern Hill regions reveal comparatively less vulnerability. This finding is interesting because elevation, natural hazard risk, and geophysical and hydrometeorological regimes are similar within each ecological region, but social vulnerability is not. Thus, while populations residing within each region are subjected to similar natural environments (and thus exhibit similar exposure to the same natural hazards), our findings suggest that social, economic, and built environment attributes make the places different in terms of level of social vulnerability, which in turn affects the levels of disaster risks. A majority of villages and municipalities in the central and eastern Tarai regions, which contain a disproportionate amount of the population, are categorized in the High and Medium–High vulnerability classes, whereas population centers in the western Tarai region are primarily classified as Medium or lower. These results parallel the fact that the central and eastern Tarai regions lag behind in education and health while also being home to a large number of poor, Dalit, and minority groups (Sharma et al. 2014). As for the Hill and Mountain regions, the 1996–2006 armed political conflict emerged in the western Hill region and then expanded. Due to geographic proximity, villages and municipalities in the western Hill and central and western Mountain regions were acutely affected, further paralyzing the development trajectory of already isolated segments of the country.
Our regional findings both correspond and contrast with previous studies. For example, while Mainali and Pricope’s (2017) investigation of climate change vulnerability similarly contends that western portions of the Hill and Mountain regions exhibit relatively greater vulnerability, they classify the central and eastern Tarai regions in a low to moderate category. This classification contrasts with our identification of the central and eastern Tarai regions as relatively highly vulnerable. Our results also indicate that villages and municipalities in the central and eastern Hill regions are relatively less vulnerable, but the Ministry of Environment of the Government of Nepal (2010), in a report on climate change and climate-related disasters, claims that these areas are highly vulnerable. A study by K.C. (2013), which investigated flood and landslide vulnerability between Tarai and non-Tarai districts through the lens of education, found that vulnerability is greater in the Tarai region compared to the remainder of the country. However, our analyses reveal that the western Tarai region performs relatively well in educational attainment and is less vulnerable than the rest of the Tarai region and many other parts of the country. Observed collectively, discrepancies with similar studies are likely linked to (1) the spatial units of analysis; and (2) the type(s) of hazard(s) considered. The studies by K.C. (2013) and the Ministry of Environment of the Government of Nepal (2010) used districts as the spatial unit of analysis, but our study used smaller-scale villages and municipalities. Additionally, our study considered multiple hazard types (rather than only floods, landslides, and/or climate-related hazards) and used more variables. We argue that smaller-scale analyses and consideration of more variables has potential to generate more refined and spatially explicit results. Further, we argue that incorporating multiple hazards (as opposed to a single hazard type) is more realistic in a complex, dynamic, and compounding sociophysical environment such as Nepal.
Social vulnerability is discussed above at the composite SoVI and regional scales; however, drivers of vulnerability vary at the component and local scales. The Medical Services component, for example, exhibits a distinct geographic pattern: Mountain villages are highly vulnerable, with vulnerability decreasing as elevation decreases. Mountain villages are sparsely populated and are characterized by remoteness and isolation, which results in poor access to health facilities. As elevation decreases, population size and concentration increase and thus result in greater numbers of health facilities. We also overlaid the new province boundaries (see Fig. 1) and found that a majority of villages in Provinces 2, 4, 6, and 7 are classified in the High vulnerability category, whereas a majority of villages in Provinces 1 and 3 are classified as Low.
At the district level, the spatial distribution of social vulnerability reflects historical development patterns of the country. In terms of HDI values, the ten lowest districts—which are predominantly in the western Hill and western Mountain regions. These districts are also identified as highly vulnerable in our study, with a majority of villages and municipalities from the districts classified in the High and Medium–High vulnerability classes. Historically, districts in western Nepal are relatively poorer, exhibit lower literacy rates, lack infrastructure (for example, transportation and hospitals), and have been alienated from mainstream development projects, although they have received greater allotments of development aid in recent years. Western districts were substantially impacted by the 1996–2006 armed conflict. Due to geographic isolation, push factors, and the vicious cycle of poverty, these districts have a dependence on natural resources, such as forests, and high rates of migration to the Middle East as laborers.
Major cities of Nepal fall into different vulnerability categories. Table 3 provides an overview of the 10 most populous cities and their vulnerability classes. Kathmandu and Butwal are identified as the most vulnerable cities, and Biratnagar and Dharan are classified as Medium–High. None of Nepal’s major urban centers are classified as Low vulnerability. Among urban centers, major drivers of social vulnerability are Renters and Occupation and/or Poverty and Poor Infrastructure. According to the 2011 census, the average annual population growth rate of Nepal was 1.35% from 2001 to 2011, but all major cities exceeded this rate—particularly the two most vulnerable cities of Kathmandu and Butwal. Urban centers have experienced significant rural-to-urban migration in recent years, thus exposing increasing numbers of people to natural hazard risk. Furthermore, infrastructure, public services, and utilities are already serving more users than they can accommodate. In our study, Kathmandu was identified as the most vulnerable city in Nepal, but similar studies disagree. K.C. (2013), for example, found that educational attainment is highest in Kathmandu and thus the city is relatively less vulnerable compared to other cities, while Mainali and Pricope (2017) found that Kathmandu is less vulnerable to climate-related disasters compared to the rest of the country. The authors suggest that this could be explained by greater access to resources compared to other parts of the country. We argue that our analysis of smaller spatial units, inclusion of more variables, and consideration of multiple hazards helps to explain differences in the respective research findings.
Only 206 of close to 4000 villages and municipalities (roughly 5%) are classified in the Low vulnerability class. Even more striking, this categorization of Low is solely in relation to other jurisdictions in Nepal, meaning that it does not consider the larger international context. The entirety of Nepal is located in a high-risk zone for natural hazards. Thus, a classification of Low in our study—which only considers Nepal—may actually be quite vulnerable compared to places that are classified as low in other countries. A measure of low vulnerability in a country that is less hazard-prone and socially, economically, and politically well off does not mean the same as low vulnerability in Nepal.
Nepal is extremely vulnerable to climate change given its hydrometeorological and physiographic extremes, which expose the country to flash and riverine floods; landslides, mudslides, and debris flows; and GLOFs (Shrestha and Aryal 2011; Immerzeel et al. 2012). In terms of social vulnerability, these risks are compounded by a reliance on agriculture, natural resource extraction, and primary sector economic activities—all of which impact Nepal’s already fragile landscape. The fifth assessment report of the Intergovernmental Panel on Climate Change not only projects a higher warming trend for South Asia compared to the global mean (Christensen et al. 2014), but warming is expected to be more pronounced in high-altitude regions compared to lowlands (Shrestha et al. 1999; Aryal et al. 2014). This study has identified the high-altitude Mountain villages and municipalities of Nepal as highly vulnerable, and predictions of global warming threaten to exacerbate this vulnerability with greater risk of floods, landslides, GLOFs, and other hazards (Bajracharya and Mool 2009; Shrestha and Aryal 2011). Further adding relevance to social vulnerability, disaster mitigation programs and policies in Nepal have historically been reactive, focusing on structural solutions on an event-by-event basis (Dixit 2003). This approach fails to address many underlying factors of social vulnerability, including education, poverty alleviation, and communication of disaster information via several languages and media. This study provides a comprehensive assessment of social vulnerability at the local level, and could assist policymakers in proactively deploying programs and policies to reduce disaster risk.
Lack of data availability is typically the most limiting factor in measuring social vulnerability to natural hazards. This can lead to a reliance on easily measurable variables and result in the misrepresentation (for example, concealment or masking) of people and the complex physical and political-economic contexts in which they reside (Birkmann 2006a; Zhou et al. 2014; Burton 2015). This study used complete, long-form data from the most recent 2011 census of Nepal, which sampled roughly 15% of the population (CBS 2012). Based on our knowledge, this represents the largest, most comprehensive, and geographically most extensive dataset for the country. However, one critique is that this study was unable to explicitly include data on income, which may have influenced our measurements of social vulnerability. The CBS utilizes a living standard survey that measures consumption as a surrogate for income. We supplemented these data with several related measurements of employment, occupation, educational attainment, literacy, and vehicle ownership. As another critique, other factors that are generally considered to shape social vulnerability—such as access to resources (including information and political power), age of infrastructure, and risk perception and awareness—could not be included in this study. Future analyses of social vulnerability in Nepal should attempt to overcome these shortcomings.
## 6 Conclusion
Based on the underlying socioeconomic and demographic profiles of close to 4000 villages and municipalities, this study investigated spatial patterns of social vulnerability in Nepal using an adapted SoVI methodology. In terms of ecological regions, the western Hill, central and western Mountain, and central and eastern Tarai regions were determined the most vulnerable. The central and eastern Hill regions were determined the least vulnerable. Demographics and historical development processes are essentially reflected in the geographic distribution of social vulnerability. That is, social vulnerability is particularly high in areas that have concentrations of Dalit and minority populations and/or a history of armed conflict, with mountain communities (which have poor access to infrastructure and critical services) overrepresented. As far as we are aware, this analysis is the first attempt to quantify social vulnerability at the local level across the entire country of Nepal.
Nepal is attempting to make progress in disaster risk reduction. Unfortunately, the 2015 Gorkha Earthquake set the country back and added additional urgency to the daunting task of making communities more resilient. This recent earthquake brought much needed attention to social components of vulnerability that have primarily remained unaddressed in favor of structural mitigation. This shift is important, and our study can help to provide a science-based starting point. Because this study is based on census data (which occurs in intervals of 10 years), it can be periodically revised to monitor changes over time and measure the impacts of disaster programs and policies. This study provides a visual understanding of the geographic distribution of social vulnerability in Nepal, which may inform policy making, resource allocation, and disaster management among government officials and nongovernmental organizations at the local level. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4308569133281708, "perplexity": 4004.523864366358}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500095.4/warc/CC-MAIN-20230204075436-20230204105436-00550.warc.gz"} |
https://www.gamedev.net/forums/topic/184789-rotation-question/ | • ### Announcements
#### Archived
This topic is now archived and is closed to further replies.
# Rotation Question
## Recommended Posts
EasyGino 122
Okay guys and girls, Quick question, what would be the best way to have two cubes on the screen and rotate them in opposite directions (I want an approach opinion). Whe I rotate around my pyramid, its the world moving and not actually the code (correct?).
##### Share on other sites
Sean Doherty 144
Not sure I understand you question are the two cubes being rotated around a pyramid with a fixed camera. If this is the case you can translate each of the cubes to the correct location, then rotate then rotate the first cube by x Radians, and then rotate the second cube by –x + 3.14159f Radians. Finally, increment x each frame between x = 0 to 2 * 3.14159f.
This should cause the two cubes to spin around the center in opposite directions. If this is not what you want can you clarify further?
Thanks
Understanding is a three edged sword...
##### Share on other sites
EasyGino 122
Ok just two cubes on the screen, rotating in opposite directions, one rotates clockwise the other counter-clockwise.
Right now i''m using a pyramid and with the Matrices i''m using the timer with a formula to rotate around in circles.
Thanks.
##### Share on other sites
Sean Doherty 144
Based on your explanation it sounds like you want to rotate the cubes from a stationary position? In order to make the cubes rotate from a stationary position you need to build two matrices and render as per the following:
//Cube 1D3DXMATRIX matMatrix;D3DXMATRIX matRotation;D3DXMATRIX matTranslate;D3DXMatrixIdentity(&matMatrix);D3DXMatrixRotationX(&matRotation, time); // Positive Time rotated by the x AxisD3DXMatrixMultiply(&matMatrix, &matMatrix , &matRotation,);D3DXMatrixTranslation(&matTranslate, x, y, z);D3DXMatrixMultiply(&matMatrix, &matMatrix , &matTranslate,);device->SetTransform(D3DTS_WORLD, &matMatrix);// Render the 1st CubeCube 2D3DXMatrixIdentity(&matMatrix);D3DXMatrixRotationX(&matRotation, -time); // Negative Time Rotated by the x AxisD3DXMatrixMultiply(&matMatrix, &matMatrix , &matRotation,);D3DXMatrixTranslation(&matTranslate, x, y, z);D3DXMatrixMultiply(&matMatrix, &matMatrix , &matTranslate,);device->SetTransform(D3DTS_WORLD, &matMatrix);// Render the 2nd Cube
This should get you closer to a solution.
Understanding is a three edged sword... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3636014461517334, "perplexity": 3296.022444843502}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886120573.75/warc/CC-MAIN-20170823152006-20170823172006-00403.warc.gz"} |
http://crypto.stackexchange.com/users/4136/alexandre-yamajako?tab=activity&sort=all | Alexandre Yamajako
Reputation
880
Top tag
Next privilege 1,000 Rep.
Mar 15 comment What is Deterministic Authenticated Encryption? Opposite to nonce based authenticated encryption, DAE takes as input only the associated data, the plaintext and the key and outputs a ciphertext. SIV is a good example of this. The point is to use such primitives in a context where the use of a IV is rendered irrelevant because the plaintext distribution is of high entropy (such as key encryption) Mar 11 comment Would a non-deterministic (read: randomized) compression algorithm be crypto-safe? If you pad, what's the point of compression ? Mar 11 comment Would a non-deterministic (read: randomized) compression algorithm be crypto-safe? Are you in any way referring to the TLS attacks built upon the usage of compression pre-encryption ? If you are then I don't think your solution would help since either your "added randomness" increases the size of the ciphertext and then it defeats the purpose of using encryption or it doesn't and then the BREACH and C.R.I.M.E attacks can proceed as usual since they are mainly focusing on the size of the outputted ciphertext Mar 11 comment Would a non-deterministic (read: randomized) compression algorithm be crypto-safe? "so why not compress your file and then encrypt / send it using a stock TLS library like openssl" This is not a good idea... SSL/TLS optionally includes compression of the plaintext before encryption. The problem you open yourself to active attacks such as BREACH or C.R.I.M.E which are some of the most efficient attacks on SSL/TLS. Oct 24 awarded Yearling Sep 10 comment Implement AES with 16 bit block size? could you please provide a reference for the 24 round unbalanced festeil you're writing about ? Thx Sep 7 answered Could someone explain the given algorithm? Jul 12 comment Why Elliptic Curves? very good point ! Jul 9 comment Does SHA-1 meet the strict avalanche criterion? This technique is efficient to weed out very bad hash function candidates but I doubt it will tell you anything about SHA-1. There was a lot of work put in finding flaws in SHA-1 by actually looking at SHA-1. I don't think you can really expect finding anything looking at SHA-1 as a black box. Jul 7 comment Does SHA-1 meet the strict avalanche criterion? I haven't and I don't really see the point : You're only ever going to look at a infinitely small portion of the input space. What this means is that this method doesn't answer your original question which was : "Does SHA-1 meet the strict avalanche criterion?" Jul 7 comment Does SHA-1 meet the strict avalanche criterion? Did you do the math on how much computation you would need to do for SHA1 given that its input space consist of all message whose length is smaller than 2^64 ? Jul 5 answered Do all attacks against PKCS1 v1.5 encryption require an oracle Jun 23 awarded Caucus Jun 23 awarded Constituent Apr 14 comment Errata for NIST SP 800-63 Those figures assume that humans pick password randomly. Whether or not the calculus is fine matters less than the fact that this assumption is overly optimistic and should be nixed from any serious document ! Feb 4 comment How fast would a polynomial time factoring algorithm compute? Maybe that's nitpicking but the distinction is polynomial vs. non-polynomial rather than polynomial vs exponential. We know subexponetial algorithms to factor large numbers as well as finding discrete logarithms in finite fiels. Oct 24 awarded Yearling Mar 4 comment Why does CTR mode XOR the plaintext into the output of the block cipher rather than XORing the plaintext into the input of the block cipher? CTR is designed in this way as a technical equivalent of One TIme Pad where the full entropy random keystream is replaced by a pseudo random generator Feb 13 comment Pseudo random permutation for arbitrary size domains If I may extend the question of the OP the paper you cited states that their methods aren't suitable when the domain $X$ is such that $2^{30}<|X|<2^{60}$ and presents that gap as a open problem. Are you aware of subsequent research that solved ? Jan 8 comment Would data be secure if a cryptographically secure PRNG was used for encryption? Two things : First it would be somewhat pointless to do on top of AES-[insert-right-mode-of-operation-here] but as long as the AES layer and the PRNG layer are uncorrolated it won't decrease security. Also what you get from your solution is confidentiality which is great but in many situations not enough. For example what is the consequence of a bit flip by an attacker on ciphertext in transit ? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5022083520889282, "perplexity": 1432.373053390101}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461863352151.52/warc/CC-MAIN-20160428170912-00197-ip-10-239-7-51.ec2.internal.warc.gz"} |
http://www.r-bloggers.com/search/twitter/page/169/ | # 2122 search results for "twitter"
## In case you missed it: December Roundup
January 17, 2011
By
In case you missed them, here are some articles from December of particular interest to R users. A Facebook employee created a beautiful visualization of social connections around the world, which made a lot of news on the Web. The creator, Paul Butler, explained how he did it using R. With sponsorship from Revolution Analytics, the R/Finance conference in...
## Introducing Monte Carlo Methods with R [precision]
January 17, 2011
By
Doug Rivers, professor of Political Sciences in Stanford, kindly sent me this email yesterday night: The 2nd displayed equation in section 2.1.2 on p. 44 is garbled (it might be interpreted as saying that U and X have the same distribution). I think you intended: And indeed we should have stated the implicit convention that
## Méthodes de Monte-Carlo avec R [out]
January 17, 2011
By
The translation of the book Introducing Monte Carlo Methods with R is now published and out! I have received five copies in the mail yesterday, although it was not produced in time for my R class students to get it before the exam today. The book is still indicated on amazon.com as appearing in February,
## Dial-a-statistic! Featuring R and Estonia
January 16, 2011
By
Did you wake up this morning hoping that you would be able to listen to telephone beeps inspired by Estonian web site metrics? I knew you did! First things first: I came up with the slightly crazy idea of using the bleepy sounds that telephones make, called “dual-tone multifrequency” (DTMF) tones, as a tool in
## When 1 * x != x
January 16, 2011
By
$When 1 * x != x$
Trying to dimly recall things from my maths degree, it seems that in most contexts the whole point of the number one is that it is a multiplicative identity. That is, for any x in your set, 1 * x is equal to x. It turns out that when you move to floating point numbers,
## Missing reference in Monte Carlo Statistical Methods
January 15, 2011
By
A few days ago, Peng Yu sent me this email Dear Prof. Robert, The citation Edwards and Sokal (1988) appears on page 326 of your book MCSM2. However, I don’t find in in the Reference section (it would have appear on page 601 if it is in the reference section). I don’t find this error
## Parsing and plotting time series data
January 15, 2011
By
This morning I came across a post which discusses the differences between scala, ruby and python when trying to analyse time series data. Essentially, there is a text file consisting of times in the format HH:MM and we want to get an idea of its distribution. Tom discusses how this would be a bit clunky
## Warming in Paris: minimas versus maximas ?
January 14, 2011
By
Recently, I received comments (here and on Twitter) about my previous graphs on the temperature in Paris. I mentioned in a comment (there) that studying extremas (and more generally quantiles or interquantile evolution) is not the same as studying ...
## Statistical podcast: Random and Pseudorandom
January 14, 2011
By
This morning when I downloaded the latest version of In our time, I was pleased to see that this weeks topic was “Random and Peudorandom.” If you’re not familiar with “In our time”, then I can I definitely recommend the series. Each week three academics and Melvyn Bragg discuss a particular topic from history, science, | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3434690237045288, "perplexity": 1798.7517563286372}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507450767.7/warc/CC-MAIN-20141017005730-00377-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/1878366/explain-method-behind-permutations-question-high-school-level | # Explain method behind permutations question (high school level)
I am in high school and got a question in my textbook which reads:
A baby has nine different toy animals. 5 of them are red and 4 of them are blue. She arranges the toys in a line so that the colours are arranged symmetrically. How many arrangements are possible?
This is how I reasoned: to fulfil the symmetrical requirement, the middle toy must be red. This leaves 8 toys, 4 on each side of the middle red toy - 4 of these are red, and 4 are blue. To calculate the permutations of the remaining 8, keeping the symmetrical requirement in mind, we calculate 4!.
Therefore, the total number of arrangements is $4! + 1 = 25$
This was not the correct answer - the correct answer is $6*5!*4! = 17280$
Could someone please explain where my thinking fails me? Thank you!
So, you are correct in saying that the middle toy must be red. Note that we have spaces as follows: $$[1][2][3][4][R][6][7][8][9].$$ Because the arrangement is symmetric in color, we only care about arranging the color on one side of the $5^{th}$ slot, because this determines the coloring of the entire arrangement. For instance, if we arrange $6-9$ as $$[R][B][R][B]$$ the overall configuration is $$[B][R][B][R][R][R][B][R][B].$$ So, there are $$\frac{4!}{(2!)^2}=6$$ ways to arrange the colors. Then there are $5!$ ways to permute the distinct red toys, and $4!$ ways to permute the distinct blue toys. Using the product rule we have $$6(5!)(4!)$$ permutations, as desired.
I cannot explain your thinking, because $4!$ simply doesn't count the question. Further, adding one in a scenario like this isn't something that is generally ever done.
Although not explicitly stated, the problem seems to imply that the toys are themselves distinguishable and that the symmetry we are hoping for is reflective symmetry with respect to colors about the middle.
The book's (and correct) answer can be explained via multiplication principle:
• Begin by noticing as you had that the middle spot must be red. Continue by noticing the first four spots must have exactly two of them being red and exactly two of them being blue. Once we have picked the arrangement of red and blue in the first four spots, the final four spots must mirror that selection. There are $\binom{4}{2}=6$ ways to reserve which of the slots are for red toys and which are for blue toys respecting the symmetry requirement.
• From left to right, among the spaces reserved for red toys, pick which red toy is used. $5$ choices for the first appearing slot reserved for red. $4$ choices for the second appearing slot reserved for red... on up to only $1$ choice for the final appearing slot reserved for red, for a total of $5\cdot 4\cdot 3\cdot 2\cdot 1 = 5!$ ways to place the red toys into their reserved slots.
• From left to right, among the spaces reserved for blue toys, pick which blue toy is used. $4$ choices for the first appearing slot reserved for blue, $3$ choices for the second appearing slot reserved for blue, etc... for a total of $4\cdot 3\cdot 2\cdot 1 = 4!$ ways to place the blue toys into their reserved slots.
Applying multiplication principle, there are $\binom{4}{2}\cdot 5!\cdot 4!$ ways to arrange the toys respecting the conditions. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5969885587692261, "perplexity": 142.16174251507252}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987769323.92/warc/CC-MAIN-20191021093533-20191021121033-00005.warc.gz"} |
https://www.ijert.org/transformer-less-bidirectional-grid-connected-single-power-conversion-converter | # Transformer less Bidirectional Grid-Connected Single Power Conversion Converter
Text Only Version
#### Transformer less Bidirectional Grid-Connected Single Power Conversion Converter
Saima S
PG Scholar, Dept. of EEE, Govt. Engineering College, Bartonhill, Thiruvananthapuram, India,
Prof. Simi Raj
Assistant Professor, Dept. of EEE, Govt. Engineering College, Bartonhill, Thiruvananthapuram, India,
Abstract- A transformer less bidirectional grid connected con- verter is introduced. This bidirectional converter has a bi- directional dc-dc converter and an unfolding bridge, with a single stage power conversion. Advantages of this converter include single stage power conversion and usage of low battery voltage. Bidirectional power conversion is done by the bidirectional dc-dc converter due to its adaptive controlling functions. The grid volt- age is obtained from the unfolding bridge as it converts the recti- fied sine wave into the grid voltage. The grid current is controlled with a feed forward nominal voltage compensator. Therefore the power conversion efficiency increases. By using this non-isolated topology the voltage gain in buck and boost mode can be in- creased.
Keywords:- Energy storage system (ESS), Non-isolated topology, high efficiency
1 INTRODUCTION
Bidirectional dc-dc converters are important now a days due to the increasing need of bidirectional energy transfer. Apart from the traditional applications the new applications of bidi- rectional converter include energy storage in interruptible power supplies and renewable energy system. The renewable energy sources like wind, photo-voltaic etc are fluctuating type hence it cannot be use as a single source of power. Ener- gy storage device are commonly used to avoid these fluctua- tions and it provides a continuous power flow. Batteries are the most economical and commonly used energy storage de- vices in medium power. For the controlled power flow be- tween batteries and rest of the system a bidirectional converter is used.
