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https://brainsanswers.co.uk/physics/find-c-and-i-choose-the-right-answe-14033835
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, 02.12.2019 22:10 soccerjessie8701
# Find c and i. choose the right answers. hint: c = total of payments - amount financed amount financed (m) = \$3,500 number of payments per year (y) = 12 number of payments (n) = 36 36 payments of \$104.50 each.
### Another question on Physics
Physics, 04.02.2019 21:57
Now that the first three steps have been explained, identify the next three steps, in order. calculate the magnitude of r sum vector components calculate a and b magnitudes calculate the direction of r, calculate x,y components step 4 step 5 step 6
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# Another pathing problem
P
#### Patrik Grinsvall
##### Guest
Since i solved my orignial question which was creating a new path in each step event (dont know why it only affected a few enemies, but sitll good).
I go directly to the :
*BONUS QUESTION*
Code:
``````mp_grid_path(id, path, xstart, ystart, xgoal, ygoal, allowdiag);
x start Starting x coordinate of the new path
y start Starting y coordinate of the new path
xgoal Finishing x coordinate of the new path
ygoal Finishing y coordinate of the new path``````
However i have always used absolute coordinates and not coordinates divided by cell size. Anyone know the answer to this? It would be really buggy if the xgoal and ygoal was coordinates and not pixels.
Any ideas?
I spawn 5 enemies at x = 0. Their y are random. They all use pathing and here is the relevant code:
Spawning code:
Code:
``````// if it is time to spawn the enemies.
if(time == spawn_time && enemies_alive == 0) {
// spawn enemies
for(tmpx = 0; tmpx <= spawn_amount; tmpx++) {
var randomy = irandom_range(0, window_get_height());
randomy = irandom_range(0, window_get_height());
var tmpinstance = instance_create_depth(1, randomy, 100, o_enemy1);
}
// increase difficulty...
level++;
spawn_amount = spawn_amount + level;
enemy1_hp = enemy1_hp + (level * 2);
enemy1_speed = enemy1_speed + (level / 10)
enemy1_attack_damage = 10 + (level*2);
}``````
Code that creates the path (create of enemy1):
Code:
``````if(instance_exists(nearestInstance)) {
mp_grid_path(global.grid, myPath, x, y, nearestInstance.x, nearestInstance.y, true);
path_start(myPath,2, path_action_stop, true);
show_debug_message("we have a path!");
} else {
show_debug_message("we dont dont 1! have a path!");
}``````
Now to the problem. Only some of the enemies move. All have their path layed out but they just refuse to move...
See attached screenshot. The red tiles are impassable tiles. The lines are the paths and i have marked what objects are moving and what is not. I have also tried to set a fixed speed to 2 and a bunch of other things even removing all obstacles from the game. Still same result.
#### Attachments
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Last edited by a moderator:
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# Maths
posted by .
Margie is responsible for buying a week's supply of food and medication for the dogs and cats at a local shelter. The food and medication for each dog costs twice as much as those supplies for a cat. She needs to feed 164 cats and 24 dogs. Her budget is K4,240. How much can Margie spend on each dog for food and medication?
• Maths -
cost of cat --- x
cost for dog -- 2x
164x + 24(2x) = 4240
212x = 4240
x = 20
spends 20 on a cat and 40 on a dog
check:
20(164) + 40(24) = 4240
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Use the rule of 72 to determine how long it will take the principal in this example to double. According to the rule of 72 how often will an individuals investment double.
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# 99%
1. ### 99% one sided upper bound confidence interval for mean?
I have a random sample X1....X24 from normal distribution with mean u and variance sigma^2 = .73. If Xbar = 3.3 then what is a 99% one sided upper bound confidence interval for u?
2. ### how do i know if i should choose 90% 95% 99% ?
I'm doing this hypthesis testing, I should do a one sided t-test and i have to do it with 5% significance level. And according the answer key, i should be using 90% CI interval values from the table for the calculations. BUT i was about to choose 95%, because its 5% sign. level. So how do i know...
3. ### 99% Confident Level
I have gotten some basics from this question, but cannot think of the formula to match it. Too much information and I am lost.. PLEASE HELP!!!! At the time she was hired as a server at the Grumney Family restaurant, Beth Brigden was told, “You can average more than \$20 a day in tips.” Over...
4. ### 99% confidence interval ????????????
Hi there, im doing report on mobile phone use and i want to use some clever statistics in it. Heres the basic info: It was claimed that 65% of people wanted a regulation to ban mobile phone usage on public transport. 94 people, as far as possible selected randomly from the population, were...
5. ### Find 99% confidence interval estimate of....
Help!! Seemed to be stuck on this problem, can anyone help?? Thanks! In order to help identify baby growth pattern that are unusual we need to construct a confidence interal estimate of the mean head circumference of all babies that are two months old. A random sample of 100 babies is...
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Question
# 1) Two professors compare their commute times to work. The first professor takes a random sample...
1) Two professors compare their commute times to work. The first professor takes a random sample of 25 days and finds an average commute time of 13.4 minutes and a standard deviation of 55 seconds. The second professor takes a random sample of 20 days and finds an average commute time of 19.6 minutes and a standard deviation of 40 seconds At the .1 significance level, conduct a full and appropriate hypothesis test for the professors to see if the VARIABILITY in the first professor's commute is higher than that of the 2nd.
a) What are the appropriate null and alternative hypotheses?
A H0:σ1=σ2H1:σ1>σ2 B H0:σ1=σ2H1:σ1<σ2 C H0:σ1=σ2H1:σ1≠σ2 D H0:μ1=μ2H1:μ1>μ2 E H0:μ1=μ2H1:μ1<μ2 F H0:μ1=μ2H1:μ1≠μ2
b) Identify the other values given in the problem:
1) ? = 25
2) ? = 13.4
3) ? = 55
4) ? = 20
5) ? = 19.6
6) ? = 40
7) ? = 1
c) Calculate the value of the test statistic. Round your response to at least 2 decimal places.
F=
d) What is the corresponding P-value for the test statistic? Round your response to at least 4 decimal places.
e) Make a decision:
Since α (<, >, =, =/) P, we (reject, accept) the null hypothesis (H0, H1)
f) Help write a summary of the results of this hypothesis test:
(There is, There is not, We do not whether there is) enough evidence in this sample to conclude the standard deviation in the first professor's (class length, commute time, coffee drinking, grades) is (greater than, less than, different from) the second professor's at the α= (.05, .01, .1) significance level because P=
a) The appropriate null and alternative hypotheses are : H012 against H112
b) Given
c) The test statistic can be written as
which under H0 follows a F distribution with (n1 -1, n2 -1) df.
We reject H0 at α significance level if P-value < α
Now,
The value of the test statistic =
The corresponding P-value for the test statistic
Since P-value < 0.10, so we reject H0 at 0.1 significance level.
Conclusion : There is enough evidence in this sample to conclude the standard deviation in the first professor's commute time is greater than the second professor's at the α = 0.10 significance level
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## Friday, May 15, 2009
### A neat trick for ray collisions in nonuniform media
Mattias Rabb showed me a really neat trick a few years ago that this post will share. He found it in a paper I had never seen by Coleman in 1967. Kudos to Mattias for not only finding this paper, but managing to find this trick in it (I would not have understood it had he not told me what was there). It gives a way to compute an unbiased random hitpoint for a light particle and a nonuniform density.
Recall that for a uniform density volume this can be done analytically. Given a canonical random number X (e.g., a call to drand48()), and a medium with interaction coefficient s (the probability of a collision in a small distance d is sd), we have distance = -log(1-X)/s (see Dutre et al., p 241 for a derivation of this classic result).
In a photon tracing program we would use this as follows:
X = drand48()
d = -log(1-X)/s
newposition = rayorigin + d*raydirection // assumes unit length direction
scatter or absorb
No suppose s(x,y,z) is a function of position like a call to noise or whatever. Usually we would resort to ray maching with small steps that assume s is locally constant. This is a pain in the same family as ray epsilons. But the Coleman paper has a lovely trick when s(x,y,z) is always less than a known smax. Pretend the medium is all constant smax, take a step as above, and sometimes reject the result:
d = 0
while (1) {
X = drand48()
d += -log(1-X)/smax
Y = drand48()
newposition = rayorigin + d*raydirection
if (s(newposition)/smax > Y) break
}
This takes a bunch of random steps and is unbaised (I would love to see a clean proof of this-- I don't follow Coleman's). I think it saved us something like 5X in our adjoint photon tracer.
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Main Fuzzy PID controllers for industrial applications
# Fuzzy PID controllers for industrial applications
Language: english
Pages: 23
File: PDF, 2.96 MB
You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.
1
### Real-time systems. Scheduling, analysis and verification
Year: 2002
Language: english
File: PDF, 3.51 MB
2
### Interpretive OpenGL for computer graphics
Year: 2005
Language: english
File: PDF, 674 KB
```Fuzzy PID Controllers
for Industrial Applications
G. Ron Chen
Lecture for EE 6452
City University of Hong Kong
Summary
• Proportional-Integral-Derivative (PID) controllers are the
most widely used controllers in industries today
• Statistics: > 90% controllers in industries are PID or PIDtype of controllers (the rest are programmable logical
controllers (PLC))
• Merits of PID controllers: simple, cheap, reliable, and
effective
• For lower-order linear time-invariant systems and processes,
PID controllers have good set-point tracking performance
with guaranteed stability
• Fuzzy logic provides a certain level of artificial intelligence
to the conventional PID controllers
• Fuzzy PID controllers have self-tuning ability and on-line
adaptation to nonlinear, time-varying, and uncertain systems
• Fuzzy PID controllers provide a promising option for
industrial applications with many desirable features
Outline of the Presentation
• Overview of the Fuzzy Logic Technology
• Overview of Conventional PID Controllers
• Introduction to Fuzzy PID Controllers
• Some Successful Examples of Applications
• Concluding Remarks
Overview of the Fuzzy Logic Technology
Closed-Loop Set-Point Tracking System
Consider the typical set-point tracking system:
r
+
Σ
(reference
signal)
e
−
u
Controller
(error
signal)
y
Plant
(control
signal)
(output
signal)
Figure 1 A typical closed-loop set-point tracking system
Objective:
e(t) : = r(t) − y(t) → 0
(t→∞)
Approach: Design a fuzzy logic controller (FLC)
e
Fuzzification
Fuzzy Rule Base
Defuzzification
controller
input
u
controller
output
Fuzzy Logic Controller (FLC)
Figure 2 General structure of a fuzzy logic controller
temperature
b
r = 45 o
c
y (t )
d
e (t )
a
0
t
Figure 3 Temperature set-point tracking example
(i) If e > 0 then
e=r −y> 0
or
r>y
the output y is at position a or d
(ii) Furthermore, if e& < 0 then
e& = r& − y& = 0 − y&
or
y& > 0
(iii) Therefore, the output y is at position a
Fuzzy Logic Rule Base:
R1:
IF e > 0 AND e& < 0 THEN u(t+) = u(t)
R2:
IF e < 0 AND e& < 0 THEN u(t+) = − u(t)
R3:
IF e < 0 AND e& > 0 THEN u(t+) = u(t)
R4:
IF e > 0 AND e& > 0 THEN u(t+) = − u(t)
Fuzzy Controller Design
A. Fuzzification
Purpose: Enable the input physical signal to use the rule base
Approach: Use membership functions
1
0
µ
µ
PL
µPS
NL
µNS 1
.
e, e
H
(a)
−H
0
(b)
Figure 4 Four membership functions for signals e and e&
B. Programmable Rule Base
R1:
IF e = PL AND e& < 0 THEN u(t+) = µP L(e) . u(t)
R2:
IF e = PS AND e& < 0 THEN u(t+) = (1−µPS(e)) . u(t)
R3:
IF e = NL AND e& < 0 THEN u(t+) = −µNL(e) . u(t)
R4:
IF e = NS AND e& < 0 THEN u(t+) = −(1−µNS(e)) . u(t)
R5:
IF e = NL AND e& > 0 THEN u(t+) = µNL(e) . u(t)
R6:
IF e = NS AND e& > 0 THEN u(t+) = (1−µNS(e)) . u(t)
R7:
IF e = PL AND e& > 0 THEN u(t+) = −µPL(e) . u(t)
R8:
IF e = PS AND e& > 0 THEN u(t+1) = −(1−µPS(e)) . u(t)
.
e, e
To implement the FLC on a digital computer:
u(t) = u(kT)
and
u(t+) = u((k+1)T)
where T is the sampling time.
R1:
IF e(kT) = PL AND e& (kT) < 0
THEN u((k+1)T ) = µPL(e(kT)) . u(kT)
R2:
IF e(kT) = PS AND e& (kT) < 0
THEN u((k+1)T) = (1−µPS(e(kT))) . u(kT)
R3:
IF e(kT) = NL AND e& (kT) < 0
THEN u((k+1)T ) = −µNL(e(kT)) . u(kT)
R4:
IF e(kT) = NS AND e& (kT) < 0
THEN u((k+1)T ) = −(1−µNS(e(kT))) . u(kT)
IF e(kT) = NL AND e& (kT) > 0
THEN u((k+1)T ) = µNL(e(kT)) . u(kT)
R5:
R6:
IF e(kT) = NS AND e& (kT) > 0
THEN u((k+1)T ) = (1−µNS(e(kT))) . u(kT)
R7:
IF e(kT) = PL AND e& (kT) > 0
THEN u((k+1)T ) = −µP L(e(kT)) . u(kT)
R8:
IF e(kT) = PS AND e& (kT) > 0
THEN u((k+1)T) = −(1−µPS(e(kT))) . u(kT)
where e& (kT) ≈
1
T
[e(kT) − e((k−1)T)], with initial conditions
y(0) = 0, e(−T) = e(0) = r − y(0), e& (0) =
1
T
[e(0) − e(−T)] = 0
C. Defuzzification
Select membership functions for the different control outputs from
the rule base
µN
1 µZO
–H
0
µP
u
H
Figure 5 Typical membership functions for u
Then, the overall control signal, u, is generated by a weighted
average formula:
N
∑ µ u (kT )
i =1
u((k+1)T) =
i i
N
∑µ
N
,
i
(µi ≥ 0,
∑µ
i =1
i
> 0)
i =1
where control outputs ui(kT), i = 1, ..., N=8 are from the rule base.
Overview of Conventional PID Controllers
In the time domain:
(i) P-controller
u(t) = KP e(t)
t
(ii) I-controller
u(t) = KI
∫ e(τ) dτ
0
d
(iii) D-controller u(t) = KD dt e(t)
Control gains, KP, KI, and KD, are constants to be determined in the
design for set-point tracking and stability consideration.
r
+
e
–
KP
u
system
y
(a) Proportional controller
r
+
e
–
t
KI∫
u
system
y
0
(b) Integral controller
r
+
e
–
d
KD
dt
u
system
(c) Derivative controller
Figure 6. Conventional PID controllers
y
In the frequency domain:
(i) P-controller
U(s) = KP E(s)
K
U(s) = sI E(s)
(iii) D-controller U(s) = KD s E(s)
(ii) I-controller
Use Laplace transform L{⋅} for continuous-time signals:
U(s) = L{ u(t) } and
E(s) = L{ e(t) }
Use z-transform Z{⋅} for discrete-time signals.
r
+
e
−
KI∫ t
0
+
u
system
y
+
KP
(a) PI controller
d
KDdt
r
+
e
+
−
u
system
y
+
KP
(b) PD controller
KP
r
+
e
−
t
K∫I 0
+
+
u
system
y
+
d
KD dt
(c) PID controller
t
r
+
e
−
K∫I 0
KP
+
+
u
system
−
+
d
KDdt
(d) PI+D controller
Figure 7 Some typical combination of P, I, D controllers.
y
Introduction to Fuzzy PID Controllers
A. Discretization of Convetional PID Controllers
First, digitize the conventional analog PID controllers by
2 z −1
S = T z +1
where T > 0 is the sampling time.
For the PI controller:
u(nT) = u(nT–T) + T∆u(nT)
~
KI
~
∆u(nT) = K P v(nT) +
e(nT)
T
1
T
e(nT)
+
~
KI
+
z−1
−
∆u(nT)
T
+
+
1
T
v(nT)
~
KP
Figure 8. The digital PI controller
u(nT)
+
z−1
u(nT−T)
Similarly, for the PD controller:
~
~
∆u(nT) = K P d(nT) + K D v(nT)
where
e(nT ) + e(nT − T )
T
e(nT ) − e(nT − T )
v(nT) =
T
d(nT) =
1
T
+
d(nT)
~
KP
+
z− 1
e(nT)
+
∆u(nT)
T
+
+
z− 1
u(nT)
−
z−1
+
−
1
T
u(nT−T)
v(nT)
~
KD
Figure 9. The digital PD controller
B. Example: Designing the Fuzzy PI Controller
r(nT) e(nT)
+
1
T
-
d(nT)
Ki
Fuzzy PI
Controller
z-1
+
+
KuPI
u(nT)
-
1
T
z-1
Kp
ev (nT
Figure 10. The Fuzzy PI control system
Fuzzification and Defuzzification fuzzy membership functions
negative
positive
1
0.5
-L
0
L
∆ u PI (nT )
Figure 11. Output membership functions
negative
positive
1
0.5
-L
0
L
ep , ev
Figure 12. Input membership functions
Process
y(nT)
K p ev (nT )
IC18
IC12
L IC11
IC4
IC3
IC17
IC13
IC10
IC5
IC2
-L
K i d (nT )
L
IC6
IC1
IC14
IC9
IC7
IC8
-L
IC15
IC19
IC16
IC20
Figure 13. IC regions for the fuzzy PI controller
∆u PI (nT )
=
=
=
=
=
=
=
=
=
[
L K i d ( nT ) + K p ev ( nT )
[
2(2 L − K i d ( nT ) )
L K i d ( nT ) + K p ev ( nT )
2(2L − K p e v ( nT ) )
[
],
in IC1, IC2, IC5, IC6
],
in IC3, IC4, IC7, IC8
]
1
L + K p ev ( nT ) ,
2
1
[L + K i d (nT )] ,
2
1
− L + K p ev ( nT ) ,
2
1
[− L + K i d ( nT )] ,
2
[
]
0,
−L,
L,
Note: Rigorous stability can be guaranteed
in IC9, IC10
in IC11, IC12
in IC13, IC14
in IC15, IC16
in IC18, IC20
in IC17
in IC19
Some Successful Examples of Applications
There are many successful examples of fuzzy PID controllers.
1. Robotics
* Six-legged Insect Robot
(Dr. P. Sooraksa, G. R. Chen, and students)
King Mongkut’s Institute of Technology, Bangkok, Thailand
* Multi-purpose Autonomous Robust Carrier for Hospitals
(MARCH)
(Dr. P. Sooraska, Prof. S. K. Tso, Dr. B. L. Luk, G. R. Chen, and students)
Centre for Intelligent Design, Automation and Manufacturing
City University of Hong Kong
* Uncertain Robot-Arm Control
(next page)
(G. R. Chen and students)
University of Houston, Texas, USA
* Uncertain Double-Pendulum Control
(DEMO)
(Prof. Edgar Sanchez, G. R. Chen, and students)
CINVESTAV, Mexico
2. Temperature Control
(next page)
(G. R. Chen and students)
University of Houston, Texas, USA
Other Application Examples
A. Process Control (temperature, flow rate, injection)
B. Vehicles Control (parking, docking, backing truck-trailers)
C. Electronic Appliances (washer, dryer, camcorder-camera)
D. Life-Support Systems (space shuttle, submarine)
E. … … many more … …
374
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 5, NO. 3, MAY 1997
Fig. 6. The output membership functions for the I component.
(R4) IF
AND
Then PD-output
.
In these rules,
is the error, where
is the
is the rate of the change of the error,
set-point,
“PD-output” is the fuzzy PD control output
,“
”
means “error positive” and “
” means “output positive,”
etc. Finally, “AND” is the Zadeh’s logical “AND” defined by
.
Similarly, from the membership functions of the fuzzy
I controller, the following control rules are used for the I
component, where
is the delayed error signal.
(R5) IF
AND
THEN I-output
.
(R6) IF
AND
THEN I-output
.
(R7) IF
AND
THEN I-output
.
(R8) IF
AND
THEN I-output
.
In the above rules, “I-output” is the fuzzy I control output
, and the other terms are defined similarly to the PD
component.
These eight rules altogether yield the control actions for the
fuzzy PD I control law.
3) Defuzzification: In the defuzzification step, for both
fuzzy PD and I controllers, the commonly used “center of
mass” formula is employed to defuzzify the incremental
control of the fuzzy control law, (15) as shown in (17)
Fig. 7. Regions of the fuzzy PD and I controllers’ input-combination values.
Fig. 8. Block diagram and physical setup for the robot arm experiment.
geometry of Fig. 7:
we obtain the following nine formulas for the ten IC regions:
input membership value membership value of output
membership value of output
(17)
For the fuzzy PD controller, the value-ranges of the two
inputs, the error and the rate of change of the error, are
actually decomposed into ten adjacent input-combination (IC)
regions, as shown in Fig. 7. The control rules for the fuzzy
PD controller (R1)–(R4), with membership functions and IC
regions together, are used to evaluate appropriate fuzzy control
law’s for each region.
Now, by applying the values
,
,
,
and the following straight line formulas obtained from the
in IC A
(18)
in IC B
(19)
in IC C
(20)
in IC D
(21)
in IC E
(22)
in IC F
(23)
in IC G, J
(24)
in IC H
(25)
in IC I
(26)
Similarly, defuzzification of the fuzzy I controller follows
the same procedure as described above for the PD component,
except that the input signals in this case are different. The
376
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 5, NO. 3, MAY 1997
Fig. 10.
Tracking performance of the fuzzy PID-controlled system (I).
Fig. 11.
Tracking performance of the conventional PID-controlled system (II).
the mass-center of the axis of rotation, and
the gravity
constant.
The actual data that we used in the experiment were:
(kgm ),
(kgm ),
(Nm),
IV. EXPERIMENT
AND
RESULTS
In the experiment, the robot arm system was run using two
control methods: using the conventional digital PID controller
and the fuzzy PID controller, respectively, both based on
the same configuration and under the same conditions. The
conventional digital PID controller was unable to satisfactorily
run the robot arm system (with a nonlinear load) no matter
what combinations of control gains were used. Plots of the
system output with the tuned PID gains that achieved the best
results by trial-and-error are shown in Fig. 9, where and below
s. The fuzzy PID controller, in contrast, controlled
the robot arm system with reasonably good results, obtained
also by trial-and-error, as shown in Fig. 10. In this and the
,
,
other fuzzily controlled simulation figures,
, and
and
are fuzzy gains defined in
Section II-B (see Fig. 2). In Figs. 9 and 10, the robot arm was
not connected to the spring, where the units used are oltage
400 r/min) versus second.
(1 V
Another comparison, at a different speed and with the spring
added to the arm, is shown in Figs. 11 and 12, where the units
used are voltage (1 V 400 r/min) versus s in Fig. 11 while
versus second in Fig. 12. In these experiments, parameters
for the fuzzy PID control gains were found such that there
Concluding Remarks
• Fuzzy logic provides a certain level of artificial intelligence
to the conventional PID controllers, leading to the effective
fuzzy PID controllers
• Fuzzy PID controllers are easy to use (plug-and-play)
• Fuzzy PID controllers can be implemented by both
o software (matured)
o hardware (pre- matured)
• Fuzzy PID controllers have strong self-tuning ability and online adaptation to nonlinear, time-varying, and uncertain
systems.
• Fuzzy PID controllers have a promising future for various
industrial applications
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Thursday
May 5, 2016
# Homework Help: Algebra
Posted by A.W. on Sunday, March 1, 2009 at 7:12pm.
Is this right? Examine the rise in gasoline prices from 1997 to 2006. The price of regular unleaded gasoline price in January 1997 was \$1.26 and in January 2006 was \$2.31 (Bureau of Labor Statistics, 2006). Use the coordinates (1997, 1.26) and (2006, 2.31) to find the slope (or rate of change) between the two points. Describe how you arrived at your answer. Slope is y=mx+b. So I took m= 2006-1997/2.31-1.26= 1.05/9= .116666666= to about .12 cents per year.
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# Imaginer1
Senior Members
35
1. ## E.r.d.
ERD, Energy Renewal Device. Of course, what I made was impossible because a force cannot make more than it is. It was a circuit that consisted of a battery which had two outputs- one to the lightbulb, another to a motor. The motor was connected to a generator, which connected back to the battery. But I assumed it was 100% clean energy that wouldn't run out. I just watched it not-long-enough-to-see-the-battery run out. Aww, I was so close to clean energy!
2. ## hoverboards
Well, I think that this would be the only way, because weight has to be number 1 in your experiment. So if you made a huge magnet platform, took a skateboard, and put the same poled magnet on the bottom, and removed the wheels, it would.. STILL definitely not work. Seriously I don't think it's really possible to make something that will keep you up, that's easy to balance on- it is going to be hard.
3. ## Problem in Isaac Newton's Theory
.... I'm at eighth grade science, can you sort of explain for me? is that at eighth grade science? you know, I AM likely just in my grade (6th) but I'm a little too scientifically advanced sometimes.
4. ## What is nothing?
Nothing is more than likely somewhere, but it;s near impossible to make nothing. It would be an intense vacuum. INTENSE. like, man could never make it. ever.
5. ## Laser discussion
You know, I got a theory about lazer beams that we could make them by condensing protons into bullets. If we get to a quark, and condense a couple million of them into a bullet? I didn't really think about quarks being in protons- and that they're little molecular charges.
6. ## High School Holography
Ironic- I just bought this two dollar mirror- look into it for me, I have no idea how it works- Two mirrors. Now, make it so if you were looking at the mirror it would be convex (facing inward) Do that with both of them. Now cut a little hole in one of them. Put them on top of each other so the hole is facing up. Heres the cool part- if you put a small object inside, a copy comes up. You want to try to touch it? blam, it's a hologram. look at how this could be working, I bet your project would pass with the right info.
7. ## find number of atoms
I agree with insane alien- and I'm pretty sure C3H8 would be carbon three atoms, hydrogen eight atoms. I don't really see those numbers. P.S. I could be wrong. I'm eleven. I just am more advanced than most
8. ## Imaginer 1's Scientific Theories
Well, I'm only really interested in science because I keep on thinking up theories. Then I want to see if they have been tested, then I'll proboably never figure out because I would mostly have to spend bajillions of dollars to test it. But here are some sci-fi things and my theories for them, and why I think it's possible or not. I THINK IS POSSIBLE- Lazer Beams This is warfare, but I do have a theory for this, but it leads to something else impossible. After I saw the movie "War of the Worlds" I wondered how the lazer beams could be real. Well, I know this too is likely impossible, but- what if we condensed protons to something like a bullet? would that be what people now call "lazer beams?" Cloning Really, it's already happening- but only for females at the time. A while ago (2001?) a scientist removed the egg cell from a lamb. He then let body cells stay around it for a while. The result? a fetus DID start to grow. it was the exact duplicate of the lamb because there was no other genes to be mixed besides hers. Teleportation Really, you got to think about it more simple. People in Quantum Physics are already developing scanners that can tell oxygen from hydrogen or whatever. So if you took all the elements of yourself, turned them into electric signals like a phone does, and send it to another pod- Well, now I'm stuck. at this point there is a clone of you who likely doesn't have a beating heart somewhere across the country or something. If you have any ideas, help me out! Preventing age I read a book saying that people die of natural causes- old age, really- is because DNA strands fall and die (I don't think I can really believe that book, huh) so if we prevented the strands to fall, what would happen? eternal life? (SEE FRANKENSTIEN UNDER IMPOSSIBLE) I THINK IS NOT POSSIBLE- Frankenstien- the animation of dead tissue TOO scary for me to think about. and if I DID get a theory, alot of people would really be angry or upset at me. So I don't really want to get in trouble. (but I am thinking about it. SHH!) Time Travel Completely impossible. I doubt that in zillions of years, man will have a time machine. I already have proof. No one is coming to visit us, and they talk as if time is a solid. It's not. It's something that is in your mind. it doesn't exist.
9. ## Problem in Isaac Newton's Theory
I admit, this was on a television show. But it IS very perplexing. Isaac Newton was the scientist who discovered gravity. Well, the TV show said he also went into atoms, but he was almost TOO long ago to know about that. Anyway, supposedly he thought that electrons circled the nucleus of an atom because of gravity. A few minutes after I watched that, I noticed something: If the electrons orbited the electron because of gravity, then they would also have to eventually collide with the nucleus, and the atom would likely no longer exist. Every object would be imploding really fast- and I really think that I would be consisting of two or three atoms right now if that was happening. So if the electrons aren't held to the nucleus by gravity, by what?
10. ## The Official "Introduce Yourself" Thread
Hello! I'm only eleven years old in sixth grade, but my reading level is at 8th grade. And, well, I'm pretty interested in science. Actually, my interest started at 5 years old. Well, now I'm also considered by my teachers a 8th grade level (approximately) at science too. I don't mean to talk too much but hey how else is anyone going to know me? Anyway, I mostly have scientific theories. (DID A SIXTH GRADER MAKE A HYPOTHESIS?) Really, I also do some science experimenting. Well, hope to get to know YOU on the forums!
11. ## Beginner Curious About Chromosomes
So you're a beginner to the forums? well, me too. But you're lucky- I know quite a bit about chromosones. (Well, it's mostly your opinion) Ask me a question!
×
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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020
# Calculus A2
Code Completion Credits Range Language
01MAA2 Z,ZK 10 4+4 Czech
Lecturer:
Edita Pelantová (guarantor)
Tutor:
Edita Pelantová (guarantor), Pavel Eichler, Jiří Fejlek, Petr Gális, Jakub Kořenek, Václav Košík, Jiří Mikyška, Severin Pošta
Supervisor:
Department of Mathematics
Synopsis:
The subject is devoted mainly to the integral calculus of the real functions with one real variable and to the theory of the number series and the power series.
Requirements:
Succesfull completion of the course Mathematical analysis I, i.e. familiarity with differential calculus.
Syllabus of lectures:
Continuation of differential calculus: Taylor´s Polynomials, Taylor´s formula; Theory of integrals: primitives, definite integral (Riemann definition), techniques of integration and application of integrals; Infinite series: criteria of convergence, operations on series, absolute and conditional convergence, real and complex power series, the Cauchy-Hadamard theorem, expansion of function into power series, summation of infinite series.
Syllabus of tutorials:
Content of excercises consists in solving problems with emphasis on using theoretical results. The domains of problems: evaluation fo limits by the l´Hospital rule, uniform continuity, approximation of function by the Taylor polynomial, technics for determination of primitive functions, evaluation of volumes and areas, expansion of function into a power series
Study Objective:
Acquired knowledge: a rigorous construction of integral, to focus on properties of power series.
Acquired skills: application of the theoretical results in geometry, discrete mathematics and in physics.
Study materials:
Obligatory:
[1] E. Pelantová: Matematická analýza II, skriptum ČVUT, 2007
[2] E.Pelantová, J.Vondráčková: Cvičení z matematické analýzy - Integrální počet a řady, skriptum ČVUT 2006
Optional:
[3] I. Černý, M. Rokyta: Differential and Integral Calculus of One Real Variable, Karolinum, Praha 1998
[4] I.Černý, Úvod do inteligentního kalkulu I, Academia 2005
Note:
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-08-12
For updated information see http://bilakniha.cvut.cz/en/predmet11353405.html
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12 Questions
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# Core Concepts in Classical Physics
Created by
@CozyPersonification
### What does the first law of thermodynamics state?
• Work done is equal to internal energy change
• Internal energy change is equal to heat supplied minus work done (correct)
• Internal energy change is equal to heat supplied
• Work done is equal to heat supplied
• ### Which scientist developed the four equations known as Maxwell's Equations?
• Nikola Tesla
• Albert Einstein
• James Clerk Maxwell (correct)
• Isaac Newton
• ### How are flows classified in fluid dynamics?
• Based on their temperature
• Based on the arrangement of fluid layers relative to the flow direction (correct)
• Based on their color
• Based on their viscosity
• ### What type of flows involve parallel layers sliding past each other without mixing?
<p>Laminar flows</p> Signup and view all the answers
### In fluid dynamics, what characterizes turbulent flows?
<p>Random eddies in the fluid</p> Signup and view all the answers
### What does Ampère's Circuital Law describe in electromagnetism?
<p>Relationship between magnetic fields and electrical currents</p> Signup and view all the answers
### According to Newton's Law of Inertia, what happens to objects in motion?
<p>They remain in motion unless acted upon by a net external force</p> Signup and view all the answers
### What concept in Newtonian mechanics relates to the product of mass and acceleration?
<p>Force</p> Signup and view all the answers
### Which Newtonian law describes the relationship between net force, acceleration, mass, and distance for rotational motion?
<p>Law of Force Equilibrium</p> Signup and view all the answers
### What does the Law of Acceleration state about changes in an object's velocity vector?
<p>Velocity changes in direction or magnitude</p> Signup and view all the answers
### What is the main focus of thermodynamics in relation to energy?
<p>Irreversible transformation of energy from one form to another</p> Signup and view all the answers
### In thermodynamics, what principle states that the sum of exchanged energies remains conserved?
<p>First Law of Thermodynamics</p> Signup and view all the answers
## Mechanics in Physics
Mechanics is a core branch of classical physics that deals with the motion and forces acting on objects. It includes Newtonian mechanics, thermodynamics, electromagnetism, and fluid dynamics, among other subjects. Let's delve deeper into its key aspects.
### Newtonian Mechanics
Newtonian mechanics describes the relationship between motion, mass, force, energy, work, power, and torque of physical bodies. Isaac Newton established three laws of motion that govern how physical entities interact in space:
1. Law of Inertia: Objects in motion remain in motion unless acted upon by a net external force; objects at rest stay at rest unless disturbed.
2. Law of Acceleration: Acceleration occurs whenever net force acts on an object, causing changes in the velocity vector direction or magnitude.
3. Law of Force Equilibrium: Net force equals acceleration multiplied by mass times a constant (and multiplied by distance when considering rotations).
These laws form the foundation of understanding mechanical behavior in everyday life and underpin technological advancements.
### Thermodynamics
Thermodynamics deals with heat transfer processes involving temperature and thermal energy. It addresses the transformation of energy from one form to another through irreversible processes. These transformations occur under the condition that the sum of exchanged energies remains conserved, known as the First Law of Thermodynamics. This law states that the internal energy change of a system is equal to the heat supplied minus the work done on the system.
### Electromagnetism
Electromagnetism explains the interaction between electrically charged particles and magnetic phenomena. James Clerk Maxwell developed four equations, collectively called Maxwell's Equations, which explain the behavior of electric and magnetic fields. They are:
1. Gauss's Law
2. Gauss's Law for Magnetic Fields
4. Ampère's Circuital Law
These equations reveal how charges create fields that attract or repel other charges and how changing fields induce electrical currents.
### Fluid Dynamics
Fluid dynamics focuses on the flow properties of fluids, including liquids and gases. Flows can be classified as either laminar or turbulent based on the arrangement of fluid layers relative to the direction of flow. Laminar flows involve parallel layers sliding past each other without mixing, while turbulent flows consist of random eddies in the fluid. Understanding fluid dynamics helps engineers design aircraft wings, improve fuel efficiency, and develop weather forecast models.
