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Calculating DensityYou can calculate density by finding the mass of an object and dividing it by its volume. To find the volume of a solid is easy. You just multiply length times width times heigth. To find the mass of an object, you can place it on a balance scale to determine its mass. But, what if you are trying to find the density of an object like a marble or a nail? This is an irregularly shaped object. You cannot just measure the sides of a marble or a nail and multiply the length times the width times the heigth. So, the density of an irregular solid is determined by using the same formula for density, only you must find the volume of the object by water displacement. Calculating the density of a regular solid such as a cube is easy. You measure the sides of the object with a metric ruler and calculate the volume: length times width times heigth. How can you find the volume of an irregularly shaped object? Curtiss is using a graduated cylinder to determine the volume of an irregularly shaped object by water displacement. Emily and John are measuring the mass of a bolt. Kayla and Mandie work together to find the mass of a nail by using a balance scale. They will use a graduated cylinder to find the volume of the nail by water displacement. Now that they have these measurements, they can calculate the density of an irregularly shaped object. Density equals mass divided by volume. Andrea slowly lowers the bolt into the graduated cylinder. Chelsea watches the water level increase. They record the water displacement by finding the difference in the first and second water levels. Jason is trying very hard to read the volume of water in the graduated cylinder. To get an accurate measurement, Jason knows he must find the meniscus or the bottom of the curve. Teams work together using a balance to find the mass of a bolt. Clinton is using his balance to find the mass of a bolt. Stevie and Dani work together to find the volume of the bolt. First, you read the water level in the graduated cylinder. Second, place the bolt into the graduated cylinder. If you tie a string around the bolt, you will be able to lower it into the cylinder without splashing out any water. Next, get a second reading of the water level and find the difference. The difference in the water level is called water displacement and you can use this to find the volume of an irregularly shaped object like a bolt. Erin and Brandon work together to find the volume of a marble. Sarah and Emily watch Colin and Cody find the mass of a nail.
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# 2014 YZ450
"Significant" is a subjective word. I don't know about you, but in my mind, moving the muffler (probably 70% of the exhaust system weight) forward 4-5" is significant. In spite of the fact that the muffler hasn't been moved forward of the CG, it has unquestionably moved forward, as well as downward.
Which is great for centralizing mass and giving the bike a lighter feel overall, however I don't believe it will put any noticeable amount back on the front end.
Which is great for centralizing mass and giving the bike a lighter feel overall, however I don't believe it will put any noticeable amount back on the front end.
After moving a 5 pound silencer 5" forward, you'd be able to measure the front/rear weight distribution change with a scale, I expect. Besides no one said that it was done to put weight on the front wheel, only that it moves weight forward, which it unquestionably does. When you're talking about moving weight located behind the CG towards the CG it both centralizes the mass AND moves weight forward, no matter how you want to spin it.
Fair enough!
Still seems like we would be taking about ounces and not pounds though.
Edited by FinchFan394
After moving a 5 pound silencer 5" forward, you'd be able to measure the front/rear weight distribution change with a scale, I expect. Besides no one said that it was done to put weight on the front wheel, only that it moves weight forward, which it unquestionably does. When you're talking about moving weight located behind the CG towards the CG it both centralizes the mass AND moves weight forward, no matter how you want to spin it.
This is the proper way to think about it. It's about weight (or force) in relation to CG that is the crux of the issue with the YZ.
Another way to look at it is with reference to the engine mod.
Using the formula of Weight X Arm = Moment (weight X distance = force) Moving the 70lb. engine forward 2.5 mm equals a moment (force) reference of 175.
Now using an example assuming the "tornado" portion of the exhaust weighs 3 lbs. and is located 6" (150mm)behind the CG and the new pipe layout puts much of that weight 6" forward of the CG you're talking about a change of moment (force about CG) of 3 lbs. X 12" (300mm) = a force reference of 900 where 450 units that were aft of CG are now forward of it.
A big difference. Even more than the engine mod.
Wow look at what three pounds can do...imagine what your 180# can do moved forward an inch.......
You see this whole wrapping the header around the cylinder reminds of the guys putting CF on their bikes to save weight. I could not drink Coke for a week and probably save double what the CF will.
Wow look at what three pounds can do...imagine what your 180# can do moved forward an inch.......
You see this whole wrapping the header around the cylinder reminds of the guys putting CF on their bikes to save weight. I could not drink Coke for a week and probably save double what the CF will.
Preachin to the choir bro.
Hope that Josh Grant and Brayton can give the yz450f some good results ! I cant believe all the crap this great bike gets after Stewarts drama show.
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×
Get Full Access to Precalculus With Trigonometry: Concepts And Applications - 1 Edition - Chapter 6-6 - Problem 1
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# For 1-3, translate one vector so that the two vectors are head-to-tail, and then use
ISBN: 9781559533911 468
## Solution for problem 1 Chapter 6-6
Precalculus with Trigonometry: Concepts and Applications | 1st Edition
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Problem 1
For 1-3, translate one vector so that the two vectors are head-to-tail, and then use appropriate triangle trigonometry to find and the angle the resultant vector makes with (Figure 6-6k).1. = 7 cm, = 11 cm, and = 73
Step-by-Step Solution:
Step 1 of 3
Carole Pateman: The Sexual Contract 3.15.16 She looks at the social contract and views how it affects inequality between genders. Her piece is called Women & Consent. Context: feminist critiques of liberalism Pateman is responding to a dilemma that feminists call a “double bind” o Should women attempt to seek to obtain absolute equality with men Does this mean women should become more like men Does this not reproduce inherently male standards of evaluation & qualification for positions of power/authority/respectability Does this not accept social devaluation of practices, characteristics & value that
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##### ISBN: 9781559533911
Precalculus with Trigonometry: Concepts and Applications was written by and is associated to the ISBN: 9781559533911. This full solution covers the following key subjects: . This expansive textbook survival guide covers 106 chapters, and 2321 solutions. Since the solution to 1 from 6-6 chapter was answered, more than 233 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 1 from chapter: 6-6 was answered by , our top Calculus solution expert on 03/16/18, 04:16PM. The answer to “For 1-3, translate one vector so that the two vectors are head-to-tail, and then use appropriate triangle trigonometry to find and the angle the resultant vector makes with (Figure 6-6k).1. = 7 cm, = 11 cm, and = 73” is broken down into a number of easy to follow steps, and 39 words. This textbook survival guide was created for the textbook: Precalculus with Trigonometry: Concepts and Applications, edition: 1.
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# Dimensional (Unit) Analysis and Problem Solving
A convenient check on your work, or even a way to determine the best approach to a problem, is to use dimensional analysis. This simply means to include all of the units for each factor in an equation, and then to check to see that the units on both sides of the equation are equal.
Example: How many centimeters are there in one foot?
Known: 1 ft = 12 inches (defined, therefore exactly); 2.54 cm = 1 inch (defined).
Set up: (1 ft)(12 inches/ft)(2.54 cm/inch)
note that ft cancels ft and inches cancels inches to give cm!
Solve: (1 ft)(12 inches/ft)(2.54 cm/inch) = 30.48 cm.
How about sig figs? In this problem there are no significant figures the way its set up, because there are no measurements! That is, all of the numbers are part of definitions, so they are exact, and that means the answer is exact as well.
Extra Example: Assume it is 293 miles to your destination in the Bay Area. If you are driving a car that gets 27 miles per gallon and gas costs an average of \$3.45/gallon for the trip, how much will it cost you to drive there and back? Again, look at units. Want answer in dollars, so \$3.45/gallon ?? = \$ So we have \$ on both sides, but we need to get rid of (/gallon), so let's try dividing by 27 miles/gallon: (\$3.45/gallon) / (27 miles/gallon) ? = \$ We can now cancel gallons, as shown, and all we need to do now is multiply by miles to cancel miles: (293 miles)(\$3.45) / (27 miles) = \$ We now have the same units on each side, and can do the math, which I will leave to you.
# SI Units (metric system)
SI Units: The metric system originated around the French Revolution as a rational system of measurements to rescue France from the chaos of pre-revolutionary measurements and thus prevent tax collectors from cheating.
Wanted to base system on "natural" universal standards. Thus for length they chose the size of the Earth: specifically the meter was defined as one ten-millionth (10-7) of the Earth's meridian (line from the S to the N pole) through Paris. For mass the Kilogram was defined as the mass of a cube of water 0.1 meter on a side. Of course these are not convenient, so standards were quickly created: the meter became the distance between two lines on a platinum-iridium bar stored in a vault in Paris, while the kilogram became a cylindrical mass of platinum-iridium stored in the same vault.
Today the various units are defined by international agreement to give the SI (Systéme International) units:
• Length: the meter (m) is defined as the distance light travels in a vacuum in 1/299,792,458 sec (note that this is truly universal: in principle it can be determined by anyone, anytime, anywhere in the Universe).
• Mass: the kilogram (kg) however is still based on the International Prototype Kilogram in Paris and the derived standard kilogram standards held by governments around the world.
• Time: the second (s) is defined today as the duration of 9,192,631,770 periods of the radiation of two hyperfine levels of the ground state of the cesium 133 atom.
• Amount of substance: the mole (mol) is defined as the number of atoms in 0.012 kg (defined, so sig figs not restricted) of carbon 12 atoms.
• Temperature: the kelvin (K) is defined as 1/273.15 of the thermodynamic temperature of the triple point of water.
• Electric current: the ampere is defined as the the current which carries one coulomb (6.24146 x 1018 times the charge on an electron or proton) of charge through a conductor in one second.
Prefixes: Note Table 1.2 in your text (p 10). You should know (memorize) and be able to interconvert the prefixes in the table below:
Prefix Symbol Magnitude tera- T 1012 giga- G 109 mega- M 106 kilo- k 103 base 100 deci- d 10-1 centi- c 10-2 milli- m 10-3 micro- (or mc) 10-6 nano- n 10-9 pico- p 10-12 fempto- f 10-15
Memorize: 1 mL = 1 cm3; 1 inch = 2.54 cm (defined); 1 liter is about 1 quart; density of water = 1 g/mL; 0° C = 32 °F, 100°C = 212 °F, -40 °C = -40 °F.
## Temperature
Look in your text for conversions between °C and °F and example problems
# Density
Density is defined as the mass of a given volume of a substance: Density = mass/volume. Note that this weeks laboratory exercise give practice in Density, significant figures etc.
Let's try some density problems. First note that the units of density are g/cm3 or g.cm-3.
• A student found that 20.0 mL of a liquid weighed 35.987 g. What is its density?
Known: Density = mass/volume, generally expressed as g/mL = g/cm3
Solve: (35.987 g) / (20.0 mL) = 1.79935 g/mL
note that the units are those of density so we are confident we set it up correctly.
How about sig figs? Use multiplication/division rules, so count: 3 for 20.0 and 5 for 35.987, therefore should have three sig figs:
1.79935 g/mL = 1.80 g/mL
Extra Example: Using a jewelers balance a student found that a coin weighed 2.34 carats in air. By weighing it again submerged in water she found it had a volume of 0.034 mL. What is its density? (1 carat = 200 mg, defined)* Known: 1 carat = 200 mg (defined), density is g/mL Solve: (2.34 carats)(200 mg/carat)(1 g/1,000 mg) / 0.034 mL = 13.764706 g/mL How about sig figs? Both conversion factors are defined, so exact. Two measurements: 2.34 and 0.034 = 3.4 x 10-2. Thus the answer will have only two sig figs since using counting rule - least number of sig figs. 13.764706 g/mL = 14 g/mL
# Matter
What is matter? Stuff. Has mass and occupies space.
## Mass
Mass is the measure of quantity for matter. Mass is the property of matter resulting in its inertia and and attraction via gravity.
Do not confuse mass and weight. Weight is the force acting on an object due to gravity. We often interchange these terms in conversation, but they are quite different - you have the same mass whether you are weightless in space on here on Earth (taking a shuttle flight is no substitute for a diet!). To confuse us further we call the determination of mass "weighing"!
Matter has both physical properties and chemical properties. These are properties which do not depend on the quantity of substance and therefore they can be used to identify a substance (sometimes referred to as intensive properties).
• Physical properties of substances can be observed without, in principle, changing their compositions. Physical properties include mass, color, density etc. Note that physical changes such as melting, cutting, etc. do not change composition. When you perform a physical operation such as melting or cutting, you have changed the object, but you still have the same kind of stuff - chop a wooden stick in half, you have two sticks, not a newkind of thing like a rock or piece of metal. Physical operations are also often readily reversible - if you melt ice the water can be readily returned to ice, though not necessarily the same shape, it is obviously the same stuff!
### NEXT
Syllabus / Schedule C109 Home
© R A Paselk
Last modified 28 January 2011
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A question often posed by operators of anaerobic digesters is “what should I be looking for?”. This is often in the context of process plant with a myriad of expensive instrumentation and computer control. I have always been of the view that anaerobic digestion is a simple process looked after by nature and with its slow reaction rate needs little attention, but in the words of the management guru: “measure more by measuring less”.
Ratio 1 – Gas : Sludge
There are 2 ways of measuring gas production : the instrumentation way and the operator way. If you can rely on your gas meter, please use it, but there is another way. Nowadays, for safety reasons and to reduce greenhouse gas emissions, all biogas is burned, either in boilers, gas engines or waste gas burners. The trick is to calibrate the consumption rate of each gas appliance (m3/hr) and to ensure that there is an hours run meter for each appliance. There is no need to monitor gas consumption more regularly than daily, so the daily gas production from the digester(s) is the sum total of the hours run by each appliance and its gas consumption rate. A log book and a calculator or a spreadsheet will do the job for you.
Likewise, there are 2 ways of measuring the raw sludge feed to the digester : the instrumentation way and the operator way. If you are unhappy with reliance on a series of flowmeters, calibrate your feed pump(s), record the hours run, and there you are with the daily raw sludge feed volume.
Now you can calculate Ratio 1 – divide the daily (or weekly or whatever time interval you choose) gas production by the raw sludge feed volume. What is the significance ? If your raw sludge is consistent, then the ratio will be. If the ratio is not consistent day by day, either your raw sludge dry matter is varying or your digester is not performing, because Ratio 1 is approximately equal to:
(Raw Sludge % TS) x (% VS) x (% Volatile Destruction) / 1000
For example a raw sludge with a TS of 6%, a VS of 80% and a VSD of 45% will give a value for Ratio 1 of 21.6.
Ratio 2 – Gas : Digester Capacity
Again monitor the gas production, expressed as m3/day. Divide this figure by the digester capacity (m3) to give you your second ratio. This tells you how hard your digester is working.
In the example above a digester working on a 15 day retention time will give a value for Ratio 2 of 1.44. A figure less than 1.0 means that you could be working your digester much harder; a figure more than 1.5 is good for a conventional sewage sludge digester; high solids digesters have been known to achieve a figure of more than 4.
Ratio 3 – CH4: CO2
There are two ways of monitoring gas quality – yes, you guessed it, using an expensive instrument, either permanent or portable, to measure the CH4 content of the gas, or a “Draeger” tube with a portable set of bellows to measure the CO2 content; it can be assumed for this ratio that the biogas comprises only CH4 and CO2. Whether you measure CH4 or CO2 the important issue is that Ratio 3 is consistent from day to day; for a sludge digester it is normally about 1.5. The alarm bells should ring if Ratio 3 falls because this indicates a rising CO2 content, which in turn indicates that the methane forming stage of the anaerobic digestion process is becoming less stable, which might lead to failure. Measuring the pH will tell you that your digester has already failed and measuring VFA’s is more complex.
Measure the 3 ratios regularly; if your digester is happy the ratios will not vary.
Anaerobic Digester
Diagram of anaerobic digester
Michael Chesshire, Greenfinch Ltd, Burford House, Tenbury Wells, Worcs, WR15 8HQ (Tel: 01584 810777)
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# Linear Regression
Statistics Solutions provides a data analysis plan template for the linear regression analysis. You can use this template to develop the data analysis section of your dissertation or research proposal.
The template includes research questions stated in statistical language, analysis justification and assumptions of the analysis. Simply edit the blue text to reflect your research information and you will have the data analysis plan for your dissertation or research proposal.
Data Analysis Plan: Linear Regression
Copy and paste the following into a word document to use as your data analysis plan template.
Research Question:
RQ: Does independent variable predict dependent variable?
HoIndependent variable does not predict dependent variable.
HaIndependent variable predicts dependent variable.
Data Analysis
To examine the research question, a linear regression will be conducted to investigate whether or not independent variable predicts dependent variable. A linear regression is an appropriate analysis when the goal of research is to assess the extent of a relationship between a dichotomous or interval/ratio predictor variable on an interval/ratio criterion variable. In this case, the predictor variable is the independent variable and the criterion variable(s) is the dependent variable. The following regression equation will be used: y = b1*x + c; where y = estimated dependent variable, c = constant, b = regression coefficient and x = independent variable . The F-test will be used to assess whether the independent variable predicts the dependent variable. R-squared will be reported and used to determine how much variance in the dependent variable can be accounted for by the independent variable. The t-test will be used to determine the significance of the predictor and beta coefficients will be used to determine the magnitude and direction of the relationship. For statistically significant models, for every one unit increase in the predictor, the dependent variable will increase or decrease by the number of unstandardized beta coefficients. The assumptions of a linear regression —linearity and homoscedasticity—will be assessed. Linearity assumes a straight line relationship between the predictor variables and the criterion variable and homoscedasticity assumes that scores are normally distributed about the regression line. Linearity and homoscedasticity will be assessed by examination of a scatter plots.
Reference
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02 Jul 2007, 23:21
stevegt wrote:
1. In June, 1981, six teenagers in the village of Medjugorje, Yugoslavia, claimed to have had visions of the Virgin Mary, who they say has continued to appear to them over the ensuing years.
(A) claimed to have had visions of the Virgin Mary, who
(B) claimed to have visions of the Virgin Mary, whom
(C) claimed to have had visions of the Virgin Mary, whom
(D) claimed to have visions of the Virgin Mary, who
(E) had claimed to have had visions of the Virgin Mary, whom
guess A for "who ........... has".
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### Show Tags
02 Jul 2007, 23:23
1. In June, 1981, six teenagers in the village of Medjugorje, Yugoslavia, claimed to have had visions of the Virgin Mary, who they say has continued to appear to them over the ensuing years.
(A) claimed to have had visions of the Virgin Mary, who
(B) claimed to have visions of the Virgin Mary, whom
(C) claimed to have had visions of the Virgin Mary, whom
(D) claimed to have visions of the Virgin Mary, who
(E) had claimed to have had visions of the Virgin Mary, whom
Need possesive pronoun 'whom' here as virgin mary is object and not subject
B,C,E - left
E - had claimed ... have had - awkward and not correct tense - out
B & C - tough choice
C - 'had' refers to past perfect tense and we do not have a past action here - may not be right. Please correct me if i am wrong with this choice.
B looks best.
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03 Jul 2007, 09:33
stevegt wrote:
1. In June, 1981, six teenagers in the village of Medjugorje, Yugoslavia, claimed to have had visions of the Virgin Mary, who they say has continued to appear to them over the ensuing years.
(A) claimed to have had visions of the Virgin Mary, who
(B) claimed to have visions of the Virgin Mary, whom
(C) claimed to have had visions of the Virgin Mary, whom
(D) claimed to have visions of the Virgin Mary, who
(E) had claimed to have had visions of the Virgin Mary, whom
I'll go with (A) here.
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### Show Tags
03 Jul 2007, 12:02
"Whom" is incorrect usage so eliminate B, C, E
Down to A or D I go w/ A as "have had" is parallel to "has continued"
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### Show Tags
03 Jul 2007, 12:25
What's the OA?
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03 Jul 2007, 12:31
I feel C. Virgin Mary is the object so whom is requireed. Also had is required as there are 2 events. One is having the visions and the other is the claiming.
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### Show Tags
16 Oct 2010, 07:35
This one is up for debate
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### Show Tags
17 Oct 2010, 16:31
I am with A.
HAVE HAD is correct because it is a continuous thing but of the past which is still true today (so it cannot be past perfect HAD HAD dreams) and takes good bearing on the verb CLAIMED. They CLAIMED to HAVE HAD dreams. it cannot be "they CLAIMED to HAVE dreams" as it indicates they are having dreams now and it cannot be "they CLAIMED to HAD dreams". So out go everything except A and C.
Now for the pronoun for Mary, it is a WHO since it is the subject of the subordinate clause " who they say has continued to appear to them over the ensuing years." Whenever we have the subject being referred the correct pronoun is WHO not WHOM. So C is out.
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26 Oct 2010, 02:49
Straight A ...as 'who/whom' refers to 'teenagers' in the subject of the verb, hence 'who' is correct.
Since the visions continue to appear ... use of Present perfect(have) is correct and to denote the sequence of events the use of Past perfect (had) is also correct.
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16 Nov 2010, 06:51
I'll go with A as well. Also, I'm from Yugoslavia and we haven't seen Mary, at least not the virgin one
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16 Nov 2010, 21:37
'C'.
two things happening in past. claimed, and visions. hence had visions is correct.
also mary is the object hence whom is required.
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Re: teenagers [#permalink] 16 Nov 2010, 21:37
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# Spanish 1st Grade Number of the Day March NO PREP!
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(7 MB|28 pages)
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1. You will not be disappointed with these NO PREP, Number of the Day activities IN SPANISH. This means no hassle for you...Just print and GO! Place value, problem-solving, fractions, skip counting, money, addition problems to 20, greater than, and less than, just to name a few! This resource has ever
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• Product Description
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If you are looking for a way for your 1st graders to practice Common Core Math and TEKS objectives (for our Texans), this NO PREP resource is for you! The activities are all black and white for easy printing. These are skills my first graders are learning and reviewing. Every month the skills build on each other.
This has been created to help students begin to think about math (numbers) in different ways. On days where we don't get to one of the pages, I send it home for homework, use it as an assessment, or place it in a center. Common Core Math and TEKS objectives (for our Texans) are practiced in this resource.
***DISCLAIMER: This product has been translated into academic Spanish by Monica M. Falcon. We realize there are many different ways to say words in Spanish and/or many terms that people are familiar with. However, we deliberately avoided regional Spanish. Teacher directions are written in English. Please email us at thefunfactoryontpt@gmail.com if you want different words.***
March has numbers 112-127.
**These numbers are NOT meant to coordinate with the number of days in school!**
This has been created to help students begin to think about math (numbers) in different ways.
Objectives covered:
• Written form
• Expanded form
• Place value
• Addition (using the part/part/whole) Number Bonds
• Subtraction
• Money -recognizing coins and their value, counting
Other skills practiced for March:
• Shapes (both 2 and 3 dimensional)
• Measurement,/strong> (non-standard) and math vocabulary
• Word Problems
• Estimation
• Skip Counting
• Fractions - halves and fourths
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Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ▯ - 3, 6 + 6 = ▯.
Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
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Convert Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot
Kyle's Converter > Density > Kilograms Per Thousand Cubic Feet > Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot
Kilograms Per Thousand Cubic Feet (kg/MCF) Long Tons Per Acre-foot (t (Imp)/ac ft) Precision: 0 1 2 3 4 5 6 7 8 9 12 15 18
Reverse conversion?
Long Tons Per Acre-foot to Kilograms Per Thousand Cubic Feet
(or just enter a value in the "to" field)
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Unit Descriptions
1 Kilogram per Thousand Cubic Feet:
Mass of 1 kilogram per volume of one thousand cubic feet. International foot of exactly 0.3048 meters. Approximate density of 0.035 314 666 721 4886 kilograms per cubic meter. 1 kg/MCF = 0.0353146667214886 kg/m3.
1 Long Ton per Acre-Foot:
Mass of 1 long ton per volume of an acre-foot. Long ton UK of 2240 pounds. International pound and foot. 1 t (US)/ac ft ? 0.823722634473616 kg/m3.
Conversions Table
1 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 0.042970 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 3.001
2 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 0.085780 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 3.4298
3 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 0.128690 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 3.8585
4 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 0.1715100 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 4.2872
5 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 0.2144200 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 8.5744
6 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 0.2572300 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 12.8616
7 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 0.3001400 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 17.1488
8 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 0.343500 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 21.436
9 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 0.3858600 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 25.7232
10 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 0.4287800 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 34.2976
20 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 0.8574900 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 38.5848
30 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 1.28621,000 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 42.872
40 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 1.714910,000 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 428.7204
50 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 2.1436100,000 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 4287.2036
60 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 2.57231,000,000 Kilograms Per Thousand Cubic Feet to Long Tons Per Acre-foot = 42872.0363
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# Planck's Law, Quantum mechanics help
1. Oct 13, 2011
### hxcguitar101
1. The problem statement, all variables and given/known data
(2) The orbiting space shuttle moves around the Earth well above 99% of the atmosphere, yet it still accumulates an electric charge on its skin due (in part) to the loss of electrons caused by the photoelectric effect from sunlight. Suppose the skin of the shuttle is coated with nickel for which the work function is φ = 4.87 eV at the temperatures encountered while in orbit. (A) What is the maximum wavelength of solar radiation that can result in electron emission from the shuttle’s skin? (B) What is the maximum fraction of the total power falling on the shuttle that could potentially produce photoelectrons?
I Found the answer to part A to be 255 nm... how do you find part B?
2. Relevant equations
Planks law: u(λ) = 8πhcλ^-5)/(e^(hc/λkT)-1)
3. The attempt at a solution
I set up the integral: Int(8πhcλ^-5)/(e^(hc/λkT)-1)) from 0 to 255nm all over the same integral from 0 to infinity (planck's law) but I have NO IDEA how to solve it! THANKS
Last edited: Oct 13, 2011
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HWK 16 - F = 22.16 P-value = 0.00 Conclusion Rejection Ho...
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Homework #16 Problem #10 Business Issue Judgement of errors made by auditors Business Question Can we conclude that the auditors judgemets were better than actual results Data Direct Indirect Combination 17.0 16.6 25.2 18.5 22.2 24.0 15.8 20.5 21.5 18.2 18.3 26.8 20.2 24.2 27.5 16.0 19.8 25.8 13.3 21.2 24.2 Analysis Hypotheses Ho: Ho: mu1 = mu2 = mu3 Ha: Ha: at least 2 means differ Test Stat If Ho is true the sample means should be similar If Ha is true the sample means might be very different Sum of Squared Treatment differences Mean Squared Treatment differences Mean Squared Error Differences F = MST/MSE If Ho is true, this ratio has the F distribution with df1=k-1 and df2=n-k Sig Level Alpha = .05 Reject Rule Reject Ho if F > FINV = 3.55 F > 3.555 Calculations
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Unformatted text preview: F = 22.16 P-value = 0.00 Conclusion Rejection Ho Business Answer According to the sample taken there is overwhelming evidence to conclude that the auditors judgements were better than the acutal Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 7 119 17 5.01 Column 2 7 142.8 20.4 6.26 Column 3 7 175 25 4.01 ANOVA SS df MS F P-value F crit 225.68 2 112.84 22.16 3.55 SST = Sum of Squares --" treatments " = [n j *(xbar j- xdoublebar)^2], j=1,2,3 MST = SST/(k-1) , where k=number of treatments SSE = Sum of Squares -- Errors for all three samples = Sum[(n j-1)*s j ^2], j=1,2,3 MSE = SSE/(n-k) where n = n1+n2+n3. (Here, n=20+20+20=60) 91.66 18 5.09 317.34 20...
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# How far is Latakia from Deir ez-Zor?
The distance between Deir ez-Zor (Deir ez-Zor Airport) and Latakia (Bassel Al-Assad International Airport) is 239 miles / 384 kilometers / 208 nautical miles.
The driving distance from Deir ez-Zor (DEZ) to Latakia (LTK) is 325 miles / 523 kilometers, and travel time by car is about 6 hours 13 minutes.
239
Miles
384
Kilometers
208
Nautical miles
## Distance from Deir ez-Zor to Latakia
There are several ways to calculate the distance from Deir ez-Zor to Latakia. Here are two standard methods:
Vincenty's formula (applied above)
• 238.898 miles
• 384.469 kilometers
• 207.597 nautical miles
Vincenty's formula calculates the distance between latitude/longitude points on the earth's surface using an ellipsoidal model of the planet.
Haversine formula
• 238.365 miles
• 383.611 kilometers
• 207.133 nautical miles
The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points).
## How long does it take to fly from Deir ez-Zor to Latakia?
The estimated flight time from Deir ez-Zor Airport to Bassel Al-Assad International Airport is 57 minutes.
## Flight carbon footprint between Deir ez-Zor Airport (DEZ) and Bassel Al-Assad International Airport (LTK)
On average, flying from Deir ez-Zor to Latakia generates about 60 kg of CO2 per passenger, and 60 kilograms equals 133 pounds (lbs). The figures are estimates and include only the CO2 generated by burning jet fuel.
## Map of flight path and driving directions from Deir ez-Zor to Latakia
See the map of the shortest flight path between Deir ez-Zor Airport (DEZ) and Bassel Al-Assad International Airport (LTK).
## Airport information
Origin Deir ez-Zor Airport
City: Deir ez-Zor
Country: Syria
IATA Code: DEZ
ICAO Code: OSDZ
Coordinates: 35°17′7″N, 40°10′33″E
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## t Distributions
The Student's t-Distribution (more simply the t-distribution) is the distribution of sample means when the population standard deviation is unknown. Estimates of a population mean based on a sample will use this distribution. The distribution received the name "Student's t" because its discoverer, William Gosset, published his work under the pseudonym "Student".
### The Formulas
If the random variable $T$ has an t-distribution over the interval $(-\infty, \infty)$, with $n$ degrees of freedom, then the PDF of the distribution is given by the following formula.
$f_T(t) = \dfrac{ \Gamma\left(\dfrac{n+1}{2}\right) }{ \Gamma\left(\dfrac{n}{2}\right) \sqrt{n \pi} \left(1 + \dfrac{t^2}{n} \right)^{(n+1)/2}}$
### Computing with the t-Distribution
As with many important distributions, computations involving the t-distribution are typically left to available technology. The Texas Instruments calculator syntax for the CDF is $\operatorname{tcdf}(x_1,x_2,n)$.
• For the t-distribution with 7 degrees of freedom, the area under the curve between 2.5 and 7.3 is $P(2.5 < t < 7.3) = \operatorname{tcdf}(2.5,7.3,7) = 0.0204$.
• For the t-distribution with 15 degrees of freedom, the area under the curve less than 1.25 is $P(t < 1.25) = \operatorname{tcdf}(-\infty, 1.25, 15) = 0.8848$.
### Derivation of the t Distribution
Standard scores for sample means are normally distributed with $z = \dfrac{\bar{x} - \mu}{\sigma/\sqrt{n}}$. However, the population standard deviation $\sigma$ is most often unknown, and the sample standard deviation $s$ is used in its place. In that case, we have $t = \dfrac{\bar{x} - \mu}{s/\sqrt{n}}$, a slightly different formula, and we cannot expect it to be normally distributed as $z$ was.
Let the random variable $S$ represent the sample standard deviation (whose value depends on the random sample obtained), and consider the random variable $T^2$. Algebraically, we find:
$$T^2 = \dfrac{(\bar{x} - \mu)^2}{\dfrac{S^2}{n}} \dfrac{\dfrac{n}{\sigma^2}}{\dfrac{n}{\sigma^2}} = \dfrac{\dfrac{(\bar{x} - \mu)^2}{\sigma^2/n}}{\dfrac{S^2}{\sigma^2} \dfrac{n-1}{n-1}} = \dfrac{ Z^2 / 1}{ \left[ (n-1)\dfrac{S^2}{\sigma^2} \right] / (n-1)}$$
We know that squared standard scores have a chi-square distribution with one degree of freedom. We also know that the random variable $\dfrac{(n-1)S^2}{\sigma^2}$ has a chi-square distribution with $n-1$ degrees of freedom. And we have found that the random variable $T^2$ is the ratio of two chi-square distributions, each divided by their degrees of freedom. Therefore, $T^2$ has an F-distribution with degrees of freedom 1 and $n-1$.
Since probabilities of each distribution can be found with its CDF, we have the following result.
\begin{align} F_{T^2}(u) &= P(T^2 < u) \\ &= P( -\sqrt{u} < T < \sqrt{u} ) \\ &= F_T(\sqrt{u}) - F_T(-\sqrt{u}) \end{align}
The PDFs of these distributions can be found by taking derivatives.
$$f_{T^2}(u) = \dfrac{1}{2\sqrt{u}} \left[ f_T(\sqrt{u}) + f_T(-\sqrt{u}) \right]$$
But the $T$ distribution is symmetric, because of the underlying symmetry of the normal distributions from which it was formed. Therefore $f(t) = f(-t)$, and we have:
\begin{align} f_{T^2}(u) &= \dfrac{1}{\sqrt{u}} f_T(\sqrt{u}) \\ \sqrt{u} f_{T^2}(u) &= f_T(\sqrt{u}) \end{align}
Making the substitution $u = t^2$ and swapping sides of the equation, we obtain:
$$f_T(t) = |t| f_{T^2}(t^2)$$
The left side of this equation is the PDF of the random variable $T$, while the right hand side gives us a formula in terms of the PDF of $T^2$, which has an F-distribution. Using that formula produces the PDF of a t-distribution with $n-1$ degrees of freedom.
\begin{align} F_T(t) &= (t^2)^{1/2} \dfrac{ \Gamma\left(\dfrac{n}{2}\right) \left(\dfrac{1}{n-1}\right)^{1/2} (t^2)^{1/2-1} }{ \Gamma\left(\dfrac{n-1}{2}\right) \Gamma\left(\dfrac12\right) \left(1 + \dfrac{1}{n-1} t^2 \right)^{n/2} } \\ &= \dfrac{ \Gamma\left(\dfrac{n}{2}\right)}{ \Gamma\left(\dfrac{n-1}{2}\right) \sqrt{(n-1)\pi} \left(1 + \dfrac{t^2}{n-1} \right)^{n/2} } \end{align}
Replacing $n$ by $n+1$ in this result will produce the PDF of a t-distribution with $n$ degrees of freedom.
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# Physics exercises_solution: Chapter 42
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## Physics exercises_solution: Chapter 42
Mô tả tài liệu
Bộ tài liệu bài tập tham khảo môn vật lý bậc đại học bằng tiếng anh Chapter 42
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## Nội dung Text: Physics exercises_solution: Chapter 42
1. 3 2 K 2(7.9 10 4 eV)(1.60 10 19 J eV) 42.1: a) K kT T 2 3k 3(1.38 10 23 J K) T 6.1 K 2(4.48 eV) (1.60 1019 J eV) b) T 34,600 K. 3(1.38 10 23 J K ) c) The thermal energy associated with room temperature (300 K) is much greater than the bond energy of He 2 (calculated in part (a)), so the typical collision at room temperature will be more than enough to break up He 2 . However, the thermal energy at 300 K is much less than the bond energy of H 2 , so we would expect it to remain intact at room temperature. 1 e2 42.2: a) U 5.0 eV. 4πε0 r b) 5.0 eV (4.3 eV 3.5 eV) 4.2 eV. 42.3: Let 1 refer to C and 2 to O. m1 1.993 10 26 kg, m2 2.656 10 26 kg, r0 0.1128 nm m2 r1 m m r0 0.0644 nm (carbon ) 1 2 m1 r2 m m r0 0.0484 nm (carbon) 1 2 b) I m1r12 m2 r22 1.45 10 46 kg m 2 ; yes, this agrees with Example 42.2. 42.4: The energy of the emitted photon is 1.01 10 5 eV, and so its frequency and wavelength are E (1.01 105 eV)(1.60 1019 J eV) f 2.44 GHz h (6.63 1034 J s) c (3.00 108 m s) λ 0.123 m. f (2.44 109 Hz) This frequency corresponds to that given for a microwave oven.