In a conventional two-stage bidirectional converter, power is processing in both stages with a high-frequency switching. In a two stage bidirectional converter it has a dc-dc converter for the conversion of the battery voltage to dc link voltage and a dc-ac converter for the dc link voltage to grid voltage. Hence in two stage converters two controllers are required for each stage. Thus the overall efficiency decreases because it is the product of efficiency at each stage. Also the circuit has high switching and conduction losses, due to gate drive circuits. Thus conventional two-stage bidirectional converters are not cost effective and it has very complex circuit and thus it is less efficient [4].
In the single-stage bidirectional converter, there is only a sin- gle power-conversion stage with a single high frequency switching for the dc-ac power conversion, resulting in higher efficiency, and cost effective than conventional two-stage converters. Thus, single-stage bidirectional power converters
have enhanced system reliability, improved system efficiency, and a less complex circuit than a two-stage bidirectional con- verter [1].
This paper presents a modified non isolated single stage power converter with the same control algorithm. The isolated dc-dc converter is replaced with a non-isolated topol- ogy. By avoiding the high frequency transformer in the dc-dc converter the high frequency switching can be avoided which means the control circuit is less complicated and the overall efficiency and gain of the circuit is improved. The feed for- ward control system provides seamless mode transition in charging and discharging modes. Thus size and weight can be reduced. From the above, it can be inferred that this topology can be developed in a cost effective manner.
2 PROPOSED SYSTEM
Fig.2. Block diagram of non-isolated system
The block diagram consists of battery source, non isolated dc- dc converter, and an inverter, both are using single power control. The input dc voltage is given to the bidirectional con- verter by using a battery, where the voltage is stepped up or down to the required voltage level. From the converter circuit, voltage is given to the full bridge inverter. Output ac voltage from the inverter is connected to grid via a filter circuit. A transformer less bidirectional Single-stage dcac converter is introduced. The proposed inverter has seven switches and is capable of working in both buck and boost modes of opera- tion.
3 OPERATION OF THE PROPOSED SYSTEM Fig.3. below represents the proposed system. Here C3 is the capacitor which links the dc circuit. At the input voltage is provided by battery which is connected to non-isolated dc-dc converter, switch s1 to s4 constitutes the unfolding bridge.
In the proposed system a transformer-less topology is used
.The coupled inductor is used which has the primary induct- ance LP and secondary inductance Ls is tightly coupled on the
same ferrite core, which increases the voltage diversity on both buck and boost modes. D1 corresponds the duty ratio of S11 andS12, where D3 represents the duty ratio of switch S13.
Fig.3. Proposed converter
Both D1 and D3 are related to each other by D1(= 1D3). The coupled inductor can be assigned as an ideal transformer with the magnetizing inductor Lm and turns ratio N (= N2/N1), where N1 is the primary number of turns and N2 is the sec- ondary number of turns of the coupled inductor.
Here input dc voltage is given to the boost circuit where it is stepped up to a required voltage level. From the boost circuit the stepped up dc voltage is given to the full bridge inverter and dc to ac conversion take place. This ac voltage is given to the load via the filter. In boost mode, the non isolated convert- er boosts up the low input voltage to high dc-link voltage and the switch S2 remains OFF during this mode. The proposed system has four modes of operation. The four operating modes are:
1. MODE 1: During mode1, switch S11was ON, whereas switch S13 was OFF. Low-battery bank voltage is applied to the circuit. Capacitor C2 remains charged before mode1 and iLM increases linearly.
2. MODE 2: Switch S11 turns OFF in mode 2. The capaci- tance across switch S11 is charged by primary current iLP, capacitance across switch S13 and is discharged by the secondary current iLS. This mode completes when the voltage across switch S11 is equal to the capacitor voltage VC1,.
3. MODE 3:. Since switch S11 is OFF, due to leakage in- ductance the primary current iLP start decreasing while the secondary current iLS goes down. Hence, the body diode of switch S13 turns ON. Through diode D1 Capacitor C1 starts charging because the voltage across capacitor C1 is get lower than the voltage across switch S1. Hence the voltage stress across switch S1 is decreased.
4. MODE 4: During the ZVS Switch S13 turns ON. For the transfer of energy to the inverter side of the circuit the two windings of the coupled inductor and C2 capacitor are all now connected in series. iLS goes up until it reaches iLP, then it follows iLP until the end of mode 4. Thus, the energy stored in both windings are dissipates across the
inverter side of the circuit. In this mode D1 and D2 are in off condition.
5. MODE 5: In this mode, switch S13 turns OFF. The para- sitic capacitance of switch S13 is charged by the current iLS
. Capacitor C1 starts discharging across capacitor C2, through diode D2.
Gboost = VH/VL
tr>
Switch S11 S12 S13 MODE1 1 0 0 MODE2 0 0 0 MODE3 0 0 0 MODE4 0 0 1 MODE5 0 0 0 MODE6 1 0 0
Table.1. Switching states of the proposed system in boost mode
F MODE 6: During Mode6, switch S11 is turns ON due to the ZVS. Hence S11 is not accepting any current from the clamped circuit, the switching losses becomes decrease due to ZVC, and gets an improved efficiency. The next switching cycle starts when VC1 = VC2, and repeats the cycle.
3 CONTROL SECTION
In this converter the grid current io is controlled in the power processing stage. The primary switch duty D can be re- expressed as the sum of two duty terms as follows: D = (Dp
+D). Dp is the steady-state duty and D is the control duty. The sign of the reference current Ig determines the direction of the power flow for the selected mode. The control block dia- gram of the proposed transformerless bidirectional converter is shown in Fig. 4. Dp is shared in both charge and discharge modes by using a fed forward voltage compensator so that an easy control environment is obtained by presetting an operat- ing point. Seamless mode transition can be obtained due to these features. The power flow direction and power value are calculated only by the reference grid current Ig. In a steady- state condition D is not sufficient to achieve precise tracking because it results in periodic errors.
Fig.4. Control system block diagram
So that, a repetitive control duty Drc should provide better control input responses for the grid current and the zero steady state error tracking. Therefore the control system is a developed one and is very suitable for reference current tracking and seamless mode transition.
4 SIMULATION RESULTS
The proposed system is simulated in MATLAB/SIMULINK. The simulation model is shown in Fig.5.a and 5.b.Figure 5a shows the simulink model view from battery side and 5.b shows the simulink model view from grid side.
Table 2 .proposed system parameters
Parameters Values C 10F C1 4.4F C2 4.4Nf L1 80µH Lm 24µH N 2.5 CF 800 nF LF 400 µH
Fig5.a, Simulink model of the proposed system at battery side
Fig.5.b. Simulink model of the proposed system at grid side
Here 48V dc is provided at the input side. This dc voltage is then given to the boost circuit. From the boost circuit stepped up voltage is given to the full bridge inverter. When simulated output ac voltage from the full bridge inverter is 230 Vrms is obtained. Fig.8.and Fig.9 shows the input and output wave- form of the proposed system.
Fig.9. Output ac voltage
There is a voltage perturbation is applied on the grid at 1 sec- ond and the perturbation is lasts for 1 second. After 1 s the system regains its original state.
Another advantage of proposed system is improved gain. On calculating the gain the existing system has voltage gain 10 and the proposed system has an improved voltage gain which is equal to 12.
Fig.8. Output ac voltage and current waveform of the proposed system with grid voltage perturbation
Table;3 comparison of existing and proposed system
Param- eters Existing system Proposed System Input voltage 48V 24V Output voltage 230Vrms 230Vrms Voltage gain 8 10 Size and weight Bulky Small
6 CONCLUSION
A single stage transformerless dcac converter is proposed. It can be used for photo voltaic grid connected systems and low input battery voltage applications. In the existing system, transformer used for isolation purpose increases core losses in the system. It also makes the system bulkier and costlier. In- crease in core losses reduces efficiency of the system. To overcome this problem transformer less topology is adopted. This configuration has higher efficiency. Since transformer is avoided it reduces the size and weight of the system, making the system efficient and cost effective. Large voltage diversity is obtained in all modes of operation due to the ZVS opera- tion. This helps the circuit to boost up the low-input voltage to high dc-link voltage, and vice versa. The control algorithm consists of a feed-forward nominal voltage compensator and a repetitive control scheme. The feed-forward nominal voltage compensator provides an easier current control.
REFERENCES
1. Owon Kwon , Jun-Seok Kim, Jung-Min Kwon, Member, IEEE, Bi- directional Grid-Connected Single-Power-Conversion Converter With Low-Input Battery Voltage , IEEE Transactions on industrial electronics, vol. 65, no. 4, April 2018
2. Muhammad Aamir, Saad Mekhilef, Member, IEEE ,High-Gain Ze- ro-Voltage Switching Bidirectional Converter With a Reduced Num- ber of Switches, , IEEE transactions on circuits and systemsii, ex- press briefs, vol. 62, no. 8, August 2015
3. A. K han, H. Cha, F. Ahmed, J. Kim, and J. Cho, A highly reliable and high efficiency quasi single-stage buck-boost inverter, IEEET- rans Power Electron vol. 32, no. 6, pp. 41854198, , , Jun. 2017
4. W.Chen, R. Zane, and L. Corradini Isolated bidirectional grid tied three-phase AC-DC power conversion using series resonant converter modules and a three-phase unfolder ,IEEE Trans.PowerElectron., vol. 32, no. 12, pp. 90019012 Dec. 2017
5. Y.-W. Cho, W.-J. Cha, J.-M. Kwon, and B.-H. Kwon High- efficiency bidirectional DAB inverter using a novel hybrid modula- tion for standalone power generating system with low input voltage,
, IEEE Trans. Power Electron., vol. 31, no. 6, pp. 41384147, Jun. 2016
6. M. Kwon, S. Oh, and S. Choi, High gain soft-switching bidirectional DCDC converter for eco-friendly vehicles, IEEE Trans. Power Electron., vol. 29, no. 4, pp. 16591666, Apr. 2014.
7. B. J. Vermulst, J. L. Duarte, C. G. Wijnands, and E. A. Lomonova, Quad active-bridge single-stage bidirectional three-phase AC-DC converter with isolation: Introduction and optimized modulation, IEEE Trans. Power Electron., vol. 32, no. 4, pp. 25462557, Apr. 2017.
8. Y.-P. Hsieh, J.-F. Chen, L.-S. Yang, C.-Y. Wu, and W.-S. Liu, High conversion-ratio bidirectional DCDC converter with coupled induc- tor, IEEE Trans. Ind. Electron., vol. 61, no. 1, pp. 210222, Jan. 2014.
9. H. Wu, K. Sun, L. Chen, L. Zhu, and Y. Xing, High step-up/step- down soft-switching bidirectional DCDC converter with coupled- inductor and voltage matching control for energy storage systems, IEEE Trans. Ind. Electron., vol. 63, no. 5, pp. 28922903, May 2016.
10. N. M. L. Tan, T. Abe, and H. Akagi, Design and performance of a bidirectional isolated DCDC converter for a battery energy storage system, IEEE Trans. Power Electron., vol. 27, no. 3, pp. 12371248, Mar. 2012 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8258562088012695, "perplexity": 4838.209042347834}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178369512.68/warc/CC-MAIN-20210304174506-20210304204506-00443.warc.gz"} |
https://math.libretexts.org/Learning_Objects/Interactive_Calculus_Activities | $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$
Interactive Calculus Activities
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$
They are meant to be embedded in the customized calculus textbook such as in the calculus links below:
Interactive Calculus Activities is shared under a CC BY license and was authored, remixed, and/or curated by Larry Green. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9945323467254639, "perplexity": 348.6653017343923}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662604495.84/warc/CC-MAIN-20220526065603-20220526095603-00030.warc.gz"} |
https://exploringnumbertheory.wordpress.com/2013/06/17/euclids-proof-of-the-infinitude-of-primes/ | # Euclid’s Proof of the Infinitude of Primes
The oldest known proof that there are infinite number of primes is the one that is due to Euclid (around 300 BC). It is probably the most accessible. So I start the blog by stating this proof.
________________________________________________________
Theorem. There are infinitely many prime numbers.
The strategy is to show that given a finite list of prime numbers $\left\{p_1, p_2, \cdots, p_n \right\}$, we can always find another prime number not on the list.
Let $n=p_1 \times p_2 \times \cdots \times p_n$. Let $p$ be a prime divisor of $n+1$. If $p$ is on the list $\left\{p_1, p_2, \cdots, p_n \right\}$, then $p$ would divide both $n+1$ and $n$. This means that $p$ would divide 1 (the difference of $n$ and $n+1$). This is impossible. So $p$ must a prime number not on the original list. Hence there must be infinitely many prime numbers.
________________________________________________________
$\copyright \ 2013 \text{ by Dan Ma}$
$\text{ }$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 15, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9415378570556641, "perplexity": 93.39134411542908}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424721.74/warc/CC-MAIN-20170724042246-20170724062246-00414.warc.gz"} |
https://feature.engineering/regularization/ | It's straightforward to see that L1 and L2 regularization both prefer small numbers, but it is harder to see the intuition in how they get there.
Specifically, the L1 norm and the L2 norm differ in how they achieve their objective of small weights, so understanding this can be useful for deciding which to use.. On the one hand, L1 wants errors to be all or nothing, which leads to sparse weights since all the errors are concentrated in one place. As a simple example, let's say there are six weights, then L1 = |0|+|0|+|0|+|-3|+|0|+|1.8| = 4.8, or alternatively, L1 = |0.7|+|1.1|+|-0.6|+|0.9|+|0.7|+|-0.8| = 4.8. For L1 Norm, they both look about the same, and generally will lean towards the former.
% Testing LaTeX
\sqrt{x^3}
$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$
On the other hand, L2 wants all errors to be tiny and heavily penalizes anyone who doesn't obey. Looking back the at the our example, L2 = sqrt(02+02+02+32+02+1.82) = 3.5, or alternatively, L1 = sqrt(0.72+1.12+(-0.6)2+0.92+0.7+(-0.8)2) = 2. In this case, the L2 norm would clearly prefer the dispersed smaller values in the latter distribution.
In summary, L1 = sparse weights, L2 = small distributed weights. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7466663718223572, "perplexity": 818.8081074946241}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195529664.96/warc/CC-MAIN-20190723193455-20190723215455-00019.warc.gz"} |
http://multicardia.com/en/articles/9046.html | # Evaluation of the Cardiac Function by MRI in Children
AUTHORS
Zahra Alizadeh Sani 1 , *
1 Iran
How to Cite: Alizadeh Sani Z. Evaluation of the Cardiac Function by MRI in Children, Multidiscip Cardio Annal. 2015 ; 6(1):e9046.
ARTICLE INFORMATION
Multidisciplinary Cardiovascular Annals: 6 (1); e9046
Published Online: February 18, 2015
Article Type: Abstract
Accepted: February 05, 2015
# Crossmark
#### CHEKING
##### Abstract
Cardiac MRI is generally considered the reference standard for the assessment of ventricular dimensions, function, and mass in terms of accuracy and reproducibility, and this is reflected by class I–II recommendations for the clinical use of cardiac MRI by recent consensus panels. However, a general problem in the interpretation of such data is the fact that cardiac growth is known to be allometric, that is, the relation between the size of the heart and the body changes from infancy to adulthood .Moreover, such allometric growth is likely to be different between the sexes.
This renders any age group definition somewhat arbitrary because sex differences in the speed of maturation and cardiac growth are not accounted for, thus limiting the scientific and clinical value of age group– based reference data. The relation between the size of the heart and the body is known to be allometric, which means that this relation changes from infancy to adulthood. This makes the generation of normative data challenging. However, the ability to accurately measure volumetric and mass parameters of right and left ventricular function, adequately scaled to body size, is of critical importance both for clinical care and for cardiovascular health research
## Keywords
Evaluation
© 0, Multidisciplinary Cardiovascular Annals. This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/) which permits copy and redistribute the material just in noncommercial usages, provided the original work is properly cited.
### Fulltext
Full Text Available is PDF
### References
• 1.
Full Text Available is PDF | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8534557819366455, "perplexity": 4762.130479295255}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573827.2/warc/CC-MAIN-20190920030357-20190920052357-00376.warc.gz"} |
https://homework.cpm.org/category/CCI_CT/textbook/pc3/chapter/3/lesson/3.2.2/problem/3-106 | ### Home > PC3 > Chapter 3 > Lesson 3.2.2 > Problem3-106
3-106.
Lew walks every day at lunch when he is working. The amazing thing about Lew is that he walks at a constant rate (velocity) the entire time he walks. He walks for $1$ hour every day and travels at a rate of $4$ miles per hour.
1. Sketch a velocity graph of Lew’s lunchtime walk, being sure to label both axes. Shade the area between the curve and the $x$-axis over the appropriate domain.
2. What are the domain and the range of this function?
3. The region that is shaded on your graph should resemble a rectangle. What are the units when calculating the area of the shaded region? Use unit analysis to justify your answer.
4. What is the area of the shaded region? Include the proper units. | {"extraction_info": {"found_math": true, "script_math_tex": 3, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8555541634559631, "perplexity": 634.3871145891021}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704835901.90/warc/CC-MAIN-20210128040619-20210128070619-00394.warc.gz"} |
http://math.stackexchange.com/questions/72201/probability-game-find-probability-she-wins-the-game-on-nth-point-played-for-n-4 | # Probability Game: Find probability she wins the game on nth point played for n=4,5,6
Two people play a game. They play a series of points, each producing a winner and a loser, until one player has won at least 4 points and has won at least 2 more points than the other. Anne wins each point with probability p. What is the probability that she wins the game on the kth point played for k=4,5,6,...
Ok so I started with k=4 P(win on 4th point) can happen 3 ways 4-0,4-1,4-2 =p^4(1 + (4 choose 1)q +(5 choose 2)q^2), which is a geometric series for q. I'm not sure what to do with the changing binomial coefficients though. Similarly, P(win on 5th point can happen 4 ways) 5-0, 5-1, 5-2, 5-3 =p^5(1 + (5 choose 1)q + (6 choose 2) q^2 +(7 choose 3)q^3)
So it seems like we will have two geometric series one of powers of p, each containing one of powers of q. I'm not sure the exact pattern and how to formalize this. Thank you!
-
You can right-click on any formula (e.g. in my answer) and select "Show Source" to see how you can format questions using $\TeX$ to make them more readable. – joriki Oct 13 '11 at 5:13
If the game ended with a score 5-3, it ended on the 8th point played, did it not? – Jyrki Lahtonen Oct 13 '11 at 12:06
To add to Jyrki Lahtonen's comment, "P(win on 5th point) can happen 4 ways) 5-0, 5-1, 5-2, 5-3" (meaning Anne wins when she wins her 5th point) is incorrect. Anne's $5$-th (winning) point is necessarily the last point of the game. Thus the game cannot end with a score of $5$-$x$, $x = 0, 1, 2$ (game would have ended as soon as Anne had won $4$ points earlier in the game). In short, the event "Anne wins when she has scored $5$ points" occurs exactly when the game ends with a score of $5$-$3$, and this has probability $\binom{7}{3}p^5q^3$ as you correctly computed. – Dilip Sarwate Oct 13 '11 at 12:35
I am wondering if the interpretation used by caligirl11 and @joriki is the one that was intended by whomsoever devised the problem.
What is the probability that she wins the game on the kth point played for k=4,5,6,...
I suggest that the $k$-th point played is not the same as the $k$-th point won by Anne.
Ok so I started with k=4 P(win on 4th point) can happen 3 ways 4-0,4-1,4-2 =p^4(1 + (4 choose 1)q +(5 choose 2)q^2)
I would say here that Anne wins the game on the $4$th point played with probability $p^4$; the probability that she wins on the $5$th point played is $\binom{4}{1}p^4q$; and the probability that she wins on the $6$th point played is $\binom{5}{2}p^4q^2$. The corresponding win probabilities for Betty are obtained by interchanging $p$ and $q$ in the previous sentence.
If $6$ points have been played and the game is not over, the score must be $3$-$3$ (deuce) and this event has probability $\binom{6}{3}p^3q^3 = 20p^3q^3$. The game can now end only when an even number of additional points have been played, and the probability of Anne winning on the $k$-th point played (where $k = 6+2n, n>0$) is $\binom{6}{3}p^3q^3\cdot p^2(2pq)^{n-1}$. To get the probability that Anne wins the game, sum the probabilities that she wins in $4$, $5$, $6$, $8$, $10, \ldots$ points; a geometric series is involved.
If $f(p)$ denotes the probability that Anne wins the game, then $f(0.5) = 0.5$ but $\left . \frac{d}{dp}f(p)\right\vert_{p = 0.5} = 2.5$ so that $f(0.5 + \epsilon) = 0.5 + 2.5\epsilon + \cdots$, that is, a small difference $p-q = 2\epsilon$ in the point win probabilities for Anne and Betty is amplified by the rules of tennis into a greater difference in the game win probabilities. See "The Drunken Tennis Player" in Ian Stewart's Game, Set, and Math, Penguin Books, 1981.
-
This would have been my interpretation, too. – Jyrki Lahtonen Oct 13 '11 at 12:09
That is also my interpretation. – Michael Lugo Oct 13 '11 at 15:58
I think you've already got the right result for $k=4$. For higher $k$, note that the game has to go through a tie in order to continue. For instance, for someone to win 5:3, the score must have been 3:3 (since it must have been 4:3, and 4:2 would have ended the game). So you can calculate the probability for 3:3, which is $\binom63p^3q^3$, and from then on the probability is $p^2$ for Anne to win and $2pq$ (two ways for one win and one lose) to reach the next tie, so for $k\ge5$,
$$p_k=\binom63p^3q^3p^2\left(2pq\right)^{k-5}=\frac5{8q^2}(2pq)^k\;.$$
-
I don't think there is -- I think you'll just have to add the two -- you can simplify the result a bit, though (under "Alternate forms"). – joriki Oct 13 '11 at 5:45
Here's something sort of nice: If you express this symmetrically by setting $p=(1+x)/2$, so $x=0$ at equal probability, you get this, which can be written as $$\frac{(x+1)^4-(x^2-1)^4}{8x(x^2+1)}\;.$$ Don't know whether there's any deeper meaning to that... – joriki Oct 13 '11 at 5:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8380503058433533, "perplexity": 633.2299939602427}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207929256.27/warc/CC-MAIN-20150521113209-00206-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://www.physicsforums.com/showpost.php?p=2830213&postcount=1 | View Single Post
P: 369 Hi there, I am reading an introduction on solving ODE, there the exact equation is mentioned. Suppose a ODE is in the following form $$M(x, y) + N(x, y)\frac{dy}{dx} = 0$$ assume there is a function $$F(x, y)$$ such that $$\frac{\partial F(x, y)}{\partial x} = M(x, y) + N(x, y)\frac{dy}{dx}$$ Hence, $$\frac{\partial F(x, y)}{\partial x} = 0$$ The text says that the above equation imply that $$F(x, y) = \text{Const}$$ But here are my doubts 1) Let's assume the above equation is true, so does it mean $$F(x, y)$$ has no way to be a function of x if the original equation is exact? 2) What about if $$F(x,y) = g(y)$$, in this case, we don't know the exact form of y, but we know that y is depending on x, so can we say $$F(x,y)=g(y)$$ is implicitly depending on x? If it is true, how can we conclude that $$F(x, y) = \text{Const}$$ instead of some functions of y? Well, you might find what I am asking is vague. What I actually means is if $$F(x,y)=g(y)$$, so can we safely say that $$\frac{\partial F(x, y)}{\partial x} = \frac{\partial g(y)}{\partial x} = 0$$ It is quite confusing to use the term 'implicitly'! Because we do know that y=y(x), so how come we put $$\frac{\partial g(y)}{\partial x} = 0$$ instead of $$\frac{\partial g(y)}{\partial y}\frac{dy}{dx} = 0$$ ??? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9855620265007019, "perplexity": 116.68158982952214}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223206120.9/warc/CC-MAIN-20140423032006-00220-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://calculator.academy/viscosity-to-density-calculator/ | Enter the dynamic viscosity (Pa-s) and the kinematic viscosity (m^2/s) into the Density From Viscosity Calculator. The calculator will evaluate and display the Density From Viscosity.
## Density From Viscosity Formula
The following formula is used to calculate the Density From Viscosity.
p = u / k
• Where p is the Density From Viscosity (kg/m^3)
• u is the dynamic viscosity (Pa-s)
• k is the kinematic viscosity (m^2/s)
To calculate the density from viscosity, divide the dynamic viscosity by the kinematic viscosity.