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## Description
Explore key concepts in classical physics such as Newtonian mechanics, thermodynamics, electromagnetism, and fluid dynamics. Learn about laws governing motion, forces, energy transformations, and fluid flow properties.
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simple solution?
• May 9th 2009, 09:16 AM
krispiekream
simple solution?
i have a simple question.
can someone please tell me how to get there?
I just dont get it.
http://i709.photobucket.com/albums/w...ntitled5-1.jpg
• May 9th 2009, 09:27 AM
krispiekream
Also,
What can i do in this case?
c(j)c(j + 2)???
• May 9th 2009, 10:34 AM
HallsofIvy
Quote:
Originally Posted by krispiekream
i have a simple question.
can someone please tell me how to get there?
I just dont get it.
http://i709.photobucket.com/albums/w...ntitled5-1.jpg
$\sum_{j= 0}^\infty \left(0.9\right)^{2j}= \sum_{j=0}^\infty \left(0.9^2\right)^j= \sum_{j= 0}^\infty \left(0.81\right)^j$
is a geometric series with a= 1 and r= 0.81. Use the formula for the sum of a geometric series: $\sum_{j=0}^\infty ar^j= \frac{a}{1- r}$
• May 9th 2009, 10:43 AM
krispiekream
thank you..i needed that..
• May 9th 2009, 11:56 AM
krispiekream
I understand the first step now..
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# Op Ed: A Cryptographic Design Perspective of Blockchains: From Bitcoin to Ouroboros
How does one design a blockchain protocol? Back in 2013, while in Athens, I set out to design a non-proof-of-work-based blockchain protocol motivated by the debt crisis in Greece, looming bank liquidity problems and the increasing discussions about the possibility of having a parallel currency. The new protocol had to be based on proof of stake to make sure that it can run even on cellphones and be secure independent of any computational power existing that is external to it.
Very soon it became clear that the problem was going to need much more than a few months' work. Fast-forward three years to 2016: I was at the University of Edinburgh and had joined forces with IOHK whose CEO, Charles Hoskinson, was poised to solve the same problem. The protocol, "Ouroboros" as it would be eventually named, was there but the core of the security proof was still elusive when my good friend Alexander Russell visited me.
Together, we tackled the problem of proving the security of the system. Whiteboards were filled over and over again until we felt we mined a true gem: a clean combinatorial argument that enabled us to argue mathematically the security of the scheme.
#### Diving Into the Mindset of a Cryptographer
Security is an elusive concept. Take a system that is able to withstand a given set of adverse operational conditions. When can we call it secure? What if it collapses in the next moment when it is subjected to a slightly different set of conditions? Or when it is given inputs different from any that have been tried before?
Security cannot be demonstrated via experiment alone since attacker ingenuity can rarely be completely enumerated within any reasonable timeframe. Cryptographic design, thus, has to somehow scale this "universal quantifier": the system should be called secure only if it withstands all possible attacks.
In response to this fundamental problem, "provable security" emerged as a rigorous discipline within cryptography that promotes the co-development of algorithms and (so-called) proofs of security. Such proofs come in the form of theorems that, under certain assumptions and threat models that describe what the attacker can and cannot do, establish the security of cryptographic algorithms. In this fashion, modern cryptographic design pushes the "burden of proof" to the proposer of an algorithm.
In the world of academic cryptography, gone are the days when someone could propose a protocol or algorithm and proclaim it secure because it was able to withstand a handful of known attacks. Instead, modern cryptographic design requires due diligence by the designers to ensure that no attack exists within a convincing and well-defined threat model.
This approach has been a tremendously powerful and inspiring paradigm within cryptography. For instance, the notion of a secure channel has been studied for more than 40 years. This is the fundamental cryptographic primitive that allows the proverbial Alice and Bob to send messages to each other safely in the presence (and possibly active interference) of an attacker. Today's provable security analysis, even using automated tools, has unearthed attacks against secure channel protocols like TLS that were unanticipated by the security community.
Back in 2009 though, the blockchain was a concept that was presented outside regular academic cryptographic discourse. A brief white paper and a software implementation were sufficient to fuel its initial adoption that expanded rapidly. In retrospect, this was perhaps the only way for this fringe idea to ripple the waters of scientific discourse sufficiently and force a paradigm shift (in the sense of Thomas S. Kuhn's " Structure of Scientific Revolutions ") in terms of how the consensus problem was to be studied henceforth.
As the shift settled though, a principled approach became direly needed. The newly discovered design space appears to be vast and the avenues of exploring it too numerous. The "burden of proof" needs to return to the designer.
Blockchain protocols need to become systematized, as they have gradually become one of the dominant themes in distributed consensus literature. The blockchain is not the problem; it is the solution. But in this case, one may wonder, what was the problem?
In 2014, jointly with Juan Garay and Nikos Leonardos, we put forth a first description of "the problem" in the form of what we called a "robust transaction ledger." Such a ledger is implemented by a number of unauthenticated nodes and provides two properties, called persistence and liveness. Persistence mandates that nodes never disagree about the placement of transactions once they become stable, while liveness requires that all (honestly generated) transactions eventually become stable. Using this model, we provided a proof of security for the core of the Bitcoin protocol (a suitably simplified version of the protocol that we nicknamed the "bitcoin backbone").
Given this proof, a natural question a cryptographer will ask is whether this protocol is really the best possible solution to the problem. "Best" here is typically interpreted in two ways: first, in terms of the efficiency of the solution; and second, in terms of the relevance and applicability of the threat model and the assumptions used in the security proof.
Efficiency is a particular concern for the Bitcoin blockchain. With all its virtues, the protocol is not particularly efficient in terms of processing time or resource consumption. This is exactly where "proof of stake" emerged as a possible alternative and a more efficient primitive for building blockchain protocols.
So, is it possible to use proof of stake to provably implement a robust transaction ledger? By 2016, with our Bitcoin backbone work already presented, this was a well-defined question; and the answer came with Ouroboros: our proof-of-stake-based blockchain protocol.
#### Ouroboros
The unique characteristic of Ouroboros is that the protocol was developed in tandem with a proof of security that aims to communicate in a succinct way that the proposed blockchain protocol satisfies the properties of a robust transaction ledger. Central to the proof is a combinatorial analysis of a class of strings that admit a certain discrete structure that maps to a blockchain fork. We called "forkable" those strings that admit a non-trivial such structure, and our proof shows that their density becomes minutely small as the length of the string grows.
With this argument, we showed how there is an opportunity for the nodes running the protocol to converge to a unique history. The protocol then dictates how to take advantage of this opportunity by running a cryptographic protocol that enables the nodes to produce a random seed, which, in turn, is used to sample the next sequence of parties to become active. As a result, the protocol facilitates the next convergence step to take place; in this way, it can continue ad infinitum following a cyclical process that was also the inspiration for its name. Ouroboros is the Greek word for the snake that eats its tail, an ancient Greek symbol for re-creation.
Having the protocol and its proof in hand gave us the unique opportunity for peer review, i.e., asking fellow cryptographers to evaluate the construction and its associated security proof as part of the formal submission process to a major cryptology conference.
Peer reviewing at the top cryptology venues is a painstakingly rigorous process that goes on for months. Papers are first reviewed independently by at least three experts, and afterward a discussion for each paper rages on as the three reviewers, as well as other members of the scientific committee, get involved and try to converge on the intellectual merits of each submission.
As a result of successfully passing this rigorous peer review process, Ouroboros was accepted and included in the program of Crypto 2017 , the 37th annual cryptology conference. Crypto is one of the flagship conferences of the International Association for Cryptologic Research (IACR) and is one of the most exciting places for a cryptographer to be, as the program always contains research on the cutting edge of the discipline.
Furthermore, Ouroboros will be the settlement layer of the Cardano blockchain to be rolled out by IOHK in 2017, making it one of the swiftest technology transfer cases from a basic research publication to a system to be used by many thousands in just one year.
While all this may seem like a happy conclusion to the quest for a proof-of-stake blockchain, we are far from being done. On the contrary, we are still, as a community, at the very beginning of this expedition that will delve deep into blockchain design space. There are still too many open questions to solve, and new systems will be built on the foundations of the research that our community is laying out today.
The views expressed in this op ed are those of its author, Aggelos Kiayias , and do not necessarily reflect those of Bitcoin Magazine or BTC Media.
Ouroboros image courtesy of Wikimedia Commons .
The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of Nasdaq, Inc.
The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of Nasdaq, Inc.
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# Problem Set 1 Answers - Exercise 2A.2 Demonstrate how my...
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Exercise 2A.2 Demonstrate how my budget constraint would change if, on the way into the store, I had lost \$300 of the \$400 my wife had given to me. Does my opportunity cost of pants (in terms of shirts) or shirts (in terms of pants) change? What if prices of pants and shirts had doubled while I was driving to the store? Exercise 2A.3 How would my budget constraint change if, instead of a 50% off coupon for pants, my wife had given me a 50% off coupon for shirts? What would the opportunity cost of pants (in terms of shirts) be? Exercise 2A.4 Suppose that the two coupons analyzed above were for shirts instead of pants. What would the budget constraints look like? 2.1 Suppose my brother and I both go on a week-long vacation in Cayman and, when we arrive at the airport on the island, we have to choose between either renting a car or taking a taxi to our hotel. Renting a car involves a fixed fee of \$300 for the week, with each mile driven afterwards just costing 20 cents — the price of gasoline per mile. Taking a taxi involves no fixed fees, but each mile driven on the island during the week now costs \$1 per mile. A: Suppose both my brother and I have brought \$2,000 on our trip to spend on “miles driven on the island” and “other goods”. On a graph with miles driven on the horizontal and other consumption on the vertical axis, illustrate my budget constraint assuming I chose to rent a car and my brother’s budget constraint assuming he chose to take taxis. (a) What is the opportunity cost for each mile driven that I faced? (b) What is the opportunity cost for each mile driven that my brother faced? B: Derive the mathematical equations for my budget constraint and my brother’s budget constraint, and relate elements of these equations to your graphs in part A. (a) Where in your budget equation for me can you locate the opportunity cost of a mile driven? (b) Where in your budget equation for my brother can you locate the opportunity cost of a mile driven? 2.3 Suppose the only two goods in the world are peanut butter and jelly. A: You have no exogenous income but you do own 5 jars of peanut butter and 2 jars of jelly. The price of peanut butter is \$4 per jar, and the price of jelly is \$6 per jar. (a) On a graph with jars of peanut butter on the horizontal and jars of jelly on the vertical axis, illustrate
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# Definition of Return of A Long/short Portfolio
This can either be a silly question or a question with no sure rigorous answer but defined with some convention. Any way, here it is.
What is the (industrial recognized) definition of the return of a long-short portfolio? Normally, return is defined as profit/initial investment. The initial portfolio may be predominantly short or even neutral (net zero dollar). Should we take the initial investment as the sum of the absolute value of the investment, because the short most likely requires collateral? If so, should one take the leverage rate into account?
• You should be able to find the money weighted return if you get the inflows / outflows correctly. Mar 14, 2014 at 23:52
• @user1869020: Could you be more specific with a formula?
– Hans
Mar 15, 2014 at 0:13
The initial investment is the capital in the account used to support the portfolio, not the cost of the assets in the portfolio. For example, when you sell a stock or bond short, your account doesn't actually accrue any cash. Instead you start receiving a regular cash flow.
There isn't necessarily a difference between these quantities in a long-only portfolio but for a long-short portfolio of any kind you automatically must make some assumption about the leverage -- the amount of cash required to support a given position size.
If your portfolio is a set of positions with notional values $A_i$ (possibly including cash $A_0$) and it is supported by capital $K$ then the gross leverage is
$$L_G =\frac1K \sum_{i>0} |A_i|$$
After a month, if your positions are now worth $\tilde{A}_i$ then your one-month return on capital is
$$r =\frac1K \sum_i (\tilde{A}_i-{A}_i)$$.
This obviously depends on the capital $K$, so return is dependent on leverage assumptions.
Depending on the riskiness of a strategy and how well it can be measured within their existing risk control software, prime brokers will typically allow leverage between 2:1 and 20:1.
If your position exceeds the agreed leverage ratio at any time, you will receive a margin call, where you will either have to come up with some further long positions to assign to the portfolio, or liquidate some existing positions to cash.
• I suppose for each $A_i$ there is a support capital $K_i$? It is always positive (nonnegative), correct? Is this the collateral to the bank for loans for either long or short? If I define leverage $L_i=\frac{A_i}{K_i}$, is it reasonable to assume the positive leverages are mostly of similar absolute magnitude, and the negative ones are as well but quite distinct from the former?
– Hans
Mar 15, 2014 at 18:35
• It really depends on the type of assets in the portfolio. For example, futures hedges on futures options will reduce capital charges. Mar 15, 2014 at 19:44
* For a given period t and a set of securities and cash denoted with index i which individually have returns r and weights w in a portfolio the portfolio return could be computed as
$$R = \sum_i w^s _i r^s _i + w_i^l r_i^l$$ where the sups l and s mean short and and long respectively. Note that the weights need to sum up to unity
$$\sum_i (w^s_i + w^l_i) =1$$
Also note that the weights of the shorts are negative
hope this helps.
*adding an example. time = 0, sec1 = 0, sec2 = 0, margin cash = 0, available cash = 100.
time = 1, sec1 = 80, sec2 = 0, margin cash = 0, available cash = 20.
time = 2, sec1 = 80, sec2 = -40, margin cash = 60, available cash = 0.
weights thus can be read as: sec1 = 80% sec2 = -40% margin cash = 60% sum= 100%
This sort of normalization makes attribution with short positions possible, so it may help you as well.
*Source: 'Performance Attribution with Short Positions' Dr. Jose Menchero, The Journal of Performance Measurement
• This is not valid. For a long-short portfolio, you can not impose extraneously the total portfolio value be always positive. Not only positive would be a problem, even positive net weight but close to zero would wreak havoc.
– Hans
Mar 20, 2014 at 20:26
• Also, a purely short portfolio would real the absurdity of this formulation whether one allows $w_i$'s to take on arbitrary signs or not. What you have written here is the definition of return on a net long portfolio. I would not have posed the question, had that definition been fit for extending to general long-short portfolio.
– Hans
Mar 20, 2014 at 21:05
• check out the example for clarity Apr 1, 2014 at 22:50
• Are your examples supposed to resolve the two objections I have raised in my two comments? I do not see that. Please explain in detail if you do think they do resolve them.
– Hans
Apr 2, 2014 at 3:47
• "This is not valid. For a long-short portfolio, you can not impose extraneously the total portfolio value be always positive" Ans: They are normalized weights, so they sum up to 1 or 100% Apr 3, 2014 at 0:26
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# Nilpotent groups #
An API for nilpotent groups, that is, groups for which the upper central series reaches ⊤.
## Main definitions #
Recall that if H K : Subgroup G then ⁅H, K⁆ : Subgroup G is the subgroup of G generated by the commutators hkh⁻¹k⁻¹. Recall also Lean's conventions that ⊤ denotes the subgroup G of G, and ⊥ denotes the trivial subgroup {1}.
• upperCentralSeries G : ℕ → Subgroup G : the upper central series of a group G. This is an increasing sequence of normal subgroups H n of G with H 0 = ⊥ and H (n + 1) / H n is the centre of G / H n.
• lowerCentralSeries G : ℕ → Subgroup G : the lower central series of a group G. This is a decreasing sequence of normal subgroups H n of G with H 0 = ⊤ and H (n + 1) = ⁅H n, G⁆.
• IsNilpotent : A group G is nilpotent if its upper central series reaches ⊤, or equivalently if its lower central series reaches ⊥.
• nilpotency_class : the length of the upper central series of a nilpotent group.
• IsAscendingCentralSeries (H : ℕ → Subgroup G) : Prop and
• IsDescendingCentralSeries (H : ℕ → Subgroup G) : Prop : Note that in the literature a "central series" for a group is usually defined to be a finite sequence of normal subgroups H 0, H 1, ..., starting at ⊤, finishing at ⊥, and with each H n / H (n + 1) central in G / H (n + 1). In this formalisation it is convenient to have two weaker predicates on an infinite sequence of subgroups H n of G: we say a sequence is a descending central series if it starts at G and ⁅H n, ⊤⁆ ⊆ H (n + 1) for all n. Note that this series may not terminate at ⊥, and the H i need not be normal. Similarly a sequence is an ascending central series if H 0 = ⊥ and ⁅H (n + 1), ⊤⁆ ⊆ H n for all n, again with no requirement that the series reaches ⊤ or that the H i are normal.
## Main theorems #
G is defined to be nilpotent if the upper central series reaches ⊤.
• nilpotent_iff_finite_ascending_central_series : G is nilpotent iff some ascending central series reaches ⊤.
• nilpotent_iff_finite_descending_central_series : G is nilpotent iff some descending central series reaches ⊥.
• nilpotent_iff_lower : G is nilpotent iff the lower central series reaches ⊥.
• The nilpotency_class can likewise be obtained from these equivalent definitions, see least_ascending_central_series_length_eq_nilpotencyClass, least_descending_central_series_length_eq_nilpotencyClass and lowerCentralSeries_length_eq_nilpotencyClass.
• If G is nilpotent, then so are its subgroups, images, quotients and preimages. Binary and finite products of nilpotent groups are nilpotent. Infinite products are nilpotent if their nilpotent class is bounded. Corresponding lemmas about the nilpotency_class are provided.
• The nilpotency_class of G ⧸ center G is given explicitly, and an induction principle is derived from that.
• IsNilpotent.to_isSolvable: If G is nilpotent, it is solvable.
## Warning #
A "central series" is usually defined to be a finite sequence of normal subgroups going from ⊥ to ⊤ with the property that each subquotient is contained within the centre of the associated quotient of G. This means that if G is not nilpotent, then none of what we have called upperCentralSeries G, lowerCentralSeries G or the sequences satisfying IsAscendingCentralSeries or IsDescendingCentralSeries are actually central series. Note that the fact that the upper and lower central series are not central series if G is not nilpotent is a standard abuse of notation.
def upperCentralSeriesStep {G : Type u_1} [] (H : ) [H.Normal] :
If H is a normal subgroup of G, then the set {x : G | ∀ y : G, x*y*x⁻¹*y⁻¹ ∈ H} is a subgroup of G (because it is the preimage in G of the centre of the quotient group G/H.)
Equations
• = { carrier := {x : G | ∀ (y : G), x * y * x⁻¹ * y⁻¹ H}, mul_mem' := , one_mem' := , inv_mem' := }
Instances For
theorem mem_upperCentralSeriesStep {G : Type u_1} [] (H : ) [H.Normal] (x : G) :
∀ (y : G), x * y * x⁻¹ * y⁻¹ H
theorem upperCentralSeriesStep_eq_comap_center {G : Type u_1} [] (H : ) [H.Normal] :
The proof that upperCentralSeriesStep H is the preimage of the centre of G/H under the canonical surjection.
instance instNormalUpperCentralSeriesStep {G : Type u_1} [] (H : ) [H.Normal] :
.Normal
Equations
• =
def upperCentralSeriesAux (G : Type u_1) [] :
(H : ) ×' H.Normal
An auxiliary type-theoretic definition defining both the upper central series of a group, and a proof that it is normal, all in one go.
Equations
Instances For
def upperCentralSeries (G : Type u_1) [] (n : ) :
upperCentralSeries G n is the nth term in the upper central series of G.
Equations
• = ().fst
Instances For
instance upperCentralSeries_normal (G : Type u_1) [] (n : ) :
().Normal
Equations
• =
@[simp]
theorem upperCentralSeries_zero (G : Type u_1) [] :
@[simp]
theorem upperCentralSeries_one (G : Type u_1) [] :
theorem mem_upperCentralSeries_succ_iff (G : Type u_1) [] (n : ) (x : G) :
x upperCentralSeries G (n + 1) ∀ (y : G), x * y * x⁻¹ * y⁻¹
The n+1st term of the upper central series H i has underlying set equal to the x such that ⁅x,G⁆ ⊆ H n
class Group.IsNilpotent (G : Type u_2) [] :
A group G is nilpotent if its upper central series is eventually G.
• nilpotent' : ∃ (n : ),
Instances
theorem Group.IsNilpotent.nilpotent' {G : Type u_2} [] [self : ] :
∃ (n : ),
theorem Group.IsNilpotent.nilpotent (G : Type u_2) [] :
∃ (n : ),
def IsAscendingCentralSeries {G : Type u_1} [] (H : ) :
A sequence of subgroups of G is an ascending central series if H 0 is trivial and ⁅H (n + 1), G⁆ ⊆ H n for all n. Note that we do not require that H n = G for some n.
Equations
Instances For
def IsDescendingCentralSeries {G : Type u_1} [] (H : ) :
A sequence of subgroups of G is a descending central series if H 0 is G and ⁅H n, G⁆ ⊆ H (n + 1) for all n. Note that we do not require that H n = {1} for some n.
Equations
Instances For
theorem ascending_central_series_le_upper {G : Type u_1} [] (H : ) (hH : ) (n : ) :
H n
Any ascending central series for a group is bounded above by the upper central series.
The upper central series of a group is an ascending central series.
theorem upperCentralSeries_mono (G : Type u_1) [] :
theorem nilpotent_iff_finite_ascending_central_series (G : Type u_1) [] :
∃ (n : ) (H : ), H n =
A group G is nilpotent iff there exists an ascending central series which reaches G in finitely many steps.
theorem is_decending_rev_series_of_is_ascending (G : Type u_1) [] {H : } {n : } (hn : H n = ) (hasc : ) :
IsDescendingCentralSeries fun (m : ) => H (n - m)
theorem is_ascending_rev_series_of_is_descending (G : Type u_1) [] {H : } {n : } (hn : H n = ) (hdesc : ) :
IsAscendingCentralSeries fun (m : ) => H (n - m)
theorem nilpotent_iff_finite_descending_central_series (G : Type u_1) [] :
∃ (n : ) (H : ), H n =
A group G is nilpotent iff there exists a descending central series which reaches the trivial group in a finite time.
def lowerCentralSeries (G : Type u_2) [] :
The lower central series of a group G is a sequence H n of subgroups of G, defined by H 0 is all of G and for n≥1, H (n + 1) = ⁅H n, G⁆
Equations
Instances For
@[simp]
theorem lowerCentralSeries_zero {G : Type u_1} [] :
@[simp]
theorem lowerCentralSeries_one {G : Type u_1} [] :
theorem mem_lowerCentralSeries_succ_iff {G : Type u_1} [] (n : ) (q : G) :
q lowerCentralSeries G (n + 1) q Subgroup.closure {x : G | p, q, p * q * p⁻¹ * q⁻¹ = x}
theorem lowerCentralSeries_succ {G : Type u_1} [] (n : ) :
lowerCentralSeries G (n + 1) = Subgroup.closure {x : G | p, q, p * q * p⁻¹ * q⁻¹ = x}
instance lowerCentralSeries_normal {G : Type u_1} [] (n : ) :
().Normal
Equations
• =
The lower central series of a group is a descending central series.
theorem descending_central_series_ge_lower {G : Type u_1} [] (H : ) (hH : ) (n : ) :
H n
Any descending central series for a group is bounded below by the lower central series.
theorem nilpotent_iff_lowerCentralSeries {G : Type u_1} [] :
∃ (n : ),
A group is nilpotent if and only if its lower central series eventually reaches the trivial subgroup.
noncomputable def Group.nilpotencyClass (G : Type u_1) [] [hG : ] :
The nilpotency class of a nilpotent group is the smallest natural n such that the n'th term of the upper central series is G.
Equations
Instances For
@[simp]
theorem upperCentralSeries_nilpotencyClass {G : Type u_1} [] [hG : ] :
The nilpotency class of a nilpotent G is equal to the smallest n for which an ascending central series reaches G in its n'th term.
The nilpotency class of a nilpotent G is equal to the smallest n for which the descending central series reaches ⊥ in its n'th term.
theorem lowerCentralSeries_length_eq_nilpotencyClass {G : Type u_1} [] [hG : ] :
The nilpotency class of a nilpotent G is equal to the length of the lower central series.
@[simp]
theorem lowerCentralSeries_nilpotencyClass {G : Type u_1} [] [hG : ] :
theorem lowerCentralSeries_map_subtype_le {G : Type u_1} [] (H : ) (n : ) :
Subgroup.map H.subtype (lowerCentralSeries (H) n)
instance Subgroup.isNilpotent {G : Type u_1} [] (H : ) [hG : ] :
A subgroup of a nilpotent group is nilpotent
Equations
• =
theorem Subgroup.nilpotencyClass_le {G : Type u_1} [] (H : ) [hG : ] :
The nilpotency class of a subgroup is less or equal to the nilpotency class of the group
@[instance 100]
instance Group.isNilpotent_of_subsingleton {G : Type u_1} [] [] :
Equations
• =
theorem upperCentralSeries.map {G : Type u_1} [] {H : Type u_2} [] {f : G →* H} (h : ) (n : ) :
theorem lowerCentralSeries.map {G : Type u_1} [] {H : Type u_2} [] (f : G →* H) (n : ) :
theorem lowerCentralSeries_succ_eq_bot {G : Type u_1} [] {n : } (h : ) :
theorem isNilpotent_of_ker_le_center {G : Type u_1} [] {H : Type u_2} [] (f : G →* H) (hf1 : f.ker ) (hH : ) :
The preimage of a nilpotent group is nilpotent if the kernel of the homomorphism is contained in the center
theorem nilpotencyClass_le_of_ker_le_center {G : Type u_1} [] {H : Type u_2} [] (f : G →* H) (hf1 : f.ker ) (hH : ) :
theorem nilpotent_of_surjective {G : Type u_1} [] {G' : Type u_2} [Group G'] [h : ] (f : G →* G') (hf : ) :
The range of a surjective homomorphism from a nilpotent group is nilpotent
theorem nilpotencyClass_le_of_surjective {G : Type u_1} [] {G' : Type u_2} [Group G'] (f : G →* G') (hf : ) [h : ] :
The nilpotency class of the range of a surjective homomorphism from a nilpotent group is less or equal the nilpotency class of the domain
theorem nilpotent_of_mulEquiv {G : Type u_1} [] {G' : Type u_2} [Group G'] [_h : ] (f : G ≃* G') :
Nilpotency respects isomorphisms
instance nilpotent_quotient_of_nilpotent {G : Type u_1} [] (H : ) [H.Normal] [_h : ] :
A quotient of a nilpotent group is nilpotent
Equations
• =
theorem nilpotencyClass_quotient_le {G : Type u_1} [] (H : ) [H.Normal] [_h : ] :
The nilpotency class of a quotient of G is less or equal the nilpotency class of G
theorem nilpotencyClass_quotient_center {G : Type u_1} [] [hH : ] :
Quotienting the center G reduces the nilpotency class by 1
theorem nilpotencyClass_eq_quotient_center_plus_one {G : Type u_1} [] [hH : ] [] :
The nilpotency class of a non-trivial group is one more than its quotient by the center
theorem of_quotient_center_nilpotent {G : Type u_1} [] (h : ) :
If the quotient by center G is nilpotent, then so is G.
theorem nilpotent_center_quotient_ind {P : (G : Type u_2) → [inst : ] → [inst : ] → Prop} (G : Type u_2) [] (hbase : ∀ (G : Type u_2) [inst : ] [inst_1 : ], P G) (hstep : ∀ (G : Type u_2) [inst : ] [inst_1 : ], P ()P G) :
P G
A custom induction principle for nilpotent groups. The base case is a trivial group (subsingleton G), and in the induction step, one can assume the hypothesis for the group quotiented by its center.
theorem derived_le_lower_central {G : Type u_1} [] (n : ) :
@[instance 100]
instance CommGroup.isNilpotent {G : Type u_2} [] :
Abelian groups are nilpotent
Equations
• =
theorem CommGroup.nilpotencyClass_le_one {G : Type u_2} [] :
Abelian groups have nilpotency class at most one
def commGroupOfNilpotencyClass {G : Type u_1} [] (h : ) :
Groups with nilpotency class at most one are abelian
Equations
Instances For
theorem lowerCentralSeries_prod {G₁ : Type u_2} {G₂ : Type u_3} [Group G₁] [Group G₂] (n : ) :
lowerCentralSeries (G₁ × G₂) n = ().prod ()
instance isNilpotent_prod {G₁ : Type u_2} {G₂ : Type u_3} [Group G₁] [Group G₂] [] [] :
Group.IsNilpotent (G₁ × G₂)
Products of nilpotent groups are nilpotent
Equations
• =
theorem nilpotencyClass_prod {G₁ : Type u_2} {G₂ : Type u_3} [Group G₁] [Group G₂] [] [] :
The nilpotency class of a product is the max of the nilpotency classes of the factors
theorem lowerCentralSeries_pi_le {η : Type u_2} {Gs : ηType u_3} [(i : η) → Group (Gs i)] (n : ) :
lowerCentralSeries ((i : η) → Gs i) n Subgroup.pi Set.univ fun (i : η) => lowerCentralSeries (Gs i) n
theorem isNilpotent_pi_of_bounded_class {η : Type u_2} {Gs : ηType u_3} [(i : η) → Group (Gs i)] [∀ (i : η), Group.IsNilpotent (Gs i)] (n : ) (h : ∀ (i : η), Group.nilpotencyClass (Gs i) n) :
Group.IsNilpotent ((i : η) → Gs i)
products of nilpotent groups are nilpotent if their nilpotency class is bounded
theorem lowerCentralSeries_pi_of_finite {η : Type u_2} {Gs : ηType u_3} [(i : η) → Group (Gs i)] [] (n : ) :
lowerCentralSeries ((i : η) → Gs i) n = Subgroup.pi Set.univ fun (i : η) => lowerCentralSeries (Gs i) n
instance isNilpotent_pi {η : Type u_2} {Gs : ηType u_3} [(i : η) → Group (Gs i)] [] [∀ (i : η), Group.IsNilpotent (Gs i)] :
Group.IsNilpotent ((i : η) → Gs i)
n-ary products of nilpotent groups are nilpotent
Equations
• =
theorem nilpotencyClass_pi {η : Type u_2} {Gs : ηType u_3} [(i : η) → Group (Gs i)] [] [∀ (i : η), Group.IsNilpotent (Gs i)] :
Group.nilpotencyClass ((i : η) → Gs i) = Finset.univ.sup fun (i : η) => Group.nilpotencyClass (Gs i)
The nilpotency class of an n-ary product is the sup of the nilpotency classes of the factors
@[instance 100]
instance IsNilpotent.to_isSolvable {G : Type u_1} [] [h : ] :
A nilpotent subgroup is solvable
Equations
• =
theorem normalizerCondition_of_isNilpotent {G : Type u_1} [] [h : ] :
theorem IsPGroup.isNilpotent {G : Type u_1} [hG : ] [] {p : } [hp : Fact ()] (h : IsPGroup p G) :
A p-group is nilpotent
theorem isNilpotent_of_product_of_sylow_group {G : Type u_1} [hG : ] [] (e : ((p : { x : // x ().primeFactors }) → (P : Sylow (p) G) → P) ≃* G) :
If a finite group is the direct product of its Sylow groups, it is nilpotent
theorem isNilpotent_of_finite_tfae {G : Type u_1} [hG : ] [] :
[, , ∀ (H : ), H.Normal, ∀ (p : ), Fact ()∀ (P : Sylow p G), (P).Normal, Nonempty (((p : { x : // x ().primeFactors }) → (P : Sylow (p) G) → P) ≃* G)].TFAE
A finite group is nilpotent iff the normalizer condition holds, and iff all maximal groups are normal and iff all Sylow groups are normal and iff the group is the direct product of its Sylow groups.
@[deprecated isNilpotent_of_finite_tfae]
theorem isNilpotent_of_finite_tFAE {G : Type u_1} [hG : ] [] :
[, , ∀ (H : ), H.Normal, ∀ (p : ), Fact ()∀ (P : Sylow p G), (P).Normal, Nonempty (((p : { x : // x ().primeFactors }) → (P : Sylow (p) G) → P) ≃* G)].TFAE
Alias of isNilpotent_of_finite_tfae.
A finite group is nilpotent iff the normalizer condition holds, and iff all maximal groups are normal and iff all Sylow groups are normal and iff the group is the direct product of its Sylow groups.
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# Numpy Array Equal Method : How to check if numpy arrays are equal
Numpy Array Equal Method
Sometimes we have two or more NumPy arrays and want to validate the equality between them. To do so there is a method in NumPy and that is numpy.array_equal(). In this entire tutorial, I will show you the implementation of this method to check NumPy array is equal or not. All things will be done step by step.
## Steps to Check Numpy Array Equal or Not
### Step 1: Import the library
Here in this entire post, I am using only NumPy module. So let’s import it.
import numpy as np
### Step 2: Create a Sample Numpy array
I want to check whether a NumPy array is equal or not. To do so you have let’s create three NumPy arrays and then implement the method. Two arrays will be equal and one is different.
Array 1
array_1 = np.array([1,2,3,4,5,6])
Output
array([1, 2, 3, 4, 5, 6])
Array 2
array_2 = np.array([1,2,3,4,5,6])
Output
array([1, 2, 3, 4, 5, 6])
Array 3
array_3 = np.array([1,2,3])
Output
array([1, 2, 3])
### Step 3: Check the Numpy Array is Equal or Not
After the above two steps let’s check the equality of the NumPy array. I will show you all the methods to do so. Let me see it.
#### Method 1: Check equality of Numpy array elementwise
You can check whether a single element in the array is equal or not using the logical == operator. For example, If I check array_1 and array_2 then all the output will be True, and if array_1 and array_3 then you will get a single output False if it doesn’t match.
Execute the below lines of code.
array_1 == array_2
Output
array_1 == array_3
Output
False
#### Method 2: Check equality of Numpy array using numpy.array_equal function
The other method to check Numpy Array is Equal or not is using the numpy.array() method. Here you have to just pass the two arrays as an argument to get the output.
Comparison of Array 1 and Array 2
Let’s compare array_1d and array_2d and see the output.
np.array_equal(array_1,array_2)
Output
Comparison of Array 1 and Array 3
In the same way, If I will compare array_1 and array_3 then you will get the output as False.
np.array_equal(array_1,array_3)
Output
## Conclusion
Numpy array_equal() is a mostly used function to validate any duplicacy of the array. There are two methods I have compiled for you. If you will ask me which method to use then I will suggest choosing the second method.