2. 42.5: a) From Example 42.2, E1 0.479 meV 7.674 10 23 J and I 1.449 10 46 kg m 2 K 1 Iω 2 and K E gives ω 2 E1 I 1.03 1012 rad s 2 b) v1 r1ω1 (0.0644 109 m)(1.03 1012 rad s) 66.3 m s (carbon) v2 r2 ω2 (0.0484 10 9 m)(1.03 1012 rad s) 49.8 m s (oxygen) c) T 2π ω 6.10 10 12 s 1 1 42.6: a) E0 ω (0.2690 eV) 2.083 10 20 J 2 2 1 2 E0 2(2.083 10 2 J) E0 mr vmax gives vmax 2 26 1.91 103 m s 2 mr 1.139 10 kg b) According the Eq. 42.7 the spacing between adjacent vibrational energy levels is twice the ground state energy: 1 En (n ) ω, 2 E En 1 En ω hf . Thus, using the E specified in Example 42.3, it follows that its vibrational period is 1 h (6.63 1034 J s) T 1.54 1014 s. f E (0.2690 eV)(1.60 1019 J eV) c) The vibrational period is shorter than the rotational period.
3. m m 42.7: a) I mr r 2 Li H r 2 m m Li H (1.17 10 26 kg)(1.67 10 27 kg)(1.59 10 10 m) 2 (1.17 10 26 kg 1.67 10 27 kg) 3.69 10 47 kg m 2 2 42 E E4 E3 (4(4 1) (3) (3 1)) 2I I 34 4(1.054 10 J s) 2 E 3.69 10 47 kg m 2 E 1.20 10 21 J 7.53 10 3 eV. hc (6.63 1034 J s)(3.00 108 m s) b) λ 21 λ 1.66 10 4 m. E 1.20 10 J 42.8: Each atom has a mass m and is at a distance L 2 from the center, so the moment of inertia is 2(m)( L 2) 2 mL2 2 2.21 10 44 kg m 2 . l (l 1)2 l (l 1)2 2 2 l2 42.9: a) El , El 1 E (l l l 2 l ) 2I 2I 2I I ΔE ΔE l b) f . h 2π 2πI hc 42.10: a) E k mr , and solving for k , λ 2 2πc k mr 205 N m. λ
4. 1 2 42.11: Energy levels are E En El n ω l (l 1) 2 2I 1 n (0.269 eV) l (l 1) (2.395 10 4 eV) where the values are from 2 Examples 42.2 and 42.3. a) n 0, l 1 n 1, l 2 : E E f Ei (1)(0.2690 eV) (4)(2.395 104 eV) 0.2700 eV hc (6.626 1034 J s)(2.998 108 m s) λ E (0.2700 eV)(1.602 1019 J eV) 4.592 10 6 m. b) n 0, l 2 n 1, l 1 : E E f Ei (1)(0.2690 eV) (4)(2.395 104 eV) 0.2680 eV hc (6.626 10 34 J s)(2.998 108 m s) λ E (0.2680 eV)(1.602 1019 J eV) λ 4.627 10 6 m c) n 0, l 3 n 1, l 2 : E E f Ei (1)(0.2690 eV) (6)(2.395 104 eV) 0.2676 eV hc (6.626 1034 J s)(2.998 108 m s) λ 19 4.634 10 6 m. ΔE (0.2676 eV)(1.602 10 J eV) 42.12: ω k mr 2k m 3.14 10 20 J 0.196 eV, where mr m 2 has been used.
5. ω 1 k 42.13: a) f 2π 2π mr m1m2 2πf 2 k mr 2πf 2 m1 m2 (1.67 10 27 kg ) (3.15 10 26 kg)[2π (1.24 1014 Hz)]2 k (1.67 10 27 kg 3.15 10 26 kg) k 963 N m 3 1 b) E n ω n ω ω hf 2 2 E 6.63 1034 J s 1.24 1014 Hz 8.22 1020 J 0.513 eV c 3.00 108 m s c) λ 2.42 10 6 m infrared f 1.24 10 Hz 14 42.14: a) As a photon, λ hc 6.63 1034 J s 3.00 108 m s 0.200 nm. E 6.20 103 eV 1.60 1019 J eV b) As a matter wave, λ h h 6.63 10 J s 34 0.200 nm and p 2mE 2 9.11 10 31 kg 37.6 eV 1.60 10 19 J eV c) as a matter wave, λ h 6.63 1034 J s 0.200 nm . 2mE 2 1.67 10 27 kg 0.0205 eV 1.60 1019 J eV 42.15: The volume enclosing a single sodium and chlorine atom 2 2.82 1010 m 3 4.49 1029 m 3 . So the density m mCl 3.82 1026 kg 5.89 1026 kg ρ Na V 4.49 10 29 m3 ρ 2.16 103 kg m3 .
6. 42.16: For an average spacing a, the density is ρ m a 3 , where m is the average of the ionic masses, and so a 3 m 6.49 10 26 kg 1.33 10 25 kg 2 3.60 10 29 m 3 , ρ (2.75 10 kg m ) 3 3 and a 3.30 10 10 m 0.330 nm . b) The larger (higher atomic number) atoms have the larger spacing. hc (6.63 10 34 J s) (3.00 108 m s) 42.17: E 13 2.14 10 13 J λ 9.31 10 m 1.34 106 eV 1.34 106 eV So the number of electrons that can be excited to the conduction band is n 1.12 eV 1.20 106 electrons. hc 42.18: a) 2.27 10 7 m 227 nm , in the ultraviolet. E b) Visible light lacks enough energy to excite the electrons into the conduction band, so visible light passes through the diamond unabsorbed. c) Impurities can lower the gap energy making it easier for the material to absorb shorter wavelength visible light. This allows longer wavelength visible light to pass through, giving the diamond color. 42.19: a) To be detected the photon must have enough energy to bridge the gap width E 1.12 eV λ hc 6.63 1034 J s 3.00 108 m s 1.11 10 6 m , in the infrared. E 1.12 eV 1.60 10 J eV 19 b) Visible photons have more than enough energy to excite electrons from the valence to conduction band. Thus visible light is absorbed, making silicon opaque. 42.20: vrms 3kT m 1.17 105 m s , as found in Example 42.9. The equipartition theorem does not hold for the electrons at the Fermi energy. Although these electrons are very energetic, they cannot lose energy, unlike electrons in a free electron gas.
7. 2 2ψ 2ψ 2ψ 42.21: a) 2 2 2 Eψ x 2m y z nx πx n πy n πz where ψ A sin sin y sin z L L L 2 2ψ n π 2ψ 2ψ x ψ , and similarly for and 2 . x 2 L y 2 z 2 n x π n y π n z π 2 22 ψ Eψ 2m L L L E nx n y nz π 2 2 2 2 2 2mL2 3π 2 2 b) Ground state nx n y nz 1 E , 2mL2 The only degeneracy is from the two spin states. The first excited state 2, 1, 1 or 1, 2, 1 3π 2 2 or 1, 1, 2 E and the degeneracy is 2 3 6 . mL2 9π 2 2 The second excited state 2, 2, 1 or 2, 1, 2 or 1, 2, 2 E and the 2mL2 degeneracy is 2 3 6 . 1 ψ dV 2 42.22: L 2 nx πx L 2 n y πy L 2 nz πz A sin 2 dx sin L dy sin L dz 0 L 0 0 3 L A , 2 2 so A 2 L (assuming A to be real positive). 32
8. 42.23: Density of states: g E 2m 3 2 V E 1 2 2π 2 3 (2(9.11 10 31 kg)) 3 2 (1.0 10 6 m 3 )(5.0 eV)1 2 (1.60 10 19 J eV)1 2 g E 2π 2 (1.054 10 34 J s) 3 9.5 10 40 states J 1.60 10 19 J eV 1.5 10 states eV. 22 42.24: Equation (42.13) may be solved for nrs 2mE L π , and substituting this 12 into Eq. (42.12), using L3 V , gives Eq. (42.14). n 2 π 2 2 42.25: Eq.(42.13): E rs 2 2mL L nrs 2mE π 0.010 m 2(9.11 10 31 kg) (7.0 eV) (1.60 10 19 J eV) π (1.054 10 34 J s) nrs 4.3 10 7. 3 42.26: a) From Eq. (42.22), Eav EF 1.94 eV. 5 b) 2E m 21.94 1.60 10 19 J eV 8.25 105 m s . 9.11 10 31 kg c) EF 3.23 eV 1.60 1019 J eV 3.74 104 K. k 1.38 10 23 J K π 2 kT π 2 1.38 10 23 J K 300 K 42.27: a) CV 2E R 25.48 eV 1.60 1019 J eV R F CV 0.0233 R 0.194 J mol K. 0.194 J mol K b) 7.68 10 3 . 25.3 J mol K c) Mostly ions (see Section 18.4).
9. 42.28: a) See Example 42.10: The probabilities are 1.78 10 7 , 2.37 10 6 , and 1.51 105 . b) The Fermi distribution, Eq. (42.17), has the property that f EF E 1 f E (see Problem (42.46)), and so the probability that a state at the top of the valence band is occupied is the same as the probability that a state of the bottom of the conduction band is filled (this result depends on having the Fermi energy in the middle of the gap). 1 42.29: f E E EF kT e 1 1 EF E kT ln f E 1 EF E 1.38 10 23 J K 300 K ln 1 4 1 4.4 10 EF E 3.20 10 20 J E 0.20 eV. So the Fermi level is 0.20 eV below the conduction band. 42.30: a) Solving Eq. (42.23) for the voltage as a function of current, kT I kT 40.0 mA V ln 1 I e ln 3.60 mA 1 0.0645 V. e S b) From part (a), the quantity eeV kT 12.11 , so far a reverse-bias voltage of the same magnitude, 1 I I S e eV kT 1 I S 1 3.30 mA . 12.11
10. 42.31: I IS eeV kT 1 IS e 1 eV kT 1 a) eV 1.60 1019 C 1.50 102 V 0.580 kT 1.38 10 23 J K 300 K 9.25 103 A IS 0.0118 A. e0.580 1 Now for V 0.0100 V, eV kT 0.387 I 0.0118 A e 0.387 1 5.56 10 3 A 5.56 mA eV b) Now with V 15.0 mV, 0.580 kT I 0.0118 A e 0.580 1 5.18 103 A . eV If V 10.0 mV 0.387 kT I 0.0118 A e 0.387 1 3.77 10 3 A . 22 hλ 42.32: See Problem (42.7): I 2 7.14 10 48 kg m 2 . E 2π c 42.33: a) p qd 1.60 10 19 C 2.4 10 10 m 3.8 10 29 C m p 3.0 10 29 C m b) q 10 1.3 10 19 C d 2.4 10 m c) q e 0.78 p 1.5 1030 C m q 10 9.4 10 21 C d) d 1.6 10 m q e 0.059 This is much less than for sodium chloride (part (c)). Therefore the bond for hydrogen iodide is more covalent in nature than ionic.
11. 42.34: The electrical potential energy is U 5.13 eV, and 1 e2 r 2.8 10 10 m. 4πε0 U 42.35: a) For maximum separation of Na and Cl for stability: e2 U 4πε0 r 5.1 eV 3.6 eV 1.60 10 19 J eV 2.40 10 19 J (1.60 10 19 C) 2 r 19 9.6 10 10 m. 4πε0 (2.40 10 J ) b) For K and Br : U e2 4πε0 r 4.3 eV 3.5 eV 1.60 10 19 J eV 1.28 10 19 J (1.60 10 19 C) 2 r 1.8 10 9 m. 4πε0 (1.28 10 19 J) 42.36: The energies corresponding to the observed wavelengths are 3.29 1021 J, 2.87 10 21J, 2.47 10 21 J, 2.06 10 21 J and 1.65 10 21 J. The average spacing of these energies is 0.410 10 21 J and using the result of Problem (44-4), these are seen to correspond to transition from levels 8, 7, 6, 5 and 4 to the respective next lower levels. 2 Then, 0.410 10 21 J , from which I 2.71 10 47 kg m 2 . I
12. I I (mH mCl ) 42.37: a) Pr. (44.36) yields I 2.71 10 47 kg m 2 , and so r mr mH mCl (2.71 10 47 kg m 2 ) (1.67 10 27 kg 5.81 10 26 kg) r (1.67 10 27 kg 5.81 10 26 kg) r 1.29 10 10 m. 2 l2 b) From l l 1 : E l l 1 l 1l . But E hc l 2πcI 2I I λ λ 4.84 10 4 m . So the l-values that lead to the wavelength of Pr. (44-32) are: λ 4.84 10 4 m λ 6.04 10 5 m : l 8. 6.04 10 5 m Similarly for: λ 6.90 10 5 m : l 7; λ 8.04 10 5 m : l 6 λ 9.64 10 5 m : l 5; λ 1.204 10 4 m : l 4. c) The longest wavelength means the least transition energy (l 1 l 0) (1) (1.054 10 34 J s) 2 E 47 4.10 10 22 J 2.71 10 kg m 2 hc λ 4.85 10 4 m. E d) If the hydrogen atom is replaced by deuterium, then the reduced mass changes to mr 3.16 1027 kg. Now, l2 hc 2πcI 2πcmr r 2 E λ I λ l l m 3.16 10 kg 27 λ r λ m 1.62 10 27 kg λ (1.95)λ r So for l 8l 7: λ (60.4 μm) (1.95) 118 μm. l 7 l 6: λ (69.0 μm) (1.95) 134 μm. l 6 l 5: λ (80.4 μm) (1.95) 156 μm. l 5l 4: λ (96.4 μm) (1.95) 188 μm. l 4 l 3: λ (120.4 μm) (1.95) 234 μm.
13. 42.38: From the result of Problem (42.9), the moment inertia of the molecule is 2l hlλ I 2 6.43 10 46 kg m 2 E 4π c and from Eq. (42.6) the separation is I r0 0.193 nm. mr
14. L2 2l (l 1) 42.39: a) Eex . 2I 2I E g 0 (l 0), and there is an additional multiplicative factor of 2l + 1 because for each l state there are really 2l 1 ml states with the same energy. l ( l 1) 2 nl kT So (2l 1)e 2 I n0 b) T 300 K, I 1.449 10 46 kg m 2 . 2 (1) (1 1) (i) El 1 46 7.67 10 23 J. 2(1.449 10 kg m ) 2 El 1 7.67 10 23 J 0.0185. kT (1.38 10 23 J K) (300 K) (2l 1) 3 n so l 1 (3)e 0.0185 2.95. n0 El 2 2 (2) (2 1) (ii) 0.0556. kT 2(1.449 10 46 kg m 2 ) (1.38 10 23 J K ) (300 K) (2l 1) 5. nl 1 (5)(e 0.0556 ) 4.73. n0 El 10 2 (10) (10 1) (iii) 1.02. kT 2(1.449 10 46 kg m 2 ) (1.38 10 23 J K ) (300 K) n (2l 1) 21 so l 10 (21) (e 1.02 ) 7.57. n0 El 20 2 (20) (20 1) (iv) 3.89. kT 2(1.449 10 46 kg m 2 ) (1.38 10 23 J K ) (300 K) (2l 1) 41. nl 20 (41)e 3.89 0.838. n0
15. 42.40: a) I co 1.449 10 46 kg m 2 . 2l (l 1) 1.054 1034 J s) 2 (1) (1 1) El 1 7.67 10 23 J. 2I 2(1.449 10 46 kg m 2 ) El 0 0. E 7.67 10 23 J 4.79 10 4 eV. hc (6.63 10 34 J s) (3.00 108 m s) λ 2.59 10 3 m 2.59 mm. E (7.67 10 23 J) b) Let’s compare the value of kT when T=20 K to that of E for the l 1 l 0 rotational transition: kT (1.38 10 23 J K) (20 K) 2.76 10 22 J. kT E 7.67 10 23 J (from part (a)). So 3.60. E Therefore, although T is quite small, there is still plenty of energy to excite CO molecules into the first rotational level. This allows astronomers to detect the 2.59 mm wavelength radiation from such molecular clouds.
16. mNa mCl 2 42.41: a) I mr r 2 r mNa mCl (3.8176 10 26 kg) (5.8068 10 26 kg) (2.361 10 10 m) 2 (3.8176 10 26 kg 5.8068 10 26 kg) I 1.284 10 45 kg m 2 For l 2 l 1 : 2 2(1.054 10 34 J s) 2 E E2 E1 (6 2) 1.730 10 23 J 2 I 1.284 10 45 kg m 2 hc λ 0.01148 m 1.148 cm. E 2 1 For l 1 l 0 : E E1 E0 (2 0) (1.730 10 23 J) 2I 2 8.650 10 24 J hc λ 2.297 cm. E b) Carrying out exactly the same calculation for Na 37 Cl, where mr (37) 2.354 10 26 kg and I(37) 1.312 10 45 kg m 2 we find for l 2 l 1: E 1.693 10 23 J and λ 1.173 cm. For l 1 l 0 : E 8.465 10 24 J and λ 2.347 cm. So the differences in wavelength are: l 2 l 1 : λ 1.173 cm 1.148 cm 0.025 cm. l 1 l 0: λ 2.347 cm 2.297 cm 0.050 cm. E 42.42: The vibration frequency is, from Eq. (42.8), f 1.12 1014 Hz. The force h constant is k (2πf ) 2 mr 777 N m . 1 k 1 2k 42.43: En n E0 2 mr 2 mH 1 2(576 N m) E0 (1.054 10 34 J s) 4.38 10 20 J 0.274 eV. 2 1.67 10 27 kg This is much less than the H 2 bond energy.
17. 42.44: a) The frequency is proportional to the reciprocal of the square root of the reduced mass, and in terms of the atomic masses, the frequency of the isotope with the deuterium atom is 12 12 m m (mH mF ) 1 (mF mD ) f f0 F H m m ( m m ) f 0 1 (m m ) . F D D F F H Using f 0 from Exercise (42.13) and the given masses, f 8.99 1013 Hz. mH mI r 2 42.45: a) I mr r 2 (1.657 10 27 kg) (0.160 10 9 m) 2 mH mI 4.24 10 47 kg m 2 b) Vibration-rotation energy levels are: 2 1 k El l (l 1) h 2I 2 mr 2 1 k l (l 1) n hf since : ω 2πf 2I 2 mr i) n 1, l 1 n 0, l 0 : 2 3 1 2 E (2 0) hf hf . 2I 2 2 I hc hc c 3.00 108 m s λ 2 . E 3.96 1011 Hz 6.93 1013 μ hf f I 2I λ 4.30 10 6 m. ii) n 1, l 2 n 0, l 1 : 2 E (6 2) hf 2I c 3.00 108 m s λ 4.28 10 6 m. 2 2(3.96 1011 Hz) 6.93 1013 Hz 2 2πI f iii) n 2, l 2 n 1, l 3 2 E (6 12) hf 2I c 3.00 108 m s λ 4.40 10 6 m. 2 3(3.96 1011 Hz) 6.93 1013 Hz 3 2I f
18. 42.46: The sum of the probabilities is 1 1 f ( EF E ) f ( EF E ) E kT E kT e 1 e 1 E / kT 1 e E kT e 1 1 e E kT 1. 42.47: Since potassium is a metal we approximate E F E F0 . 32 3 π 4 3 2 n 2 3 EF 2m ρ But the electron concentration n m 851 kg m 3 n 26 1.31 10 28 electron m 3 6.49 10 kg 32 3 π 4 3 (1.054 10 34 J s) 2 (1.31 10 28 /m 3 ) 2 3 EF 31 3.24 10 19 J 2.03 eV. 2(9.11 10 kg) 42.48: a) First we calculate the number-density of neutrons from the given mass-density: n (7.0 1017 kg m 3 ) / 1.67 10 27 kg neutron ) 4.2 10 44 m 3 . Now use Eq. 44.21 2 4 1 2 4 2 3 3 π 3 2 n 3 3 3 π 3 (6.63 10 34 J s 2π ) 2 (4.2 10 44 m 3 ) 3 EF 0 27 1.8 10 11 J. 2m 2(1.67 10 kg ) b) Set kT EF0 (see Exercise 42.26) to obtain EF 0 (1.8 10 11 J ) T 1.3 1012 K. k (1.38 10 28 J K ) 42.49: a) Each unit cell has one atom at its center and 8 atoms at its corners that are each shared by 8 other unit cells. So there are 1 8 8 2 atoms per unit cell. n 2 9 4.66 10 28 atoms m 3 V (0.35 10 m) 3 23 32 3 π 4 3 2 N b) E F0 2m V In this equation N V is the number of free electrons per m 3 . But the problem says to assume one free electron per atom, so this is the same as n V calculated in part (a). m 9.109 10 31 kg (the electron mass), so EF0 7.563 10 19 J 4.7 eV
19. d αe 2 1 1 42.50: a) U tot 2 8A 9 . dr 4πε0 r r Setting this equal to zero when r r0 gives 8 A4πε0 r07 αe 2 and so αe 2 1 r07 U tot . 4πε0 r 8r 8 At r r0 , 7αe 2 U tot 1.26 10 18 J 7.85 eV. 32πε0 r0 b) To remove a Na Cl ion pair from the crystal requires 7.85 eV. When neutral Na and Cl atoms are formed from the Na and Cl atoms there is a net release of energy 5.14 eV 3.61 eV 1.53 eV, so the net energy required to remove a neutral Na, Cl pair from the crystal is 7.85 eV 1.53 eV 6.32 eV. 23 3 3 32 3 π 4 3 2 N 42.51: a) Eav EF 0 . Etot NEav . 5 5 2m V 1 3 dEtot 2 3 32 3 π 4 3 2 N N N dV 3 5 2m V V 2 53 32 3 π 4 3 2 N . 5m V 53 dEtot 32 3 π 4 3 2 N P . dV 5m V N b) 8.45 10 28 m 3 V 32 3 π 4 3 (1.054 10 34 J s) 2 p (8.45 10 28 m 3 ) 5 3 5(9.11 10 31 kg) 3.80 1010 Pa 3.76 105 atm (!) c) There is a large attractive force on the electrons by the copper ions.
20. 42.52: a) From Problem (42.51): 53 32 3 π 4 3 2 N p . 5m V dp 5 32 3 π 4 3 2 N 2 3 N B V V 2 dV 3 5m V V 5 p. 3 N b) 8.45 10 28 m 3 . V 5 32 3 4 32 B (8.45 10 28 m 3 ) 5 3 6.33 1010 Pa. 3 5m 6.33 1010 Pa c) 0.45. The copper ions themselves make up the remaining 1.4 1011 Pa fraction. 23 32 3 π 4 3 2 N 42.53: a) EF0 . 2m V 32 1 N 2m 2 c 2 23 2 m 3c 3 23 2 m 3c 3 Let EF 0 mc 2 23 43 2 100 V (100)3 π 1003 23π 2 3 3000π 2 3 3 1.67 10 m . 33 8.45 10 28 m 3 b) 5.06 10 5. 1.67 1033 m 3 Since the real concentration of electrons in copper is less than one part in 10 4 of the concentration where relativistic effects are important, it is safe to ignore relativistic effects for most applications. 6(2 1030 kg) c) The number of electrons is N e 6.03 1056. The 1.99 10 26 kg Ne 6.03 1056 concentration is 4 6.66 1035 m 3 . V 3 π (6.00 106 m) 3 6.66 1035 m 3 d) Comparing this to the result from part (a) 400 so relativistic effects 1.67 1033 m 3 will be very important.
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# Find the area of the region bounded by the given curves.$y = x^2 e^{-x}$ , $y = xe^{-x}$
## $\frac{3}{e}-1 \approx 0.104$
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the problem is find this higher ear off region bonded, even curves wise before to x squared being Have you connected wax? Why is there too ex terms in tow? Make two backs first. We light isn't your functions. Uh, you cool and blind. The intersection point this square. My ice. Where to? Next Zero. So we have X is equal to zero. Work actually is a good one. The interval. There are only two. Why? Come on. Axe is between these two points. We have extensive connective box is rich is on I square has to make remarks, sells air rear of this region is into girl from one to two eyed smiles X square. I have seen toe naked backs Jax. Now, for this problem, we can use division. My parts honor is integral off. You would have to be from the ex. It's the call to do camp spinning Wyness into through your prom. Have bean, Jax. Then we can light. You see? Could I smile us X square? Andi reprise records into next works. Ben, you prom is equal to one last two lakhs being using connective too. Make it two. This into your own too this foreigner, This is Echo Two negative X minus. Excluded Hamson into ninety bucks. Wanted to minus and to grow up your prime times. These is class into a twenty to one minus two lives. You two make the box next. So think on too. But here the first term notices negative reply to unwind with dysfunctions. Thatis invective. Two month or into negative too. And minus zero. And then plus this integral. We can also use new substitution on that you is too one minus two ax on being promised. They would too mixed works. So you promised they would connect to the they could connective into the backs. Then is this integral? Has the cold too? You'd have swing. This's one month's too likes times active in connect LAX. I want to too minus into a girl of your prom. Temps, please. This is to you to make marks. I wanted to announces from zero to one. Sorry. Just found the right. One zero to one. There are two lines. And then this money with this zero minus zero with Krista term his zero. And it's a cycle. The chair, miss one last two likes. I have selected negative vibes from zero to one minus into Europe. From zero to one, you're crowned. How spaces to perhaps interconnected lacks yaks. This is Cho Choo loving one zero two dysfunction we have This is this next two one times negative to make. You want to make you one minus. This is one times next to you. What? This is possible. Thiss minus active to to take your marks from you. No one. This is control you can make to Juan. Plus one one minus connected to have to want pass two. There it is three times to make you want and minus one.
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# User:Shahriar Alam
I'm currently enrolled in the Master's program in Mechanical Engineering at Michigan Technological University. I've started my graduate studies in fall'18 and my course-works are centered around design and manufacturing.
Completion of my bachelor's was done from Islamic University of Technology, Dhaka, Bangladesh. Studying from one of the best from my country has given me the opportunity to explore my topics of interests and I had the privilege to work in South Asia's biggest mechanical lab. Where I got hands on experience to different mechanical equipment and projects which resulted in my enhancing fixation upon a research oriented career.
# Projects & Research Experiences
## Modeling Micro Resonator Dynamics
During my fall'18 semester I got the opportunity to work on a project under the supervision of Dr. Fei Long and Dr. Radheshyam Tewari. My work was to develop a single degree of freedom model and check the shifting of resonating frequency with variation in dimension using bode plot. Modeling of the single DOF was done using simulink. Upon the results, the influence of dimension of the micro-resonator was analyzed as a part of Design of Experiments.
## Analytical Assessment of Sweet Spot and Performance of a Cricket Bat
As an athlete, I had an immense interest in sports equipment and accessories, which led me to my undergrad research, “Analytical Assessment of Sweet Spot and Performance of Cricket Bat”. Cricket bats were designed using SOLIDWORKS and in ANSYS16 workbench, modal analysis was done considering Free-Free boundary condition. Material properties of English Willow were used. Different values (mass, the center of mass, fundamental frequency and moment of inertia) were calculated experimentally and matched with the values in Finite Element Analysis for free-free boundary condition. Batsmen use differently designed bats with different Edge Thicknesses according to their shot preferences and match situations. The maximum edge thickness of a bat is typically 330mm-390mm from the bat shoulder and so is the sweet spot found to exist in the simulation. I saw batters changing their bats according to the game conditions which in almost every case hampered both the flow of game and batsmen. Then I came up with an idea of designing a bat with a uniform edge thickness, having a comfortable pick-up weight, which batters of every playing style can use. Now, I’m working on how much force is transferred to the bat handle when a ball hits the sweet spot of the bat while playing different shots using Explicit Dynamics and I want to find out how much strain is imposed upon a batter’s wrist and elbow while playing different shots.
## ISCEA (International Supply Chain Education Alliance) Case Competition
In 2015, I participated in global case competition arranged by ISCEA. My work was to implement an efficient supply chain management in the apparel industry of Bangladesh. This competition widened my idea and perception regarding corporate world. My team IUTB-0108 placed in the top 20 global and top 8 regional teams. As a result of this brilliant outcome, my team was offered scholarship and our course fee of Certified Supply Chain Analyst was 100% waived. I got to acquire a lot about lean manufacturing and combining mid-level management for the maximum profit with minimum resource available and that too in reduced time.
## Color Sensing Auto Actuated Robot
My robotics project, “Auto-actuated Color Sensing Robot” was well appreciated in the different national project showcasing competitions. I came out runner-up in project showcasing competition at Mecceleration, country's biggest mechanical festival. The robot’s function was to automatically detect if an object is placed in-front of it. Then sensing color of the object its function was to put the objects in their respective pots. I used three servo-motors for actuations, one for the rotation of the base, one for the oscillation of the mechanical arm and the other one was for the opening and closing of the claw. The whole robot was hand-made, using plywood. Two sensors (Sonar sensor and RGB color sensor) were used. Design and measurements were done in SolidWorks. Coding and calibration were done using Arduino-Uno. Calibration was done in four colors (Red, Green, Black, White). The main theme of my project was to bring automation to the sorting of containers in shipyards.
# Research Interests
During my undergrad I had the opportunity to work as a trainee in country's renowned power-plant, fertilizer factory, Automotive Industry and Apparel Industry. This training made me interested in different research topics, upon which I want to pursue my PhD.
Additive Manufacturing was something rarely known in Bangladesh. But I was lucky enough. Training done in Beximco Textiles, gave me the opportunity to experience the extensiveness of 3D printing. I was sure by then that AM is going to be the next big thing and there are lot of aspects that may be improved in this field and lot of sectors can be explored, which in turn is sure to bring about revolution in the field of Technology.
### Bio-printing
Bio-printing to me is something that's going to change everything. While applying for grad school I came to know about the advancement of 3D printing in this sector. I was amazed how bio-printing is going to make our medical science grow and flourish. Printing of cartilage tissues, vascular channels, heart etc really amazed me. The most that made me interested that these printed organs were ready to be used and functioned well, just like real ones.
### Bio-materials
Bio-material makes the bio-printing viable. Bio-ink and their ability to support living cells was something mention-worthy. While going through research and publication related to bio-printing, I came to know about Hydrogel, pluronic 127 etc fugitive inks that aid the extrusion based organ printing. I also have some ideas to create vascular channels in organs with nano-fibers stamped with them to increase the ability of the organs to withstand more stress.
### Metal 3D Printing
Printed object in Additive Manufacturing being ready for use attracts my curiosity towards metal printing. Metal printing makes the printed object being ready for use. It enhances the utility of 3D printing. As 3D printing can make complex geometries to be printed in a single and simple step, I think selection of perfect printable metal in this case will add a new dimension to AM.
## Energy Storage Systems
Currently I'm working on a project on using super-capacitor with energy storage systems. As super-capacitor's peak voltage and current are very high, they can absorb maximum energy and then pass it towards the storage system without affecting the life-cycle of battery-like energy storage systems. I'm also interested in Hydrogen Energy Storage and going through the latest research works on Hydrogen collection and storing them for usage in electric vehicle or in industries to reduce carbon foot-print.
## Electrification in Automotive Systems
Course on Intro to Hybrid Electric Vehicle and Propulsion system drove towards the electrification of automotive systems. I found that most of the regenerative braking is lost in heat to save the battery in an HEV or BEV. I thought that selection of material in super-capacitor and using them in parallel to battery can enhance life-cycle and also make the most use of regenerative braking.
# Goals
Applying what I learnt during my course of study and depicting them to the reality is my aim. I'll be soon done with my master's. Before my graduation I want to have hands-on experience. I want to give a shape to my ideas that will boost my confidence and make me an accomplished candidate while I go for a research-oriented career.
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# Model Building
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I have built 5 garages that do not have roofs that I am placing in a sandbox for students to use. Their assignment is to add one of the 5 roof truss designs that they drew to the top of their garage. I think I used a common original building but just modified the texture on each version. All objects are linked and the building will support fourteen 28 foot roof trusses.
When I was attempting to fine tune the placement of the garages within the sandbox I noticed that the building origin was not at the same location for one of the buildings. All z locations are the same but either x or y should be the same with one of the locations adjusted for the spacing between the garages.
SL is down right now but why would the origin of one build be different that anther one?
• Replies 184
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1 hour ago, IvyTechEngineer said:
SL is down right now but why would the origin of one build be different that anther one?
things to check for:
position and/or size of root prim
position and/or size of linked prims relative to root prim
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That is the puzzle. It doesn't male sense. All the building were created from the same base model. The first model is created and all the building elements are linked. Floor and walls are textured and it is ready for a new roof.
The first building is place in my sandbox @ x = 190, y=250 and z=1.623
The second building is then copied from the first @ x = 180, y=250 and z=1.623
Then I unlink the second building, re-texture and relink. Everything look good.
The third building is then copied from the first @ x = 170, y=250 and z=1.623
Then I unlink the third building, re-texture and relink the origin has changed to
x = 174.238, y=250.022 and z=0.050.
I believe the last item selected sets the origin for the building but I could be wrong...
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14 hours ago, IvyTechEngineer said:
I believe the last item selected sets the origin for the building but I could be wrong...
The last prim selected will be the root prim. And it's the root prims ccordinates that will be displayed.
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My students have been working on 5 garage design in Solidworks and Second Life. So far so good. The design below is a King post roof truss with a width of 28 feet and pitch of 25 degrees.
Thanks for everyone's help
ivytechengineer
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On 11/15/2021 at 5:16 PM, ChinRey said:
You can always use Ctrl+Shift+Alt+4 to hide and show avatars but I think most builders simply cam away from their avatar.
Camera control is a rather important skill for builders btw. So:
• To focus on and object: Click on it while holding down the Ctrl and Alt keys.
• To shift camera sideways or up and down, hold down Ctrl, Alt and Shift and use arrow keys or move the mouse
• To rotate camera, hold down Ctrl, and Alt and use arrow keys or move the mouse
• To cam in and out, either use the mouse wheel or old down Alt and use arrow keys or move the mouse
• To revert to default camera position, hit the Escape key
One of the requirements to become a real SL builder is to fall off your work platform without noticing because you and your camera are too focused on your build.
There are several free builder grid textures available. Carl Metropolitan's is probably the most common and you can pick it up at MP: https://marketplace.secondlife.com/p/Basic-Builders-Grid-Texture/8534776 or here: https://marketplace.secondlife.com/p/Basic-Builders-Grid-Decimeter-Scaled/8667959
Or maybe you want to make your own. Metropolitan's grids only cover a 10x10 msurface since that was the size limit back when he made it. I used to solve that limitation with texture repeats but maybe it's time to come u with a new 64x64 m one?
I was also wondering if there are shortcuts to standard orthographic views like there is in CAD programs? Also, in the drawing of assemblies there are a number of mates than can be used to align the part faces, edges, etc. in CAD tools. Does SL have something like that?
Thanks
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3 hours ago, IvyTechEngineer said:
I was also wondering if there are shortcuts to standard orthographic views like there is in CAD programs?
You can't do this with large objects so easily, but with many objects you can use the build tool and rotate the object through 90 degrees on some of the axes to get aligned in different ways. Assuming you are standing facing your garage in the picture earlier, rotating it around the Z axis will get you side and front elevation views, rotating it around it's X-axis will put it into the position of a top-down view. If you really felt the need to replicate the CAD-style three-views you could have four copies of the model and put them in different alignments, however, feel trying to work in the CAD-style is not going to get you the smoothest of experiences here.
3 hours ago, IvyTechEngineer said:
lso, in the drawing of assemblies there are a number of mates than can be used to align the part faces, edges, etc. in CAD tools. Does SL have something like that?
The Builders-Buddy type aids help with precise positioning, but for a lot of us it's as easy to look at a prim's X,Y,Z positions and dimensions and from that calculate how far along one of those axes a different sized prim must be positioned so that the adjacent faces are coincident.
In some of the Third-party viewers is a command-line calculator so that you can type in expressions such as "calc 105.65 + 0.5/2.0 + 0.75/2.0" which will give you a value showing where on the axis in question you place a 0.75 cube so that one face will be up against a face of the 0.5 cube centred on 105.65 on that particular axis. It's much faster than using a calculator.
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• 1 month later...
I am looking into building a small old west town, maybe 6 buildings. The Second Life Marketplace has some builders that have buildings that might work but I am a little unclear about how to evaluate the significance of Land Impact. For example, RE Blueprint Design has a 16x16 building that has a Land Impact of 47. Is this ok? I am a little leery about buying something that has no reviews. I could spend some time and create buildings in SL myself but this may take some time to do. I have attempted to also reach out to some of the builders and only a few respond in SL. (Sent them notecards via IM but I am not sure they are still active SL users.) Suggestions?