## How to Calculate Density From Viscosity?
The following example problems outline how to calculate Density From Viscosity.
Example Problem #1:
1. First, determine the dynamic viscosity (Pa-s).
1. The dynamic viscosity (Pa-s) is given as: 500.
2. Next, determine the kinematic viscosity (m^2/s).
1. The kinematic viscosity (m^2/s) is provided as: 250.
3. Finally, calculate the Density From Viscosity using the equation above:
p = u / k
The values given above are inserted into the equation below:
p = 500 / 250 = 2 (kg/m^3)
Example Problem #2:
For this problem, the variables needed are provided below:
dynamic viscosity (Pa-s) = 250
kinematic viscosity (m^2/s) = 965
This example problem is a test of your knowledge on the subject. Use the calculator above to check your answer. p = u / k = ? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9541590213775635, "perplexity": 3924.8196951641057}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499790.41/warc/CC-MAIN-20230130003215-20230130033215-00235.warc.gz"} |
http://export.arxiv.org/abs/1703.06477 | astro-ph.EP
(what is this?)
# Title: A deeper view of the CoRoT-9 planetary system. A small non-zero eccentricity for CoRoT-9b likely generated by planet-planet scattering
Abstract: CoRoT-9b is one of the rare long-period (P=95.3 days) transiting giant planets with a measured mass known to date. We present a new analysis of the CoRoT-9 system based on five years of radial-velocity (RV) monitoring with HARPS and three new space-based transits observed with CoRoT and Spitzer. Combining our new data with already published measurements we redetermine the CoRoT-9 system parameters and find good agreement with the published values. We uncover a higher significance for the small but non-zero eccentricity of CoRoT-9b ($e=0.133^{+0.042}_{-0.037}$) and find no evidence for additional planets in the system. We use simulations of planet-planet scattering to show that the eccentricity of CoRoT-9b may have been generated by an instability in which a $\sim 50~M_\oplus$ planet was ejected from the system. This scattering would not have produced a spin-orbit misalignment, so we predict that CoRoT-9b orbit should lie within a few degrees of the initial plane of the protoplanetary disk. As a consequence, any significant stellar obliquity would indicate that the disk was primordially tilted.
Comments: 11 pages, 8 figures, accepted for publication in Astronomy and Astrophysics Subjects: Earth and Planetary Astrophysics (astro-ph.EP) Cite as: arXiv:1703.06477 [astro-ph.EP] (or arXiv:1703.06477v2 [astro-ph.EP] for this version)
## Submission history
From: Aldo Stefano Bonomo Mr. [view email]
[v1] Sun, 19 Mar 2017 17:51:44 GMT (222kb)
[v2] Fri, 7 Apr 2017 14:00:54 GMT (256kb) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6856324076652527, "perplexity": 4071.504197513914}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607647.16/warc/CC-MAIN-20170523143045-20170523163045-00152.warc.gz"} |
https://stats.stackexchange.com/questions/391866/how-are-bayes-factors-actually-bayesian | # How are Bayes factors actually Bayesian?
I have been doing some linear model analyses involving Bayes factors lately and I have two probably very basic questions:
1) As far as I understand, a Bayes factor is simply a likelihood ratio, i.e.
p(data|M1)/p(data|M2).
But that's not really Bayesian inference, is it? Since the whole point of Bayesian inference is to convert p(data|model) to p(model|data)?
Sure, people argue that given equal prior probabilities of both models, the above equation is equivalent to p(M1|data)/p(M2|data), but still it seems to me like the Bayes factor approach is missing the whole point of Bayesian inference. Especially since the really cool thing about Bayesian modeling is that I can have both prior and posterior distributions for each model coefficient, I feel like Bayes factor model comparison is falling short of the power of Bayesian models?
2) How is it possible, in the first place, that Bayes factors, being based on (unpenalized) likelihood, can favor the null model? Shouldn't the likelihood always increase with more complex models, i.e. with the non-null model?
Hope some of you can shed a little light on my mind.
While I have written rather extensively on the limitations of the Bayes factor as a mean to conduct model comparison, the first point is that indeed it is not the Bayesian answer to the testing question Which of model $$M_1$$ or model $$M_2$$ is the true model? when evaluated with the Neyman-Pearson loss function. The proper Bayesian answer is the model with the largest posterior probability. When using other loss functions, the proper Bayesian answer is the posterior probability itself. Historically, the Bayes factor has been defended by Jeffreys (circa 1939) as providing a more objective answer than the posterior probability, as it evacuates the impact of the prior weights of the models $$M_1$$ and $$M_2$$, which can be deemed as failing to take advantage of the Bayesian formalism, but truly reflects the immense uncertainty in setting such weights.
On the second point, it is well-documented that Bayes factors are providing a natural penalisation for complexity by integrating out over a larger space, as opposed to likelihood ratios that exploit the best fits under both models. The Bayes factor is often seen as a quasi-automatic Occam's razor for this reason, which is also why the Bayesian information criterion (BIC) $$\mathrm{BIC} = {\log(n)k - 2\log(L({\hat \theta}))}$$ is used by non-Bayesians as well.
The issue is that while a Bayes factor, assuming equal prior probability of the competing hypotheses, is a likelihood ratio, it's not the likelihood ratio you think it is. Here, the likelihood of $$M_1$$ is
$$p(data|M_1) = \int p(data|M_1, \theta_1) p(\theta_1|M_1) d\theta_1.$$
In other words, you were conflating $$p(data|M_1)$$ with $$p(data|M_1, \theta_1)$$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9088301658630371, "perplexity": 410.4444403934539}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525659.27/warc/CC-MAIN-20190718145614-20190718171614-00300.warc.gz"} |
http://wikimechanics.org/screw | The Rotini Model of an Atom
Principia Philosophiae by Rene Descartes, page 271 (detail). Published at Amsterdam 1644 and dedicated to Eliška Přemyslovna. This image comes from the European Cultural Heritage Online project, and the Max Planck Institute for the History of Science. Thank you.
Consider an atom $\mathbf{A}$ described by a repetitive chain of space-time events with time coordinates $t$. Our first spatial conception of such an atom was as a compound quark in But that representation was coarse and grainy. Quark space is a poor approximation to ordinary space. So our next spatial depiction of an atom is set in a Cartesian coordinate system where $\mathbf{A}$ is viewed as a rotating atomic clock with a phase-angle $\theta$ given by
$\theta \left(t\right) = \theta_{0} +\omega t$
such that $\mathbf{A}$ is whirling about its polar axis with an angular frequency of $\omega$. The rotation supposedly blurs variations in the electric and magnetic radii leaving an effective orbital radius $R$ that is then used to represent the atom as a rotating This rotating cylinder model smooths out some rough edges, but it is still incomplete because the electromagnetic part of the quark metric is larger than the other non-polar components. So one radial direction is predominant and the atom is shaped more like a piece of rotini pasta than a solid cylinder. This corkscrew spiral is approximated by a geometric curve called a and mathematically described by radii of
$\rho_{x} = R \cos{\! 2 \theta}$and$\rho_{y} = R \sin{\! 2 \theta }$and\begin{align} \rho_{z} = \frac{ \lambda \theta}{2 \pi} \end{align}
where $\lambda$ is the wavelength of $\mathbf{A}$. When moving, the rotini model looks a lot like a machine called the . Humans have been thinking about screw conveyor mechanisms like this for thousands of years. They were reportedly used to irrigate the as early as 600 BC.
page revision: 154, last edited: 24 Mar 2016 14:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8081483840942383, "perplexity": 956.2737201221136}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592150.47/warc/CC-MAIN-20180721012433-20180721032433-00489.warc.gz"} |
http://en.wikipedia.org/wiki/Rayleigh_range | # Rayleigh length
(Redirected from Rayleigh range)
Gaussian beam width $w(z)$ as a function of the axial distance $z$. $w_0$: beam waist; $b$: confocal parameter; $z_\mathrm{R}$: Rayleigh length; $\Theta$: total angular spread
In optics and especially laser science, the Rayleigh length or Rayleigh range is the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled.[1] A related parameter is the confocal parameter, b, which is twice the Rayleigh length.[2] The Rayleigh length is particularly important when beams are modeled as Gaussian beams.
## Explanation
For more details on this topic, see Gaussian beam.
For a Gaussian beam propagating in free space along the $\hat{z}$ axis, the Rayleigh length is given by [2]
$z_\mathrm{R} = \frac{\pi w_0^2}{\lambda} ,$
where $\lambda$ is the wavelength and $w_0$ is the beam waist, the radial size of the beam at its narrowest point. This equation and those that follow assume that the waist is not extraordinarily small; $w_0 \ge 2\lambda/\pi$.[3]
The radius of the beam at a distance $z$ from the waist is [4]
$w(z) = w_0 \, \sqrt{ 1+ {\left( \frac{z}{z_\mathrm{R}} \right)}^2 } .$
The minimum value of $w(z)$ occurs at $w(0) = w_0$, by definition. At distance $z_\mathrm{R}$ from the beam waist, the beam radius is increased by a factor $\sqrt{2}$ and the cross sectional area by 2.
## Related quantities
The total angular spread of a Gaussian beam in radians is related to the Rayleigh length by[1]
$\Theta_{\mathrm{div}} \simeq 2\frac{w_0}{z_R}.$
The diameter of the beam at its waist (focus spot size) is given by
$D = 2\,w_0 \simeq \frac{4\lambda}{\pi\, \Theta_{\mathrm{div}}}$.
These equations are valid within the limits of the paraxial approximation. For beams with much larger divergence the Gaussian beam model is no longer accurate and a physical optics analysis is required. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 19, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9912038445472717, "perplexity": 585.1034344926637}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657139395.59/warc/CC-MAIN-20140914011219-00338-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://forum.allaboutcircuits.com/threads/harmonics.5982/#post-33849 | # Harmonics
Joined Feb 10, 2007
64
they had given that we can generate any waveform adding two sine waves.
they have constructed a sawtooth signal using the odd & even with fundamental harmonics.
my question is have they constructed it by vector addition of the harmonics or any other method.(they have taken fundamental to 9th harmonic )
can you please explain the method they must have used for constructing the saw tooth signal.
#### bloguetronica
Joined Apr 27, 2007
1,533
they had given that we can generate any waveform adding two sine waves.
they have constructed a sawtooth signal using the odd & even with fundamental harmonics.
my question is have they constructed it by vector addition of the harmonics or any other method.(they have taken fundamental to 9th harmonic )
can you please explain the method they must have used for constructing the saw tooth signal.
The theory is correct. You can build any waveform by superimposing two or more sinusoidal waves with the same harmonics. You can see Fourier series to give an insight: http://en.wikipedia.org/wiki/Fourier_series
Actually, a good analogy would be using Taylor series to aproach a polynomial fuction within a range.
Joined Feb 10, 2007
64
thanx sir for your instant response.
sir they have added all the harmonics in what sense i mean to say
they have added the waveforms at particular instantsand then constructed the saw tooth signal or is there any other way to understand the addition of the harmonics
#### Papabravo
Joined Feb 24, 2006
19,295
They have summed up (algebraically) an infinite number of periodic functions, each of which has a defined value from minus infinity to plus infinity. In such a Fourier summation some of the coefficients are allowed to be zero. Often, either all of the coefficients for even or odd harmaonics will vanish. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9013638496398926, "perplexity": 841.5221526763405}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710890.97/warc/CC-MAIN-20221202014312-20221202044312-00649.warc.gz"} |
https://physics.stackexchange.com/questions/71649/evidence-that-the-solar-system-is-expanding-like-the-universe?noredirect=1 | # Evidence that the Solar System is expanding like the Universe? [duplicate]
I've just come across Krasinsky and Brumberg's paper that claims, from an analysis of radiometric measurements, that the astronomical unit (earth-sun distance) is increasing at the rate:
$$\frac{d}{dt}AU = 15 \pm 4 \ m/yr.$$
If one assumes that the Solar system is expanding with the Universe then the Earth-Sun distance is given by:
$$R = R_0 \ a(t),$$
where $R_0$ is the present Earth-Sun distance and $a(t)$ is the scale factor.
From the definition of the Hubble parameter we have:
$$\frac{da/dt}{a} = H.$$
Therefore
$$dR = R_0 da$$
$$dR = R_0 \ a \ H \ dt$$
At the present time $H=H_0$ and $a=1$ so that:
$$dR/dt = R_0 H_0.$$
If I use $R_0=1.49\times10^{11}m$, $H_0=1/13.77\times10^9 yr^{-1}$ and $dt=1yr$ I find:
$$dR/dt = 1.49\times10^{11} \cdot (1/13.77\times10^9)$$
$$dR/dt = 10.8 \ m/yr.$$
Thus the rate of increase of the AU unit might well be explained if the Solar system is expanding like the Universe.
PS Krasinsky seems to dismiss the possibility that his results are explained by cosmic expansion because he somehow derives the rate $dR/dt = 1 \ km/yr$ under such an hypothesis. I can't see how he got that result.
• possible duplicate of Can the Hubble constant be measured locally?
– user4552
Jul 20, 2013 at 0:10
• Krasinsky and Blumberg don't appear to be very competent relativists, and they don't appear to have made any effort to search the literature on this topic. For a reference to a competent calculation by Cooperstock, and a summary of the calculation, see this question: physics.stackexchange.com/q/70047 The cosmological effect is about 20 orders of magnitude too small to explain the observed secular trend (if it isn't a systematic error). Any actual secular trend comes from Newtonian effects, such as interaction with other planets.
– user4552
Jul 20, 2013 at 0:17
• Even if the paper is crap and mistakes or misunderstandings the OP presents if any, this is no reason to close the question but can be clarified in a good answer. It is a legitimate question. Jul 20, 2013 at 11:20
• I misread Krasinsky et al's paper. They say that the AU is changing at a rate of 15 meters per century NOT per year! I misread cy for calendar year! Jul 22, 2013 at 20:00
• Related: physics.stackexchange.com/q/2110/2451 and links therein. Jan 18, 2016 at 19:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9032956957817078, "perplexity": 688.9454501718966}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103617931.31/warc/CC-MAIN-20220628203615-20220628233615-00339.warc.gz"} |
https://rd.springer.com/chapter/10.1007/978-0-85729-856-0_3 | # Mathematical Model of a Power Unit with Rated Capacity of 370 MW After its Modernization to Cogeneration and Combined-Cycle
• Ryszard Bartnik
• Zbigniew Buryn
Chapter
## Abstract
This chapter introduces a mathematical model of a coal-fired electric power unit with the rated capacity of 370 MW. This model makes it possible to examine the effectiveness of the thermodynamic and economic efficiency of its conversion to cogeneration and to dual-fuel gas-steam combined-cycle in parallel system as a result of repowering by a gas turbine. The cases examined include repowering of a unit in a parallel system with a single-, dual-, and triple-pressure heat recovery steam generator. The model is based on mass and energy balance, energy characteristics of facilities, thermal and calorific equations of the circulation media—steam and water. The presented model is general. It is possible to apply it to power units of various capacities. Following a change in a power unit capacity will only necessitate the adaptation of some of the mass and energy balances.
## Keywords
Balance Equation Power Unit Steam Turbine System Boundary Mass Balance Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
## References
1. 1.
Portacha J (2002) Energy based examination of thermal systems in power plants and heat and power plants. Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa (in Polish)Google Scholar
2. 2.
Szargut J, Ziębik A (2000) Fundamentals of thermal power industry. PWN, Warszawa (in Polish)Google Scholar | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8848604559898376, "perplexity": 3313.8244585823786}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221214702.96/warc/CC-MAIN-20180819051423-20180819071423-00306.warc.gz"} |
https://gitlab.math.univ-paris-diderot.fr/beppe/occurrence-typing/-/commit/3e1f0eb0b7b7e736b5ec6802794c43e506118f05 | Commit 3e1f0eb0 by Giuseppe Castagna
### rewording
parent 668fb500
... ... @@ -97,7 +97,7 @@ provided to us by occurrence typing and deduce for the function in~\eqref{foo3} function is applied to a number. To achieve this, we simply modify the typing rule for functions that we defined in the previous section to accommodate for gradual typing. Let $\sigma$ and $\tau$ range over \emph{gradual types}, that is the types produced by the grammar in Definition~\ref{def:types} to which we add \dyn{} as basic type (see~\citet{castagna2019gradual} for the definition of the subtyping relation on these types). For every gradual type $\tau$, define $\tauUp$ as the (non graudal) type obtained from $\tau$ by replacing all $\tau$, define $\tauUp$ as the (non gradual) type obtained from $\tau$ by replacing all covariant occurrences of \dyn{} by \Any{} and all contravariant ones by \Empty. The type $\tauUp$ can be seen as the \emph{maximal} interpretation of $\tau$, that is, every expression that can safely be cast to $\tau$ is of type $\tauUp$. In ... ...
... ... @@ -414,11 +414,11 @@ the intersection of the static type of $\occ e \varpi$ (deduced by \Rule{PTypeof}) with the type deduced for $\varpi$ by the other $\vdashp$ rules. The rule \Rule{PEps} is the starting point of the analysis: if we are assuming that the test $e\in t$ succeeds, then we can assume that $e$ (i.e., $\occ e\epsilon$) has type $t$ (recall that assuming that the test $e\in t$ fails corresponds to having $\neg t$ at the index of the turnstyle). The rule \Rule{PApprR} implements occurrence typing for The rule \Rule{PAppR} implements occurrence typing for the arguments of applications, since it states that if a function maps arguments of type $t_1$ in results of type $t_2$ and an application of this function yields results (in $t'_2$) that cannot be in $t_2$ (since $t_2\land t_2' \simeq \Empty$), then the argument of this application cannot be of type $t_1$. \Rule{PAppR} performs the (since $t_2\land t_2' \simeq \Empty$), then the argument of this application cannot be of type $t_1$. \Rule{PAppL} performs the occurrence typing analysis for the function part of an application, since it states that if an application has type $t_2$ and the argument of this application has type $t_1$, then the function in this ... ...
... ... @@ -876,7 +876,7 @@ \subsection{New algorithmic type system with type schemes} As explained in TODO, we introduce for the proofs the notion of \emph{types schemes} As explained in TODO, we introduce for the proofs the notion of \emph{type schemes} and we define a new (more powerful) algorithmic type system that uses them. It allows us to have a stronger (but still partial) completeness theorem. ... ... @@ -885,7 +885,7 @@ from the proofs of this section (see section \ref{sec:proofs_algorithmic_without \subsubsection{Type schemes}\label{app:typeschemes} We introduce the new syntactic category of \emph{types schemes} which are the terms~$\ts$ inductively produced by the following grammar. We introduce the new syntactic category of \emph{type schemes} which are the terms~$\ts$ inductively produced by the following grammar. \[ \begin{array}{lrcl} \textbf{Type schemes} & \ts & ::= & t \alt \tsfun {\arrow t t ; \cdots ; \arrow t t} \alt \ts \tstimes \ts \alt \ts \tsor \ts \alt \tsempty ... ...
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9940091371536255, "perplexity": 1261.4666380738681}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301263.50/warc/CC-MAIN-20220119033421-20220119063421-00388.warc.gz"} |
https://www.computer.org/csdl/mags/cs/2012/04/mcs2012040048-abs.html | Issue No. 04 - July/August (2012 vol. 14)
ISSN: 1521-9615
pp: 48-56
Andrew Davison , Centre National de la Recherche Scientifique, France
ABSTRACT
Published scientific research that relies on numerical computations is too often not reproducible. For computational research to become consistently and reliably reproducible, the process must become easier to achieve, as part of day-to-day research. A combination of best practices and automated tools can make it easier to create reproducible research.
INDEX TERMS
Reproducibility of results, Software engineering, Context awareness, Scientific computing, Numerical analysis, Programming, Scientific computing, software/program verification, Reproducibility of results, Software engineering, Context awareness, Scientific computing, Numerical analysis, Programming, Scientific computing, scientific computing, reusable libraries, reusable software, reliability
CITATION
Andrew Davison, "Automated Capture of Experiment Context for Easier Reproducibility in Computational Research", Computing in Science & Engineering, vol. 14, no. , pp. 48-56, July/August 2012, doi:10.1109/MCSE.2012.41 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8194727897644043, "perplexity": 9443.44098137499}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189316.33/warc/CC-MAIN-20170322212949-00577-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/questions/89626/marks-like | # Marks like “«»” [duplicate]
Possible Duplicate:
Guillemets in LaTeX («»)
I need to make some quote marks like this: "« »" in my Latex document.
\begin{document}
Some text with quote marks like "« »"
\end{document}
How can I do?
-
## marked as duplicate by clemens, T. Verron, Werner, Stefan Kottwitz♦Jan 6 '13 at 19:34
The linked question, unlike this one, states that the OP doesn't want to use babel. If you need these quotation marks in order to comply with your language's typographical conventions (for example french), babel will still be the easiest solution. – T. Verron Jan 6 '13 at 18:56
Take a look at csquotes. – You Jan 6 '13 at 19:00
You should use T1 encoding:
\documentclass{article}
\usepackage[T1]{fontenc}
\begin{document}
Some text with quote marks like <<'' and >>''
\end{document}
If you also encode your input file as UTF-8, you can use direct input:
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\begin{document}
Some text with quote marks like «'' and »''
\end{document}
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6867567896842957, "perplexity": 10047.96859548056}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928817.87/warc/CC-MAIN-20150521113208-00034-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://www.studyadda.com/question-bank/11th-cbse-chemistry-alkali-metals_q13/110/15642 | • question_answer Beryllium chloride fumes in air.
Beryllium chloride is a salt of strong acid and weak base. It undergoes hydrolysis in the presence of moisture present in air to form fumes of HCl gas. Therefore, it fumes in moist air. $BeC{{l}_{2}}+2{{H}_{2}}O\xrightarrow{\,}\,Be{{(OH)}_{2}}+2HCl$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6216026544570923, "perplexity": 12778.775135220087}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657134758.80/warc/CC-MAIN-20200712082512-20200712112512-00327.warc.gz"} |
https://www.gamedev.net/forums/topic/428046-viewprojection-matrix-in-ortho-woes/ | # View/Projection matrix in ortho woes!
This topic is 4234 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
I have spend days literally on this, I have now come to a conclusion, but the logic seems strange, therefore could some one in the know please confirm if my understanding is correct, thank you very much. My problem area is that the near and far clipping planes, are changing in a major way depending on the position of the camera. Some code to demonstrate:
Me.Device.Transform.View = Matrix.LookAtLH(New Vector3(0, 0, 0), New Vector3(0, 0, 1), New Vector3(0, 1, 0))
Me.Device.Transform.Projection = Matrix.OrthoLH(Me.Width, Me.Height), -50, 50)
'Clipping occurs
Dim mesh As Mesh = Mesh.Cylinder(Me.Device, 20, 10, 101, 20, 1)
'Clipping does not occur
Dim mesh As Mesh = Mesh.Cylinder(Me.Device, 20, 10, 99, 20, 1)
Being ortho rather than perspective projection, we are dealing with a view cube as opposed to a viewing frustum. Leaving the view matrix for a moment, all seems straight forward, we have a cube 100 units deep, so to test I draw a cylinder 99 in the Z and no clipping occurs, if I use a cylinder 101 in the Z clipping occurs, so far so good! But the code below produces exactly the same results:
Me.Device.Transform.View = Matrix.LookAtLH(New Vector3(0, 0, -25), New Vector3(0, 0, 1), New Vector3(0, 1, 0))
Me.Device.Transform.Projection = Matrix.OrthoLH(Me.Width, Me.Height), -25, 75)
I have positioned the camera at -25 this time and what seems to be happening is that the near and far clipping plane is relative to the cameraPosition. The cameraTarget value makes no difference as long as it indicates the direction. There you go, I can’t see any documentation to back this up, but I would be grateful if someone could confirm either way if am on the right track!! Julian
##### Share on other sites
This is what is expected, aside from negative near plane values not being useful.
The near and far plane refer to the view space Z values (ie: after the world and view transforms). They represent how near and far something can be to the camera to be rendered. If these value were in world space, you'd have trouble quickly. Imagine turning your camera 90 degrees, looking down + or - X. How far would we see if near/far were referring to world space Z? No distance clipping would occur, instead it would become left/right clipping. Right there we can see that the values are not world space.
Since the near and far are based on Z distance from camera, a near value of less than 0 isn't useful. Anything less than 0 is behind the camera. A value of 0 is on the camera. A value greater than 0 is in front of the camera.
Due to how the math works, you actually want the near plane set to as high a value as you can. A value of 0 will break depth buffering. Very small values will introduce precision problems. The far plane can be large without affecting precision much.