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sci.electronics.basics
[Top] [All Lists]
## Re: Diode in series with light bulb
Subject: Re: Diode in series with light bulb "Ralph Mowery" Tue, 20 Dec 2005 18:02:05 GMT sci.electronics.basics
```"steve" wrote in message news:1135101130.732259.280690@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx > I was reading a web site that has information about light bulbs. Here > is a quote relating to a question I wanted to ask. > > -- Quote --- > "Reducing the voltage applied to a light bulb will reduce the filament > temperature, resulting in a dramatic increase in life expectancy. > One device sold to do this is an ordinary silicon diode built into a > cap that is made to stick to the base of a light bulb. A diode lets > current through in only one direction, causing the bulb to get power > only 50 percent of the time if it is operated on AC. This effectively > reduces the applied voltage by about 30 percent. (Reducing the voltage > to its original value times the square root of .5 results in the same > power consumption as applying full voltage half the time.) The life > expectancy is increased very dramatically. However, the power > consumption is reduced by about 40 percent (not 50 since the cooler > filament has less resistance) and light output is reduced by reduced by > about 70 percent (cooler filaments are less efficient at radiating > visible light)." > > --- > My question is really just a just wondering kind of question. I have no > interest in doing this. > > I have seen the type of "Savings " devices written about above. Would > the same thing be achieved if I simply took a diode of the proper > rating and put it in line in one of the wires running to an > incandescent light bulb? > Yes, you would get the same effect. Unless the bulb is in a hard to reach place you would be beter off just reducing the wattage of the bulb. The calculations I have seen (not verified) say you will save more on electricity than the extra bulb replacements will cost. ```
Current Thread Diode in series with light bulb, steve Re: Diode in series with light bulb, Ralph Mowery <= Re: Diode in series with light bulb, Don Bruder Re: Diode in series with light bulb, steve Re: Diode in series with light bulb, Don Bruder Re: Diode in series with light bulb, Warren Weber Re: Diode in series with light bulb, cornytheclown Re: Diode in series with light bulb, steve Re: Diode in series with light bulb, redbelly
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# Metric vs. other measurement systems - chart
Show 40 post(s) from this thread on one page
Page 12 of 46 First 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 ... Last
• Dec 18, 2020, 05:11 PM
hemmjo
Why is it that most to the "Metric" countries sell "pints" in the pubs?
"A pint glass is a form of drinkware made to hold either a British ("imperial") pint of 20 imperial fluid ounces (568 ml) or an American pint of 16 US fluid ounces (473 ml). Other definitions also exist, see below. These glasses are typically used to serve beer, and also often for cider."
• Dec 18, 2020, 06:00 PM
IntheGroove
• Dec 18, 2020, 06:05 PM
mklotz
and exceeds the volume of three Olympic swimming pools.
• Dec 18, 2020, 06:42 PM
Karl_H
And weighs more than 12 jumbo jets!
• Dec 19, 2020, 08:37 AM
metric_taper
I'll never understand why the USA is still stuck in the old system. I was trained to be bi-lingual with SAE and SI in all my engineering and physics classes in the early 80s. But work did everything in Imperial, and put unit dimensions in parenthesis for metric.
And the worlds pilots are still using altitude in feet, barometric pressure in inches of Hg, and airspeed in knots. At least unit temperature operating ranges was in Celsius.
All the POTUS Jimmy Carter signs are gone from the roadways. And my latest auto does not have the dual speedometer range of earlier, only in MPH (and it's a Japanese design made in Mexico). If you live in states that incorporated as section road use of land, the mile will be stuck with us forever. As every mile, the state owns a 60 foot right of way, even across federal lands.
My only issue with the metric system is the size of the mm is wrong. Arbitrary. It should have been based on human factors of what the unaided eye can see, and be marked on a steel rule *. But like every other mistake, they become permanent errors that are supported forever.
.
.
* I'm not aware of any quantum length that could set an absolute standard. Human factor is why water is used for a temperature scale, metric weight used that as well. And it's only an issue when correct dimension analysis is not done.
At least my newer lathe has both scales, and a mix of Imperial and metric feed screws. It has change gears for metric and SAE thread, but I can't disengage the half nuts during metric, and that makes me razzle frazzle, and cuss.
• Dec 19, 2020, 11:05 AM
bruce.desertrat
Quote:
Originally Posted by metric_taper
All the POTUS Jimmy Carter signs are gone from the roadways.
Not entirely. Interstate 19 (which runs south from Interstate 10 where it makes that turn east at the southwest corner of Tucson) is labeled in mph for speed, but km for distance, still. I think it's the last one left.
• Dec 19, 2020, 06:40 PM
TheElderBrother
Let's make a list of all worthwhile inventions that come from France.
I'll wait.
• Dec 19, 2020, 06:48 PM
IntheGroove
Fries
Toast
Dips
Windows
Doors
and of course, Kiss...
• Dec 19, 2020, 07:06 PM
bruce.desertrat
Pasteurization
Canned food
The rabies vaccine
The germ theory of disease
The monoplane
The bunsen burner (developed in Pasteur's laboratory)
Lets not forget the Razor of Democracy itself, Dr Guillotine's invention...
that's just off the top of my head...
• Dec 19, 2020, 07:19 PM
IntheGroove
...also Democracy and Existentialism...
Show 40 post(s) from this thread on one page
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# [R] Compare two normal to one normal
Rolf Turner r.turner at auckland.ac.nz
Wed Sep 23 04:45:47 CEST 2015
```On 23/09/15 13:39, John Sorkin wrote:
> Charles, I am not sure the answer to me question, given a dataset,
> how can one compare the fit of a model of the fits the data to a
> mixture of two normal distributions to the fit of a model that uses a
> single normal distribution, can be based on the glm model you
> suggest.
>
> I have used normalmixEM to fit the data to a mixture of two normal
> curves. The model estimates four (perhaps five) parameters: mu1, sd^2
> 1, mu2, sd^2, (and perhaps lambda, the mixing proportion. The mixing
> proportion may not need to be estimated, it may be determined once
> once specifies mu1, sd^2 1, mu2, and sd^2.) Your model fits the data
> to a model that contains only the mean, and estimates 2 parameters
> mu0 and sd0^2. I am not sure that your model and mine can be
> considered to be nested. If I am correct I can't compare the log
> likelihood values from the two models. I may be wrong. If I am, I
> should be able to perform a log likelihood test with 2 (or 3, I am
> not sure which) DFs. Are you suggesting the models are nested? If so,
> should I use 3 or 2 DFs?
You are quite correct; there are subtleties involved here.
The one-component model *is* nested in the two-component model, but is
nested "ambiguously".
(1) The null (single component) model for a mixture distribution is
ill-defined. Note that a single component could be achieved either by
setting the mixing probabilities equal to (1,0) or (0,1) or by setting
mu_1 = mu_2 and sigma_1 = sigma_2.
(2) However you slice it, the parameter values corresponding to the null
model fall on the *boundary* of the parameter space.
(3) Consequently the asymptotics go to hell in a handcart and the
likelihood ratio statistic, however you specify the null model, does not
have an asymptotic chi-squared distribution.
(4) I have a vague idea that there are ways of obtaining a valid
asymptotic null distribution for the LRT but I am not sufficiently
knowledgeable to provide any guidance here.
(5) You might be able to gain some insight from delving into the
literature --- a reasonable place to start would be with "Finite Mixture
Models" by McLachlan and Peel:
@book{mclachlan2000finite,
title={Finite Mixture Models, Wiley Series in
Probability and Statistics},
author={McLachlan, G and Peel, D},
year={2000},
publisher={John Wiley \& Sons, New York}
}
(6) My own approach would be to do "parametric bootstrapping":
* fit (to the real data) the null model and calculate
the log-likelihood L1, any way you like
* fit the full model and determine the log-likelihood L2
* form the test statistic LRT = 2*(L2 - L1)
* simulate data sets from the fitted parameters for the null model
* for each such simulate data set calculate a test statistic in the
foregoing manner, obtaining LRT^*_1, ..., LRT^*_N
* the p-value for your test is then
p = (m+1)/(N+1)
where m = the number of LRT^*_i values that greater than LRT
The factor of 2 is of course completely unnecessary. I just put it in
"by analogy" with the "real", usual, likelihood ratio statistic.
Note that this p-value is *exact* (not an approximation!) --- for any
value of N --- when interpreted with respect to the "total observation
procedure" of observing both the real and simulated data. (But see
below.) That is, the probability, under the null hypothesis, of
observing a test statistic "as extreme as" what you actually observed is
*exactly* (m+1)/(N+1). See e.g.:
@article{Barnard1963,
author = {G. A. Barnard},
title = {Discussion of ``{T}he spectral analysis of point processes''
by {M}. {S}. {B}artlett},
journal = {J. Royal Statist. Soc.},
series = {B},
volume = {25},
year = {1963},
pages = {294}
}
or
@article{Hope1968,
author = {A.C.A. Hope},
title = {A simplified {M}onte {C}arlo significance test procedure},
journal = {Journal of the Royal Statistical Society, series {B}},
year = 1968,
volume = 30,
pages = {582--598}
}
Taking N=99 (or 999) is arithmetically convenient.
However I exaggerate when I say that the p-value is exact. It would be
exact if you *knew* the parameters of the null model. Since you have to
estimate these parameters the test is (a bit?) conservative. Note that
the conservatism would be present even if you eschewed the "exact" test
and an "approximate" test using a (very) large value of N.
Generally conservatism (in this context! :-) ) is deemed to be no bad thing.
cheers,
Rolf Turner
P. S. I think that the mixing parameter must *always* be estimated.
I.e. even if you knew mu_1, mu_2, sigma_1 and sigma_2 you would still
have to estimate "lambda". So you have 5 parameters in your full model.
Not that this is particularly relevant.
R. T.
--
Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276
```
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The Indie Hacker Grind
Content development is not an easy task and it is hard to stay motivated. There is still a significant amount of work for us to finish the methods and flow development and it is overwhelming sometimes. On the bright side, we got our first few organic search traffic clicks! We got our first Google image […]
Lots of Progress!
It’s been a month, so it’s time for another update. The past month has been pretty busy and lots of fun. Here is what we’ve been up to: I added another person to the StatsTest team. I wasn’t moving quite as fast as I wanted to, so I brought another person on board to help
Focusing on the problem rather than the solution
I’ve been moving a bit more slowly over the holidays, but with the start of the new year I’m back at it again. I finished the proportional difference methods today, which means all of the “Difference” methods are now finished. This is 25 methods out of the total 45 methods projected for the StatsTest workflow–that’s
Mapping Out An Intro To Stats Domain
StatsTest.com is making great progress. I just finished the 16th statistical method. All 16 of these methods fall under difference, meaning you want to see whether two groups are significantly different on your variable of interest, rather than relationship or prediction. All 16 of these methods also fall under continuous, meaning the variable that you
Making Statistics Easy And Simple Is Not So Simple
This week I finished all of the one sample and two sample (continuous dependent variable) tests. Moving on, I just spent a few hours diving into ANOVA, ANCOVA, MANOVA, and MANCOVA analyses in all of their parametric vs non-parametric, repeated measures vs independent, covariate vs no covariate, multiple dependent variables vs single dependent variable, and
Which statistical test should I use?
Visit Choose Your Test to answer a few questions to choose the appropriate test for your specific data and question. If you are interested in my process or reasoning in developing this, read on below. I’m scouring the web for statistical flow charts and introduction to statistics books to get a sense for what questions
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In my exploration for other companies and websites devoted to easy-to-understand statistics and easy-to-use statistical software I came across StatWing: Efficient and Delightful Data Science. StatWing was created by a few Stanford graduates (plus a few others). They went on to get Y-Combinator funding in 2012 and were acquired by Qualtrics in 2016 (who were
Hello World, this is StatsTest
StatsTest is meant to be extremely user-friendly and practitioner oriented. The goal of StatsTest is to enable anyone that needs to run a statistical test to understand which method they should be using, what assumptions come along with the method, and why the method is the best way to analyze their data. Most stats resources
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## A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from its end determine the spring constant in N/m
Question
A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from its end determine the spring constant in N/m
in progress 0
3 years 2021-08-02T01:22:04+00:00 1 Answers 76 views 0
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disappointed by Kaplan GMAT 800 : General GMAT Questions and Strategies
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# disappointed by Kaplan GMAT 800
Author Message
Director
Joined: 02 Mar 2006
Posts: 580
Location: France
Followers: 1
Kudos [?]: 99 [0], given: 0
disappointed by Kaplan GMAT 800 [#permalink]
### Show Tags
26 May 2006, 00:54
I've recently bought GMAT800 2006-2007 edition because I read everywhere that it was a very challenging material to get prepared for >700 scores.
I have following critics:
1.
Indeed the verbal part is somehow more difficult, but not as expected. I'm doing right now the SC and CR1000, and I must say they are of better quality and many are much harder.
The quant part is not so difficult.
They just compiled the difficult problems from their other books/cdrom!
2.
The book is big, heavy but in quantity poorly filled.
eg: For the RC, the same text is repeated on all the pages where questions are asked. I believe it is to be more convenient for the reader, who doesnt have to turn the pages back. So typically one question for RC takes one page!
For the CR, 2 pb/pages and the explanation/answer takes almost one page each.
Moreover, there are huge white/blank areas which could have been easily filled with text.
3. The last and big problem is that this book takes problems from Kaplan regular gmat book 2003 and from the cd room. I had 3 CAT left, now I assume it will distort the results. Thus, I stopped reading the book to not make the things worse.
Conclusion. I paid 21Euros for this book which doesnt bring any added value compared with the kaplan material I had already. same advices, problems... And for hard pbs, I just need to go in the 1000s and one questions....
For info, until now I worked on OG10 and 11, kaplan CD, 1000 docs and didnt start yet the PR CATs. I worked at the beginning with Cliff CAT and Barron, but they are not worth to work with(verbal part)
Cheers
Kaplan GMAT Prep Discount Codes Math Revolution Discount Codes Magoosh Discount Codes
disappointed by Kaplan GMAT 800 [#permalink] 26 May 2006, 00:54
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## 10 Search Results
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## How many years will it take a principal of \$400 to generate simple interest of \$112 at a rate of 14% per annum?
Question
How many years will it take a principal of \$400 to generate simple interest of \$112 at a rate of 14% per annum?
in progress 0
45 mins 2021-09-15T10:43:03+00:00 2 Answers 0
Step-by-step explanation:
Simple interest means the increment is constant. 112 * .14 = 15.68
How much do we need to increase by ?
400-112= 288
288/15.68 approx 18.4. Since we can’t have .4 of a year, it is 19 years.
Principle = \$400
Simple Interest = \$112
Rate of interest = 14%
Amount =\$512
S.I =P*T*R/100
112=400*T*14/100
112=4*14*T
112/56=T
T =2
T = 2 years
Step-by-step explanation:
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# Lesson 7
Fracciones no unitarias en la recta numérica
## Warm-up: Conteo grupal: Cuartos (10 minutes)
### Narrative
The purpose of this Choral Count is to invite students to practice counting by $$\frac{1}{4}$$ and notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to locate fractions on the number line using their knowledge of unit fractions. Save the recorded count to compare to a count in an upcoming lesson.
### Launch
• “Cuenten de $$\frac{1}{4}$$ en $$\frac{1}{4}$$, empezando en $$\frac{1}{4}$$” // “Count by $$\frac{1}{4}$$, starting at $$\frac{1}{4}$$.”
• Record as students count. Record 4 fractions in each row, then start a new row. There will be 4 rows.
• Stop counting and recording at $$\frac{16}{4}$$.
### Activity
• “¿Qué patrones ven?” // “What patterns do you see?” (The bottom part of the fraction never changes. The top part of the fraction is increasing by 1. The rows end at counts of four in the top like 4, 8, 12, 16.)
• 1–2 minutes: quiet think time
• Record responses.
### Activity Synthesis
• “¿En qué se parece contar de fracción en fracción a contar de número entero en número entero? ¿En qué es diferente?” // “How is counting by fractions the same as counting by whole numbers? How is it different?” (The top part of the fraction is just like counting by whole numbers, going up one. The bottom part is different because it doesn’t change.)
• “¿Alguien puede describir el patrón con otras palabras?” // “Who can restate the pattern in different words?”
• “¿Alguien quiere agregar otra observación sobre por qué ocurre ese patrón aquí?” // “Does anyone want to add an observation on why that pattern is happening here?”
• “¿Están de acuerdo o en desacuerdo? ¿Por qué?” // “Do you agree or disagree? Why?”
• “Es útil hablar de la parte de arriba de la fracción y de la parte de abajo de la fracción. Tenemos nombres para esas partes. La parte de abajo de una fracción se llama el denominador. Nos dice en cuántas partes iguales está partida la unidad. La parte de arriba de una fracción se llama el numerador. Nos dice cuántas de esas partes iguales están descritas. Busquen lugares en la lección de hoy en los que esa terminología les puede ayudar a explicar su razonamiento” // “This is a place where it’s helpful to talk about the top part of the fraction and the bottom part of the fraction. We have words for those parts. The bottom part of a fraction is called the denominator. It tells how many equal parts the whole was partitioned into. The top part of a fraction is called the numerator. It tells how many of the equal parts are being described. Look for places in today's lesson where that terminology might help you explain your reasoning.”
• Display the terms “denominador” // “denominator” and “numerador” // “numerator” and their definitions, and keep displayed throughout the lesson.
## Activity 1: Carrera sobre rectas numéricas (15 minutes)
### Narrative
The purpose of this activity is for students to practice identifying fractional intervals along a number line. This is Stage 2 of the center activity, Number Line Scoot. This activity encourages students to count by the number of intervals (the numerator). Students have to land exactly on the last tick mark, which represents 4, to encourage them to move along different number lines. While this activity does not focus on equivalence, it gives students exposure to this idea before they work more formally with it in the next section. In the synthesis, students relate counting on a number line marked off in whole numbers to their number lines marked off in fractional-sized intervals.
It may be helpful to play a few rounds with the whole class to be sure students are clear on the rules of the game. Keep the number line game boards for center use.
Engagement: Develop Effort and Persistence. Check in and provide each group with feedback that encourages collaboration and community. For example, check in after the first round of Number Line Scoot.
Supports accessibility for: Attention, Social-Emotional Functioning
### Required Materials
Materials to Gather
Materials to Copy
• Number Line Scoot Stage 2 Directions, Spanish
• Number Line Scoot Stage 2 Gameboard
### Required Preparation
• Each group of 2 students needs a number cube.
• Each student needs at least 5 base-ten cubes to use as game pieces.
### Launch
• Groups of 2
• Give each group of 2 a gameboard, two recording sheets, a number cube, and at least 10 base-ten cubes.
• “Ahora van a jugar un juego en el que se van a mover, de fracción en fracción, sobre diferentes rectas numéricas. Para comenzar, cada jugador pone un cubo pequeño sobre el cero de cada recta numérica. El objetivo del juego es llevar tantos cubos como puedan hasta el 4 de cualquiera de las rectas numéricas” // “Now you will play a game where you move, by fractions, along different number lines. To start, each player places a small cube on zero on each number line. The goal of the game is to get as many small cubes as you can to the 4 on any of the number lines.”
• Roll the number cube, demonstrate where to record the rolled number and move that fraction along one of the number lines.
### Activity
• 10 minutes: partner work time
• As students work, monitor for students who count by the numerator once they have chosen a number line.
### Activity Synthesis
• Display a gameboard with a marker on $$\frac{3}{4}$$.
• “Si yo sacara 4 y escogiera mover $$\frac{4}{4}$$, ¿cómo contarían la movida?” // “If I rolled a 4, and chose to move $$\frac{4}{4}$$, how would you count the move?” (I would count 1, 2, 3, 4.)
• “¿Cómo supieron que se habían movido $$\frac{4}{4}$$?” // “How did you know you have moved $$\frac{4}{4}$$?” (Because each space is $$\frac{1}{4}$$, so I need to move 4 times.)
• Display a number line marked with only 0, 1, 2, 3, 4.
• “¿En qué se parecen contar sobre esta recta numérica y contar sobre sus rectas numéricas? ¿En qué son diferentes?” // “How is counting along this number line the same and different than counting along your number lines?” (On the whole number one each space is 1 so we just count 1, 2, 3, 4. On our number lines we still count the jumps, but now each space is smaller than 1 so we need the denominator to tell us the size of each space.)
## Activity 2: Fracciones en la recta numérica (10 minutes)
### Narrative
The purpose of this activity is for students to locate a variety of fractions on the number line. Students are given a fraction less than 1 and greater than 1 with the same denominator to locate on each number line. The activity synthesis focuses on counting the number of unit fractions in a fraction to locate it on a number line and how to determine whether fractions are less than 1 or greater than 1. As they locate the fractions on the number lines, students strengthen their understanding of the meaning of the numerator and denominator of a fraction (MP6).
MLR8 Discussion Supports. Synthesis: Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
### Launch
• Groups of 2
• Display the number line for fourths from Number Line Scoot.
• “¿Qué saben sobre $$\frac{3}{4}$$ y $$\frac{6}{4}$$?” // “What do you know about $$\frac{3}{4}$$ and $$\frac{6}{4}$$?” (They both have 4 on the bottom. Three is less than 4 and 6 is greater than 4. They are both numbers of fourths.)
• Share and record responses.
### Activity
• “Con su compañero, ubiquen las fracciones en cada recta numérica y contesten las preguntas sobre su trabajo” // “Work with your partner to locate the fractions on each number line and answer the questions about your work.”
• 4–6 minutes: partner work time
• Monitor for students who locate non-unit fractions on the number line by partitioning into equal parts of size $$\frac{1}{b}$$ and count the number of those parts.
### Student Facing
1. Ubica y marca $$\frac{3}{4}$$ y $$\frac{6}{4}$$.
2. Ubica y marca $$\frac{7}{8}$$ y $$\frac{12}{8}$$.
3. Ubica y marca $$\frac{2}{3}$$ y $$\frac{4}{3}$$.
4. Ubica y marca $$\frac{2}{6}$$ y $$\frac{7}{6}$$.
5. ¿Cómo partiste la recta numérica cuando ibas a ubicar los números $$\frac{7}{8}$$ y $$\frac{12}{8}$$? Explica tu razonamiento.
6. ¿Qué patrones observaste en las fracciones que ubicaste?
### Student Response
If students partition the interval from 0 to 2 into fourths instead of the interval from 0 to 1 (or a similar error with another fraction), consider asking:
• “Dime cómo encontraste $$\frac{3}{4}$$ en la recta numérica” // “Tell me about how you found $$\frac{3}{4}$$ on the number line?”
• “¿Cómo nos ayuda el denominador a saber cómo partir la recta numérica?” // “How does the denominator help us know how to partition the number line?”
### Activity Synthesis
• “¿Qué patrones observaron en las fracciones que ubicaron?” // “What patterns did you notice in the fractions you located?”
• “¿Cómo saben cuándo una fracción es menor que 1?” // “How do you know when a fraction is less than 1?”
• “¿Cómo saben cuándo una fracción es mayor que 1?” // “How do you know when a fraction is greater than 1?”
• “¿Cómo les ayudó contar de fracción unitaria en fracción unitaria a ubicar las otras fracciones en la recta numérica?” // “How did counting by unit fractions help you locate the other fractions on the number line?” (I counted by $$\frac{1}{4}$$ three times to find $$\frac{3}{4}$$. I counted by $$\frac{1}{6}$$ as I moved along the number line, like $$\frac{1}{6}$$, $$\frac{2}{6}$$, $$\frac{3}{6}$$, $$\frac{4}{6}$$, $$\frac{5}{6}$$, $$\frac{6}{6}$$, $$\frac{7}{6}$$ to find $$\frac{7}{6}$$.)
## Activity 3: ¿Cuál es la fracción? (10 minutes)
### Narrative
The purpose of this activity is for students to determine how a number line is partitioned and what fraction is marked on it with only 0, 1, and 2 labeled. Students partition and locate and mark, but don’t label, a fraction on a number line and then trade with a partner to determine the fraction their partner has marked. Remind students to mark, but not to label their partitions and their fraction, so that their partner only has the 0, 1, and 2 to use to determine what fraction is on their number line.
### Launch
• Groups of 2
• “Completen la primera parte de la actividad individualmente. Partan la recta numérica y pongan una marca que represente una fracción, pero no escriban el número. No le digan a su compañero cómo partieron la recta numérica ni qué número representa la marca” // “Complete the first part of the activity on your own. Partition the number line and mark, but don’t label, a fraction on the number line. Don’t tell your partner how you are partitioning or what number you are marking.”
• 2 minutes: independent work time
### Activity
• “Ahora, intercambien rectas numéricas con su pareja y respondan las preguntas sobre la recta numérica de su compañero. Cuando ambos terminen, compartan cómo razonaron” // “Now, trade number lines with your partner and answer the questions about their number line. When you are both finished, share your reasoning”
• 1–2 minutes: independent work time
• 1–2 minutes: partner work time
### Student Facing
1. Haz una partición de la recta numérica en cualquier número de partes de igual tamaño. Escoge una fracción y ubícala. Pon una marca que la represente, pero no escribas el número.
2. Intercambia tu recta numérica con un compañero.
1. ¿Cómo partió su recta numérica tu compañero?
2. ¿Qué número representa la marca de tu compañero en su recta numérica? Explica tu razonamiento.
Si te queda tiempo: juega otra vez.
### Activity Synthesis
• Display a number line partitioned by a student.
• “Hablen con su compañero sobre qué fracción está representada” // “Talk to your partner about what fraction is represented.”
• Share and record responses.
• “¿Cómo decidieron de qué manera partir su recta numérica y qué fracción poner en su recta numérica?” // “How did you decide how to partition your number line and what fraction you’d put on your number line?”
• “¿Cómo decidieron de qué manera estaba partida la recta numérica de su compañero y qué fracción estaba marcada?” // “How did you decide how your partner’s number line was partitioned and decide what fraction was marked?”
## Lesson Synthesis
### Lesson Synthesis
“Hoy ubicamos más fracciones en la recta numérica. En una lección anterior, aprendimos cómo se construyen las fracciones a partir de fracciones unitarias. ¿Cómo vemos esto en la recta numérica?” // “Today we located more fractions on the number line. In an earlier lesson, we learned how fractions are built from unit fractions. How do we see this on the number line?” (I counted the unit fractions, like 3 one-fourths, to get to $$\frac{3}{4}$$. I partition the number line into unit fractions and then I can count parts up to the fraction I am locating.)
Draw or have students draw a number line with $$\frac{3}{4}$$ marked, such as:
Trace or have them trace through and count the 3 one-fourths to get to $$\frac{3}{4}$$, such as:
“Recuerden que cuando ubicamos $$\frac{3}{4}$$ en la recta numérica, es útil mostrar o pensar en las tres partes (3 cuartas partes). Luego, ponemos la marca y escribimos el número $$\frac{3}{4}$$ al final de esas partes. Cuando ubicamos y marcamos fracciones, no hay que marcar la longitud, se puede simplemente contar las fracciones unitarias y, luego, poner el punto al final y marcarlo” // “Remember, when we are locating a fraction on the number line, it might be helpful to think about or show the 3 one-fourth parts, and then we mark and label the number $$\frac{3}{4}$$ at the end of those parts. When we locate and label fractions, you don’t have to mark the length, you can just count the unit fractions and then mark and label the point at the end.”
Point to the location of each fraction on the number line and count: “$$\frac{1}{4}$$, $$\frac{2}{4}$$, $$\frac{3}{4}$$.”
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## Conversion formula
The conversion factor from minutes to weeks is 9.9206349206349E-5, which means that 1 minute is equal to 9.9206349206349E-5 weeks:
1 min = 9.9206349206349E-5 wk
To convert 3783 minutes into weeks we have to multiply 3783 by the conversion factor in order to get the time amount from minutes to weeks. We can also form a simple proportion to calculate the result:
1 min → 9.9206349206349E-5 wk
3783 min → T(wk)
Solve the above proportion to obtain the time T in weeks:
T(wk) = 3783 min × 9.9206349206349E-5 wk
T(wk) = 0.37529761904762 wk
The final result is:
3783 min → 0.37529761904762 wk
We conclude that 3783 minutes is equivalent to 0.37529761904762 weeks:
3783 minutes = 0.37529761904762 weeks
## Alternative conversion
We can also convert by utilizing the inverse value of the conversion factor. In this case 1 week is equal to 2.6645519429025 × 3783 minutes.
Another way is saying that 3783 minutes is equal to 1 ÷ 2.6645519429025 weeks.
## Approximate result
For practical purposes we can round our final result to an approximate numerical value. We can say that three thousand seven hundred eighty-three minutes is approximately zero point three seven five weeks:
3783 min ≅ 0.375 wk
An alternative is also that one week is approximately two point six six five times three thousand seven hundred eighty-three minutes.
## Conversion table
### minutes to weeks chart
For quick reference purposes, below is the conversion table you can use to convert from minutes to weeks
minutes (min) weeks (wk)
3784 minutes 0.375 weeks
3785 minutes 0.375 weeks
3786 minutes 0.376 weeks
3787 minutes 0.376 weeks
3788 minutes 0.376 weeks
3789 minutes 0.376 weeks
3790 minutes 0.376 weeks
3791 minutes 0.376 weeks
3792 minutes 0.376 weeks
3793 minutes 0.376 weeks
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Black Americans are, on the whole, about twice as likely as : GMAT Critical Reasoning (CR)
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Black Americans are, on the whole, about twice as likely as
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Black Americans are, on the whole, about twice as likely as [#permalink]
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18 Oct 2003, 18:52
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Black Americans are, on the whole, about twice as likely as White Americans to develop high blood pressure. This likelihood also holds for westernized Black Africans when compared to White Africans.
Researchers have hypothesized that this predisposition in westernized Blacks may reflect an interaction between western high-salt diets and genes that adapted to an environmental scarcity of salt.
Which of the following statements about present-day, westernized Black Africans, if true, would most tend to confirm the researchersтАЩ hypothesis?
(A) The blood pressures of those descended from peoples situated throughout their history in Senegal and Gambia, where salt was always available, are low.
(B) The unusually high salt consumption in certain areas of Africa represents a serious health problem.
(C) Because of their blood pressure levels, most White Africans have markedly decreased their salt consumption.
(D) Blood pressures are low among the Yoruba, who, throughout their history, have been situated far inland from sources of sea salt and far south of Saharan salt mines.
(E) No significant differences in salt metabolism have been found between those people who have had salt available throughout their history and those who have not.
If you have any questions
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19 Oct 2003, 03:40
Well... an interesting question.
As for me I was struggling between B and E, but chose E. Here's my thoughts:
Imo A is incorrect.
The blood pressures of those descended from peoples situated throughout their history in Senegal and Gambia, where salt was always available, are low. First of all, I do not like those explicit geografical pointers (Senegal and Gambia). Next, the argument talks about hypothising that Black Americans are coming from regions with scarce salt. But Choice A offers quite oppisite facts. Out of the Scope.
B. The same story. This answer choice suggests "certain areas of Africa" as a reference point. We are analysing the Black Africans in general, "certain areas" are deceptive.
C is tempting, but how can we be sure that it assumes HIGH blood pressure, but not LOW?
D is tempting as well, but it doesn't bear on genes (I treat "genes" as Subject-specific qualifier).
E I took me quite a long time to land with this choice, but look: if we know that both groups of people have similar salt methabolism level, we may conclude that even if there are different levels of salt consumption in both groups, African people organism itself produces sufficient level of salt. That gives us 100% proof that high salt American diets are killing for Black Africans, who thus expose temselves to high levels of salt inputs.
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19 Oct 2003, 08:48
ye, the correct answer is A, but, to me too, at the first instance, it seemed like this particular choice is refuting the hypothesis presented by the author.
But, if you look closer, you 'll figure out the reason behind. As, the cause of BP--that author marks--is interaction between high-salt diet and genes from salt scare places. But for people who are from salt rich places, hypothesis should be wrong and the first choice says in line with the hypothesis.
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19 Oct 2003, 09:08
d_batra79
thanx, you are right
19 Oct 2003, 09:08
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http://alumnus.caltech.edu/~shippert/DR/DR_method.html
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# Defensive Runs: the Method
This article describes the method I have used to convert Sherri Nichol's Defensive Average (DA) numbers, using Palmer and Thorn's Linear Weights, into something I call "Defensive Runs". This is the number of runs that a player would give up at his position over league average.
My method consists of determining how many hits (of each type) and double plays the player would have given up if he had had a league average number of opportunities for the season. I define "league average opps" (LAopps) as total opps per position for the whole league divided by the number of teams in the league, i.e. the average number of opps at each position for each team for the whole year.
Here are all the intermediate and final numbers I calculate. Most of the primary information comes from the DA data, and are described here. Note that these quantities all represent events allowed (or made, in the case of double plays) above the league average rate; therefore, a negative NorH means you gave up fewer hits than a league average fielder, and a negative NorDP means you made fewer double plays than the average fielder.
The number of non-outs the player would give up above average in LAopps.
Nor2B = LAopps*(2B/APO) - LA2B.
Number of doubles that would be given up above average in LAopps.
Nor3B = ...
Same as Nor2B, only for triples.
Number of double plays that would be made above average in LADPopps.
MDP = DPI - Popps * LADP%
"Marginal double plays." This is the number of double plays the player made over what a league average player would have made in the actual number of DP opps the player had.
DR(hits) = (0.27+0.46)*NorH + (.34)*Nor2B +(.56)*Nor3B
Defensive Runs from hits (using T&P's Linear Weights). Double plays aren't factored in yet.
DR/G = [DR(hits) + .5*NorDP]/AGP
"Defensive Runs per Game". The number of runs the player would give up per game (above average) if he had an average number of opps (both regular and DP) and played the full game.
TDR = DR(hits)*Popps/LAopps + .5*MDP
"Total Defensive Runs", for the player's season (i.e. number of actual opps). Essentially DR/G pro-rated by player opps.
The Nor prefix means "Normalized to league average opps". LA... means "League Average", and Popps is "Player opportunties".
The AGP in DR/G is "average number of games for each team", which is generally close to 162 except for strike affected seasons (1994 and 1995).
DR/G should give us a ranking of how "good" the fielder is, regardless of actual playing time or balls hit to him. TDR puts the Popps back in, giving us a measure of how valuable the player's entire defensive season was. This gives us defensive equivalents of Dave Tate's MR/G and TMR from the MLV method, which was what I was trying to accomplish.
The difference between NorDP and MDP is in the number of opps used for the comparison. NorDP uses the league's average DP opps over a full season at the player's position; MDP uses the actual number of DP opps the player saw in his playing time. I had to split it out like this because DR/G assumes an average number of opps, while TDR uses the player's real number of opps. In practice, double plays don't affect the final DR values very much, but I didn't know that when I started, and doing things this way is more rigorous.
The weights are from The Hidden Game of Baseball, and are slightly different than the ones in TBIII. Too bad - I started before I got TBIII, and its a pain to change all the formulas in the spreadsheet, so I just left it the way it was. (It also appears that the TBIII weights are smoothed out to make each XB worth a standard increment above a single, which seems fishy to me).
You may have noticed that for the DPs, I used T&P's "Outs on base" weight of 0.5 runs. I don't know if this is a legitimate weight or if it is one of T&P's famous made up numbers (like for the fielding runs - the roundness of this number makes me suspicious), but I couldn't find a better one, so I decided to just use it. If anybody has a better idea, let me know.
Note that I have lumped errors, hits, and what not into "NorH" (which really should be NorNO for "non-outs", but its too late now). I don't know how to weight errors, so I decided to pretend they are singles. The number of real hits given up dwarfs the number of fielding errors anyway, so I'm not too worried about this assumption.
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https://tryalgo.org/en/permutations/2016/09/05/permutation-rank/
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Given a permutation on {0,1,…,n-1} find its rank for the lexicographical order. Given a rank find the corresponding permutation.
## Example
Say n=4, then the 4!=24 permutations are lexicographically ordered as follows.
rank permutation
0 0,1,2,3
1 0,1,3,2
2 0,2,1,3
3 0,2,3,1
4 0,3,1,2
5 0,3,2,1
….