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2 hours ago, IvyTechEngineer said:
The Second Life Marketplace has some builders that have buildings that might work but I am a little unclear about how to evaluate the significance of Land Impact.
Well, you know how many prims you have for your land. There's no need to save on them unless you risk running out.
2 hours ago, IvyTechEngineer said:
For example, RE Blueprint Design has a 16x16 building that has a Land Impact of 47. Is this ok?
That doesn't sound too bad for a good ol' prim house. It probably isn't convexed so you should be able to cut the LI down to about half too.
2 hours ago, IvyTechEngineer said:
I am a little leery about buying something that has no reviews.
I wouldn't trust MP reviews either if I was you.
But with old prim builds like these, you can usually expect that what you see is what you get. It's mainly mesh you should be a bit more careful about.
Also, consider the price. I don't know exactly which building you have in mind but most of them cost 50 or 100 L\$ each. That's roughly 20-50 US cents. Can you afford to risk that much money?
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15 hours ago, ChinRey said:
Well, you know how many prims you have for your land. There's no need to save on them unless you risk running out.
That doesn't sound too bad for a good ol' prim house. It probably isn't convexed so you should be able to cut the LI down to about half too.
I wouldn't trust MP reviews either if I was you.
But with old prim builds like these, you can usually expect that what you see is what you get. It's mainly mesh you should be a bit more careful about.
Also, consider the price. I don't know exactly which building you have in mind but most of them cost 50 or 100 L\$ each. That's roughly 20-50 US cents. Can you afford to risk that much money?
I am not so much worried about the money, it is really the land impact and the fact that some of the buildings have not been reviewed nor do they respond to my attempts to ask them questions. Also, I was thinking that some of these building could be built in SL or Blender and they might allow more customization. Some of the buildings from other builders include signage which I might need to add if it is not included. In addition, I wanted to do a rough layout of the building before buying them. This would be a great class project for my students maybe.
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If I have an object, like a coin, that has two sides, can the both the head and tail sides be merged in Blender using uploaded as a single image image in SL?
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27 minutes ago, IvyTechEngineer said:
If I have an object, like a coin, that has two sides, can the both the head and tail sides be merged in Blender using uploaded as a single image image in SL?
You may be thinking of a flat mesh which can have different textures on different sides. I have a few of those on my Marketplace for free/fullperm. You'll be able to use them for what you described.
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1 hour ago, IvyTechEngineer said:
If I have an object, like a coin, that has two sides, can the both the head and tail sides be merged in Blender using uploaded as a single image image in SL?
If it has to be one texture, it's as simple as copy pasting the 2 images into one image in an image editor. Preferably an oblong texture such as 256x512. Creating a coin in Blender and mapping the UVs onto the new image.
A slightly more complicated way is to create a coin in Blender with 2 materials and 2 UV channels. You could then bake the 2 images from 1st UV channel, to the 2nd UV channel, into one texture.
You will have to create a new coin either way, though.
Of course, if it's a prim cylinder (or a mesh unwraped in a similar way) you can just edit the texture scale to 0.5, and the offset to 0.250, in-world, when using an oblong texture.
Edited by arton Rotaru
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Sorry, one more question about uploading models with textures. If I upload a file that should include a texture, can I select the texture or should it have the same file name?
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16 minutes ago, IvyTechEngineer said:
Sorry, one more question about uploading models with textures. If I upload a file that should include a texture, can I select the texture or should it have the same file name?
While you CAN upload the textures along with the mesh object, I think the majority of people simply upload them separately and then apply them to the faces of the mesh in world.
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Maybe I'm misunderstanding something, but if he made a coin like object in blender with a cylinder. Unwrapped it and applied those texures to each side of the UV map and baked it. Wouldn't that be all he needed to do?
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33 minutes ago, IvyTechEngineer said:
Sorry, one more question about uploading models with textures. If I upload a file that should include a texture, can I select the texture or should it have the same file name?
What Fluffy said, uploading the texture separately. I pretty much always check textures with the local texture feature in-world anyway.
If the texture is applied onto the model when exporting, this texture has to be in the same folder where the exported mesh is, to be found by the importer. You need to check Include Textures in the importers Options tab as well.
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4 minutes ago, arton Rotaru said:
always check textures with the local texture feature in-world
100%! Especially once you start delving into normal and specular maps, but even with just a diffuse map I can't think of any instance where you shouldn't test with local textures before uploading.
I tend to work in 3D Coat a lot and find it really helpful to upload the mesh as soon as I'm done with retopo and LOD making. That way I can check the base AO/normal/diffuse maps to make sure they work in SL before I start texturing, and then while you're creating the textures all you have to do is hit save in whatever app you're using and the textures will automatically update on your mesh in SL, which is exceptionally useful!
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22 minutes ago, Janet Voxel said:
Maybe I'm misunderstanding something, but if he made a coin like object in blender with a cylinder. Unwrapped it and applied those texures to each side of the UV map and baked it. Wouldn't that be all he needed to do?
With the coin images as they are, it would require to scale, and move them in Blender, to avoid overlapping UVs. Doing that will lead to the same result when baking indeed.
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Just wanted to add since I mentioned normal maps, etc. you could also look into using one of several tools available to generate depth and cavity maps for the coin texture which you could then use to create the normal and specular maps needed for SL materials.
Anyway, it would be a really nice touch, but it's best to stick to mastering the basics first, especially when it comes to sensible texture resolutions based on object size, because as nice and shiny as those coins may look with 3 high resolution 1024 x 1024 textures on your creative efforts will most certainly draw the ire of others. 😄
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3 hours ago, Janet Voxel said:
Maybe I'm misunderstanding something, but if he made a coin like object in blender with a cylinder. Unwrapped it and applied those texures to each side of the UV map and baked it. Wouldn't that be all he needed to do?
I have used Blender but am no expert. Textures are something new for me so I watch a lot of YouTube videos. I typically do more CAD work outside of Blender. To create the texture I ultimately used I started with
and then moved onto
I used Photoshop and paint.net to merge the two sides of the coin and that worked ok. Photoshop was used to crop the images and paint,net was used to merge all the images together into a single image.
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3 hours ago, arton Rotaru said:
What Fluffy said, uploading the texture separately. I pretty much always check textures with the local texture feature in-world anyway.
If the texture is applied onto the model when exporting, this texture has to be in the same folder where the exported mesh is, to be found by the importer. You need to check Include Textures in the importers Options tab as well.
Thanks, I wanted to minimize the cost (i know that is lame) but thought if I could create a single texture that it would be better. When you upload a model the Include Textures can be selected as well and somehow SL knows what texture needs to be uploaded. Maybe that info is embedded in the DAE file?
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2 hours ago, Fluffy Sharkfin said:
100%! Especially once you start delving into normal and specular maps, but even with just a diffuse map I can't think of any instance where you shouldn't test with local textures before uploading.
I tend to work in 3D Coat a lot and find it really helpful to upload the mesh as soon as I'm done with retopo and LOD making. That way I can check the base AO/normal/diffuse maps to make sure they work in SL before I start texturing, and then while you're creating the textures all you have to do is hit save in whatever app you're using and the textures will automatically update on your mesh in SL, which is exceptionally useful!
Thanks. I am not sure I totally understand what you said. My background is really CAD (Solidworks) and Blender to translate to a DAE file. Not much experience with textures per se. I have used Photoshop and paint.net (free) but still just a hack ... lol
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1 hour ago, IvyTechEngineer said:
I used Photoshop and paint.net to merge the two sides of the coin and that worked ok. Photoshop was used to crop the images and paint,net was used to merge all the images together into a single image.
You can do all that in PS easily. What I would do is resizing the images to 128x128 (Bilinear). Create a new image with the size of 128x256. Ctrl-A > Ctrl-C > Ctrl-V into the new image. Move one up, and one down (hold Shift to keep it in the middle). Merge the layers (Ctrl-E). Add some padding by duplicating the layer. Move it below the original layer and give it some gaussian blur. Copy the blurred layer several times until you have something like this.
Activate the background layer and save as Targa 24 bits/pixel.
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7 hours ago, IvyTechEngineer said:
Thanks. I am not sure I totally understand what you said. My background is really CAD (Solidworks) and Blender to translate to a DAE file. Not much experience with textures per se. I have used Photoshop and paint.net (free) but still just a hack ... lol
I was just extolling the virtues of the Local Textures feature which you can (and should) learn more about from this wiki page
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# The probability of two random points on a plane being closer than a certain distance?
• Oct 13th 2011, 01:58 AM
ingenious
The probability of two random points on a plane being closer than a certain distance?
Hi,
I've been struggling with the following problem for some time now, and it seems that I need some pro help:
I have a process that generates a point $\displaystyle x$ on a plane, and I need to find the pdf $\displaystyle p(x)$ of that point. The process goes like this: First, points $\displaystyle x_1$ and $\displaystyle x_2$ are independently generated on the plane with pdfs $\displaystyle p_1(x_1)$ and $\displaystyle p_2(x_2)$. Then, only if the two points are closer than a certain distance $\displaystyle r$, i.e. $\displaystyle ||x_1 - x_2|| < r$, I take as my point $\displaystyle x \equiv x_1$.
This point $\displaystyle x$ is used for Monte Carlo integration, and if I use the pdf $\displaystyle p(x) = p_1(x_1) p_2(x_2) \pi r^2$ it all works nicely. However, I'm having a hard time justifying this particular pdf. I see two possible ways: (1) this pdf is a decent approximation of the real pdf; (2) this pdf is an unbiased estimate of the real pdf. More specifically, $\displaystyle \pi r^2$ is the result of a one-sample Monte Carlo estimation of the integral that appears due to the distance probability.
I'm having a hard time mathematically formulating this pdf. Any ideas? Thanks very much in advance!
• Oct 14th 2011, 10:17 AM
Laurent
Re: The probability of two random points on a plane being closer than a certain dista
Hi,
As far as I understand, you define $\displaystyle X$ to be $\displaystyle X_1$ conditioned to be at distance smaller than $\displaystyle r$ to $\displaystyle X_2$, right? In other words, you sample $\displaystyle X_1$ and $\displaystyle X_2$ repeatedly until they are closer than $\displaystyle r$ from each other and then you set $\displaystyle X=X_1$. Is that indeed it?
If so, first the law of $\displaystyle X$ should not symmetric with respect to $\displaystyle p_1$ and $\displaystyle p_2$ as they have different roles. And second there is no meaning to writing $\displaystyle p(x)$ as a function of $\displaystyle x_1,x_2$ which are not defined in terms of $\displaystyle x$? So something has to be wrong; it may be my understanding, but let's carry on.
Given my rewriting of the problem, the pdf of $\displaystyle X$ is derived as follows (I use a slightly sloppy notation "dx" that stands for an "infinitesimal subset around x"; you can turn it to fully rigorous by writing a Borel set A instead of dx, but I feel this writing with dx gives more feeling of what happens):
$\displaystyle P(X\in dx)=P(X_1\in dx |\, \|X_2-X_1\|<r)=\frac{P(X_1\in dx, X_2\in D(x,r))}{P(\|X_2-X_1\|<r)}$ $\displaystyle =\frac{P(X_1\in dx)P(X_2\in D(x,r))}{P(\|X_1-X_2\|<r)}$
hence
$\displaystyle P(X\in dx)=\frac{p_1(x) \int_{D(x,r)}p_2(y)dy}{\int_{\{\|z-y\|<r\}}p_1(y)p_2(z)dy dz}\,dx$
so the pdf is the function on the right hand side.
If $\displaystyle p_2$ is continuous at $\displaystyle x$, the integral at the numerator is close to $\displaystyle p_2(x)\pi r^2$ when $\displaystyle r$ is small. Then, for small $\displaystyle r$, one may say that the pdf $\displaystyle p$ of $\displaystyle X$ is close to $\displaystyle \frac1C p_1(x)p_2(x)$, where $\displaystyle C=\int p_1(y)p_2(y)dy$ (so that $\displaystyle p$ integrates to 1).
I hope this answers your question. Feel free to ask for further details. Or to make your question more specific, if I got it wrong.
• Oct 14th 2011, 11:43 AM
ingenious
Re: The probability of two random points on a plane being closer than a certain dista
The generated point will be used for Monte Carlo integration of a function that is defined everywhere where $\displaystyle x_1$ can be (e.g. the whole plane). Actually, I can already use $\displaystyle x \equiv x_1$ for the MC integration with PDF $\displaystyle p(x) = p_1(x_1)$. Just that I want to have another sampling strategy that takes $\displaystyle x_1$ only if a random point $\displaystyle x_2$ with PDF $\displaystyle p_2(x_2)$ lands within a distance $\displaystyle r$ of $\displaystyle x_1$.
Therefore, I'm not sure about whether this normalization is needed. Otherwise the nominator looks OK: If I assume that $\displaystyle p_2$ is constant within the $\displaystyle r$-neighborhood around $\displaystyle x_1$, then I can take $\displaystyle p_2(y)$ out of the integral as $\displaystyle p_2(x_2)$ and then I get my result $\displaystyle p_1(x_1) p_2(x_2) \pi r^2$.
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HW _8 Solutions
# HW _8 Solutions - Problem 3.67 Determine the maximum power...
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Problem 3.67 Determine the maximum power that can be extracted by the load resistor from the circuit in Fig. P3.67. 2000 I x 6 k Ω 3 k Ω 4 k Ω R L I x 15 V + _ _ Figure P3.67: Circuit for Problem 3.67. Solution: To find the Th´evenin equivalent circuit, we start by determining V Th = V oc . 2000 I x 6 k Ω 3 k Ω 4 k Ω I x 15 V _ _ V oc a b V 1 + _ Voltage division: V 1 = 15 ( 3 + 6 ) k × 6k = 10 V I x = V 1 6k = 10 6 mA . The dependent voltage source is: 2000 I x = 2 × 10 6 × 10 3 × 10 3 = 20 6 V . With ( a , b ) an open circuit, no current flows through the 4-k resistor. Hence, there is no voltage drop across it. V Th = V oc = V 1 2000 I x = 10 20 6 = 40 6 = 6 . 67 V . 2000 I x 6 k Ω 3 k Ω 4 k Ω 15 V _ _ I sc a b I 1 I 2 Next, we find I sc : 15 + 3k I 1 + 6k ( I 1 I 2 ) = 0
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6k ( I 2 I 1 )+ 4k I 2 + 2000 I x = 0 Also, I x = I 1 I 2 Solution yields: I 1 = 2 . 5 mA , I 2 = 1 . 25 mA . I
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# What, When & Why of Regularization in Machine Learning?
In this post, we will try and understand some of the following in relation to regularizing the regression machine learning models to achieve higher accuracy and stable models:
• Background
• What is regularization?
• Why & when does one need to adopt/apply the regularization technique?
## Background
At times, when one is building a multi-linear regression model, one uses the least squares method for estimating the coefficients of determination or parameters for features. As a result, some of the following happens:
• Often, the regression model fails to generalize on unseen data. This could happen when the model tries to accommodate for all kind of changes in the data including those belonging to both the actual pattern and, also the noise. As a result, the model ends up becoming a complex model having significantly high variance due to overfitting thereby impacting the model performance (accuracy, precision, recall, etc) on unseen data. The diagram below represents the high variance regression model
Fig 1. Regularization needed for reducing overfitting in the regression model
The goal is to reduce the variance while making sure that the model does not become biased (underfitting). After applying the regularization technique, the following model could be obtained.
Fig 2. The regression model after regularization is applied
• A large number of features and the related coefficients (at times large enough) result in computationally intensive models.
The above problems could be tackled using regularization techniques which are described in later sections.
## What is Regularization?
Regularization techniques are used to calibrate the coefficients of determination of multi-linear regression models in order to minimize the adjusted loss function (a component added to least squares method). Primarily, the idea is that the loss of the regression model is compensated using the penalty calculated as a function of adjusting coefficients based on different regularization techniques.
Adjusted loss function = Residual Sum of Squares + F(w1, w2, …, wn) …(1)
In the above equation, the function denoted using “F” is a function of weights (coefficients of determination).
Thus, if the linear regression model is calculated as the following:
Y = w1*x1 + w2*x2 + w3*x3 + bias …(2)
The above model could be regularized using the following function:
Adjusted Loss Function = Residual Sum of Squares (RSS) + F(w1, w2, w3) …(3)
In the above function, the coefficients of determination will be estimated by minimizing the adjusted loss function instead of simply, RSS function.
In later sections, you will learn about why and when regularization techniques are needed/used. There are three different types of regularization techniques. They are as following:
1. Ridge regression (L2 norm)
2. Lasso regression (L1 norm)
3. Elastic net regression
For different types of regularization techniques as mentioned above, the following function, as shown in equation (1) will differ:
F(w1, w2, w3, …., wn)
In later posts, I will be describing different types of regression mentioned above. The difference lies in the adjusted loss function to accommodate the coefficients of parameters.
## Why does one need to apply Regularization technique?
Often the linear regression model comprising of a large number of features suffers from some of the following:
• Overfitting: Overfitting which results in model failing to generalize on the unseen dataset
• Multicollinearity: Model suffering from multicollinearity effect
• Computationally Intensive: A model becomes computationally intensive
The above problem makes it difficult to come up with a model which has higher accuracy on unseen data and which is stable enough.
In order to take care of the above problems, one goes for adopting or applying one of the regularization techniques.
## When does one need to apply regularization techniques?
Once the regression model is built and one of the following symptoms happen, one could go for applying one of the regularization technique.
• Model lack of generalization: Model found with higher accuracy fails to generalize on unseen or new data.
• Model instability: Different regression models can be created with different accuracies. It becomes difficult to select one of them.
## Summary
In this post, you learned about the regularization techniques, and, why and when are they applied. Primarily, if you have come across the scenario that your regression models are failing to generalize on unseen or new data or the regression model is computationally intensive, you may try and apply regularization techniques. Applying regularization techniques make sure that unimportant features are dropped (leading to a reduction of overfitting) and also, multicollinearity is reduced.
## Ajitesh Kumar
I have been recently working in the area of Data analytics including Data Science and Machine Learning / Deep Learning. I am also passionate about different technologies including programming languages such as Java/JEE, Javascript, Python, R, Julia, etc, and technologies such as Blockchain, mobile computing, cloud-native technologies, application security, cloud computing platforms, big data, etc. I would love to connect with you on Linkedin. Check out my latest book titled as First Principles Thinking: Building winning products using first principles thinking.
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# Ounces to Pounds conversion
oz
: lb
+:
lb
oz
Calculation:
Pounds to Ounces ►
#### Ounces to Pounds
Ounce Definition: An ounce (symbol: oz) is a unit of mass in the imperial and US customary systems of measurement. The avoirdupois ounce (the common ounce) is defined as exactly 28.349523125 grams and is equivalent to one sixteenth of an avoirdupois pound.
Current use: The ounce is still a standard unit of mass in the US customary system of measurement. It is mostly used in the United States for measuring packaged food products, food portions, and postal items, among other things. The ounce is still used in some other countries around the world that have roots in British history and culture. Due to metrication, the United Kingdom (UK) no longer officially uses the ounce. It is however, still used in some settings in the UK, such as restaurants.
Pound Definition: A pound (symbol: lb) is a unit of mass used in the imperial and US customary systems of measurement. The international avoirdupois pound (the common pound used today) is defined as exactly 0.45359237 kilograms. The avoirdupois pound is equivalent to 16 avoirdupois ounces.
Current use: The pound as a unit of weight is widely used in the United States, often for measuring body weight. Many versions of the pound existed in the past in the United Kingdom (UK), and although the UK largely uses the International System of Units, pounds are still used within certain contexts, such as labelling of packaged foods (by law the metric values must also be displayed). The UK also often uses both pounds and stones when describing body weight, where a stone is comprised of 14 pounds.
#### How to convert Ounces to Pounds
1 ounce (oz) is equal to 0.0625 pounds (lb).
1 oz = (1/16) lb = 0.0625 lb
The mass m in pounds (lb) is equal to the mass m in ounces (oz) divided by 16:
m(lb) = m(oz) / 16
#### Example
Convert 5 oz to pounds:
m(lb) = 5 oz / 16 = 0.3125 lb
Pounds to Ounces ►
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Edit Article
# How to Calculate Normality
Community Q&A
Many chemical substances are available in a dissolved liquid form, rather than a solid form. Liquid chemicals are easier to dispense and measure than solid ones, especially since the solid form is usually a powder. However, the stoichiometry of chemical reactions is complicated by the liquid delivery method. Stoichiometry performs calculations using the amount of the desired substance being placed into the equations. The liquid used to dissolve the substance will not participate in the reaction, and stoichiometry will not take that liquid in to account in the reaction. The amount of the reacting substance being delivered can be determined by finding the normality of the solution. Use these tips to learn how to calculate normality.
## Steps
1. 1
Gather information about the equivalent weight of the reacting substance. Consult chemical reference books to find out the valence and the molecular weight of the substance. Molecular weight is the ratio of the mass of 1 molecule of the substance to the mass (one carbon12 molecule divided by 12.) Valence is determined by the maximum number of subatomic valence or atom to atom bonds that the substance may form with other substances. This information will be required to determine normality.
2. 2
Figure the equivalent weight of the substance. The equivalent weight of the substance is equal to the molecular weight divided by the valence.
3. 3
Calculate normality. Normality is the concentration of the substance of interest in a dissolving liquid. Therefore, normality is a property of the mixture, and will vary with the use of more or less dissolving liquid to place the substance of interest into a solution. Normality is the number of grams of the substance of interest divided by (the equivalent weight of the substance times the amount of dissolving liquid).
4. 4
Try an example. Dissolve sodium chloride (NaCl) in water. Sodium chloride has a valence of 1 and a molecular weight of 58.443. Therefore, the equivalent weight is 58.443/1 or 58.443. 1 gram of NaCl is dissolved into 0.05 L of water, so the normality of the solution is 1/(58.443 x 0.05) or 0.342.
## Community Q&A
Search
• How can I prepare 0.02N H2SO4?
wikiHow Contributor
You prepare a 0.01 molarity solution of sulphuric acid. It itself will be a 0.02N H2SO4 solution because normality=molarity*(no of H+ ions it can provide)---(for an acid). H2SO4 has 2H+ ions, so you will get the desired solution.
• How to prepare sodium hydroxide with 0.1 molarity?
• What is the normality of 1000 mL of H2SO4?
• How could the normality of HCl be 11.5?
• If 2.65 grams of anhydrous sodium carbonate is dissolved in 500 ml of solution what is the normality?
• How to prepare 0.1mol/L sodium phosphate buffer?
## Article Info
Categories: Chemistry
In other languages:
Русский: рассчитать нормальность раствора, Español: calcular la normalidad, Português: Calcular a Normalidade, Italiano: Calcolare la Normalità, Deutsch: Die Normalität berechnen, Français: calculer la normalité
Thanks to all authors for creating a page that has been read 199,222 times.
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Outlook: Newcourt Acquisition Corp Warrant is assigned short-term B1 & long-term Ba3 estimated rating.
AUC Score : What is AUC Score?
Short-Term Revised1 :
Dominant Strategy : Buy
Time series to forecast n: for Weeks2
Methodology : Multi-Task Learning (ML)
Hypothesis Testing : Paired T-Test
Surveillance : Major exchange and OTC
1The accuracy of the model is being monitored on a regular basis.(15-minute period)
2Time series is updated based on short-term trends.
## Summary
Newcourt Acquisition Corp Warrant prediction model is evaluated with Multi-Task Learning (ML) and Paired T-Test1,2,3,4 and it is concluded that the NCACW stock is predictable in the short/long term. Multi-task learning (MTL) is a machine learning (ML) method in which multiple related tasks are learned simultaneously. This can be done by sharing features and weights between the tasks. MTL has been shown to improve the performance of each task, compared to learning each task independently. According to price forecasts for 4 Weeks period, the dominant strategy among neural network is: Buy
## Key Points
1. Buy, Sell and Hold Signals
2. What statistical methods are used to analyze data?
3. Operational Risk
## NCACW Target Price Prediction Modeling Methodology
We consider Newcourt Acquisition Corp Warrant Decision Process with Multi-Task Learning (ML) where A is the set of discrete actions of NCACW stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4
F(Paired T-Test)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Multi-Task Learning (ML)) X S(n):→ 4 Weeks $∑ i = 1 n a i$
n:Time series to forecast
p:Price signals of NCACW stock
j:Nash equilibria (Neural Network)
k:Dominated move
a:Best response for target price
### Multi-Task Learning (ML)
Multi-task learning (MTL) is a machine learning (ML) method in which multiple related tasks are learned simultaneously. This can be done by sharing features and weights between the tasks. MTL has been shown to improve the performance of each task, compared to learning each task independently.
### Paired T-Test
A paired t-test is a statistical test that compares the means of two paired samples. In a paired t-test, each data point in one sample is paired with a data point in the other sample. The pairs are typically related in some way, such as before and after measurements, or measurements from the same subject under different conditions. The paired t-test is a parametric test, which means that it assumes that the data is normally distributed. The paired t-test is also a dependent samples test, which means that the data points in each pair are correlated.
For further technical information as per how our model work we invite you to visit the article below:
How do AC Investment Research machine learning (predictive) algorithms actually work?
## NCACW Stock Forecast (Buy or Sell)
Sample Set: Neural Network
Stock/Index: NCACW Newcourt Acquisition Corp Warrant
Time series to forecast: 4 Weeks
According to price forecasts, the dominant strategy among neural network is: Buy
Strategic Interaction Table Legend:
X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)
Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)
Z axis (Grey to Black): *Technical Analysis%
### Financial Data Adjustments for Multi-Task Learning (ML) based NCACW Stock Prediction Model
1. The characteristics of the hedged item, including how and when the hedged item affects profit or loss, also affect the period over which the forward element of a forward contract that hedges a time-period related hedged item is amortised, which is over the period to which the forward element relates. For example, if a forward contract hedges the exposure to variability in threemonth interest rates for a three-month period that starts in six months' time, the forward element is amortised during the period that spans months seven to nine.
2. When using historical credit loss experience in estimating expected credit losses, it is important that information about historical credit loss rates is applied to groups that are defined in a manner that is consistent with the groups for which the historical credit loss rates were observed. Consequently, the method used shall enable each group of financial assets to be associated with information about past credit loss experience in groups of financial assets with similar risk characteristics and with relevant observable data that reflects current conditions.
3. If, at the date of initial application, it is impracticable (as defined in IAS 8) for an entity to assess a modified time value of money element in accordance with paragraphs B4.1.9B–B4.1.9D on the basis of the facts and circumstances that existed at the initial recognition of the financial asset, an entity shall assess the contractual cash flow characteristics of that financial asset on the basis of the facts and circumstances that existed at the initial recognition of the financial asset without taking into account the requirements related to the modification of the time value of money element in paragraphs B4.1.9B–B4.1.9D. (See also paragraph 42R of IFRS 7.)
4. However, depending on the nature of the financial instruments and the credit risk information available for particular groups of financial instruments, an entity may not be able to identify significant changes in credit risk for individual financial instruments before the financial instrument becomes past due. This may be the case for financial instruments such as retail loans for which there is little or no updated credit risk information that is routinely obtained and monitored on an individual instrument until a customer breaches the contractual terms. If changes in the credit risk for individual financial instruments are not captured before they become past due, a loss allowance based only on credit information at an individual financial instrument level would not faithfully represent the changes in credit risk since initial recognition.
*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.
### NCACW Newcourt Acquisition Corp Warrant Financial Analysis*
Rating Short-Term Long-Term Senior
Outlook*B1Ba3
Income StatementB2Caa2
Balance SheetCaa2Ba3
Leverage RatiosCBaa2
Cash FlowBaa2B2
Rates of Return and ProfitabilityBaa2Ba3
*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?
## Conclusions
Newcourt Acquisition Corp Warrant is assigned short-term B1 & long-term Ba3 estimated rating. Newcourt Acquisition Corp Warrant prediction model is evaluated with Multi-Task Learning (ML) and Paired T-Test1,2,3,4 and it is concluded that the NCACW stock is predictable in the short/long term. According to price forecasts for 4 Weeks period, the dominant strategy among neural network is: Buy
### Prediction Confidence Score
Trust metric by Neural Network: 85 out of 100 with 791 signals.
## References
1. Matzkin RL. 1994. Restrictions of economic theory in nonparametric methods. In Handbook of Econometrics, Vol. 4, ed. R Engle, D McFadden, pp. 2523–58. Amsterdam: Elsevier
2. G. Theocharous and A. Hallak. Lifetime value marketing using reinforcement learning. RLDM 2013, page 19, 2013
3. Bera, A. M. L. Higgins (1997), "ARCH and bilinearity as competing models for nonlinear dependence," Journal of Business Economic Statistics, 15, 43–50.
4. Mnih A, Kavukcuoglu K. 2013. Learning word embeddings efficiently with noise-contrastive estimation. In Advances in Neural Information Processing Systems, Vol. 26, ed. Z Ghahramani, M Welling, C Cortes, ND Lawrence, KQ Weinberger, pp. 2265–73. San Diego, CA: Neural Inf. Process. Syst. Found.
5. M. J. Hausknecht and P. Stone. Deep recurrent Q-learning for partially observable MDPs. CoRR, abs/1507.06527, 2015
6. D. Bertsekas and J. Tsitsiklis. Neuro-dynamic programming. Athena Scientific, 1996.
7. Nie X, Wager S. 2019. Quasi-oracle estimation of heterogeneous treatment effects. arXiv:1712.04912 [stat.ML]
Frequently Asked QuestionsQ: What is the prediction methodology for NCACW stock?
A: NCACW stock prediction methodology: We evaluate the prediction models Multi-Task Learning (ML) and Paired T-Test
Q: Is NCACW stock a buy or sell?
A: The dominant strategy among neural network is to Buy NCACW Stock.
Q: Is Newcourt Acquisition Corp Warrant stock a good investment?
A: The consensus rating for Newcourt Acquisition Corp Warrant is Buy and is assigned short-term B1 & long-term Ba3 estimated rating.
Q: What is the consensus rating of NCACW stock?
A: The consensus rating for NCACW is Buy.
Q: What is the prediction period for NCACW stock?
A: The prediction period for NCACW is 4 Weeks
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# What convention shows $R_{XYZ} = R_ZR_YR_X$
In the book Introduction to Robotics by John J. Craig, the explanation of multiplying matrices for fixed-angle rotation is a bit confusing. I understand fixed-angle rotation order $XYZ$ is equal to Euler angle $ZYX$, but I am wondering why the equation is written as following, or what mathematical convention describes this way of writing so I know in the future what it means.
It is described as:
The derivation of the equivalent rotation matrix, $_B^AR_{XYZ}(\gamma,\beta,\alpha)$ is straight-forward, because all rotations occur about axes of the reference frame; that is, $$_B^AR_{XYZ}(\gamma,\beta,\alpha) = R_Z(\alpha)R_Y(\beta)R_X(\gamma)$$
Since rotation operations do not commute, the order is important, so I would imagine it should be obvious for a notation to imply it is multiplied in reverse order.
• @OnceUponACrinoid I am asking if there is a convention for why the order is then written backwords. Reading right to left or left to right is the same, since it is still the matrix RxRyRz not RzRyRx, and since ABC = A(BC), the order of reading is irrelevant. Maybe the answer is just 'how to think about it', but i was looking if there was a specific explanation – user1938107 Jun 15 '15 at 6:58
• Well, when describing Euler rotations, it says Rx'y'z' = RxRyRz , and subsequent operations are added to the right side, in both cases (so if you rotate first, then translate based on the rotation, translation is appended to right side) – user1938107 Jun 15 '15 at 7:07
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# What is the equation of parabola
2
by nikhu
2014-08-22T03:02:39+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.
The following are some examples of equations of parabolas in x-y plane.
the vertex is at origin and a gives the distance focus from vertex.
passes through origin vertex at A/2B
another one
vertex at (x1,y1) and focal length = a
well, the following
represents parabola if B² = 4 AC and more conditions ....
• Brainly User
2014-08-22T09:04:00+05:30
Y^2=4ax and x^2=4ay is the equation of parabola
Comment has been deleted
this should never be marked as best... face the truth......
Comment has been deleted
don't cry....
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Latest Banking jobs » Revision Test Reasoning Ability Quiz For...
# Revision Test Reasoning Ability Quiz For SBI Clerk Prelims 2021- 6th June
Directions (1-5): Study the following information carefully and answer the given questions.
Seven persons A, B, C, D, E, F and G have exam on seven different days of the same week starting from Sunday to Saturday.
More than three person has exam before E. G has exam before D and only two people has exam between them. C has exam immediate before A and none of them has exam on Monday. B has exam immediate before F. The number of persons has exam between F and G is less than number of persons has exam between D and A.
Q1. Who has exam on Monday?
(a) A
(b) B
(c) C
(d) D
(e) None of these
Q2. Who has exam just before F?
(a) A
(b) B
(c) C
(d) D
(e) None of these
Q3. How many persons have exam in between B and C?
(a) More than three
(b) One
(c) Two
(d) Three
(e) No one
Q4. Who has exam on Saturday?
(a) A
(b) B
(c) C
(d) D
(e) None of these
Q5. Who has exam just after E?
(a) A
(b) B
(c) C
(d) D
(e) None of these
Directions (6-10): Study the following arrangement carefully and answer the questions given below:
N 4 7 T U J K 3 % F @ © L N 5 P 1 8 U \$ E 2 D C 6 # 9 Z Q 8 Y * M A
Q6. Which of the following is sixth to the left of the fifteenth from the left end of the given arrangement?
(a) 2
(b) #
(c) %
(d) \$
(e) None of these
Q7. How many such numbers are there in the given arrangement each of which is immediately preceded by a consonant but not immediately followed by a letter?
(a) One
(b) None
(c) three
(d) Two
(e) Four
Q8. How many such symbols are there in the arrangement, each of which is immediately followed by a letter but not immediately preceded by a number?
(a) One
(b) Three
(c) None
(d) Two
(e) More than three
Q9. What should come in place of question mark (?) in the following series based on the above arrangement?
(a) 69Q
(b) #Z8
(c) 6#Q
(d) #9Z
(e) None of these
Q10. Four of the following five are alike in a certain way based on their positions in the given arrangement and so from a group. Which is the one that does not belong to that group?
(a) DC6
(c) 9ZQ
(d) 5P1
(e) #MA
Directions (11-15): Study the following information carefully and answer the questions given below:
In a certain code language
‘grabbling and target’ is written as ‘yo vo na’,
‘team is higher’ is written as ‘sa ra ta’,
‘target is bad’ is written as ‘la vo sa’, and
‘victory are grabbling’ is written as ‘yo ha ja’.
Q11.What is the code for ‘grabbling’?
(a) ja
(b) ha
(c) yo
(d) na
(e) None of these
Q12. ‘victory are team’ can be written as
(a) ja ha ta
(b) ta ra ha
(c) ha ja ra
(d) Either (a) or (c)
(e) None of these
Q13.What is the code for ‘victory’?
(a) ja
(b) yo
(c) la
(d) ha
(e) Can’t be determined
Q14.What does ‘la’ stand for?
(a) is
(c) and
(d) are
(e) None of these
Q15. What is the code for ‘is’?
(a) ja
(b) yo
(c) sa
(d) ha
(e)None of these
Practice More Questions of Reasoning for Competitive Exams:
###### SBI Clerk Study Plan 2021
Solutions
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# 10.3: Use Graphs to Solve Quadratic Equations
Difficulty Level: Basic Created by: CK-12
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### Notes/Highlights Having trouble? Report an issue.
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### Vocabulary Language: English Spanish
TermDefinition
solutions of a quadratic equation The $x-$intercept of a quadratic equation is also called a root, solution, or zero.
Double Root A solution that is repeated twice.
Quadratic Formula The quadratic formula states that for any quadratic equation in the form $ax^2+bx+c=0$, $x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$.
Roots The roots of a function are the values of x that make y equal to zero.
Zero Product Rule The zero product rule states that if the product of two expressions is equal to zero, then at least one of the original expressions much be equal to zero.
Zeroes The zeroes of a function $f(x)$ are the values of $x$ that cause $f(x)$ to be equal to zero.
Zeros The zeros of a function $f(x)$ are the values of $x$ that cause $f(x)$ to be equal to zero.