This is the same for perspective cameras too, not just ortho cameras.
##### Share on other sites
Thank you very much, your explanation was very clear
Cheers
1. 1
Rutin
24
2. 2
3. 3
JoeJ
18
4. 4
5. 5
• 38
• 23
• 13
• 13
• 17
• ### Forum Statistics
• Total Topics
631710
• Total Posts
3001846
× | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2390216886997223, "perplexity": 1442.5772290474533}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589536.40/warc/CC-MAIN-20180716232549-20180717012549-00315.warc.gz"} |
https://robjhyndman.com/publications/on-continuous-time-threshold-autoregression/ | # On continuous-time threshold autoregression
Peter J Brockwell and Rob J Hyndman
(1992) International Journal of Forecasting, 18(3), 439-454
DOI
The use of non-linear models in time series analysis has expanded rapidly in the last ten years, with the development of several useful classes of discrete-time non-linear models. One family of processes which has been found valuable is the class of self-exciting threshold autoregressive (SETAR) models discussed extensively in the books of Tong (1983, 1990). In this paper we consider problems of modelling and forecasting with continuous-time threshold autoregressive (CTAR) processes. Techniques for analyzing such models have been proposed by Tong and Yeung (1991) and Brockwell, Hyndman and Grunwald (1991). In this paper we define a CTAR($p$) process $X(t)$ with boundary width $2\delta>0$ as the first component of a $p$-dimensional Markov process $X(t)$, defined by a stochastic differential equation. We are primarily concerned with the problems of model-fitting and forecasting when observations are available at times $1, 2, \dots, N$; however, the techniques considered apply equally well to irregularly spaced observations. For practical computations with CTAR processes we approximate the process $X(t)$ by a linearly interpolated discrete-time Markov process whose transitions occur at times $j/n$, $j = 1, 2, \dots$ with $n$ large. This model is used to fit ‘narrow boundary’ CTAR models to both simulated and real data. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8952234983444214, "perplexity": 733.3613282044059}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827963.70/warc/CC-MAIN-20181216165437-20181216191437-00055.warc.gz"} |
https://www.umr-cnrm.fr/spip.php?article125&lang=en | Last update: February 2020
### Quick description
The numerical model ALADIN (Aire Limitée Adaptation dynamique Développement InterNational) is a limited area bi-spectral model.
Since the beginning of the years 2000s, the ALADIN model is used at CNRM as a Regional Climate Model (RCM) with the name CNRM-ALADIN (or ALADIN-Climat). In the climate model family of CNRM, ALADIN can be seen as the limited area version of the ARPEGE-Climate model with which it shares most of the dynamics and physics or as the hydrostatique version of AROME.
The main advantage of RCMs is to limit the numerical cost of simulations with respect to global climate model at the same resolution. Therefore they allow to explore the climate representation at very fine scale.
At CNRM, we are currently developing and using the version 6 of CNRM-ALADIN that is based on cycle 37t1 of ARPEGE-IFS and on the version 6 of the CNRM climate physics that is common to ARPEGE-Climat, CNRM-CM6 or CNRM-ESM2, all global models used in CMIP6. In its simplest version, CNRM-ALADIN represent the atmosphere component of the climate as well as the land surface and its interactions with the atmosphere thanks to the SURFEX-ISBA model.
### Main uses
In climate mode, CNRM-ALADIN can be used in different configurations:
• Contribution of CNRM to the international programme WCRP CORDEX (lien) in particular over the Mediterranean and European domains (Med-CORDEX, Euro-CORDEX).
• Contribution to the version 2020 of the web portal of the French national climate service (DRIAS) and to the European climate service (Climate Data Store of C3S)
• Dedicated simulations for geographical areas of interest: metropolitan France (Colin et al. 2010, Daniel et al. 2019), South-East Atlantic Ocean (Mallet et al. 2019), La Réunion, Guadeloupe (Cantet et al. 2014), Martinique, Nouvelle Calédonie, Polynésie Française (Hopuare et al. 2015), North America (Lucas-Picher et al. 2013, 2015).
• Simulations at very low resolution (125 or 150 km, Herrmann et al. 2011)
• Simulations at very high résolution (12 km, Déqué and Somot 2008, Colin et al. 2010, Herrmann et al. 2011, Bador et al. 2017).
• Frequent use of the spectral nudging option (Radu et al. 2008, Colin et al. 2010, Herrmann et al. 2011)
• Use in forced mode by sea surface temperature and sea ice coverage (Herrmann et al. 2011, Bador et al. 2017)
• Use in coupled mode with interactive aerosol scheme (ALADIN-TACTIC, Nabat et al. 2015b, 2020, Mallet et al. 2019, Drugé et al. 2019, 2021) or in a fully-coupled regional climate system model CNRM-RCSM including the representation of surface hydrology and of the regional ocean (Sevault et al. 2014, Nabat et al. 2014, Somot et al. 2018, Darmaraki et al. 2019b).
• Use in academic mode (Big-Brother/Little-Brother) in which CNRM-ALADIN is driven by CNRM-ARPEGE at the same resolution and with the same physics (Colin et al. 2010)
• Use in perfect boundary condition mode in which the lateral and surface boundary forcings come from global reanalyses (Nabat et al. 2014, Sanchez-Gomez and Somot 2018, Daniel et al. 2019).
• Use in scenario mode in which the lateral and surface boundary conditions come from global climate models (CNRM-CM5, CNRM-ESM2 ou de GCMs issus de CMIP) to perform historical and scenario simulations (Sanchez-Gomez et al. 2009b, Déqué et al. 2012, Tramblay et al. 2013, Bador et al. 2017, Boé et al. 2020, Gutiérrez et al. 2020, Vautard et al. 2021, Coppola et al. 2021).
### Scientific applications using CNRM-ALADIN in climate mode
The scientific studies carried out with ALADIN-Climate at CNRM cover:
• Study of the strengths and limits of the regional climate models: academic study in Big-Brother/Little-Brother experiments (Radu et al. 2008, Colin et al. 2010), sensitivity study to the domain size (Colin et al. 2010, Herrmann et al. 2011), sensitility study to the model physics (Fardà et al. 2010), sensitivity study to the use of spectral nudging (Radu et al. 2008, Colin et al. 2010, Herrmann et al. 2011), study of the RCM internal variability (Sanchez-Gomez and Somot, 2018), added-value study with respect to the driving model (Déqué and Somot 2008, Herrmann et al. 2011, Ruti et al. 2016), large-scale reproductibility study (Sanchez-Gomez et al. 2009a), aerosol forcing study (Boé et al. 2020, Gutierrez et al. 2020).
• The evaluation and sometimes improvement of the model for the representation of the mean climate state (Sevault et al. 2014, Nabat et al. 2015a, Daniel et al. 2019), the heavy precipitation events (Déqué and Somot 2008, Colin et al. 2010, Fumière et al. 2019, Caillaud et al. 2021), the regional winds over sea (Herrmann et al. 2011), the intense air-sea fluxes (Waldman et al. 2017a), the urban heat island over Paris (Daniel et al. 2019), the floods (Lucas-Picher et al. 2015), the heat waves (Lemonsu et al. 2014, Bador et al. 2017), the Mediterranean Sea water and heat budgets (Sanchez-Gomez et al. 2011), the Mediterranean cyclogenesis (Sanchez-Gomez and Somot 2018), the weather regimes (Sanchez-Gomez et al. 2009a).
• the study and the attribution of past trends (Nabat et al. 2014, Drugé et al. 2019)
• the characterization of the future climate evolution during the 21st century at the regional scales and of the associated uncertainties (Sanchez-Gomez et al. 2009, Déqué and Somot 2010, Driouech et al. 2010, Déqué et al. 2012, Jacob et al. 2013, Tramblay et al. 2013, Gutiérrez et al. 2020, Boé et al. 2020, Coppola et al. 2021, Evin et al. 2021)
• the study of the regional impacts of climate change on the water resources (Tramblay et al. 2013), on the photovoltaic energy production (Gutiérrez et al. 2020).
### Where can I find outputs of ALADIN-Climat ?
The outputs (netcdf format) of the CNRM-ALADIN climate model can be found on :
• the Interactive Atlas of the IPCC-AR6. here
• the ESGF (Earth System Grid Federation) for example the CNRM ESGF datanode or the ESGF IPSL datanode. Se also the web page CORDEX ESGF.
• the Med-CORDEX database (www.medcordex.eu)
• on the Climate Data Store of the European climate service C3S (ici)
• (for the historians,) the dedicated databases of the European projects ENSEMBLES (data) and CECILIA (data)
### Some illustrations and movies using CNRM-ALADIN model outputs
• Movie of a tropical cyclone track close to La Réunion island (South-West Indian Ocean) at a resolution of 150km by the global climate model CNRM-ESM2-1 (left) and at a resolution of 12km y the regional climate model CNRM-ALADIN63 (right). Big thank to M-D. Leroux and D. Salas for this movie. here
• Historically, ALADIN development started at the beginning of the 1990s within a broad consortium gathering numerous weather centres in Europe. In its "operational numerical weather forecast" version, it is presented on the following web pages: First link Second link Third link
The very first reference articles presenting ALADIN are Bubnova et al. 1995 (Monthly Weather Review, n.123) and Radnoti 1995 (Mon. Wea. Rev., n.123).
• Since the beginning of the years 2000s, the ALADIN model is used at CNRM as a Regional Climate Model (RCM) with the name CNRM-ALADIN (or ALADIN-Climat). The first climate version of ALADIN is based on the cycle 24t1 of ARPEGE-ALADIN and on the version 4 of the climate physics (physics of the ARPEGE-Climat model version 4). This model (called at that time ALADIN-Climat v4) allowed to participate to the European projects ENSEMBLES and CECLIA, to the national project SCAMPEI, to the French national portal DRIAS and to publish the first scientific articles using ALADIN-Climate (Spiridonov et al. 2005, Déqué and Somot 2008, Radu et al. 2008, Sanchez-Gomez et al. 2009a, 2009b, 2011, Fardà et al. 2010).
• The version 5 of CNRM-ALADIN (also called ALADIN-Climat v5) is based on the cycle 32t0 of ARPEGE-ALADIN and on the version 5 of the CNRM climate. This climate physics is also used in CMIP5 with ARPEGE-Climate and CNRM-CM5. CNRM-ALADIN5 has been widely used in the first phase of the international CORDEX initiative for the domains Mediterranean (Med-CORDEX, version 5.2, CNRM-ALADIN52, Tramblay et al. 2013, Jacob et al. 2013, Nabat et al. 2014a, 2014b, Sevault et al. 2014), Europe (Euro-CORDEX, version 5.3, CNRM-ALADIN53, Bador et al. 2017), Africa (CORDEX Africa, CNRM-ALADIN52) and North America (CORDEX North-America, Lucas-Picher et al. 2013). We also use it in the European projects CLIM-RUN and IMPACT2C as well as in the national projects ANR MEDUP and ANR REMEMBER. Finally, CNRM-ALADIN5 served to feed the version 2014 of the web portal of the French national climate servce DRIAS with dedicated simulations over France including the French outermost territories.
### Some key reference publications for CNRM-ALADIN
Intercomparaison study of CNRM-ALADIN with the other European RCMs:
Coppola E., Nogherotto R., Ciarlò J.M., Giorgi F., van Meijgaard E., Kadygrov N., Iles C., Corre L., Sandstad M., Somot S., Nabat P., Vautard R., Levavasseur G., Schwingshackl C., Sillmann J., Kjellström E., Nikulin G., Aalbers E., Lenderink G., Christensen O.B., Boberg F., Lund Sørland S., Demory M.-E., Bülow K., Teichmann C., Warrach-Sagi K., Wulfmeyer V. (2020) Assessment of the European Climate Projections as Simulated by the Large EURO-CORDEX Regional and Global Climate Model Ensemble. Journal of Geophysical Research – Atmospheres, http://doi.org/10.1029/2019JD032356 or pdf
Vautard R., Kadygrov N., Iles C., Boberg F., Buonomo E., Bülow K., Coppola E., Corre L., van Meijgaard E., Nogherotto R., Sandstad M., Schwingshackl C., Somot S., Aalbers E., Christensen O.B., Ciarlo J.M., Demory M.-E., Giorgi F., Jacob D., Jones R.G., Keuler K., Kjellström E., Lenderink G., Levavasseur G., Nikulin G., Sillmann J., Solidoro C., Lund Sørland S., Steger C., Teichmann C., Warrach-Sagi K., Wulfmeyer V. (2021) Evaluation of the large EURO-CORDEX regional climate model ensemble. Journal of Geophysical Research – Atmospheres, https://doi.org/10.1029/2019JD032344
Nabat, P., Somot, S., Cassou, C., Mallet, M., Michou, M., Bouniol, D., Decharme, B., Drugé, T., Roehrig, R., and Saint-Martin, D. (2020) Modulation of radiative aerosols effects by atmospheric circulation over the Euro-Mediterranean region. Atmos. Chem. Phys., 20, 8315–8349, https://doi.org/10.5194/acp-20-8315-2020.
Daniel M., Lemonsu A., Déqué M., Somot S., Alias A., Masson V. (2019) Benefits of explicit urban parameterization in regional climate modeling to study climate and city interactions. Climate dynamics, 52(5-6), 2745-2764, doi:10.1007/s00382-018-4289-x
Herrmann M., Somot S., Calmanti S., Dubois C., Sevault F. (2011) Representation of daily wind speed spatial and temporal variability and intense wind events over the Mediterranean Sea using dynamical downscaling : impact of the regional climate model configuration. Nat. Hazards Earth Syst. Sci., 11, 1983-2001, doi:10.5194/nhess-11-1983-2011
Colin J., Déqué M., Radu R., Somot S. (2010) Sensitivity study of heavy precipitations in Limited Area Model climate simulation: influence of the size of the domain and the use of the spectral nudging technique. Tellus-A, 62(5), 591-604. doi:10.1111/j.1600-0870.2010.00467.x | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8565438389778137, "perplexity": 11872.596373878107}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662587158.57/warc/CC-MAIN-20220525120449-20220525150449-00556.warc.gz"} |
https://codereview.stackexchange.com/questions/217197/to-find-if-a-character-is-a-delimiter/217202 | # To find if a character is a delimiter
I have a function to check if a character is a delimiter and I wonder if it is consistent or can be improved:
int chDelimit(int ch)
{
return
(ch == '\n' || ch == '\t') ||
(ch >= ' ' && ch <= '/') ||
(ch >= ':' && ch <= '@') ||
(ch >= '[' && ch <= '') ||
(ch >= '{' && ch <= '~') ||
(ch == '\0');
}
• Can you add a description of what a delimiter is in this case? What one program considers a delimiter, another might not. – pacmaninbw Apr 10 at 12:34
## 3 Answers
There's no particular ordering of characters' code-points in C (other than the digits 0..9). This code assumes (for example) that '[' is less than '', but that's not the case in EBCDIC at least.
I think you might be better off creating a table of boolean values, and indexing into that with the (unsigned value of) ch, in the way that standard <ctype.h> functions are normally implemented. This will probably improve performance (one lookup, rather than up to 11 comparisons, per call).
Alternatively, and depending on what characters are considered "delimiters", you may be able to use standard library functions (e.g. isalnum()) in combination.
1. Function Name It isn't clear that chDelimit() is a function that tests whether a character is a delimiter character. For functions that return boolean, it's generally accepted to call it Is<Condition>() where condition is phrased in the affirmative. For example, I'd name this function IsDelimiter() and not IsNonDelimiterCharacter()
2. Depending on your application, it might be worthwhile to create macros for boolean values (or enums). See SO: Using Boolean Values in C
3. If the list of delimiter characters isn't going to grow too large, create a character array, DelimiterCharacters, and have your function do a one-pass search.
Strictly speaking you can't assume that the various characters are in range, portably. The only characters actually guaranteed to be located in a continuous range in the symbol table are '0' to '9'. That's mostly a nitpick though, since 99.9% of all systems are ASCII or UTF.
What's more serious is that this look-up is slow. You have numerous branches which the CPU must execute. If you have to call this function repeatedly from a loop, it will be performance-heavy. Instead, you can replace all of this with a look-up table.
For boolean checks, you should be using bool.
A fixed function might look like this:
#include <stdbool.h>
bool isdelimit (char ch)
{
ch &= 0x7F; // ensure 7 bit
const bool DELIMIT[128] =
{
['\n'] = true,
['\t'] = true,
[' '] = true,
['\0'] = true,
// ...
};
return DELIMIT[ch];
}
The table DELIMIT will per default initialize all items to false save for those that you explicitly initialize. By using the character value as the search key, the algorithm turns branchless and efficient.
The above trick with using designated initializers means that you only need to type out those delimiters you are interested in, rather than typing out a big table of 127 values.
Also check out the rarely used but 100% standard C functions strpbrk and strcspn (string.h) that can be used for this very purpose too.
• This designated initializer is a very cool idea. – machine_1 Apr 12 at 13:46
• 99+% of systems are Extended ASCII, like UTF-8, Latin-1, ASCII+Don'tCare, and so on, at least leaving out other wider UTFs. Few are vanilla ASCII. – Deduplicator Apr 12 at 13:58
• @Deduplicator With ASCII being a subset of them all. – Lundin Apr 12 at 14:02
• I'd expect values outside the 0...7F range to return false, not ignore the 8th bit. Simple enough to use const bool DELIMIT256[UCHAR_MAX + 1] and static const bool DELIMIT[(unsigned char) ch]; – chux - Reinstate Monica Apr 12 at 22:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1536250114440918, "perplexity": 3278.057502297435}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496671053.31/warc/CC-MAIN-20191121231600-20191122015600-00305.warc.gz"} |
http://www.bushcraftsociety.com/who-sang-oaluvo/bews2.php?795662=normal-approximation-to-poisson-proof | normal approximation to poisson proof
Solution. If $$Y$$ denotes the number of events occurring in an interval with mean $$\lambda$$ and variance $$\lambda$$, and $$X_1, X_2,\ldots, X_\ldots$$ are independent Poisson random variables with mean 1, then the sum of $$X$$'s is a Poisson random variable with mean $$\lambda$$. Suppose $$Y$$ denotes the number of events occurring in an interval with mean $$\lambda$$ and variance $$\lambda$$. More formally, to predict the probability of a given number of events occurring in a fixed interval of time. Poisson Approximation for the Binomial Distribution • For Binomial Distribution with large n, calculating the mass function is pretty nasty • So for those nasty “large” Binomials (n ≥100) and for small π (usually ≤0.01), we can use a Poisson with λ = nπ (≤20) to approximate it! If you’ve ever sold something, this “event” can be defined, for example, as a customer purchasing something from you (the moment of truth, not just browsing). Let X be the random variable of the number of accidents per year. More about the Poisson distribution probability so you can better use the Poisson calculator above: The Poisson probability is a type of discrete probability distribution that can take random values on the range $$[0, +\infty)$$.. Gaussian approximation to the Poisson distribution. To predict the # of events occurring in the future! It turns out the Poisson distribution is just a… It is normally written as p(x)= 1 (2π)1/2σ e −(x µ)2/2σ2, (50) 7Maths Notes: The limit of a function like (1 + δ)λ(1+δ)+1/2 with λ # 1 and δ \$ 1 can be found by taking the 2.1.6 More on the Gaussian The Gaussian distribution is so important that we collect some properties here. Normal Approximation to Poisson is justified by the Central Limit Theorem. At first glance, the binomial distribution and the Poisson distribution seem unrelated. But a closer look reveals a pretty interesting relationship. 28.2 - Normal Approximation to Poisson . The fundamental difficulty is that one cannot generally expect more than a couple of places of accuracy from a normal approximation to a Poisson distribution. Because λ > 20 a normal approximation can be used. 1. Proof of Normal approximation to Poisson. For sufficiently large values of λ, (say λ>1000), the normal distribution with mean λ and variance λ (standard deviation ) is an excellent approximation to the Poisson distribution. Normal Approximation for the Poisson Distribution Calculator. Why did Poisson invent Poisson Distribution? Use the normal approximation to find the probability that there are more than 50 accidents in a year. For your problem, it may be best to look at the complementary probabilities in the right tail. Lecture 7 18 A comparison of the binomial, Poisson and normal probability func-tions for n = 1000 and p =0.1, 0.3, 0.5. Thread starter Helper; Start date Dec 5, 2009; Dec 5, 2009 #1 Helper. The normal and Poisson functions agree well for all of the values of p, and agree with the binomial function for p =0.1. 1 0. I have been looking for a proof of the fact that for a large parameter lambda, the Poisson distribution tends to a Normal distribution. In a factory there are 45 accidents per year and the number of accidents per year follows a Poisson distribution. Just as the Central Limit Theorem can be applied to the sum of independent Bernoulli random variables, it can be applied to the sum of independent Poisson random variables. Are 45 accidents per year a given number of events occurring in the right tail approximation. We collect some properties here, and agree with the binomial distribution the. On the Gaussian the Gaussian the Gaussian the Gaussian the Gaussian distribution is so important we... May be best to look at the complementary normal approximation to poisson proof in the future given... A year normal probability func-tions for n = 1000 and p =0.1, 0.3, 0.5, and... Interesting relationship with the binomial function for p =0.1, 0.3, 0.5 than... The complementary probabilities in the right tail in the right tail, to the! Glance, the binomial distribution and the number of events occurring in a fixed interval of.! Are 45 accidents per year follows a Poisson distribution Poisson and normal probability func-tions n. To look at the complementary probabilities in the future and agree with the binomial function for p =0.1,,... The number of accidents per year approximation to find the probability of a given number of accidents per year the... Accidents per year and the Poisson distribution Gaussian distribution is so important we! Comparison of the binomial, Poisson and normal probability func-tions for n = 1000 and p =0.1, 0.3 0.5! Are 45 accidents per year let X be the random variable of the function. Problem, it may be best to look at the complementary probabilities in the tail! More on the Gaussian distribution is so important that we collect some properties here on. ; Dec 5 normal approximation to poisson proof 2009 ; Dec 5, 2009 ; Dec,! Of events occurring in the future and normal probability func-tions for n = 1000 and =0.1... Given number of accidents per year follows a Poisson distribution seem unrelated > 20 a normal approximation to the. Dec 5, 2009 # 1 Helper, Poisson and normal approximation to poisson proof probability func-tions for n 1000! Approximation can be used 20 a normal approximation can be used seem unrelated Poisson seem... Dec 5, 2009 ; Dec 5, 2009 ; Dec 5, 2009 ; Dec 5, #! At first glance, the binomial function for p =0.1, 0.3, 0.5, to predict the probability a... Poisson and normal probability func-tions for n = 1000 and p =0.1,,... Can be used at first glance, the binomial function for p =0.1 predict the probability that there more. With the binomial, Poisson and normal probability func-tions for n = and... Of accidents per year 2009 ; Dec 5, 2009 # 1 Helper 1 Helper a normal approximation to the..., 0.3, 0.5 more than 50 accidents in normal approximation to poisson proof factory there are more than 50 in! A pretty interesting relationship = 1000 and p =0.1, 0.3, 0.5 2009 ; 5. Gaussian distribution is so important that we collect some properties here important that we collect some properties here here. A year and agree with the binomial, Poisson and normal probability func-tions for n = 1000 p... To predict the probability that there normal approximation to poisson proof more than 50 accidents in a year the variable... Closer look reveals a pretty interesting relationship the # of events occurring in the future 1 Helper follows a distribution. A given number of events occurring in a factory there are 45 accidents year... All of the binomial distribution and the number of accidents per year follows a Poisson distribution unrelated. To look at the complementary probabilities in the right tail, the function! Gaussian the Gaussian the Gaussian distribution is so important that we collect some properties here a! Of accidents per year more on the Gaussian the Gaussian distribution is so important we! To find the probability that there are 45 accidents per year of a given number of accidents per year a. Look reveals a pretty interesting relationship 20 a normal approximation to find the probability that there are 45 per. Agree with the binomial, Poisson and normal probability func-tions for n = 1000 and p =0.1 normal..., the binomial distribution and the number of accidents per year follows a Poisson.... Distribution seem unrelated that there are 45 accidents per year and the of. There are more than 50 accidents in a fixed interval of time normal approximation to poisson proof of the of! Important that we collect some properties here > 20 a normal approximation can be used agree well for of. Occurring in a year seem unrelated Poisson functions agree well for all of values. Distribution is so important that we collect some properties here binomial function for p.. Approximation to find the probability of a given number of accidents per year and the number of per. # 1 Helper can be used to look at the complementary probabilities in the right tail of p and... Be best to look at the complementary probabilities in the future your problem it... Interval of time are more than 50 accidents in a fixed interval of time the distribution. Factory there are more than 50 accidents in a fixed interval of time formally, to predict the of. The random variable of the binomial function for p =0.1, 0.3, 0.5 λ > a... Look reveals a pretty interesting relationship ; Start date Dec 5, 2009 # 1.. Normal approximation can be used are more than 50 accidents in a interval... Well for all of the values of p, and agree with the binomial for. Glance, the binomial distribution and the number of events occurring in a year 5, #!, it may be best to look at the normal approximation to poisson proof probabilities in the tail! For your problem, it may be best to look at the complementary probabilities in right... And the Poisson distribution seem unrelated ; Dec 5, 2009 # 1.. Interesting relationship than 50 accidents in a fixed interval of time can be used p..., and agree with the binomial, Poisson and normal probability func-tions for n = 1000 and p.... More than 50 accidents in a year agree well for all of number! Seem unrelated =0.1, 0.3, 0.5 a pretty interesting relationship are than! Problem, it may be best to look at the complementary probabilities in the future at the complementary in. Binomial function for p =0.1 year follows a Poisson distribution # of events in. Approximation to find the probability that there are 45 accidents per year follows Poisson! On the Gaussian the Gaussian distribution is so important that we collect some properties here, and! The random variable of the number of accidents per year follows a Poisson distribution seem.., 0.5 are 45 accidents per year 5, 2009 ; Dec 5, 2009 ; Dec 5, #. 2.1.6 more on the Gaussian distribution is so important that we collect some properties.. But a closer look reveals a pretty interesting relationship fixed interval of time 0.3 0.5... Normal approximation to find the probability of a given number of events occurring in the right tail # events! Probability that there are 45 accidents per year follows a Poisson distribution number... > 20 a normal approximation can be used functions agree well for all of the of. Dec 5, 2009 ; Dec 5, 2009 ; Dec 5, 2009 ; Dec 5, 2009 1! And p =0.1 that there are more than 50 accidents in a factory there are 45 accidents year..., to predict the # of events occurring in the future = 1000 and p =0.1, 0.3,.... # 1 Helper p =0.1 2009 ; Dec 5, 2009 # 1 Helper the. Of accidents per year let X be the random variable of the values of p, and agree the. To predict the probability that there are 45 accidents per year follows a distribution. In a factory there are 45 accidents per year follows a Poisson distribution unrelated. The Gaussian the Gaussian the Gaussian distribution is so important that we collect some properties here distribution seem.... At the complementary probabilities in the right tail starter Helper ; Start date Dec 5 2009. Thread starter Helper ; Start date Dec 5, 2009 ; Dec 5, 2009 # Helper..., to predict the # of events occurring in a year 2009 # Helper. Comparison of the number of accidents per year collect some properties here be used binomial for. Of events occurring in the right tail Dec 5, 2009 ; Dec 5 2009! Of events occurring in the future number of events occurring in the right tail Gaussian the Gaussian the Gaussian is. # of events occurring in the future fixed interval of time use normal! Poisson and normal probability func-tions for n = 1000 and p =0.1 0.3... Of a given number of events occurring in a fixed interval of time p, agree. For p =0.1 the probability of a given number of accidents per year follows a Poisson distribution seem.!, 0.5 factory there are 45 accidents per year and the Poisson distribution seem.! A year Poisson distribution seem unrelated the complementary probabilities in the future values of p and. Λ > 20 a normal approximation to find the probability that there are more than 50 in!, and agree with the binomial function for p =0.1 interesting relationship the future for p,... First glance, the binomial distribution and the Poisson distribution seem unrelated formally, to predict the probability there!, 0.3, 0.5 of p, and agree with the binomial, Poisson and normal probability for. A year for p =0.1 binomial, Poisson and normal probability func-tions for n = and... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9321728348731995, "perplexity": 449.5398467243298}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704843561.95/warc/CC-MAIN-20210128102756-20210128132756-00630.warc.gz"} |
https://en.wikipedia.org/wiki/Fed_model | Fed model
Original graphic from Humphrey-Hawkins report of July 22, 1997
The "Fed model" is a theory of equity valuation that has found broad application in the investment community. The model compares the stock market’s earnings yield (E/P) to the yield on long-term government bonds. In its strongest form the Fed model states that bond and stock market are in equilibrium, and fairly valued, when the one-year forward-looking earnings yield equals the 10-year Treasury note yield ${\displaystyle (Y_{\text{10}})}$:
${\displaystyle {\frac {E}{P}}=Y_{\text{10}}}$
The model is often used as a simple tool to measure attractiveness of equity, and to help allocating funds between equity and bonds. When for example the equity earnings yield is above the government bond yield, investors should shift funds from bonds into equity. The Fed model was so named by Ed Yardeni,[1][2] at Deutsche Morgan Grenfell, based on a statement made in the Humphrey-Hawkins report of July 22, 1997 [2] issued by the Federal Reserve that warned:
“…changes in this ratio [P/E of the S&P 500 index] have often been inversely related to changes in the long-term Treasury yields, but this year's stock price gains were not matched by a significant net decline in interest rates. As a result, the yield on ten-year Treasury notes now exceeds the ratio of twelve-month-ahead earnings to prices by the largest amount since 1991, when earnings were depressed by the economic slowdown.”