23 3,2,1,0
## An observation
Suppose we are given a permutation $(p_{n-1},\ldots,p_1,p_0)$ and which to compute its rank.
How many permutations start with a 0? Well the remainder is a permutation over {1,..,n-1}, and all these permutations are valid completions of the initial 0. Hence there are $(n-1)!$ permutations that start with a 0. Similarly there are $(n-1)!$ permutations that start with a 1, and in the lexicographical order they come after those that start with a 0. This means that a first contribution to the rank is $p_{n-1} \cdot (n-1)!$.
The situation for the next value $p_{n-2}$ is slightly different. Again there are $(n-2)!$ permutation that start with fixed values $p_{n-1},p_{n-2}$. However there are only $n-1$ possibilities for $p_{n-2}$, namely all n values excluding $p_{n-1}$. This means that the second contribution to the rank is $r_{n-2} \cdot (n-2)!$, where $r_{n-1}$ is the rank of $p_{n-2}$ among the set $\{0,1,\ldots,n-1\} \setminus \{p_{n-1}\}$. The key is then to translate a vector $p$ defining a permutation into a vector of ranks $r$ such that $r_i$ is the rank of $p_i$ among the values $\{p_{i},\ldots,p_1,p_0\}$. For example if p=(2,0,3,1), then r=(2,0,1,0). The rank of p is then
$r_{n-1} \cdot (n-1)! + \cdots + r_2 \cdot 2! + r_1 \cdot 1! \cdot + r_0.$
Note that $r_0$ can safely be omitted in the expression since it is always zero.
The trick is then to compute the ranks $r_i$ from the values $p_i$.
## An $O(n^2)$ algorithm
For this purpose we parse the permutation p, keeping track of the values which have not yet be seen so far and search among them to determine the rank. We maintain a list digits contains all values which have not yet seen in the given permutation. Note that the last element of the permutation can be ignored, it does not provide any information for the rank.
For the inverse, decompose r into
$r_{n-1} (n-1)! + \cdots + r_2 \cdot 2! + r_1 \cdot 1! + r_0$
with $0\leq r_i \leq i$ and map each $r_i$ to the value of rank i among the values {0,…n-1} which have not seen so far.
## An $O(n \log n)$ algorithm
In order to compute the rank of a permutation we use a table called rank which maps a value $p_i$ to a rank $r_i$ as explained above. Initially the table has the identity ranks, i.e. rank[x]=x. Then after each processed value $p_i$ we need to decrement all ranks in rank between the indices $p_i$ and $n-1$. We can use a segment tree for this purpose. Then the decrement and access operations to the rank table can be done in logarithmic time.
## Variant
Let s be some string of length n. We can ask the same question about permutations of s. The difficulty is that there can be repetitions of a same letter in s. Do you know how compute the rank-permutation bijection for this variant?
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http://mathhelpforum.com/algebra/224506-square-root-i.html
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# Thread: square root of i
1. ## square root of i
Find the square roots of i
?
would the modulus = i ? and not sure how to work out its argument?
any help apprecited
2. ## Re: square root of i
Originally Posted by Tweety
Find the square roots of i ?
Well of course as with any complex number there are two square roots:
$\sqrt {|z|} \exp \left( {\frac{{\arg (z)i}}{2} + \pi ki} \right),~k=0,~1$
3. ## Re: square root of i
$e^{i\theta} = \cos \theta + i \sin \theta$
Plug in $\dfrac{\pi}{2} + 2\pi n$:
$e^{i \left(\pi/2 + 2\pi n\right)} = i$
Take the square root of both sides:
$e^{i\left(\pi/4 + \pi n\right)} = \sqrt{i}$
There are two solutions in the range $[0,2\pi)$:
$e^{\pi i/4},e^{5\pi i/4}$
4. ## Re: square root of i
why plug in pi/2 ?
5. ## Re: square root of i
why cant I just work it out like this, the above looks quite complicated,;.....
let z = 0 + 1*i
than the modulus of z = $\sqrt{0^{2} + 1^{2}} = 1$
arg(z) = $tan \alpa = 1 = \frac{\pi}{4}}$
but not sure how to go from here, the correct answers are
$\frac{1}{\sqrt{2}}(1+i)$
$-\frac{1}{\sqrt{2}}(1+i)$
6. ## Re: square root of i
First, what made you think, originally, that there were four square roots of i?
Second, while the modulus of z= i is 1, its argument is NOT $\pi/4$. I don't know where you got that "1" in " $arctan(1)$". Surely you don't think argument is the arctangent of the modulus? The argument of "a+ bi" is the arctangent of b/a, if a is not 0. Of course, if a= 0 then a+ bi= bi which has modulus $\frac{\pi}{2}$ if b> 0, $-\frac{\pi}{2}$ if b< 0. (0 has no "argument").
So if z= i, $arg(z)= \frac{\pi}{2}$. HALF of that is $\frac{\pi}{4}$ and half of $\frac{\pi}{2}+ 2\pi= \frac{5\pi}{2}$ is $\frac{5\pi}{4}$. Those are the arguments of the two square roots of i which, of course, have modulus $1^{1/2}= 1$, so the two square roots are $\frac{\sqrt{2}}{2}(1+ i)$ and $\frac{\sqrt{2}}{2}(1- i)$.
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1. I am doing a math work sheet to help prepare for my upcoming semester in school and I need help with a math problem.
Question is....
The HCP prescribes 1.7 mcg/kg/body weight/day. Client's weight is 150 lbs.
What is the dose of medication ? ( round to nearest hundredth.)
I tried 115.91 and it is incorrect
150/2.2=68.18
68.18*1.7=115.91(rounded)
Can someone please show me how this problem is done.
Thank you!
Joined: Jul '17; Posts: 11
from FL , US
5. Sorry for the confusion but that's the answer I came up with and they said it's incorrect, I still
do not have the correct answer because I can not see the answer on the computer until I answer it correctly.
6. Can you show me how to solve the problem please?
7. No I do not have the correct answer that's what I'm searching for now.
8. I wonder if they're being picky about significant digits? Strictly speaking, you shouldn't be rounding to a hundredth of a kilo because you don't know what hundredth of a pound you have. Maybe try 150/2.2 = 68 kg, then 68*1.7 = 115.6?
9. uhmmmm - the only other possibilities that I could think of would be that the answer may be converting the units from mcg to mg... or maybe dividing the total into equal doses (tid, bid?) and the answer would be how much each dose should be.... and like someone else pointed out, the answer key could just be wrong.
10. No not the correct answer either
11. Its daily dose.
12. Quote from Ashleyherberth
Its daily dose.
yeah I understand that.. I'm just posting ideas to help you get past this question. you're math is correct....
13. 115.60? If they really want it to the hundredth?
Also, please use the "quote" button so we know who you're responding to, when you say an answer is wrong.
14. Try no rounding of anything until the end. I got 115.66613 mcg/day. So try 115.7 or 115.67.
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#### IMAGES
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3. Basic Division Word Problems
4. Division
5. White Rose Maths
6. Division 4 (problem solving)
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4. 😊 Can You Solve These Tricky Missing Number Puzzles?Test Your Logical Reasoning solving ability
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6. Year 4 Divide by 100 Reasoning and Problem Solving
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7. Year 4 Divide 2-Digits by 1-Digit 1 Reasoning and Problem Solving
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13. Year 4 Divide 3 Digits by 1 Digit Reasoning and Problem Solving
Questions 1, 4 and 7 (Problem Solving). Developing Find the missing numbers when dividing 3 digits by 1 digit using pictorial support.
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Ex 8.4
Chapter 8 Class 6 Decimals
Serial order wise
Get live Maths 1-on-1 Classs - Class 6 to 12
### Transcript
Ex 8.4, 4 Express as km using decimals. (c) 8888 m8888 m = 8888 × 1 m = 8888 × 1/1000 km = 8888/1000 km = 8.888 km As 1000 m = 1 km 1 m = 1/1000 km
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https://www.hellovaia.com/textbooks/math/introductory-statistics-oer-2018/hypothesis-testing-with-one-sample/q103-la-leche-league-international-reports-that-the-mean-age/
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### Select your language
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Q.103
Expert-verified
Found in: Page 554
### Introductory Statistics
Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208
# La Leche League International reports that the mean age of weaning a child from breastfeeding is age four to five worldwide. In America, most nursing mothers wean their children much earlier. Suppose a random survey is conducted of 21 U.S. mothers who recently weaned their children. The mean weaning age was nine months (3/4 year) with a standard deviation of 4 months. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is less than four years old.
(0.60 years, 0.90 years) or approximately (7.2 months, 10.8 months), when the sample standard deviation is rounded to 0.33.
See the step by step solution
## Step 1: Find H0 and Ha: We want to test if if the mean weaning age in the U.S. is less than four years old.
${H}_{0}:\mu =4;{H}_{a}:\mu <4$
## Step 2: Determine the distribution needed: In words, CLEARLY state what your random variable represents. Let μ represent the mean age at which American mothers wean their children
Normal: $N\left(4,\frac{0.333}{\sqrt{21}}\right)$
Test Statistic: $t=–44.7$
## Step 3: Calculate the p-value using the normal distribution for mean RV
$p-value=0.0000$
In one to two complete sentences, explain what the p-value means for this problem.
If the null hypothesis is true (the mean age is 4), then there is a 0.0000 probability that the sample (estimated) mean age is 3 or more.
## Step 4: Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.
alpha decision reason for decision 0.01 Reject the null hypothesis. $p-value<0.01$
Conclusion: There is sufficient evidence to conclude that the mean age at which American mothers wean their children is less than four years old.
## Step 5: Confidence Interval
(0.60 years, 0.90 years) or approximately (7.2 months, 10.8 months), when the sample standard deviation is rounded to 0.33.
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TRIANGLES upon the same base, and between the same parallels, are equal to one another.
A complete set of male pupil teachers' examination questions in Euclid [book ... - Σελίδα 12
των W J. Dickinson - 1879 - 36 σελίδες
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## The Popular Educator, Τόμοι 1-2;Τόμος 12
1867
...to show. The reader will remember that in Problem XXIV (page 308) it was shown that triangles on the same base and between the same parallels are equal to one another, and that triangles on equal bases and between the same parallels are also equal to one another. Now...
## Elements of Geometry: Containing the First Six Books of Euclid, with a ...
John Playfair - 1806 - 311 σελίδες
...also the parallelogram ABCD is equal to EFGH. Wherefore, parallelograms, &c. QED PROP. XXXVII. THEOR. TRIANGLES upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DEC be upon the same base BC, and between the same parallels AD, BC; the triangle...
## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...
Euclid, Robert Simson - 1806 - 518 σελίδες
...parallelogram ABCD is equal to EFGH. Wherefore, parallelograms, &c. QED An ; . PROP. XXXVII. THEOR. TRIANGLES upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC be upon the same base RC"and between the same parallels AD, BC : the triangle...
## Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5
John Mason Good - 1813
...diameter bisects them, that is, divides them in two equal parts. Prop. XXXV. Theor. Parallelograms upon the same base and between the same parallels, are equal to one another. Prop. XXXVI. Theor. Parallelograms upon equal basis, and between the same parallels, are equal to one...
## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...
Euclides - 1816 - 528 σελίδες
...also the parallelogram ABCD is equal to EFGH. Wherefore parallelograms, &c. QED PROP. XXXVII. THEOR. TRIANGLES upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC, be upon the same base BC, and between thesame p \ r\ parallels AD, BC :...
## Elements of Geometry: Containing the First Six Books of Euclid: With a ...
John Playfair - 1819 - 317 σελίδες
...the parallelogram ABCD is equal to EFGH. Wherefore, parallelograms, &c. Q, ED PROP. XXXVII. THEOR. Triangles upon the same base, and between the same parallels, are equal to one another. AD Let the triangles ABC, DBC be upon the same base BC, and between the same parallels AD, BC : The...
## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...
Peter Nicholson - 1825 - 372 σελίδες
...divides the parallelogram ACDB into two eqoal parts, QED Proposition XXXV. Theorem. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF BC ;...
## Elements of Geometry, Containing the First Six Books of Euclid
Euclid - 1826 - 180 σελίδες
...shall the two trapeziums be equal to one another. PROPOSITION XXXVII. THEOREM. Triangles constituted upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC, be constituted upon the same base вс, and between the same parallels...
## Euclid's Elements of geometry, transl. To which are added, algebraic ...
Euclides - 1826
...shall the two trapeziums be equal to one another. PROPOSITION XXXVII. THEOREM. Triangles constituted upon the same base, and between the same parallels, are equal to one another. » 3i. i. parallel to сл, " and through c draw CF, parallel to в D. Therefore each of them EBCA,...
## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...
Robert Simson - 1827 - 513 σελίδες
...diameter BC divides the parallelogram ACDB into two equal parts.' ei. ED PROP. XXXV. THEOR. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parnllelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC :...
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# Fourier transform of $e^{-\lvert \lambda x\rvert}$
I'm working on an exercise from Rudin's Real and Complex Analysis: Chapter 9, Exercise 14. The problem is to prove the theorems about the Fourier transform on $\mathbf{R}^{1}$ discussed in the chapter in $\mathbf{R}^{k}$ instead. I'm trying to generalize Section 9.7 to $\mathbf{R}^{k}$. Let $H$ be defined in $\mathbf{R}^{k}$ by $$H(x) = e^{-\lvert x\rvert},$$ and for every positive number $\lambda$, let $h_{\lambda}$ be defined by $$h_{\lambda}(x) = \int_{\mathbf{R}^{k}} H(\lambda y)e^{ix\cdot y} dm(y).$$
I was able to show that $H$ is integrable by using polar coordinates: $$\int_{\mathbf{R}^{k}} H(x) \:dm(x) = \int_{0}^{\infty} r^{k-1} \:dr \int_{\mathbf{S}_{k-1}} e^{-\lvert ru\rvert} d\sigma(u) = k\cdot m(\mathbf{B}_{k})\int_{0}^{\infty} e^{-r}r^{k-1}\: dr = k\Gamma(k)m(\mathbf{B}_{k}),$$ where $\mathbf{S}_{k-1}$ is the unit $k$-sphere, $\sigma$ is the Borel measure defined in $\mathbf{S}_{k-1}$ by $$\sigma(E) = k\cdot m\{ru~:~0<r<1,~u\in E\},$$ and $\mathbf{B}_{k}$ is the unit $k$-ball. But I'm having trouble computing $h_{\lambda}$ in a closed form expression as is done in the section: when $k=1$, it follows from symmetry and integration by parts that $$h_{\lambda}(x) = \sqrt{\frac{2}{\pi}} \int_{0}^{\infty} e^{-\lambda t}\cos(tx) \:dt = \sqrt{\frac{2}{\pi}} \frac{\lambda}{\lambda^{2}+x^{2}}$$ (here ordinary Lebesgue measure is scaled by $1/\sqrt{2\pi}$). I'm not sure how to do the calculation for $k>1$.
• If you use $$\lvert x\rvert_1 = \sum_{\kappa = 1}^k \lvert x_{\kappa}\rvert$$ rather than the Euclidean norm, you get an easy-to-handle function. – Daniel Fischer Aug 7 '17 at 21:00
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Montreal Math ClubMathematics students in Montreal - Étudiants de mathématiques à Montréal
Montreal Math Club :: Mathematics :: Combinatorics Share |
# Combinatorial Fields
AuthorMessage
Euclid
Posts : 95
Join date : 2009-09-15
Age : 56
Location : Alexandria
Subject: Combinatorial Fields Thu Aug 25, 2011 12:04 pm hi, here is another good news,I just found in the Carmichael book 1937 http://books.google.ca/books/about/Introduction_to_the_theory_of_groups_of.html?id=sd5QAAAAMAAJchapter XIII is dedicated to the one-to-one correspondence between sharply double transitive groups and near-fields.hence, we have another algebraical structure to be described in combinatorial terms:aNear-field' = aGrouprecall that aField' = aCyc (defining the combinatorial fields) take the tetrahedron as example : there are 12 rotations that permute 4 verticesTetrahedron' = Cyc[3]after fixing a vertex with the finger, the remaining liberty of rotation (relabeling) is a cyc[3] here (page 7) is shown how to introduce coordinates (is a very fast job) http://books.google.com/books?id=7DdJaZcJ0bIC&printsec=frontcover&dq=near+rings&hl=en&ei=U9BXToPdK6nb0QHYyZjDDA&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDQQ6AEwAQ#v=onepage&q&f=false- choose a 0- choose a 1since the structure there is a stick-two-stuck-all structure (a combinatorial field), every point got now an identity, a unique determination. Let' take another example, a triangular prism with 6 vertices and 6 rotation,If we choose a vertex (combinatorial stuff) and we name it - let's say A, the other vertices became- the left side of A one- the right side of A one- the correspondent of A in the other triangle- the correspondent of the left side of A one- the correspondent of the right side of A one We have a name-one-all-named process.my conclusion isIf someone wants to do what teacher Descartes asked, i.e. to introduce coordinates, he will need stick-one-stuck-all structures, and stick-two-stuck-all structures,i. e. the primitives of Lin species.After pinning a 0 (and a 1), all the other points get an identity, a unique determination.Being well determined, one can carry now further algebraical operations. In fact, the primitives of Lin, (stick-one-stick-all) structures are studied for 150 years now, and they are known today as groups and fields.In the finite area, the record of sharp-transitivity are detained by the Mathieu groups M11 - the only stick-four-stuck-all groupM12 - the only stick-five-stuck-all group
Euclid
Posts : 95
Join date : 2009-09-15
Age : 56
Location : Alexandria
Subject: Re: Combinatorial Fields Wed Aug 31, 2011 3:03 am Fano_plane'' = X.Klein_four-groupAfter pinning any two points in the Fano plane, a third one is determined.The remaining geometry is described by the Klein group acting on itself (also, the P4bic species).======================here is another remark, that could be useful to explain what a combinatorial field (and, thus, a field) is :the so called Complex Plane is not a plane, but is the complex line.Yes, that surface on the blackboard, containing a C letter, a circle, a 0, a 1 and two axes is a LINE, not a PLANE.
Euclid
Posts : 95
Join date : 2009-09-15
Age : 56
Location : Alexandria
Subject: Re: Combinatorial Fields Thu Sep 08, 2011 11:40 am (modified - I have opened a new topic on projectivity)Last edited by nick on Tue Sep 20, 2011 5:45 am; edited 1 time in total
Euclid
Posts : 95
Join date : 2009-09-15
Age : 56
Location : Alexandria
Subject: Re: Combinatorial Fields Thu Sep 15, 2011 9:35 pm let me mention some other ones,the stick-3-stuck-all structures are already known, they are the projective lines : http://en.wikipedia.org/wiki/Projective_linebut a nice surprise is VectorSpace[n^k]' = Cyc[n-1](Lin [k]) = Cylinderwhere k(n-1) + 1 = n^k,yes, the container for vector spaces is a primitive of a cylinder,given a vector (affine) space V over a field K, one may built the transformations x ----> ax+b wherea is a coefficient in Kb is a vector in Vthis is an imprimitive permutation group, with transitivity higher than 1 and lower than 2.A vector (affine) space is the group #5 of degree 9 in the Conway (Maple) table; the blocks in the table are representatives of lines parallelism classes.If we pin a point in a normal R^2 space, all the translations are killed. However, it remains the overall scaling with some lambda (warning, not rotations, a vector space with rotations is something else) ==============here is a nice notation for a cyc(lin) :start from a permutation - let's say (1 2 3)(4 5 6)(7 8 9)(0 A B) and optimize like this :(1470 258A 369B) <------- this is a cyc3(lin4), the derivative of 9T5 is something like (1234 4678).there are four lines 14, 26, 37, 48 passing through 0, and after pinning the 0 one can synchronously permute the 8 symbols
Subject: Re: Combinatorial Fields
Combinatorial Fields
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# chemistry
posted by .
explain the following observations;
A. an open can of soda loses its fizz quicker at room temperature than in the frig.
B. chlorine gas in tap water escapes as the water warms to room temperature.
C. less sugar dissolves in iced coffee than in hot coffee.
• chemistry -
A and B. Gases are less soluble in warm water than in cold water.
C. Sugar is more soluble in warm water than cold water.
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# Hypothetical way to travel faster than light, but not technically exceed lightspeed
by knicely
Tags: expansion, lightspeed, space
P: 2 From what I understand, space (not matter) can expand at a speed faster than that of light, and when it does, it goes in all directions. Would it be possible to create a controlled expansion of space behind a vehicle along a single path, like a corridor, that would change your position in space technically faster than light? And a follow up question, what is believed to cause the expansion of space?
PF Patron Sci Advisor Thanks Emeritus P: 38,424 Hmm, that way, you would be moving away from your starting point faster than c, but you would NOT be approaching your end point any faster! You would just be making the distance between start and end greater.
P: 334
Quote by knicely From what I understand, space (not matter) can expand at a speed faster than that of light, and when it does, it goes in all directions. Would it be possible to create a controlled expansion of space behind a vehicle along a single path, like a corridor, that would change your position in space technically faster than light? And a follow up question, what is believed to cause the expansion of space?
I gather you mean the warp drive or Alcubierre drive involving space itself transporting the ship along with it at FTL speed to a predetermined destination. Well, it would be nice if it were as easy as the Star Trek episodes make it seem. Unfortunately the obstacles that such a method of travel would have to overcome are so daunting as to make it seem totally impossible not only with current technology but with any technology we can presently realistically envision.
For example one method requires preparing the trajectory for the ship beforehand. Obviously such preparation demands FTL capabilities. Other problems involve the inability of the crew to control the ship. Still others involve the application of mind-boggling impossible energies required to manipulate the fabric of space that way. The article below discusses these and others.
Alcubierre drive http://en.wikipedia.org/wiki/Alcubierre_drive
The Glen research center site has an article about what it claims to be the general scientifically-derived consensus on the FTL idea based on warp drive.
Glen Research Center Status of "Warp Drive" "Warp Drives", "Hyperspace Drives", or any other term for Faster-than-light travel is at the level of speculation, with some facets edging into the realm of science. We are at the point where we know what we do know and know what we don’t, but do not know for sure if faster than light travel is possible. The bad news is that the bulk of scientific knowledge that we have accumulated to date concludes that faster than light travel is impossible. http://www.nasa.gov/centers/glenn/te.../warpstat.html
Mentor
P: 8,262
## Hypothetical way to travel faster than light, but not technically exceed lightspeed
Quote by knicely And a follow up question, what is believed to cause the expansion of space?
You mean the expansion of the universe, or the accelerated expansion of the universe that we measure at the current epoch? If the former, then it's essentially an initial condition of the big bang models; the latter is attributed to an unknown called 'dark energy'. This could either be some mysterious fluid with negative pressure, or require a modification of general relativity on the relevant scales.
P: 154 This universe sucks. We can't go faster than light. All we can hope for is to build a race of robots similar to the ones in Asimov's robot stories that would take our place and explore the galaxy for us.
PF Patron
P: 10,394
Quote by Dr_Morbius This universe sucks. We can't go faster than light. All we can hope for is to build a race of robots similar to the ones in Asimov's robot stories that would take our place and explore the galaxy for us.
Perhaps. But maybe it's that exact limitation that has kept any aliens from invading the planet already!
P: 227
Quote by Dr_Morbius This universe sucks. We can't go faster than light. All we can hope for is to build a race of robots similar to the ones in Asimov's robot stories that would take our place and explore the galaxy for us.
We will probably be that race in a few hundred years.
P: 149 well if you love fiction, who knows we ourselves are robots of more intelligent creatures.
P: 366
Quote by Drakkith Perhaps. But maybe it's that exact limitation that has kept any aliens from invading the planet already!
Arthur C Clarke once said: "A sufficiently advanced technology is indistinguishable from magic"
If such limitations did not exist for another race - (they had overcome the seemingly impossible hurdles) then I dont see why they would invade us both from a practical and moral perspective.
In terms of physical materials there are much more abundant and easier invaded places. The recent abysmal Battle:LA was a terrible premise - the aliens invaded Earth for our water and seemingly ignored every other source of water in our solar system!
Then again I like the idea in the Day the Earth Stood Still where it is the life sustaining planet that is the resource.
Mentor
P: 5,227
Quote by Cosmo Novice Then again I like the idea in the Day the Earth Stood Still where it is the life sustaining planet that is the resource.
Interesting premise, shame about everything else in that film. The only thing these supposedly magically advanced aliens could think of was total extermination even though they value life and have the ability to mystically change animal behaviour in order to make them come into the "arcs." Though I suppose a story where aliens give us the technology to live a totally eco-friendly existence and gently dismantle our weapons and current industries with their swarm wouldn't be such a sellable idea.
P: 366
Quote by Ryan_m_b Interesting premise, shame about everything else in that film. The only thing these supposedly magically advanced aliens could think of was total extermination even though they value life and have the ability to mystically change animal behaviour in order to make them come into the "arcs." Though I suppose a story where aliens give us the technology to live a totally eco-friendly existence and gently dismantle our weapons and current industries with their swarm wouldn't be such a sellable idea.
A few really nice premises in that film; its just a shame its such a bad remake; the idea of aliens growing into human bodies and becoming more human was, IMO, a nice idea.
I think in honesty looking at the options then destruction from their perspective would be the most efficient and humane thing to do - but then we are judging through our own mores and values and whose to say that has any relevance to the alien view. (Maybe in fact it was the humen side of Klaatu that wanted to destroy!?) Anyway the original and lesser known film was actually a lot better!
I think if a magically advance alien race was to come down and give us answers to energy problems/global warming, hunger, immunity to disease, then how much more dangerous would the human race become - its like giving a child magical powers he has little comprehension of; at least thats how I see it.
P: 2 HallsofIvy : I see what you mean. If you were to aim directly at your destination and cause space to expand, it would be pointless. Everything along this hypothetical corridor would be pushed apart. My thought is to aim to the side of your destination (and not at anything important behind you). That way, as space expanded and 'propelled' you forward, the object you're trying to reach wouldn't be kept the same distance away. Radrook : I have never heard of an Alcubierre drive before, but it sounds fairly similar to my thought. Thank you cristo : thank you for the info. That clarifies some stuff for me. Pretty much with this idea, I was just trying to think of a way to technically move faster than light without actually moving faster than light and breaking the laws of physics, like a work around.
Mentor
P: 5,227
Quote by knicely I have never heard of an Alcubierre drive before, but it sounds fairly similar to my thought. Thank you
You might also be interested to read about NASA's Breakthrough Propulsion Program. Part of the problem in the ideas proposed by the BPP is that they are based on hugely speculative premises such as the ability to manipulate the gravitational constant, to acquire and manipulate negative mass or to develop superluminal signalling none of which is indicated to be possible (and if it were would severely undermine our understanding of the universe, not to mention introduce time travel).
P: 7
Quote by Ryan_m_b or to develop superluminal signalling none of which is indicated to be possible
Well if I read right, this is conceivably possible: http://www.guardian.co.uk/science/20...cles-neutrinos
If you might somehow patiently manage to line up a long string black holes, using slingshots, that "might" be able to get you to reach the speed of gravity depending on the set-up; which is supposed to be the same as light. Giant qualifier quotes have been placed purposely. :D
Mentor P: 8,262 This thread's gone from inquisitive to speculative, therefore no longer adheres to PF rules.
Mentor
P: 5,227
Quote by LKD_ Well if I read right, this is conceivably possible: http://www.guardian.co.uk/science/20...cles-neutrinos If you might somehow patiently manage to line up a long string black holes, using slingshots, that "might" be able to get you to reach the speed of gravity depending on the set-up; which is supposed to be the same as light. Giant qualifier quotes have been placed purposely. :D
I know the thread is locked but just for the record the neutrino result is yet to be confirmed http://physicsforums.com/showthread.php?t=532620 and no matter what you do an object with mass cannot reach the speed of light.
Related Discussions Special & General Relativity 6 Special & General Relativity 13 Astrophysics 3 Special & General Relativity 13 Special & General Relativity 6
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Reference.PulseIn History
August 29, 2009, at 12:35 PM by David A. Mellis -
Changed lines 16-17 from:
value: type type of pulse to read: either HIGH or LOW. (int)
to:
value: type of pulse to read: either HIGH or LOW. (int)
November 02, 2008, at 10:58 AM by David A. Mellis -
Changed line 9 from:
pulseIn(pin, value)
to:
pulseIn(pin, value) \\
Deleted lines 39-41:
November 02, 2008, at 10:57 AM by David A. Mellis -
Changed lines 1-3 from:
to:
pulseIn()
Changed lines 8-12 from:
to:
Syntax
pulseIn(pin, value) pulseIn(pin, value, timeout)
Changed lines 21-22 from:
the length of the pulse (in microseconds) or 0 if no pulse started before the timeout
to:
the length of the pulse (in microseconds) or 0 if no pulse started before the timeout (unsigned long)
March 29, 2008, at 04:09 PM by David A. Mellis -
Changed lines 2-3 from:
to:
unsigned long pulseIn(pin, value, timeout)
Changed lines 5-9 from:
Reads a pulse (either HIGH or LOW) on a pin. For example, if value is HIGH, pulseIn() waits for the pin to go HIGH, starts timing, then waits for the pin to go LOW and stops timing. Returns the length of the pulse in microseconds.
The timing of this function has been determined empirically and will probably show errors in longer pulses. Works on pulses from 10 microseconds to 3 minutes in length. Note that this function will not return until a pulse is detected.
to:
Reads a pulse (either HIGH or LOW) on a pin. For example, if value is HIGH, pulseIn() waits for the pin to go HIGH, starts timing, then waits for the pin to go LOW and stops timing. Returns the length of the pulse in microseconds. Gives up and returns 0 if no pulse starts within a specified time out.
The timing of this function has been determined empirically and will probably show errors in longer pulses. Works on pulses from 10 microseconds to 3 minutes in length.
timeout (optional): the number of microseconds to wait for the pulse to start; default is one second (unsigned long)
Changed lines 18-19 from:
the length of the pulse (in microseconds)
to:
the length of the pulse (in microseconds) or 0 if no pulse started before the timeout
Changed lines 39-41 from:
to:
September 27, 2007, at 05:10 AM by David A. Mellis - describing what the function does, not what it doesn't do.
Changed lines 6-8 from:
The timing of this function has been determined empirically and will probably show errors in longer pulses.Works on pulses from 10 microseconds to 3 minutes in length. Note that this function does not have a timeout built into it, so can appear to lock the Arduino if it misses the pulse.
to:
The timing of this function has been determined empirically and will probably show errors in longer pulses. Works on pulses from 10 microseconds to 3 minutes in length. Note that this function will not return until a pulse is detected.
April 18, 2007, at 02:20 PM by Paul Badger -
April 18, 2007, at 02:20 PM by Paul Badger -
Deleted lines 37-38:
April 18, 2007, at 02:14 PM by Paul Badger -
Changed lines 6-8 from:
Works on pulses from 10 microseconds to 3 minutes in length.
to:
The timing of this function has been determined empirically and will probably show errors in longer pulses.Works on pulses from 10 microseconds to 3 minutes in length. Note that this function does not have a timeout built into it, so can appear to lock the Arduino if it misses the pulse.
April 18, 2007, at 02:07 PM by Paul Badger -
Works on pulses from 10 microseconds to 3 minutes in length.
April 14, 2006, at 02:56 PM by David A. Mellis - Documented pulseIn()
unsigned long pulseIn(pin, value)
Description
Reads a pulse (either HIGH or LOW) on a pin. For example, if value is HIGH, pulseIn() waits for the pin to go HIGH, starts timing, then waits for the pin to go LOW and stops timing. Returns the length of the pulse in microseconds.
Parameters
pin: the number of the pin on which you want to read the pulse. (int)
value: type type of pulse to read: either HIGH or LOW. (int)
Returns
the length of the pulse (in microseconds)
Example
```
int pin = 7;
unsigned long duration;
void setup()
{
pinMode(pin, INPUT);
}
void loop()
{
duration = pulseIn(pin, HIGH);
}
```
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We use the MAP prep packs in class. We currently use TestPrep-Online's materials to help students prepare for MAP 2nd, 3rd, 4th, and 5th grade tests. We believe the prep packs have had a positive influence on the students.
Guide To Using Our Free MAP Diagnostic Tests
Note: If your child gets 7-8 on our MAP sample test, congratulations! they're on the right track. Continue practicing to keep that knowledge strong and intact.
## Free MAP Test for 2nd Grade- Preview
Our Free 2nd Grade MAP Practice Test consists of ten multiple-choice questions which cover every section of the exam. Once your child has clicked on an answer option, check the explanation to see if it was the correct one.
Our Free 2nd Grade MAP Practice Test consists of ten multiple-choice questions which cover every section of the exam. Once your child has clicked on an answer option, check the explanation to see if it was the correct one.
At the end of each question, please rate the answer explanation. This helps us improve our service and provide the best possible practice material for your child.
### 2nd Grade MAP Question Preview
What number is missing from the following equation?
? + 7 = 18
A. 9
B. 10
C. 11
A number sentence can be expressed in many ways. For example, you know that 1 + 2 = 3. Similarly, you can say that 1 = 3 – 2 or 2 = 3 – 1.
An equation has two sides separated by an equal sign, and both sides must be equal for the equation to be correct.
Addition and subtraction are inverse relationships. If you add and subtract the same number, then your expression will not change. In fact, if you apply the same change to both sides of the equation, it remains correct. You can subtract seven from both sides and the equation will not change.
Subtracting seven from each side makes the following equivalent equation:
? + 7 – 7 = 18 – 7
The sevens on the left side cancel each other out because addition and subtraction are inverse. Since the sevens cancel each other, this is what is left of the equation.
? = 18 – 7 = 11
The NWEA 2nd Grade MAP Exam is one of the top assessment exams used in elementary schools throughout the United States. The test itself is taken on a computer and evaluates students’ skills in language usage, math, and reading comprehension.
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## 8 Tips for Preparing your child for the 2nd Grade MAP Test
• Map out deadlines and priorities. Once your child has taken our initial sample test it will be much easier for you to know what topics to prioritize in your studying plan prior to the test. If your child struggled most with the vocabulary questions and least with math questions, for instance, you may want to begin with the MAP Reading comprehension section.
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3,503 views
Context-free languages are:
1. closed under union
2. closed under complementation
3. closed under intersection
4. closed under Kleene closure
Context-Free languages are not closed under intersection and complementation.
CFG are closed under Union , Kleen closure & Concatenation .
Also CFG are closed under Regular intersection
BUT , are CFG closed under Regular Union ?
I think yes...coz..every regular is CFG & CFG are closed under union ....
correct me if I am wrong
So take two regular language sigma* over {a,b} and other as {a}then their union is sigma* ,which is not cf.
Correct me if I am wrong.
@air1ankit I have some doubt in the above table
1. DCFL closed under reversal?
1. CSL closed under set difference?
2. REC under epsilon free substitution?
According to the above table we can say , A and D is correct answer
wat is GSM mapping ??
Gsm mapping Short for generalized sequential machine mapping. A function that is the response function of a generalized sequential machine, and therefore generalizes the notion of sequential function. Without constraining the machine to have a finite state-set, generalized sequentiality is equivalent to the following property of initial subwords preservation
for all u,v in I*, f(uv) has the form f(u)w for some w in O*, where I* and O* are the sets of all input and output strings.
What is Substitution Operation?