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View Single Post
09-04-2012, 08:18 PM #171
corners
Legend
Join Date: Jul 2008
Posts: 5,440
The following were questions posed to Travlerajm, but I'd like to add a bit of response as well.
Quote:
Originally Posted by stoneage Thanks for the clarification! I have had two problems with MgR/I: 1. I have yet to hear an explanation why this parameter is relevant to the mechanical behavior of the racquet in tennis. MgR/I describes how the racquet swings freely in a gravitational field, i.e. like a pendulum. MgR/I=21 means that frequency of a racquet swinging from the but is 0.73 Hz. But unless you are building a cuckoo clock of the racquet I have difficulties to see the relevance. Gravity is the least of forces involved in a tennis swing. But if you have some explanation that could shed some light on this I would be most interested (no irony intended).
Rod Cross has been modeling tennis strokes, including the serve, as double pendulums for several years, with two papers appearing in the past twelve months.
Quote:
2. There are an infinite number of racquet configurations that fulfill MgR/I=21 most of them very strange and unplayable. So if you use only that to find an optimal racquet you could easily go wrong.
This isn't the case. Many racquets on the market are reasonably close to 21.0, especially traditional players' frames like the Pro Staff 6.0 and the Prestiges. I support your skepticism but I think you're misinterpreting this notion of MgR/I and its use. It's not meant as a stand-alone, be all/end all.
I suspect that if you try some on-court experiments, like the following two, you'll find some value in the approach:
Experiment #1: Alternate between two frames with very different MgR/I values but with very similar swingweights and static weights. The two frames will differ only in balance point.
For example: Racquet A at 335 grams / 31.5 cm balance / 320 swingweight (MgR/I = 20.8 ) and Racquet B at 335 grams / 33.0 cm balance / 320 swingweight (MgRI = 21.37).
Experiment #2: Alternate between two frames with the same MgR/I values (how about 21.0?) but with very different static weight, balance and swingweights, such as:
Racquet A at 350 grams / 31.5 cm balance / 330 swingweight (MgRI = 21.0), and Racquet B at 335 grams / 32.0 cm balance /320 swingweight (MgRI = 21.0). Or better yet, your preferred specs and another very different configuration with the same MgR/I ratio as your preferred specs.
If the ratio doesn't make some sense to you after these experiments then we can confidently add your report to the "MgR/I is rubbish." pile of anecdotes.
__________________________________________________ _________
racquetTune, stringBed and swingTool racquet apps for the iPhone/iPad.[/QUOTE]
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# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.
2 Pages
### type214
Course: TRNLIB 16, Fall 2009
School: Wisconsin
Rating:
Word Count: 602
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214: Component Three-Way Valve with Actuator by HVACSIM+ General Description This component represents a valve with two inlet ports and one outlet port. The position of the valve is determined by an input control signal, C. Port 1 of the valve is closed when C=0 and open when C=1. The sixth parameter, MODE, determines the inherent characteristics of the two inlet ports. If MODE=0, both ports are linear....
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Coursehero >> Wisconsin >> Wisconsin >> TRNLIB 16
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214: Component Three-Way Valve with Actuator by HVACSIM+ General Description This component represents a valve with two inlet ports and one outlet port. The position of the valve is determined by an input control signal, C. Port 1 of the valve is closed when C=0 and open when C=1. The sixth parameter, MODE, determines the inherent characteristics of the two inlet ports. If MODE=0, both ports are linear. If MODE=1, port 1 is exponential (equal percentage) and port 2 is linear. If MODE=2, both ports are exponential. As discussed in section 4.0 of reference [1], the actual behavior of the valve model in a system simulation will depend on the valve's authority over the system. Nomenclature C - requested relative valve position (0 < C < 1) Ca - relative actuator position (0 <= Ca <= 1) Ch1 - relative opening of port 1 (0 <= Ch <= 1) Ch2 - relative opening of port 2 (0 <= Ch <= 1) hys - fraction of actuator's range over which Ch remains constant when actuator's direction of travel reverses K1 - flow resistance parameter for inlet port 1, when port 1 is open (Ch=1) K2 - flow resistance parameter for inlet port 2, when port 2 is open (Ch=0) MODE - determines port 1 / port 2 inherent characteristics: 0 => linear / linear 1 => exponential / linear 2 => exponential / exponential w1 - mass flow rate at inlet port 1 w2 - mass flow rate at inlet port 2 w3 - mass flow rate at outlet port 3 y - leakage parameter: fractional leakage when DeltaP = 1. Toll - actuator time constant Mathematical Description The relationship between the input control signal, C, and the actuator position, Ca, is defined by: d(Ca)/dt = (C - Ca) / Toll This differential equation is solved by MODSIM, the main HVACSIM+ program, unless the time constant, Toll, is less than one second, in which case the following solution is used: IF (Toll/Deltat) < OR 0.05 | Css - C- | < 10^(-10) THEN Ca = C ELSE Ca = C - (C - Ca-)*exp(-Deltat/Toll) where Ca- is the value of Ca one time step ago. The actuator position differs from the valve position due to hysteresis effects, which are determined by the utility function HYSTER (described in section 3.2 of reference [1]). Ch1 = HYSTER(Ca, hys) Ch2 = 1. - Ch1 The outlet flow rate is the sum of the inlet flow rates, and the outlet temperature is a weighted average of the inlet temperatures: w3 = w1 + w2 T3 = (w1*T1 + w2*T2) / w3 Calculation of the inlet pressures depends upon the mode. Mode = 0: P1 = P3 + sign(w1)*K1*w1^2*[(1 - y)*Ch1 + y]^(-2) P2 = P3 + sign(w2)*K2*w2^2*[(1 - y)*Ch2 + y]^(-2) Mode = 1: P1 = P3 + sign(w1)*K1*w1^2*y^(-2*Ch2) P2 = P3 + sign(w2)*K2*w2^2*[(1 - y)*Ch2 + y]^(-2) Mode = 2: P1 = P3 + sign(w1)*K1*w1^2*y^(-2*Ch2) P2 = P3 + sign(w2)*K2*w2^2*y^(-2*Ch1) Component 515 Configuration InputsDescription 1w1- mass flow rate, inlet port 1 2w2- mass flow rate, inlet port 2 3P3- pressure at outlet 4T1- temperature, inlet port 1 5T2- temperature, inlet port 2 6C- input control signal (0 <= C <= 1) 7Ca- actuator rel...
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# Football with Frobenius: The Super Bowl Math Problem
••• Peter G. Aiken/Getty Images Sport/GettyImages
Print
With the Super Bowl just around the corner, athletes and fans of the world have their focus fixed firmly on the big game. But for _math_letes, the big game might bring to mind a little problem relating to the possible scores in a game of football. With only limited options for the amount of points that you can score, some totals simply cannot be reached, but what is the highest? If you want to know what links coins, football and McDonald’s chicken nuggets, this is a problem for you.
## The Super Bowl Math Problem
The problem involves the possible scores either the Los Angeles Rams or the New England Patriots could possibly achieve on Sunday without a safety or a two-point conversion. In other words, the allowable ways to increase their scores are 3-point field goals and 7-point touchdowns. So, without safeties, you can’t achieve a score of 2 points in a game with any combination of 3s and 7s. Similarly, you can’t achieve a score of 4 either, nor can you score 5.
The question is: What’s the highest score that can’t be achieved with only 3-point field goals and 7-point touchdowns?
Of course, touchdowns without a conversion are worth 6, but since you can get to that with two field goals anyway, it doesn’t matter for the problem. Also, since we’re dealing with math here, you don’t have to worry about the specific team’s tactics or even any limits on their ability to score points.
Try to solve this yourself before moving on!
## Finding a Solution (the Slow Way)
This problem has some complex mathematical solutions (see Resources for full details, but the main result will be introduced below), but it’s a good example of how this isn’t needed to find the answer.
All you have to do to find a brute-force solution is to simply try each of the scores in turn. So we know you can’t score 1 or 2, because they’re less than 3. We already established that 4 and 5 aren’t possible, but 6 is, with two field goals. After 7 (which is possible), can you score 8? Nope. Three field goals gives 9, and a field goal and a converted touchdown makes 10. But you can’t get 11.
From this point onwards, a little work shows that:
\begin{aligned} 3 × 4 &= 12\\ 7 + (3 × 2) &= 13 \\ 7 × 2 &= 14\\ 3 × 5 &= 15\\ 7 + (3 × 3) &= 16\\ (7 × 2) + 3 &= 17 \end{aligned}
And in fact, you can keep going like this for as long as you want. The answer seems to be 11. But is it?
## The Algebraic Solution
Mathematicians call these problems “Frobenius coin problems.” The original form related to coins, such as: If you only had coins valued 4 cents and 11 cents (not real coins, but again, that’s math problems for you), what is the largest amount of money you couldn’t produce.
The solution, in terms of algebra, is that with one score worth p points and one score worth q points, the highest score you can’t get (N) is given by:
N = pq \; – \;(p + q)
So plugging in the values from the Super Bowl problem gives:
\begin{aligned} N &= 3 × 7\; – \;(3 + 7) \\ &= 21 \;–\; 10\\ &= 11 \end{aligned}
Which is the answer we got the slow way. So what if you could only score touchdowns with no conversion (6 points) and touchdowns with one-point conversions (7 points)? See if you can use the formula to work it out before reading on.
In this case, the formula becomes:
\begin{aligned} N &= 6 × 7\; – \;(6 + 7) \\ &= 42 \;–\; 13\\ &= 29 \end{aligned}
## The Chicken McNugget Problem
So the game is over and you want to reward the winning team with a trip to McDonald's. But they only sell McNuggets in boxes of 9 or 20. So what’s the highest number of nuggets you can’t buy with these (outdated) box numbers? Try to use the formula to find the answer before reading on.
Since
N = pq \; – \;(p + q)
And with p = 9 and q = 20:
\begin{aligned} N &= 9 × 20\; – \;(9 + 20) \\ &= 180 \;–\; 29\\ &= 151 \end{aligned}
So provided you were buying more than 151 nuggets – the winning team will probably be pretty hungry, after all – you could buy any number of nuggets you wanted with some box combination.
You might be wondering why we’ve only covered two-number versions of this problem. What if we incorporated safeties, or if McDonalds sold three sizes of nugget boxes? There is no clear formula in this case, and while most versions of it can be solved, some aspects of the question are completely unsolved.
So maybe when you’re watching the game or eating bite-sized bits of chicken you can claim you’re trying to solve an open problem in mathematics – it’s worth a try to get out of chores!
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# 2x16 LCD Shield 'select' button and project code problem
Hello,
I’ve been looking online for awhile now, and I just can’t seem to figure out how to set a function for the ‘select’ button on the 2x16 LCD Shield (connected to an Arduino Uno). I have tried a number of codes from similar projects, altering them to suit mine, but it doesn’t do what I tell it to do.
My end goal is for the user to press ‘select’ (on the LCD) which will allow the ultrasonic sensor (US) to measure the distance from its placement on the wall (e.g 40cm, above the bathtub’s top edge) to the bottom of the empty bathtub. The code will then take away that 40cm + another 10cm (as an overflow barrier) equalling 50cm in total, revealing the maximum depth (for example 60cm- which equals the distance from the bottom of the bathtub to 10cm from the top). The arduino now knowing the distance, will minus the height/depth the user sets for their water height (e.g 35cm) from the maximum depth measurement (60cm).
The simple calculation would be something like this 60cm (maximum depth) – 35cm (distance set by user) = 25cm (which is the gap, between the water’s surface/level (35cm) and the 10cm mark before the top).
The code below shows some of my work, however I’d need some help altering the code to fit want I stated above.
Code:
``````// include the library code:
#include <LiquidCrystal.h>
#define echoPin 1
#define trigPin 2
#define solenoidPin 3
#define buttonsPin A0
// initialize the library by associating any needed LCD interface pin
// with the arduino pin number it is connected to
const int rs = 8, en = 9, d4 = 4 , d5 = 5, d6 = 6, d7 = 7;
LiquidCrystal lcd(rs, en, d4, d5, d6, d7);
void setup() {
Serial.begin (9600);
pinMode(trigPin, OUTPUT);
pinMode(echoPin, INPUT);
pinMode(3, OUTPUT); // connected to S terminal of Relay
pinMode(A0, INPUT);
}
void loop() {
// set up the LCD's number of columns and rows:
lcd.begin(16, 2);
lcd.setCursor (1, 1); // put your setup code here, to run once:
lcd.setCursor (0, 0);
// Print a message to the LCD.
delay (250);
lcd.setCursor (0, 0);
lcd.print("Maximum Distance:");
lcd.setCursor(1, 1);
lcd.print("(Hold Select)");
delay (2000);
lcd.clear ();
lcd.setCursor(1, 0);
lcd.print("Wait till the");
lcd.setCursor (1, 1);
lcd.print("screen clears");
delay (1200);
int x;
lcd.setCursor(10, 1);
if (x < 800) {
lcd.clear ();
delay (10000);
Serial.println(x, DEC);
}
// Ultrasonic sensor function
float duration, distance;
digitalWrite(trigPin, LOW);
delayMicroseconds(2);
digitalWrite(trigPin, HIGH);
delayMicroseconds(10);
digitalWrite(trigPin, LOW);
duration = pulseIn(echoPin, HIGH);
distance = (duration / 2) * 0.0344;
}
``````
Thank you for tidying up your posting of code. I use “boilerplate” prompt messages to remind people, so my comments will have moved on to “nudge” someone else.
Hi.
I'll have to take your word for it, so i'm assuming now you already tried, and played with this display shield of yours.
In your sketch, you are reading A0 and as i've started assuming already i'll also assume that's where your button presses come in to your Arduino (it is with the shield i've got here).
But in your code, you are making no attempt to do something with it.
If you don't know how to handle each button, here's some advice:
Do what i did when i got the shield years ago.
You've got the display.
That's a great debug tool.
Use the display to show what values you get when pressing the buttons.
Make notes while pressing the buttons.
Expect to see slight variations while pressing the same button multiple times.
So look for a value range instead of some absolute value when processing the button presses.
By the way i'm 100% sure this info is already available, as this is not the first time i'm writing this.
Again: Use that display while debugging your sketches.
It's a powerful tool to use, certainly when it is already available in your design.
MAS3:
But in your code, you are making no attempt to do something with it.
Hello, yes I'm not quite sure how actually to do this function. I updated the code if that changes anything, but when I try and use the US it doesn't work like it would with other codes aimed towards getting the component to read the distance, and shut off the solenoid/relay.
I'm not sure what you want to know right now.
Your updated code shows that you are displaying the values you get from the key presses, and that you only will show these key presses if that value is less than 800.
So other keys won't generate a value lower than 800 ?
I'm sure that's not true.
Your code starts telling something about a maximum distance, but doesn't show anything holding such value.
Instead you're instructing to press a key and wait until the screen clears, after which you'll make an attempt to read the button which might already be released by then (because you instructed so).
There's no need to re-initialise the screen every iteration, and there's no need to waste huge amounts of time.
3.2 seconds to the controller is like waiting 3.2 days to you.
That part is probably just an attempt to read the key and show it, i'd add some comment to remind myself and others what's going on there.
This would make it easier for you to find, and to comment out once you don't need it any more.
Your Ultrasonic function is no function, so do not name it that way.
The word function has a meaning in code, and what you've shown thus far doesn't have a function at that place.
Because your sketch is quite short, i'd make 2 sketches out of them.
A sketch dedicated to testing the key presses, and a sketch measuring your distance and displaying it.
The key press test sketch should tell you the value coming in from each of the keys, and would help you for all future sketches handling these keys.
Use comment lines to clarify what you've found out, and save your sketch for future reference whenever you'll need to use those keys again.
Thanks for the advice, the code was really just bits and pieces of other codes put together, so I truly had no idea what such terminology meant. Despite my efforts exploring the internet, I still hadn't grasped a proper understanding, nor had the time to do so. Even now, I don't completely understand the sections I need to change (its my first project), with a limited time period I might need to do trial and error.
Do you recommend any helpful online sources/examples?
Well all i can tell you, is what works for me.
If i find some interesting code, i'll study it to try and understand what's exactly going on.
I'll test what i think i've learned by altering the code and see if that does what i wanted it to do, and why it doesn't.
I won't start using bits and pieces of code before i'm confident i understand what it does.
Sometimes that means i'll figure out another way to do what i had in mind, and sometimes i can alter some code i found and studied.
So to gather a heap of code, shake it up a bit and expect it to work is not a very effective way to get things done.
It'll frustrate you and make you want to give up, so it's just a waste of time.
Studying code to understand it, takes time.
But it'll be time well spent, as opposed by the alternative mentioned above.
Thanks for the advice. May I ask how you got just the 'select' button to work? Am I doing it right?
Hi.
I can’t tell for sure from the code so far.
You are testing for a value of less than 800 on A0.
The range of an analog input is 0 - 1023 (so 1024 possible results).
There’s 5 buttons on my shield (which isn’t necessarily the same as yours), so if the range from the buttons would be between 800 and 1023, that would be waste of over half the range.
So i’m sure there’s some buttons which will have a result lower than 800.
These buttons would be processed as the “select” button, if you don’t test that too.
So you’d need to be sure you’re within the range belonging to that “select” button.
Let’s assume your button does resolve to a value of 789 (so <800).
You’d want to know what the next lower value is.
That’s why i pitched the test sketch which will print the read out value to the display already present in your setup; you’ll know all values of each key press.
After that, and if you only need to know whether the “select” button was pressed, you need to check if the value at A0 is between your known values of these buttons.
This way you allow for some deviations which could occur from different causes (like power dips on your Arduino board, for whatever reason).
If you (later) would like to use the other buttons, you’d need to test each of the buttons.
That would be possible with a small loop, a smart order of values to test, and results in a button number which would then be translated to whatever button was pressed.
Remember that no press is also a possibility (like 0 is also a number).
Also, dump the delays.
You don’t need them and there’s a much more elegant way to get the same result without a total waste of processing power.
Do take a look at my signature (which means it is part of each and all of my forum postings).
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Welcome! On this website you can find information about each number.
Number 327504521
Number 327504521 basic info
Number 327504521 has 9 digits. Number 327504521 can be formatted as 327,504,521 or 327.504.521 or 327 504 521 or in case this was a phone number 327-504-521 or 32-750-4521 to be easier to read. Number 327504521 in English words is "three hundred and twenty-seven million, five hundred and four thousand, five hundred and twenty-one". Number 327504521 can be read by triplets (groups of 3 digits) as "three hundred and twenty-seven, five hundred and four, five hundred and twenty-one". Number 327504521 can be read digit by digit as "three two seven five zero four five two one". Number 327504521 is odd. Number 327504521 is not divisible by any single digit number. Number 327504521 is a composite number (non-prime number).
Number 327504521 conversions
Number 327504521 in binary code is 10011100001010101001010001001. Number 327504521 in octal code is: 2341251211. Number 327504521 in hexadecimal (hexa): 13855289.
The sum of all digits of this number is 29. The digital root (repeated digital sum until you get single-digit number) is 2. Number 327504521 divided by two (halved) equals 163752260.5. Number 327504521 multiplied by two (doubled) equals 655009042. Number 327504521 multiplied by ten equals 3275045210. Number 327504521 raised to the power of 2 equals 1.0725921127544E+17. Number 327504521 raised to the power of 3 equals 3.5127876611601E+25. The square root (sqrt) of 327504521 is 18097.085980898. The sine (sin) of 327504521 degree is -0.98162718344593. The cosine (cos) of 327504521 degree is 0.19080899538545. The base-10 logarithm of 327504521 equals 8.5152172995394. The natural logarithm of 327504521 equals 19.607012417524. The number 327504521 can be encoded to characters as CBGEJDEBA. The number 327504521 can be encrypted to chemical element names as lithium, helium, nitrogen, boron, neon, beryllium, boron, helium, hydrogen.
Numbers simmilar to 327504521
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Number 327504521 typographic errors with one digit missing: 275045213750452132504521327045213275452132750521327504213275045132750452
Number 327504521 typographic errors with one digit doubled: 332750452132275045213277504521327550452132750045213275044521327504552132750452213275045211
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Several randomly selected numbers:
82407104716447215575440023084149804161162045611987751339510598545193387608698001668310262592894496684812883497477348905681016273968199922226556400819602853363000499519579463595447793180199317685293903348151301492816722566365297744105651462081848984145799782511173647773432340959865260481158825799492819146677881400899168774150291680574588594210627263540218248623561629089798797481569738718.
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Lesson 4-6: Consistent & Dependent Systems - PowerPoint PPT Presentation
Don’t be a hater!. Lesson 4-6: Consistent & Dependent Systems. Objective: Students will: Determine whether a system of equations is consistent, inconsistent, or dependent. Consistent Systems At least 1 solution Two possibilities: 1) Lines intersect 2) Same line Inconsistent system
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Lesson 4-6: Consistent & Dependent Systems
Objective:
Students will:
Determine whether a system of equations is consistent, inconsistent, or dependent.
At least 1 solution
Two possibilities:
1) Lines intersect 2) Same line
Inconsistent system
If lines are parallel they are called inconsistent
There is no solution to the system
Lines have same slope but are not same line (different intercepts)
Dependent System: Infinite number of solutions
►lines that are actually the same
►one equation is a scalar of the other
(can multiply by a factor to become the other)
How to find consistent systems: (Ones having 1 or more solutions)
Compare Slopes
►if they are different
► if they are the same & dependent (same line)
Example 1 Consistent? x – y = 2
x + y = 4
What is the slope?
What is the slope?
1
-1
They do not have the same slope so they are consistent (only one solution)
Example 2 Consistent? 2x + y = 4
4x + 2y = 16
What is the slope?
What is the slope?
-2
-2
Since the slopes are the same we need to determine if they are the same line consistent or parallel lines inconsistent
Is one of the equations a scalar of the other?
No, if you multiply the top equation by 2 you get 4x +2y =8 so they are not the same line and therefore inconsistent (no solution)
1) x + 2y + z =1
2) 3x + 3y + z = 2
3) 2x + y = 2
Multiplying 2) by -1 and adding to 1) yields:
-2x – y = -1
Multiplying 3) by -1 yields:
-2x –y = -2
What is the slope?
-2
What is the slope?
-2
Since they have the same slope but are not the same line they are inconsistent
Example 3 Is this system dependent?
x – 3y = 2
3x – 9y = 6
If we multiply the top equation by a scalar of 3 we get:
3x - 9y = 6 which is equation 2!!
The two lines are the same and the system is dependent (infinite number of solutions)
Make sure both equations are in the same form-
Either slope-intercept or standard before checking!
Combine 2 equations to eliminate a variable
If this new equation is a multiple of the 3rd equation → DEPENDENT
Example 4 Dependent? x + y = 1
-x + z = 1
y + z = 2
Which equations are easiest to combine?
1 and 2 to get y + z =2
This is already the 3rd equation!! (scalar of 1) so dependent
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# Ray Tracing with Cones: coverage, overlapping and abutting triangles
In his classic paper Ray Tracing with Cones, John Amanatides describes a variation on classical ray tracing. By extending the concept of a ray by an aperture angle, making it a cone, aliasing effects (including those originating from too few Monte Carlo samples) can be reduced.
During cone-triangle intersection, a scalar coverage value is calculated. This value represents the fraction of the cone that is covered by the triangle. If it is less than $1$, it means that the triangle doesn't fully cover the cone. Further tests are required. Without the usage of more advanced techniques however, we only know how much of the cone is covered, but not which parts.
Amanatides states:
Since at present only the fractional coverage value is used in mixing the contributions from the various objects, overlapping surfaces will be calculated correctly but abutting surfaces will not.
This does not make sense to me. From my point of view it is the other way around. Let's take an example: We have two abutting triangles, a green and a blue one, each of which covers exactly 50% of our cone. They are at the same distance from the viewer.
The green triangle is tested first. It has a coverage value of 0.5, so the blue triangle is tested next. With the blue one's coverage value of 0.5 our cone is fully covered, so we're done and end up with a 50:50 green-blue mixture. Great!
Now imagine that we kill the blue triangle and add a red one some distance behind the green one - overlapping. Greeny gives us a coverage value of 0.5 again. Since we don't have the blue one to test anymore we look further down the cone and soon find the red one. This too returns some coverage value greater than 0, which it shouldn't because it is behind the green one.
So, from this I conclude that abutting triangles work fine, while overlapping triangles would need some more magic like coverage masks to be correct. This is the opposite of what Amanatides says. Did I misunderstand something or is this a slip in the paper?
I did implement a ray tracer based on Amantides' work but, as that was years ago, my memory of the paper is a little rusty.
However, ignoring this particular case, in general when it comes to working with fractional coverage e.g. Alpha compositing, (see "A over B") my understanding is that the usual assumption is that the items being composited are uncorrelated.
Thus if A with X% coverage is on top of B with Y% coverage and C in the background, then it's assumed that one will see
X%*A + (100-X%)*Y% * B + (100-X%)(100-Y%)*C
Does that make sense? Obviously this will give "leaks" in the case where A and B are strongly correlated.
I think I might have put a small bit mask on the rays to avoid these problems, but it was a very long time ago.
• With that explanation it totally makes sense, thank you! In case you remember, how was your experience with cone tracing in comparison to normal ray tracing? Of course it's an approximation, but does it achieve a considerable speedup at acceptable quality? Commented Sep 3, 2015 at 19:07
• Oh, gosh, it was a long time ago. Actually, I only implemented the cone tracing. Whether I actually tried turning off the radius part I simply can't recall but, if I get time, I'll try to remember the pros and cons of going down the cone-tracing route. Commented Sep 4, 2015 at 9:55
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Physics Honors/AP 1 and 2
Physics Lab
# Physics Lab: Spring Constant
## Goal: To determine the spring constant for a 5" spring.
#### Materials
• One or more 5" springs (available at a hardware store)
• Other equipment as you deem necessary!
#### Procedure
1. Design a lab to determine the spring constant k for a narrow 5-6" spring [if you have the Physics lab kit, use the Hooke's constant spring so that you can compare data with your peers]. You may consult with your fellow students use similar or different methods. Come up with a way to suspend the spring, attach your weights, and measure the displacement x caused by force of the weights. The spring constant k will be F/x.
2. How many trials should you make?
3. What components of the spring force equation can you vary? What should you vary? What are the limits of your variations? [Remember that stretch the spring too far will destroy its springyness and change its constant.]
4. Determine the spring constant using you method for at least two other springs. If possible, collaborate (identify similar springs in your kit and compare your results with your peers).
#### Data Handling
1. Explain your calculations.
2. Show how plotting data such as force against extension can give you a value for k, the spring constant.
#### Report
1. Describe your materials, equipment, an dprocedures in sufficient detail that your fellow students could repeat your experiment.
2. Report your data. Be sure to indicate the amount of error in your measurements. For example, if you can only measure a mass of 25 gms within 1 grm, your error would be 25 ± 1, or 1/25 = 4%.
3. Present your data in an organized form, preferably in a table, in such a way it is easy to compare results as you repeate trials or vary a specific contributing factor.
4. Show a sample calculation, if you have calculated values.
5. If you did a series of experiments, varying something by increasing or decreasing a factor, try to plot your data (y-axis) as a function of the factor (x-axis).
6. You may use a spreadsheet to calculate your information and create your table.
7. Summarize your results.
8. Draw conclusions about what is happening.
9. Suggest at least one way to improve your experiment.
Post your report to the Moodle Lab Assignment for this Lab.
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Presentation is loading. Please wait.
# What is a Bus? One of the set of conductors (wires, PCB tracks, or connections in an integrated circuit) connecting the various functional units in a computer.
## Presentation on theme: "What is a Bus? One of the set of conductors (wires, PCB tracks, or connections in an integrated circuit) connecting the various functional units in a computer."— Presentation transcript:
What is a Bus? One of the set of conductors (wires, PCB tracks, or connections in an integrated circuit) connecting the various functional units in a computer. There are busses both within the CPU and connecting it to external memory and peripheral devices. The width of the data bus, i.e., the number of parallel connectors, and its clock rate determine its data rate (the number of bytes per second which it can carry). This is one of the factors limiting a computers performance.
Computers do their work with Ones and Zeroes This is called the binary number system A single binary digit (a one or a zero) is called a bit Binary works for computers because switches are on or off Eight bits make up a byte We'll see more about this soon... DecimalBinary 0 0 1 1 2 10 3 11 4100 5101 etc
Serial Parallel
Printed Circuit Boards
Cross section of multilayer printed circuit board
CPU RAM or ROM The buss address wires: 10010111 The buss data wires: 00110010 Hey RAM! Get me whatever is stored at address 10010111 Ok boss... that would be the number 00110010 bus's read/write wire 0 (read from memory) (Data on data wires would go in the other direction if read/write wire was 1 – CPU would send, RAM would receive)
Okay, so thats what the circuit board is about... What goes on behind the closed doors of the chips?
The clock set the pace, and keeps the chips in sync...
Some metaphors for how a computer is organized...
A Little More About the CPU... All a CPU does is: fetch instructions from RAM or ROM execute those instructions Executing an instruction generally involves either: reading data from memory into a register (a very small chunk of extremely fast volatile memory built into the CPU), or modifying the data in a register (adding two values, comparing them, testing if a value is zero, etc), or storing the contents of a register back into memory Instructions are just ones and zeroes For instance, in an 8086 microprocessor, the instruction 10110000 01100001 means "put the value 01100001 into register AL"
Booting a PC...
Adding Two One-Bit Binary Numbers Input AInput BDecimal Output Binary Output In Other Words... 000000 + 0 = 0 101011 + 0 = 1 011010 + 1 = 1 112101 + 1 = 2 Think of the binary output as two separate bits: Rule for the right (ones) bit: (A and not B) or (B and not A) Rule for the left (twos) bit: ??
Getting Tricky with Ones and Zeroes AND OR 2-way switchflashlight
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# A Short Guide to Robot Path Planning
##### The times they are a-changin’.
This post seems to be older than 15 years—a long time on the internet. It might be outdated.
Pick your favorite path planning approach and explain why you prefer it. Give an example of how it works. Identify its strengths and weaknesses, compared to other methods. Describe how you might apply it.
My favorite path planning approach is the visibility graph. I enjoy the visibility graph because it is one the primary methods I use to when performing my own human version of “path planning.” Last summer, I worked in a cubicle office space. There were two doors leading into the office space and the door to the restroom was more or less situated between the two doors. I was constantly trying to figure out which door required the least amount of steps. Although I didn’t know it at the time, I was basically creating a visibility graph and attempting to determine the shortest path, all in my head.
The Visibility Graph works by plotting straight line paths between the start, goal, and all the vertices of the all the objects in the workspace. The paths may cross over each other; however they may not intersect an object. There are several methods to actually calculate the visibility graph; however the most common method is the rotational plane sweep algorithm. Once constructed, the visibility graph can be searched for the shortest path from the start to the goal. Searching for a path usually requires weighting each segment of the line. Typically, the weight would just be its distance. However, other factors such as quality of terrain or amount of energy needed could also be taken into account.
One of the most obvious weaknesses of the visibility graph is that its complexity greatly increases as the number of objects increases. Additionally, many of the edges in the visibility graph are unneeded, such as when a vertex occurs in a convex area. There are methods to remove these additional edges; however, they will require additional computation efforts. If a workspace is expected to have many objects with convex vertices, it would probably be more efficient to use trapezoidal decomposition.
One of the benefits of the visibility graph, especially when compared to trapezoidal decomposition, is that the path planner does not care about the boundaries of the workspace. This could be especially helpful in situations where the edges of the workspace are complex. And let’s face it, looking at the visibility graph is pretty cool in and of itself.
7
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# Definite Integral – Finding area between a polynomial and a line – Exercise 6793
Exercise
Find the area of the region bounded by the graphs of the equations:
$$y=x^3-3x+1, y=x+1$$
$$S=8$$
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MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi
# How to convert a vector to a row of a matrix and resize it at the same time in a special situation?
Asked by Ayob on 19 Apr 2013
I want to convert a vector to a row of a matrix in a special situation which is necessary to resize it too as I explain.
for example:
```vector A=[1 2 3]
```
should be the second row of matrix B in a special situation as shown below,as you see in the second row of the matrix B,after every two element zero we have a element of vector A.
```B=[a b c d e f g h i;
0 0 1 0,0 2 0 0 3;
a1 b1 c1 d1 e1 f1 g1 h1 i1;
.. .. .. .. .. .. .. .. ..;]
```
My program is a large one and I need the way which is fast.
## Products
No products are associated with this question.
Answer by Matt J on 19 Apr 2013
``` B(2,:)=0;
B(2,3:3:end)=A;```
## 1 Comment
Ayob on 19 Apr 2013
Yes,it works
Answer by Azzi Abdelmalek on 19 Apr 2013
``` A=[1 2 3]
B=[5 5 5 5 5 5 5 5 5;0 0 0 0 0 0 0 0 0;4 4 4 4 4 4 4 4 4]
n=size(B,2)
id=fix(n/3);
B(2,id:id:n)=A```
## 1 Comment
Ayob on 19 Apr 2013
Good but not as much Matt. method.
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# What is 0.999 in percent form
### Decimal to Percentage (%) Calculator
Enter a decimal value:
% Ex.: 0.25, 0.7, 3/5, 2, etc.
Percent result
### Quote of the day ...
Here is the answer to the question: What is 0.999 in percent form or how to convert 0.999 into a percent equivalent.
## How to convert from decimal to percent
### Let's see this example:
We want to write the decimal number 0.999 in percent form. So, to convert this value to percent, we just multiply it by 100.
In this example multiplying 0.999 by 100 we get 99.9 (the value in percent).
➥ There is an ease way to accomplish this:
• Step1: Move the decimal point two places to the right: 0.999 → 9.99 → 99.9.
• Step2: Add a % sign: 99.9%
So, 0.999 is equivalent to 99.9% in percent form.
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# Booleans
Booleans are True or False statements. Unlike strings or numbers, booleans store statements of truth: is what I’m saying true or false?
For example, if I say, “You are a robot”, a boolean can store whether this statement is true. In this case, since you are not a robot (hopefully!), False would be stored.
1. I am a human. _______
2. I have 25 fingers. _______
4. My favorite color is blue. ______
The most common forms of boolean operators are comparisons like less than or greater than. How these are written in python are listed below.
OperatorDescriptionOperatorDescription
<Less than>Greater than
<=Less than or equal to>=Greater than or equal to
==Equal to!=Not equal to
### Challenge 1
As usual, use print to print out your results to the following:
print(5 + 8 < 10)
print((3 + 5) * 6) == (65 - 17)
The first statement should return False. And the second should return True.
### Challenge 2
Try printing out the answers to the following expressions using print. If the results for any of these statements don’t make sense, please ask for help!
• 54 < (10 + 32)
• (37 / 5) != 7
• “Hello” + “World” == “Hello World”
• False == False
### Fun Fact: Connecting Booleans with AND and OR operators
You can also connect boolean expressions together using the AND and the OR operator. Here’s a chart that describes what happens when we connect booleans together:
ExpressionResult
True and TrueTrue
True and FalseFalse
False and TrueFalse
False and FalseFalse
True or TrueTrue
True or FalseTrue
False or TrueTrue
False and FalseFalse
To summarize, AND requires both boolean expressions to be true, while OR only requires one of the two Boolean expressions to be true. Here are some more examples:
• (5 < 8) and (9 != 10) produces True since both 5 is less than 8 and 9 is not equal to 10.
• (8 <= 2) or (“h” + “e” == “he”) produces True since “h” + “e” results in “he”, even though 8 is not less than or equal to 2.
• (6 != 2 * 3) or (8 < 2 * 4) produces False since both 6 not equal to 2 * 3, and 8 being less than 2 * 4, produce False.