The Fed model was never officially endorsed by the Fed, but former Fed chairman Alan Greenspan[3] seemed to make reference to it in his memoirs: “The decline of real (inflation adjusted) long-term interest rates that has occurred in the last two decades has been associated with rising price-to-earnings ratios for stocks, real estate, and in fact all income-earnings assets.” A bond yield versus equity yield comparison has been used in practice long before the Fed published the graph and Yardeni gave it a name. A variant of this, first the expected AAA bond yield from the Blue Chip survey versus the forward-earnings yield on the S&P 500, and then later versus the 10-year Treasury was developed by Dirk van Dijk at I/B/E/S in the mid-1980s.
Support for the Fed model
While not unanimous, there is broad consensus in the non-academic investing community that the basic comparison underlying the Fed model is valid. A number of arguments are listed by different authors in favor of the Fed model:
Competing assets argument
Stocks and bonds are competing asset classes for investors. When stocks yield more than bonds, investors are better off investing in stocks. When funds flow from bonds into stocks on a large scale, the yield on bonds should increase and the yield on stocks decrease, until the Fed model equilibrium is reached.
Present value
Another argument often mentioned in favor of the Fed model is the present value of stocks should be equal to the sum of its discounted future cash flows. The government bond rate can be seen as a proxy for the risk-free rate. When the government bond rate falls, the discount rate falls, and the present value rises. And this implies that when interest rates fall, E/P also falls.
Historical data
One of the most compelling arguments in favor of the Fed model is the almost 30 years of data from the S&P 500 index showing a high correlation between the two parameters. For example, Salomons[4] shows a correlation of 75% over the 1995–2002 period. However, over the 1881–2002 period the correlation was only 19% and in recent years the correlation has broken down completely.[5]
Users
MoneyWeek (April 28, 2010) argued that
“The Fed model matters because important people use it. Analysts across the board, from JP Morgan, to ING, to Prudential – I could go on and on – use the Fed model in their calculations. […] The fact is, influential market players embrace the Fed model. Whether they truly believe in it or not is immaterial. The net result is that the Fed model is a significant valuation tool which prominent investors use to check whether they should be buying stocks or bonds. And when those inflection points come about, markets move. Because when the advocates say it's time to buy, a wave of trading orders are placed.”
Inflation and money illusion
Clifford Asness[6] argues that investors actually set stock market P/Es based on nominal interest rates (see also criticism below) but that they do so in error. By confusing real and nominal investors suffer from ‘money illusion’. Asness ‘fights the Fed model’ as a normative model but acknowledges that the model has certain descriptive validity and as a positive model cannot simply be dismissed. Other authors see inflation as the driver behind the Fed model but hypothesize it is not investor stupidity but accounting rules[7] or investor risk aversion during times of inflation[8] that causes the Fed model equilibrium.
Criticism
Criticism on the Fed model has been harsh, and a number of papers with creative titles were published by academia such as "The fed model: The bad, the worse, and the ugly" and "Fight the FED model". Academics have concluded that the model is inconsistent with rational valuation of the stock market.
Lack of theoretical support
The competing asset argument listed above argues that only when stocks have the same yield as government bonds, both asset classes are equally attractive to investors. But the earnings yield (E/P) of a stock does not describe what an investor actually receives as not all earnings are paid out to the investor. And how do corporate bonds (with a yield above the government bond yield) fit into this picture? A number of assumptions need to be made to go from the constant growth dividend discount model to the Fed model. Estrada starts with the Gordon growth model[9]
${\displaystyle P={\frac {D(1+G)}{R_{\text{f}}+RP-G}}}$
where P is the current price and D the current dividend, G the expected long-term growth rate, ${\displaystyle R_{\text{f}}}$ the risk free rate (10-year treasury notes) and RP the equity risk premium. If one now assumes that 100% of the earnings are paid as dividend (D=E), the growth rate is equal to zero, and the equity risk premium is also equal to zero, one gets the Fed model: E/P=${\displaystyle R_{\text{f}}}$. The three assumptions seem unrealistic at best. It is also pointed out that the Fed model compares a real magnitude (E/P) with a nominal interest rate.[6][10][11] Inflation should affect the bond yield, but not the earnings yield.
Data selection and international markets
The Fed model equilibrium was only observed in one market, and for a limited time window. More specifically, the relationship is observed for the S&P 500 index between ~1980 and ~2005 but data outside of this time window, or in different international markets do not show the same pattern. The correlation between earnings yield and government bond yields was only 19% over the 1881–2002 period.[4] Over the period from 1999 to 2010 was reported to be –0.80 with statistical significance [3]. The Fed model equilibrium specifically seemed to break down during the height of the financial crisis in 2008, when the yield on 10-year Treasuries reached an all-time low at 2.4% whereas the S&P 500 earnings yield reached a 20-year-high at more than 8%, a gap of 6 percentage points. And a study of international data showed that the Fed model equilibrium only shows up in 2 out of 20 evaluated international markets.[9] It seems that the empirical support for the Fed model is then based on carefully chosen and limited evidence.
Lack of predictive power
If the Fed model is indeed an equity valuation theory with descriptive validity, it should be able to identify over-valued and under-valued assets. But it turns out that the Fed model has no power to forecast long term stock returns. Traditional value investing methods using only the market's P/E have significantly more efficacy than the Fed model.[6]
As an example Tom Lauricella applied the Fed model to S&P500 index on January 19, 2008.[12] He writes:
With the past week's downturn, stocks in the Standard and Poor's 500-stock index are trading at 13 times their expected earnings for 2008. Last June, when the S&P index was 12% higher than it is now, stocks were priced at 14.2 times this year's earnings. Meanwhile, with a U.S. recession now widely expected and the Federal Reserve thought likely to cut short-term rates further, U.S. Treasury yields have fallen sharply. The 10-year Treasury note is yielding 3.64%, its lowest level since July 2003, and down from 3.81% a week ago.
Thus S&P500 forward earning yield (1/13=7.69%) is higher than 10-year Treasury note yield (3.64%), suggesting S&P500 is significantly undervalued. However, over the next twelve months, the S&P500 index fell from 1,325.19 (January 18, 2008) to 805.22 points (January 20, 2009), a drop of more than 39%.
Is the Fed model mis-specified?
The Fed model equilibrium remains an enigma. On one hand 30 years of data is available that shows how S&P earnings yield and 10-year government bond yield move in tandem. On the other hand, there is no theoretical foundation to explain the relationship, and the best explanation academics came up with is that investors collectively suffer from 'money illusion'. A number of questions remain unanswered. Why was the relationship observed in the US and not in most other international markets?[9] Do investors in the US (the world's largest equity market) suffer more from 'illusions' than investors in for example Austria and Finland? Why did the relationship not exist in the US before 1980 (or 1965) and why did the equilibrium break down during the 2008 crisis? And if government bonds and stocks are competing assets, what is the role of corporate bonds?
The recently proposed capital structure substitution theory argues that the Fed model indeed needs to be re-specified. It suggests that supply (company management), rather than demand (investors) drives the relationship between E/P and interest rates. Stock market earnings yield tends to equilibrium not with the government bond yield but with the average after-tax corporate bond yield as companies adjust capital structure (mix of equity and bonds) to maximize earnings per share.[13] If managements consistently optimize capital structure by substituting stocks (repurchasing shares) for bonds or vice versa, equilibrium is reached when:
${\displaystyle {\frac {E_{\text{x}}}{P_{\text{x}}}}=R_{\text{x}}\ [1-T]}$
where E is the earnings-per-share of company x, P is the share price, R is the nominal interest rate on corporate bonds and T is the corporate tax rate. For a long time the after-tax interest rate on corporate bonds was roughly equal to the 10-year Treasury rate. But during the 2008 financial crisis this relationship broke down, as Baa rated corporate bonds peaked at over 9%, and 10-year treasuries bottomed under 2.5% (see figure 3). In the US, SEC Rule 10b-18 (explicitly allowing share repurchases) enabled fine adjustment toward equilibrium as of 1982, explaining why the equilibrium emerged around that time and not before. And in many other countries share repurchases were prohibited until 1998 or are still considered illegal, explaining why the Fed model equilibrium was observed in the US but not in many other international markets.
Fed model equilibrium comparing S&P 500 earnings yield and 10-year Treasury yield. The descriptive validity of the model is limited before 1982 and after 2007.
Re-specified Fed model comparing S&P 500 earnings yield with after-tax corporate bond yield (average rating=Baa). Before 1982 the equilibrium could not be reached due to legal limitations in repurchasing shares (SEC Rule 10b-18).
Is the Fed model miss-specified? Thirty years of investor money illusion (left) or deliberate company policy (right)?
References
1. ^ Yardeni, Ed (1997). "Fed's stock market model finds overvaluation". US Equity Research, Deutsche Morgan Grenfell.
2. ^ Yardeni, Ed (1999). "New, improved stock valuation model". US Equity Research, Deutsche Morgan Grenfell.
3. ^ Greenspan, Alan (2007). The Age of Turbulence: Adventures in a New World. New York: Penguin Press. p. 14. ISBN 1-59420-131-5.
4. ^ a b Salomons, R. (2006). "A Tactical Implication of Predictability: Fighting the FED model". The Journal of Investing.
5. ^ [1]
6. ^ a b c Asness, Clifford (2003). "Fight the FED model". Journal of Portfolio Management.
7. ^ Thomas, J.; Zhang, F (2007). "Don't fight the Fed Model" (PDF).
8. ^ Bekaert, Geert; Engstrom, Eric (April 2008). "Inflation and the Stock Market: Understanding the 'Fed Model'". SSRN 1125355.
9. ^ a b c Estrada, J. (2006). "The Fed model: A note". Finance Research Letters: 14–22.
10. ^ Feinman, J. (2003). "Inflation illusion and the (mis)pricing of assets and liabilities" (PDF). Journal of Investing: 29–36.
11. ^ Ritter, J.R.; Warr, R.S. (2002). "The decline of inflation and the bull market of 1982–1999" (PDF). Journal of Financial and Quantitative Analysis: 29.
12. ^ Lauricella, Tom (19 January 2008). "When Is It Time to Buy Stocks Again?". Wall Street Journal.
13. ^ Timmer, Jan (2011). "Understanding the Fed Model, Capital Structure, and then Some".
• Lander, Joel; Orphanides, Athanasios; Douvogiannis, Martha (1997). "Earnings, Forecasts and the Predictability of Stock Returns: Evidence From Trading the S&P". Journal of Portfolio Management. 23 (4): 24–35. doi:10.3905/jpm.1997.409620. Cite uses deprecated parameter |coauthors= (help) [The research paper by three Federal Reserve economists that gave rise to the somewhat misleading name 'Fed Model' to describe the idea of comparing earnings yields to treasury yields]. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 6, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40409454703330994, "perplexity": 4877.34785614432}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738663202.87/warc/CC-MAIN-20160924173743-00263-ip-10-143-35-109.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/208930-limit-composite-function.html | # Math Help - Limit of a composite function
1. ## Limit of a composite function
I don't want an easy answer to this problem. However, I would be happy if you could provide me with theorems and/or techniques required to solve it.
$\lim _{x\to \infty }x^2(ln({x+1\over x}) +ln({2x+3\over 2x}))$
I know that $\lim _{x\to \infty }({x+1\over x})^x = \lim _{x\to \infty }(1+{1\over x})^x = e$ But the natural logarithm is in the way and I think that you can't calculate the limit IN the logarithm first.
P.S. Oh, and by the way could anyone recommend a book on calculus with challenging problems, because most of the usual calculus textbooks aren't rigorous enough for my college course. (My lecturer always finds a way to give much more complicated problems than those in textbooks)
2. ## Re: Limit of a composite function
Hello, Doubled144314!
We need these two theorems:
. . $\lim_{x\to\infty}\left(1 + \tfrac{1}{x}\right)^x \;=\;e$
. . $\lim_{x\to\infty}\left(1 + \tfrac{a}{x}\right)^x \;=\;e^a$
$\displaystyle \lim _{x\to\infty}x^2\bigg[\ln\left(\tfrac{x+1}{x}\right) +\ln\left(\tfrac{2x+3}{2x}\right)\bigg]$
We have: . $\lim_{x\to\infty}x\cdot x\bigg[\ln\left(1+\tfrac{1}{x}\right) + \ln\left(1 + \tfrac{3}{2x}\right)\bigg]$
. . . . . . $=\;\lim_{x\to\infty}x\bigg[x\ln\left(1+\tfrac{1}{x}\right) + x\ln\left(1 + \tfrac{3}{2x}\right)^x\bigg]$
. . . . . . $=\;\lim_{x\to\infty}x\bigg[\ln\left(1 + \tfrac{1}{x}\right)^x + \ln\left(1 + \tfrac{\frac{3}{2}}{x}\right)^x\bigg]$
. . . . . . $=\;\lim_{x\to\infty}x\cdot \bigg[\ln\left(\lim_{x\to\infty}\left[1 + \tfrac{1}{x}\right]^x\right) + \ln\left(\lim_{x\to\infty}\left[1 + \tfrac{\frac{3}{2}}{x}\right]^x\right)\bigg]$
. . . . . . $=\;\infty\cdot \ln(e)\cdot \ln(e^{\frac{3}{2}}) \;=\;\infty\cdot1\cdot\tfrac{3}{2} \;=\;\infty$
3. ## Re: Limit of a composite function
Originally Posted by Doubled144314
I don't want an easy answer to this problem. However, I would be happy if you could provide me with theorems and/or techniques required to solve it.
$\lim _{x\to \infty }x^2(ln({x+1\over x}) +ln({2x+3\over 2x}))$
I know that $\lim _{x\to \infty }({x+1\over x}) = \lim _{x\to \infty }(1+{1\over x})^1 = e$ But the natural logarithm is in the way and I think that you can't calculate the limit IN the logarithm first.
I would rewrite the function as \displaystyle \begin{align*} \lim_{x \to \infty} \frac{\ln{\left(\frac{x+1}{x}\right)} + \ln{\left(\frac{2x+3}{2x}\right)}}{\frac{1}{x^2}} \end{align*}, and since this goes to \displaystyle \begin{align*} \frac{0}{0} \end{align*} you can apply L'Hospital's Rule. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9873493909835815, "perplexity": 276.50908158472004}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394010916587/warc/CC-MAIN-20140305091516-00024-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://www.semanticscholar.org/paper/Lifting-Methods-in-Mass-Partition-Problems-Sober'on-Takahashi/3285d346bfeaa0035c8ddfb3fa0a903957e1efea | # Lifting Methods in Mass Partition Problems
@article{Soberon2022LiftingMI,
title={Lifting Methods in Mass Partition Problems},
author={Pablo Sober'on and Yuki Takahashi},
journal={International Mathematics Research Notices},
year={2022}
}
• Published 8 September 2021
• Mathematics
• International Mathematics Research Notices
Many results about mass partitions are proved by lifting $\mathds {R}^d$ to a higher-dimensional space and dividing the higher-dimensional space into pieces. We extend such methods to use lifting arguments to polyhedral surfaces. Among other results, we prove the existence of equipartitions of $d+1$ measures in $\mathds {R}^d$ by parallel hyperplanes and of $d+2$ measures in $\mathds {R}^d$ by concentric spheres. For measures whose supports are sufficiently well separated, we prove results…
1 Citations
## Figures from this paper
### Bisections of mass assignments using flags of affine spaces
• Mathematics
• 2021
We use recent extensions of the Borsuk–Ulam theorem for Stiefel manifolds to generalize the ham sandwich theorem to mass assignments. A k-dimensional mass assignment continuously imposes a measure on
## References
SHOWING 1-10 OF 50 REFERENCES
### Convex equipartitions: the spicy chicken theorem
• Mathematics
• 2013
We show that, for any prime power $$n$$n and any convex body $$K$$K (i.e., a compact convex set with interior) in $$\mathbb{R }^d$$Rd, there exists a partition of $$K$$K into $$n$$n convex sets with
### Equipartitions with Wedges and Cones
A Borsuk-Ulam theorem for flag manifolds is introduced, which the author believes to be of independent interest, and a stronger statement, namely that any $d$ mass distributions in $\mathbb{R}^d$ can be simultaneously bisected by a single hyperplane is proved.
### Borsuk-Ulam theorems for products of spheres and Stiefel manifolds revisited
• Mathematics
Topological Methods in Nonlinear Analysis
• 2020
We give a different and possibly more accessible proof of a general Borsuk--Ulam theorem for a product of spheres, originally due to Ramos. That is, we show the non-existence of certain
### More Bisections by Hyperplane Arrangements
• Mathematics
Discret. Comput. Geom.
• 2022
A different proof of the Hubard and Karasev result is given using the framework of Blagojević, Frick, Haase & Ziegler (2016), based on the equivariant relative obstruction theory of tom Dieck, which was developed for handling the Grünbaum–Hadwiger–Ramos hyperplane measure partition problem.
### BALANCED CONVEX PARTITIONS OF MEASURES IN ℝ d
We prove the following generalization of the ham sandwich theorem, conjectured by Imre Barany. Given a positive integer k and d nice measures μ 1 , μ 2 ,…, μ d in ℝ d such that μ i (ℝ d )= k for all
### Appollonius Revisited: Supporting Spheres for Sundered Systems
• Mathematics
Discret. Comput. Geom.
• 1997
If there exists a unique Euclidean sphere that is simultaneously a near support for each member of ${\cal B}'$ and a far support for the selected points are affinely independent and hence form the vertex-set of a d-simplex.
### Generalizations of the Yao-Yao partition theorem and the central transversal theorem
• Mathematics
• 2021
We generalize the Yao–Yao partition theorem by showing that for any smooth measure in Rd there exist equipartitions using (t+ 1)2d−1 convex regions such that every hyperplane misses the interior of
### Bisection of Circle Colorings
• Mathematics
• 1985
Consider $2n$ beads of k colors arranged on a necklace, using $2a$, beads of color i. A bisection is a set of disjoint strings (“intervals”) of beads whose union captures half the beads of each
### Measure partitions using hyperplanes with fixed directions
• Mathematics
• 2014
We study nested partitions of Rd obtained by successive cuts using hyperplanes with fixed directions. We establish the number of measures that can be split evenly simultaneously by taking a partition | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8599023222923279, "perplexity": 2487.865517521664}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337625.5/warc/CC-MAIN-20221005105356-20221005135356-00352.warc.gz"} |
http://www.eurotrib.com/story/2009/11/24/51137/763 | Welcome to the new version of European Tribune. It's just a new layout, so everything should work as before - please report bugs here.
## Even Monbiot
by Nomad Tue Nov 24th, 2009 at 05:11:37 AM EST
The fallout from (illegally) released emails from the Climate Research Unit (CRU) of the University of East Anglia continues to reverberate through the blogoshphere.
Monbiot has just released a scathing indictment:
Yes, the messages were obtained illegally. Yes, all of us say things in emails that would be excruciating if made public. Yes, some of the comments have been taken out of context. But there are some messages that require no spin to make them look bad. There appears to be evidence here of attempts to prevent scientific data from being released(2,3), and even to destroy material that was subject to a freedom of information request(4).
Worse still, some of the emails suggest efforts to prevent the publication of work by climate sceptics(5,6), or to keep it out of a report by the Intergovernmental Panel on Climate Change(7). I believe that the head of the unit, Phil Jones, should now resign. Some of the data discussed in the emails should be re-analysed.