A is right
D is right because
$(CFL)^* = Regular$
all regular are CFL’s
by
A & D
CFL’s are NOT CLOSED under INTERSECTION, COMPLEMENTATION, DIFFERENCE.
DCFS’s are NOT CLOSED under INTERSECTION, UNION, CONCATENATION, KLEENE CLOSURE, DIFFERENCE, REVERSAL, HOMOMORPHISM.
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# What is the correct way to modify the bin-counts given a threshold for a chi-squared test?
When performing a chi-square test, one inputs the expected counts (via integrating probability distribution over respective bin bounds) and observed counts into the chi-square formula (denoted below).
I am told by a friend that when performing a chi-square test, one must impose a threshold such that any bin counts less than the threshold are consolidated into the next bin.
I tried looking this up via various permutations of search keywords “adaptive binning threshold count chi-square” but without much success.
I am unclear on whether a bin count less than the threshold means that bin count is effectively zero, or if the bin (or bin-width) merges. As an example, suppose the bin count threshold is 5:
original bin-edges = [0, 5, 10, 15, 20, 25]
original bin-midpoints = [2.5, 7.5, 12.5, 17.5, 22.5]
original bin counts = [3, 15, 26, 18, 2]
The first option is to consolidate the bins like so:
modified bin-edges = original bin-edges
modified bin-midpoints = original bin-midpoints
modified bin counts = [0, 18, 26, 20, 0]
The second option is to consolidate the bins like so:
modified bin-edges = [0, 10, 15, 25]
modified bin-midpoints = [5, 12.5, 20]
modified bin counts = [18, 26, 20]
# note the unequal bin-widths
Are either of these two methods correct when considering a minimized chi-squared?
This brings me to my next related question. Assuming a distribution with a central peak, should one consolidate bins to their respective next-right bin if in the left-side tail and consolidate bins to their respective next-left bin if in the right-side tail? If not, what is the proper procedure?
While the threshold is supposed to be small (typically ~5, sometimes less), can this hide information in a distribution tail in other distributions (say, lognormal distribution)?
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# Amazon SDE I Off-campus Hiring
I have applied to multiple positions on LinkedIn. Finally, I got a mail stating that I can give my online test on Hackerearth platform.
Round 1:
It was for 90 minutes, consisting of 20 multiple-choice(negative marks for wrong answers) and 2 coding questions. The questions were asked from Data Structures, Operating Systems, Computer Networks, DBMS, Time complexity and recurrence relations. Most of them were taken from Gate preparation guide from GeeksforGeeks. Some of the questions include,
1. Circular Queue: find the front and rear after specific operations?
2. Increasing RAM increases performance because?
3. CPU handles an interrupt by executing an interrupt service routine by checking what?
4. Binary search recurrence relation?
5. Quicksort worst-case complexity when the pivot is the n/4 smallest element using an O(n) algorithm?
6. The best time complexity for finding the nth Fibonacci number?
7. Tightest upper bound for binary search tree insertion?
8. Given some statements about ER and relational models, find the false statements.
Coding Questions include,
1. Chocolates distribution problem
2. Check if any sub-string and its reverse exist in a given array of strings.
After three days, I got the result and I was told to come to Amazon Bangalore campus for further technical discussions.
Round 2:
3. Find the number of disconnected components in the given directed graph.
4. Discussion about Dynamic programming and recursion.
5. Discussion about the team, that I was giving my interview for.
This round went for an hour and I was told to write the working code. I coded in Java writing all the necessary comments, importing all the necessary packages, handling all the exceptions and edge-cases. The interviewer was really impressed.
Round 3:
2. Given two nodes, find the shortest path in the given binary tree and binary search tree.
3. Given an infix expression as a string, evaluate it. We need to handle invalid strings, operator precedence, space characters, non-numeric characters, etc. Much importance was given to data structure as well.
4. Given a 2D maze, a man with a starting position, list of possible moves and a number k, find the probability after k moves the man will stand inside the maze.
This round went for more than 2 hours. For all the above questions, I was told to handle all the edge cases, and the interviewer was focused on the optimal solution and working code for all the problems.
Round 4:
2. Count ways to reach the n’th stair
3. Print all Jumping Numbers smaller than or equal to a given value
4. Questions on deadlock, handling, and its prevention.
5. Questions on Java Strings and string pool.
6. How SSH works?
This round went for more than an hour questions I was asked about the reasons for which I was using specific data structures for the about coding questions.
HR told me that I was doing really good and I was told that I will have one more round and that will be a bar-raiser. After two weeks I got a mail saying that I will have the next round in three days. It was on Amazon Chime.
Round 5:
2. Deep dive into my internship project and my individual contribution.
3. Questions on HashTable.
4. Deep dive into LRU, and its working in real computers like what is stored in the cache.
5. Questions on page faults, thrashing.
6. Two numbers with sum closest to zero
This round was with a Senior Manager and a recruiter from Jordan. All the questions were focused on the depth of knowledge I had.
The first four rounds, I did really well and I was able to impress the interviewers and they were also happy with my performance. I felt that I was not performed well in the final round. Make sure you have a really good Internet connection. Amazon considers each and every round before rejecting a candidate. Most of the rounds were focused on Data structures, algorithms, time complexity and problem-solving. I prepared for System Design questions, but I was not asked anything about it as I’m a fresher.
Companies like Amazon has policies that state that if a candidate has appeared for the interview and if he/she is not selected, then the candidate cannot apply for the next six months. Also, once you are in the interview process, you will never know when the further rounds will be scheduled and you will not get ample time to prepare. So, before applying for jobs, make sure you have prepared well.
Result: Selected.
Write your Interview Experience or mail it to contribute@geeksforgeeks.org
My Personal Notes arrow_drop_up
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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JohnATL
Members
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1. Dynamics supplement question 19
Thanks for the insights! I appreciate the help.
2. Dynamics supplement question 19
Thank you! While waiting for your answer I discovered another shortcut that is a bit quicker, but only works when the two angles equal 90°. Simply take the sin of each angle and multiply them times mg to get T1 and T2. I think your solution is universal however, even if the angles don't add up to 90°. How often do AP1 questions include this type of question where the angles don't sum up to 90°?
3. Dynamics supplement question 19
On problem 19(c) of the supplemental questions for AP1 Dynamics I must be doing something wrong with the Trig functions to solve for the tension in each wire, but the problem is not worked out in the answer, it simply says to substitute the appropriate trig functions to solve. Can someone show me the steps for that so I achieve the correct answer? Thanks! AP1 Dynamics 19.pdf
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# Fuel evaporation
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June 24, 2002, 08:04 Fuel evaporation #1 Julie Polyakh Guest Posts: n/a I deal with injected fuel evaporation modeling. n-Heptane injected into air @T=293K (both of them). Chemical model of combustion initiated. The results are very strange, e.g. the droplets evaporate very quickly and achieve the temperature of 45K (i.e.-228C). I think the problem is saturation pressure set in Droplet Properties (Psat=10e+5 Pa (?) ). The questions are: 1) what are the units of pressure? 2) where is the value of the saturation pressure used in the calculations? 3) at what temperature it should be given (i.e. initial, mean, etc.) and 4) what is the saturation pressure for my fuel? The most confusing here is that in handbooks I found there is no saturation pressure given, but only the vapor pressure. Is this the same? Thanks, Julie
June 24, 2002, 08:13 Re: Fuel evaporation #2 Ossi Guest Posts: n/a 1) Pressure is in Pascals [Pa]. 2) The vapor pressure is used in the mass and heat transfer computations between the drop and the surroundings. 3) It should be computed according to the drop temperature in dropro.f. 4) The vapor pressure depends on the temperature. What kind of injection velocities are you encountering ? Extremely high velocities would maybe lead to such low temperatures or very incorrect vapor pressure.
June 24, 2002, 09:48 Re: Fuel evaporation #3 Julie Polyakh Guest Posts: n/a The velocities are about 150 m/sec. Ossi, you say that the vapor pressure should be computed according to the drop temperature in dropro.f. But there is the saturation pressure value that I should supply in the Droplets Properties. The default value is 10e+5. I have performed the computations with the sat. pres. = 0.5e+5. It yelds better result, but the temperature is still incredibly low (~76 K). May be there is a bug in dropro.f? Thank you, Julie
June 25, 2002, 04:22 Re: Fuel evaporation #4 rogeha Guest Posts: n/a You have an example in dropro.f for n-dodecane how saturation pressure changes with temperature as well as latent heat of evaporation. regards, Dragan
June 26, 2002, 04:21 Re: Fuel evaporation #5 Julie Polyakh Guest Posts: n/a Thank you. I'll check that
June 27, 2002, 07:11 Re: Fuel evaporation #6 Malcolm Guest Posts: n/a The saturation pressure set for each droplet type is used as a default in case dropro doesn't return anything; the same applies to the other properties.
June 28, 2002, 09:26 Re: Fuel evaporation #7 Stefan Hildenbrand Guest Posts: n/a Hi, I guess your saturation pressure is wrong. I found this about Heptane. (http://webbook.nist.gov). You should probably have a look at this. Furthermore, the sat. pressure is very much dependent on temperature. Antoine Equation Parameters log10(P) = A - (B / (T + C)) P = vapor pressure (bar) T = temperature (K) Temperature (K) A B C Reference 299.07 - 372.43 4.02832 1268.636 -56.199 Williamham, Taylor, et al., 1945
June 28, 2002, 10:25 Re: Fuel evaporation #8 Julie Polyakh Guest Posts: n/a Stefan, Thank you for the answer. Can you tell me for what temperature range the Antoine equation is valid? Regards, Julie
June 28, 2002, 11:24 Re: Fuel evaporation #9 Julie Polyakh Guest Posts: n/a I have tried this and it doesn't work. The pressure obtained by the equation is 4760 Pa @ T=293 K. The calculation just stops at the 3rd iteration. Have any idea? Julie
June 28, 2002, 14:17 Re: Fuel evaporation #10 Volker Guest Posts: n/a Hi, You can use a few values of vapour pressure and derive some sort of function of temperature (eg. poynomial) as the input for your dropro. These are values I found in 'VDI-Wärmeatlas': 371,6 K - 101,3 kPa (this is the 'normal' boiling temperature); 380 K - 130 kPa; 400 K - 219 kPa; 420 K - 349 kPa; 440 K - 529 kPa; 460 K - 721 kPa; 480 K - 1094 kPa; 500 K - 1513 kPa; 520 K - 2046 kPa; 540,3 K - 2736 kPa. At the critical temperature (540,3 K), Heptane is gaseous at any pressure, so this value is quite important in the droplet property setup. Another possibilty to calculate the vapour pressure is this (again from 'VDI Wärmeatlas'): ln p,sr=f0(Tr)+omega*f1(Tr), where: p,sr=ps/pc (reduced vapour pressure) ps - vapour pressure pc - critical pressure (i.e. 27,4e+5 Pa for heptane) Tr=T/Tc (reduced temperature) Tc - critical temperature (i.e. 540,3 K for heptane) omega - acentric factor (i.e. 0,349 for heptane) f0(Tr)=5,92714-(6,09648/Tr)-1,28862*ln(Tr)+0,169347*Tr**6 f1(tr)=15,2518-(15,6875/Tr)-13,4721*ln(Tr)+0,43577Tr**6 It's a bit of a monster but it worked alright for n-dodecan. Are there any ohter possible reasons for your problem? You could try and check the void fraction of your droplets (should be below 40% of the cell volume). Did you try to run your case without the chem. module (maybe with a high initial temperature to see if your droplets evaporate as expected)? Another thing that might cause you problems are thin wall layer cells. Hope that helps. Regards, Volker
June 28, 2002, 15:36 Re: Fuel evaporation #11 Julie Polyakh Guest Posts: n/a Volker, Can you tell me what happens to the vapor pressure at 273K? The problem is that I have to simulate droplets evaporation inside the vaporiser, so they are not suppose to evaporate before they hit the vaporizer's hot wall. However, in the model I build for today droplets evaporate far away before the wall... Could you, please, explain me the sence of the void fraction in STAR-CD? I think I don't understand it properly. What means that it should be below 40% of the cell volume? Thanks for the help, Julie
June 28, 2002, 15:54 Re: Fuel evaporation #12 Julie Polyakh Guest Posts: n/a I have checked the void fraction. It changes from 0.003 to 0.01. Is it ok? Regards, Julie
June 30, 2002, 05:40 Re: Fuel evaporation #13 Julie Polyakh Guest Posts: n/a Hi, May be the result depends upon number of droplets per parcel (i.e. total mass of drops per parcel)? What do you think? Regards, Julie
July 1, 2002, 06:16 Re: Fuel evaporation #14 Stefan Hildenbrand Guest Posts: n/a It's valid in the range 299.07 - 372.43 K, so your 293 K are not accounted for.
July 1, 2002, 08:05 Re: Fuel evaporation #15 Volker Guest Posts: n/a Have you tried that function to get an idea of the vapour pressure at 273 K? Anyway, it should be well below standard pressure. What did you use in dropro to define the vapour pressure? Have you defined the critical temperature? The void fraction is the fraction of the volume of a cell that is filled by droplets. The droplet model in Star does only work properly when the volume of the droplet is small compared to the cell volume, i.e. The user guide recommends a maximum fraction of 40%. Volker
July 1, 2002, 08:15 Re: Fuel evaporation #16 Volker Guest Posts: n/a It should be better (with respect to accuracy) to have many parcels with only few droplets in them but that will result in longer CPU time. One more tip for droplet calculations. Try the Switches SW 70 (impl. treatment of dropl mass transfer source, don't use with ignition model), 71 (impl. treatm. of dropl. heat transf. source) and 199 (disable evaporation). Furthermore set the Rconstants RCONS 34 = 0.1 - 0.7 (Under-relaxation of coupling terms between disp. and cont. phase) and RCONS 185 = 1 (Gradient based interpolation of vel. for dropl. tracking, with this one you have to use the -3 option in starlink). Hope that helps. Volker
July 1, 2002, 09:03 Re: Fuel evaporation #17 Julie Polyakh Guest Posts: n/a Hi! The answers to your questions: 1) Q: Have you tried that function to get an idea of the vapour pressure at 273 K? Anyway, it should be well below standard pressure. A: Yes, you are right. It is about 5 kPa and STAR does not want to perform any calculaions with this value. 2) Q: What did you use in dropro to define the vapour pressure? Have you defined the critical temperature? A: I do not use dropro.f subroutine. All parameters defined as "Standard" at initial temperature (273 K). Some new questions to you: 1) Is there any detailed description of Switches and Real Constants? 2) I have checked the void fraction. It changes from 0.003 to 0.01. Is it ok? Is there some "lower limit" for it? Thank you, Julie
July 1, 2002, 10:10 Re: Fuel evaporation #18 Volker Guest Posts: n/a Hi, I think if you want to get any meaningful results for droplet evaporation you have to define the vapour pressure as a function of temperature (in dropro). You have to tell the code at which temperature-pressure couples heptane is going to evaporate. If you don't do that it will take the value you provide for the vapour pressure (under standard) and the droplet will evaporate whereever the pressure in your domain is below or equal that pressure regardless of the temperature (or maybe it will stop do anything sensible). If you use the standard value of 100 kPa and use the same pressure as your inlet pressure the droplets will evaporate as soon as they enter the domain. If you want to prevent boiling altogether just switch the boiling model off. Your void fraction sounds ok (I don't know of any lower limit). There is no description of the switches and constants to my knowledge, try and get in touch with Star. Volker crevoise likes this.
July 1, 2002, 11:32 Re: Fuel evaporation #19 Julie Polyakh Guest Posts: n/a Volker, How did you got to know about the switches and constants, if tere is no description available? Do you have an experience of writing any subroutines for the STAR? There are some functions, which I can not figure out where they are defined. (E.g. FUELFN(,,).) May I ask what kind of work do you do? Regards, Julie
July 1, 2002, 12:59 Re: Fuel evaporation #20 Volker Guest Posts: n/a Julie, I found out about those switches on a Star CD training course. The user guide says that they 'activate beta-level features in the code', so they will probably become properly documented and introduced in later releases of the code. I am not quite sure myself how that FUELFN works but apparently it works alright. If you don't trust these functions you can always include your own function. In this example you click on 'user' in that saturation pressure field and Star will set up the folder 'ufile' and copy the dropro into that folder. You will find a bit of sample code in dropro that gives you an idea how to set the thing up. I hope you are a little familiar with the joys of Fortran programming. I am just getting involved with liquid fuel combustion myself (automotive industry). Regards, Volker
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Messages in this thread
Date Mon, 29 Apr 2002 08:33:45 -0400 (EDT) From "Richard B. Johnson" <> Subject RE: FPU, i386
`On Fri, 26 Apr 2002, Kerl, John wrote:> There is an error here which shouldn't be propagated:> > if (fabs(a-b) < 1.0e-38)> ...It is not an error at all.> > "Machine epsilon" for doubles (namely, the difference between 1.0 and> the next largest number) is on the order of 2e-16. This is a rough> estimate of the granularity of round-off error; and in fact 1.0 / 0.2> and 5.0 can't possibly be as close as 1.0e-38, unless they're exactly> equal.This is not correct. The FPU in (even) the i486 stores 'tiny' (defined inthe Intel book) in extended real format. Quantities as small as +/- 3.37* 10 -4932 are represented internally. Any comparison of real numbers is(or certainly should be) done internally. The hard-coded example of1.0e-38 is well within the dynamic range of both the FPU and the doublefabs().As explained on page 16-3 of the Intel 486 Programmer's ReferenceManual, the FPU tries to prevent denormalization. Denormalizationproduces either a denormal or a zero. Even single precisiondenormals all have exponents of -46 or more negative, also wellwithin the -38 cited.> > There are four epsilon-ish things to be aware of:> > * Difference between 0.0 and next float above: ~= 1.4e-45> * Difference between 0.0 and next double above: ~= 4.9e-324> * Difference between 1.0 and next float above: ~= 1.2e-7> * Difference between 1.0 and next double above: ~= 2.2e-16> > The first two are more useful for things like detecting underflow; the> last two (some numerical folks suggest using their square roots) are> more useful for implementing an "approximately equals".> I agree with your explainations on everything following:> ----------------------------------------------------------------> > The poster was incorrect in expecting 1.0 / 0.2 to be exactly equal to> anything, as was explained to him. But the problem doesn't have to do> with whether a number is transcendental, or irrational, or rational:> the number must be rational *and* must have a mantissa whose> denominator is a power of two *and* that power of two must be less than> or equal to 23 (for single) or 52 (for double). And of course 1/5 is> 2^-3 * 8/5, of which the mantissa has denominator 5, which isn't a power> of two.> > So we all should know not to expect floating-point numbers to be> exactly equal to anything; that's been established. However, another> more basic question was not answered; curiosity (if nothing else)> demands an answer. Namely, it's OK to say we can't expect 1.0/0.2 ==> 5.0. But why is the result of (what is apparently) the same> computation *sometimes* the same, and *sometimes* different? That's the> question.> > And I think it's fair for the poster to want to know why.> > If you disassemble the sample program, you'll see that without> optimization, 1.0 is divided by 0.2 at *run* time, and compared with> 5.0; with optimization, the division is done, and the "<" and> "==" comparisons are done, at *compile* time. OK, but: If we're not> cross-compiling (most people don't), then the compiler creating a.out> is running on perhaps the same box as a.out is! Why does gcc, folding> the constant in the optimized a.out, get a different answer for 1.0/0.2> than the unoptimized a.out gets for 1.0/0.2?> > Not only that, without optimization:> > if (1/h < 5.0)> ...> > gives a different answer inside a.out than> > x = 1/h;> if (x < 5.0)> ...> > The key is that Pentiums (Pentia?) have 80-bit floating-point numbers> in the FPU. Without optimization, at compile time, gcc represents 5.0> as 0x4014000000000000. 0.2 is 0x3fc999999999999a. These are both> 64-bit doubles -- 1 sign bit, 11 exponent bits, & 52 explicit mantissa> bits (and 1 implicit leading mantissa bit, not stored in memory.)> > In the case "if (1/h < 5.0)", at run time, 1.0 is loaded into the FPU> using fld1; then "fdivl {address of 0.2 in memory}". The result is the> *80-bit* number 0x40019ffffffffffffd80. The 64-bit number 5.0> (0x4014000000000000) is loaded into the FPU to become the 80-bit number> 0x4001a000000000000000. Then, these two 80-bit numbers are compared in> the FPU; they're of course not the same.> > What's different in the case "x = 1/h; if (x < 5.0) ..." is that both> 80-bit numbers are stored from the FPU to memory as 64-bit (rounding> off the mantissa bits which differ), at which point they're both> 0x4014000000000000, then loaded *back* into the FPU where they're> both 0x4001a000000000000000.> > This isn't an FPU bug, by any stretch of the imagination, nor is it a> compiler bug. But it's a subtle difference between the Pentium's FPU> and other FPUs, of which it may occasionally be useful to be aware.> > > > > -----Original Message-----> From: Richard B. Johnson [mailto:root@chaos.analogic.com]> Sent: Thursday, April 25, 2002 7:23 AM> To: rpm> Cc: Jesse Pollard; Nikita@Namesys.COM; Andrey Ulanov;> linux-kernel@vger.kernel.org> Subject: Re: FPU, i386> > > On Thu, 25 Apr 2002, rpm wrote:> > > On Wednesday 17 April 2002 08:10 pm, Jesse Pollard wrote:> > > --------- Received message begins Here ---------> > >> > > > > if (int(1/h * 100) == int(5.0 * 100))> > >> > > will give a "proper" result within two decimal places. This is still> > > limited since there are irrational numbers within that range that COULD> > > still come out with a wrong answer, but is much less likely to occur.> > >> > > Exact match of floating point is not possible - 1/h is eleveated to a> > > float.> > >> > > If your 1/h was actually num/h, and num computed by summing .01 100> times> > > I suspect the result would also be "wrong".> > >> > > > why is exact match of floating point not possible ?> > Because many (read most) numbers are not exactly representable> in floating-point. The purpose of floating-point it to represent> real numbers with a large dynamic range. The trade-off is that> few such internal representations are exact.> > As a simple example, 0.33333333333..... can't be represented exactly> even with paper-and-pencil. However, as the ratio of two integers> it can be represented exactly, i.e., 1/3 . Both 1 and 3 must> be integers to represent this ratio exactly.> > All real numbers (except trancendentials) can represented exactly> as the ratio of two integers but floating-point uses only one> value, not two integers, to represent the value. So, an exact> representation of a real number, when using a single variable> in a general-purpose way, is, for all practical purposes, not> possible. Instead, we get very close.> > When it comes to '==' close is not equal. There are macros in> <math.h> that can be used for most floating-point logic. You> should check them out. If we wanted to check for '==' we really> need to do something like this:> > double a, b;> some_loop() {> if(fabs(a-b) < 1.0e-38)> break;> }> Where we get the absolute value of the difference between two> FP variables and compare against some very small number.> > To use the math macros, the comparison should be something like:> > if (isless(fabs(a-b), 1.0e-38))> break;> > > Cheers,> Dick Johnson> > Penguin : Linux version 2.4.18 on an i686 machine (797.90 BogoMips).> > Windows-2000/Professional isn't.> > -> To unsubscribe from this list: send the line "unsubscribe linux-kernel" in> the body of a message to majordomo@vger.kernel.org> More majordomo info at http://vger.kernel.org/majordomo-info.html> Please read the FAQ at http://www.tux.org/lkml/> Cheers,Dick JohnsonPenguin : Linux version 2.4.18 on an i686 machine (797.90 BogoMips). Windows-2000/Professional isn't.-To unsubscribe from this list: send the line "unsubscribe linux-kernel" inthe body of a message to majordomo@vger.kernel.orgMore majordomo info at http://vger.kernel.org/majordomo-info.htmlPlease read the FAQ at http://www.tux.org/lkml/`
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5 Replies Latest reply on Jan 3, 2019 11:34 AM by Paul Wachtler
# Legend Calculation
Hi
i would like to show the comparison of quantity with the Technology and Furniture.
Issue: if Technology sales greater than Furniture then it supposed to be Green Else Red.
My Trial Logic: IF COUNT(IF [Category] = 'Furniture' THEN [Quantity] END) <=
COUNT(IF [Category] = 'Technology' THEN [Quantity] END) THEN 1 ELSE 0 END
But i am unable to achieve the same.
• ###### 1. Re: Legend Calculation
Hi Naryb,
You can accomplish this with an LOD expression. Right now the level of detail of your viz is at the State and Category level - each category can never be the other which is why your current calculation isn't working. We can get it working with an LOD though like this:
IF
{FIXED [State]: sum(IF [Category] = 'Furniture' THEN [Quantity] END)}
<=
{FIXED [State]: sum(IF [Category] = 'Technology' THEN [Quantity] END)}
THEN 1 ELSE 0
END
Best,
Paul
• ###### 2. Re: Legend Calculation
Hi Paul,
Thank you
• ###### 3. Re: Legend Calculation
That looks like it's working as you described it. If Technology sales are higher the bars are one color and if Furniture is higher than it's another - you can change these two colors to whatever you'd like.
Do you mean that you only want the technology bar to be colored? In that case, you can do this:
IF [Category] = "Technology" then
IF {FIXED [State]: sum(IF [Category] = 'Furniture' THEN [Quantity] END)}
<=
{FIXED [State]: sum(IF [Category] = 'Technology' THEN [Quantity] END)}
THEN "Green" else "Red"
END
else "Blue"
end
Also, as a tip, putting red and green on the same chart isn't recommended since color blind people tend to be unable to see the difference. Blue and Orange is preferable (and you can use grey for the non-colored bars).
• ###### 4. Re: Legend Calculation
Hi Paul,
Really appreciate your time and help.
Happy New year Paul.
Thank you
• ###### 5. Re: Legend Calculation
You're welcome Naryb, happy to help! Happy New Year to you too!
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+0
# 1,000
0
38
1
How do you make 1,000,no more,no less,with only 750,8,6,and 100? You can use each number as many times as you want. Use all numbers at least 1 time.
Guest May 19, 2017
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Scilab Home page | Wiki | Bug tracker | Forge | Mailing list archives | ATOMS | File exchange
Scilab 5.5.1
Change language to: English - Português - 日本語 - Русский
meanf
weighted mean of a vector or a matrix
Calling Sequence
```m = meanf(x, fre, [orien])
m = meanf(x, fre, 'r') or m = meanf(x, fre, 1)
m = meanf(x, fre, 'c') or m = meanf(x, fre, 2)```
Arguments
x
A real or complex, full or sparse matrix, or an integer matrix, or an hypermatrix.
fre
A real or complex, full or sparse matrix, or an integer matrix, or an hypermatrix.
orien
The orientation of the computation. Valid values are
• 1 or "r": result is a row, after a column-wise computation.
• 2 or "c": result is a column, after a row-wise computation.
• "*": full undirectional computation.
m
The mean.
Description
This function computes the mean of a vector or matrix `x`, each of them counted with a frequency given by the corresponding values of the integer vector or matrix `fre`.
For a vector or matrix `x`, `m = meanf(x, fre)` or `m = meanf(x, fre, "*")` returns in scalar `m` the mean of all the entries of `x`, each value counted with the multiplicity indicated by the corresponding value of `fre`.
`m = meanf(x, fre, 'r')` (or, equivalently, `m = meanf(x, fre, 1)`) returns in each entry of the row vector `m` the mean of each column of `x`.
`m = meanf(x, fre, 'c')` (or, equivalently, `m = meanf(x, fre, 2)`) returns in each entry of the column vector `m` the mean of each row of `x`.
Examples
```x=[0.2113249 0.0002211 0.6653811;0.7560439 0.3303271 0.6283918]
m=meanf(x,rand(x))
m=meanf(x,[10 10 10;1 1 1],'r')
m=meanf(x,[10 10 10;1 1 1],'c')```
• mean — mean (row mean, column mean) of vector/matrix entries
• stdevf — standard deviation
• variancef — variance (et moyenne) d'un vecteur ou d'une matrice réelle ou complexe de nombres pondérés en fréquence
Bibliography
Wonacott, T.H. & Wonacott, R.J.; Introductory Statistics, fifth edition, J.Wiley & Sons, 1990.
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IIT-JEE
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Question From class 12 Chapter DETERMINANTS
Let A be a square matrix of order n; then the sum of the product of elements of any row (column) with their cofactors is always equal to
Let A be a square matrix of order n; then the sum of the product of elements of any row (column) with the cofactors of the corresponding elements of some other row (column) is 0.
5:32
Let be a square matrix of order so that sum of elements of each row is . Then the sum elements of matrix is
5:09
The sum of the products of the elements of any row of a matrix A with the corresponding cofactors of the elements of the same row is always equal to
0:00
The sum of products of elements of any row with the cofactors of corresponging elements is equal to……………
2:03
If A and B are two matrices of the same order; then
5:25
Let A be a square matrix of order such that each element in a row(column) of A is 0, then .
1:57
Let denote a square matrix of order with every element a; Then, the sum of all elements of the product matrix is
5:12
Let matrix and let denote the matrix of the cofactors of elements of matrix A and be the matrix of cofactors of elements of matrix and so on. If denote the matrix of cofactros of elements of matrix , then equals
1:42
Let A be a square matrix of order n and let B be a matrix obtained from A by multiplying each element of a row/columnn of A by a scalar k then
6:02
Let be a square matrix of order 3. Then for any positive integer n, what is equal to ?
3:09
Let A be a square matrix and B be a matrix obtained from A by adding to a row/column of A a scalar multiple of another row/column of A, then
4:30
Let A be a square matrix of order n n where n 2. Let B be a matrix obtained from A with first and second rows interchanged. Then which one of the following is correct ?
4:31
Let 'A' is matrix such that the sum of elements in each row is 1. Find out sum of the all the elements in .
In a matrix the sum of each row, column and both the main diagonals is . Then the sum of the four corner elements
2:51
Let A be a square matrix of order n. Then;
4:08
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## Take My Convexity Topics Class
A "Convexity Topics Class" QE" is a standard mathematical term for a generalized constant expression which is used to solve differential equations and has solutions which are routine. In differential Class resolving, a Convexity Topics function, or "quad" is utilized.
The Convexity Topics Class in Class form can be expressed as: Q( x) = -kx2, where Q( x) are the Convexity Topics Class and it is an essential term. The q part of the Class is the Convexity Topics consistent, whereas the x part is the Convexity Topics function.
There are 4 Convexity Topics functions with appropriate service: K4, K7, K3, and L4. We will now look at these Convexity Topics functions and how they are resolved.
K4 - The K part of a Convexity Topics Class is the Convexity Topics function. This Convexity Topics function can likewise be written in partial fractions such as: (x2 - y2)/( x+ y). To resolve for K4 we increase it by the appropriate Convexity Topics function: k( x) = x2, y2, or x-y.
K7 - The K7 Convexity Topics Class has a service of the type: x4y2 - y4x3 = 0. The Convexity Topics function is then multiplied by x to get: x2 + y2 = 0. We then have to increase the Convexity Topics function with k to get: k( x) = x2 and y2.
K3 - The Convexity Topics function Class is K3 + K2 = 0. We then multiply by k for K3.
K3( t) - The Convexity Topics function equationis K3( t) + K2( t). We increase by k for K3( t). Now we multiply by the Convexity Topics function which offers: K2( t) = K( t) times k.
The Convexity Topics function is also referred to as "K4" because of the initials of the letters K and 4. K implies Convexity Topics, and the word "quad" is pronounced as "kah-rab".
The Convexity Topics Class is one of the main approaches of fixing differential equations. In the Convexity Topics function Class, the Convexity Topics function is first increased by the appropriate Convexity Topics function, which will offer the Convexity Topics function.
The Convexity Topics function is then divided by the Convexity Topics function which will divide the Convexity Topics function into a genuine part and a fictional part. This provides the Convexity Topics term.
Lastly, the Convexity Topics term will be divided by the numerator and the denominator to get the ratio. We are left with the right-hand man side and the term "q".
The Convexity Topics Class is an important concept to comprehend when solving a differential Class. The Convexity Topics function is just one approach to fix a Convexity Topics Class. The techniques for fixing Convexity Topics equations consist of: particular worth decay, factorization, ideal algorithm, numerical option or the Convexity Topics function approximation.
## Hire Someone To Do Your Convexity Topics Class
If you wish to end up being knowledgeable about the Quartic Class, then you require to very first start by browsing the online Quartic page. This page will reveal you how to use the Class by using your keyboard. The description will likewise reveal you how to produce your own algebra equations to help you study for your classes.
Before you can understand how to study for a Convexity Topics Class, you need to initially understand making use of your keyboard. You will find out how to click on the function keys on your keyboard, in addition to how to type the letters. There are 3 rows of function keys on your keyboard. Each row has four functions: Alt, F1, F2, and F3.
By pushing Alt and F2, you can multiply and divide the value by another number, such as the number 6. By pushing Alt and F3, you can use the 3rd power.
When you push Alt and F3, you will enter the number you are attempting to increase and divide. To multiply a number by itself, you will push Alt and X, where X is the number you wish to multiply. When you push Alt and F3, you will enter the number you are trying to divide.
This works the exact same with the number 6, other than you will just enter the two digits that are 6 apart. Lastly, when you push Alt and F3, you will utilize the 4th power. Nevertheless, when you press Alt and F4, you will utilize the real power that you have found to be the most suitable for your issue.
By utilizing the Alt and F function keys, you can increase, divide, and after that utilize the formula for the 3rd power. If you require to increase an odd variety of x's, then you will require to enter an even number.
This is not the case if you are attempting to do something complex, such as multiplying two even numbers. For example, if you want to increase an odd number of x's, then you will require to get in odd numbers. This is especially true if you are attempting to determine the response of a Convexity Topics Class.
If you wish to convert an odd number into an even number, then you will need to press Alt and F4. If you do not know how to multiply by numbers on their own, then you will require to utilize the letters x, a b, c, and d.
While you can multiply and divide by use of the numbers, they are a lot easier to use when you can take a look at the power tables for the numbers. You will have to do some research study when you first start to use the numbers, however after a while, it will be second nature. After you have produced your own algebra equations, you will have the ability to develop your own reproduction tables.
The Convexity Topics Solution is not the only way to fix Convexity Topics equations. It is necessary to find out about trigonometry, which utilizes the Pythagorean theorem, and after that use Convexity Topics formulas to resolve issues. With this approach, you can learn about angles and how to solve problems without having to take another algebra class.
It is essential to attempt and type as rapidly as possible, due to the fact that typing will help you know about the speed you are typing. This will help you write your responses faster.
## Hire Someone To Take My Convexity Topics Class
A Convexity Topics Class is a generalization of a direct Class. For example, when you plug in x=a+b for a given Class, you get the value of x. When you plug in x=a for the Class y=c, you obtain the worths of x and y, which offer you an outcome of c. By using this fundamental idea to all the equations that we have attempted, we can now fix Convexity Topics equations for all the values of x, and we can do it rapidly and effectively.
There are many online resources offered that offer complimentary or budget friendly Convexity Topics formulas to solve for all the worths of x, including the cost of time for you to be able to take advantage of their Convexity Topics Class task aid service. These resources usually do not require a subscription charge or any sort of financial investment.
The answers offered are the result of complex-variable Convexity Topics formulas that have actually been solved. This is also the case when the variable utilized is an unidentified number.