#### What do you think the following expressions produce?
• (11-2 < 10) and (7+3 > 10)
• (True or 3 < 1) and (False or 3>1)
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## Search found 572 matches
Thu Oct 10, 2019 1:39 pm
Forum: BASIC programs
Topic: Digital Signal Processing
Replies: 4
Views: 834
Flag:
### Re: Digital Signal Processing
"Your" FFT code is adapted to and published in BestBASIC: https://bestbasic.net/forum/viewtopic.php?f=4&t=41
In speed it is superior. Seehttps://bestbasic.net/forum/viewtopic.php?f=4&t=42
Sat May 11, 2019 8:22 am
Forum: BASIC programs
Topic: IBM mainframe 360/30 vs. iPad 2019
Replies: 13
Views: 1369
Flag:
### Re: IBM mainframe 360/30 vs. iPad 2019
I remember making a large stress analisys program (Finite Element Method) in Fortran IV on the new IBM 360/30 mainframe in the late sixties. The process involved a large number of simultaneous linear equations to be solved. Intensive use of a hard disk (7.2 Mb) was necessary due to the limited amou...
Fri May 03, 2019 9:17 am
Forum: BASIC programs
Topic: Whisky app, Final version
Replies: 8
Views: 952
Flag:
### Re: Whisky app, Final version
@ Henko »30 Apr 2019, 12:45
I think you make a mistake in the sentence: "If we take a dram as 3 cc or whiskey, then one dram costs € 2.69"
3cc is equal to 3ml. I suppose you are counting here with 3cl?
A dram of 3cc is only a small sip and € 2.69 is very expensive for that.
Mon Apr 01, 2019 8:28 am
Forum: BASIC programs
Topic: Minesweeper, final version 29-02-2019
Replies: 3
Views: 657
Flag:
### Re: Minesweeper, final version 29-02-2019
Thank you Henko for the detailed explanation. As a mac user I didn't know the game.
I will definitely try it now, hoping it won't become an addiction.
Fri Mar 08, 2019 10:00 am
Forum: Libraries
Topic: Rounded Rectangles
Replies: 7
Views: 774
Flag:
### Re: Rounded Rectangles
matt7 wrote:
Thu Mar 07, 2019 9:12 pm
… Any draw and fill settings (including color, alpha, dash, and shadow) must be set before calling one of the functions, just like normal DRAW and FILL commands.
… snip
You do not have to be a fool to forget that
Thu Mar 07, 2019 11:36 am
Forum: Libraries
Topic: Rounded Rectangles
Replies: 7
Views: 774
Flag:
### Re: Rounded Rectangles
Game, set match!
Thu Mar 07, 2019 9:35 am
Forum: Libraries
Topic: Rounded Rectangles
Replies: 7
Views: 774
Flag:
### Re: Rounded Rectangles
old alternative solution: viewtopic.php?f=20&t=449&p=1470
Tue Mar 05, 2019 9:57 am
Forum: BASIC programs
Topic: "Quick & dirty" file selector
Replies: 7
Views: 641
Flag:
### Re: "Quick & dirty" file selector
Thanks Henko,
My own solution to find and select files is far too complex for easy use. viewtopic.php?f=20&t=1530&p=9321
This solution is very elegant and useful in most cases.
Tue Feb 19, 2019 10:25 am
Forum: PDF manual (by Dutchman)
Topic: PDF manual 5-8
Replies: 7
Views: 2074
Flag:
### Re: PDF manual 5-8
I have added subchapter "Sprite order rules" on page 55
Tue Feb 19, 2019 8:53 am
Forum: BASIC programs
Topic: The game of Hamurabi with a new coat
Replies: 20
Views: 1205
Flag:
### Re: The game of Hamurabi with a new coat
Nice "coat" for that old interesting game
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100 719
Assignments Done
97.9%
Successfully Done
In July 2021
# Answer to Question #4302 in AJAX | JavaScript | HTML | PHP for Johann
Question #4302
Print out all numbers between 0 & 1000 which are evenly divisible by three OR seven. Print them on different lines.Print out all numbers between 0 & 1000 which are evenly divisible by three OR seven. Print them on different lines.
7) Write a loop which prints out every third number between 11 & 21 inclusive.
8) Write a loop which calculates 5 factorial.
9) Write a loop which calculates the average of all of the numbers which are evenly divisible by 3 and lie between 70 & 101 inclusive. The average should be a double.
10) Write a loop which sums up 1/20 + 1/19 + 1/18 +...1/2.
1
2011-10-07T08:21:05-0400
#include <stdio.h>
//~ Print out all numbers between 0 and 1000
which are evenly divisible by three OR seven.
//~ Print them on different
lines.
void PrintDiv3_7()
{
int i=0;
int cnt3=0; // counter of
period 3
int cnt7=0; // counter of period 7
while (i<1001)
{
if ((cnt3==0) || (cnt7==0))
printf("%d \n", i);
cnt3=(cnt3<2)?
cnt3+1 : 0;
cnt7=(cnt7<6)? cnt7+1 :
0;
i++;
};
printf("\n\n");
};
//~ 7) Write a loop which
prints out every third number between 11 and 21 inclusive.
void
PrintEveryThird()
{
int i;
for (i=11+2; i<22;
i+=3)
{
printf("%d ", i);
};
printf("\n\n");
};
//~ 8)
Write a loop which calculates 5 factorial.
void Calc5Fact()
{
int
i;
int f=1;
for(i=2; i<6; i++)
f*=i;
printf("5! =
%d\n\n",f);
};
Need a fast expert's response?
Submit order
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
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New Zealand
Level 8 - NCEA Level 3
# Applications of sine and cosine functions
## Interactive practice questions
The population (in thousands) of two different types of insects on an island can be modelled by the following functions: Butterflies: $f\left(t\right)=a+b\sin\left(mt\right)$f(t)=a+bsin(mt), Crickets: $g\left(t\right)=c-d\sin\left(kt\right)$g(t)=cdsin(kt)
$t$t is the number of years from when the populations started being measured, and $a$a,$b$b,$c$c,$d$d,$m$m, and $k$k are positive constants. The graphs of $f$f and $g$g for the first $2$2 years are shown below.
a
State the function $f\left(t\right)$f(t) that models the population of Butterflies over $t$t years.
b
State the function $g\left(t\right)$g(t) that models the population of Crickets over $t$t years.
c
How many times over a $18$18 year period will the population of Crickets reach its maximum value?
d
How many years after the population of Crickets first starts to increase, does it reach the same population as the Butterflies?
e
Solve for $t$t, the number of years it takes for the population of Butterflies to first reach $200000$200000.
Easy
Approx 19 minutes
Three objects, $X$X, $Y$Y and $Z$Z are placed in a magnetic field such that object $X$X is $2$2 cm from object $Y$Y and $4$4 cm from object $Z$Z. As object $X$X is moved closer to line $YZ$YZ, object $Y$Y and $Z$Z move in such a way that the lengths $XY$XY and $XZ$XZ remain fixed.
Let $\theta$θ be the angle between sides $XY$XY and $XZ$XZ, and let the area of triangle $XYZ$XYZ be represented by $A$A.
A circular Ferris wheel that is $40$40 meters in diameter contains several carriages. Hannah and Michael enter a carriage at the bottom of the Ferris wheel, and get off $6$6 minutes later after having gone around completely $3$3 times. When a carriage is at the bottom of the wheel, it is $1$1 meter above the ground.
The tide rises and falls in a periodic manner, and Brad needs to chart tide levels to determine when he can sail his ship into a bay. He begins measuring at low tide at $8$8am, and sees the marking that the bay is $7$7 metres deep. He measures high tide at $2$2pm, when the bay is $15$15metres deep.
### Outcomes
#### M8-2
Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions
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https://www.mathematicshub.edu.au/search/resolve-bakery-3/
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Go to website
# reSolve bakery 3
Models and compares different multiplication strategies for solving the 'The cupcake order' problem. It then launches the 'Cupcake boxes' problem, which draws on various concepts including two-digit multiplication, shape and area.
Year level(s) Year 5
Audience Student, Teacher
Purpose Teaching resource, Teaching strategies
Format Video
Teaching strategies and pedagogical approaches Questioning, Concrete Representational Abstract model, Targeted teaching, Worked examples
Keywords strategy, partitioning, multiplication, renaming, doubling, problem solving, reasoning, understanding, fluency, centimetres, area, explicit teaching
## Curriculum alignment
Curriculum connections Numeracy
Strand and focus Number, Build understanding
Topics Multiplication and division, Operating with number
AC: Mathematics (V9.0) content descriptions
AC9M5N06
Solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate; check the reasonableness of answers
AC9M5M02
Solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units
AC9M5N02
Express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another
Numeracy progression Multiplicative strategies (P6, P7)
Understanding units of measurement (P7)
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# Kinematics of thrown chalk - find time to hit the floor
#### jacyh
Using only one equation of motion, how will you solve this:
Suppose a the tteacher's hand is 1m from the floor, and the teacher flicked a chalk upwards at 2m/s. How long will it take for the chalk to reach the floor?
I can't seem to use only one equation, it's always two equations or three.
Related Introductory Physics Homework Help News on Phys.org
#### Dr.Brain
Its simple.If the teacher throws the chalk upwards with velocity 2 m/s , then on downward motion, while at the same point on its return motion , its velocity would be 2 m/s . Now apply v=u+at .
BJ
#### HallsofIvy
Homework Helper
Dr.Brain said:
Its simple.If the teacher throws the chalk upwards with velocity 2 m/s , then on downward motion, while at the same point on its return motion , its velocity would be 2 m/s . Now apply v=u+at .
BJ
But to find the time at which it hit the floor you would have to use a second "equation of motion" and apparently this question requires only one.
I would vote for d= -(1/2)gt2+ 2t+ 1 where d is the height above the floor. Set d= 0 and solve for t.
#### mukundpa
Homework Helper
Take h= -1m(downward), u = +2 m/s (upward) and "g" negative(downward) and solve eq h = ut + (1/2)gt^2.
it is quadratic in t gives two values of t, the positive value is the answer.
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# LUP Student Papers
## LUND UNIVERSITY LIBRARIES
### Map change detection using GPS position data
and Andersson, Fanny LU (2018) In Master's Theses in Mathematical Sciences FMAM05 20181
Mathematics (Faculty of Engineering)
Abstract
Technology advancement in autonomous driving is accelerating. For the technology to be safe it is crucial for the vehicles to have an updated map, meaning all vehicles should have a correct and identical representation of the current road network. This makes change detection in the maps of great importance, in order to continuously understand and recognize the features that need to be updated.
This thesis aims to develop and evaluate methods to continuously and automatically update maps using only crowd-sourced Global Positioning System (GPS) data. The approach was to create inferred maps using a method based on an approximate Kernel Density Estimation (KDE). The road network is represented using a mathematical graph. A Hidden Markov... (More)
Technology advancement in autonomous driving is accelerating. For the technology to be safe it is crucial for the vehicles to have an updated map, meaning all vehicles should have a correct and identical representation of the current road network. This makes change detection in the maps of great importance, in order to continuously understand and recognize the features that need to be updated.
This thesis aims to develop and evaluate methods to continuously and automatically update maps using only crowd-sourced Global Positioning System (GPS) data. The approach was to create inferred maps using a method based on an approximate Kernel Density Estimation (KDE). The road network is represented using a mathematical graph. A Hidden Markov Model (HMM) and the Viterbi algorithm are used to map match GPS data to the road network.
In the updating routine, new roads are added and old ones are removed. Furthermore, temporary changes are flagged. Three evaluation methods, two set-based and one path-based, are proposed which complement one another by taking different aspects into account—both geometric and topologic.
The proposed map-inference method is robust to noise compared to many other map-generation algorithms, however, it is computationally heavy. Therefore, we propose creating geographically smaller maps and fusing multiple maps together. One of the main challenges was the parameter tuning of various thresholds, since the implemented algorithms are sensitive with respect to the accuracy of the data. The path-based evaluation is the only method where parameter tuning is not needed.
Evaluation results show successful map updates on road level, where the accuracy was further increased when using an OpenStreetMap (OSM) as base map. However, results show that the methodology is not appropriate to obtain lane-level accuracy. (Less)
Popular Abstract (Swedish)
Självkörande bilar är ett hett forskningsområde och utvecklingen går snabbt framåt. För att teknologin ska vara säker krävs det att alla bilar har en uppdaterad karta över hur vägnätverket ser ut. Om bilen ska kunna använda kartan för navigering behöver den innehålla information om mer än bara var man kan svänga. Information ner på centimeterprecision om vägskyltar, trafikljus, vägmarkeringar och vägräcken är livsnödvändigt för att bilen ska kunna köra själv.
De flesta nyare bilar samlar hela tiden in information om sin omgivning med hjälp av ett antal sensorer såsom kameror, RADAR och GPS. Med denna information kan förändringar i vägnätverket upptäckas. Dessa förändringar kan vara både temporära såsom vägarbeten eller permanenta såsom... (More)
Självkörande bilar är ett hett forskningsområde och utvecklingen går snabbt framåt. För att teknologin ska vara säker krävs det att alla bilar har en uppdaterad karta över hur vägnätverket ser ut. Om bilen ska kunna använda kartan för navigering behöver den innehålla information om mer än bara var man kan svänga. Information ner på centimeterprecision om vägskyltar, trafikljus, vägmarkeringar och vägräcken är livsnödvändigt för att bilen ska kunna köra själv.
De flesta nyare bilar samlar hela tiden in information om sin omgivning med hjälp av ett antal sensorer såsom kameror, RADAR och GPS. Med denna information kan förändringar i vägnätverket upptäckas. Dessa förändringar kan vara både temporära såsom vägarbeten eller permanenta såsom nya vägar. Att manuellt hitta och korrigera dessa ändringar i motsvarande karta är kostsamt och tidskrävande.
I detta arbete utforskas metoder för automatisk kartuppdatering. Idén är att utnyttja en stor mängd GPS-data som samlas in från många bilar. Med hjälp av denna data kan en karta skapas över hur vägnätverket ser ut. Denna används sedan för att hitta förändringar i en äldre existerade karta. Detta kan vara antingen en högkvalitativ manuellt verifierad karta, exempelvis Google Maps, eller en karta skapad med data insamlad under en tidigare period. När förändringarna har identifierats uppdateras den äldre kartan med hjälp av den nya kartan. Genom att kontinuerligt samla in ny data kan vi se till att kartan de autonoma bilarna kör efter är uppdaterad så att de kan köra säkert. (Less)
author
supervisor
organization
alternative title
Utilising inferred maps to continuously and automatically detect changes in road networks for autonomous vehicles
course
FMAM05 20181
year
type
H2 - Master's Degree (Two Years)
subject
keywords
autonomous driving, change detection, map inference, GPS, road network, HMM, Viterbi algorithm, OSM, map matching, crowd-sourced data, update maps
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFMA-3353-2018
ISSN
1404-6342
other publication id
2018:E35
language
English
id
8948007
2018-06-12 16:47:46
date last changed
2018-06-12 16:47:46
```@misc{8948007,
abstract = {Technology advancement in autonomous driving is accelerating. For the technology to be safe it is crucial for the vehicles to have an updated map, meaning all vehicles should have a correct and identical representation of the current road network. This makes change detection in the maps of great importance, in order to continuously understand and recognize the features that need to be updated.
This thesis aims to develop and evaluate methods to continuously and automatically update maps using only crowd-sourced Global Positioning System (GPS) data. The approach was to create inferred maps using a method based on an approximate Kernel Density Estimation (KDE). The road network is represented using a mathematical graph. A Hidden Markov Model (HMM) and the Viterbi algorithm are used to map match GPS data to the road network.
In the updating routine, new roads are added and old ones are removed. Furthermore, temporary changes are flagged. Three evaluation methods, two set-based and one path-based, are proposed which complement one another by taking different aspects into account—both geometric and topologic.
The proposed map-inference method is robust to noise compared to many other map-generation algorithms, however, it is computationally heavy. Therefore, we propose creating geographically smaller maps and fusing multiple maps together. One of the main challenges was the parameter tuning of various thresholds, since the implemented algorithms are sensitive with respect to the accuracy of the data. The path-based evaluation is the only method where parameter tuning is not needed.
Evaluation results show successful map updates on road level, where the accuracy was further increased when using an OpenStreetMap (OSM) as base map. However, results show that the methodology is not appropriate to obtain lane-level accuracy.},
author = {Sjöstrand, Lina and Andersson, Fanny},
issn = {1404-6342},
keyword = {autonomous driving,change detection,map inference,GPS,road network,HMM,Viterbi algorithm,OSM,map matching,crowd-sourced data,update maps},
language = {eng},
note = {Student Paper},
series = {Master's Theses in Mathematical Sciences},
title = {Map change detection using GPS position data},
year = {2018},
}
```
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# ABC and ADC are two right triangles with common hypotenuse AC.
Question. ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.
Solution:
In $\triangle \mathrm{ABC}$,
$\angle A B C+\angle B C A+\angle C A B=180^{\circ}$ (Angle sum property of a triangle)
$\Rightarrow 90^{\circ}+\angle B C A+\angle C A B=180^{\circ}$
$\Rightarrow \angle B C A+\angle C A B=90^{\circ} \ldots(1)$
In $\triangle \mathrm{ADC}$
$\angle C D A+\angle A C D+\angle D A C=180^{\circ}$ (Angle sum property of a triangle)
$\Rightarrow 90^{\circ}+\angle A C D+\angle D A C=180^{\circ}$
$\Rightarrow \angle A C D+\angle D A C=90^{\circ} \ldots(2)$
Adding equations (1) and (2), we obtain
$\angle B C A+\angle C A B+\angle A C D+\angle D A C=180^{\circ}$
$\Rightarrow(\angle B C A+\angle A C D)+(\angle C A B+\angle D A C)=180^{\circ}$
$\angle B C D+\angle D A B=180^{\circ}$
However, it is given that
$\angle B+\angle D=90^{\circ}+90^{\circ}=180^{\circ} \ldots(4)$
From equations (3) and (4), it can be observed that the sum of the measures of opposite angles of quadrilateral ABCD is 180°. Therefore, it is a cyclic quadrilateral.
Consider chord CD.
$\angle C A D=\angle C B D$ (Angles in the same segment)
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https://www.maplesoft.com/support/help/maple/view.aspx?path=GaussInt/GIsmith&L=E
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crawl-data/CC-MAIN-2024-22/segments/1715971058709.9/warc/CC-MAIN-20240524091115-20240524121115-00556.warc.gz
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GIsmith - Maple Help
GaussInt
GIsmith
Gaussian Integer-only Smith Normal Form
Calling Sequence GIsmith(A) GIsmith(A, U, V)
Parameters
A - Matrix of Gaussian integers U - name (optional) V - name (optional)
Description
• The function GIsmith computes the Smith normal form S of an n by m Matrix of Gaussian integers.
• If two n by n Matrices have the same Smith normal form, they are equivalent.
• The Smith normal form is a diagonal Matrix $S$ where
$\mathrm{rank}\left(A\right)$ = number of nonzero rows (columns) of $S$
${S}_{i,i}$ is in the first quadrant for $0
${S}_{i,i}$ divides ${S}_{i+1,i+1}$ for $0
$\prod _{i=1}^{r}{S}_{i,i}$ divides $\mathrm{det}\left(M\right)$ for all minors $M$ of rank $0
• The Smith normal form is obtained by doing elementary row and column operations. This includes interchanging rows (columns), multiplying through a row (column) by a unit in ${Z}_{i}$, and adding integral multiples of one row (column) to another.
• In the case of three arguments, the second argument U and the third argument V will be assigned the transformation Matrices on output, such that GIsmith(A) = U . A . V.
Examples
> $\mathrm{with}\left(\mathrm{GaussInt}\right):$
> $H≔\mathrm{Matrix}\left(\left[\left[-4+7I,8+10I,-6-8I\right],\left[-5+7I,6-6I,5I\right],\left[-10+I,1-3I,-10+5I\right]\right]\right)$
${H}{≔}\left[\begin{array}{ccc}{-4}{+}{7}{}{I}& {8}{+}{10}{}{I}& {-6}{-}{8}{}{I}\\ {-5}{+}{7}{}{I}& {6}{-}{6}{}{I}& {5}{}{I}\\ {-10}{+}{I}& {1}{-}{3}{}{I}& {-10}{+}{5}{}{I}\end{array}\right]$ (1)
> $\mathrm{GIsmith}\left(H\right)$
$\left[\begin{array}{ccc}{1}& {0}& {0}\\ {0}& {1}& {0}\\ {0}& {0}& {1797}{+}{791}{}{I}\end{array}\right]$ (2)
> $A≔\mathrm{Matrix}\left(\left[\left[-4-8I,-1-10I,2+3I\right],\left[-1-9I,8+4I,-5+10I\right]\right]\right)$
${A}{≔}\left[\begin{array}{ccc}{-4}{-}{8}{}{I}& {-1}{-}{10}{}{I}& {2}{+}{3}{}{I}\\ {-1}{-}{9}{}{I}& {8}{+}{4}{}{I}& {-5}{+}{10}{}{I}\end{array}\right]$ (3)
> $B≔\mathrm{GIsmith}\left(A,U,V\right)$
${B}{≔}\left[\begin{array}{ccc}{1}& {0}& {0}\\ {0}& {1}& {0}\end{array}\right]$ (4)
> $U$
$\left[\begin{array}{cc}{-1}{+}{4}{}{I}& {-1}{-}{I}\\ {5}{-}{10}{}{I}& {2}{+}{3}{}{I}\end{array}\right]$ (5)
> $V$
$\left[\begin{array}{ccc}{0}& {43}{+}{30}{}{I}& {101}{+}{8}{}{I}\\ {0}& {-28}{-}{29}{}{I}& {-75}{-}{21}{}{I}\\ {1}& {66}{-}{21}{}{I}& {89}{-}{99}{}{I}\end{array}\right]$ (6)
> $\mathrm{LinearAlgebra}:-\mathrm{Equal}\left(\mathrm{.}\left(U,A,V\right),B\right)$
${\mathrm{true}}$ (7)
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http://www.math.niu.edu/~rusin/known-math/95/info-summary
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From: M.Voorneveld@kub.nl (VOORNEVELD M.) Newsgroups: sci.math Subject: continuity of information summarizing function Date: Tue, 3 Oct 1995 08:54:38 GMT Suppose we are given a positive, finite number n of variables, each having possible values in [0,1] and real valued functions w^i:[0,1]^n ---> R (i = 1,...,n) assigning to each possible combination of these variables a number representing something attached to the i-th variable (i=1,...,n). These functions w^i are continuous. We are working in a laboratory environment where all these variables can change, but only one at a time (never 2 or more at the same time). This provides us with a lot of information, but we are only interested in the situations in which we cannot imcrease any of the w^i's under the permitted changes (i.e. one at a time). We have found functions containing the necessary information, real valued functions M:[0,1] --> R which is such that M(x_{-i}, x_{i}) - M(x_{-i}, y_{i}) > 0 iff w^i(x_{-i}, x_{i}) - w^i({x_{-i}, x_{i}) > 0 for each x_{-i} = (x_1,...,x_{i-1},x_{i+1},...,x_n) in [0,1]^(n-1) and x_{i} in [0,1]. In other words, this function M exactly represents what happens to w^i when any variable i is changed. What we are interested in, is whether or not there is a function M which is continuous, given that the w^i are continuous on [0,1]^n and M satisfies the property given above. We thought about proving this by induction. The result is trivial if n = 1, since P = w^i has the desired property. If we try to extend this result to higher n, the problem is that we only know of continuous M's for the 'smaller' experiments involving at most n-1 variables, but we have to extract from these functions a single function that is continuous. Any information, references to relevant literature, etc. would be greatly appreciated. Please e-mail to M.Voorneveld@kub.nl Thanks! Mark Voorneveld ============================================================================== From: rusin@washington.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Re: continuity of information summarizing function Date: 5 Oct 1995 15:02:42 GMT In article , VOORNEVELD M. wrote: >Suppose we are given a positive, finite number n of variables, each having >possible values in [0,1] and real valued functions w^i:[0,1]^n ---> R >(i = 1,...,n) assigning to each possible combination of these variables a >number representing something attached to the i-th variable (i=1,...,n). > ... >We have found functions containing the necessary information, real valued >functions M:[0,1] --> R which is such that > > M(x_{-i}, x_{i}) - M(x_{-i}, y_{i}) > 0 iff > w^i(x_{-i}, x_{i}) - w^i({x_{-i}, x_{i}) > 0 > >for each x_{-i} = (x_1,...,x_{i-1},x_{i+1},...,x_n) in [0,1]^(n-1) and x_{i} >in [0,1]. Let me see if I've got this straight, say for n=2. You've got two real-valuesd functions w1 and w2 defined on the square and you're looking for a third one M with the property that M(x1,x2) > M(y1,x2) iff w1(x1,x2) > w1(y1,x2) M(x1,x2) > M(x1,y2) iff w2(x1,x2) > w2(x1,y2) What happens if, say, w1(x,y)=(1/2-y)x and w2(x,y)=(x-1/2)y ? Then you want M(2/3,2/3) > M(2/3, 1/3) because w2(2/3, 2/3) > w2(2/3, 1/3), but also M(2/3,1/3) > M(1/3, 1/3) because w1(2/3, 1/3) > w1(1/3, 1/3); so your M must have M(2/3,2/3) > M(1/3,1/3). On the other hand you also want M(2/3,2/3) < M(1/3, 2/3) because w1(2/3, 2/3) < w1(1/3, 2/3), but also M(1/3,2/3) < M(1/3, 1/3) because w2(1/3, 2/3) < w2(1/3, 1/3); so your M must have M(2/3,2/3) < M(1/3,1/3). Now you're trapped in a contradiction. You can scale these examples to keep the outputs in any desired range. Continuity has nothing to do with it. Perhaps I've overlooked something obvious? dave ============================================================================== From: "M.Voorneveld" To: rusin@math.niu.edu (Dave Rusin) Date: Fri, 6 Oct 1995 11:15:54 MET Subject: Re: continuity of information summarizing function > In article , > VOORNEVELD M. wrote: > >Suppose we are given a positive, finite number n of variables, each having > >possible values in [0,1] and real valued functions w^i:[0,1]^n ---> R > >(i = 1,...,n) assigning to each possible combination of these variables a > >number representing something attached to the i-th variable (i=1,...,n). > > > ... > >We have found functions containing the necessary information, real valued > >functions M:[0,1]^n --> R which is such that > > > > M(x_{-i}, x_{i}) - M(x_{-i}, y_{i}) > 0 iff > > w^i(x_{-i}, x_{i}) - w^i({x_{-i}, x_{i}) > 0 > > > >for each x_{-i} = (x_1,...,x_{i-1},x_{i+1},...,x_n) in [0,1]^(n-1) and x_{i} > >in [0,1]. > > Let me see if I've got this straight, say for n=2. You've got two real-valuesd > functions w1 and w2 defined on the square and you're looking for a third one > M with the property that > M(x1,x2) > M(y1,x2) iff w1(x1,x2) > w1(y1,x2) > M(x1,x2) > M(x1,y2) iff w2(x1,x2) > w2(x1,y2) > No, we HAVE functions w1 and w2 such that a third function with the above property exists. When it exists, there is a whole convex cone of such functions (Easy: aM has the desired property for any a>0 and if M and M~ have the desired property, so does M+M~. Notice that this cone is typically not pointed, since the zero function usually does not satisfy the desired property.). But does this cone contain a continuous one? > What happens if, say, w1(x,y)=(1/2-y)x and w2(x,y)=(x-1/2)y ? Then you want > M(2/3,2/3) > M(2/3, 1/3) because w2(2/3, 2/3) > w2(2/3, 1/3), but also > M(2/3,1/3) > M(1/3, 1/3) because w1(2/3, 1/3) > w1(1/3, 1/3); so your > M must have M(2/3,2/3) > M(1/3,1/3). On the other hand you also want > M(2/3,2/3) < M(1/3, 2/3) because w1(2/3, 2/3) < w1(1/3, 2/3), but also > M(1/3,2/3) < M(1/3, 1/3) because w2(1/3, 2/3) < w2(1/3, 1/3); so your > M must have M(2/3,2/3) < M(1/3,1/3). Now you're trapped in a contradiction. > > Perhaps I've overlooked something obvious? Sorry for this misunderstanding! Mark. ============================================================================== From: M.Voorneveld@kub.nl (VOORNEVELD M.) Newsgroups: sci.math Subject: Re: continuity of information summarizing function Date: Fri, 6 Oct 1995 10:27:12 GMT In article <450s2i\$g6j@muir.math.niu.edu> rusin@washington.math.niu.edu (Dave Rusin) writes: >In article , >VOORNEVELD M. wrote: >>Suppose we are given a positive, finite number n of variables, each having >>possible values in [0,1] and real valued functions w^i:[0,1]^n ---> R >>(i = 1,...,n) assigning to each possible combination of these variables a >>number representing something attached to the i-th variable (i=1,...,n). >> >... >>We have found functions containing the necessary information, real valued >>functions M:[0,1]^n --> R which is such that >> >> M(x_{-i}, x_{i}) - M(x_{-i}, y_{i}) > 0 iff >> w^i(x_{-i}, x_{i}) - w^i({x_{-i}, x_{i}) > 0 >> >>for each x_{-i} = (x_1,...,x_{i-1},x_{i+1},...,x_n) in [0,1]^(n-1) and x_{i} >>in [0,1]. >Let me see if I've got this straight, say for n=2. You've got two real-valuesd >functions w1 and w2 defined on the square and you're looking for a third one >M with the property that > M(x1,x2) > M(y1,x2) iff w1(x1,x2) > w1(y1,x2) > M(x1,x2) > M(x1,y2) iff w2(x1,x2) > w2(x1,y2) We assume that w1 and w2 are such that a function M with the desired property exists. When it exists there is a whole convex cone of such functions (Easy: if M has the desired property, then so does aM for any a>0 and if M and M~ both have the desired property, then so does M+M~. Notice that this cone is typically not pointed, since the zero function usually does not satisfy the desired property). The question is if this cone of functions with the desired property contains a CONTINUOUS one. Sorry for this misunderstanding! Mark M.Voorneveld@kub.nl ============================================================================== From: "M.Voorneveld" To: rusin@math.niu.edu (Dave Rusin) Date: Mon, 9 Oct 1995 14:46:44 MET Subject: Re: continuity of information summarizing function > got it now. let me think about it some more later today. > dave Okay, I hope you can figure it out. My knowledge of math is really not that phenomenal and even though I spent lots of time on it, I couldn't solve it. Intuitively, there should be such a continuous function, considering that the domain [0,1]^n and the functions w^i are so 'nice', but it wouldn't be the first time my intuition was wrong! Mark ============================================================================== From: rusin@washington.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Ordered topologies (Was Re: continuity of information summarizing function) Date: 9 Oct 1995 22:28:45 GMT I'm sort of tuckered out on this one, but I thought I'd re-cast the problem so that someone else can see what needs to be done. The following would resolve the original problem (attached below). Y is a topological space with a partial ordering "<", such that all the sets A_p = { q in Y : q < p } are open. The question then is, is there necessarily a _continuous_ embedding of Y into R? Jacobson's _Algebra_ notes that a finite partially ordered set embeds in a totally ordered set. Since he bothers attributing this result (to Szpilrajn-Marczewski (!) ) I assume there must be a broader context for this kind of thing. Of course you need to know something about Y (e.g. its cardinality). Here's the setup of the original poster. A (transitive!) partial order is established on the cube X = [0,1]^n . The ordering is specified by a set of n real-valued functions w_i: we say p < q iff p and q have all coordinates equal except the i-th, and w_i(p) < w_i(q). I believe the w_i were assumed to be smooth. Unless I've missed some nuance here, this leads to an equivalence relation on X such that Y = X/~ has the stated property. ("~" is generated by: p~q iff w_i(p)=w_i(q) and p and q have all but the i-th coordinates equal.) An excerpt of the original post is attached. dave In article , VOORNEVELD M. wrote: >Suppose we are given a positive, finite number n of variables, each having >possible values in [0,1] and real valued functions w^i:[0,1]^n ---> R >(i = 1,...,n) assigning to each possible combination of these variables a >number representing something attached to the i-th variable (i=1,...,n). > ... >We have found functions containing the necessary information, real valued >functions M:[0,1]^n --> R which is such that > > M(x_{-i}, x_{i}) - M(x_{-i}, y_{i}) > 0 iff > w^i(x_{-i}, x_{i}) - w^i({x_{-i}, x_{i}) > 0 > >for each x_{-i} = (x_1,...,x_{i-1},x_{i+1},...,x_n) in [0,1]^(n-1) and x_{i} >in [0,1]. ============================================================================== From: M.Voorneveld@kub.nl (VOORNEVELD M.) Newsgroups: sci.math Subject: Topology question Date: Wed, 21 Feb 1996 08:26:03 GMT Let X and Y be compact metrizable topological spaces (so that XxY, the product of X and Y, is compact in the product topology) and f = (f1,f2) : XxY --> R^2 a continuous function into two-dimensional Euclidean space. One is given that there exists a real-valued function g: XxY --> R such that for each a and b in X and each c and d in Y: g(a,c) > g(b,c) iff f1(a,c) > f1(b,c) and g(a,c) > g(a,d) iff f2(a,c) > f2(a,d) QUESTION: Is there a function h: XxY --> R with the same property as g which has a maximum on XxY? I tried this problem first by looking if I could show there is a function h which is continuous, but for the existence of a maximum it will suffice to show that there is a function h which is upper semi-continuous in the sense that {(x,y) in XxY | h(x,y) >= c} is closed for every c in R. But I can't show this, each time getting stuck because the only thing one knows about this function g (or h) is how it behaves in two 'directions' as dictated by the property of g: it increases iff the first (resp. second) coordinate changes and the first (resp. second) coordinate function increases. On the other hand, I couldn't find a counterexample either! Can someone maybe give some hints on how to solve this problem? Maybe looking at continuity properties is not the easiest way! Please mail to M.Voorneveld@kub.nl Thanks! Mark Voorneveld (M.Voorneveld@kub.nl) ============================================================================== From: rld@math.ohio-state.edu (Randall Dougherty) Newsgroups: sci.math Subject: Re: Topology question Date: 21 Feb 1996 19:46:11 -0500 In article , VOORNEVELD M. wrote: >Let X and Y be compact metrizable topological spaces (so that XxY, the >product of X and Y, is compact in the product topology) and >f = (f1,f2) : XxY --> R^2 a continuous function into two-dimensional >Euclidean space. > >One is given that there exists a real-valued function g: XxY --> R such that >for each a and b in X and each c and d in Y: >g(a,c) > g(b,c) iff f1(a,c) > f1(b,c) and >g(a,c) > g(a,d) iff f2(a,c) > f2(a,d) > >QUESTION: Is there a function h: XxY --> R with the same property as g which >has a maximum on XxY? Not necessarily. Let X = Y = [0,1]. Let f1(0,0) = f2(0,0) = g(0,0) = 0 and, for (x,y) different from (0,0), f1(x,y) = xy^6/(x^2+y^2)^3 f2(x,y) = yx^6/(x^2+y^2)^3 g(x,y) = xy/(x^2+y^2)^3. Then f1,f2,g have the stated properties. Now suppose h has the same property as g. Let Z be the zigzag path from (1,1) to (1/2,1) to (1/2,1/2) to (1/4,1/2) to (1/4,1/4) to ... . Then h(x,y) must strictly increase as (x,y) moves along Z toward (0,0). Also: h(x,0) = h(1,0) < h(1,1); h(0,y) = h(0,1) < h(1,1); if (x,y) lies to the right of Z, and (x',y) is on Z, then h(x,y) < h(x',y); if (x,y) lies above Z, and (x,y') is on Z, then h(x,y) < h(x,y'). Therefore, for any (x,y) we have h(x,y) < h(1/2^n,1/2^n) for some n. Since the numbers h(1/2^n,1/2^n) strictly increase as n increases, h has no maximum. Randall Dougherty rld@math.ohio-state.edu Department of Mathematics, Ohio State University, Columbus, OH 43210 USA "I have yet to see any problem, however complicated, that when looked at in the right way didn't become still more complicated." Poul Anderson, "Call Me Joe" ============================================================================== From: "M.Voorneveld" To: rusin@math.niu.edu (Dave Rusin) Date: Fri, 8 Mar 1996 14:00:43 MET Subject: Groebner bases and Info summary Admittedly, I had noticed the connection between linear algebra and game theory. The Groebner base idea sounds interesting. I don't know the concept, but will look in our library. Do you have any good references to it? Here's the counterexample of our correspondence on information summarizing functions. It was given by Randall Dougherty (Dept Mathematics, Ohio State University): Consider [0,1]^2 as domain, take w_1(x,y) = 0 if (x,y) = (0,0) xy^6/(x^2 + y^2)^3 otherwise w_2(x,y) = 0 if (x,y) = (0,0) yx^6/(x^2 + y^2)^3 otherwise M(x,y) = 0 if (x,y) = (0,0) xy/(x^2 + y^2)^3 otherwise Clearly, w = (w_1,w_2) is continuous, M satisfies the desired property. Consider any function M with the desired property and consider the zig zag path Z from (1,1) to (1/2,1) to (1/2,1/2) to (1/4,1/2) to (1/4,1/4) to ... M strictly increases along this path. Also M(x,0) = M(1,0) < M(1,1) M(0,y) = M(0,1) < M(1,1) If (x,y) lies to the right of Z and (x',y) is on Z, then M(x,y) < M(x',y). If (x,y) lies to the left of Z and (x,y') is on Z, then M(x,y) < M(x,y'). Therefore, for any (x,y) in [0,1]^2 we have M(x,y) < M(1/2^n, 1/2^n) for some n. Since the sequence {M(1/2^n, 1/2^n)}_{n = 0}^{\infty} strictly increases, M has no maximum. But then M cannot be continuous! Best, Mark =================== Mark Voorneveld M.Voorneveld@kub.nl =================== ============================================================================== From: "M.Voorneveld" Organization: Tilburg University To: rusin@math.niu.edu (Dave Rusin) Date: Mon, 11 Mar 1996 11:24:30 MET Subject: Re: Groebner bases and Info summary > There is a very readable introduction to Groebner bases in the Springer > Undergraduate Texts in Mathematics series. The authors are (I think) > Little, O'Shea, and one other whose name escapes me right now. Okay, I know which book you mean! As usual, it is not present at our library; the only study at our university which is closely related to mathematics is econometrics (I'm in the mathematical economics program of the econometrics department) and our supply of good books on mathematics is unfortunately rather limited. > Thanks for sending the example. I noticed in on sci.math. I should append > it to the file in which we discussed this problem. The zigzag path is essential since we only have data concerning the properties of the functions in the directions of the 'coordinate axes'; There may be simpler examples. I'll let you know if I find a particularly clear one! Mark =================== Mark Voorneveld M.Voorneveld@kub.nl ===================
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# Alternatives to motorized variable capacitor?