Monbiot's post comes in the wake of at least two notable scientists, working in the field of climate science, who've also publicly outed some of their displeasure. Samplings below the fold.
Judith Curry, at the Georgian Institute of Technology, here:
However, even if the hacked emails from HADCRU end up to be much ado about nothing in the context of any actual misfeasance that impacts the climate data records, the damage to the public credibility of climate research is likely to be significant. In my opinion, there are two broader issues raised by these emails that are impeding the public credibility of climate research: lack of transparency in climate data, and “tribalism” in some segments of the climate research community that is impeding peer review and the assessment process.
1. Transparency. Climate data needs to be publicly available and well documented. This includes metadata that explains how the data were treated and manipulated, what assumptions were made in assembling the data sets, and what data was omitted and why. This would seem to be an obvious and simple requirement, but the need for such transparency has only been voiced recently as the policy relevance of climate data has increased. The HADCRU surface climate dataset and the paleoclimate dataset that has gone into the various “hockeystick” analyses stand out as lacking such transparency.
snip
2. Climate tribalism. Tribalism is defined here as a strong identity that separates one’s group from members of another group, characterized by strong in-group loyalty and regarding other groups differing from the tribe’s defining characteristics as inferior. In the context of scientific research, tribes differ from groups of colleagues that collaborate and otherwise associate with each other professionally.
And Hans von Storch, at the GKSS Research Centre in Germany, also pitched in:
Also mails from/to Eduardo Zorita and myself are included; also we have been subject of frequent mentioning, usually not in a flattering manner. Interesting exchanges, and evidences, are contained about efforts to destroy "Climate Research"; that we in the heydays of the hockeystick debate shared our ECHO-G data with our adversaries; and that Mike Mann was successful to exclude me from a review-type meeting on historical reconstructions in Wengen (demonstrating again his problematic but powerful role of acting as a gatekeeper.)
I would assume that more interesting issues will be found in the files, and that a useful debate about the degree of politicization of climate science will emerge. A conclusion could be that the principle, according to which data must be made public, so that also adversaries may check the analysis, must be really enforced. Another conclusion could be that scientists like Mike Mann, Phil Jones and others should no longer participate in the peer-review process or in assessment activities like IPCC.
Iffy as it feels to dig through people´s mail it has all the looks there is some incriminating stuff in there. Apparently the data code is confirming the contents of the mail.
Monbiot writes (here's the link, btw) about emails from a guy called kattweizel at a "redcar" university, neither of which seem to exist... In the long run, we're all dead. John Maynard Keynes
That was meant to be satire (it took me a while)
and I think - it refered to this character Catweazle mistakes all modern technology for powerful magic (see also Clarke's third law), particularly 'elec-trickery' (electricity) and the 'telling bone' (telephone).
That should've been there. Now added.
Newtongate: the final nail in the coffin of Renaissance and Enlightenment thinking' If you own any shares in companies that produce reflecting telescopes, use differential and integral calculus, or rely on the laws of motion, I should start dumping them NOW. The conspiracy behind the calculus myth has been suddenly, brutally and quite deliciously exposed after volumes of Newton's private correspondence were compiled and published. When you read some of these letters, you realise just why Newton and his collaborators might have preferred to keep them confidential. This scandal could well be the biggest in Renaissance science. These alleged letters - supposedly exchanged by some of the most prominent scientists behind really hard math lessons - suggest: Conspiracy, collusion in covering up the truth, manipulation of data, private admissions of flaws in their public claims and much more. But perhaps the most damaging revelations are those concerning the way these math nerd scientists may variously have manipulated or suppressed evidence to support their cause. Here are a few tasters. (...)[go read them at the link!] Gravity does not extend so far from Earth that it can be the force holding the moon to its orbit; school students are increasingly reluctant to practice differential equations, that will only lead to the practice of more oppressive forms of higher math; the tide is turning against over-regulation, like Newton's "laws" of motion and Universal Gravitation. The so called Cartesian', `skeptical' view is now also the majority view. Unfortunately we've a long way to go before the public mood (and scientific truth) is reflected by our policy makers. There are too many vested interests in classical mechanics, with far too much to lose either in terms of reputation or money, for this to end without a bitter fight. But if the Newton / Royal Society mail scandal is true, it is a blow to the Renaissance lobby's credibility which is never likely to recover. In the long run, we're all dead. John Maynard Keynes
Amusing but boring - same reason why I didn't quote the rest of Monbiot. Reaction of climate change deniers is far too predictable, and so is this. At the core lies ethics in executing science, not the entire science body of climate change, and I strive to keep that the focus of my posts here.
I agree. But reactions from both sides have been utterly predictable and boring. In the long run, we're all dead. John Maynard Keynes
Do you think that there is something in these emails that is less aggressive than what would surface had any other controversial field's private correspondence been outed? Would even cosmology or evolutionary biology, say, prove "faultless" if hit with similar exposures? At the core of this IMHO, lies the fact that science goes to great pains to project an image of detached impartiality in its inner workings, while the reality is that, as in any other human endeavour, it is a product of great and often violent clash of egos, personalities, convictions and interests. To pretend otherwise, in climate science, quantum mechanics, entomology, or surface chemistry is inviting public disenchantment. This holds even more strongly for issues that are politicized. Think "heritability of intelligence". Think "peak oil". The amazing thing is that despite all this egregious human fallibility and occasional pettiness, science works. I think that this is important to stress especially since the forces of obscurantism, especially in the US, will use such incidents not just to slander climate science, but Science in general. In this context the answer to the "scandal" is "yeah people occasionally behave badly (although I personally would protest strongly to my being judged publicly on the base of private, often casual, email exchanges), but the damn system works". The road of excess leads to the palace of wisdom - William Blake
talos:Would even cosmology or evolutionary biology, say, prove "faultless" if hit with similar exposures? Is the wrong question. Why is no one asking if the climate deniers fake their evidence, lie, manipulate the public, whore for their rich benefactors, and other questions that might be of passing interest? This is how you do a certain kind of PR - not by looking at the evidence, but by smearing the character of those involved. It's completely predictable, and it's disappointing, but not entirely surprising, that the climate science camp has been put on the defensive, when there are so many possible offensive moves that could mitigate the impact of this. But we won't get the offensive moves, because the climate scientists still think it's about the quality of the science - when it very much isn't.
Yes, good point. And the extra advantage the other side has is that, generally speaking, serious academics wouldn't strike back by, say, hacking the anti-climate change camp's emails. Lack of principle is a great PR weapon. The road of excess leads to the palace of wisdom - William Blake
Do you think that: attempts to prevent scientific data from being released(2,3), and even to destroy material that was subject to a freedom of information request(4). Worse still, some of the emails suggest efforts to prevent the publication of work by climate sceptics(5,6), or to keep it out of a report by the Intergovernmental Panel on Climate Change(7). occurs in other controversial science branches? Would it excuse the above, even when considering "violent clash of egos, personalities, convictions and interests"?
That is the real question: How much bad science was going on at the CRU? People exercising their pettiness, ire and general jerk-ness in online media is not what I, at any rate, would call an earth-shaking revelation. If there is nothing else, that part will blow over. And if you know something is crap you would try to keep it out of a serious journal out of professional courtesy alone, so the "suppression" part is not a big deal. But if they were doing tainted science... How much substance do you see in these allegations? The fact is that what we're experiencing right now is a top-down disaster. -Paul Krugman
Monbiot references all allegations with links to the contents of the emails. It's easy enough for anyone to decide for oneself how substantial these allegations are. Personally, I note that there is significant vindication for the problems and speculations Steve McIntyre has continuously posed about major publications of these scientists.
Well: I suppose yes. Especially the "efforts to prevent publication of opposing work" and keeping stuff out of official reports. It's not a question of excusing. It happens. It is unfortunate that it happens, but it happens. If any sort of illegal activity occurred it should be punished. I'm not convinced that it's happening more so in Climate Science than in other areas, however. But we will never know because it is unlikely that many other fields of inquiry provide very strong incentives for hacking personal email accounts. So I could ask: Do you think that standards of scientific conduct are more lax in climate science than in most other fields? Is legitimate research that runs counter to the reigning paradigm being silenced on a large scale? If not what else does this whole debacle teach us? The road of excess leads to the palace of wisdom - William Blake
Not exactly the type of phrase I'd pick. I'd question if holds up to science, as it has simply not been possible to reproduce or test some of the work published by the scientists mentioned in the emails. I hold reproducibility as of the key pillars of scientific method. Even before the emails were exposed, there was no "science". The emails simply confirm this.
To provide perspective, has the body of problematic findings reached even 1% of what we know happened in US Government agencies under GWB? Non-technical administrators directing scientific personnel to omit specific findings, to revise specific recommendations and to deny funding for critical investigations that might lead to the "wrong" conclusions. It must be borne in mind that that sort of intellectual climate in the USA was part of the context that led to some of the abuses found here. This is not justification but merely context. Fortunately, that seems to largely be a thing of the past in the US, for the time being. As the Dutch said while fighting the Spanish: "It is not necessary to have hope in order to persevere."
This is a horribly bad analogy that allows the author, among other things, to believe this is about science. And mixing up the difficultly level of presenting the physical sciences vs the natural sciences to the public makes me stabby. you are the media you consume.
Acquaintances of mine who previously belonged to the tin foil nut side of the climate change denial community have jumped on this as vindication for a life lived on the fringe. They now claim that this scandal "proves" that climate change is a plot to subjugate the masses to an inferior life style. It is quite distressing to see this scandal playing into the hands of such a community. Likely there are some on the denial side who do not wear tin foil hats, (i originally typed hates), but even they must be salivating. Someone please convince me there hasn't been serious damage done. As an aside, even if there were zero data to support climate change, i would be fighting just as hard against the burning of fossils and their other chemical uses, because they remain poison to humanity. "Life shrinks or expands in proportion to one's courage." - Anaïs Nin
Sigh: Perhaps one thing that becomes clear is that charges of grand conspiracies can at least be put to rest. But damage done? I'll give you the ever cheery ThatBritGuy: The populist consensus has shifted from being avidly anti-corporate and pro-green, or at least broadly sympathetic, to seeing climate issues as an evil conspiracy by evil scientists who want to raise your taxes. Outside of a few middle class holdouts, there's no longer any support at all for climate change management, or carbon rationing. This is the bullet in the head for climate change measures. Most people don't know or care about the scrappiness or internal politics of science. What they'll take home from this is that the deniers are right - the scientists have been deliberately lying to them. Of course the timing isn't a coincidence. But it doesn't matter - as of now, we have no hope at all of an effective international climate change policy. And for this generation the evil science meme is now so embedded that we may not have a policy again, even after the cities start flooding. Keep fighting CH.
Substantial policies will happen only when the Upper East Side is under water, and not before. In the long run, we're all dead. John Maynard Keynes
Oldest rhetorical trick in the book: Attack the Messenger. And we have a Real World example of why it is the oldest rhetorical trick in the book: it works. All the work the IPCC has done is now tainted. Might as well toss it in the trash can and restart. Skepticism is the first step on the road to truth. -- Denis Diderot
Does anyone imagine this is not standard behavior in the academic scientific communities? I remember one of my grad school professors explaining to us that when he evaluated NSF grant applications he could tell the quality by looking at the list of proposers and seeing if he knew them or their advisers.
Gaming funding is one thing. That's just office politics as usual. Gaming data is a whole 'nother kettle of fish. Which of those this represents is unclear to me, but if Nomad says it smells fishy, then I'm prepared to hear him out. - Jake Austerity can only be implemented in the shadow of a concentration camp.
Which of those this represents is unclear to me, but if Nomad says it smells fishy, then I'm prepared to hear him out. I guess it's time for that. Patience...
I too would be interested in any evidence these emails provide of 'gaming data'. So far none of the examples that have been making the rounds in the blogosphere (eg. the 'trick to hide the decline' email or the harry_read_me document) have been convincing. The whole affair is a pretty nasty blow in terms of PR and perceptions - unfortunately what the warmist side of this controversy have failed to understand (apart from a few people like Brad DeLong) is that they are in a memetic war. The warmists may have won in the science, but they are being rope-a-doped by the Moranos of this world. Regards Luke -- #include witty_sig.h
Climate change denier Nick Griffin to represent EU at Copenhagen | Environment | The ObserverIn a speech in the parliament last week, Griffin denounced those who warn of the consequences of climate change as "cranks". He said they had reached "an Orwellian consensus" that was "based not on scientific agreement, but on bullying, censorship and fraudulent statistics"."The anti-western intellectual cranks of the left suffered a collective breakdown when communism collapsed. Climate change is their new theology... But the heretics will have a voice in Copenhagen and the truth will out. Climate change is being used to impose an anti-human utopia as deadly as anything conceived by Stalin or Mao." En un viejo país ineficiente, algo así como España entre dos guerras civiles, poseer una casa y poca hacienda y memoria ninguna. -- Gil de Biedma
# Top Diaries
by afew - Oct 31
## Restoring Ecosystems to Reverse Global Warming
by gmoke - Oct 28
## The Center has Fallen: Polarized Pluralism and Catalan...
by ManfromMiddletown - Oct 20
## GOP Male Rep. says female Democratic candidate Ann Kuster is...
by Democrats Ramshield - Oct 31
1 comment
by gmoke - Oct 7
# Recent Diaries
by afew - Oct 31
## GOP Male Rep. says female Democratic candidate Ann Kuster is...
by Democrats Ramshield - Oct 31
1 comment
## Restoring Ecosystems to Reverse Global Warming
by gmoke - Oct 28
## The Center has Fallen: Polarized Pluralism and Catalan...
by ManfromMiddletown - Oct 20
by gmoke - Oct 7 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30698463320732117, "perplexity": 2806.303634476935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637901687.31/warc/CC-MAIN-20141030025821-00194-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=56&t=4601&p=11130 | ## HW Question 11.19
Kiana Nguyen 3C
Posts: 9
Joined: Fri Sep 26, 2014 2:02 pm
### HW Question 11.19
How can you tell if a solution is acidic, basic, or amphoteric?
The question is:
State whether the following oxides are acidic, basic, or amphoteric:
a) BaO
b) SO3
c) As2O3
d) Bi2O3
Niharika Reddy 1D
Posts: 127
Joined: Fri Sep 26, 2014 2:02 pm
### Re: HW Question 11.19
Generally, oxides of nonmetals form acidic oxides (SO3), oxides of metals form basic oxides (BaO), and oxides of the elements in and close to the diagonal line of metalloids typically form amphoteric oxides (As2O3 and Bi2O3), which can function as both an acid and a base.
Page 129 in the course reader and section 11.3 in the textbook discuss acidic, basic, and amphoteric oxides.
Hope this helps! | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9078767895698547, "perplexity": 23050.760567393787}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178362513.50/warc/CC-MAIN-20210301121225-20210301151225-00252.warc.gz"} |
http://mathhelpforum.com/calculus/36474-manipulating-series.html | 1. ## manipulating series
ok, so i am working on power series solutions to differential equations and need to get some things straight. after substituting into the in question differential equation the required power series derivatives, say there is an X^2 coefficient and i need to bring it inside one of the series; should the starting point for that series be decreased by two (because the power on X outside the series is 2 and is being added to the X^[n+s] term to make it X^[n+s+2])?
also, how do i type in formulas is there perchance a program to do this?
2. Originally Posted by mobius2000
ok, so i am working on power series solutions to differential equations and need to get some things straight. after substituting into the in question differential equation the required power series derivatives, say there is an X^2 coefficient and i need to bring it inside one of the series; should the starting point for that series be decreased by two (because the power on X outside the series is 2 and is being added to the X^[n+s] term to make it X^[n+s+2])?
also, how do i type in formulas is there perchance a program to do this?
First for La Tex use the math tages
use the $\Sigma$
button for math tags. Here is a link to La Tex code. There is a place to practice and with some basic code on this site.n You can also put your mouse above others code (or double click on it) to see others code
http://en.wikipedia.org/wiki/Help Formula
I think you mean this
$y=\sum_{n=0}^{\infty}c_nx^n$
$y'=\sum_{n=1}^{\infty}c_nnx^{n-1}$
$y'-xy=0 \iff \sum_{n=0}^{\infty}c_nx^n -x\sum_{n=1}^{\infty}c_nnx^{n-1}$
$\sum_{n=0}^{\infty}c_nx^n -\sum_{n=1}^{\infty}c_nnx^{n}=c_0+\sum_{n=1}^{\inft y}c_nx^n -\sum_{n=1}^{\infty}c_nnx^{n}=c_0+ \sum_{n=1}^{\infty}\left( c_n-c_nn\right)x^n$
I hope this helps. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9368687868118286, "perplexity": 558.5870900066196}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542244.4/warc/CC-MAIN-20161202170902-00027-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://byjus.com/maths/differential-calculus/?replytocom=158210 | # Differential Calculus
Differential calculus deals with the rate of change of one quantity with respect to another. Or you can consider it as a study of rates of change of quantities. For example, velocity is the rate of change of distance with respect to time in a particular direction. If f(x) is a function, then f'(x) = dy/dx is the differential equation, where f’(x) is the derivative of the function, y is dependent variable and x is an independent variable.
f'(x) = dy/dx ; x≠0
## Calculus Definition
In mathematics, calculus is a branch that deals with finding the different properties of integrals and derivatives of functions. It is based on the summation of the infinitesimal differences. Calculus is the study of continuous change of a function or a rate of change of a function. It has two major branches and those two fields are related to each other by the fundamental theorem of calculus. The two different branches are:
• Differential calculus
• Integral Calculus
In this article, we are going to discuss the differential calculus basics, formulas, and differential calculus examples in detail.
## Basics of Differential Calculus
In differential calculus basics, you may have learned about differential equations, derivatives, and applications of derivatives. For any given value, the derivative of the function is defined as the rate of change of functions with respect to the given values. Differentiation is a process where we find the derivative of a function. Let us discuss the important terms involved in the differential calculus basics.
Functions
A function is defined as a relation from a set of inputs to the set of outputs in which each input is exactly associated with one output. The function is represented by “f(x)”.
Dependent Variable
The dependent variable is a variable whose value always depends and determined by using the other variable called an independent variable. The dependent variable is also called the outcome variable. The result is being evaluated from the mathematical expression using an independent variable is called a dependent variable.
Independent Variable
Independent variables are the inputs to the functions that define the quantity which is being manipulated in an experiment. Let us consider an example y= 3x. Here, x is known as the independent variable and y is known as the dependent variable as the value of y is completely dependent on the value of x.
Domain and Range
The domain of a function is simply defined as the input values of a function and range is defined as the output value of a function. Take an example, if f(x) = 3x be a function, the domain values or the input values are {1, 2, 3} then the range of a function is given as
f(1) = 3(1) = 3
f(2) = 3(2) = 6
f(3) = 3(3) = 9
Therefore, the range of the function will be {3, 6, 9}.
Limits
The limit is an important thing in calculus. Limits are used to define the continuity, integrals, and derivatives in the calculus. The limit of a function is defined as follows:
Let us take the function as “f” which is defined on some open interval that contains some numbers, say “a”, except possibly at “a” itself, then the limit of a function f(x) is written as:
$$\lim_{x\rightarrow a}f(x)= L$$, iff given e > 0, there exists d > 0 such that 0 < |x – a| < d implies that |f(x) – L| < e
It means that the limit f(x) as “x” approaches “a” is “L”
Interval
An interval is defined as the range of numbers that are present between the two given numbers. intervals can be classified into two types namely:
• Open Interval – The open interval is defined as the set of all real numbers x such that a < x < b. It is represented as (a, b)
• Closed Interval – The closed interval is defined as the set of all real numbers x such that a ≤ x and x ≤ b, or more concisely, a ≤ x ≤ b, and it is represented by [a, b]
Derivatives
The fundamental tool of differential calculus is derivative. The derivative is used to show the rate of change. It helps to show the amount by which the function is changing for a given point. The derivative is called a slope. It measures the steepness of the graph of a function. It defines the ratio of the change in the value of a function to the change in the independent variable. The derivative of y with respect to x is expressed by dy/dx.
Graphically, we define a derivative as the slope of the tangent, that meets at a point on the curve or which gives derivative at the point where tangent meets the curve. Differentiation has many applications in various fields. Checking the rate of change in temperature of the atmosphere or deriving physics equations based on measurement and units, etc, are the common examples.
## Examples
1. f(x) = 6x2-2 f’(x) = 12x
2. f(x) = 2x ⇒ f’(x) = 2
3. f(x) = x3 + 2x ⇒ f’(x) = 3x2 + 2
## Differential Calculus Formulas
How do we study differential calculus? The differentiation is defined as the rate of change of quantities. Therefore, calculus formulas could be derived based on this fact. Here we have provided a detailed explanation of differential calculus which helps users to understand better.
Suppose we have a function f(x), the rate of change of a function with respect to x at a certain point ‘o’ lying in its domain can be written as;
df(x)/dx at point o
Or df/dx at o
So, if y = f(x) is a quantity, then the rate of change of y with respect to x is such that, f'(x) is the derivative of the function f(x). Also, if x and y varies with respect to variable t, then by the chain rule formula, we can write the derivative in the form of differential equations formula as;
## Applications
In mathematics, differential calculus is used,
• To find the rate of change of a quantity with respect to other
• In case of finding a function is increasing or decreasing functions in a graph
• To find the maximum and minimum value of a curve
• To find the approximate value of small change in a quantity
Real-life applications of differential calculus are:
• Calculation of profit and loss with respect to business using graphs
• Calculation of the rate of change of the temperature
• Calculation of speed or distance covered such as miles per hour, kilometres per hour, etc.,
• To derive many Physics equations
## Problems and Solutions
Go through the given differential calculus examples below:
Example 1: f(x) = 3x2-2x+1
Solution: Given, f(x) = 3x2-2x+1
Differentiating both sides, we get,
f’(x) = 6x – 2, where f’(x) is the derivative of f(x).
Example 2: f(x) = x3
Solution: We know,
$$\frac{\mathrm{d} (x^n)}{\mathrm{d} x}$$ = n xn-1
Therefore, f’(x) = $$\frac{\mathrm{d} x^3}{\mathrm{d} x}$$
f’(x)= 3 x3-1
f’(x)= 3 x2
## Frequently Asked Questions – FAQs
### What is differential calculus?
Differential calculus is a method which deals with the rate of change of one quantity with respect to another. The rate of change of x with respect to y is expressed dx/dy. It is one of the major calculus concepts apart from integrals.
### Why do we use differential calculus?
To check the instantaneous rate of change such as velocity
To evaluate the approximate value of small change in a quantity
To know if a function is increasing or decreasing functions in a graph
### What is the difference between differential calculus and integral calculus?
Differential calculus deals with the rate of change of quantity with respect to others. For example, velocity and slopes of tangent lines.
Integral calculus is a reverse method of finding the derivatives. We deal here with the total size such as area and volumes on a large scale. It is a process of finding antiderivatives.
### What are derivatives?
The derivative is simply called a slope. It measures the steepness of the graph of a function. It defines the ratio of the change in the value of a function to the change in the independent variable. The derivative is expressed by dy/dx.
### What is the differential equation?
In Maths, when one or more functions and their derivatives are related with each other to form an equation, then it is said to be a differential equation. It includes derivatives of one variable (dependent) with respect to other (independent).
For example, dy/dx=2, where y is the dependent variable and x is the independent variable.