The Convexity Topics Class is a term that is an extension of a direct Class. One benefit of using Convexity Topics equations is that they are more basic than the direct equations. They are easier to resolve for all the worths of x.
When the variable used in the Convexity Topics Class is of the type x=a+b, it is simpler to solve the Convexity Topics Class because there are no unknowns. As a result, there are less points on the line defined by x and a constant variable.
For a right-angle triangle whose base indicate the right and whose hypotenuse indicate the left, the right-angle tangent and curve chart will form a Convexity Topics Class. This Class has one unknown that can be discovered with the Convexity Topics formula. For a Convexity Topics Class, the point on the line specified by the x variable and a constant term are called the axis.
The existence of such an axis is called the vertex. Because the axis, vertex, and tangent, in a Convexity Topics Class, are an offered, we can find all the worths of x and they will sum to the provided values. This is attained when we utilize the Convexity Topics formula.
The aspect of being a continuous element is called the system of equations in Convexity Topics equations. This is sometimes called the central Class.
Convexity Topics formulas can be resolved for other values of x. One way to resolve Convexity Topics equations for other values of x is to divide the x variable into its element part.
If the variable is provided as a favorable number, it can be divided into its aspect parts to get the normal part of the variable. This variable has a magnitude that amounts to the part of the x variable that is a constant. In such a case, the formula is a third-order Convexity Topics Class.
If the variable x is negative, it can be divided into the same part of the x variable to get the part of the x variable that is multiplied by the denominator. In such a case, the formula is a second-order Convexity Topics Class.
Option assistance service in resolving Convexity Topics equations. When utilizing an online service for resolving Convexity Topics formulas, the Class will be fixed instantly.
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## Udacity
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### Course: College Algebra>Unit 13
Lesson 5: Interpreting the rate of change of exponential models
# Interpreting change in exponential models
Sal finds the factor by which a quantity changes over a single time unit in various exponential models.
## Want to join the conversation?
• Why 1.75 is as the same as 75% instead of 0.75?
• 75% does = 0.75
The problem is dealing with exponential growth in the number of branches.
So tree has its original number of branches (100% or 1) + growth of 75% (0.75)
1 (original) + 0.75 (growth) = new percentage = 1.75%
For example: 200 branches * 100% + 75% growth = 200(1) + 200 (0.75) = 200 (1.75) = 350
If the problem just used 0.75, then the number of branches would actually be shrinking by 25%
For example: 200 * 0.75 = 150 branches
This is fewer branches than we started with. So, the tree is not growing, its shrinking.
Hope this helps.
• I don't understand why the bear population would shrink by a factor of 2/3 rather than 1/3. When it asked, "what factor is the bear population shrinking by" isn't it asking for the factor in function of the population lost rather than the one remained?
• The question is asking for the factor. In this case the factor is (2/3). The population is decreasing by 1/3, but to get the third, you would multiply by two thirds.
example: 1 * 2/3 = 2/3
The 1 has decreased by one third to a solution of 2/3
• Sal says the bear population shrinks by a factor of 2/3, but this statement is just a double negative, if something shrinks by a factor <1, then it increases. So would it shrink by the reciprocal of 2/3? (So 3/2), or would it shrink by the difference of 1 and the original factor added to 1. Which would be (1 - 2/3 + 1 or 4/3).
• No, shrinking by a factor of 2/3 means the original amount is MULTIPLIED by 2/3, which means you have 2/3 of the original left.
• In the practice "Interpret change in exponential models" when given a question about finding percentage, if we are handed sat (0.75), why would this not be 75% for an answer. I've tried looking at the explanation but it doesn't make sense.
• How do you do the (0.81)^t ones, he doesn't explain that
• If you've got something like f(x) = 43*(0.81)^t, then it's like the second last example with 2/3 as a factor. If you have a factor that is smaller than 1, then the number still decreases.
• In the first exercise, something is increasing, so we get "...increases by a factor 1.5" or so. In the second exercise something decreases. Decreasing is the opposit of increasing, so we'd expect "...decreases nu a factor 1.5". Instead we get a decrease by a factor less than 1. Isn't a decrease by a factor less than one an increase? Just like an increase by a factor less than one is a decrease?
• Yes... to decrease a value using multiplication, you need to multiply by a value less than 1. Any value over 1 would increase the number.
• Why is Math so darn hard all the time?
:(
• Does the population of bears shrink by a factor or 2/3 or 1/3? It seems if there are 2/3 as many bears the next year, the population shrank by 1/3.
(1 vote)
• It did shrink by 1/3, but not by a factor of 1/3. A 'factor' is a term of multiplication. Since there are 2/3 as many bears, the population was multiplied by 2/3, so we say it shrunk by a factor of 2/3.
• So if n is 1 or more it grows and if it is less than one it shrinks?
(1 vote)
• Basically, if you have a function f that is exponential and can be expressed as:
`f(x) = a * b^x`, b determines the factor.
`If b < 1, then f(x) will decrease as x increases.If b > 1, then f(x) will increase as x increases.If b = 1, then no matter what x is, 1^x = 1, so it stays flat.`
• How can exponential growth and decay help us solve problems in the real world? How does this math subject affect and impact us throughout our lives? What is an example of exponential growth or decay in the real world?
• As we see in the video, exponential growth and decay can help us measure anything from the amount of a drug left in the body to the amount of radiation in an area.
(1 vote)
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# Concrete LEGO
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161
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How to make your own 10:1 scale LEGO brick out of concrete!
You'll need:
• 4 - 5 liters of concrete (when mixed)
• Some scrap wood
• Saw
• Hammer and nails / screws and screwdriver
• Ruler (or something else to take measures)
## Step 1: Messure Up!
So, how large is a LEGO block?
These links ought to give us some clues..:
http://nobsjustabs.wordpress.com/2009/03/24/converting-lego-measurements-to-scale-lengths/
http://stason.org/TULARC/games/mindstorms-lego/13-Material-Technology-and-Measurements-Lego.html
To make a 3 x 2 brick we get the following measurements:
Height of block: 9.6 mm
Width of block: 15.9 mm
Length of block: 23.8 mm
spacing of knob centers: 8 mm
Diameter of knobs: 5 mm
Height of knobs: 1.7 mm
To scale this up, we just change "mm" to "cm". Easy, huh?
10:1 block:
Height of block: 9.6 cm
Width of block: 15.9 cm
Length of block: 23.8 cm
spacing of knob centers: 8 cm
Diameter of knobs: 5 cm
Height of knobs: 1.7 cm
## Step 2: Building the Frame
Remember that you want to be able to disassembly the molding box after the concrete has set, so dont go overkill with the size of the nails. (Or, just use screws instead)
1) Start out with a peace of wood that is approx. 18 x 26 cm and drill out the six 50 mm holes using a hole saw.
2) Nail another 18 x 26 cm peace of wood to the underside of the previous one.
3) Add the 96 mm high walls to complete the jig for molding.
## Step 3: Molding
1) Follow the instructions on the bag of the concrete on how to make the proper mix. You will need at least 4 liters.
2) Fill the box up.
3) Why not add a copyright infringing logo to the wet concrete?
4) Set aside for a few days or what ever the bag of the concrete states, in order for the .
5) Carefully remove the box, starting with the sides and the "bottom".
To remove the wood with the six holes, its easiest to try to break the wood apart. Carefully.
6) If you chose to paint it, use the proper paint!
Candy red would probably look sweet!
## Recommendations
• ### Lamps Class
9,270 Enrolled
## 95 Discussions
How about mini legos? You can even build a house out of those?
I was surprised to see this as, for the past couple of months, I've been working on a seating project similar to this. We had a budget and lot longer for development (we also had copyright issues to avoid) But I thought people might like to see what we did. We had to consider durability, mass production and re-use of the molds. I have hundreds more pictures if anyone's interested. Obviously these look slightly different to actual LEGO bricks but they stack properly :)
12 replies
btw I did eventually get around to making this into a full concrete seating instructable. https://www.instructables.com/id/Modular-Concrete-Bench/
Beautiful work. If they were rectangular they would be able to lock across blocks better/have more diverse use. Maybe make those in addition to these?
Yeah, that would be cool. we didn't need the blocks to overlap for this project, but longer bricks would allow you to make more sound structures, if you wanted.
There was a reply here I DID NOT POST (but it had my screen name). Anyone else have a problem with having their screen name hijacked?
Your mold seems to have the same shortcoming that I noticed in the original. You seem to have the same spacing from the raised squares to the edge of the block as you have between the squares. If the outside margin was half the space between the squares, then you could stack your blocks in staggered rows, like a regular brick wall. Although it would mean you'd also need to make a mold for a half-size block if you wanted to make a rectangular wall, so maybe that's why you didn't do it that way.
DUDE!!! I am going to do this to make a fire pit!!! I have been trying to decide how I wanted to construct it and I didn't see anything compelling. The custom concrete block design is awesome.
We did consider this (lots of design meetings and eventually decided against it), but the idea was to make abstract seating arrangements and not a large brick wall. Plus (I won't explain why) offsetting the lugs in that way makes producing the molds more complicated.
I don't know about stacking "properly" — the first principle of LEGO building is "cross your lines" (that is, offset each row relative to the one below it so you don't have vertical interfaces running more than one row high through your structure). It doesn't look to me like these blocks can even do that, because the studs are too close together in the center and not close enough to the sides. Still looks like a neat project though!
I like this version a lot. Looks very clean, sleek. Do you have a link to more pictures? What about tinting the concrete? And if you did build a mold that was interlockable sideways like bricks then use a lighter weight material like hypertufa maybe for short walls? Could be good for making raised gardening beds?
To prevent the concrete from sticking to the form and make it easier to remove the form after the concrete is set, line the form with a sheet of plastic. Hefty garbage bags might suffice, or a bit of visquene sheet. Fold the sheet carefully in the corners to minimize unsightly creases in the concrete. To make a lot of these blocks, you should probably invest in making a few silicone molds instead of wood. They'll be more work and more expensive to make than wood, but should be much easier to pull off the concrete and should last longer.
4 replies
i think the concrete is too heavy for silicone, think it just stretches the mold instead of just filling it up.
They usually use a firm urethane rubber for concrete molds. Smooth-on.com probably has a video or two of concrete molding and stamping.
I used another instructable https://www.instructables.com/id/How-To-Make-Your-Own-Sugru-Substitute/ to make stepping stone molds from a plasticene over Styrofoam original. The 'oogoo can be layered on even after the base coat dries on the mold and if you are worried about stretching and strength, you can put fibreglass drywall tape down as you lay up the mold. The modelling clay original easily pops out of the silicone mold. This was an easy & inexpensive way to make unique stepping stones for a fundraiser. Btw those cement legos are awesome!
the easiest way to keep cement from sticking to the forms is to cote them with diesel fuel. when working with a local contractor we always had diesel in a five gallon bucket and used a paint brush to apply.
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```-Axiom: ---------
- A |- A
-
-Structural Rules:
-
-Exchange: Γ, A, B, Δ |- C
- ---------------------------
- \$Gamma;, B, A, Δ |- C
+Question: why do thunks work? We know that `blackhole ()` doesn't terminate, so why do expressions like:
-Contraction: Γ, A, A |- B
- -------------------
- Γ, A |- B
+ let f = fun () -> blackhole ()
+ in true
-Weakening: Γ |- B
- -----------------
- Γ, A |- B
+terminate?
-Logical Rules:
+Bottom type, divergence
+-----------------------
---> I: Γ, A |- B
- -------------------
- Γ |- A --> B
+Expressions that don't terminate all belong to the **bottom type**. This is a subtype of every other type. That is, anything of bottom type belongs to every other type as well. More advanced type systems have more examples of subtyping: for example, they might make `int` a subtype of `real`. But the core type system of OCaml doesn't have any general subtyping relations. (Neither does System F.) Just this one: that expressions of the bottom type also belong to every other type. It's as if every type definition in OCaml, even the built in ones, had an implicit extra clause:
---> E: Γ |- A --> B Γ |- A
- -----------------------------------------
- Γ |- B
-```
+ type 'a option = None | Some of 'a;; + type 'a option = None | Some of 'a | bottom;; -`A`, `B`, etc. are variables over formulas. -Γ, Δ, etc. are variables over (possibly empty) sequences -of formulas. `Γ |- A` is a sequent, and is interpreted as -claiming that if each of the formulas in Γ is true, then `A` -must also be true. +Here are some exercises that may help better understand this. Figure out what is the type of each of the following: -This logic allows derivations of theorems like the following: + fun x y -> y;; -
```-------- Id
-A |- A
----------- Weak
-A, B |- A
-------------- --> I
-A |- B --> A
------------------ --> I
-|- A --> B --> A
-```
+ fun x (y:int) -> y;; -Should remind you of simple types. (What was `A --> B --> A` the type -of again?) + fun x y : int -> y;; -The easy way to grasp the Curry-Howard correspondence is to *label* -the proofs. Since we wish to establish a correspondence between this -logic and the lambda calculus, the labels will all be terms from the -simply-typed lambda calculus. Here are the labeling rules: + let rec blackhole x = blackhole x in blackhole;; -
```-Axiom: -----------
- x:A |- x:A
+ let rec blackhole x = blackhole x in blackhole 1;;
-Structural Rules:
+ let rec blackhole x = blackhole x in fun (y:int) -> blackhole y y y;;
-Exchange: Γ, x:A, y:B, Δ |- R:C
- --------------------------------------
- Γ, y:B, x:A, Δ |- R:C
+ let rec blackhole x = blackhole x in (blackhole 1) + 2;;
-Contraction: Γ, x:A, x:A |- R:B
- --------------------------
- Γ, x:A |- R:B
+ let rec blackhole x = blackhole x in (blackhole 1) || false;;
-Weakening: Γ |- R:B
- ---------------------
- Γ, x:A |- R:B [x chosen fresh]
+ let rec blackhole x = blackhole x in 2 :: (blackhole 1);;
-Logical Rules:
-
---> I: Γ, x:A |- R:B
- -------------------------
- Γ |- \xM:A --> B
+By the way, what's the type of this:
---> E: Γ |- f:(A --> B) Γ |- x:A
- ---------------------------------------------
- Γ |- (fx):B
-```
+ let rec blackhole (x:'a) : 'a = blackhole x in blackhole -In these labeling rules, if a sequence Γ in a premise contains -labeled formulas, those labels remain unchanged in the conclusion. -Using these labeling rules, we can label the proof -just given: +Back to thunks: the reason you'd want to control evaluation with thunks is to +manipulate when "effects" happen. In a strongly normalizing system, like the +simply-typed lambda calculus or System F, there are no "effects." In Scheme and +OCaml, on the other hand, we can write programs that have effects. One sort of +effect is printing (think of the [[damn]] example at the start of term). +Another sort of effect is mutation, which we'll be looking at soon. +Continuations are yet another sort of effect. None of these are yet on the +table though. The only sort of effect we've got so far is *divergence* or +non-termination. So the only thing thunks are useful for yet is controlling +whether an expression that would diverge if we tried to fully evaluate it does +diverge. As we consider richer languages, thunks will become more useful. -
```------------- Id
-x:A |- x:A
----------------- Weak
-x:A, y:B |- x:A
-------------------------- --> I
-x:A |- (\y.x):(B --> A)
----------------------------- --> I
-|- (\x y. x):A --> B --> A
-```
-We have derived the *K* combinator, and typed it at the same time! +Towards Monads +-------------- -[To do: add pairs and destructors; unit and negation...] +This has now been moved to the start of [[week7]]. -Excercise: construct a proof whose labeling is the combinator S.
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Rupert
Sorted by New
# Wiki Contributions
Rupert10
However, because topology on is finer than topology on here, this still shows how the proof of the Lawvere fixed point theorem can be applied here to give Brouwer fixed point theorem as corollary, which could conceivably be a publishable result (see what "Geometry and Topology" think about that), and this could still be sorta kinda maybe relevant to Scott's original motivation for looking at the problem (if you're okay with working with two different topologies on the space of agents, one finer than the other). But this is a very big space of agents you're talking about here.
Correction: need not only that topology on is finer than topology on , but also, given arbitrary open subset of , take pre-image under evaluation map in , projection onto first factor and then pre-image of that under the continuous surjection , it needs to be shown that this set is open in both topologies. I believe that this can indeed be done for an appropriate class of spaces for the pair of topologies in question.
Rupert10
Let be with generalised Cantor space topology, and be with product topology, a closed disc in a finite-dimensional Euclidean space. Then there is a continuous surjection . I don't know how to show that there is a topological space with carrier set and a continuous surjection . Thanks to Alex Mennen for pointing out the problem.
Rupert10
When I look at my post the LaTeX code isn't formatting properly; if anyone can let me know how to fix that.
Rupert20
I have just now submitted an attempted solution to this problem to "Geometry and Topology". I claim that the space you are looking for is ( being the least uncountable cardinal) with the generalised Cantor space topology", that is for each countable well-ordered bit-string you have a basic open set consisting of all bit-strings of length with as an initial fragment. Since this topological space has quite a large cardinality I'm somewhat unclear whether this is helpful for your proposed application and would need to think about it more. (Matthew Barnett just now directed me to this post of yours.) I sent you an early draft of my paper, which argues the point in detail, on FB Messenger, and can send the latest version to you if you wish.
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BUILT-IN MATHEMATICA SYMBOL
# ListFourierSequenceTransform
ListFourierSequenceTransform[list, ]
gives the discrete-time Fourier transform (DTFT) of a list as a function of the parameter .
ListFourierSequenceTransform[list, , k]
places the first element of list at integer time k on the infinite time axis.
ListFourierSequenceTransform[list, {1, 2, ...}, {k1, k2, ...}]
gives the multidimensional discrete-time Fourier transform
## ExamplesExamplesopen allclose all
### Basic Examples (2)Basic Examples (2)
Discrete-time Fourier transform of a constant vector:
Out[1]=
Two-dimensional DTFT:
Out[2]=
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# PHI 103
posted by .
Mrs. Orlof teaches two history classes, one in the morning and one in the afternoon. Yesterday she gave the same test to both classes. Anyone who failed the test must take a retest. Since a greater percentage of students who took the morning test failed the test than students who took the afternoon test, more of Orlof’s morning history students than afternoon history students will have to take the retest.
The conclusion above is not necessarily valid because
• PHI 103 -
A larger percentage doesn't mean more students. The morning class may be larger than the afternoon class.
## Similar Questions
1. ### phi 103
mrs orlof teaches 2 history classes one in the afternoon and one in the morining yesturday she gave the same test to both classses anyone who failed the test must retake since a greater percentage of students who took the morining …
2. ### Critical Thinking (philosophy)
1. 21{1[2(24)24]}> The average height of members of the high school basketball team is six feet, three inches. Jerry is on the high school basketball team, so Jerry must be taller than six feet. The argument above is flawed because …
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A prof. teaches 2 calc. classes. The first class has 25 students and their mean on the 1st test was an 82. The 2nd class has 15 students and their mean on the same test was a 74. What is the mean on this test if the prof. combines …
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4. Gregory teaches martial arts. He charges a one-time processing fee of \$5.00 and the cost of the classes is shown below. Let x represent the number of classes and y represent the cost of classes. Based on this information, what will …
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Mrs. Orlof teaches two history classes, one in the morning and one in the afternoon. Yesterday she gave the same test to both classes. Anyone who failed the test must take a retest. Since a greater percentage of students who took the …
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Mrs. Orlof teaches two history classes, one in the morning and one in the afternoon. Yesterday she gave the same test to both classes. Anyone who failed the test must take a retest. Since a greater percentage of students who took the …
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››Sodium carbonate molecular weight
Molar massive of Na2CO3 = 105.98844 g/mol
Convert grams salt Carbonate to mole or moles salt Carbonate to grams
Molecular load calculation:22.989770*2 + 12.0107 + 15.9994*3
››Percent ingredient by element
Element Symbol Atomic Mass # of Atoms Mass Percent Sodium Na 22.989770 2 43.382% Carbon C 12.0107 1 11.332% Oxygen O 15.9994 3 45.286%
››Similar chemistry formulasNote the all formulas space case-sensitive.Did you average to uncover the molecular load of one of these comparable formulas?Na2CO3Na2Co3
››Calculate the molecular weightof a chemical link 0) location="/molarmass/" + urlencode(this.q.value); rather alert("Please get in a chemistry formula or surname of a substance."); return false;">
Enter a chemistry formula: 0) location="/molarmass/" + urlencode(this.form.q.value); rather alert("Please enter a chemical formula or surname of a substance."); return false;">
Browse the perform ofcommon chemical compounds.
You are watching: What is the molar mass of sodium carbonate
In chemistry, the formula load is a quantity computed by multiplying the atomic weight (in atomic mass units) the each element in a chemical formula by the number of atoms of that aspect present in the formula, then adding all the these assets together.
The atom weights provided on this website come indigenous NIST, the national Institute the Standards and Technology. We usage the most usual isotopes. This is exactly how to calculate molar mass (average molecule weight), which is based upon isotropically weighted averages. This is no the exact same as molecular mass, i beg your pardon is the mass of a single molecule that well-defined isotopes. For mass stoichiometric calculations, we are usually identify molar mass, i m sorry may additionally be referred to as standard atomic load or average atomic mass.
If the formula provided in calculating molar mass is the molecule formula, the formula weight computed is the molecule weight. The percentage by load of any atom or group of atoms in a compound deserve to be computed by dividing the complete weight that the atom (or team of atoms) in the formula by the formula weight and also multiplying by 100.
A common request ~ above this website is to convert grams come moles. To finish this calculation, you need to know what substance you are trying to convert. The factor is the the molar fixed of the substance affects the conversion. This site defines how to uncover molar mass.
Using the chemical formula of the compound and also the regular table the elements, us can include up the atomic weights and also calculate molecular load of the substance.
Finding molar massive starts through units that grams every mole (g/mol). When calculating molecular weight of a chemical compound, it tells us how many grams space in one mole of that substance. The formula weight is just the load in atomic mass devices of every the atoms in a given formula.
See more: How Much Does A Chevy Cruze Weigh T Of Chevy Cruze, Used 2019 Chevrolet Cruze Specs & Features
Formula weights room especially helpful in identify the family member weights that reagents and also products in a chemical reaction. These relative weights computed native the chemistry equation room sometimes referred to as equation weights.
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HP Prime: Black Hole Characteristics – Hawking Radiation
01-05-2018, 03:32 AM (This post was last modified: 01-23-2018 03:02 PM by Eddie W. Shore.)
Post: #1
Eddie W. Shore Senior Member Posts: 1,596 Joined: Dec 2013
HP Prime: Black Hole Characteristics – Hawking Radiation
HP Prime: Black Hole Characteristics – Hawking Radiation
Equations Used
Given the mass (either in kg or solar masses), the following equations can estimate these black hole characteristics:
R = M * G/c^2
Life time left as the black hole slowly radiates (in s):
t = M^3 * 5120 * π * G^2 / (hbar * c^4)
The HP Prime uses the conversion for seconds to years:
1 year ≈ 31556925.9747 s
Average temperature of the black hole (K):
temp = (hbar * c^3)/(M * 8 * k * π * G)
If you need to convert to °C subtract 273.15 from this result.
Surface area of the black hole (m^2):
sa = (M^2 * 16 * π * G^2)/c^4
Surface gravity of the black hole (m/s^2), as you can imagine, this will be a huge number:
gr = c^4 / (M * 4 * G)
Constants Used
Values are taken from the HP Prime
Universal Gravitation Constant
G = 6.67384 * 10^-11 m^3/(kg * s^2)
Speed of Light
c = 299792458 m/s
Plank Constant Divided by 2*π
hbar = 1.054571726 * 10^-34 J*s
Boltzmann Constant
k = 1.3806488 * 10^-23 J/K
HP Prime Program BLACKHOLE
Code:
EXPORT BLACKHOLE() BEGIN // EWS 2018-01-04 // Hawking Radiation // Input of mass LOCAL ch,M; INPUT({M,{ch,{"kg","Solar Mass"}}}, "Mass",{"Mass: ","Unit: "}); IF ch=2 THEN M:=1.988435ᴇ30*M; END; LOCAL k,G,c,hbar; // from 4 Constants // Shift, Units, Constant k:=1.3806488ᴇ−23; // Chemistry G:=6.67384ᴇ−11; // Physics c:=299792458; // Physics hbar:=1.054571726ᴇ−34; // Quantum // Swartzchild radius (m) LOCAL R:=(2*G*M)/c^2; // Life (years) LOCAL t:=M^3*5120*π*G^2/ (hbar*c^4*31556925.9747); // Temperature (K) LOCAL temp:=(hbar*c^3)/ (M*8*k*π*G); // Surface Area (m^2) LOCAL sa:=M^2*16*π*G^2/c^4; // Gravity LOCAL gr:=c^4/(4*G*M); // Results PRINT(); PRINT("Schwartzchild Radius:"); PRINT(R+" m"); PRINT("Life:"); PRINT(t+" years"); PRINT("Temperature:"); PRINT(temp+" K"); PRINT("Surface Area:"); PRINT(sa+" m^2"); PRINT("Surface Gravity:"); PRINT(gr+" m/s^2"); // List RETURN {R,t,temp,sa,gr}; END;
Examples
Cygnus X-1: 14.8 solar masses
Life: 6.79261706057 * 10^70 years
Temperature: 4.16932978074 * 10^-9 K (near absolute zero, very cold!)
Surface Area: 24004068275.4 m^2
Surface Gravity: 1.02819127807 * 10^12 m/s^2
Sagittarius A*, the center of our Milky Way Galaxy: 4.31 million solar masses
Life: 1.67758214773 * 10^87 years
Temperature: 1.43169560917 * 10^-14 K
Surface Area: 2.03571024785 * 10^21 m^2
Surface Gravity: 3530680.02679 m/s^2
Source:
Jim Wisniewski. “Hawking Radition Calcualtor” Xaonon. January 3, 2017. http://xaonon.dyndns.org/hawking/ Retrieved December 26, 2017
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Messages In This Thread HP Prime: Black Hole Characteristics – Hawking Radiation - Eddie W. Shore - 01-05-2018 03:32 AM RE: HP Prime: Black Hole Characteristics – Hawking Radiation - salvomic - 01-05-2018, 09:05 AM RE: HP Prime: Black Hole Characteristics – Hawking Radiation - KeithB - 03-12-2024, 02:42 PM RE: HP Prime: Black Hole Characteristics – Hawking Radiation - hfw - 01-20-2018, 12:23 PM RE: HP Prime: Black Hole Characteristics – Hawking Radiation - Eddie W. Shore - 01-23-2018, 03:01 PM RE: HP Prime: Black Hole Characteristics – Hawking Radiation - morvaoutig - 03-12-2024, 10:55 AM RE: HP Prime: Black Hole Characteristics – Hawking Radiation - rprosperi - 03-12-2024, 12:08 PM RE: HP Prime: Black Hole Characteristics – Hawking Radiation - morvaoutig - 03-12-2024, 12:50 PM RE: HP Prime: Black Hole Characteristics – Hawking Radiation - carey - 03-12-2024, 03:22 PM
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# [R] A vectorization question
Christos Hatzis christos at nuverabio.com
Tue Jan 9 23:24:12 CET 2007
```That's true. Just need to negate the difference. Actually, straight diff
can be used after reversing the vector:
apply(mat, 1, function(x) diff(sort(x, decreasing = TRUE)[2:1]))
I only have 3 columns in my matrix so sorting should not add much overhead,
but I will time both versions.
Thanks again.
-Christos
-----Original Message-----
From: Marc Schwartz [mailto:marc_schwartz at comcast.net]
Sent: Tuesday, January 09, 2007 5:07 PM
To: christos at nuverabio.com
Cc: 'R-help'
Subject: RE: [R] A vectorization question
Welcome Christos.
Note that my first example can actually be simplified to:
apply(mat, 1, function(x) -diff(sort(x, decreasing = TRUE)[1:2]))
Since we really just need to negate the difference, rather than take the
abs().
The advantage of this approach is that the two max values will always be the
first and second values, so will be independent of the length of 'x' (number
of columns in the matrix).
Using the second example more generally, you would have to use something
like:
apply(mat, 1, function(x) diff(sort(x)[-c(1:(length(x) - 2))]))
in the subsetting of the sort() results or precalcuate the indices (ie.
ncol(mat) and ncol(mat) - 1).
Might add a bit more overhead, but testing would give you more empiric
timing data. That might have to be balanced by whether the rows tend to be
random in order or closer to being sorted in increasing/decreasing order,
which would affect the sort time. Worst case scenario is generally having to
reverse the sort order. Of course, if the matrices are "relatively" small,
sorting time would likely be a non-issue.
HTH,
Marc
On Tue, 2007-01-09 at 16:39 -0500, Christos Hatzis wrote:
> Thanks, Marc.
> This is what I was trying to do but could not get it to work.
>
> -Christos
<snip>
```
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# Questions tagged [recreational-mathematics]
Puzzles, curiosities, brain teasers and other mathematics done "just for fun".
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### Something that I found, and would like to see if it's known.
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# SC
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Could some one please explain the correct answers!! Explanation is what I need!!
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VP
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13 May 2007, 18:42
LM wrote:
Could some one please explain the correct answers!! Explanation is what I need!!
B.
"concern" is the obstacle.Hence "concern' is required.
->A,C,E are out
Since the original sentence contains "that" comma is not required after passage.
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Could you please explain all the SC questions>?
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# Excel modulo value for index/match
I’m using MATCH within the INDEX fn to come up the column number…within MATCH I’m using a modulo calculation.
I have a two dimensional table with a decade of factors so that once they hit the 11th duration it goes to the next line to pick up the next decade.
I can figure out the “row” part of it easy enough. For the column part I’m using this…
IF(MOD(\$G3,10)=0,10,MOD(\$G3,10))
…where G3 is the duration.
Assume the table is what it is and there’s no changing it now.
I’m just wondering if there is a more elegant/clever way to find that column number?
This method works & it’s not a production-level work product…more scratch paper than anything…I’m just curious if there’s a better mouse trap out there.
If I am understanding correctly, think I have faced this before and did 1+mod(x-1,10). Still not elegant, but felt better than the “if” way.
3 Likes
Actually I think that is elegant, other than being able to change quadIO to 1.
1 Like
What are you some kind of high fallutin’ abstract calculus professor?
Around here we use right()+0.
Another solution, if you have cells to spare, is column = g3-row*10.
1 Like
If I’m understanding the problem correctly, wouldn’t the following do the trick?
= MOD(\$G3 - 1, 10) + 1
Edited to add: I see procrastinator has given lie to their name and beaten me to it. Yes, this is what I do too.
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# Does light speed apply to all waves traveling in vacuum?
by Crazy Tosser
Tags: apply, light, speed, traveling, vacuum, waves
P: 175 Seriosly, waves have different frequencies, and light is somewhere in the middle of the EM spectrum, then maybe the right or left side could travel faster than c
P: 277 Light is generally the term used to refer to electromagnetc waves in the visual spectrum (but its really the same as other E&M waves, just at different energies). They all behave generally the same, i.e. all E&M waves travel at the speed of light.
P: 87 All massless waves (and all massless particles) travel at the speed of light.
PF Patron
P: 8,963
## Does light speed apply to all waves traveling in vacuum?
That includes gravity, by the way.
I think that in one regard, you can say that not all waves travel at c in vacuum, but I'm not sure if my reasoning applies. It seems to me that the matter waves associated with a particle can't do so, since the particle itself can't.
P: 816
CT, all EM waves travel at the same speed in a vacuum. As far as I am aware this is not the case when dealing with a medium in which the waves are travelling slower.
Quote by Phlogistonian All massless waves (and all massless particles) travel at the speed of light.
If by speed of light you mean around $3\times10^8$ then I can't see how that is correct.
P: 249
Quote by Crazy Tosser Seriosly, waves have different frequencies, and light is somewhere in the middle of the EM spectrum, then maybe the right or left side could travel faster than c
The phase velocity of a wave is a product of the frequency and wavelength:
L*f=v
The electromagnetic wave equation has solutions with different frequences, but the wavelength must be inversely proportional to the frequency, so the product is always the same:
L*f=c
P: 422
Quote by Danger That includes gravity, by the way. I think that in one regard, you can say that not all waves travel at c in vacuum, but I'm not sure if my reasoning applies. It seems to me that the matter waves associated with a particle can't do so, since the particle itself can't.
Has it been experimentally proven that gravity waves travel at the speed of light.
P: 87
Quote by _Mayday_ If by speed of light you mean around $3\times10^8$ then I can't see how that is correct.
The original question was about waves in a vacuum.
P: 816
Quote by Phlogistonian The original question was about waves in a vacuum.
That doesn't make what you said correct.
P: 87
Quote by _Mayday_ That doesn't make what you said correct.
You can think what you want. I won't engage in a pointless argument over semantics.
P: 175 Well, how about traveling slower than the speed of light? If you are in a car that's goin at 100mph and you light a flashlight backwards, does the light travel at c-(100mph)?
Mentor
P: 27,563
Quote by Crazy Tosser Well, how about traveling slower than the speed of light? If you are in a car that's goin at 100mph and you light a flashlight backwards, does the light travel at c-(100mph)?
http://hyperphysics.phy-astr.gsu.edu...iv/einvel.html
The speed of light is constant in all inertial frames, no matter the speed of the source.
Zz.
P: 2,237
Quote by bassplayer142 Has it been experimentally proven that gravity waves travel at the speed of light.
only to within 20%, IIRC.
P: 286
Quote by Crazy Tosser Well, how about traveling slower than the speed of light? If you are in a car that's goin at 100mph and you light a flashlight backwards, does the light travel at c-(100mph)?
Excellent question, CT, and the answer is very important (ZapperZ already mentioned it). Make sure to keep reading every text you can get your hands on, because we've all asked this question at one time or another; if you can accept the true answer it will blow your mind.
Related Discussions Special & General Relativity 43 General Physics 9 Astrophysics 5 Special & General Relativity 2 General Physics 12
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3 Phase Energy Meter Connection Diagram With Ct
Here you can discover details about the 3 Phase Energy Meter Connection Diagram With Ct, pointers, and frequently asked questions. We have actually made this page for people browsing for a 3 Phase Energy Meter Connection Diagram With Ct.
A wiring diagram will reveal you where the wires should be attached, so you do not have to presume.
You don’t have to presume, a wiring diagram will show you just how to link the cables.
Contents
3 Phase Energy Meter Connection Diagram With Ct
See the 3 Phase Energy Meter Connection Diagram With Ct images below
Tips and techniques for reading wiring diagrams
• Put a blank sheet of paper next to the wiring diagram and just draw the simple circuit. All complex wiring diagrams are simply a series of simple diagrams, and it makes it hard to look at if you do not narrow down to the circuit that you’re doing.
• Print the wiring diagram off and use highlighters to trace the circuit. When you utilize your finger or follow the circuit with your eyes, it’s simple to mistrace the circuit. One trick that I utilize is to print the same wiring diagram off twice.
• To effectively check out a wiring diagram, one has to understand how the elements in the system operate. Following diagrams is fairly simple, however using it within the scope of how the system runs is a various matter.
• Read wiring diagrams from negative to positive and redraw the circuit as a straight line. All circuits are the same– voltage, ground, single component, and switches.
• Before reading a schematic, get familiar and comprehend all the signs. Check out the schematic like a roadmap. I print the schematic and highlight the circuit I’m diagnosing to make certain I’m staying on the right path.