I want to dynamically fine-tune the capacitor (about 100pF) of an RLC series resonant circuit, so as to keep it tuned despite variations of the coil's environment. Operating frequency is f = 13.56MHz, Q ≈ 30, about 0.1W power dissipation in R (mostly hidden in the coil). I only need like ±10% adjustment of C.
I see that I could use a motorized capacitor (approriately scaled with fixed capacitors), but what I find is way overkill and over-expensive.
What are my options ?
I vaguely see that a varicap may help (although polarization might be tricky), but I have no experience with these, and I even wonder if a varicap is at all compatible with my high-Q requirement.
I'm pointed that the voltage across the capacitor is critical in the varicap scenario. It can be estimated from the givens; I get:
(Q R)2 C = L and (2π f) 2 L C = 1,
thus R = 1/(2π f C Q) ≈ 3.9Ω
thus IEFF = (P/R)1/2 ≈ 160mA,
thus UEFF = IEFF/(2π f C) ≈ 19VEFF across the capacitor.
With some margin, I believe 80VPP will never be exceeded.
Currently my capacitor has no grounded side; but that polarization issue seems fixable.
• Depending on the steps you need something similar to a decade could work, or maybe a golomb ruler like setup Commented Apr 18, 2016 at 11:27
• A proper varicap may help. Modern diodes have very high Q value (low losses), it is not a problem for your Q=30 requirement. The problem is the operating voltage. What RF voltage do you have on this ~100 pF capacitor? Commented Apr 18, 2016 at 11:54
• Motorized inductor? Commented Apr 18, 2016 at 12:24
• @Master: I guess operating voltage is <80Vpp (see addition in question). Commented Apr 18, 2016 at 16:41
You have a large number of options.
a) Your link to motorised cap is indeed way over the top. However, if you can buy, or rescue from a junked radio, a vane-type variable tuning capacitor, you can buy a geared stepper motor for a few \$£euro from fleaBay, and couple them yourself.
b) Although you say you only need 10% variation in C, it is usually unwise to use a variable capacitor as the entire tuning C. Far better to used a fixed capacitor, and connect a variable capacitor with a relatively large capacitance swing to it with a small capacitor. This has a number of advantages.
The stability and resolution of the resulting combination is far better than that of the variable capacitor alone.
The RF voltage across the variable element is lower than that across the combination. This is not so important if the variable is a vane-type, but could be very significant if the variable is a varactor.
If the variable is a varactor with a low Q, the Q of the combination will tend to the Q of the fixed capacitor, which you could choose to be higher.
c) You can adjust the inductor, perhaps by moving a ferrite core in and out of a solenoid, perhaps by making the inductor from two solenoids in series, and rotating one to change their mutual inductance, so changing the total inductance.
• Perfect suggestions! 80 V pp is far too much for normal varactors. I would put forward one more solution, but it is really rather complicated. You can use PIN diodes for stepping through the required range by connecting / disconnecting fixed ceramic capacitors. And the remaining small adjustment range can be covered by varactor. This is stable and the most compact solution. However it is not a simple one. Commented Apr 18, 2016 at 22:08
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# CR: Property tax (CR 1000, TestA, Q17)
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
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15 Feb 2008, 08:36
kyatin wrote:
gixxer1000 wrote:
incognito1 wrote:
(D) If Proposition 13 is not repealed, identical properties will continue to be taxed at different rates. Incorrect. The reason why identical properties in our example are taxed differently is because they were bought during different times. The reference to "identical properties" is misleading here, what if two identical houses were bought in the same year - would Proposition 13 tax them differently? No. Even though they are identical.
That's the whole point D is trying to make. The reason that people are paying different rates under prop 13 is because they bought the identical properties at different years. Without propisition 13 you would pay the exact same rate no matter what. That means that every year the value of the property would be assed and you would pay 3% of that. So even if you bought the house 11 years ago for \$75,000 it is now worth \$200,000 because the identical property was just purchased for that amount. You now pay \$6,000(3% of \$200,000) just like the homeowner who purchased the property this year.
With Proposition 13, if you bought your house 11 years ago for \$75,000, your property tax would be approximately \$914 a year (1 percent of \$75,000 increased by 2 percent each year for 11 years); and if your neighbor bought an identical house next door to you for \$200,000 this year, his tax would be \$2,000 (1 percent of \$200,000). Without Proposition 13, both you and your neighbor would pay \$6,000 a year in property taxes (3 percent of \$200,000).
I wish we can get in a room to discuss...it would be fun.
I am convinced now that its B, for me.
If you read carefully the underlined text in above comment....you and your neighbour bought "identical" houses in different year....if you both sell it this year then new owners will pay same tax with proposition 13....SO D does NOT have to be true.
I agree, it so hard to convey things with only written words.
I also agree that IF you bought identical properties in the same year under prop 13 you would pay the same amount it taxes. So for prop 13 everyone would always have to buy identical properties at the same time or they will pay different rates.
Without prop 13 you are guaranteed to pay the same rate on identical properties no matter when you purchase the house.
Statement B says without prop 13 EVERY home owner will experience an increase in taxes.
If you bought a home 11 years ago you would be paying 22% for property tax. If they repeal it your tax rate would drop to 3%. That is a substantial decrease not increase.
Here would be the options for the home owner who bought the house 11 years ago:
With: \$75,000 x 22% = \$16,500
Without:\$200,000 x 3% = \$6,000
B is clearly wrong.
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
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15 Feb 2008, 11:18
gixxer1000 wrote:
If you bought a home 11 years ago you would be paying 22% for property tax.
............
Here would be the options for the home owner who bought the house 11 years ago:
With: \$75,000 x 22% = \$16,500
.........
Sorry, I don't understand your logic:
"if you bought your house 11 years ago for \$75,000, your property tax would be approximately \$914 a year (1 percent of \$75,000 increased by 2 percent each year for 11 years)"
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
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15 Feb 2008, 12:02
walker wrote:
gixxer1000 wrote:
If you bought a home 11 years ago you would be paying 22% for property tax.
............
Here would be the options for the home owner who bought the house 11 years ago:
With: \$75,000 x 22% = \$16,500
.........
Sorry, I don't understand your logic:
"if you bought your house 11 years ago for \$75,000, your property tax would be approximately \$914 a year (1 percent of \$75,000 increased by 2 percent each year for 11 years)"
I see my error
I was increasing the rate by 2% a year instead of increasing the tax by 2%.
Still the point I was trying to make is EVERY homeowner will NOT experience a substantial increase
Another ex. (I'll double check my math) :
If you purchased a house 11 years ago for \$75,000 and now it's worth \$80,000.
With prop 13 you would pay \$914 (\$75,000 x 1%= \$750 then increase \$750 by 2% for 10 more years)
If they repealed it you would pay \$2400 (\$80,000 x 3% = \$2400)
So inorder for B to be true that would mean that everyones properties would have to increase in value at a considerable rate.
I dont see how you can guarantee that by the passage.
The only thing that leads me to think that your right is that it says every homeowner is likely to experience a substantial increase in property taxes. I guess you could interpret that as 'definitely maybe'.
So I guess that gives you some room to make assumptions. And without D I would go with B. The problem is that I can find any scenario to disprove D. The only way D would not be correct is if under prop 13 everyone ALWAYS bought identical properties at the exact same time. Because if that doesnt happen, identical properties will be taxed at different rates.
I know B is the OA so I'm beginning to thing this was just a problem that was not thought all the way through.
Sorry for dragging this out.
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
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15 Feb 2008, 13:17
This question was in my mind for whole day
Some fresh remarks:
1. The question is LSAT question rather than GMAT one. in GMAT "conclusion" questions are "must be true" questions. I'm not a guru in LSAT but I read some links and found that LSAR Logical Reasoning "conclusion" questions are not necessarily "must be true" one. (Please, correct me if I'm wrong). But I did not find good logic for such LSAT questions (due to lack of time and LSAT skills).
A,C are out - "unconstitutional" and "preventing inflation" are far away from the argument.
(B) If Proposition 13 is repealed, every homeowner is likely to experience a substantial increase in property taxes.
Here we have extreme generalization (every) with very tricky word "likely" that defends the generalization.
(D) If Proposition 13 is not repealed, identical properties will continue to be taxed at different rates.
I see two problems:
1. "identical properties" vs. "identical properties with different year of buying". There were some "identical properties" with the same year of buying that were and will be taxed at the same rates.
2. "continue". We have to assume that the Proposition 13 is a proposition to existing low rather than new one.
(E) Proposition 13 has benefited some homeowners more than others.
Here we also generalization (homeowners) with word "some" that defends the generalization. I cannot find something wrong with E. Only "benefited" bothers me.
So I between B and E. E is slightly better
Any ideas?
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
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15 Feb 2008, 13:50
Walker between B and E ...I would still go with B
Read question stem again....what is author likely arguing for?
The tone of the arguments is not about "some people getting benefited more than others"
It is more about increase in tax due to repealing of proposition 13.
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
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15 Feb 2008, 15:48
kyatin wrote:
...I would still go with B
Read question stem again....what is author likely arguing for?
The tone of the arguments is not about "some people getting benefited more than others"
It is more about increase in tax due to repealing of proposition 13.
I've tried to go back: from conclusion to the argument.
(B) If Proposition 13 is repealed, every homeowner is likely to experience a substantial increase in property taxes.
I don't understand why the author has to introduce "an identical house". it does not help to arrive at the conclusion.
It would be very great to find OE
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
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15 Feb 2008, 17:58
walker wrote:
Wasi, N. and White, M.J. (2005). Property tax limitations and mobility: The lock-in effect of California’s Proposition 13, NBER Working Paper No. W11108.
or
INTERNATIONAL REAL ESTATE REVIEW
2007 Vol. 10 No. 1: pp. 26 - 47
Residential Stability or Rational Bubble: Proposition 13 in Southern California
Mark Hoven Stohs
For example, a buyer A purchases a house for \$100,000 in 1975. Suppose
further that the property tax rate is 1%, property value increases at the rate of
10% per year and the inflation rate is 2%.4 In 2005 buyer A’s taxes would
have risen to \$1,811. In 2005 buyer B would pay \$1,744,940 for an
identical house and receive a property tax bill of \$17,449. Therefore, buyer
A’s annual property subsidy is \$15,638 (= \$17,449 – \$1,811). ..........
walker, I think you just nailed it!
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
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15 Feb 2008, 20:57
incognito1 wrote:
walker, I think you just nailed it!
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
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16 Feb 2008, 11:36
So whats the conclusion here
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
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16 Feb 2008, 11:43
kyatin wrote:
So whats the conclusion here
walker located Proposition 13 on the net, and having read the relevant excerpt, it looks like (E) is the correct answer since it explicitly mentions A's subsidy in the last statement (hence A benefited more than B). The OA is incorrect.
One can argue that this question is incomplete as the author does not make any argument in the given statements. Which is why they should refrain from having such answer choices in the actual exam.
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
### Show Tags
16 Feb 2008, 12:03
incognito1 wrote:
One can argue that this question is incomplete as the author does not make any argument in the given statements. Which is why they should refrain from having such answer choices in the actual exam.
I agree. I read some posts of guys that passed GMAT and guys often said: "CR was pretty straightforward". Of all OG CR I fount only one CR that was not airtight (for me, of course ).
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
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21 Feb 2014, 22:34
I do not agree with B for the sole reason that it used the extreme word "every" in the choice.
In a scenario, where a homeowner has bought a property for \$500K, without proposition 13, he will end up paying 3% of 200K (doesn't state anywhere in the argument that it will be any different than this percentage value) which eventually leads me to believe that not everyone ends up paying high property tax without proposition 13.
Suggestions?
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
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25 Feb 2014, 11:21
Hey Asseem.
Let me see if I can help.
In general - good spot. the word 'every' is a key one to watch out for as it is often a signifier of a response that is too extreme.
HOWEVER - that is not the case here.
The key thing to understanding this is (as is often the case) to look closely at the question being asked.
Here it asks 'which argument is the author most likely trying to support'
What we are NOT looking for is 'which is the logical conclusion'
As we are just looking for the author's intentions, our burden of proof is lower. We can see which makes most sense from the evidence we have.
In this case it is clearly B. All the others make no sense at all
Does that help?
James
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink]
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10 Mar 2014, 07:06
Thanks James for pointing out what i was missing while reading this question repeatedly.
Here it asks 'which argument is the author most likely trying to support
What we are NOT looking for is 'which is the logical conclusion
I am now in agreement with you and others who opted for B on this one.
In the past few days, i looked at few CR exercises and realized that we are not supposed to derive any logic based on real world scenarios.
We absolutely must stick to the context and details presented in the argument. In the example provided, the property tax for both homeowners increases if proposition 13 is repealed.
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Re: CR: Property tax (CR 1000, TestA, Q17) [#permalink] 10 Mar 2014, 07:06
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## digitalmars.D.learn - remaping arrays
• BCS (13/13) Aug 02 2005 What is the easiest way to paint something like "real[5][]" over somethi...
• Regan Heath (33/47) Aug 02 2005 import std.stdio;
• BCS (5/8) Aug 02 2005 In article , Regan Heath says...
• Regan Heath (10/19) Aug 02 2005 I realised this, I thought maybe you had it backwards.
• Derek Parnell (30/48) Aug 02 2005 At first I thought you couldn't do this, but I did some tests and here i...
• Regan Heath (6/50) Aug 02 2005 You've made a liar out of me. I should learn to read all the replied
```What is the easiest way to paint something like "real[5][]" over something like
"real[]".
What I’m looking for would result in this:
real[] a;
real [5][] b;
b.length = a.length/b[0].length;
b.ptr = a.ptr; // or whatever
now:
b[0] == a[0..5];
b[1] == a[5..10];
..
b[last] == a[(b.last-1)*5 .. b.last*5];
this should not requier any copying.
```
Aug 02 2005
"Regan Heath" <regan netwin.co.nz> writes:
```On Tue, 2 Aug 2005 20:38:21 +0000 (UTC), BCS <BCS_member pathlink.com>
wrote:
What is the easiest way to paint something like "real[5][]" over
something like
"real[]".
What I’m looking for would result in this:
real[] a;
real [5][] b;
b.length = a.length/b[0].length;
b.ptr = a.ptr; // or whatever
now:
b[0] == a[0..5];
b[1] == a[5..10];
..
b[last] == a[(b.last-1)*5 .. b.last*5];
this should not requier any copying.
import std.stdio;
void main()
{
static int[] a =
[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24];
int[][5] b;
//paint
foreach(int i, inout int[] row; b)
row = a[(i*5)..(i*5)+5];
//display
foreach(int line, int[] row; b)
{
writef(line,": ");
foreach(int i; row)
{
writef("%02d ",i);
}
writefln("");
}
writefln("");
//proof
writefln("No copying, see:");
writefln("a: %x",a.ptr);
foreach(int line, int[] row; b)
writefln("%d: ",line,"%x",row.ptr);
}
Regan
```
Aug 02 2005
```In article <opsuwik1iy23k2f5 nrage.netwin.co.nz>, Regan Heath says...
Not quite.
I need a dynamic array of arrays-of-const size
real [5][] b;
you used an array-of-const size of dynamic arrays
int[][5] b;
BTW, I havn't run you code yet, but I'll try it later.
```
Aug 02 2005
"Regan Heath" <regan netwin.co.nz> writes:
```On Tue, 2 Aug 2005 23:51:48 +0000 (UTC), BCS <BCS_member pathlink.com>
wrote:
In article <opsuwik1iy23k2f5 nrage.netwin.co.nz>, Regan Heath says...
Not quite.
I need a dynamic array of arrays-of-const size
real [5][] b;
you used an array-of-const size of dynamic arrays
int[][5] b;
I realised this, I thought maybe you had it backwards.
The basic problem is that a const-size array has a fixed memory location,
so you cannot make it refer to another existing array, you have to copy
into it.
So your options are, fixed-array and copy or dynamic array and no copy.
AFAIKS.
BTW, I havn't run you code yet, but I'll try it later.
NP.
Regan
```
Aug 02 2005
Derek Parnell <derek psych.ward> writes:
```On Tue, 2 Aug 2005 20:38:21 +0000 (UTC), BCS wrote:
What is the easiest way to paint something like "real[5][]" over something like
"real[]".
What I’m looking for would result in this:
real[] a;
real [5][] b;
b.length = a.length/b[0].length;
b.ptr = a.ptr; // or whatever
now:
b[0] == a[0..5];
b[1] == a[5..10];
..
b[last] == a[(b.last-1)*5 .. b.last*5];
this should not requier any copying.
At first I thought you couldn't do this, but I did some tests and here is
my result...
<code>
import std.stdio;
void main()
{
real[5][] a;
real[] b;
// Populate the unmapped array with some test data.
real k = 6.996; // starting number
for (int i = 0; i < 7; i++) // create 7 real[5] arrays.
{
a.length = a.length + 1;
for( int j = 0; j < 5; j++, k+=1.569)
a[\$-1][j] = k;
}
// Remap the array.
b = cast(real[])a;
b.length = a.length * 5;
// Display the remapped array.
foreach(int i, real x; b)
writefln("Elem[%2d] = %s", i, x);
}
</code>
--
Derek
Melbourne, Australia
3/08/2005 10:32:50 AM
```
Aug 02 2005
"Regan Heath" <regan netwin.co.nz> writes:
```On Wed, 3 Aug 2005 10:34:23 +1000, Derek Parnell <derek psych.ward> wrote:
On Tue, 2 Aug 2005 20:38:21 +0000 (UTC), BCS wrote:
What is the easiest way to paint something like "real[5][]" over
something like
"real[]".
What I’m looking for would result in this:
real[] a;
real [5][] b;
b.length = a.length/b[0].length;
b.ptr = a.ptr; // or whatever
now:
b[0] == a[0..5];
b[1] == a[5..10];
..
b[last] == a[(b.last-1)*5 .. b.last*5];
this should not requier any copying.
At first I thought you couldn't do this, but I did some tests and here is
my result...
<code>
import std.stdio;
void main()
{
real[5][] a;
real[] b;
// Populate the unmapped array with some test data.
real k = 6.996; // starting number
for (int i = 0; i < 7; i++) // create 7 real[5] arrays.
{
a.length = a.length + 1;
for( int j = 0; j < 5; j++, k+=1.569)
a[\$-1][j] = k;
}
// Remap the array.
b = cast(real[])a;
b.length = a.length * 5;
// Display the remapped array.
foreach(int i, real x; b)
writefln("Elem[%2d] = %s", i, x);
}
</code>
You've made a liar out of me. I should learn to read all the replied
before posting.
The memory layout of "real[5][]" and the fact that a "real[5]" is not an
'array struct' makes painting as real[] possible, very clever.
Regan
```
Aug 02 2005
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# Detect quasi-parallel lines with spurs in a binary image
I'm looking for a way to remove quasi-parallel curves from the net, as depicted in the figure. Not only the original nets (upper row in figure) contain many spurs, but also the curves to be detected are not necessary straight lines. Ideally, I'd like to keep only the border of each such a region (lower row in figure).
I've came across solutions like hit-or-miss with line structuring element, Hough transform and Radon transform - but they were aimed at either detecting long straight lines or arbitrary shapes (like ellipses).
My idea was to represent a net as a graph, linearly approximate each edge (and split it into smaller segments if it deviates from the approximated line too much), for each pixel store the slope of an approximated edge in a matrix, and finally for each pixel I'd search such a matrix in a given neighborhood for other pixels (belonging to a different edge) with a similar slope.
Could you recommend me any method already used to accomplish such a task or tell me whether my approach seems reasonable?
## 1 Answer
I would start with a pruning algorithm (see skeleton pruning) in order to erase small segments, then use:
• the Hough transform, but segments are not really straights.
• if the pruning was a success, then you separate each segment and use the first and last point to compute the orientation, which will define when line are parallel. You will have to introduce a tolerance because you want quasi-parallel lines.
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# Proofs of Theorems and Glossary of Terms - PowerPoint PPT Presentation
Proofs of Theorems and Glossary of Terms. Just Click on the Proof Required. Menu. Theorem 4 Three angles in any triangle add up to 180°. Theorem 6 Each exterior angle of a triangle is equal to the sum of the two interior opposite angles.
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## PowerPoint Slideshow about 'Proofs of Theorems and Glossary of Terms' - portia
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Presentation Transcript
Theorem 4 Three angles in any triangle add up to 180°.
Theorem 6 Each exterior angle of a triangle is equal to the sum of the two interior opposite angles
Theorem 9 In a parallelogram opposite sides are equal and opposite angle are equal
Theorem 14 Theorem of Pythagoras : In a right angle triangle, the square of the hypotenuse is the sum
of the squares of the other two sides
Theorem 19 The angle at the centre of the circle standing on a given arc is twice the angle at any point of the circle standing on the same arc.
Go to JC Constructions
5
3
1
2
Theorem 4:Three angles in any triangle add up to 180°C.
Use mouse clicks to see proof
Given: Triangle
Proof:Ð3 + Ð4 + Ð5 = 1800Straight line
Ð1 = Ð4 and Ð2 = Ð5 Alternate angles
ÞÐ3 + Ð1 + Ð2 = 1800
Ð1 + Ð2 + Ð3 = 1800
Q.E.D.
To Prove:Ð1 + Ð2 + Ð3 = 1800
Construction:Draw line through Ð3 parallel to the base
Constructions
Quit
45
135
3
0
180
1
2
4
Theorem 6:Each exterior angle of a triangle is equal to the sum of the two interior opposite angles
Use mouse clicks to see proof
To Prove:Ð1 = Ð3 + Ð4
Proof:Ð1 + Ð2 = 1800 …………..Straight line
Ð2 + Ð3 + Ð4 = 1800 ………….. Theorem 2.
Þ Ð1 + Ð2 = Ð2 + Ð3 + Ð4
Þ Ð1 = Ð3 + Ð4
Q.E.D.
Constructions
Quit
c
a
d
Theorem 9:In a parallelogram opposite sides are equal and opposite angle are equal
Use mouse clicks to see proof
Given: Parallelogram abcd
To Prove:|ab| = |cd| and |ad| = |bc|
3
4
Construction:Draw the diagonal |ac|
1
Proof: In the triangle abc and the triangle adc
2
Ð1 = Ð4 …….. Alternate angles
Ð2 = Ð3 ……… Alternate angles
|ac| = |ac| …… Common
Þ The triangle abc is congruent to the triangle adc……… ASA = ASA.
Þ |ab| = |cd| and |ad| = |bc|
Q.E.D
Constructions
Quit
a
a
c
b
c
c
c
a
b
b
a
Theorem 14:Theorem of Pythagoras : In a right angle triangle, the square of the hypotenuse is the sum of the squares of the other two sides
Use mouse clicks to see proof
Given: Triangle abc
To Prove:a2 + b2 = c2
Construction: Three right angled triangles as shown
Proof: ** Area of large sq. = area of small sq. + 4(area D) (a + b)2 = c2 + 4(½ab)
a2 + 2ab +b2 = c2 + 2ab
a2 + b2 = c2
Q.E.D.
Constructions
Quit
o
r
c
b
Theorem 19:The angle at the centre of the circle standing on a given arc is twice the angle at any point of the circle standing on the same arc.
Use mouse clicks to see proof
To Prove:| Ðboc | = 2 | Ðbac |
5
2
Construction:Join a to o and extend to r
Proof: In the triangle aob
4
1
3
| oa| = | ob | …… Radii
Þ | Ð2 | = | Ð3 | …… Theorem 4
| Ð1 | = | Ð2 | + | Ð3 | …… Theorem 3
Þ | Ð1 | = | Ð2 | + | Ð2 |
Þ | Ð1 | = 2| Ð2 |
Similarly| Ð4 | = 2| Ð5 |
Q.E.D
Þ | Ðboc | = 2 | Ðbac |
Constructions
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## Four color theorem: about edges selection
For the decomposition of a graph representing a map, I’m trying to use different algorithms to select the edge to remove.
The question is:
• When you have multiple valid choices, which is the best edge to select … if any?
Some basic rules are:
• Avoid new F5 to be created
• Get rid of F5 whenever is possible, selecting the edge of a face with 2, 3 or 4 edges
• Consider to remove an edge from an F5 face only if no faces with 2, 3, 4 edges exist
Here are all possibilities. Last 2 groups (removing edges from F5 and F6) don’t have to be taken into account. I just wanted to see how it continued after the cases with faces made of 2, 3, 4 and 5 edges:
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Chemistry 12th Edition
pOH is the negative logarithm of the $OH^-$ concentration ($M$). $pOH = -log[OH^-]$ The equation that relates pOH and pH is: $pH + pOH = 14$
This equation is the derivation of the $K_w$ equation: $[H^+] \times [OH^-] = 10^{-14}$ $log ([H^+] \times [OH^-]) = log(10^{-14})$ $log[H^+] + log[OH^-] = -14$ $-pH + (-pOH) = -14$ $pH + pOH = 14$
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Access HW 11-17
# Access HW 11-17 - Lindsey Duff GI Gifts Query Homework...
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Lindsey Duff GI Gifts Query Homework Assignment 11/16/2010 1. What is the cash balance? Query1 Cash Balance \$235.00 SQL: SELECT Sum([Cash_Receipt Table].Amount) AS [Cash Balance] FROM [Cash_Receipt Table]; 2. What is the revenue GI Gifts can recognize? Query1 Revenue 314 SQL: SELECT Sum([Sales_Order_Detail Table].[Price]*[Shipment_Detail Table]. [Quantity_Shipped]) AS Revenue FROM ([Sales_Order Table] INNER JOIN [Sales_Order_Detail Table] ON [Sales_Order Table].[Order#] = [Sales_Order_Detail Table].[Order#]) INNER JOIN ([Shipment Table] INNER JOIN [Shipment_Detail Table] ON [Shipment Table].[Shipment#] = [Shipment_Detail Table].[Shipment#]) ON ([Sales_Order_Detail Table].[Item#] = [Shipment_Detail Table].[Item#]) AND ([Sales_Order_Detail Table].[Order#] = [Shipment Table].[Sales Order#]); 3. What is the current A/R balance? Query 1 A/R \$79.00 SQL: SELECT Sum([Recognizable Revenue]![Revenue]-[Collected Cash]![Collected Cash]) AS [A/R] FROM [Collected Cash], [Recognizable Revenue]; 4. What is the detailed A/R by customer? A/R by Customer
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# The head loss in a sudden expansion from 6 cm diameter pipe to 12 cm diameter pipe, in terms of velocity V1, in the 6 cm dia pipe is
This question was previously asked in
UPPSC AE Civil 2013 Official Paper I
View all UPPSC AE Papers >
1. $$\frac{{15}}{{16}} \times \frac{{{{\rm{V}}^2}}}{{2{\rm{g}}}}$$
2. $$\frac{3}{4} \times \frac{{{\rm{V}}_1^2}}{{2{\rm{g}}}}$$
3. $$\frac{1}{4} \times \frac{{{\rm{V}}_1^2}}{{2{\rm{g}}}}$$
4. $$\frac{9}{{16}} \times \frac{{{\rm{V}}_1^2}}{{2{\rm{g}}}}$$
Option 4 : $$\frac{9}{{16}} \times \frac{{{\rm{V}}_1^2}}{{2{\rm{g}}}}$$
## Detailed Solution
Concept:
Head loss occurs in the expansion zone.
The general formula for minor head loss is given as $$\frac{{{\rm{k}}{{\rm{V}}^2}}}{{2{\rm{g}}}}$$
where, V = velocity in smaller dia pipe
For sudden expansion head loss is given as,
$${{\rm{h}}_{\rm{L}}}{\rm{\;}} = {\rm{\;}}\frac{{{{\left( {{{\rm{V}}_1} - {{\rm{V}}_2}} \right)}^2}}}{{2{\rm{g}}}}$$
$$\Rightarrow {{\rm{h}}_{\rm{L}}}{\rm{\;}} = {\rm{\;}}\frac{{{\rm{V}}_1^2}}{{2{\rm{g}}}}{\left( {1 - \frac{{{{\rm{V}}_2}}}{{{{\rm{V}}_1}}}} \right)^2}{\rm{\;}} = {\rm{\;}}\frac{{{\rm{V}}_1^2}}{{2{\rm{g}}}}{\left( {1 - \frac{{{{\rm{A}}_1}}}{{{{\rm{A}}_2}}}} \right)^2}{\rm{\;}}$$
Comparing with the general formula for minor head loss $${{\rm{h}}_{\rm{L}}} = {\rm{k}}\frac{{{{\rm{V}}^2}}}{{2{\rm{g}}}}$$
$${\rm{K\;}} = {\rm{\;}}{\left( {1 - \frac{{{{\rm{A}}_1}}}{{{{\rm{A}}_2}}}} \right)^2}$$
Given:
$${{\rm{A}}_1}{\rm{\;}} = {\rm{\;}}\frac{{\rm{\pi }}}{4} \times {6^2}{\rm{\;}} = {\rm{\;}}9{\rm{\pi }}$$
$${{\rm{A}}_2}{\rm{\;}} = {\rm{\;}}\frac{{\rm{\pi }}}{4} \times {12^2}{\rm{\;}} = {\rm{\;}}36{\rm{\;\pi }}$$
$$\therefore {\rm{\;}}{{\rm{h}}_{\rm{L}}}{\rm{\;}} = {\rm{\;}}\frac{{{\rm{V}}_1^2}}{{2{\rm{g}}}}\left( {1 - \frac{{9{\rm{\pi }}}}{{36{\rm{\pi }}}}} \right)^2{\rm{\;}} = {\rm{\;}}\frac{{{\rm{V}}_1^2}}{{2{\rm{g}}}}\left( {\frac{3}{4}} \right)^2= \frac{9}{16}\frac{{{\rm{V}}_1^2}}{{2{\rm{g}}}}$$
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Videos and questions for Chapter 1c of the course "Market Analysis with Econometrics and Machine Learning" at Ulm University (taught by Sebastian Kranz)
### Multiple Linear Regression with Control Variables
Consider the model from the video above and assume prices $$p_t$$ are uncorrelated with $$u_t$$ but positively correlated with $$s_t$$. Do we get a consistent estimator $$\hat \beta_1$$ if we estimate the short regression $$q_t = \beta_0 + \beta_1 p + \varepsilon$$ via OLS?
Assume we estimate the multiple regression $q_t = \beta_0 + \beta_1 p_t + \beta_2 s_t + u_t$ where $$p_t$$ is uncorrelated with the error term $$u_t$$ but correlated with the other explanatory variable $$s_t$$. Is $$p$$ then exogenous or endogenous?
Now assume we change the model in the video such that $$p$$ is uncorrelated with both $$u$$ and $$s$$. Assume we estimate again the short regression $$q_t = \beta_0 + \beta_1 p + \varepsilon$$. Is the estimator $$\hat \beta_1$$ now consistent?
Assume you have a perfectly randomized pricing experiment. Do you need to add control variables to your regression to consistently estimate the causal effect of price on expected demand?
Nevertheless control variables are often added in randomized experiments. First, because perfect randomization is often not possible and second because control variables can allow you to reduce the standard errors of your estimator.
If you add control variables in the regression, you can also run non-perfectly randomized price experiments. For example, if you already know that it is more profitable to set higher price on sunny days, you may want to run an experiment where you set higher prices on sunny days than on non-sunny days but still add some random price fluctuation each day. If you then control in the regression for sunny and non-sunny days, you still can consistently estimate the causal effect of prices.
### Matrix formula for multiple linear regression
Take a look on the lecture slides for chapter 1c to see that the OLS estimator $$\hat \beta$$ can be computed with the same matrix formula that we have introduced for the simple linear regression. One only needs to add one column to the matrix $$X$$ for each explanatory variable.
For more advanced intuition for the multiple regression, the following regression anatomy result is useful.
### Illustration of Regression Anatomy in R
On the slides you find more details and interpretation of the regression anatomy. If you are new to econometrics this may sound all a bit abstract. But if you already have a some experience, the regression anatomy can be really helpful for a better intuitive understanding of what it means to add a control variable.
But let's move on...
## Which control variables to include...
And finally an example that is not about estimating ice cream demand!
Here are some quiz questions about which control variables you would include in a regression.
Assume you want to study if and how much wage discrimination based on gender exists. Would you add channel variables like having studied a quantitative subject to your regression?
Assume you want to analyse the effect of obtaining a university degree on wages. Would you add as control variable whether people later have a management position in their firm?
Assume you want to analyse the effect of obtaining a university degree on wages. Would you add high-school grades as control variable?
Video remark on the difficulty to estimate causal effect of a university degree on wages:
Assume a producer sells his product at a producer price $$p^p$$ to stores and the stores set a retail price $$p^r$$ for final customers. You are the producer and want to estimate how the demand for your product depends on your producer price $$p^p$$. Should you add the retail price $$p^r$$ as a control variable to your regression?
Assume you know that prices $$p$$ depend on variables describing the demand conditions and on costs $$c$$. You also know that costs are uncorrelated with demand conditions. You want to estimate a demand function. Would you add costs $$c$$ as control variable to your regression?
### R Example about Estimating Heterogeneous Effects
Consider the regression with interaction effects:
$q = \beta_0 + \beta_1 p + \beta_2 s + \beta_3 p \cdot s + \varepsilon$
To what will the estimated coefficient $$\hat \beta_1$$ in the regression with interaction terms be equal to?
### Non-linear Effects
Asssume we estimate a regression in which an explanatory variable $$x$$ has a quadratic effect: $y = \beta_0 + \beta_1 * x + \beta_1 x^2 + \varepsilon$ Is this still called a linear regression?
### Conditions for a valid instrumental variable
An instrumental variable (in the example above costs), must satisfy two conditions. An exogeneity condition and a relevance condition.
What do you think is the exogeneity condition that an instrumental variable must satisfy?
What do you think is the relevance condition that an instrumental variable must satisfy?
Which condition of an instrument $$z$$ for an endogenous variable $$x$$ could you check statistically with a real world data set?