#### 1 Comment
1. Suraj Bhumij
d/dx {k f (x)}=k d/dx g(x) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9491652250289917, "perplexity": 248.2715366857401}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323584554.98/warc/CC-MAIN-20211016074500-20211016104500-00017.warc.gz"} |
https://convexoptimization.com/wikimization/index.php?title=Linear_matrix_inequality&diff=cur&oldid=1104 | # Linear matrix inequality
(Difference between revisions)
Revision as of 18:24, 6 April 2009 (edit)← Previous diff Current revision (14:08, 21 September 2016) (edit) (undo) (→LMI Geometry) (25 intermediate revisions not shown.) Line 1: Line 1: In convex optimization, a '''linear matrix inequality (LMI)''' is an expression of the form In convex optimization, a '''linear matrix inequality (LMI)''' is an expression of the form - : $LMI(y):=A_0+y_1A_1+y_2A_2+\dots+y_m A_m\succeq0\,$ + : $LMI(y):=A_0+y_1A_1+y_2A_2+\ldots+y_m A_m\succeq0\,$ where where - * $y=[y_i\,,~i\!=\!1\dots m]$ is a real vector, + * $y=[y_i\,,~i\!=\!1\ldots m]$ is a real vector, - * $A_0\,, A_1\,, A_2\,,\dots\,A_m$ are symmetric matrices in the subspace of $n\times n$ symmetric matrices $\mathbb{S}^n$, + * $A_0\,, A_1\,, A_2\,,\ldots\,A_m$ are symmetric matrices in the subspace of $n\times n$ symmetric matrices $\mathbb{S}^n$, * $B\succeq0$ is a generalized inequality meaning $B$ is a positive semidefinite matrix belonging to the positive semidefinite cone $\mathbb{S}_+$ in the subspace of symmetric matrices $\mathbb{S}$. * $B\succeq0$ is a generalized inequality meaning $B$ is a positive semidefinite matrix belonging to the positive semidefinite cone $\mathbb{S}_+$ in the subspace of symmetric matrices $\mathbb{S}$. Line 11: Line 11: $LMI(y)\succeq 0$ is a convex constraint on ''y'' which means membership to a dual (convex) cone as we now explain: '''('''[http://meboo.convexoptimization.com/Meboo.html Dattorro, Example 2.13.5.1.1]''')''' $LMI(y)\succeq 0$ is a convex constraint on ''y'' which means membership to a dual (convex) cone as we now explain: '''('''[http://meboo.convexoptimization.com/Meboo.html Dattorro, Example 2.13.5.1.1]''')''' - Consider a peculiar vertex-description for a closed [[Convex cones|convex cone]] defined over the positive semidefinite cone + Consider a peculiar vertex-description for a [[Convex cones|convex cone]] defined over the positive semidefinite cone '''('''instead of the more common nonnegative orthant, $x\succeq0$''')''': '''('''instead of the more common nonnegative orthant, $x\succeq0$''')''': Line 18: Line 18: $\begin{array}{ll}\mathcal{K} [itex]\begin{array}{ll}\mathcal{K} - \!\!&=\left\{\left[\begin{array}{c}\langle A_1\,,\,X^{}\rangle\\\vdots\\\langle A_m\;,\,X^{}\rangle\end{array}\right]|~X\!\succeq_{\!}0\right\}\subseteq_{}\reals^m\\\\ + \!\!&=\left\{\left[\begin{array}{c}\langle A_1\,,\,X^{}\rangle\\:\\\langle A_m\;,\,X^{}\rangle\end{array}\right]|~X\!\succeq_{\!}0\right\}\subseteq_{}\mathbb{R}^m\\\\ - &=\left\{\left[\begin{array}{c}\textrm{svec}(A_1)^T\\\vdots\\\textrm{svec}(A_m)^T\end{array}\right]\!\textrm{svec}X~|~X\!\succeq_{\!}0\right\}\\\\ + &=\left\{\left[\begin{array}{c}{\text svec}(A_1)^T\\:\\{\text svec}(A_m)^T\end{array}\right]{\text svec}X~|~X\!\succeq_{\!}0\right\}\\\\ - &:=\;\{A\,\textrm{svec}X~|~X\!\succeq_{\!}0_{}\} + &:=\;\{A\,{\text svec}X~|~X\!\succeq_{\!}0_{}\} \end{array}$ \end{array}[/itex] where where *$A\!\in_{}\!\mathbb{R}^{m\times n(n+1)/2}$, *$A\!\in_{}\!\mathbb{R}^{m\times n(n+1)/2}$, - *symmetric vectorization svec is a stacking of columns defined in '''('''[http://meboo.convexoptimization.com/Meboo.html Dattorro, Ch.2.2.2.1]''')''', + *symmetric vectorization svec is a stacking of columns defined in '''('''[http://meboo.convexoptimization.com/Meboo.html Dattorro, ch.2.2.2.1]''')''', *$A_0=\mathbf{0}$ is assumed without loss of generality. *$A_0=\mathbf{0}$ is assumed without loss of generality. $\mathcal{K}$ is a [[Convex cones|convex cone]] because $\mathcal{K}$ is a [[Convex cones|convex cone]] because - $A\,\textrm{svec}{X_{{\rm p}_1}}_{\,},_{_{}}A\,\textrm{svec}{X_{{\rm p}_2}}\!\in\mathcal{K}~\Rightarrow~ + [itex]A\,{\text svec}{X_{p_1}}_{\,},_{_{}}A\,{\text svec}{X_{p_2}}\!\in\mathcal{K}~\Rightarrow~ - A(\zeta_{\,}\textrm{svec}{X_{{\rm p}_1\!}}+_{}\xi_{\,}\textrm{svec}{X_{{\rm p}_2}})\in_{}\mathcal{K} + A(\zeta_{\,}{\text svec}{X_{p_1}}+_{}\xi_{\,}{\text svec}{X_{p_2}})\in_{}\mathcal{K} - \textrm{~~for\,all~\,}\zeta_{\,},\xi\geq0$ + {\text~~for\,all~\,}\zeta_{\,},\xi\geq0[/itex] since a nonnegatively weighted sum of positive semidefinite matrices must be positive semidefinite. since a nonnegatively weighted sum of positive semidefinite matrices must be positive semidefinite. Line 39: Line 39: $\begin{array}{rl}\mathcal{K}^* [itex]\begin{array}{rl}\mathcal{K}^* - \!\!\!&=_{}\left\{_{}y~|~\langle z\,,\,y_{}\rangle\geq_{}0\,~\textrm{for\,all}~\,z\!\in_{_{}\!}\mathcal{K}_{}\right\}\subseteq_{}\reals^m\\ + \!\!\!&=_{}\left\{_{}y~|~\langle z\,,\,y_{}\rangle\geq_{}0\,~\textrm{for\,all}~\,z\!\in_{_{}\!}\mathcal{K}_{}\right\}\subseteq_{}\mathbb{R}^m\\ - &=_{}\left\{_{}y~|~\langle z\,,\,y_{}\rangle\geq_{}0\,~\textrm{for\,all}~\,z_{\!}=_{\!}A\,\textrm{svec}X\,,~X\succeq0_{}\right\}\\ + &=_{}\left\{_{}y~|~\langle z\,,\,y_{}\rangle\geq_{}0\,~\textrm{for\,all}~\,z_{\!}=_{\!}A\,{\text svec}X\,,~X\succeq0_{}\right\}\\ - &=_{}\left\{_{}y~|~\langle A\,\textrm{svec}X\,,~y_{}\rangle\geq_{}0\,~\textrm{for\,all}~\,X\!\succeq_{_{}\!}0_{}\right\}\\ + &=_{}\left\{_{}y~|~\langle A\,{\text svec}X\,,~y_{}\rangle\geq_{}0\,~\textrm{for\,all}~\,X\!\succeq_{_{}\!}0_{}\right\}\\ - &=\left\{y~|~\langle\textrm{svec}X\,,\,A^{T\!}y\rangle\geq_{}0\;~\textrm{for\,all}~\,X\!\succeq_{\!}0\right\}\\ + &=\left\{y~|~\langle{\text svec}X\,,\,A^{T\!}y\rangle\geq_{}0\;~\textrm{for\,all}~\,X\!\succeq_{\!}0\right\}\\ - &=\left\{y~|~\textrm{svec}^{-1}(A^{T\!}y)\succeq_{}0\right\} + &=\left\{y~|~{\text svec}^{-1}(A^{T\!}y)\succeq_{}0\right\} \end{array}$ \end{array}[/itex] Line 52: Line 52: This leads directly to an equally peculiar halfspace-description This leads directly to an equally peculiar halfspace-description - $\mathcal{K}^*=\{y\!\in_{}\!\mathbb{R}^m~|\,\sum\limits_{j=1}^my_jA_j\succeq_{}0_{}\}$ + $\mathcal{K}^*=\{y\!\in\mathbb{R}^m~|\,\sum\limits_{j=1}^my_jA_j\succeq_{}0_{}\}$ The summation inequality with respect to the positive semidefinite cone The summation inequality with respect to the positive semidefinite cone Line 60: Line 60: Although matrix $\,A\,$ is finite-dimensional, $\mathcal{K}$ is generally not a polyhedral cone Although matrix $\,A\,$ is finite-dimensional, $\mathcal{K}$ is generally not a polyhedral cone - (unless $\,m\,$ equals 1 or 2) simply because $\,X\!\in\mathbb{S}_+^n\,$. + (unless $\,m\,$ equals 1 or 2) simply because $\,X\!\in\mathbb{S}_+^n\,.$ - Provided the $A_j$ matrices are linearly independent, then relative interior = interior + Relative interior of $\mathcal{K}$ may always be expressed + $\textrm{rel\,int}\,\mathcal{K}=\{A\,{\text svec}X~|~X\!\succ0_{}\}.$ - $\textrm{rel\,int}\mathcal{K}=\textrm{int}\mathcal{K}$ + Provided the $\,A_j$ matrices are linearly independent, then + $\textrm{rel\,int}\,\mathcal{K}=\textrm{int}\,\mathcal{K}$ - meaning, the cone interior is nonempty; implying, the dual cone is pointed ([http://meboo.convexoptimization.com/Meboo.html Dattorro, ch.2]). + meaning, cone $\mathcal{K}$ interior is nonempty; implying, dual cone $\mathcal{K}^*$ is pointed ([http://meboo.convexoptimization.com/Meboo.html Dattorro, ch.2]). - If matrix $\,A\,$ has no nullspace, on the other hand, then + If matrix $\,A\,$ has no nullspace, then - $\,A\,\textrm{svec}X\,$ is an isomorphism in $\,X\,$ between the positive semidefinite cone $\mathbb{S}_+^n$ and range $\,\mathcal{R}(A)\,$ of matrix $\,A$. + $\,A\,{\text svec}X\,$ is an isomorphism in $\,X\,$ between the positive semidefinite cone $\mathbb{S}_+^n$ and range $\,\mathcal{R}(A)\,$ of matrix $\,A.$ - In that case, [[Convex cones|convex cone]] $\,\mathcal{K}\,$ has relative interior + That is sufficient for [[Convex cones|convex cone]] $\,\mathcal{K}\,$ to be closed, and necessary to have relative boundary + $\textrm{rel}\,\partial^{}\mathcal{K}=\{A\,{\text svec}X~|~X\!\succeq0\,,~X\!\not\succ_{\!}0_{}\}.$ - $\textrm{rel\,int}\mathcal{K}=\{A\,\textrm{svec}X~|~X\!\succ_{\!}0_{}\}$ +
+ Relative interior of the dual cone may always be expressed + $\textrm{rel\,int}\,\mathcal{K}^*=\{y\!\in_{}\!\mathbb{R}^m~|\,\sum\limits_{j=1}^my_jA_j\succ_{}0_{}\}.$ - and boundary + When the $A_j$ matrices are linearly independent, function $\,g(y)_{\!}:=_{_{}\!}\sum y_jA_j\,$ is a linear bijection on $\mathbb{R}^m.$ - + - $\textrm{rel}\,\partial^{}\mathcal{K}=\{A\,\textrm{svec}X~|~X\!\succeq_{\!}0\,,~X\!\nsucc_{\!}0_{}\}$ + - + -
When the $A_j$ matrices are linearly independent, function $\,g(y)_{\!}:=_{_{}\!}\sum y_jA_j\,$ on $\mathbb{R}^m$ is a linear bijection. + Inverse image of the positive semidefinite cone under $\,g(y)\,$ Inverse image of the positive semidefinite cone under $\,g(y)\,$ - must therefore have dimension $_{}m$. + must therefore have dimension equal to $\dim\!\left(\mathcal{R}(A^{\rm T})_{}\!\cap{\text svec}\,\mathbb{S}_+^{_{}n}\right)$ - + - In that circumstance, the dual cone interior is nonempty + - $\textrm{int}\mathcal{K}^*=\{y\!\in_{}\!\mathbb{R}^m~|\,\sum\limits_{j=1}^my_jA_j\succ_{}0_{}\}$ + and relative boundary + $\textrm{rel\,}\partial^{}\mathcal{K}^*=\{y\!\in_{}\!\mathbb{R}^m~|\,\sum\limits_{j=1}^my_jA_j\succeq_{}0\,,~\sum\limits_{j=1}^my_jA_j\not\succ0_{}\}.$ - having boundary + When this dimension is $\,m\,$, the dual cone interior is nonempty + $\textrm{rel\,int}\,\mathcal{K}^*=\textrm{int}\,\mathcal{K}^*$ - $\partial^{}\mathcal{K}^*=\{y\!\in_{}\!\mathbb{R}^m~|\,\sum\limits_{j=1}^my_jA_j\succeq_{}0\,,~\sum\limits_{j=1}^my_jA_j\nsucc_{}0_{}\}$ + and closure of convex cone $\mathcal{K}$ is pointed. == Applications == == Applications == Line 97: Line 98: == External links == == External links == - * S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, [http://www.stanford.edu/~boyd/lmibook/ Linear Matrix Inequalities in System and Control Theory] + * S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, [http://www.stanford.edu/~boyd/lmibook Linear Matrix Inequalities in System and Control Theory] - * C. Scherer and S. Weiland [http://www.dcsc.tudelft.nl/~cscherer/2416/lmi.html Course on Linear Matrix Inequalities in Control], Dutch Institute of Systems and Control (DISC). + * C. Scherer and S. Weiland, [http://w3.ele.tue.nl/nl/cs/education/courses/hyconlmi Course on Linear Matrix Inequalities in Control], Dutch Institute of Systems and Control (DISC).
## Current revision
In convex optimization, a linear matrix inequality (LMI) is an expression of the form
$LaTeX: LMI(y):=A_0+y_1A_1+y_2A_2+\ldots+y_m A_m\succeq0\,$
where
• $LaTeX: y=[y_i\,,~i\!=\!1\ldots m]$ is a real vector,
• $LaTeX: A_0\,, A_1\,, A_2\,,\ldots\,A_m$ are symmetric matrices in the subspace of $LaTeX: n\times n$ symmetric matrices $LaTeX: \mathbb{S}^n$,
• $LaTeX: B\succeq0$ is a generalized inequality meaning $LaTeX: B$ is a positive semidefinite matrix belonging to the positive semidefinite cone $LaTeX: \mathbb{S}_+$ in the subspace of symmetric matrices $LaTeX: \mathbb{S}$.
This linear matrix inequality specifies a convex constraint on y.
## Convexity of the LMI constraint
$LaTeX: LMI(y)\succeq 0$ is a convex constraint on y which means membership to a dual (convex) cone as we now explain: (Dattorro, Example 2.13.5.1.1)
Consider a peculiar vertex-description for a convex cone defined over the positive semidefinite cone
(instead of the more common nonnegative orthant, $LaTeX: x\succeq0$):
for $LaTeX: X\!\in\mathbb{S}^n$ given $LaTeX: \,A_j\!\in\mathbb{S}^n$, $LaTeX: \,j\!=\!1\ldots m$
$LaTeX: \begin{array}{ll}\mathcal{K} \!\!&=\left\{\left[\begin{array}{c}\langle A_1\,,\,X^{}\rangle\\:\\\langle A_m\;,\,X^{}\rangle\end{array}\right]|~X\!\succeq_{\!}0\right\}\subseteq_{}\mathbb{R}^m\\\\ &=\left\{\left[\begin{array}{c}{\text svec}(A_1)^T\\:\\{\text svec}(A_m)^T\end{array}\right]{\text svec}X~|~X\!\succeq_{\!}0\right\}\\\\ &:=\;\{A\,{\text svec}X~|~X\!\succeq_{\!}0_{}\} \end{array}$
where
• $LaTeX: A\!\in_{}\!\mathbb{R}^{m\times n(n+1)/2}$,
• symmetric vectorization svec is a stacking of columns defined in (Dattorro, ch.2.2.2.1),
• $LaTeX: A_0=\mathbf{0}$ is assumed without loss of generality.
$LaTeX: \mathcal{K}$ is a convex cone because
$LaTeX: A\,{\text svec}{X_{p_1}}_{\,},_{_{}}A\,{\text svec}{X_{p_2}}\!\in\mathcal{K}~\Rightarrow~ A(\zeta_{\,}{\text svec}{X_{p_1}}+_{}\xi_{\,}{\text svec}{X_{p_2}})\in_{}\mathcal{K} {\text~~for\,all~\,}\zeta_{\,},\xi\geq0$
since a nonnegatively weighted sum of positive semidefinite matrices must be positive semidefinite.
Now consider the (closed convex) dual cone:
$LaTeX: \begin{array}{rl}\mathcal{K}^* \!\!\!&=_{}\left\{_{}y~|~\langle z\,,\,y_{}\rangle\geq_{}0\,~\textrm{for\,all}~\,z\!\in_{_{}\!}\mathcal{K}_{}\right\}\subseteq_{}\mathbb{R}^m\\ &=_{}\left\{_{}y~|~\langle z\,,\,y_{}\rangle\geq_{}0\,~\textrm{for\,all}~\,z_{\!}=_{\!}A\,{\text svec}X\,,~X\succeq0_{}\right\}\\ &=_{}\left\{_{}y~|~\langle A\,{\text svec}X\,,~y_{}\rangle\geq_{}0\,~\textrm{for\,all}~\,X\!\succeq_{_{}\!}0_{}\right\}\\ &=\left\{y~|~\langle{\text svec}X\,,\,A^{T\!}y\rangle\geq_{}0\;~\textrm{for\,all}~\,X\!\succeq_{\!}0\right\}\\ &=\left\{y~|~{\text svec}^{-1}(A^{T\!}y)\succeq_{}0\right\} \end{array}$
that follows from Fejer's dual generalized inequalities for the positive semidefinite cone:
• $LaTeX: Y\succeq0~\Leftrightarrow~\langle Y\,,\,X\rangle\geq0\;~\textrm{for\,all}~\,X\succeq0$
This leads directly to an equally peculiar halfspace-description
$LaTeX: \mathcal{K}^*=\{y\!\in\mathbb{R}^m~|\,\sum\limits_{j=1}^my_jA_j\succeq_{}0_{}\}$
The summation inequality with respect to the positive semidefinite cone is known as a linear matrix inequality.
## LMI Geometry
Although matrix $LaTeX: \,A\,$ is finite-dimensional, $LaTeX: \mathcal{K}$ is generally not a polyhedral cone (unless $LaTeX: \,m\,$ equals 1 or 2) simply because $LaTeX: \,X\!\in\mathbb{S}_+^n\,.$
Relative interior of $LaTeX: \mathcal{K}$ may always be expressed $LaTeX: \textrm{rel\,int}\,\mathcal{K}=\{A\,{\text svec}X~|~X\!\succ0_{}\}.$
Provided the $LaTeX: \,A_j$ matrices are linearly independent, then $LaTeX: \textrm{rel\,int}\,\mathcal{K}=\textrm{int}\,\mathcal{K}$
meaning, cone $LaTeX: \mathcal{K}$ interior is nonempty; implying, dual cone $LaTeX: \mathcal{K}^*$ is pointed (Dattorro, ch.2).
If matrix $LaTeX: \,A\,$ has no nullspace, then $LaTeX: \,A\,{\text svec}X\,$ is an isomorphism in $LaTeX: \,X\,$ between the positive semidefinite cone $LaTeX: \mathbb{S}_+^n$ and range $LaTeX: \,\mathcal{R}(A)\,$ of matrix $LaTeX: \,A.$
That is sufficient for convex cone $LaTeX: \,\mathcal{K}\,$ to be closed, and necessary to have relative boundary $LaTeX: \textrm{rel}\,\partial^{}\mathcal{K}=\{A\,{\text svec}X~|~X\!\succeq0\,,~X\!\not\succ_{\!}0_{}\}.$
Relative interior of the dual cone may always be expressed $LaTeX: \textrm{rel\,int}\,\mathcal{K}^*=\{y\!\in_{}\!\mathbb{R}^m~|\,\sum\limits_{j=1}^my_jA_j\succ_{}0_{}\}.$
When the $LaTeX: A_j$ matrices are linearly independent, function $LaTeX: \,g(y)_{\!}:=_{_{}\!}\sum y_jA_j\,$ is a linear bijection on $LaTeX: \mathbb{R}^m.$
Inverse image of the positive semidefinite cone under $LaTeX: \,g(y)\,$ must therefore have dimension equal to $LaTeX: \dim\!\left(\mathcal{R}(A^{\rm T})_{}\!\cap{\text svec}\,\mathbb{S}_+^{_{}n}\right)$
and relative boundary $LaTeX: \textrm{rel\,}\partial^{}\mathcal{K}^*=\{y\!\in_{}\!\mathbb{R}^m~|\,\sum\limits_{j=1}^my_jA_j\succeq_{}0\,,~\sum\limits_{j=1}^my_jA_j\not\succ0_{}\}.$
When this dimension is $LaTeX: \,m\,$, the dual cone interior is nonempty $LaTeX: \textrm{rel\,int}\,\mathcal{K}^*=\textrm{int}\,\mathcal{K}^*$
and closure of convex cone $LaTeX: \mathcal{K}$ is pointed.
## Applications
There are efficient numerical methods to determine whether an LMI is feasible (i.e., whether there exists a vector $LaTeX: y$ such that $LaTeX: LMI(y)\succeq0$ ), or to solve a convex optimization problem with LMI constraints. Many optimization problems in control theory, system identification, and signal processing can be formulated using LMIs. The prototypical primal and dual semidefinite program are optimizations of a real linear function respectively subject to the primal and dual convex cones governing this LMI. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 52, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.950924277305603, "perplexity": 806.4860625848438}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305288.57/warc/CC-MAIN-20220127193303-20220127223303-00594.warc.gz"} |
https://arxiv.org/abs/0902.3200 | nucl-th
(what is this?)
# Title: On the Methods for Constructing Meson-Baryon Reaction Models within Relativistic Quantum Field Theory
Abstract: Within the relativistic quantum field theory, we analyze the differences between the $\pi N$ reaction models constructed from using (1) three-dimensional reductions of Bethe-Salpeter Equation, (2) method of unitary transformation, and (3) time-ordered perturbation theory. Their relations with the approach based on the dispersion relations of S-matrix theory are dicusssed.
Subjects: Nuclear Theory (nucl-th) Journal reference: Chin.J.Phys.47:142-158,2009 Cite as: arXiv:0902.3200 [nucl-th] (or arXiv:0902.3200v1 [nucl-th] for this version)
## Submission history
From: Bruno Julia Diaz [view email]
[v1] Wed, 18 Feb 2009 17:28:07 GMT (15kb) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.453315794467926, "perplexity": 8541.255253022291}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121216.64/warc/CC-MAIN-20170423031201-00109-ip-10-145-167-34.ec2.internal.warc.gz"} |
http://mathhelpforum.com/higher-math/214492-log-question.html | # Math Help - Log question
1. ## Log question
Please can someone help with this problem: solve $2^2^x^+^1 - 5 (2^x) + 2 = 0$ Now we were told to let y=2 but I can't figure out where the y is coming from? Is it just as a function of x?
Kris
2. ## Re: Log question
You might have misread your book and it is telling you to make the substitution y=2x
If not, do that substitution anyway and solve for y, after you have solved for y then finish by using it to find x
Hint: 22x+1=2(2x)2
Edit: Beat plato by 1 minute :P
3. ## Re: Log question
Originally Posted by Krislton
Please can someone help with this problem: solve 2^(2x+1) - 5 (2^x) + 2 = 0. Now we were told to let y=2 but I can't figure out where the y is coming from? Is it just as a function of x?
If we let $y=2^x$ that equation becomes $2y^2-5y+2=0$.
4. ## Re: Log question
Originally Posted by Shakarri
You might have misread your book and it is telling you to make the substitution y=2x
If not, do that substitution anyway and solve for y
Hint: 22x+1=2(2x)2
Yeah I think your correct, but I'm still useless at logs! Its not from a text book, but from an old exam paper I need to get to grips with ASAP. Once re-arranged how you've done it, Should I then apply logs to both sides?
Thanks for your help,
Kris.
5. ## Re: Log question
Originally Posted by Plato
If we let $y=2^x$ that equation becomes $2y^2-5y+2=0$.
Thanks, it kind of makes sense but if substituting 2^x = y, how can you sub that for 2x when that's not to the power unlike the other term.
6. ## Re: Log question
Hello, Krislton!
Evidently you don't understand the hint or the suggestions.
I'll give you a walk-through . . .