3 Phase 4 Wire Energy Meter Connection Diagram With Ct
FAQ
Where is a wiring diagram used?
Wiring diagrams are generally used when attempting to show the connection system in a circuit. It is majorly used by building organizers, architects, and electrical experts to provide the wiring connections in a structure, a room, or even a simple gadget.
Why is wiring diagram crucial?
It reveals the elements of the circuit as simplified shapes, and how to make the connections in between the devices. A wiring diagram usually provides more info about the relative position and plan of devices and terminals on the devices.
What should a schematic consist of?
Schematics ought to consist of the total description and places of all developing code aspects, such as the heating/ventilation/air conditioning (also referred to as HVAC), plumbing, and electrical systems. Schematic styles are just a standard design to communicate a design plan to the owner.
Is AWG aluminum or copper?
Common household copper wiring is AWG number 12 or 14. The greater the gauge number, the smaller the size and the thinner the wire.
Can you touch a live black wire?
If you are available in contact with a stimulated black wire– and you are also in contact with the neutral white wire– current will travel through your body. You will receive an electrical shock. You will receive a shock if you touch 2 wires at various voltages at the same time.
42 Single Phase Meter Connection – Wiring Diagram Harness Info
Wiring Diagram Kwh Meter 1 Fasa – Wiring Diagram Schemas
Connection 3 Phase Ct Meter Wiring Diagrams – KODAKDIGITALCAMERAKIT
How to connect CT and PT in Energy meter || CT & PT connection
Wiring diagram types
• Schematic Diagrams.
• Wiring diagrams.
• Block diagrams.
• Pictorial diagrams.
What is an architectural wiring diagram?
Architectural wiring diagrams show the approximate areas and affiliations of receptacles, lighting, and permanent electrical services in a structure.
How are wiring diagrams read?
The electrical schematics read from left to right, or from top to bottom. This is necessary to get right, as the signal direction indicates the flow of current in the circuit. It is then simple for a user to understand when there is a modification in the course of the circuit.
How do you read electrical wire numbers?
An electrical cable is categorized by two numbers separated by a hyphen, such as 14-2. The first number represents the conductor’s gauge; the second represents the number of conductors inside the cable. 14-2 has two 14-gauge conductors: a hot and a neutral.
How do you read wire size charts?
Wire gauges range from low numbers to high numbers, with smaller numbers referring to smaller sizes and larger numbers representing larger diameters. AWG 4 is 0.2043 inches in size, and AWG 40 is. 0031 inches in diameter.
How is wire numbered?
American Wire Gauge (AWG) is the standard way to denote wire size in The United States and Canada. In AWG, the larger the number, the smaller the wire diameter and density. The largest basic size is 0000 AWG, and 40 AWG is the smallest standard size.
Why do we require wiring diagrams?
A wiring diagram is often utilized to repair issues and to make certain that all the connections have been made which everything is present.
Are all wiring diagrams similar?
Wiring diagrams may follow different standards depending on the country they are going to be used. They may have different designs depending upon the company and the designer who is creating that. They also may be drawn by various ECAD software application such as EPLAN or AutoCAD electrical.
What is the schematic format?
A schematic, or schematic diagram, is a representation of the elements of a system utilizing abstract, graphic symbols rather than realistic images.
What is the distinction in between a schematic and wiring diagram?
The schematic diagram does not show the practical connection between the components or their position. It contains only symbols and lines. A wiring diagram is a generalized pictorial representation of an electrical circuit. The parts are represented utilizing simplified shapes in wiring diagrams.
How do you read auto wiring diagrams?
An automobile wiring diagram is a map. To read it, determine the circuit in question and beginning at its power source, follow it to the ground. Use the legend to understand what each symbol on the circuit means.
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# FOURTH QUARTER WORKSHEET 4 - COLLEGE ALGEBRA
## 20 questions
See Preview
• 1. Multiple Choice
5 minutes
1 pt
Given: $\frac{5\sqrt{8}}{\sqrt{18}}$
The first step in simplifying could be:
$\frac{5\sqrt{8}}{\sqrt{18}}$ x $\frac{\sqrt{8}}{\sqrt{8}}$
$\frac{5\sqrt{4\ \ .\ \ 2}}{\sqrt{9\ \ .\ \ 2}}$
$\frac{10\sqrt{2}}{\sqrt{18}}$ x $\frac{\sqrt{2}}{\sqrt{2}}$
$\frac{5\sqrt{4\ \ .\ \ 2}}{\sqrt{6\ \ .\ \ 3}}$
• 2. Multiple Choice
30 seconds
1 pt
Rationalize the denominator:
$\frac{7\sqrt{3}}{\sqrt{10}}$
$\frac{70\sqrt{3}}{10}$
$\frac{7\sqrt{3}}{100}$
$\frac{7\sqrt{30}}{10}$
$7\sqrt{3}$
• 3. Multiple Choice
2 minutes
1 pt
$\ Simplify:\ \ \ 6\sqrt{2}\cdot5\sqrt{14}$
$32\sqrt{7}$
$60\sqrt{7}$
$2\sqrt{7}$
$30\sqrt{7}$
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# Main Categories
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# Seismology: Seismogrphic: Seismic Data: Finding Earth's Layers with Seismic Data
Product Description
This product includes 4 days of cut and glue mini assignments and answer keys plus a vocabulary worksheet lesson on the variations of the prefix seis-. Students are ask to glue the diagrams into their journals and then use refraction and reflection points to identify the layers in the diagrams. There are two planet-like diagrams and two small depth graphs.
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typodupeerror
## Four-Dimensional Rubik's Cube Craziness296
roice writes "Rubik's junkies and puzzlers will be interested in this software rendered four-dimensional analog of Rubik's Cube. With over 1.75E120 possible combinations, it's a mind bender. Free versions are available for both Windows and Linux, and they even publish their source code for download. Solving it will get your name listed in their Hall Of Fame, and there is also a running competition for the most efficient solution. To help get you started, you can check out a solution algorithm based on techniques used to solve the popular three-dimensional version."
This discussion has been archived. No new comments can be posted.
## Four-Dimensional Rubik's Cube Craziness
Comments Filter:
• #### Great. (Score:5, Funny)
on Monday June 09, 2003 @01:03AM (#6147619) Homepage Journal
Heck with solving it. There are some things that just aren't worth solving. Now where can I find a software rendered four dimensional analog of a hammer and nail?
• #### nooo (Score:5, Funny)
on Monday June 09, 2003 @01:03AM (#6147622) Journal
it took me long enough to finish the real thing.
• #### Re:Great. (Score:5, Funny)
on Monday June 09, 2003 @01:05AM (#6147630)
instead of greasing it to make it go faster, you ad space-time fabric softener.
• #### Not interested... (Score:4, Funny)
<(ur.tahc) (ta) (doowesor)> on Monday June 09, 2003 @01:06AM (#6147633) Homepage Journal
I can't even figure out the regular one. Hell, I am lucky I can tie my shoelaces in the morning!
• #### Technique number one (Score:5, Funny)
on Monday June 09, 2003 @01:06AM (#6147634) Homepage Journal
Apply a screwdriver to it; reassemble in the proper order.
Um, though that may be a little hard with the program, I'll admit.
Maybe if I apply the screwdriver to the ~~++5#Q%NO CARRIER
• #### Re:nooo (Score:5, Funny)
<jessica AT supjessica DOT com> on Monday June 09, 2003 @01:06AM (#6147636)
Haha, it only took me a minute to solve the 3D version!
I'm sure this 4D version will be just as easy...
Although I'm not sure how I'll peel off the colored stickers and rearrange them with this software version.
Hmmm
• #### thats an easy one (Score:5, Funny)
on Monday June 09, 2003 @01:07AM (#6147639)
and there is also a running competition for the most efficient solution.
duh...just peel off the stickers.
• #### Umm (Score:2, Funny)
by Anonymous Coward on Monday June 09, 2003 @01:08AM (#6147643)
Can someone plz send me a link to a trainer for this. Thx. also no-cd version much appericated.
• #### *Four* dimensional Rubiks Cube? (Score:5, Funny)
on Monday June 09, 2003 @01:09AM (#6147652) Homepage Journal
What, you have to step into the future to solve it? :-D
• #### Re:thats an easy one (Score:3, Funny)
on Monday June 09, 2003 @01:09AM (#6147655) Homepage Journal
Wouldn't that be a violation of the DMCA ?
• #### Be pepared... (Score:5, Funny)
on Monday June 09, 2003 @01:13AM (#6147678) Homepage
Just a word of warning to the foolish and brave. Before you tackle the 4^4 hypercube, make sure you buy an ergonomic mouse and mousepad. My guess is you'll probably develop super-carpal tunnel syndrome before you even you match one side of the damn cube. Also be sure to stockpile a few extra mouses, there's no knowing how many of them you'll be throwing against the wall.
• #### When I was a kid (Score:5, Funny)
by Anonymous Coward on Monday June 09, 2003 @01:17AM (#6147701)
I memorized the solutions to the Rubik's Cube so everyone would think I was smart! Haha, fooled them!
Now I just get drunk and masturbate a lot.
• #### Re:Lego Solution (Score:5, Funny)
by Anonymous Coward on Monday June 09, 2003 @01:24AM (#6147726)
Ahhhhhhhh!
It's LEGO, not LEGO's, not Lego's, not lego's, not lEGO's, not leGO's, not legO's, not lego'S, not LeGo's, not lEgO'S.
It's not LEGOS, legos, LEGOS'.. ITS LEGO
"I have one LEGO, I have two LEGO, I have many LEGO. I enjoy playing with LEGO"
1 LEGO = LEGO
2 LEGO = STILL LEGO
No farking S!!
Ok I feel better now. :)
• #### Re:Not interested... (Score:5, Funny)
on Monday June 09, 2003 @01:36AM (#6147770)
You sound like you could borrow my Rubik's Square. It only took me about half an hour to solve, once I realized that all the squares are the same color.
• #### Re:*Four* dimensional Rubiks Cube? (Score:2, Funny)
by Anonymous Coward on Monday June 09, 2003 @01:44AM (#6147800)
Most slashdot readers don't know about in and out...
• #### Most efficient solution (Score:5, Funny)
<.moc.amrakduab. .ta. .todhsals.> on Monday June 09, 2003 @01:50AM (#6147820) Journal
1) Click OPTIONS
2) Click SOLVE
Two clicks... anyone do better?
• #### No it won't (Score:2, Funny)
on Monday June 09, 2003 @01:58AM (#6147853) Homepage
Um, though that may be a little hard with the program, I'll admit.
No it won't, we just have to wait for someone to come up with a software implimented 4 dimensional hammer...there's probably already one written for emacs...
• #### Re:damn it.... (Score:5, Funny)
on Monday June 09, 2003 @02:01AM (#6147860)
Maybe somebody subjected you to one of my favorite old tricks. Take one corner off of a solved cube and rotate it so that the colors don't match the rest of the cube. Reassemble in this orientation. Presto: unsolveable cube.
Kinda funny -- I've inadvertently subjected myself to this same trick as a child. It always took so long to scramble the thing, it was easier to take it apart and put it back together in random order. Little did I realize there was a very good chance of creating an unsolvable cube.
Furthermore, I went so far as to buy a "how to solve the rubik's cube" book. Followed every goddamn step in that thing, and was pissed when it wasn't working. Eventually I tried it on my sibling's and it worked, and I came to the conclusion that mine was defective. Not sure how long it took me to figure out how mine became defective, but the blame was fully mine. :)
Gotta say, trying to solve an unsolveable puzzle sure kept me busy. It may have gotten my frustration tolerance up high enough that I can stand to debug those really nasty programs....
• #### Re:Most efficient solution (Score:5, Funny)
on Monday June 09, 2003 @02:10AM (#6147886)
1) Click OPTIONS
2) Click SOLVE
Two clicks... anyone do better?
Umm..
3) PROFIT?
• #### Re:Technique number one (Score:5, Funny)
on Monday June 09, 2003 @02:13AM (#6147895) Homepage Journal
That's a violation of your End-User License Agreement and the DMCA.
Please lie face down on the ground, with your legs and arms apart. BSA agents will be arriving shortly to take you into custody.
Schwab
• #### Re:Technique number one (Score:3, Funny)
on Monday June 09, 2003 @02:34AM (#6147939)
Here's a solving technique that works everytime: Simply twist and turn the cube until all sides match up. No additional tools required or embarassing adhesive related situations to deal with...
• #### Re:damn it.... (Score:1, Funny)
by Anonymous Coward on Monday June 09, 2003 @03:27AM (#6148053)
Geez, now you tell me...
I thought I was a moron. Months of trying to solve it, then giving up and buying the book, then spending months trying to understand the book.... never success...
I could have saved a year of my childhood!
All because i was too lazy to just scramble it properly!
Or, maybe I am just a moron.
• #### Re:nooo (Score:2, Funny)
on Monday June 09, 2003 @03:32AM (#6148058) Homepage
Right. So you get a blank cube and a set of stickers...
Why are the Do-it-yourself instructions needed?
Hmm, who are these people who open the box and say "What no directions?! How will I tell which yellow sticker goes where?"
• #### Re:Not interested... (Score:3, Funny)
on Monday June 09, 2003 @04:07AM (#6148120) Homepage
There's your problem...a Rubik's cube isn't to be used to tie your shoes. Pshhh some people.
• #### SOLVE it? (Score:1, Funny)
by Anonymous Coward on Monday June 09, 2003 @04:32AM (#6148165)
Stuff that, I'm having trouble enough reading the
black text upon the black background.
• #### Ok, where's the 5D and 6D? (Score:2, Funny)
on Monday June 09, 2003 @04:36AM (#6148176) Homepage
Heck, It was just too easy.. solved it in less than a minute.
But I won't submit my entry into the hall of fame, otherwise the FBI will come looking for this "human computer" that can perform 10^30 trops, and exceeds export regulations :P
• #### Re:damn it.... (Score:3, Funny)
on Monday June 09, 2003 @05:54AM (#6148388) Homepage
Maybe somebody subjected you to one of my favorite old tricks. Take one corner off of a solved cube and rotate it so that the colors don't match the rest of the cube. Reassemble in this orientation. Presto: unsolveable cube.
Way back in the mists of time I tried that on my school's Rubik's wizard. I took three pieces and rotated them. Gave it to the wizard and waited. Five minutes later he returned the almost complete cube, pointing out the _one_ piece he was unable to get right as it had been rotated.
• #### 1-D Rubik's Cube! (Score:5, Funny)
on Monday June 09, 2003 @06:29AM (#6148467) Journal
I found this great 1-D Rubik's Cube, here, I can embed it here on this page:
.
The interface is simple: just look at it. Quantum mechnaics dictates that observing it changes it's state so just assume it's solved.
Here is a magnified version:
.
If you still have trouble with it, my book will be coming out pretty soon.
• #### Re:Lego Solution (Score:2, Funny)
on Monday June 09, 2003 @05:26PM (#6155020)
> It's not LEGOS, legos, LEGOS'.. ITS LEGO
It's not "ITS", it's "IT'S".
#### Related LinksTop of the: day, week, month.
"Never face facts; if you do, you'll never get up in the morning." -- Marlo Thomas
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# Pie Charts and Ratios Task Cards
Subject
Grade Levels
Resource Type
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Also included in:
1. Included in this bundle are a collection of 8 sets of task cards. Files included in this bundle: ⭐ Finding the Percent of a Number Task Cards ⭐ Unit Rates Task Cards ⭐ Scale Drawings Task Cards ⭐ Ratios and Equivalent Ratios Task Cards ⭐ Proportions Task Cards ⭐ Pie Charts and Ratios Task Card
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Product Description
Pie Charts and Ratios
Task Cards
Included in this resource are 24 cards, a blank card set (if you want to add your own math problems), a recording sheet for students, and an answer key. I also solved the problems by hand using cross product and included that answer key. Additionally, I included an answer key with only the answers if you prefer to teach a different method of problem solving.
These cards can be used as task cards, independent practice, math centers or for a game of scoot.
Topics covered:
Find the missing quantity that corresponds with a percent on a pie chart when given the total number of participants, votes, etc. of the pie chart.
When given the number of votes, participants, etc. find the corresponding percent on a pie chart.
When given a set of data, figure out what percent of the data would take up on a pie chart.
When given a set of data, figure out which piece of data matches with a certain percent on the pie chart.
You might like these resources, too!
Proportions Task Cards
Ratios and Equivalent Ratios Task Cards
Unit Rates Task Cards
Scale Drawings Task Cards
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Average direction between two vectors
this is my first time asking a question so I'm sorry in advance for any mistake I might make.
So I have 3 points in 3D space: A, B and C. What I want to do is have an object on point B point towards a specific direction.
Here's a quick drawing of what I mean.
So fistly I have a vector that goes from point B to point A. Then the same but from B to C. And finally I want to find a direction that is kind of the "average" between those two vectors (not sure if this is the right term). But not the blue line, the RED line is basically what I want. I need to get the vector that corresponds to that direction (magnitude is not important).
Should I find the vector of the line that is painted blue and then find it's perpendicular vector? Is there an easier way to find the red vector? Is this even possible?
I'm not sure if this is a silly question or not but I hope someone can help me with it! Thanks a lot.
You can compute the average of the vectors, but if you only want the direction, you can use the sum $$\vec{AB} + \vec{BC} = \vec{AC}$$, that has the same direction and the double of the magnitude.
Since $$\vec{AB}=(B_x-A_x; B_y-A_y; B_z-A_z)$$, where $$A_x$$ is the $$x$$ coordinate of point $$A$$, etc.
And $$\vec{BC}=(C_x-B_x; C_y-B_y; C_z-B_z)$$, then, after simplification:
$$\vec{AB} + \vec{BC} = (C_x-A_x; C_y-A_y; C_z-A_z) = \vec{AC}$$.
Note that the red (straight) line has, as characteristics, passing through point $$B$$ and being parallel to the straight line that passes through $$A$$ and $$C$$.
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# Third Grade Guided Math Division
Common Core Standards
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Product Description
Guided Math Activities – Guided Math Division Third Grade
Unit 5 Division
Guided Math is the PERFECT way to hit all of the Common Core Standards while challenging each and every learner in the appropriate way! If you are looking for an ENGAGING, DIFFERENTIATED, and MEANINGFUL guided math unit then this resource is for you!
The variety of activities included in this unit will ensure student success and take your students to the next level!
Reach and teach EVERY student in your class with our:
*Differentiated Instruction Ideas and Suggestions for TWO WEEKS of instruction
*Pre-Assessment with suggestions for grouping your students
*8 Interactive Notebook Templates and Lesson Suggestions
Included in this unit- What is Division, Number Lines and Arrays, Unknown Numbers in Division Sentences, Solving Division Word Problems, Identity & Zero Property, Fact Pockets for all division facts 1-10
*2 Teacher Led Small Group activities with differentiated options
Array City-Make an array on a building and join buildings together to make a city
Tic Tac Divide-Tic Tac Toe with division sentences
*2 Differentiated Games for Independent Practice
Divide and Climb-Divide and move around a gameboard faster than your partner!
Spin and Color-Spin a division sentence and cover your space on a gameboard
*2 Sets of Task Cards for Independent Practice with Differentiated options for each set
Array -Identify the correct array for a given picture
*Mid Unit Quiz and Post-Assessment
*Division Fact Quizzes
*Division Charts
TWO WEEKS and 132 pages of low-prep, differentiated instruction!
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Identifying the winding number of $C$ around points in the regions shown
I am trying to understand the concept of the winding number of a curve.
As the title suggests, I would like to figure out the winding number of C around points in the regions 1, 2, 3 and 4 (It will be the best if I can do this simply by inspection with no computations).
I denote the first loop curve $C_{1}$ then $C_{2}$ and $C_{3}$ respectively. By definition, the winding number of the curve, $C$ around $a$ is defined by: $$n(C,a)=\frac{1}{2\pi i}\int_{C} \frac{1}{z-a}dz.$$ However, I did not find the formula useful. Rather, based on https://en.wikipedia.org/wiki/Winding_number, my findings are presented below.
Region 1: $n(C,a)=-1$.
Reason: Suppose a point, $z$ is in region 1 (being enclosed by loop 1). Since the curve is clockwise, by visual inspection, we have $n(C,a)=-1$.
Region 3: $n(C,a)=-1$.
Reason: Same explanation as above.
Region 2: $n(C,a)=1$.
Reason: This time, the loop is anti-clockwise.
Region 4: This is slightly tricky and I am unsure.
Can someone help me to verify if my winding number for regions 1, 2 and 3 are correct and is my way of determining winding number correct?
You are right about regions $1$, $2$, and $3$.
About region $4$: from each $p$ in that region you can draw a ray starting at $p$ and going to $\infty$ which doesn't even touch the line. Therefore, yes, the answer is $0$.
• Hi @José Carlos Santos, thank you for the verification. May I Kindly clarify what is the line you are referring to when we draw a ray at any $p$ in region 4 going to $\infty$? – Cleytus Mar 26 '18 at 14:54
• @Cleytus For me, the geometric (sort of) way of determining the winding number of $C$ with respect to $p$ is this: I consider a ray starting at $p$. For each point of intersection with $C$ I see if $C$ makes the ray turn around $p$ in a counter-clockwise or in a clockwise way and I count $+1$ in the first case and $-1$ in the second case (and $0$ if I was silly enough to pick a ray tangent to $C$). Then I add all these numbers and the sum is the winding number (it depends only on $p$, not on the direction of the ray). – José Carlos Santos Mar 26 '18 at 15:00
• Thank you Sir, have a great day! – Cleytus Mar 26 '18 at 15:03
Here's a thought experiment for you to carry out, or you can actually carry it out physically if you are so inclined.
Make a long, flexible loop of beads which cycles among three colors $RBGRBGRBG\ldots$ where $R$ is red, $B$ is blue, $G$ is green. The purpose of the color cycling is so that you can tell the orientation anywhere on the loop: the positive direction is as written above, and the negative direction is $GBRGBRGBR\ldots$.
Lay the loop down on a table top as your picture indicates, so that the positive orientation on the loop points in the same direction as the arrows on your picture.
To figure out the winding number around region 1 of the tabletop, first place the tip of one finger in region 1. Next, using the other hand, and keeping your fingertip pressed steadily on the table top, try to rearrange the loop of beads so that one of three outcomes occurs, and thereby define an integer $n \in \mathbb{Z}$, as follows:
• The loop stays on a circle of constant radius centered at your finger, going counterclockwise around that circle. The integer $n$ is positive, and it counts the number of counterclockwise rotations.
• The loop can be pulled away from your finger and bunched all up in a tiny pile far from your finger. The number $n$ is zero.
• The loop stays on a circle of constant radius centered at your finger, going clockwise around that circle. The integer $n$ is a negative integer, and its absolute value counts the number of clockwise rotations.
That integer $n$ is equal to $n(C,a)$ where $a$ is the point where your fingertip touches the top of the table.
This explanation exploits an important fact about winding number, namely that assuming $C$ misses $a$, the integer $n(C,a)$ is unchanged when $C$ is altered by a homotopy (that misses $a$).
• That is a very interesting experiment indeed! I will definitely try it out, say, during my upcoming summer break? Haha! Thank you and have a great day. – Cleytus Mar 26 '18 at 16:06
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Little star <3 <3 <3
/*
Melody
Plays a melody
circuit:
* 8-ohm speaker on digital pin 8
created 21 Jan 2010
modified 30 Aug 2011
by Tom Igoe
This example code is in the public domain.
http://arduino.cc/en/Tutorial/Tone
*/
#include “pitches.h”
// notes in the melody:
int melody[] = {
NOTE_C5,NOTE_C5,NOTE_G5,NOTE_G5,NOTE_A5,NOTE_A5,NOTE_G5,NOTE_F5,NOTE_F5,NOTE_E5,NOTE_E5,NOTE_D5,NOTE_D5,NOTE_C5,
NOTE_G5,NOTE_G5,NOTE_F5,NOTE_F5,NOTE_E5,NOTE_E5,NOTE_D5,
NOTE_G5,NOTE_G5,NOTE_F5,NOTE_F5,NOTE_E5,NOTE_E5,NOTE_D5,
NOTE_C5,NOTE_C5,NOTE_G5,NOTE_G5,NOTE_A5,NOTE_A5,NOTE_G5,NOTE_F5,NOTE_F5,NOTE_E5,NOTE_E5,NOTE_D5,NOTE_D5,NOTE_C5};
// note durations: 4 = quarter note, 8 = eighth note, etc.:
int noteDurations[] = {
4, 4, 4,4,4,4,2,4,4,4,4,4,4,2,4,4,4,4,4,4,2,4,4,4,4,4,4,2,4, 4, 4,4,4,4,2,4,4,4,4,4,4,4
};
void setup() {
// iterate over the notes of the melody:
for (int thisNote = 0; thisNote <44; thisNote++) {
// to calculate the note duration, take one second
// divided by the note type.
//e.g. quarter note = 1000 / 4, eighth note = 1000/8, etc.
int noteDuration = 1000/noteDurations[thisNote];
tone(11, melody[thisNote],noteDuration);
// to distinguish the notes, set a minimum time between them.
// the note’s duration + 30% seems to work well:
int pauseBetweenNotes = noteDuration * 1.30;
delay(pauseBetweenNotes);
// stop the tone playing:
noTone(11);
}
}
void loop() {
// no need to repeat the melody.
}
This entry was posted in Uncategorized on .
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# Why LED reversed bias voltage cannot be measured?
As I have just found out, typical LED does not behave similarly to standard diode when measuring reversed bias voltage. On typical diode, you can measure reverse bias voltage about .3 to .6V, but not on LED. I have read you can measure it using constant current source, but why? What is the physical principle behind this?
• Those sound like forward bias voltages to me... Commented Dec 5, 2014 at 11:22
LEDs behave electrically like other types of diodes, just with different parameters. They can be modeled reasonably well by the Shockley diode equation with a series resistor.
Regular diodes tend to have a reverse breakdown in the 50V-1000V range, LEDs it's on the lower end of that range. Usually we don't use LEDs reverse biased except to stand off a few volts in multiplexed circuits, so the specs tend to be very loose (maybe a 5V spec on an LED that can withstand 50V or 100V of reverse bias).
Regular diodes have a forward voltage of 0.6V or so at currents of mA, with LEDs it's more like 1V-3.5V (the lower values for IR LEDs, the higher for UV).
The ideality factor n tends to be around 2 for regular diodes, and it can be quite different for LEDs.
Sorry, but you're wrong.
The forward and reverse bias voltages and currents can be measured on an LED as easily as they can on any other diode, and all that's needed is a voltmeter, an ammeter and a voltage source.
In 2, the voltmeter is a balanced bridge which draws no current.
• Or perhaps "the voltmeter must be a balanced bridge so that no current is drawn"? Commented Dec 5, 2014 at 11:47
• Perhaps, but for the utmost in accuracy - and confusion- "In 2, 'V' is a potentiometer" works best Commented Dec 5, 2014 at 12:06
I assume you are having trouble measuring the forward voltage with your DMM Diode function. Some DMM's have enough compliance to measure LED's and some don't. So you could try another DMM. If not follow EM-fields idea and just use your power supply on the bench. Put some series resistance (maybe 1k ohm) before the LED to limit the current... and as Sphero said you will be measuring the forward voltage at only one current.
The reverse voltage of an LED is another story.. as Spehro said numbers in the 50 - 100 V range are common. (Again a series resistor will be needed so as to not damage the LED.) You can do some fun things with a reverse biased LED. (Link on request.)
• I am interested in that link about reverse biased LED applications :-) Commented Dec 7, 2014 at 3:09
• @LorenzoDonati, Well first I found that this only works (at low voltage.) with the GaP red LED's from here. purdyelectronics.com/pdf/LED-SFC.pdf AND113R or AND114R (the clear 113 is better.) Reverse bias to ~25V and it's a sinlge photon detector. (with kinda terrible efficiency.) See here, teachspin.com/newsletters/TeachSpin_MAY13FINALFOR%20WEB.pdf Commented Dec 7, 2014 at 16:26
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# What are the 5Cs of credit?
5 C's of Credit refer to the factors that lenders of money evaluate to determine credit worthiness of a borrower. They are the following:. 1. Borrower's CHARACTER. 2. Borrow (MORE)
# What does 5c stand for?
The Iphone 5C is Iphone 5Colorful 5c can also stand for thenumber 500 ("c" is the Roman numeral for 100) or for 5 degreesCelsius (centigrade) . +++ . "5c" can not stand fo (MORE)
# What animal is on a 5c coin?
There are multiple animals on 5 cent coins depending on the country and time period such as the Buffalo on the US "buffalo nickel", the Beaver on the Canadian nickel, etc.
# What is a 'Gordian Knot'?
The Gordian Knot of history was a complicated Turk's Head, tied with the bark of the Cornel Tree. Over time, the bark shrank and hardened, making it impossible to untie. Man (MORE)
# What is -5c plus 9 and how?
You can't tell a thing about -5c+9 until you know what 'c' is. And every time 'c' changes, -5c+9 changes.
In Volume
# What is 5c in milliliters?
5cc? cc means cubic centimetres which is equal to ml, so 5ml. if you mean cl, then that is equal to 50ml
# What is the answer for 5c equals -75?
The 'answer' is the number that 'c' must be, if 5c is really the same as -75. In order to find out what number that is, you could use 'algebra'. First, write the equatio (MORE)
# How many pixels does the iPhone 5c have?
The iPhone 5c is 640 x 1136 pixels. That is about 326 pixels persquare inch (ppi).
# What is minus 5c in Fahrenheit?
(-5) degrees Celsius = 23 degrees Fahrenheit. Formula: [°F] = [°C] à 9 â 5 + 32
# How many inches is a iPhone 5c?
The screen is 4" big. The height is 4.9", width is 2.33" and thedepth is 0.35"
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%%%Please try these commands. a=[1 2 3] a = 1 2 3 format compact % to suppress blank lines (format loose) % more on (more off) c=[4;5;6] c = 4 5 6 a*c % equivalent to inner product ans = 32 dot(a,c) % inner product ans = 32 A=c*a % outer product A = 4 8 12 5 10 15 6 12 18 b=a.^2 % . for elementwise b = 1 4 9 a.*b ans = 1 8 27 a = 1 2 3 exp(a) % function that acts on array ans = 2.7183 7.3891 20.0855 log(ans) ans = 1 2 3 sqrt(a) ans = 1.0000 1.4142 1.7321 format long sqrt(a) ans = 1.000000000000000 1.414213562373095 1.732050807568877 format short format % format short 2^(-24) ans = 5.9605e-008 A=reshape([1:9],3,3) A = 1 4 7 2 5 8 3 6 9 sqrt(A) ans = 1.0000 2.0000 2.6458 1.4142 2.2361 2.8284 1.7321 2.4495 3.0000 sqrtm(A) ans = 0.4498 + 0.7623i 1.0185 + 0.0842i 1.5873 - 0.5940i 0.5526 + 0.2068i 1.2515 + 0.0228i 1.9503 - 0.1611i 0.6555 - 0.3487i 1.4844 - 0.0385i 2.3134 + 0.2717i ans*ans ans = 1.0000 + 0.0000i 4.0000 + 0.0000i 7.0000 + 0.0000i 2.0000 + 0.0000i 5.0000 + 0.0000i 8.0000 - 0.0000i 3.0000 + 0.0000i 6.0000 - 0.0000i 9.0000 - 0.0000i sum(b), mean(c) ans = 14 ans = 5 y=pi % pi special variable y = 3.1416 y=tan(pi/6); B=[2 0 -1;2 5 7;-1 4 8] % form rows B = 2 0 -1 2 5 7 -1 4 8 x=B\c % solve equation x = 5.2727 -10.2727 6.5455 norm(B*x-c) % check residual ans = 7.1607e-015 B=[-3 0 1;2 5 -7;-1 4 8] B = -3 0 1 2 5 -7 -1 4 8 x=B\c x = -1.3717 1.3874 -0.1152 norm(B*x-c) ans = 0 eig(B) ans = -2.8601 6.4300 + 5.0434i 6.4300 - 5.0434i [V,D]=eig(B) V = 0.9823 -0.0400 - 0.0404i -0.0400 + 0.0404i -0.1275 0.7922 0.7922 0.1374 -0.1733 - 0.5823i -0.1733 + 0.5823i D = -2.8601 0 0 0 6.4300 + 5.0434i 0 0 0 6.4300 - 5.0434i w=2:3:10, y=1:-.25:0 w = 2 5 8 y = 1.0000 0.7500 0.5000 0.2500 0 C=[A,[8;9;10]],D=[B;a] % forming larger matrices from matrices C = 4 8 12 8 5 10 15 9 6 12 18 10 D = -3 0 1 2 5 -7 -1 4 8 1 2 3 C(2,3) ans = 15 C(2:3,1:2) ans = 5 10 6 12 I3=eye(3), Z=zeros(5,3), O=ones(2,1) I3 = 1 0 0 0 1 0 0 0 1 Z = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O = 1 1 lookfor elliptic ellipj - Jacobi elliptic functions. ellipke - Complete elliptic integral. pdepe - Solve initial-boundary value problems for parabolic-elliptic PDEs in 1-D. iirautoscaledemo - Fixed-Point Scaling of an Elliptic IIR Filter ellipk - Complete elliptic integral of first kind. ellip - Elliptic or Cauer digital and analog filter design. ellipdeg - Solves the degree equation in analog elliptic filter design. ellipap - Elliptic analog lowpass filter prototype. sne - sn elliptic function with normalized complex argument. ellipord - Elliptic filter order selection. asne - Inverse of sn elliptic function. acde - Inverse of cd elliptic function. cde - cd elliptic function with normalized complex argument. fdellip - Elliptic Module for filtdes. >> quit
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# 8.1 Exponent Multiplication
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### 8.1 Exponent Multiplication
1. 1. Algebra Warm Up: pg. 376 # 65 to 73
2. 2. 8.1 Laws Of Exponents: Multiplying Monomialspg. 370 -376 First you need to know the vocabulary: Base: The number or variable that is being raised to a power Exponent: The nunber or variable that is attached to the upper right corner of the base. --Tells how many times a number is used as a factor (# of times you need to multiply that number by itself)
3. 3. The first rule of Exponents: Product of powers: When you have like bases--you add the exponents:
4. 4. pg. 372 NOTE: what do the directions say? If they had said quot;Evaluatequot;, then what do you have to do?
5. 5. This concept can be used on more complicated problems! (recall your PEMDAS) A monomial is---an expression that is a constant, variable or a product of the 2. Essentially--to do these problems you need to : 1. Multiply the coefficients 2. Multiply the like bases(meaning you add the exponents) 3. Simplify OR because you are multiplying.... 1. Drop off the parentheses 2. Rearrange the coeffiecients together and the variables together 3. Then multiply (remember when multiplying like bases you are adding the exponents) 4. Simplify
6. 6. Sometimesyou will have to substitute things in a problem and then use the rules to simplify!
7. 7. try some..pg. 374 # 6-17 DO NOT do # 14
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Hangman: Guess the letters in a hidden word or phrase.