Is the exogenous explanatory variabe $$s$$ in the demand function $q = \beta_0 + \beta_1 p + \beta_2 s + \varepsilon$ a valid instrument for the endogenous price in this demand function?
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# Steam vs water at the same temperature
1. Nov 19, 2004
### daveed
if steam and water are both at 100 degrees celsius, why would the steam scald you more, even if they both have the same kinetic energy?
2. Nov 19, 2004
### DB
Do you mean steam as in evaporized water? Because I don' think it's possible to have water and water vapor at the same temperature. Heat is energy and would give water vapor a stronger energy than room temp. water. Making it more likely to scald you. Heat is needed to evaporate water.
I think thats what you were asking.
3. Nov 19, 2004
### DB
Oh ya, I'm pretty sure, the more kinetic energy the more heat it emits. (Kinetic Energy of molecule i.e H20, having more motion, therefore more kinectic energy)
4. Nov 19, 2004
### Staff: Mentor
Steam has more energy than water because it takes energy to break the bonds that keep it a liquid. When steam hits you, some of it condenses, and your skin absorbs all that extra energy.
5. Nov 20, 2004
### Clausius2
That's false, you can have a mixture of steam and water (vapor) at the same temperature, just the temperature of change of state.
That's a good explanation. It sounds good.
6. Nov 20, 2004
### sheldon
is it called superheated?
7. Nov 20, 2004
### brewnog
No. It's superheated once there is no longer a dryness fraction (ie once all the liquid water in the mixture has evaporated, or when the steam is 'dry'.). This is the region beyond the saturation line on a Ts diagram of water boiling.
8. Nov 20, 2004
### Dual Op Amp
Once water reached it's evaporation point, it changes into steam, and floats away into the air. This small amount of water reduces the overall temperature of water to 212 degrees F. This means no matter what water's temperature will not exceed 212 degrees F. For example, if you put a cup of water in an oven at 400 degrees F, the water would be 212 degrees F. Why? Because as, water heats to it's evaporation point, (212) it turns to steam. Steam is less dense than air, so it rises away from the cup. This reduces the overall temperature of the water, making it stay at a temperature of 212 degrees F or 100 C.
9. Nov 20, 2004
### brewnog
This is not true. Water could easily exceed this temperature, if the pressure was allowed to rise above atmospheric. For example, at 4.7atm, the boiling point of water is roughly 150 degrees Celcius.
10. Nov 20, 2004
### Staff: Mentor
When a specific mass of water reaches 100C, it isn't even close to having enough energy for all of it to turn to steam. It takes 539 cal/gram to boil water that is already at its boiling point, but to raise it one degree C (to get to the boiling point) only takes 1 cal/gram.
11. Nov 21, 2004
### OddThoughts
At standard atmospheric pressure, usually accepted as 14.7 psi, at 100 deg C. water boils and steam condenses simultaneously, 100 C is the max temperature water can reach at this pressure and it is the minimum temperature that steam can exist at this pressure. Therefore it is possible for steam to exist at many times the max temperature of water.
12. May 5, 2011
### laestat
Re: steam/water
the owen is a constant heating device, water upon constant heating beyond the Tsat will yield to super-heated tendencies, meaning the cup becomes empty & the owen is filled with steam at super-heated temperatures and the pressure rises. The Latent heat of vapourization is surpassed by constant heating easily..
13. May 5, 2011
### Drakkith
Staff Emeritus
Re: steam/water
Nov21-04, 03:12 PM <---Whew! Long time ago that this thread was brought up for air!!
14. May 5, 2011
### DaveC426913
Re: steam/water
Indeed. And it seems gibberish to me.
What's an owen?
15. May 5, 2011
### Bloodthunder
Re: steam/water
Probably an oven.
16. May 6, 2011
### laestat
Re: steam/water
17. May 6, 2011
### DaveC426913
Re: steam/water
Ok, but I still don't get how your post is shedding any light on the topic.
I guess it doesn't matter; the thread's 7 years old.
18. May 7, 2011
### laestat
Re: steam/water
just a random browse n got into it..didnt get to see when were these published in the forum..
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# 10 Fascinating Insights into the World of Reddit Q&A: Your Comprehensive Guide
An Intriguing Encounter with Complex Equations
In the early days of my journey as a software engineer, I stumbled across a significantly complex mathematical equation while working on a groundbreaking project. It was a conundrum, a riddle wrapped up in an enigma, and it took me countless hours to unravel. This experience is quite similar to most people’s initial encounter with the ever-fascinating platform, Reddit Q&A.
Reddit Q&A, a unique feature of the popular platform known as Reddit, can appear bewildering at first glance. However, just as with any complicated mathematical theorem or intricate codebase, once understood, it becomes an immensely powerful tool.
Decoding the Reddit Q&A Platform
So, what is Reddit Q&A? It’s a dedicated format within Reddit that allows for direct and structured question-and-answer sessions. It’s like the prime number in the world of social media platforms; unique, distinct, and playing by its own rules.
The Backbone of Reddit: Subreddits & Threads
Reddit is composed of countless ‘subreddits’, communities dedicated to a particular interest or topic. These subreddits are where the magic of Reddit Q&A happens. User-generated threads within these subreddits facilitate the Reddit Q&A format.
Imagine a subreddit as a complex mathematical set, and each thread is an element within that set. The interactions between members in the thread often mimic the interconnected nature of elements in a set exhibiting certain properties.
The Functionality of Reddit Q&A: A Technical Perspective
Now that you have a basic understanding of the structure of Reddit, let’s delve into the technical aspect. How does this seemingly complex system function?
In terms of functionality, Reddit Q&A format adheres to the practicality concept in programming. It operates based on the logic of an algorithm, much like a well-written function in Python or Java. Users ask questions, and other users respond with their answers. The higher the number of upvotes an answer receives from the community, the higher on the page it appears.
Navigating through Reddit Q&A: Your Personal Guide
Navigating through Reddit Q&A is like traversing through a breadth-first search algorithm. You start exploring from the topmost, most popular answers and delve deeper into other response nodes.
To add another layer of complexity, Reddit Q&A threads follow a tree-like structure, reminiscent of a binary search tree in data structures. Each comment can branch off into multiple ‘child’ comments, forming a nested thread of conversations.
Making the Most of Reddit Q&A: Insights and Applications
While Reddit Q&A can be an invaluable source of information, its true potential lies in its application. By posing thought-provoking questions, you stimulate in-depth discussions and elicit insights that wouldn’t emerge in ordinary conversation. Much like the development of an innovative algorithm, the process can be challenging but ultimately rewarding.
Reddit Q&A: The Ultimate Tool for Mathematicians
Why is Reddit Q&A particularly beneficial for mathematicians and statisticians? The key lies in its commitment to detailed, well-thought-out responses, and rigorous argumentation. Think of it as a public forum where theorems are proposed, proofs are scrutinized, and knowledge expands – a kind of open-source mathematics.
In conclusion, using Reddit Q&A can be likened to finding a solution to a complex mathematical equation or decoding an intricate algorithm. It initially appears daunting, but once you understand its intricacies, your perspective changes. Like any good mathematical problem, once you crack the code, the process becomes enjoyable and rewarding. Now, the intriguing world of Reddit Q&A awaits, ready for you to unravel its fascinating enigma. Whether you’re a software engineer, mathematician, or statistician, this unique platform offers the chance for infinite exploration and discovery.
## What is the personification of winter?
The personification of winter is often depicted as a character known as “Old Man Winter.” This character is usually portrayed as an elderly gentleman who represents the cold, frost, and chill of winter. In literature, art, and culture, he is often associated with snow, ice, and freezing temperatures. His arrival usually signals the onset of winter.
In many stories and folklore, Old Man Winter has the power to control the winter elements. He is associated with the harshness and bitter cold of the season. For example, people might say “Old Man Winter has arrived” when the weather turns cold.
It’s also worth noting that winter is often personified in other ways too. For instance, many cultures and mythologies have deities or spirits associated with the winter season. These figures might be regarded as the “rulers” of winter, capable of bringing frost, snow, and cold winds. Their characteristics and abilities vary based on different cultural beliefs and traditions.
Overall, the personification of winter can vary greatly depending on the context, but Old Man Winter is one of the most commonly recognized characters representing this season.
## What is a tooth on a gear wheel called?
A tooth on a gear wheel is called a gear tooth or cog. The shape of the tooth is crucial in transmitting torque, and its correct pairing with other gear teeth ensures efficiency and longevity of the gear system.
## What is the ingredient in a spice cookie crossword?
The main ingredient in a spice cookie is generally cinnamon. Other common ingredients include nutmeg, ginger, and cloves. These elements give the cookie its distinctive spicy flavor. Depending on the recipe, ingredients like molasses or brown sugar might also be added for sweetness.
A “padre de tu padre” crossword, in the context of Reddit, would refer to a crossword puzzle where the answer to the hint or clue “padre de tu padre” would be “Grandfather”. As used in Spanish-speaking cultures and contexts, “padre de tu padre” literally translates to “father of your father”, which in English is referred to as your “grandfather”.
Here is how you might see it in a crossword:
This type of crossword puzzle can be common on language learning subreddits like r/Spanish or r/languagelearning, where users will share different resources and games to help each other learn more effectively.
### What is Reddit and how does it relate to {topic}?
Reddit is a social networking platform where users share information, thoughts, opinions, humor, and pretty much everything under the sun. It’s organized into ‘subreddits’, subject-specific communities where like-minded individuals can discuss and share the content related to that particular topic.
How does {topic} relate to Reddit? This would depend on what exactly the topic is. If it’s a popular subject, chances are there’s a subreddit dedicated to it. Within these subreddits, you can find people discussing the ins and outs of the topic, sharing related content, asking questions, offering advice, etc. These subreddits can be an excellent resource for getting different perspectives, doing some research or simply learning more about {topic}.
### How can users engage and participate in Reddit discussions about {topic}?
Participating in Reddit discussions about any given topic, such as {topic}, is a process that requires respect for community rules and an understanding of the platform’s etiquette. Here are some steps to engage and participate effectively:
1. Understand the Platform: Reddit is a place where users can share links and initiate discussions. Each topic has its own sub-reddit, and each sub-reddit has its own rules.
2. Find the Right Sub-Reddit: The first step to participating in a Reddit discussion about {topic} is finding the appropriate sub-reddit. You can do this by using the search bar at the top of the Reddit homepage.
3. Review the Rules: Once you’ve found a potential sub-reddit, take time to review its specific rules. Not adhering to these rules may result in your posts or comments being removed, and repeated violations could lead to a ban.
4. Start by Observing: Before you start posting or commenting, spend some time observing the discussions happening within the sub-reddit. This will give you a feel for the community’s tone and what content is considered valuable.
5. Engage with Respect: When you’re ready to engage, remember to do so with respect. Avoid personal attacks, stay on topic, and contribute to the discussion in a meaningful way.
6. Post Relevant Content: If you want to start a new discussion, make sure what you’re posting is relevant to the sub-reddit and provides value to its members.
7. Be Patient: Reddit discussions often involve many different perspectives and can evolve over a period of time. Be patient, participate consistently and constructively, and you’ll gradually become a valued member of the community.
Remember, the goal of Reddit discussions is to contribute to the community and facilitate meaningful conversations. Happy Redditing!
### Could you provide examples of popular subreddit communities on {topic}?
Sure, here’s a list of popular subreddit communities related to . Due to the unspecified nature of the {topic}, I’ll use Video Games as an example.
1. /r/gaming: A general hub for all things related to video games. Here users discuss news, share related content and engage in discussions about games.
2. /r/Games: Another subreddit dedicated to gaming on a slightly more serious level. It encourages informative and interesting gaming content and discussions.
3. /r/IndieGaming: This subreddit is specifically for indie games. Users can find news about new and upcoming indie games, interviews with developers, or just share their favorite indie game with the community.
4. /r/GameDeals: A place for redditors to share information about any great deals on games.
5. /r/truegaming: More serious discussions about games. The community is aimed at those who want to talk seriously about the medium of video games.
6. /r/gamedev: This subreddit is for game developers. It’s a place for them to share, discuss, and critique each other’s work.
7. /r/MMORPG: Dedicated to Massively Multiplayer Online Role-Playing Games (MMORPGs).
8. /r/esports: Fans of esports can discuss professional players, teams, tournaments, and more in this subreddit.
9. /r/retrogaming: A subreddit for those interested in old school games.
Remember, it’s always important to read and follow the rules of each subreddit before you begin participating. It fosters healthy communication and discussion amongst its members.
### How are Reddit’s content policies applied in the context of {topic}?
Reddit’s content policies are applied universally across all topics and communities, including {topic}. These policies are designed to ensure a safe, enjoyable, and useful experience for all users. Most importantly, they are intended to foster civil, respectful discourse.
1. Respect for People: All content posted must respect human dignity and not be harmful or degrading towards any individuals or groups. This includes prohibitions on hate speech, harassment, and bullying.
2. No illegal content: Reddit prohibits the posting of illegal content or solicitation of illegal activities. This includes copyright infringement and promoting illegal activities.
3. No involuntary pornography or sexual or suggestive content involving minors: Any explicit content involving non-consenting individuals or minors is strictly forbidden.
4. Authenticity: Reddit values and encourages authentic conversation. Activities such as spamming, manipulating votes, or creating multiple accounts to evade punishment are not permitted.
5. Respect for privacy: Personal and confidential information related to others cannot be posted. This includes non-consensual pornography and threats to expose personal information.
For the specific context of {topic}, users need to follow the same guidelines alongside any additional rules set by the moderators of the subreddit in question. The enforcement of these rules can result in penalties ranging from warnings to permanent account suspension depending on the severity and frequency of infractions.
### What is the role of moderators in subreddit communities related to {topic}?
On Reddit, the role of moderators in subreddit communities related to {topic} is critical for maintaining a healthy discussion environment.
Moderators are volunteers who oversee subreddits, creating guidelines, enforcing rules, and maintaining the overall standard and vision of their respective communities.
Their responsibilities typically include:
Developing and enforcing community rules: Moderators create guidelines to fit the nature of their subreddit. These could be general Reddit rules or specific to the community. They ensure that members adhere to these rules and take action against those who violate them.
Controlling spam and approving posts: Moderators filter out spam, irrelevant or inappropriate content to keep discussions on-topic and respectful in nature.
Managing community interaction: Moderators often engage with their community, answering questions, handling disputes, and sometimes hosting events or discussions to foster a positive atmosphere.
Banning disruptive users: If a user repeatedly violates rules, moderators have the power to ban them from the subreddit, ensuring the integrity of the community.
Designing the look and feel of the subreddit: Some moderators, especially in larger communities, will also customize the appearance of their subreddit to make it unique and attractive to its audience.
Through these functions, moderators play an essential role in shaping the culture of their subreddit and providing a safe, engaging space where like-minded individuals can connect and discuss {topic}.
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# Reference Frame
Reference frame may refer to:
• Frame of reference, in physics
• Reference frame (video), frames of a compressed video that are used to define future frames
### Other articles related to "reference frames, reference frame, frame, reference":
Synchronous Frame - Simultaneity in General Relativity
... An exception are reference frames in which all components g0α are zeros ... the inability to synchronize all clocks is a property of the reference frame and not of the spacetime itself ... It is always possible in infinitely many ways in any gravitational field to choose the reference frame so that the three g0α become zeros and thus enable a complete ...
Mechanics Of Planar Particle Motion - Moving Objects and Observational Frames of Reference - Frame of Reference and Coordinate System
... The term frame of reference is used often in a very broad sense, but for the present discussion its meaning is restricted to refer to an observer's state of motion ... We first introduce the notion of reference frame, itself related to the idea of observer the reference frame is, in some sense, the "Euclidean space carried by the ... Let us give a more mathematical definition… the reference frame is.. ...
BKL Singularity - Existence of Time Singularity
... the "physically independent" functions whose number cannot be reduced by any choice of reference frame ... only known indication was related to the form of Einstein equations written in a synchronous frame, that is, in a frame in which the proper time x0 = t is. 1) written in synchronous frame gives a result in which the metric determinant g inevitably becomes zero in a finite time irrespective of any assumptions about matter distribution ...
Fictitious Centrifugal Force
... as an outward force apparent in a rotating frame of reference ... type of force is associated with describing motion in a non-inertial reference frame, and referred to as a fictitious or inertial force (a description that ... the motion is described relative to a rotating reference frame about a fixed axis at the origin of the coordinate system ...
The Monkey And The Hunter
... way of looking at the problem is by a transformation of the reference frame ... Earlier, we stated the problem in a reference frame in which the Earth is motionless ... Transform the reference frame to one that is accelerated upward by the amount g with respect to the Earth's reference frame (which is to say the acceleration of the ...
### Famous quotes containing the words frame and/or reference:
Predictions of the future are never anything but projections of present automatic processes and procedures, that is, of occurrences that are likely to come to pass if men do not act and if nothing unexpected happens; every action, for better or worse, and every accident necessarily destroys the whole pattern in whose frame the prediction moves and where it finds its evidence.
Hannah Arendt (1906–1975)
Meaning is what essence becomes when it is divorced from the object of reference and wedded to the word.
Willard Van Orman Quine (b. 1908)
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Information for Maple assignment 2
Each student will get individual data for the assignment.
Below is helpful background information for the second Maple assignment. I repeat what I wrote in the last set of instructions:
You are allowed, and indeed encouraged, to copy and modify the commands discussed here.
Packages
For this assignment you will need commands from the plots and VectorCalculus packages. Load these packages using the with command, as discussed in Packages section of the Background Information for the first Maple assignment.
Plotting Curves
We will again be using the spacecurve command from the plots package. For these instructions, we will be using as an example the curve given by:
r(t) = < 5 cos(2t) + 5 sin(t), 2 cos(2t) + 4 cos(t), sin(3t) + 4 sin(t)>
or if you prefer the parametric notation:
x=5 cos(2t) + 5 sin(t)
y=2 cos(2t) + 4 cos(t)
z= sin(3t) + 4 sin(t)
I'm beginning with this curve because it is fairly simple. More complicated curves will appear later. This curve is a closed curve (i.e. a loop) on the interval [0,2π] because the formulas are all combinations of sines and cosines with integers multiplying the parameter, t.
Since we will be doing a lot with this curve, it's wise to store it to a variable. There are several approaches to doing this, but the best for our purposes is storing it as a "live" function, r(t)
r := t -> < 5*cos(2*t) + 5*sin(t), 2*cos(2*t) + 4*cos(t), sin(3*t) + 4*sin(t)>
This should allow us to call r(t) simply by typing r(t), but also evaluate r at a value, say t=2, by typing in r(2). (Another option would have been to store the right hand expression directly to r, omitting the "t ->" portion. In this case we would need to use the subs command to evaluate r at a specific value.)
Let's start by just graphing our curve.
spacecurve(r(t),t=0..2*Pi);
We can use just r(t) because we've already stored the equation to r(t). Notice that we used the capitalization Pi to get the constant 3.141... (pi and PI do not give this constant). The result is the picture shown below.
This picture is not very useful. The rainbow coloration does not add anything and will make the curve fade away if we print out the picture in black and white. It is not clear whether that crossing in the middle is actually a crossing or just an illusion due to the viewpoint. Plus there are no axes to give reference so do not know how far to the left/right, up/down, front/back the curve stretches. Let's add some options to this command to make the picture better. You enter options in the command after the range, separated by commas.
• The thickness option will make the curve a little thicker and easier to see. The default is thickess=1, but let's make thickess=2 to beef up our curve slightly.
• We can make the whole curve a single color, say black. We do this via the option color=black. Current versions of Maple have hundreds of pre-set colors ranging from black to beige to SteelBlue. Feel free to experiment, but remember the limitations of your printer for the end result. (For the record Maple is Canadian, so it also accepts the "colour" option.)
• We will add the standard coordinate axes with the option axes=normal. Other choices for axes include axes=none (the default), axes=boxed, and axes=frame.
• We can label the x-, y-, and z-axis with the option labels=[x,y,z].
• We can make the curve smoother using the numpoints option. Maple plots curves by evaluating r(t) at many different values for t, and then connecting the dots. A higher numpoints setting makes more dots, thus smoothing the curve but lengthening the computation time. Some experimentation is often necessary to strike a balance. For this assignment numpoints=150 works well. For contrast, try numpoints=15 (chunky curve, short computation) and numpoints=1500 (smoother curve, longer computation).
• You can use the mouse to adjust the viewpoint, but you can also use the orientation command. Often the orientation command is not necessary because of the mouse, but it's good to know it's there if you need it.
• You can look up the list of all available options for three-dimensional plotting by looking up help(plot3d/options).
Putting these options into the command we get
spacecurve(r(t),t=0..2*Pi, thickness=2, color=black, axes=normal, labels=[x,y,z], numpoints=150);
Certainly the view shown is much nicer, and has some readable quantitative information (on the axes). It is still a bit deceptive, however, at the center. The picture seems to show the curve intersecting itself. In fact, this particular curve does not have any self-intersections. This is what's called a simple closed curve. If you right-click on a Maple picture, the Manipulator button allows you to rotate or scale or pan. So you can get many different views. Here is a view which shows the same curve from a different angle, and zoomed out farther. Apparently this curve does not intersect itself!
Consider the following picture of the curve, s(t)=< sin(2t), cos(2t), sin(t) >
This shares the a figure-8 shape with our original picture of our curve r(t). This curve actually has an intersection, however, as illustrated by the animation below (created by the animate command - hover your cursor over the animate for the Maple code.)
Since you cannot print an animation, you should include several views of your curve to convince the reader of any intersections.
Warning: There are curves which do not intersect themselves, but have the irritating (interesting?) property that every two dimensional view shows intersections! See the bottom of this page for examples. For example, q(t)=<sin(t),cos(3t),sin(2t)> (animated below) has this property. In this case you would include several views of your curve to convince the reader that there are no intersections.
Watch as intersections appear and disappear. Compare this to a curve with an actual intersection, such as s(t)=<sin(2t), cos(2t), sin(t)> above where the intersection does not disappear. More examples of such curious curves appear at the bottom of this page.
Analyzing Curves
We can try various views to get the size of the curve. Two images are shown below (here we used the "axes=frame" option instead of "axes=normal"). The image on the left has the z-axis sticking directly out from the viewing plane, so we are looking down from above. Alternately, you can see this as projecting (i.e. squashing) the curve into the xy-plane. The image on the right has the y-axis sticking directly out from the viewing plane. Therefore it shows a picture of the curve squashed into the xz-plane.
From these pictures I can get a rough idea of the dimensions of this curve. Apparently the curve fits inside a box with -10≤x≤6 and -3≤y≤6 and -3.6≤z≤3.6, as illustrated below. You may draw such markings by hand.
How long is this curve? This is called the arc length, which is calculated by integrating the speed of r(t) for the desired range of t (i.e. ∫ab |r'(t)| dt ). We need to differentiate r(t), and then find its length or magnitude (this is the speed). The diff command will differentiate r(t). The VectorCalculus package contains a command called Norm which computes the norm of a vector. We will use the variable speed to represent |r'(t)|.
speed:=Norm( diff(r(t),t) );
speed:=((-10*sin(2*t)+5*cos(t))^2+(-4*sin(2*t)-4*sin(t))^2+(3*cos(3*t)+4*cos(t))^2)^(1/2)
We are interested in the length of one loop of the curve. For our curve "one loop" is given by the range 0 ≤ t ≤ 2π, so we need to integrate speed from t=0 to t=2*Pi to get the length. We can integrate using the int command, so may naturally try:
int(speed, t=0..2*Pi);
Notice that when you use int here, however, Maple usually returns the original integral, not evaluated, after about 12 seconds' thought. When Maple returns the original command, it means that Maple has given up trying to evaluate whatever you asked. Usually this is because you typed in something that the program does not recognize, but in this case it is because Maple cannot solve this integral symbolically. This is not surprising -- most functions defined by formulas can't be antidifferentiated in terms of familiar functions.
Maple needs to be "convinced" to evaluate this integral approximately. You can do this via:
evalf(Int(speed,t=0..2*Pi));
56.13189562
Please note the capital I in the integrate command. This is an important difference which you can read about on a help page if you want. The numerical computation of the integral took less than a hundredth (.01) of a second. This curve is about 56 units long.
Warning: Do not confuse the Norm command in Maple with Norm from This Old House and The New Yankee Workshop, nor with Norm from Cheers. One is a command, one is a carpenter, and one is a carouser.
The VectorCalculus package also contains the Curvature command, which computes the curvature of a curve. The curvature is often a very messy formula:
Curvature(r(t),t);
((-1/2/(-200*sin(t)*cos(t)^2+144*cos(t)^6-584*cos(t)^4+498*cos(t)^2+64*cos(t)+ 16-64*cos(t)^3)^(3/2)*(-10*sin(2*t)+5*cos(t))*(-200*cos(t)^3+400*sin(t)^2*cos( t)-864*cos(t)^5*sin(t)+2336*cos(t)^3*sin(t)-996*sin(t)*cos(t)-64*sin(t)+192* sin(t)*cos(t)^2)+1/(-200*sin(t)*cos(t)^2+144*cos(t)^6-584*cos(t)^4+498*cos(t)^ 2+64*cos(t)+16-64*cos(t)^3)^(1/2)*(-20*cos(2*t)-5*sin(t)))^2+(-1/2/(-200*sin(t )*cos(t)^2+144*cos(t)^6-584*cos(t)^4+498*cos(t)^2+64*cos(t)+16-64*cos(t)^3)^(3 /2)*(-4*sin(2*t)-4*sin(t))*(-200*cos(t)^3+400*sin(t)^2*cos(t)-864*cos(t)^5*sin (t)+2336*cos(t)^3*sin(t)-996*sin(t)*cos(t)-64*sin(t)+192*sin(t)*cos(t)^2)+1/(-\ 200*sin(t)*cos(t)^2+144*cos(t)^6-584*cos(t)^4+498*cos(t)^2+64*cos(t)+16-64*cos (t)^3)^(1/2)*(-8*cos(2*t)-4*cos(t)))^2+(-1/2/(-200*sin(t)*cos(t)^2+144*cos(t)^ 6-584*cos(t)^4+498*cos(t)^2+64*cos(t)+16-64*cos(t)^3)^(3/2)*(3*cos(3*t)+4*cos( t))*(-200*cos(t)^3+400*sin(t)^2*cos(t)-864*cos(t)^5*sin(t)+2336*cos(t)^3*sin(t )-996*sin(t)*cos(t)-64*sin(t)+192*sin(t)*cos(t)^2)+1/(-200*sin(t)*cos(t)^2+144 *cos(t)^6-584*cos(t)^4+498*cos(t)^2+64*cos(t)+16-64*cos(t)^3)^(1/2)*(-9*sin(3* t)-4*sin(t)))^2)^(1/2)/(-200*sin(t)*cos(t)^2+144*cos(t)^6-584*cos(t)^4+498*cos (t)^2+64*cos(t)+16-64*cos(t)^3)^(1/2)
Ugh. This is certainly an example of why people use : instead of ;. A command ending with a colon will not display its output. Knowledge of the specific formula of the curvature is not likely to be useful, so we can safely omit it (use Ctrl+Del to delete a line from a Maple document).
We can compute the curvature at, for example, t=2 using the subs command.
evalf( subs(t=2, Curvature(r(t),t) ));
.2586332282
The subs command substitutes 2 for t in the result of the Curvature(r(t),t) command, and then evalf asks for a floating point (i.e. decimal) approximation. Pay attention to the "nesting" of the commands. Just as in algebra, Maple works outward from the inside, first calculating Curvature(r(t),t), then substituting 2 for t, then evaluating the expression to get a decimal approximation.
The curvature expression for r(t) is a (complicated) real-valued function of t, so we can plot it like any other one-variable real-valued function.
plot(Curvature(r(t),t),t=0..2*Pi,thickness=2);
The height of this function at t=t0 gives the curvature of r(t) at the point r(t0). We can use this graph to locate (approximately) the curviest (most curvy?) point on the curve. If you position your mouse cursor on the graph, and left click, the cursor position relative to the graph is shown on the left side of the toolbar at the top of the window. In this case, the coordinates that I see for the marked maximum are about (4.69, 1.81). So the highest curvature in this curve is about 1.81 and this occurs when the parameter t is about 4.69. Maple does have commands that find the minima and maxima, but they are often very slow, especially for functions as complicated as our Curvature(r(t),t). For our purposes these approximations should suffice.
Where (in space) is the curviest point? That is, what are the coordinates for the point on r(t) corresponding to the value of t that gives the highest curvature? We must substitute the value of the parameter, t=4.69, into the curve function. We can either use subs(t=4.69, r(t)) or more simply r(4.69). Both should return a vector approximately < -9.994,-2.086,-3.001 >, which means the most curvy point has coordinates approximately (-9.994,-2.086,-3.001).
To graph a point, in our case the most curvy point, we can use the pointplot3d command (in the plots package). For example, try pointplot3d([-9.994,-2.086,-3.001], symbol=box, symbolsize=20, color=blue); You will get a thoroughly unhelpful picture (although it's more interesting than if you do not include any of the options), since this point is only meaningful relative to the curve r(t). Use the display command (discussed in the Background for the first assignment) to plot both the curve and the point together.
POINT:=pointplot3d([-9.994,-2.086,-3.001], symbol=box, symbolsize=20, color=blue):
CURVE:=spacecurve(r(t),t=0..2*Pi,thickness=2, color=black, axes=normal, labels=[x,y,z], numpoints=150):
display({MCP,CURVE});
This is a bit confusing, since the little blue box is supposed to be the most curvy point, but the curve does not look very curvy at that point compared to other parts of the curve. But then I adjusted the image by adding the scaling=constrained option and the result is the more convincing picture below. So, again: pictures are wonderful but they can be deceptive unless you stay alert!
Round-off Warning: Round-off and estimation errors from earlier steps may cause the point you plot to be slightly "off" the actual point of maximum curvature. If this happens, you may want to go back to previous steps and add an extra one or two decimal digits of precision.
I chose the example above to analyze in detail because it is fairly simple. You will get randomly generated curves which may be a bit more wild. You have been given the curvature of your curve at t=2, so that you can check initially that you've entered the functions correctly.
Weird Pictures
Some strange things can happen. Let me show you a few of them.
Below is a plot of curvature for a curve which isn't very nice. The curvature has an enormous thin peak. Experiments seem to show that such behavior is common.
Below is the curve which has the curvature graph shown above. On the left is an unconstrained view, and on the right, a constrained view (observe the scale of the y-axis in the first picture). The very high curvature on the right side of the curve corresponds to the single high peak for the curvature graph. The other bends of the curve also make the curvature increase and decrease, but these are drowned out in the curvature graph above due to this single extreme bend.
Below are three pictures of another curve. I emphasize that these are all pictures of the same curve. This curve does not intersect itself, but every two dimensional view does seem to show an intersection. So detecting intersections by "just looking" may be a bit difficult. Some examination of the images is necessary.
Here are two pictures of yet another closed curve. This closed curve does have two self-intersections, each of which can appear to be an illusion. It can be difficult to convince people of these intersections without much numerical work (e.g. showing that r(t0)=r(t1) for some 0 ≤ t0 < t1 < 2 π) or many carefully chosen pictures. If you have suggestions, please let me know.
I am very curious to learn if this homework assignment will lead to any bizarre pictures and numbers. Please tell me if you think you have found some.
I thank Ms. L. Pudwell for several useful conversations about this material.
Note on torsion: After experiments with some students, I am very glad that torsion (roughly the twistiness of the curve) was not mentioned in this assignment! The torsion computations are quite elaborate, taking large amounts of memory and computational time. I think we could have frozen huge chunks of university computer resources with any general requests for torsion. I know that I caused my computers at home and at school to be very unhappy by asking for the torsion of some students' curves.
Maintained by greenfie@math.rutgers.edu and last modified 8/3/2009 by Andrew Baxter.
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# Compare and return True if two string arrays are equal in Numpy
To compare and return True if two string arrays are equal, use the numpy.char.equal() method in Python Numpy. The arr1 and arr2 are the two input string arrays of the same shape. Unlike numpy.equal, this comparison is performed by first stripping whitespace characters from the end of the string. This behavior is provided for backward-compatibility with numarray
The numpy.char module provides a set of vectorized string operations for arrays of type numpy.str_ or numpy.bytes_
## Steps
At first, import the required library −
import numpy as np
Create two One-Dimensional arrays of string −
arr1 = np.array(['Bella', 'Tom', 'John', 'Kate', 'Amy', 'Brad'])
arr2 = np.array(['Cio', 'Tom', 'Cena', 'Kate', 'Adams', 'brad'])
Display the arrays −
print("Array 1...", arr1)
print("Array 2...", arr2)
Get the type of the arrays −
print("Our Array 1 type...", arr1.dtype)
print("Our Array 2 type...", arr2.dtype)
Get the dimensions of the Arrays −
print("Our Array 1 Dimensions...",arr1.ndim)
print("Our Array 2 Dimensions...",arr2.ndim)
Get the shape of the Arrays −
print("Our Array 1 Shape...",arr1.shape)
print("Our Array 2 Shape...",arr2.shape)
To compare and return True if two string arrays are equal, use the numpy.char.equal() method. The arr1 and arr2 are the two input string arrays of the same shape −
print("Result...",np.char.equal(arr1,arr2))
## Example
import numpy as np
# Create two One-Dimensional arrays of string
arr1 = np.array(['Bella', 'Tom', 'John', 'Kate', 'Amy', 'Brad'])
# Display the arrays
print("Array 1...", arr1)
print("Array 2...", arr2)
# Get the type of the arrays
print("Our Array 1 type...", arr1.dtype)
print("Our Array 2 type...", arr2.dtype)
# Get the dimensions of the Arrays
print("Our Array 1 Dimensions...",arr1.ndim)
print("Our Array 2 Dimensions...",arr2.ndim)
# Get the shape of the Arrays
print("Our Array 1 Shape...",arr1.shape)
print("Our Array 2 Shape...",arr2.shape)
# To compare and return True if two string arrays are equal, use the numpy.char.equal() method in Python Numpy
# The arr1 and arr2 are the two input string arrays of the same shape.
print("Result...",np.char.equal(arr1,arr2))
## Output
Array 1...
['Bella' 'Tom' 'John' 'Kate' 'Amy' 'Brad']
Array 2...
Our Array 1 type...
<U5
Our Array 2 type...
<U5
Our Array 1 Dimensions...
1
Our Array 2 Dimensions...
1
Our Array 1 Shape...
(6,)
Our Array 2 Shape...
(6,)
Result...
[False True False True False False]
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# Division of polynomial matrices
Is it possible to perform euclidean division between two polynomial matrices in sage? e.g.if $A= \begin{bmatrix} x^2 +1 & x \newline 0&x-1 \end{bmatrix} , B=\begin{bmatrix} x & 2 \newline 1 &x-1 \end{bmatrix}$
are given find the matrices $Q,R$ so $A=QB +R$
in this example the answer is $Q= \begin{bmatrix} x & -1 \newline 0& 1 \end{bmatrix} , R=\begin{bmatrix} 2 & -1 \newline -1 & 0 \end{bmatrix}$
edit retag close merge delete
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# Computational Statistics (Sommersemester 2021)
Lecturer: Prof. Dr. Bernhard Renard (Data Analytics and Computational Statistics) , Dr. Sven Giese (Data Analytics and Computational Statistics) , Elizabeth Yuu (Data Analytics and Computational Statistics)
Course Website: https://hpi.de/friedrich/moodle/course/view.php?id=151
## General Information
• Weekly Hours: 4
• Credits: 6
• Enrolment Deadline: 18.03.2021 - 09.04.2021
• Teaching Form: Lecture / Exercise
• Enrolment Type: Compulsory Module
• Course Language: English
## Programs & Modules
IT-Systems Engineering MA
Data Engineering MA
Digital Health MA
Cybersecurity MA
• SECA-Konzepte und Methoden
• SECA-Techniken und Werkzeuge
• SECA-Spezialisierung
## Description
In almost all areas of life, large amounts of data are generated, requiring dedicated procedures for data analysis to allow predictions and inference for decision making. Computational statistical methods have evolved to cope with challenges arising from large datasets that are not tractable with traditional approaches, e.g. when the number of possible parameters of a model exceeds the number of observations. At the same time, this wealth of data allows replacing distributional assumptions with data-driven analyses.