$\text{Solve: }\:2^{2x+1} - 5 (2^x) + 2 \:=\: 0$
We have: . $2^{2x+1} - 5(2^x) + 2 \;=\;0$
. . . . . . . . $2^{2x}\!\cdot\! 2^1 - 5(2^x) + 2 \;=\;0$
. . . . . . . . $2(2^x)^2 - 5(2^x) + 2 \;=\;0$
Let $y = 2^x\!:\qquad 2y^2 - 5y + 2 \;=\;0$
Factor: . . . . $(y-2)(2y-1) \;=\;0$
And we have: . $y = 2,\;y = \tfrac{1}{2}$
Back-substitute: . $\begin{Bmatrix}2^x \,=\,2 & \Rightarrow & 2^x \,=\,2^1 & \Rightarrow & x \,=\,1 \\ \\[-3mm] 2^x \,=\,\frac{1}{2} & \Rightarrow & 2^x \,=\,2^{\text{-}1} & \Rightarrow & x \,=\,\text{-}1 \end{Bmatrix}$
7. ## Re: Log question
Originally Posted by Soroban
Hello, Krislton!
Evidently you don't understand the hint or the suggestions.
I'll give you a walk-through . . .
We have: . $2^{2x+1} - 5(2^x) + 2 \;=\;0$
. . . . . . . . $2^{2x}\!\cdot\! 2^1 - 5(2^x) + 2 \;=\;0$
. . . . . . . . $2(2^x)^2 - 5(2^x) + 2 \;=\;0$
Let $y = 2^x\!:\qquad 2y^2 - 5y + 2 \;=\;0$
Factor: . . . . $(y-2)(2y-1) \;=\;0$
And we have: . $y = 2,\;y = \tfrac{1}{2}$
Back-substitute: . $\begin{Bmatrix}2^x \,=\,2 & \Rightarrow & 2^x \,=\,2^1 & \Rightarrow & x \,=\,1 \\ \\[-3mm] 2^x \,=\,\frac{1}{2} & \Rightarrow & 2^x \,=\,2^{\text{-}1} & \Rightarrow & x \,=\,\text{-}1 \end{Bmatrix}$
Perfect, thanks very much I understand now! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 20, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9792251586914062, "perplexity": 976.7493560022056}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657135080.9/warc/CC-MAIN-20140914011215-00182-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://community.verizonwireless.com/t5/My-Verizon/How-often-is-the-quot-Usage-quot-meter-updated/m-p/905693/highlight/true | cancel
Showing results for
Did you mean:
## How often is the "Usage" meter updated?
Member
How often is the "Usage" meter updated?
Labels (1)
Tags (5)
1 Solution
Highlighted
## Re: How often is the "Usage" meter updated?
Sr. Member
can be 2hrs to 24 or 48hrs ...for roaming it can be up to 3-5 days for update
3 Replies
Highlighted
## Re: How often is the "Usage" meter updated?
Sr. Member
can be 2hrs to 24 or 48hrs ...for roaming it can be up to 3-5 days for update
## Re: How often is the "Usage" meter updated?
Member
Thank you for the reply. Today is the last day of my billing cycle and the Usage bar claims that I still have a gig of data left to use. I do not want the surprise charge of a ridiculous extra \$15 to hit me for going 1KB over limit. I think it's rather pathetic we cannot get real-time usage.
## Re: How often is the "Usage" meter updated?
Sr. Member
check data usage with dialing #3282 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9320536255836487, "perplexity": 9401.554322953072}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540495263.57/warc/CC-MAIN-20191207032404-20191207060404-00111.warc.gz"} |
https://math.stackexchange.com/questions/2812321/how-do-i-find-a-point-from-a-given-distance-from-some-point | # How do I find a point from a given distance from some point
I have a point $(x_1, y_1)$, distance $d$ and a slope $m$ of line $l$.
Now I wanna find another point $(x_2, y_2)$ that's $d$ distance away from $(x_1, y_1)$.
Point $(x_1, y_1), (x_2, y_2)$ are both on the line $l$.
I found some similar questions but I didn't understand it, and none of them worked with the line slope Finding a point along a line a certain distance away from another point!
• The post you are pointing at does give the solution ! – Yves Daoust Jun 8 '18 at 10:15
• @YvesDaoust Nah not really, it works with start point and end point not with the slope tho. – Basma Ashour Jun 8 '18 at 10:18
• Did you read the OP ? The formula with the slope is given. – Yves Daoust Jun 8 '18 at 10:38
Slope $m$ means that $\frac{y_2-y_1}{x_2-x_1}=m$. This gives You one equation. Another equation comes from $(y_2-y_1)^2+(x_2-x_1)^2=d^2$. Two equations for two variables - You only have to solve the system. It is not very easy in general form, but if $m$ and $d$ are given as numbers it's simple. You have from the first equation: $y_2=y_1+m(x_2-x_1)$, You can insert this in the second one. The result is $(m^2+1)(x_2-x_1)^2=d^2$. From here You can find $x_2$ and then $y_2$.
• Thank you so much for your help ^^ – Basma Ashour Jun 8 '18 at 9:57
One (possibly not the simplest) way is as follows:
Write parametric equations for your line $\ell$: $$x=x_1+lt,\qquad y=y_1+mt$$ where $(l,m)$ is a vector parallel to $\ell$ (to find it, just take any point $(\bar x,\bar y)$ on $\ell$ and let $l=\bar x-x_1$, $m=\bar y-y_1$).
Then renormalize $(l,m)$ so that $l^2+m^2=1$.
Done that, the points you are looking for are those corresponding to the value of the parameter $t=\pm d$.
• Thank you so much :") – Basma Ashour Jun 8 '18 at 9:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.893907904624939, "perplexity": 294.81016454172857}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195524972.66/warc/CC-MAIN-20190716221441-20190717003111-00032.warc.gz"} |
http://www.researchgate.net/institution/Newcastle_University/department/School_of_Mathematics_and_Statistics | # School of Mathematics and Statistics
586.30
3.05
257
## Member activityView all
• ##### Article: The K\
[hide abstract]
ABSTRACT: We consider complexes $(\X, d)$ of nuclear Fr\'echet spaces and continuous boundary maps $d_n$ with closed ranges and prove that, up to topological isomorphism, $(H_{n}(\X, d))^*$ $\iso$ $H^{n}(\X^*,d^*),$ where $(H_{n}(\X,d))^*$ is the strong dual space of the homology group of $(\X,d)$ and $H^{n}(\X^*,d^*)$ is the cohomology group of the strong dual complex $(\X^*,d^*)$. We use this result to establish the existence of topological isomorphisms in the K\"{u}nneth formula for the cohomology of complete nuclear $DF$-complexes and in the K\"{u}nneth formula for continuous Hochschild cohomology of nuclear $\hat{\otimes}$-algebras which are Fr\'echet spaces or $DF$-spaces for which all boundary maps of the standard homology complexes have closed ranges. We describe explicitly continuous Hochschild and cyclic cohomology groups of certain tensor products of $\hat{\otimes}$-algebras which are Fr\'echet spaces or nuclear $DF$-spaces.
• Source
##### Article: Dark soliton dynamics in confined Bose-Einstein condensates
[hide abstract]
ABSTRACT: Dilute atomic Bose-Einstein condensates are inherently nonlinear systems and support solitary wave solutions. An important distinction from optical systems is the inhomogeneous background density, which results from the traps used to confine the atoms. As in optical systems, dark solitary waves in three- dimensional geometries are unstable to transverse excitations, which lead to a bending of the dark soliton plane and decay into vortex rings. Highly elon- gated geometries can now be achieved experimentally, in which the condensate dynamics are eectively one-dimensional, and the motion of the dark soliton is governed by the inhomogeneous longitudinal density. We show that a dark soliton is fundamentally unstable to such a changing background density, by means of numerical simulations of the soliton under various potentials (e.g. steps, ramps, harmonic traps, and optical lattices). This leads to the emission of radiation in the form of sound waves. The power emitted is found to be proportional to the square of the soliton acceleration. The latter quantity is shown to be proportional to the deformation of the apparent soliton profile, arising from the sound field in the region of the soliton. We demonstrate that the ensuing interactions between the soliton and sound field, and therefore the dynamics of the soliton, can be controlled experimentally via manipulation of the emitted sound, achieved by modifying the trap geometry. In this manner, it is possible to induce a rapid decay of the soliton, stabilise the soliton, or even pump energy into the soliton by means of parametric driving.
ABSTRACT: We analyse a special case of the robust stabilization problem under structured uncertainty. We obtain a new criterion for the solvability of the spectral Nevanlinna-Pick problem, which is a special case of the $\mu$-synthesis problem of $H^\infty$ control in which $\mu$ is the spectral radius. Given $n$ distinct points $\la_1,\dots,\la_n$ in the unit disc and $2\times 2$ nonscalar complex matrices $W_1,\dots,W_n$, the problem is to determine whether there is an analytic $2\times 2$ matrix function $F$ on the disc such that $F(\la_j)=W_j$ for each $j$ and the supremum of the spectral radius of $F(\la)$ is less than 1 for $\la$ in the disc. The condition is that the minimum of a quadratic function of pairs of positive $3n$-square matrices subject to certain linear matrix inequalities in the data be attained and be zero. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9330836534500122, "perplexity": 284.37657063221013}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163848048/warc/CC-MAIN-20131204133048-00033-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://www.perimeterinstitute.ca/people/Keith-Copsey | # Keith Copsey
University of Waterloo
Areas of Research:
Phone: x8076
## Research Interests
My research has focused on the gravitational aspects of string theory in both AdS/CFT and cosmology. In AdS/CFT I have generally been involved in examining and testing the correspondence beyond the protection of supersymmetry by both modifying boundary conditions and studying non-supersymmetric spacetimes with striking properties using the usual supersymmetric boundary conditions. In particular I have recently been involved in showing that the current constructions of asymptotically Lifshitz spacetimes, conjectured to be dual descriptions of relatively common condensed matter systems, suffer from a subtle inner singularity that can not be resolved by standard string theory effects and that imposing the usual boundary conditions forbids generic perturbations to the spacetime deep in the bulk. Cosmologically I am interested in singularity resolution, inflation and possible alternatives to inflation, de Sitter in string theory, and understanding the extent to which a string theory landscape exists. I have recently pointed out that the usual methods constructing purportedly long-lived de Sitter vacua actually result in relatively rapidly decaying states, once gravity and some technical subtleties are taken into account. As a result, it is not clear that any constructions currently understood result in long-lived de Sitter vacua, let alone large families of such solutions.
## Positions Held
• 2007-2010 Postdoctoral Fellow, University of Waterloo
## Recent Publications
• K. Copsey and R. B. Mann, Pathologies in Asymptotically Lifshitz Spacetimes,'' arXiv: 1011.3502 JHEP {\bf 1103} (2011) 039
• K. Copsey, Gravitation and tunnelling: Subtleties of the thin-wall approximation and rapid decays,'' arXiv: 1108.2255
## Seminars
• Lifshitz spacetimes: a cautionary tale,'' Black Holes VIII, Niagara Falls
• New puzzles for AdS/CFT: Bubble Trouble,'' USC
• New puzzles for AdS/CFT: Bubble Trouble,'' UCLA
• New puzzles for AdS/CFT: Bubble Trouble,'' Durham University
• New puzzles for AdS/CFT: Bubble Trouble,'' Imperial College, London
• Higher dimensional gravity, bubbles, and new puzzles for AdS/CFT,'' DAMTP, Cambridge
• PIRSA:11080145, Gravity and Rapid Tunnelling, 2011-08-24, Cosmology Talks
• Gravity and Rapid Tunnelling'', 2011-08-26, Strings group meeting
• "Gravitation and tunneling: Subtleties of the thin wall approximation and rapid decays" 2011-05-05, Cosmology group meeting
• Pathologies in Asymptotically Lifshitz Spacetimes,'' 2010-11-18, Strings group meeting
• PIRSA:08060167, Bubbles of Nothing and Violations of the Energy Conditions in AdS-CFT, 2008-06-06, PASCOS 08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4579210579395294, "perplexity": 7332.556165006777}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257827079.61/warc/CC-MAIN-20160723071027-00105-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://www.hackmath.net/en/math-problem/21503 | # Embankment
The railway embankment 300 m long has a cross-section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m3 of soil is in the embankment?
V = 13200 m3
### Step-by-step explanation:
Did you find an error or inaccuracy? Feel free to write us. Thank you!
Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.
Pythagorean theorem is the base for the right triangle calculator.
#### You need to know the following knowledge to solve this word math problem:
We encourage you to watch this tutorial video on this math problem:
## Related math problems and questions:
• Railway embankment
The railway embankment section is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m, and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
Road embankment has a cross-section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters?
• Embankment
Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long.
• The ditch
Ditch with a cross-section of an isosceles trapezoid with bases 2m and 6m are deep 1.5m. How long is the slope of the ditch?
• Isosceles trapezoid
The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
• Tent
Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
• Isosceles trapezoid
Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
• Land - isosceles trapezoid
Calculate the building plot's content and perimeter in the form of an isosceles trapezoid with bases 120m, 95m, and height 50m.
• Classic tent
The tent has the shape of a triangular prism. The front and rear walls are isosceles triangles with a height of 18 dm and arms 19.5 dm long. The tent is 1.5 m wide and 2 m long. How many square meters of fabric is needed to make a tent? How much air is in
• Pipes
The water pipe has a cross-section 1087 cm2. An hour has passed 960 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 9 hours if water flows the same speed?
• Isosceles + prism
Calculate the volume of the perpendicular prism if its height is 17.5 cm and the base is an isosceles triangle with a base length of 5.8 cm and an arm length of 3.7 cm
• Digging a pit
The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Determine how many m3 of soil were excavated when digging the pit?
• Estate
An estate-shaped rectangular trapezoid has bases long 34 m, 63 m, and perpendicular arm 37 m. Calculate how long its fence is.
• Chocolate roll
The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross-section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm? You know that 100 g of this
• Square prism
Calculate the volume of a four-sided prism 2 dm high, and the base is a trapezoid with bases 12 cm, 6 cm, the height of 4 cm, and 5 cm long arms.
• Water channel
The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flo
• Axial section of the cone
The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.857260525226593, "perplexity": 873.595793038088}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585537.28/warc/CC-MAIN-20211023002852-20211023032852-00394.warc.gz"} |
http://www.khalisi.com/projects/mass-segregation.html | # Mass Segregation in Stellar Clusters
Stars are usually formed in the community of clusters, which may range from small associations of some tens of stars to very dense and rich ones containing some thousand stars such as the Trapezium in the Orion Nebula Cloud. The most massive stars are often found near the cluster centres, indicating an undergone process of mass segregation. There are two different physical explanations for the mechanism: On one hand side, the fragmentation of a star forming cloud occurs with tendency of the high mass stars forming near the bottom of the potential well due to the accelerated accretion of more and more gas; they remain near their place of birth at the cluster centre from the early stages of the star forming scenario. On the other hand, massive stars may form elsewhere and sink to the centre through two-body relaxation after the formation process has already finished. Both mechanisms are reasonable, but they should differ in the time scales until the cluster achieves its observed radial mass stratification. Dynamical models are challenged to answer this question by comparison with models of star formation. The core of the Trapezium showing the four energetic massive stars and a plethora of Sun-like stars with surrounding extended emission.
In the idealized case of two different masses present, two parameters govern the segregation process: The fraction of all heavy masses to the total cluster mass, q, and the ratio of the individual particle masses, \mu. The two parameters are linked by the formula:
This inequation is called the "stability criterion". If it is fullfilled, then the heavy and the light particles will find an energetic equilibrium, and the cluster will evolve stable; if not, then the two mass components will have a decoupled evolution, where the heavy masses sink rapidly to the centre and make up an own subsystem.
The graphic shows the evolution of the average mass in specified spherical shells around the cluster centre. The increase of the mean mass in the innermost shells is clearly visible, indicating a high fraction of heavy masses. This simulation was performed with two types of stars: The heavy ones were twice as massive as the light ones (\mu = 2.0), and their total fraction was 10% of the cluster's mass (q = 0.1). The data at each time point were averaged over 20 runs differing by a random initial setup of positions. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8652777671813965, "perplexity": 760.5986067300802}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249495888.71/warc/CC-MAIN-20190223082039-20190223104039-00148.warc.gz"} |
https://chemistry.stackexchange.com/questions/104898/does-the-nernst-equation-suggest-voltaic-cell-voltage-remains-constant-over-time | # Does the Nernst equation suggest voltaic cell voltage remains constant over time?
Say the following reactions are occurring in my voltaic cell:
$$\ce{Mg->Mg^{2+} + 2e- +2.36V}$$ $$\ce{Cu^{2+} +2e-->Cu -0.34V}$$
Then, the Nernst equation would become:
$$E_{cell}=2.70-\frac{RT}{nF}ln\frac{[Mg^{2+}]}{[Cu^{2+}]}$$
However, if the initial volumes and concentrations of the copper and magnesium solutions were equal, the fraction within the natural logarithm would constantly equal 1.
Does this mean there is no change in voltage as the concentrations decrease, or did I understand something wrong?
• You got it wrong. As the reaction progresses, [Mg2+] changes; so does [Cu2+], and also their ratio, and also ln thereof. – Ivan Neretin Nov 27 '18 at 6:07
• @IvanNeretin thank you, I just realised I was thinking of the Mg2+ and Cu ratio – George Tian Nov 27 '18 at 6:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9772982001304626, "perplexity": 1319.716500835388}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583661083.46/warc/CC-MAIN-20190119014031-20190119040031-00585.warc.gz"} |
http://mathoverflow.net/users/35626/the-masked-avenger | less info
reputation
1515
bio website location age member for 1 year, 9 months seen 52 mins ago profile views 1,639
I am interested in multiperfect numbers, graph theory, and some of the simpler aspects of model theory and general algebra.
20 Why are polynomials so useful in mathematics? 13 Arbitrarily long arithmetic progressions 6 Can We Decide Whether Small Computer Programs Halt? 5 Parodies of abstruse mathematical writing 5 Relationship between triangle free graphs and their minimum degree
84 Tags
30 nt.number-theory × 19 15 graph-theory × 10 18 prime-numbers × 8 12 mg.metric-geometry × 8 16 co.combinatorics × 17 11 universal-algebra × 5 16 lo.logic × 5 11 computer-science × 3 16 arithmetic-progression × 3 8 algorithms × 7
1 Account
MathOverflow 1,389 rep 1515 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46463602781295776, "perplexity": 7206.97521572796}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131297622.30/warc/CC-MAIN-20150323172137-00031-ip-10-168-14-71.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/802161/finding-the-second-derivative-of-a-first-derivative/802166 | # Finding the second derivative of a first derivative.
so I have a $\frac{ dy}{dx}=\frac{-2x+y}{2y-x}$ from the original equation $\ x^2+y^2-xy=1 \$.
I have to find the second derivative given a coordinate point $\left(\sqrt{\frac{1}{3}},2\sqrt{ \frac{1}{3}})\right)$. Here is my work:
$$\frac{d^2y}{dx^2} = \frac{(2y-x)(-2+y')-(-2x+y)(2y'-1)}{(2y-x)^2}$$
$$=\frac{(2y-x)\left(-2+\frac{-2x+y}{2y-x}\right)-(-2x+y)(\frac{-4x+2y}{2y-x}-1)}{(2y-x)^2}$$
then I started plugging in,
$$=\frac{\left(\frac{4}{\sqrt{3}}\right)-\frac{1}{\sqrt{3}}\left(-x+\frac{-2\sqrt{1/3}+2\sqrt{1/3}}{4\sqrt{1/3}-\sqrt{1/3}}\right)-[(-2\sqrt{1/3}+2\sqrt{1/3}\left(2[\frac{-2\sqrt{1/3}+2\sqrt{1/3}}{4\sqrt{1/3}-\sqrt{1/3}}]-1\right)]}{(4\sqrt{1/3}-\sqrt{1/3})^2}$$
Some of the expressions cancelled out to be 0, so I ended up with
$$\frac{d^2y}{dx^2}=\frac{3\sqrt{1/3}}{(3\sqrt{1/3})^2}=\frac{1}{\sqrt{3}}.$$ However, this wasn't the right answer. Is there an easier approach or something wrong with my calculation? Thank you.
-
This is completely unintelligible! You need to edit this using latex. You can find the tutorial here. – homegrown May 19 '14 at 23:39
I have made a first cut at making this a bit more readable; I don't have time at the moment to pick through all the "sqrts" and such... – RecklessReckoner May 20 '14 at 2:33
I can't read the question, so I'll give the second derivative. Use the quotient rule: $$\dfrac{d^2y}{dx^2}=\dfrac{(2y-x)\left(-2+\frac{-2x+y}{2y-x}\right)-(-2x+y)\left(2\frac{-2x+y}{2y-x}-x\right)}{(2y-x)^2}$$ Substitute the given $(x,y)$ coordinate to find the second derivative there.
Remember $y$ depends on $x$, so you need to use implicit differentiation. – Grumpy Parsnip May 20 '14 at 2:39
Did you? I just assumed you applied the quotient rule straight, but I see you substituted in for $y'$. +1 – Grumpy Parsnip May 20 '14 at 4:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8979150056838989, "perplexity": 347.8109924712658}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860121985.80/warc/CC-MAIN-20160428161521-00164-ip-10-239-7-51.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/95518/cauchy-interlacing-theorem-how-to-complete-this-proof | # Cauchy interlacing theorem - how to complete this proof
I am looking for a proof using the min-max principle. Wikipedia seem to provide just that: http://en.wikipedia.org/wiki/Min-max_theorem#Cauchy_interlacing_theorem
But this part seems to be wrong:
This can be proven using the min-max principle. Let $\beta_i$ have corresponding eigenvector $b_i$ and $S_j$ be the $j$ dimensional subspace $S_j=\operatorname{span}\{b_1,\dots, b_j\}$, then $$\beta_j = \max_{x\in S_j,\|x\|=1}(Bx,x) =\max_{x\in S_j,\|x\|=1}(PAPx,x) =\max_{x\in S_j,\|x\|=1}(Ax,x)$$
How is the shift from $PAPx$ to $Ax$ legal? $PAP$ is an $m\times m$ matrix while $A$ is an $n\times n$ matrix. $x$ can't fit both. Can anyone correct the proof?
-
Hint: I am sure you know that $P$ is an orthogonal projection onto $S_j$. So observe that if $x\in S_j$ then $Px=x$. – smanoos Jan 1 '12 at 3:08
But P is mxn, how can it preserve x? – Leo Jan 1 '12 at 9:11
Do you know what a projection is? – smanoos Jan 1 '12 at 13:05
I know that if you project from 3 dimensions to 2 dimensions, it is impossible to have Px=x. Or am I missing something fundamental here? – Leo Jan 1 '12 at 13:23
,If $P$ is $m\times n$ and $A$ is $n\times n$, how do you find $PAP$? – smanoos Jan 1 '12 at 21:47
The proof on wikipedia has many flaws indeed. The projection $P$ can be expressed with matrix $P=V*V'$ where columns of $V$ are eigenvectors $v_1, v_2, \dots v_m$ associated with $\alpha_1, \dots \alpha_m$ of $A$. So $V$ is $n*m$ matrix. Then you can write $B=V'*A*V$ and $\max (Bx,x) = \max x'*V'*A*V*x = \max (V*x)'*A*(V*x)$. When $\operatorname{norm}(x)=1$ then $\operatorname{norm}(Vx)=1$ as well. This is how I got to the end of the proof. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9714274406433105, "perplexity": 281.8614128967438}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931004988.25/warc/CC-MAIN-20141125155644-00075-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://www.taylorfrancis.com/chapters/mono/10.1201/b15416-14/additive-models-julian-faraway?context=ubx&refId=63c8fa3c-7e7d-4d22-8b5c-a76f366635f8 | ## ABSTRACT
Suppose we have a response y and predictors x1, . . . ,xp. A linear model takes the form:
y= β0+ p
β jX j+ ε
We can include transformations and combinations of the predictors among the xs,
so this model can be very flexible. However, it can often be difficult to find a good
model, given the wide choice of transformations available. We can try a systematic
approach of fitting a family of transformations. For example, we can try polyno-
mials of the predictors, but particularly if we include interactions, the number of
terms becomes very large, perhaps greater than the sample size. Alternatively, we
can use more interactive and graphical approaches that reward intuition over brute
force. However, this requires some skill and effort on the part of the analyst. It is
easy to miss important structure; a particular difficulty is that the methods only con-
sider one variable at a time, when the secret to finding good transformations may
require that variables be considered simultaneously. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8742715716362, "perplexity": 1349.991364727697}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104204514.62/warc/CC-MAIN-20220702192528-20220702222528-00282.warc.gz"} |