# cell
you have to get the matching cards of the following 20 cards; 4 rainbow cards, 4 rainy clouds, 4 smiles, 4 frowns, and 4 CELLS. You have to try to get as many points as possible. Rainbows=10 points, rainy clouds=5, smiles=10,frowns=5. The CELL cards (jail cell)= -20 points. If you only have 10 points you go int o a negative number which would be -10. You draw one card at a time and add up all of your points and whoever has the most points at the end of the game wins. But the game ends only when all of the cards are drawn.
kathleen
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# G.1 Number Systems
#### Binary, Octal, and Hexadecimal Number System
Table G.1 lists the integers from 0 to 16, showing their equivalents in the binary (base 2), octal (base 8), and hexadecimal (base 16) number systems. The shaded cells in each column show the digits in each number system.
##### Table G.1. Number Systems
Decimal (base 10)
Binary (base 2)
Octal (base 8)
0
0
0
0
1
1
1
1
2
10
2
2
3
11
3
3
4
100
4
4
5
101
5
5
6
110
6
6
7
111
7
7
8
1000
10
8
9
1001
11
9
10
1010
12
a
11
1011
13
b
12
1100
14
c
13
1101
15
d
14
1110
16
e
15
1111
17
f
16
10000
20
10
In addition to the decimal literals, Java also allows integer literals to be specified in octal and hexadecimal number systems, but not in the binary number system. Octal and hexadecimal numbers are specified with 0 and 0x prefix, respectively. The prefix 0X can also be used for hexadecimal numbers. Note that the leading 0 (zero) digit is not the uppercase letter O. The hexadecimal digits from a to f can also be specified with the corresponding uppercase forms (A to F). Negative integers (e.g., -90) can be specified by prefixing the minus sign (-) to the magnitude, regardless of number system (e.g., -0132 or -0X5A). The actual memory representation of the integer values is discussed in Section on page 598.
#### Converting Binary Numbers to Decimals
A binary number can be converted to its equivalent decimal value by computing the positional values of its digits. Each digit in the binary number contributes to the final decimal value by virtue of its position, starting with position 0 (units) for the right-most digit in the number. The positional value of each digit is given by
digit x base position
The number 1010012 corresponds to 4110 in the decimal number system:
1010012 = 1x25 + 0x24 + 1x23 + 0x22 + 0x21 + 1x20 = 32 + 0 + 8 + 0 + 0 + 1 = 4110
#### Converting Octal and Hexadecimal Numbers to Decimals
Similarly, octal (base 8) and hexadecimal (base 16) numbers can be converted to their decimal equivalents:
0132 = 1328 = 1x82 + 3x81 + 2x80 = 64 + 24 + 2 = 9010 Octal Decimal 0x5a = 5a16 = 5x162 + ax160 = 80 + 10 = 9010 Hex Decimal
The same technique can be used to convert a number from any base to its equivalent representation in the decimal number system.
List of Figures
List of Tables
List of Examples
Foreword
Preface
Chapter 1. Basics of Java Programming
Chapter 2. Language Fundamentals
Chapter 3. Operators and Assignments
Chapter 4. Declarations and Access Control
Chapter 5. Control Flow, Exception Handling, and Assertions
Chapter 6. Object-oriented Programming
Chapter 7. Nested Classes And Interfaces
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# Problem 55245. Calculating Student Grades
The matrix grades contains raw grades for 7 students who took your course. Each row represents a different student. The first 7 columns contain grades from 7 homework assignments, the next 3 columns contain grades from exams, and the last 5 columns contain grades from quizzes. If a student missed an assignment, their grade was recorded as 0.
The final grade for each student is calculated using the average of their raw scores weighted by how much each assignment type is worth. An example rubric would look something like:
r = [0.2 0.45 0.35]
which indicates that homework, exams, and quizzes are worth 20%, 45%, and 35% of each student's final grade, respectively.
Write a function that takes a rubric vector as an input and outputs the final grade for each student.
### Solution Stats
37.69% Correct | 62.31% Incorrect
Last Solution submitted on Sep 06, 2024
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https://cracku.in/57-what-is-the-value-of-3-times-1500-div-40-5-div-fra-x-ssc-gd-18th-feb-2019-shift-1
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Question 57
What is the value of $$(3 \times 1500 \div 40 + 5 \div \frac{2}{7} of 70)$$?
Solution
Expression : $$(3 \times 1500 \div 40 + 5 \div \frac{2}{7} of 70)$$
=Â $$(3 \times \frac{1500}{40}) + (5 \div 20)$$
= $$\frac{450}{4}+\frac{1}{4}=\frac{451}{4}$$
=> Ans - (C)
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https://www.jiskha.com/questions/1420513/i-was-given-the-following-problem-what-is-the-normality-of-a-solution-containing-6-grams
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# chemistry
I was given the following problem:
what is the normality of a solution containing 6 grams of H2SO4 in a 200ml solution? my teacher obtained a normality of 39normals while I took into account that I had two hydrogen free and obtained a result of 0.6 N, who's right?
1. 👍
2. 👎
3. 👁
1. .6 is correct ... due to H⁺ activity
1. 👍
2. 👎
2. Did you make a typo and you meant to type in that the teacher obtained 0.30 N?
Technically, you can't say. Both could be right but I disagree with Scott as to why that is so. You must know the equation involved. For example, if you titrate one(1) H then
mL x N x milliequivalent weight = grams.
200 x N x 0.098 = 6g and N = 0.31 which rounds to 0.3 N to 1 sig fig. and the equation is
NaOH + H2SO4 ==> NaHSO4 + H2O
BUT
if the equation is
2NaOH + H2SO4 ==> Na2SO4 + 2H2O then
200 x N x 0.049 = 6 and N = 0.61 which rounds to 0.6 to 1 s.f.
The equivalent weight of H2SO4 is 98 when 1 H is used but it is 98/2 = 40 when both H atoms are used.
1. 👍
2. 👎
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# Linear Equations Help : Videos | Worksheets | Word Problems
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Many students find linear equations difficult. At TuLyn, we have hundreds of free linear equations video tutorials, printable linear equations worksheets, and linear equations word problems to help you better understand linear equations and get better grades.
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https://www.encyclo.co.uk/meaning-of-BALANCE
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### balance
1. a state of equilibrium
2. a scale for weighing; depends on pull of gravity
3. an amount on the credit side of an account
4. harmonious arrangement or relation of parts or elements within a whole (as in a design)
5. equality of distribution
6. (mathematics) an attribute of a shape; exact correspondence of form on opposite sides of a dividing line or plane
...
### Balance
- Sum of DEBIT entries minus the SUM of CREDIT entries in an ACCOUNT. If positive, the difference is called a DEBIT BALANCE; if negative, a CREDIT BALANCE.
Found on http://www.nysscpa.org/prof_library/guide.htm
### Balance
(1) referring to type, an orderly and pleasing arrangements of physical characteristics so as to present a harmonious appearance.(2) referring to markings, an equal distribution of corresponding markings on marked breeds
Found on https://quitebunnyrabbitry.weebly.com/glossary.html#
### balance
(balĀ“әns) an instrument for weighing. equilibrium. postural control.
Found on http://www.encyclo.co.uk/local/21001
### balance
(ballroom) ability of the dancer to maintain an upright and controlled position of the body whether in movement or still.
Found on http://www.centralhome.com/dance-terms-b.htm
### balance
(from the article `sculpture`) The balance, or equilibrium, of freestanding sculpture has three aspects. First, the sculpture must have actual physical stability. This can be ... Rhythm and balance result from the three-dimensional arrangement of elements and materials on the site. Rhythm is a sequence or repetition of similar ... Ba...
Found on http://www.britannica.com/eb/a-z/b/10
### balance
(from the article `watch`) ...watch, or other spring-driven mechanism, is wound, the curvature of the spring is increased, and energy is thus stored. This energy is transmitted ...
Found on http://www.britannica.com/eb/a-z/b/10
### balance
[n] - a state of equilibrium 2. [n] - equality of distribution 3. [n] - an amount on the credit side of an account 4. [n] - a scale for weighing 5. [v] - be in equilibrium 6. [v] - bring into balance or equilibrium 7. [v] - compute credits and debits of an account
Found on http://www.webdictionary.co.uk/definition.php?query=balance
### Balance
• (v. i.) To move toward a person or couple, and then back. • (n.) An apparatus for weighing. • (n.) Equipoise between the weights in opposite scales. • (n.) A balance wheel, as of a watch, or clock. See Balance wheel (in the Vocabulary). • (n.) To make the sums of the debits and credits of an account equal; -- said of an i...
Found on http://thinkexist.com/dictionary/meaning/balance/
### balance
verb hold or carry in equilibrium
Found on http://wordnetweb.princeton.edu/perl/webwn?s=balance
### balance
noun a scale for weighing; depends on pull of gravity
Found on http://wordnetweb.princeton.edu/perl/webwn?s=balance
### Balance
[ability] In biomechanics, balance is an ability to maintain the line of gravity (vertical line from centre of mass) of a body within the base of support with minimal postural sway. Sway is the horizontal movement of the centre of gravity even when a person is standing still. A certain amount of sway is essential and inevitable due to small...
Found on http://en.wikipedia.org/wiki/Balance_(ability)
### Balance
[accounting] In banking and accountancy, the outstanding balance is the amount of money owed, (or due), that remains in a deposit account. ...
Found on http://en.wikipedia.org/wiki/Balance_(accounting)
### Balance
[advertisement] Balance was a 1989 television advertisement for the Lexus LS 400, which also introduced the luxury car make Lexus to television audiences. It was created by Team One, a unit of Saatchi & Saatchi. The ad was designed to promote the engineering attributes of the flagship Lexus sedan. The advertisement received several awards a...
### Balance
[game design] In game design, balance is the concept and the practice of tuning a game`s rules, usually with the goal of preventing any of its component systems from being ineffective or otherwise undesirable when compared to their peers. An unbalanced system represents wasted development resources at the very least, and at worst can underm...
Found on http://en.wikipedia.org/wiki/Balance_(game_design)
### Balance
[metaphysics] More recently, the term `balance` has come to refer to a balance of power between multiple opposing forces. Lack of balance (of power) is generally considered to cause aggression by stronger forces towards weaker forces less capable of defending themselves. In the real world, unbalanced stronger forces tend to portray themselv...
Found on http://en.wikipedia.org/wiki/Balance_(metaphysics)
### Balance
[networking] Balance is a simple but powerful generic TCP proxy with round robin load balancing and failover mechanisms. Its behaviour can be controlled at runtime using a simple command line syntax. Balance successfully runs at least on Linux(386), Linux(Itanium), FreeBSD, BSD/OS, Solaris, Cygwin, Mac-OS X, HP-UX and many more. Balance is ...
Found on http://en.wikipedia.org/wiki/Balance_(networking)
### balance
[Noun] An amount of money that remains or is left over; a steady state where forces are evenly spread.
Example: He spends too much and is always worried about his bank balance.
Found on http://www.bbc.co.uk/skillswise/glossary/
### Balance
[puzzle] A balance puzzle is a mathematical puzzle which challenges the solver to distribute a subset of numbers so that the several sides of a stylized diagram representing a balance scale are equal. The balance puzzle is a classical number puzzle in the World Puzzle Championship. It consists in a mobile or tree structure, with designated ...
Found on http://en.wikipedia.org/wiki/Balance_(puzzle)
### Balance
Bal'ance (băl' a ns) noun [ Middle English balaunce , French balance , from Latin bilanx , bilancis , having two scales; bis twice (akin to English two ) + lanx plate, scale.] 1. An apparatus for weighing. » In its simplest ...
Found on http://www.encyclo.co.uk/webster/B/7
### Balance
Bal'ance intransitive verb 1. To have equal weight on each side; to be in equipoise; as, the scales balance . 2. To fluctuate between motives which appear of equal force; to waver; to hesitate. « He would not balance or err in the determination of his choice. L...
Found on http://www.encyclo.co.uk/webster/B/7
### Balance
Bal'ance transitive verb [ imperfect & past participle Balanced ; present participle & verbal noun Balancing ] [ From Balance , noun : confer French balancer .] 1. To bring to an equipoise, ...
Found on http://www.encyclo.co.uk/webster/B/7
### balance
1. The way in which elements of a game are equalized relative to each player. Often balance is established by giving all players similar starting positions and maintained by using mechanisms to hurt the apparent leader or help the likely loser. 2. The state of a game where equally skilled players have a roughly equal chance of winning the gam...
Found on http://boardgamegeek.com/wiki/page/Glossary
### balance
1. The way in which elements of a game are equalized relative to each player. Often balance is established by giving all players similar starting positions and maintained by using mechanisms to hurt the apparent leader or help the likely loser. 2. The state of a game where equally skilled players have a roughly equal chance of winning the gam...
Found on http://www.boardgamegeek.com/wiki/page/Glossary
### balance
1. An apparatus for weighing. ... In its simplest form, a balance consists of a beam or lever supported exactly in the middle, having two scales or basins of equal weight suspended from its extremities. Another form is that of the Roman balance, our steelyard, consisting of a lever or beam, suspended near one of its extremities, on the longer arm o...
Found on http://www.encyclo.co.uk/local/20973
No exact match found
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https://www.fishbowlinventory.com/landed-cost-software?gclid=CI-64rzO47wCFRRo7Aod-EoAYQ
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# Calculating Landed Cost
How much does it cost to get products from your suppliers and into your warehouse? It is more than just the price you pay for the products themselves. The true cost of ordering products is called the Landed Cost, and this cost has much more to it than meets the eye. It includes a number of factors, including:
• Shipping Costs
• Crating, Packing, and Handling Costs
• Brokerage and Logistical Fees
• Taxes
• Insurance
• Employee Compensation
International shipments often include the following factors (in addition to the above items). These are a little more complicated, so we’ll explain them in detail:
• Customs Duties – This is a complicated topic, so buckle up. Duties are basically taxes that you pay on items that are coming into the country. In the United States, you will want to make sure that you brush up on the current law concerning duties that must be paid on imported goods. There are all kinds of regulations regarding what kinds of goods can be exempt from duties if they are purchased in a low enough quantity or if they are intended to be given as gifts. Illicit drugs and other contraband are definitely a no-no, but alcohol and tobacco products can usually be imported without too much trouble.
• Tariffs – A tariff specifies the actual amount of money that is owed on imported items that fall under the purview of customs duties. It is usually a percentage rate at which certain items (that are legally specified) are taxed.
• Harbor Fees – Did you know that no ship automatically has the right to dock in another country’s port? Each sovereign nation has the right to refuse incoming shipments if they so wish because it is their land. Incoming ships must pay for the privilege of finding port, and this payment is called a harbor fee.
• Currency Conversions – This is the rate at which one currency converts into another. Every currency is worth something in relation to every other currency. It could be more or less, meaning that, when converted into another currency, it will be worth a greater or smaller number of the new currency than it was in the other currency. These currency conversions are important to calculate because they will affect the perceived value of goods as they change hands and are sold in new markets.
Not every Landed Cost will necessarily include all of these expenses, but it is important to keep all of them in mind when calculating the true cost of the parts and products you order.
Rather than guessing about these important factors or calculating them by hand each time you place an order, wouldn’t it be nice to have all of that done for you accurately and automatically? Fishbowl calculates everything that goes into your Landed Costs, saving you a lot of time and making sure you know exactly how much you will be spending.
Plus, Fishbowl integrates directly with UPS, so you can compare shipping rates and set up a shipment directly from the Fishbowl interface without having to open a Web browser. Fishbowl is an ideal solution to handle your shipping needs.
## TL;DR SUMMARY
To calculate the landed cost of orders coming into the country from another country, you need to take into account the following fees and factors:
• Shipping costs
• Crating, packing, and handling costs
• Brokerage and logistical fees
• Taxes
• Insurance
• Employee compensation
• Customs duties
• Tariffs
• Harbor fees
• Currency versions
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Problem:Plats and Mapping: ALTA/ACSM Land Title Survey Plats
## Problem: Plats and Mapping: ALTA/ACSM Land Title Survey Plats
Which type of scale on a plat is most useful, and why?
(A) A representative fraction is most useful because it is dimensionless.
(B) A ratio scale, such as 1 in = 500 ft, is most useful since such a scale is universally understood.
(C) A bar scale is most useful since it remains valid despite enlargement or reduction of the plat.
(D) An architect’s scale, such as 1/8 in = 1 ft, is most useful since it allows the representation of the greatest detail.
This is problem 20(10-12) from the new second edition of 1001 Solved Surveying Problems by Jan Van Sickle. Reprinted with permission from 1001 Solved Surveying Problems by Jan Van Sickle (1997, 728 pp., Professional Publications Inc.). For details on this and other FLS exam-prep books, call 800/426-1178 or visit www.ppi2pass.com .
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http://www.zyra.org.uk/denslist.htm
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List of Density of Various Substances
Lists of Densities - lists of density of different stuff! and also a list of lists of density
The density of water is 1000Kg/m3 , and other substances are of different densities, some heavier and some lighter than water. To keep things easier, densities are often expressed as "specific gravity", which just means they are expressed as a ratio of the gravity of water. So, water, at 1000/m3 counts as 1 in specific gravity, and here are the densities (expressed as specific gravities) of some other substances:
For example:
Air 0.001225
Xenon Gas 0.006
Expanded Polystyrene Foam 0.015 - 0.1
Cork 0.2 - 0.3
Liquid Ammonia 0.682
Alcohol (Ethanol) 0.789 - also see booze
Oil 0.8
Liquid Nitrogen 0.808
Ice 0.92
Yes, ice is bigger than water
Water 1.000
Creosote 1.066
Glycerine 1.26
Coal 1.5
Magnesium 1.738
Beryllium 1.85
Concrete 2.4
Glass 2.6
Quartz 2.65
Aluminium 2.7
Basalt rock 3.0
Diamond 3.5
Magnetite 5.0 - 5.2
Zinc 7.1
Steel 7.85 (depending on the blend)
Iron 7.87
Copper 8.92
Silver 10.5
Mercury 13.6
Gold 19.3
Platinum 21.4
Osmium 22
etc.
To convert these to pure density measured in kilogrammes per cubic metre, multiply by 1000. So for example, gold is 19.3 times heavier than water (ie it has a specific gravity of 19.3), so it has a density of 19300Kg/m3
It would be good to have something approximating to a Complete List of Densities here, but I've found that so far there are plenty of other sites where they already do this better. So, here's a few such places listed...
www.wikipedia.org/wiki/Density
www.gkehe.8m.com/data.htm
www.iform.com.au/corp/wardrobe/tables.htm
www.vendian.org/envelope/TemporaryURL/mass_volumedensity.html
www.sciencebyjones.com/density_notes.htm
www.tesarta.com/www/resources/library/weights.html
www.simetric.co.uk/si_materials.htm
Density is Mass divided by Volume. It's usually measured in kilogrammes per cubic metre. To work out the density of something, divide mass (how much it weighs), by volume (how much space it takes up). How to Measure the Density of an Object. More about this at the page: What is Density?
If you prefer your density in the oldfashioned lb/ft3 (pounds per cubic foot), rather than in Kg/m3 (kilogrammes per cubic metre), divide the figures by 16 (or 16.018 to be more precise). So, for example mercury at 13,600 Kg/m3 works out at 13600/16 = 849lb/ft3
If you're wondering what the density of a helium balloon is, and expecting it to be negative, remember that the fact that helium balloons rise up in air is not because they have a negative weight or negative density, but because their effective lift is buoyancy because of the displacement of AIR. So in effect, balloons of light gas rise as if they had a density of minus that of air. Also see hydrogen versus helium
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https://www.teacherspayteachers.com/Product/Spider-Subtraction-4895114
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# Spider Subtraction
Subject
Grade Levels
Resource Type
File Type
PDF
(1 MB|44 pages)
Product Rating
4.0
(1 Rating)
Standards
• Product Description
• StandardsNEW
Spider Subtraction is a hands on math center to target Subtraction within 10 and within 20.
Spider Subtraction Prep:
• Print Spider Subtraction Mat
• Print Subtraction Cards (suggested: onto color cardstock to easily see.)
• Laminate Subtraction Cards
Spider Subtraction Prep/Directions:
• Flip Subtraction Card onto Spider Subtraction Mat.
• Build the Spider Subtraction Mat Number on Ten Frame(s).
• Subtract the Amount.
• Count ‘How Many’.
• Write ‘How Many’ in the Spider.
Download Includes:
1. Subtraction Cards within 10
2. Spider Subtraction Mat (10 Frame)
3. Subtraction Cards within 20
4. Spider Subtraction Mat (Double 10 Frame)
Log in to see state-specific standards (only available in the US).
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Apply properties of operations as strategies to add and subtract. If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
Total Pages
44 pages
Answer Key
N/A
Teaching Duration
N/A
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http://openstudy.com/updates/4ffc72fee4b00c7a70c53c8d
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## agentx5 3 years ago Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = t − t$$^{−1}$$, y = 6 + t$$^2$$, t = 1 The correct answer needs to be in the form of y=something... I have this (incorrect): $y=(\large\frac{2t^3}{t^2+1})x+7$ @ t=1, x=0 and y=7 $$\large\frac{dy}{dt}$$=2t $$\large\frac{dx}{dt}$$= 1+$$\large\frac{1}{t^2}$$ = $$\large\frac{t^2+1}{t^2}$$ Dividing by something, same as the product of its reciprocal, when doing $$\frac{dy}{dx}$$ Where's the error?
1. agentx5
Fixed the typo with the fraction command, press F5 to refresh and make it display properly. Am I understanding this question right @TuringTest ?
2. TuringTest
It's looking correct to me...
3. TuringTest
except that you can plug in the value for t... which just makes y=x+7
4. agentx5
Wait what? You mean just plug in 1?
5. agentx5
Ooooh!
6. TuringTest
why not, you need to know the value of the slope at that point, no?
7. agentx5
2/2 = 1 and it goes away
8. TuringTest
yeah, is that right? do you know?
9. agentx5
lol that was it /facepalm at myself >_<
10. TuringTest
haha sweet, it happens :)
11. agentx5
Well everybody got to see my work then lol
12. myko
i can't really read well your solution, but it is done like this: find point value for t=1, which is (0,7) find tanget vector at t=1 which is (2,2) write the equation: (x,y) = (0,7)+v(2,2) from here you can write it in the form y=something by eliminating v
13. agentx5
Ty myko :-) Yeah that's basically my steps too I'm doing... 1. find dy & dx with respect to dt (derivative of both) 2. find dy/dx 3. find the point for when t is as given, the x & y coords 4. put in the form of y=mx+b, solve for b using the known x & y 5. rewrite y=mx+b
14. myko
my way is shorter, :). You can avoid step 2. But ya, good job
15. myko
no need of that, becouse actually sometimes it will not work, if the dy/dx is infinity for example
16. myko
just keep y and x same level variables without considering one of them like the independent one till the end
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http://math.stanford.edu/~jzuniga/stat219.html
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STAT 219 / MATH 136 – Fall 2010
Course Goals:
This course prepares students for a rigorous study of Stochastic Differential Equations, as done in Math236/Stat316. Towards this goal, we cover – at a very fast pace – elements from the material of the (Ph.D. level) Stat310/Math230 sequence, emphasizing the applications to stochastic processes, instead of detailing proofs of theorems. A critical component of Stat219/Math136 is the use of measure theory.
The Stat217-218 sequence covers many of the same ideas and concepts as Stat219 but from a different perspective. The Stat217-218 sequence can be seen as an extension of undergraduate probability (e.g. Stat116) in both level of mathematical sophistication (i.e. no measure theory). Thus, it is possible, and in fact recommended, to take both Stat217-218 and Stat219 for credit. However, be aware that Stat217-218 alone is NOT adequate preparation for Math236.
Main topics of Stat219/Math136 include: introduction to measurable, Lp and Hilbert spaces, random variables, expectation, conditional expectation, uniform integrability, modes of convergence, stationarity and sample path continuity of stochastic processes, examples such as Markov chains, branching, Gaussian and Poisson processes, martingales and basic properties of Brownian motion.
Prerequisites:
Students should be comfortable with probability at the level of Stat116/Math105/Math151 and with real analysis (a.k.a. advanced calculus) at the level of Math115. For a good review of undergraduate probability see the optional Grimmett & Stirzaker text. Appendix A of the optional Rosenthal text includes a brief review of prerequisite material from real analysis.
Required text:
The only required text for this course is Amir Dembo's lecture notes. You will be expected to read the scheduled sections in the notes before class. Below is an estimated schedule for the course.
Week beginning Monday Wednesday Friday
9/20 1.1 1.1-1.2.2 1.2.2, 1.2.3
9/27 1.3.1,1.4.1 1.3.2, 1.4.1 1.4.2, 1.4.3
10/4 2.1,2.2 2.3 2.4
10/11 3.1 3.2 3.3
10/18 5.1 Review Midterm
10/25 4.1.1, 4.1.2 4.1.3 4.2
11/1 4.3.1 4.3.1,4.3.2 4.3.2,5.2
11/8 4.4.2, 4.5 4.4.1, 5.3 4.6
11/15 6.1 6.1 6.2
11/22
11/29 6.2 6.3 Review
12/6 Final
Suggested references:
Students are encouraged to consult other references. For your convenience, a copy of each book listed below is on hold in the Math & Computer Science library.
• Grimmett and Stirzaker, Probability and Random Processes
• Karlin and Taylor, A First Course in Stochastic Processes
• Lawler, Stochastic Processes
• Lefebvre, Applied Stochastic Processes
• Rosenthal, A First Look at Rigorous Probability Theory
• Ross, Stochastic Processes
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https://www.instructables.com/community/Motorpropeller-selection-for-quadcopter/
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313Views3Replies
### Author Options:
Hello Instructables!
We are a team of engineering students that want to get started in the world of multirotors. Our objective is to build a long endurance/high payload quadcopter for industrial applications, and we plan to innovate in the power system area.
So, without further ado here's our first problem. I've searched the internet for a while now and I've struggled to find information on how to choose an appropiate motor-propeller combination. I know the total maximun thrust should be a bit more than two times the the total weight but motor and propeller manufacturers rarely list the "thrust per rpm" of their props. Our initial estimation for the quadcopter's total weight is 3,3 kg. considering 200 g for each motor.
I did manage to find this static thrust calculator but I have no idea how reliable it is since it doesn't say how the thrust is calculated. (http://personal.osi.hu/fuzesisz/strc_eng/index.htm)
So that's about it. Any help would be greatly apreciated, no matter how small. It can be advice, information sources, or even builds that are similar to what we want to make and have already been tested.
Thank you very much for your time!
PS: Excuse me if my english sounds a bit weird, it just isn't my native language.
Tags:
The forums are retiring in 2021 and are now closed for new topics and comments.
I understand what you say, thrust calculations involve a lot science, mainly fluid mechanics, and are out of reach for hobbyists. But then, how do you decide what motors and propellers to use when building a custom quadcoter?
I think it depends on the hobbyist.
A hobbyist building a custom drone from the ground up typically has some goal in mind. Optimizing for that design starts off at the very beginning I think and continues until the end product is produced. Rotors are very generally designed so finding one that matches concepts, specifications, and such isn't impossible.
Taken a bit further, someone only interested in building a drone kits doesn't really care about what the effects to tweaks, especially small tweaks, to individual components have on their builds. After all, deviating from the kit is deviation from the kit, but if they're looking for a high powered trick drone, that's going to look a bit different.
For me, I actually have some distant aspiration to make, design, and/or pilot drones that can operate at great distances performing light industrial tasks, so I can kinda see what you're going for.
Also... one thing i kinda glossed over, the torque limit should be calculated by the forces being applied to the most distant part of the rotor from the central point. lever actions mean that forces applied near the center are multiplied as they get further out away from the central pivot. That's why CD's being spun at thousands of RPMs explode from the outside in. The force being applied on the outside edge due to drag forces is more than the plastic can tolerate.
Yeah... so there's a good reason you can't find that statistic.
Thrust, as generated by a motor and propeller combination, incorporates values from both components.
The first thing you need to look at is the overall RPM of the motor. Motors also place a constraint on torque, but, usually rotors are more limiting for torque, so that's typically where that limit is drawn from.
As far as the motor is concerned, High RPM is better. Maximize the RPMs to the weight of the engine as much as possible. Slip or slippage is not necessarily good, but it is not bad either, as it can act as a fail safe if the aircraft becomes over burdened. You need to weigh the amount of slip with the application and figure out what's correct.
Now, on to rotors... and it starts getting hairy pretty quick.
First, you're constrained by the material that the rotor is made out of. More than likely, you're going to be looking at a composite material. The bulk material properties will impose the first constraint on how much air, and thus how much force, the rotor can with stand. If you missed it, this is the absolute most ideal torque limit of the craft.
The next determinant property of the rotor is the geometry of the rotor and this is where I really can't help. The cross sectional area of the rotor and the total surface area contacting air are the next two bits, but I don't have the tools to tell you anything beyond that.
The cross sectional area that needs to be looked at is the thickest point on a propeller that looks like a tear drop, if the prop is sliced in half. This is because that determines the angle of attack and the angle of convergence of the air currents put off by the prop. There is software for this, which i do not own. This determines the amount of air moved per rotation. If memory serves, my friend who was doing a masters thesis on this stuff, said something like "Thinner is better for higher rotation, but too thin and you're unnecessarily limiting the lift generated.".
Anywho.... hope it helped.
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https://www.jiskha.com/questions/1183126/sarah-used-her-calculator-to-find-sin125-degree-she-wrote-down-sin125-degrees-57-how
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Trigonometry
Sarah used her calculator to find sin125 degree. She wrote down sin125 degrees = -.57. How could Sarah recognize that her answer is incorrect?
1. 👍
2. 👎
3. 👁
1. Sarah is wrong because her answer is for Cos(125) not Sin(125... Sin(125) equals .81915204
1. 👍
2. 👎
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# Thread: Finding a Common centre of gravity
1. ## Finding a Common centre of gravity
Hi there, i have a problem that needs solving. Put simply it goes like this:
I have lots of objects all referenced from there own centres of gravity to a point in 3D space and i need to know the common centre of gravity of all these objects combined.
I dont know if i am just not seeing the easy solution to this or whether it is genuinely a complicated problem...
Any ideas on an explanation or a formula, that Excel could handle to do this, would be awesome.
All the points have an X,Y,Z position on Right hand coordinate system.
2. Are all these constituent centers of gravity referencing the same point in 3D space? If so, let $\displaystyle \mathbf{r}_{j}$ be the vector from the common reference point $\displaystyle O$ to mass $\displaystyle m_{j}$. Then the vector $\displaystyle \mathbf{R}$ from point $\displaystyle O$ to the overall center of gravity is given by
$\displaystyle \displaystyle \mathbf{R}=\frac{\sum_{j}\mathbf{r}_{j}m_{j}}{\sum _{j}m_{j}}.$
3. Yes after doing a bit of research i came up with the same formula, thanks for confirming it.
But now im struggling in putting that into an excel format to deal with the list of co-ordinates i have!
4. You can do everything component-wise with the sumproduct and sum functions in Excel. Look at the help (hit F1 in Windows, anyway) to look up the syntax. The vector equation I gave is valid if you only look at one component at a time. Make sense?
5. Yeh that makes sense, i take it you dont have to take the mass as a vector too, as that would surely give errors (well, zeros) as it only acts in one direction? you just leave it as kg.. yeh i think i get it :P ill crack on with it tomorrow, thanks very much.
6. Right. Mass is not a vector quantity, at least not in your context. Let me know how it goes.
7. Worked a treat, Thankyou!
8. You're welcome. Have a good one!
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DAY 10
0
AI & Machine Learning
## Inspecting the model coefficients learned
``````sqft_model.get('coefficients')
``````
name index value stderr
(intercept) None -43814.8902666 5047.42632188
sqft_living None 280.360245938 2.21700145099
• 截距：直線與x相交的地方
• 斜率：單位面積的價格，每一平方要花多少錢
## Exploring other features of the data
``````#將要新增的特徵，新增到list當中
my_features = ['bedrooms','bathrooms','sqft_living','sqft_lot','floors','zipcode']
sales[my_features].show
``````
• 大部份的房子都是三間臥室
• 至於浴室在美國有個有特殊的規定，如果是套房的浴室算1個、不在套房內的(不含淋浴設備)算0.5個、如果是不再套房內的浴室(有淋浴沒浴缸)算0.75個(到底是三小= =)
• 大部份房子都是一層樓
``````#BoxWhisker Plot將會顯示兩個特徵之間的關係
#我想看看門牌與價格的關聯(我曾聽說掛上中正區的門牌50萬起跳、明明萬華就在隔壁)
sales.show(view='BoxWhisker Plot',x='zipcode',y='price')
``````
## Learning a model to predict house prices from more features
``````my_features_model = graphlab.linear_regression.create(train_data,target='price',features=my_features)
``````
``````print sqft_model.evaluate(test_data)
# {'max_error': 4142275.367360657, 'rmse': 255188.09204898693}
print my_features_model.evaluate(test_data)
# {'max_error': 3500449.806693536, 'rmse': 179356.3725536438}
``````
## Applying learned models to predict price of an average house
``````house1 = sales[sales['id'] == '5309101200']
# price:620000
``````
id date price bedrooms bathrooms sqft_living sqft_lot floors view condition grade sqft_above sqft_basement yr_built yr_renovated zipcode lat long sqft_living15 sqft_lot15
5309101200 2014-06-05 00:00:00+00:00 620000 4 2.25 2400 5350 1.5 0 4 7 1460 940 1929 0 98117 47.67632376 -122.37010126 1250.0 4880.0
``````print sqft_model.predict(house1)
# [630004.8234759354]
print my_features_model.predict(house1)
# [720058.291038626]
``````
## Applying learned models to predict price of two fancy houses
``````house2 = sales[sales['id'] == '1925069082']
# price:2200000
``````
id date price bedrooms bathrooms sqft_living sqft_lot floors view condition grade sqft_above sqft_basement yr_built yr_renovated zipcode lat long sqft_living15 sqft_lot15
1925069082 2015-05-11 00:00:00+00:00 2200000 5 4.25 4640 22703 2 4 5 8 2860 1780 1952 0 98052 47.63925783 -122.09722322 3140.0 14200.0
``````print sqft_model.predict(house2)
[1261846.2617304123]
print my_features_model.predict(house2)
# [720058.291038626]
[1451243.0229620067]
``````
## 後記
markdown table editor 顧名思義，幫你自動產生語法表格的好物
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# At the foot of the mountain the elevation of its summit is 45 degree; after ascending 1000m towards the mountain up a slope of 30 degree inclination, the elevation found to be 60 degree. Find the height of the mountain.
1
by garima9cr3
2015-03-06T15:53:49+05:30
### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
See the attached file.
height of mountain = OA =H
In ΔAOB,
tan (ABO) = AO/OB
⇒ tan 45 = AO/OB
⇒ 1 = AO/OB
⇒ OB = AO = H
In ΔPBR,
sin 30 = PR/PB
⇒ 1/2 = y/1000
⇒ y = 1000×(1/2) = 500m
Thus, AQ = AO - OQ = (H-500)m
cos 30 = RB/PB
⇒ √3 / 2 = x/1000
⇒ BR = 1000×(√3 / 2)
⇒ BR = 500√3m
thus OR = BO - BR = (H - 500√3)m
thus PQ = (H-500√3)m (since OP=PQ)
In ΔAPQ,
thanks a ton dear..!!.....:) :) :)
you are welcome!:)
:) :)
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