In this course, we will cover statistical summary of data, hypothesis testing, regression as well as statistical learning approaches with focus on clustering and classification. We will contrast traditional frequentist approaches for these tasks with non-parametric, computational more intensive alternatives and Bayesian approaches.
The lecture will be accompanied by regularly scheduled exercises, which focus on applying the covered method to real-life data from different areas of life. In the course we will work with R / Python. Basic programming knowledge is a prerequisite to successfully complete the exercises. For those students who are not familiar with any of these two languages, an introduction to R will be provided.
Learning Objectives:
• Understand concepts and methods of computational statistics
• Ability to statistically evaluate real-world data
• Ability to assess the quality and validity of a statistical method for a given analysis
• Ability to select, implement and apply appropriate statistical methods and algorithms for a given use case
## Requirements
• Fundamentals in calculus and vector analysis (at least comparable to the Mathematik I + II lectures in the ITSE Bachelor at HPI)
• Basic programming knowledge (Python or R are a plus)
• Knowledge of English (The lecture will be given in English, but you can ask questions in German and submit German solutions etc.)
## Literature
1. Hastie, Trevor ; Tibshirani, Robert ; Friedman, Jerome: The elements of statistical learning: data mining, inference and prediction. 2 : Springer, 2009 (https://web.stanford.edu/~hastie/ElemStatLearn/)
2. James, Gareth ; Witten, Daniela ; Hastie, Trevor ; Tibshirani, Robert: An Introduction to Statistical Learning -- with Applications in R. 103. New York : Springer, 2013 (Springer Texts in Statistics). - ISBN 978-1-4614-7137-0 (http://faculty.marshall.usc.edu/gareth-james/ISL/)
## Learning
Exercises will be included into the lecture times when suitable.
Lectures / Exercises will be given in zoom with interactive elements including online quizzes and questions/chats. Call-In details will be provided in time.
Due to the COVID-19 pandemic, this course will be offered online. Depending on the development of the pandemic, we will return to the lecture hall (if possible).
It is important that all participants enroll by April 12 via our Moodle page.
## Examination
Final exam covering all lecture materials (70% of final grade)
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# Cisco Placement Papers
Cisco placement papers in pdf , doc and text format to prepare for cisco company. Check following old cisco placement papers with solutions and test interview questions from year 2010 to 2015-16. Cisco is one of reputed company in india for your career. We can provide cisco aptitude syllabus for your help too. Know about cisco placement procedure and questions with aptitude test papers on this page. Best of luck for your interview in cisco company.
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Job interview Preparation TipsGeneral interview questions are a part of practically every single job interview nowadays. Despite they tell just a little about the suitability of a candidate, they have some meaning for the employers. Recruiters are able to create a good picture about your communication skills, self confidence and also attitudes. you have to yourself. General interview questions are those questions about goals, weaknesses and strengths, etc. What more to tell to general interview questions? There is practically nothing we can add. Do not waste too much time in your interview preparation with these questions. What you answer to them is not that important as most of the people believe....
1 What is the probability of getting at least one six in a single throw of three unbiased dice?(1) 1 / 6(2) 125 / 216(3) 1 / 36(4) 81 / 216(5) 91 / 216Correct choice is (5) and Correct Answer is 91 / 216Explanatory AnswerEvery die has got six sides. Each of the sides is numbered from 1 to 6.When a single unbiased die is thrown you can have six possible outcomes. When two dice are thrown simultaneously, the total number of outcomes will be 6 * 6 = 36Similarly, when three dice are thrown simultaneously, the total number of outcomes will be 6*6*6=216.We need to find out the number of cases in which at least one of the facing sides shows 6.At least one means - either one dice or two dice or all...
Cisco Placement Paper Pattern :The question paper is basically an objective type paper consisting of 50 questions out of which 20 were aptitude and 30 were technical and from the aptitude section just concentrate on the following ( just these 3 lessons nothing else ) 1)Probability in depth 2)Permutations And combinations cat level3)Sets and relations 1)A bag contains 4 red and 5 green balls find the probability of selecting 2 balls of the same color 2)Something related on sets and functions (please go through sets and functions it is very very important)3)3 ants are sitting at 3 corners of an equilateral triangle they start to move in random directions whats the probability that they wont collide...
Friends I attended for CISCO Pune ,s Recruitment Drive on 13-jan-2012 WHICH WAS CONDUCTED AT CDAC-ACTS PUNE, Here I am mentioning selection procedure... Initially they will conduct written test which consists of four sectionsNo sectional Cut Off No Negative mark Time Limit-60 Minutes No of Questions-50 Only objective QuestionsSECTION 1: Aptitude : 15 QuestionsSECTION2: C and Data Structures,Basics of CPP-15 QuestionsSECTIONS 3: Computer Networks-10 QuestionsSECTION4: Software Quality Analysis-10Questions
There were almost 40 technical questions and 10 analytical questions.Total 50 questions.Cisco Placement paper analytical QuestionsAbout analytical questions.1. Find perimeter of a trapezium with 3 sides given and distance b/w parallel sides given. 2. A triangle ABC is given, a line DE is paralel to base side and that cuts the triangle.. the ratio of area of triangle to the area of trapezium .given DE/BC=3/5.. 3. Four concentric circles r given .the radius of 1st circle is x.next is 2x,then 3x and 4x. given that area b/w 2nd and 1st is A and 4th and 3rd circles being B.find ratio of A to B 4. Difference b/w the perimeteres of two concentric circles is 66.find the difference b/w radius..ans 10.5...
CISCO PLACEMENT PAPER ON 16th DECEMBER AT BANGALORE Hai Guys,I attend this paper on dec16 The written test consists of 50 questions in 60 minutes there may be different sets. 1-6 on quantitative problems very easy on basics 7-11 on general English a passage will be given and 4 sentences will be given as ans whether the data is sufficient, not sufficient, correct conclusion, full information not given. 12-22 picture reasoning such as guess the fifth one from the four figures 23-30 missing letters in a sequence of letters very easy. <!--[if !supportLists]-->31-40 <!--[endif]-->two reasoning questions r given with some q below 41-50 some...
CISCO PAPER ON 30th OCTOBER AT BANGALORE 50 questions, 20-general aptitude 20-electronics 10-networks and c. duration -1hr 1) 28 shake hands were exchanged in a meeting, each person shakes hands with every other person only once.How many people were present in the meeting? a. 14 b. 8 c. 56 d. i dont remember. 2) There are 27 balls with one ball of heavier weight than the other balls. wats the minimum number of weighs that can be made to determine the heavier ball? a. 13 b. 4 c. 3 d. 2 3) Booksellors B1 B2 B3 and there are 5 secretaries S1, S2, S3, S4 and S5. A team must made with 2 boss, 3 secretaries by satisifying certain conditions. - B1and S1 cannot be togather. - S1 and S4 cannot be...
Some Sample questions (m.tech.) tech.--24, apti.--20 On cmos power( formula- P=CV*Vf Lowest noise margin in which logic family--a) TTL b) CMOS c) biCMOS d) all have same If CMOS has tr(rise time)=tf.find Wp/Wn. given beta(n)=2*beta(p) gm of a transistor is proportional to a)Ic b)Vt c)1/Vt d)none If A and B are given in 2,s complement find A-B in decimal. Set up time,hold time ,clock to Q delay...
Cisco test Conducted on 17th sunday october at bangalore there were almost 40 technical questions and 10 analytical questions..total 50 questions.. analytical questions find perimeter of a trapezium wit 3 sides given and distance b/w parallel sides given... A triangle ABC is given, a line DE is paralel to base side and that cuts the triangle.. the ratio of area of triangle to the area of trapezium .given DE/BC=3/5.. four concentric circles r given .the radius of 1st circle is x.next is 2x,then 3x and 4x. given that area b/w 2nd and 1st is A and 4th and 3rd circles being B.find ratio of A to B difference b/w the perimeteres of two concentric circles...
Sample Question Paper The starting location of an array is 1000. If the array[1..5/...4] is stored in row major order, what is the location of element[4][3]. Each work occupies 4 bytes. If the number of leaves in a binary tree are N, then the total number of internal nodes........(Assume complete binary tree)ANS: N-1 The locality of reference means............. If two ausigned 8 bit numbers are multiplied what is the memory space required............... The vector address of RST 7.5 is ............ANS: 003C (multiply 7.5 by 8 and convert to hex) int b = 0xAA;b>>4;printf("%x",b);What is the output of the above program.... struct s1 { struct { struct {int...
CISCO PLACEMENT PAPER CAUTION: There is a -ve marking of +1 & -1 u dont mark blindly.Mark the answer if u know exactly.cutoff will be 25 marks out of 60.So becareful. There r 2 sections in CISCO section 1: Aptitude 20 marks (10 aptitude,10analogy,oppositewords etc)) section 2:comp sc (data structue , c, theory of computation,networks,operating systems) I collected upto 20 questions; In this setion questions exact numbers I have forgotten.So this will be useful to the style of the problem only. SECTION 1: 1: A man went to market with some money.With that money he can buy 15 pencils or 25 pens.He kept 15% of that money for bus fare and with rest of the money he purchased 5 pencils,and...
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How to convert Ounces to Gram: Best ways
Ounces and grams are two common units used to measure weights in small quantities. Ounces commonly are used in the United States, where the main unit of measurement for weights is the pound. An ounce is 1/16 of a pound. Grams are the main base of measurement for weights in the metric system, which is used in many countries, including all of continental Europe. A simple calculation will easily convert weights in ounces to grams. This is the best ways to do it.
## What is Ounce – Definition
Photo: Getty Images
### Ounce Meaning
Do you know what slice of bread, a bag of chips, a pencil, and juice have in common? They can all be measured in ounces for weight. Here, the student will learn about an ounce and its definition with conversions to other units.
It is the smallest measurement unit of weight. On packages, it is referred to by the abbreviation ‘oz’ which comes from the Italian and Spanish word onza. An ounce is almost equal to the weight of a slice of bread.
### Definition of Ounce
For many years people used the unit for ounces without any standardized value. Once people understood its importance to communicate between regions efficiently, giving it a proper definition.
The definition is much easier to do within the Imperial System. Because the it is defined as 1/16 lb. Thus we can convert from lbs to kg to obtain its SI value. It is also possible to do in the other way to get ounces from kilograms.
It is 1/16 th of a pound and gram is 1/1000 th of a kilogram. Thus the definition of conversion used in the UK since 1963 and in the USA since 1959 says that one pound will be 0.45359237 kilograms exactly. This defines the ounce/gram conversion as well.
Using this definition, we get 1 ounce = 28.349523125 grams. Therefore for most of the practical purposes, we should mostly use 1ounce = 28.35g
### History of Ounce
Ounce word came into English from Anglo-Norman French. There it was unce or ounce. But its abbreviation was borrowed from Medieval Italian, where the word was onza. Nowadays, the Italian word is oncia, and the area once covered by the Roman Empire has long since switched to the metric system.
Grams and ounces both are the units of measurement that associate with the concepts of mass and weight. The gram is a metric unit to measure the mass. Ounces are typically used in the United States for measuring the mass. It results from dividing a pound into the sixteen equal parts.
### International avoirdupois ounce
The international avoirdupois ounce (abbreviated oz) is defined as exactly 28.349523125 g under the international yard and pound agreement of 1959, signed by the United States and countries of the Commonwealth of Nations.
In the avoirdupois system, sixteen ounces make up an avoirdupois pound, and the avoirdupois pound is defined as 7000 grains; one avoirdupois ounce is therefore equal to 437.5 grains.
The ounce is still a standard unit in the United States. In the United Kingdom it ceased to be a legal unit of measure in 2000, but is still in general usage on an informal basis and also as the indicator of portion sizes in restaurants.
### International troy ounce
A troy ounce (abbreviated oz t) is equal to 480 grains. Consequently, the international troy ounce is equal to exactly 31.1034768 grams. There are 12 troy ounces in the now obsolete troy pound.
Today, the troy ounce is used only to express the mass of precious metals such as gold, platinum, palladium, rhodium or silver. Bullion coins are the most common products produced and marketed in troy ounces, but precious metal bars also exist in gram and kilogram (kg) sizes. (A kilogram bullion bar contains 32.15074657 troy ounces.)
For historical measurement of gold,
• a fine ounce is a troy ounce of pure gold content in a gold bar, computed as fineness multiplied by gross weight
• a standard ounce is a troy ounce of 22 carat gold, 91.66% pure (an 11 to 1 proportion of gold to alloy material)
## What is Gram?
Photo: Study
A gram is a unit of mass in the metric system defined as one thousandth (1 x 10-3) of a kilogram. Originally, the gram was defined as a unit equal to the mass of one cubic centimeter of pure water at 4°C (the temperature at which water has maximum density). The definition was changed when the base units for the International System of Units (SI) were redefined by the 26th General Conference of Weights and Measures. The change went into effect May 20, 2019.
The symbol for the gram is the lowercase letter "g." Incorrect symbols include "gr" (the symbol for grains), "Gm" (the symbol for the gigameter), and "gm" (easily confused with the symbol for the gram-meter, g⋅m).
Gram may also be spelled gramme.
### Examples of Gram Weight
Because a gram is a small unit of weight, its size may be difficult for many people to visualize. Here are common examples of objects that have about one gram of mass:
• A small paperclip
• A thumbtack
• A piece of chewing gum
• One US bill
• A pen cap
• One cubic centimeter (milliliter) of water
• A quarter teaspoon of sugar
### Useful Gram Conversion Factors
Grams may be converted into several other units of measurement. Some common conversion factors include:
• 1 gram (1 g) = 5 carats (5 ct)
• 1 gram (1 g) = 10-3 kilograms (10-3 kg)
• 1 gram (1 g) = 15.43236 grains (gr)
• 1 troy ounce (ozt) = 31.1035 g
• 1 gram = 8.98755179×1013 joules (J)
• 500 grams = 1 Jin (Chinese unit of measurement)
• 1 avoirdupois ounce (oz) = 28.3495 grams (g)
### Uses of the Gram
The gram is widely used in science, particular chemistry and physics. Outside of the United States, the gram is used to measure non-liquid cooking ingredients and produce (e.g., flour, sugar, bananas). Relative composition for food nutrition labels is stated per 100 grams of product, even within the United States.
### History of the Gram
In 1795, the French National Convention replaced the gravet with the gramme in the metric system. While the term changed, the definition remained that of the weight of one cubic centimeter of water. The word gramme came from the Latin word gramma which in turn derived from the Greek word grámma. The grámma was a unit used in Late Antiquity (around the 4th century AD) equal to two oboli (Greek coins) or one twenty-fourth part of an ounce.
The gram was a fundamental unit of mass in the centimeter-gram-second (CGS) system in the 19th century. The meter-kilogram-second (MKS) system of units was proposed in 1901, but the CGS and MKS systems co-exists throughout the early to mid 20th century. The MKS system became the system of base units in 1960. However, the gram was still defined based on the mass of water. In 2019, the gram was defined based on the kilogram. The kilogram has a mass almost exactly equal to that of one liter of water, but its definition has been refined, too. In 2018, Planck's constant was defined. This allowed definition of the kilogram in terms of the second and the meter. Planck's constant h is defined to be 6.62607015×10−34 and equal to one kilogram meter squared per second (kg⋅m2⋅s−1). Even so, standard masses for the kilogram still exist and are used as secondary standards for kilogram and gram weights. For all practical purposes, a liter of pure water has a mass of one kilogram and a milliliter of pure water has the mass of one gram.
## Part 1: How to convert Ounces to Grams
Photo: Wikihow
Determine the kind of ounces. In most cases, the weight is referring to the avoirdupois ounce. However, precious metals are measured in the troy ounce, which weighs slightly more than the avoirdupois ounce. Unless troy ounces are specified or the item is gold, silver or a gemstone, it is usually safe to assume the item is measured in avoirdupois ounces.
Multiply the number of ounces by 28.35 to determine the weight in grams. For a more exact calculation, multiply by 28.34952313.
Multiply the number of troy ounces by 31.1 to convert the weight in grams. For a more exact calculation, as may be required for precious metals and gemstones, multiply by 31.1034768.
To convert an ounce measurement to a gram measurement, multiply the weight by the conversion ratio.
Since one ounce is equal to 28.349523 grams, you can use this simple formula to convert:
grams = ounces × 28.349523
The weight in grams is equal to the ounces multiplied by 28.349523.
For example, here's how to convert 5 ounces to grams using the formula above.
5 oz = (5 × 28.349523) = 141.747616 g
### How Many Grams are in an Ounce?
There are 28.349523 grams in an ounce, which is why we use this value in the formula above.
1 oz = 28.349523 g
Ounces and grams are both units used to measure weight.
Ounces
Grams
1 oz
28.35 g
2 oz
56.7 g
3 oz
85.05 g
4 oz
113.4 g
5 oz
141.75 g
6 oz
170.1 g
7 oz
198.45 g
8 oz
226.8 g
9 oz
255.15 g
10 oz
283.5 g
11 oz
311.84 g
12 oz
340.19 g
13 oz
368.54 g
14 oz
396.89 g
15 oz
425.24 g
16 oz
453.59 g
17 oz
481.94 g
18 oz
510.29 g
19 oz
538.64 g
20 oz
566.99 g
21 oz
595.34 g
22 oz
623.69 g
23 oz
652.04 g
24 oz
680.39 g
25 oz
708.74 g
26 oz
737.09 g
27 oz
765.44 g
28 oz
793.79 g
29 oz
822.14 g
30 oz
850.49 g
31 oz
878.84 g
32 oz
907.18 g
33 oz
935.53 g
34 oz
963.88 g
35 oz
992.23 g
36 oz
1,021 g
37 oz
1,049 g
38 oz
1,077 g
39 oz
1,106 g
40 oz
1,134 g
## Part 2: How to Convert Grams to Ounces
Photo: Toppr
To convert a gram measurement to an ounce measurement, multiply the weight by the conversion ratio.
Since one gram is equal to 0.035274 ounces, you can use this simple formula to convert:
ounces = grams × 0.035274
The weight in ounces is equal to the grams multiplied by 0.035274.
For example, here's how to convert 5 grams to ounces using the formula above.
5 g = (5 × 0.035274) = 0.17637 oz
### Grams
A gram is the mass/weight equal to 1/1,000 of a kilogram and is roughly equivalent to the mass of one cubic centimeter of water.
The gram, or gramme, is an SI unit of weight in the metric system. Grams can be abbreviated as g; for example, 1 gram can be written as 1 g.
### Ounces
One ounce is a unit of mass/weight equal to 1/16 of a pound. The common ounce should not be confused with the troy ounce, which is equal to 1/12 of a troy pound.
The ounce is a US customary and imperial unit of weight. Ounces can be abbreviated as oz; for example, 1 ounce can be written as 1 oz.
## Gram to Ounce Conversion Table
Grams Ounces
1 g 0.035274 oz
2 g 0.070548 oz
3 g 0.105822 oz
4 g 0.141096 oz
5 g 0.17637 oz
6 g 0.211644 oz
7 g 0.246918 oz
8 g 0.282192 oz
9 g 0.317466 oz
10 g 0.35274 oz
11 g 0.388014 oz
12 g 0.423288 oz
13 g 0.458562 oz
14 g 0.493835 oz
15 g 0.529109 oz
16 g 0.564383 oz
17 g 0.599657 oz
18 g 0.634931 oz
19 g 0.670205 oz
20 g 0.705479 oz
21 g 0.740753 oz
22 g 0.776027 oz
23 g 0.811301 oz
24 g 0.846575 oz
25 g 0.881849 oz
26 g 0.917123 oz
27 g 0.952397 oz
28 g 0.987671 oz
29 g 1.0229 oz
30 g 1.0582 oz
31 g 1.0935 oz
32 g 1.1288 oz
33 g 1.164 oz
34 g 1.1993 oz
35 g 1.2346 oz
36 g 1.2699 oz
37 g 1.3051 oz
38 g 1.3404 oz
39 g 1.3757 oz
40 g 1.411 oz
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C# - Find SQRT Using Algorithm
C# - Find SQRT using Algorithm
You can solve the problem in two ways with out using the built in function System.Math.Sqrt.
Method 1 - Like binary search, have a minimum and maximum possible values. Do the square operation and compare the result. Then adjust minimum or maximum until we find the correct sqrt of the given number. NOTE: This is NOT a perfect square root and it has got accuracy of 4 decimal points. To access the C# source code for method1, click here.
Method 2 - The traditional way of doing with out calculator or any assumption is using the algorithm. It will be perfect square root up to N number of decimal points meaning the limitation of float and double. Method 2 is explained on this page.
Source Code
using System;
using System.Collections.Generic;
using System.Text;
namespace SoftwareAndFinance
{
class Math
{
public static double SqrtByAlogorithm(double x)
{
long numeric = (long) x;
long n = numeric;
long fraction =(long) ((x - numeric) * 1000000); // 6 digits
long f = fraction;
int numdigits = 0, fnumdigits = 0, currdigits = 0;
int tempresult = 0;
int bOdd = 0, part = 0, tens = 1;
int fractioncount = 0;
double result = 0;
int k, f1, f2, i, num, temp, quotient;
for(numdigits = 0; n >= 10; numdigits++)
n = (n / 10);
numdigits++;
for(fnumdigits = 0; f >= 10; fnumdigits++)
f = (f / 10);
fnumdigits++;
if( (numdigits % 2) == 1)
bOdd = 1;
while(true)
{
tens = 1;
currdigits = (bOdd == 1) ? (numdigits - 1) : (numdigits - 2);
for(k = 0; k < currdigits; k++)
tens *= 10;
part = (int) numeric / tens;
// Get the Nearest Multiplication Factor
num = part;
quotient = tempresult * 2;
i = 0;
temp = 0;
for(i = 1; ;i++)
{
if(quotient == 0)
{
if(num - i * i < 0)
{
tempresult = (i - 1);
break;
}
}
else
{
temp = quotient * 10 + i;
if(num - i * temp < 0)
{
tempresult = quotient / 2 * 10 + i - 1;
break;
}
}
}
// Done with Nearest Multiplication Factor
f1 = tempresult / 10;
f2 = tempresult % 10;
if(f1 == 0)
numeric = numeric - (tempresult * tempresult * tens);
else
numeric = numeric - ((f1 * 2 * 10 + f2) * f2 * tens);
if(numeric == 0 && fraction == 0)
{
if(currdigits > 0)
{
// Handle the Zero case
tens = 1;
currdigits = currdigits / 2;
for(k = 0; k < currdigits; k++)
tens *= 10;
tempresult *= tens;
}
break;
}
if(bOdd == 1)
{
numdigits -= 1;
bOdd = 0;
}
else
numdigits -= 2;
if( numdigits <= 0)
{
if(numeric > 0 || fraction > 0)
{
if(fractioncount >= 5)
break;
// Handle the fraction part for integer numbers
fractioncount++;
numeric *= 100;
if(fraction > 0)
{
// Handle the fraction part for real numbers
fnumdigits -= 2;
tens = 1;
for(k = 0; k < fnumdigits; k++)
tens *= 10;
numeric += fraction / tens;
fraction = fraction % tens;
}
numdigits += 2;
}
else
break;
}
}
if(fractioncount == 0)
result = tempresult;
else
{
tens = 1;
for(k = 0; k < fractioncount; k++)
tens *= 10;
result = (double) tempresult / tens;
}
return result;
}
static void Main(string[] args)
{
for (double d = 0; d <= 10000; d += 50)
Console.WriteLine("sqrt({0,6:f1}) = {1,8:f4} {2,8:f4}", d, SqrtByAlogorithm(d), System.Math.Sqrt(d));
}
}
}
Output
sqrt( 0.0) = 0.0000 0.0000
sqrt( 50.0) = 7.0711 7.0711
sqrt( 100.0) = 10.0000 10.0000
sqrt( 150.0) = 12.2474 12.2474
sqrt( 200.0) = 14.1421 14.1421
sqrt( 250.0) = 15.8114 15.8114
sqrt( 300.0) = 17.3205 17.3205
sqrt( 350.0) = 18.7083 18.7083
sqrt( 400.0) = 20.0000 20.0000
sqrt( 450.0) = 21.2132 21.2132
sqrt( 500.0) = 22.3607 22.3607
sqrt( 550.0) = 23.4521 23.4521
sqrt( 600.0) = 24.4949 24.4949
sqrt( 650.0) = 25.4951 25.4951
sqrt( 700.0) = 26.4575 26.4575
sqrt( 750.0) = 27.3861 27.3861
sqrt( 800.0) = 28.2843 28.2843
sqrt( 850.0) = 29.1548 29.1548
sqrt( 900.0) = 30.0000 30.0000
sqrt( 950.0) = 30.8221 30.8221
sqrt(1000.0) = 31.6228 31.6228
sqrt(1050.0) = 32.4037 32.4037
sqrt(1100.0) = 33.1662 33.1662
sqrt(1150.0) = 33.9116 33.9116
sqrt(1200.0) = 34.6410 34.6410
sqrt(1250.0) = 35.3553 35.3553
sqrt(1300.0) = 36.0555 36.0555
sqrt(1350.0) = 36.7423 36.7423
sqrt(1400.0) = 37.4166 37.4166
sqrt(1450.0) = 38.0789 38.0789
sqrt(1500.0) = 38.7298 38.7298
sqrt(1550.0) = 39.3700 39.3700
sqrt(1600.0) = 40.0000 40.0000
sqrt(1650.0) = 40.6202 40.6202
sqrt(1700.0) = 41.2311 41.2311
sqrt(1750.0) = 41.8330 41.8330
sqrt(1800.0) = 42.4264 42.4264
sqrt(1850.0) = 43.0116 43.0116
sqrt(1900.0) = 43.5890 43.5890
sqrt(1950.0) = 44.1588 44.1588
sqrt(2000.0) = 44.7214 44.7214
sqrt(2050.0) = 45.2769 45.2769
sqrt(2100.0) = 45.8258 45.8258
sqrt(2150.0) = 46.3681 46.3681
sqrt(2200.0) = 46.9042 46.9042
sqrt(2250.0) = 47.4342 47.4342
sqrt(2300.0) = 47.9583 47.9583
sqrt(2350.0) = 48.4768 48.4768
sqrt(2400.0) = 48.9898 48.9898
sqrt(2450.0) = 49.4975 49.4975
sqrt(2500.0) = 50.0000 50.0000
sqrt(2550.0) = 50.4975 50.4975
sqrt(2600.0) = 50.9902 50.9902
sqrt(2650.0) = 51.4782 51.4782
sqrt(2700.0) = 51.9615 51.9615
sqrt(2750.0) = 52.4404 52.4404
sqrt(2800.0) = 52.9150 52.9150
sqrt(2850.0) = 53.3854 53.3854
sqrt(2900.0) = 53.8516 53.8516
sqrt(2950.0) = 54.3139 54.3139
sqrt(3000.0) = 54.7723 54.7723
sqrt(3050.0) = 55.2268 55.2268
sqrt(3100.0) = 55.6776 55.6776
sqrt(3150.0) = 56.1249 56.1249
sqrt(3200.0) = 56.5685 56.5685
sqrt(3250.0) = 57.0088 57.0088
sqrt(3300.0) = 57.4456 57.4456
sqrt(3350.0) = 57.8792 57.8792
sqrt(3400.0) = 58.3095 58.3095
sqrt(3450.0) = 58.7367 58.7367
sqrt(3500.0) = 59.1608 59.1608
sqrt(3550.0) = 59.5819 59.5819
sqrt(3600.0) = 60.0000 60.0000
sqrt(3650.0) = 60.4152 60.4152
sqrt(3700.0) = 60.8276 60.8276
sqrt(3750.0) = 61.2372 61.2372
sqrt(3800.0) = 61.6441 61.6441
sqrt(3850.0) = 62.0484 62.0484
sqrt(3900.0) = 62.4500 62.4500
sqrt(3950.0) = 62.8490 62.8490
sqrt(4000.0) = 63.2456 63.2456
sqrt(4050.0) = 63.6396 63.6396
sqrt(4100.0) = 64.0312 64.0312
sqrt(4150.0) = 64.4205 64.4205
sqrt(4200.0) = 64.8074 64.8074
sqrt(4250.0) = 65.1920 65.1920
sqrt(4300.0) = 65.5744 65.5744
sqrt(4350.0) = 65.9545 65.9545
sqrt(4400.0) = 66.3325 66.3325
sqrt(4450.0) = 66.7083 66.7083
sqrt(4500.0) = 67.0820 67.0820
sqrt(4550.0) = 67.4537 67.4537
sqrt(4600.0) = 67.8233 67.8233
sqrt(4650.0) = 68.1909 68.1909
sqrt(4700.0) = 68.5565 68.5565
sqrt(4750.0) = 68.9202 68.9202
sqrt(4800.0) = 69.2820 69.2820
sqrt(4850.0) = 69.6419 69.6419
sqrt(4900.0) = 70.0000 70.0000
sqrt(4950.0) = 70.3562 70.3562
sqrt(5000.0) = 70.7107 70.7107
sqrt(5050.0) = 71.0634 71.0634
sqrt(5100.0) = 71.4143 71.4143
sqrt(5150.0) = 71.7635 71.7635
sqrt(5200.0) = 72.1110 72.1110
sqrt(5250.0) = 72.4569 72.4569
sqrt(5300.0) = 72.8011 72.8011
sqrt(5350.0) = 73.1437 73.1437
sqrt(5400.0) = 73.4847 73.4847
sqrt(5450.0) = 73.8241 73.8241
sqrt(5500.0) = 74.1620 74.1620
sqrt(5550.0) = 74.4983 74.4983
sqrt(5600.0) = 74.8331 74.8331
sqrt(5650.0) = 75.1665 75.1665
sqrt(5700.0) = 75.4983 75.4983
sqrt(5750.0) = 75.8288 75.8288
sqrt(5800.0) = 76.1577 76.1577
sqrt(5850.0) = 76.4853 76.4853
sqrt(5900.0) = 76.8115 76.8115
sqrt(5950.0) = 77.1362 77.1362
sqrt(6000.0) = 77.4597 77.4597
sqrt(6050.0) = 77.7817 77.7817
sqrt(6100.0) = 78.1025 78.1025
sqrt(6150.0) = 78.4219 78.4219
sqrt(6200.0) = 78.7401 78.7401
sqrt(6250.0) = 79.0569 79.0569
sqrt(6300.0) = 79.3725 79.3725
sqrt(6350.0) = 79.6869 79.6869
sqrt(6400.0) = 80.0000 80.0000
sqrt(6450.0) = 80.3119 80.3119
sqrt(6500.0) = 80.6226 80.6226
sqrt(6550.0) = 80.9321 80.9321
sqrt(6600.0) = 81.2404 81.2404
sqrt(6650.0) = 81.5475 81.5475
sqrt(6700.0) = 81.8535 81.8535
sqrt(6750.0) = 82.1584 82.1584
sqrt(6800.0) = 82.4621 82.4621
sqrt(6850.0) = 82.7647 82.7647
sqrt(6900.0) = 83.0662 83.0662
sqrt(6950.0) = 83.3667 83.3667
sqrt(7000.0) = 83.6660 83.6660
sqrt(7050.0) = 83.9643 83.9643
sqrt(7100.0) = 84.2615 84.2615
sqrt(7150.0) = 84.5577 84.5577
sqrt(7200.0) = 84.8528 84.8528
sqrt(7250.0) = 85.1469 85.1469
sqrt(7300.0) = 85.4400 85.4400
sqrt(7350.0) = 85.7321 85.7321
sqrt(7400.0) = 86.0233 86.0233
sqrt(7450.0) = 86.3134 86.3134
sqrt(7500.0) = 86.6025 86.6025
sqrt(7550.0) = 86.8907 86.8907
sqrt(7600.0) = 87.1780 87.1780
sqrt(7650.0) = 87.4643 87.4643
sqrt(7700.0) = 87.7496 87.7496
sqrt(7750.0) = 88.0341 88.0341
sqrt(7800.0) = 88.3176 88.3176
sqrt(7850.0) = 88.6002 88.6002
sqrt(7900.0) = 88.8819 88.8819
sqrt(7950.0) = 89.1628 89.1628
sqrt(8000.0) = 89.4427 89.4427
sqrt(8050.0) = 89.7218 89.7218
sqrt(8100.0) = 90.0000 90.0000
sqrt(8150.0) = 90.2774 90.2774
sqrt(8200.0) = 90.5539 90.5539
sqrt(8250.0) = 90.8295 90.8295
sqrt(8300.0) = 91.1043 91.1043
sqrt(8350.0) = 91.3783 91.3783
sqrt(8400.0) = 91.6515 91.6515
sqrt(8450.0) = 91.9239 91.9239
sqrt(8500.0) = 92.1954 92.1954
sqrt(8550.0) = 92.4662 92.4662
sqrt(8600.0) = 92.7362 92.7362
sqrt(8650.0) = 93.0054 93.0054
sqrt(8700.0) = 93.2738 93.2738
sqrt(8750.0) = 93.5414 93.5414
sqrt(8800.0) = 93.8083 93.8083
sqrt(8850.0) = 94.0744 94.0744
sqrt(8900.0) = 94.3398 94.3398
sqrt(8950.0) = 94.6044 94.6044
sqrt(9000.0) = 94.8683 94.8683
sqrt(9050.0) = 95.1315 95.1315
sqrt(9100.0) = 95.3939 95.3939
sqrt(9150.0) = 95.6556 95.6556
sqrt(9200.0) = 95.9166 95.9166
sqrt(9250.0) = 96.1769 96.1769
sqrt(9300.0) = 96.4365 96.4365
sqrt(9350.0) = 96.6954 96.6954
sqrt(9400.0) = 96.9536 96.9536
sqrt(9450.0) = 97.2111 97.2111
sqrt(9500.0) = 97.4679 97.4679
sqrt(9550.0) = 97.7241 97.7241
sqrt(9600.0) = 97.9796 97.9796
sqrt(9650.0) = 98.2344 98.2344
sqrt(9700.0) = 98.4886 98.4886
sqrt(9750.0) = 98.7421 98.7421
sqrt(9800.0) = 98.9949 98.9949
sqrt(9850.0) = 99.2472 99.2472
sqrt(9900.0) = 99.4987 99.4987
sqrt(9950.0) = 99.7497 99.7497
sqrt(10000.0) = 100.0000 100.0000
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https://www.reference.com/math/algebra-used-everyday-life-de31a9060f1c30ff
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| 886,806,050
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How Is Algebra Used in Everyday Life?
# How Is Algebra Used in Everyday Life?
People use algebra in their daily lives when they make decisions about health, fitness, financial and money matters and when cooking. Algebra involves the use of known variables and fixed numbers in equations to find the values of unknown numbers.
Financial planning is an area in daily life where algebra is used. Algebra concepts are used to calculate items like interest rates and determine loan payments. They are also used to predict the growth of money.
Getting and staying physically fit often requires the use of calculations to determine if one has an appropriate level of body fat and body weight versus lean muscle and bone. It also involves determining the right amount of daily food intake and the types of foods appropriate for an individual's diet. Given known variables, such as height, activity and current percentages of body mass, algebra can be used to determine unknown variables necessary to reach and maintain fitness.
People who cook, either professionally or for personal use, use simple algebraic expressions to adjust the ingredients in a dish depending on the number of servings desired. Medical professionals use algebra in a variety of applications, such as determining drug dosage and measuring the performance of body functions, such as cardiac output.
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# Query on Natural Convection simulation
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December 10, 2010, 06:47
Query on Natural Convection simulation
#1
Member
Dynampally Pavitran
Join Date: Mar 2010
Location: India
Posts: 74
Rep Power: 9
Hello all,
I am simulating a natural convection problem in a differentially heated 2D enclosure(pls see the attachment for boundary conditions used). I am carrying out the simulations for varying Rayleigh numbers( Rayleigh number is based on the dimension of the geometry, L=H).
The rayleigh number relation used is: (g*Beta*delT*L^3)/(Kinematic viscosity*Thermal diffusivity)
All the air properties are taken at 75 C i.e at Prandtl no: 0.716
g :9.81 [m/s^2]
Beta: Thermal expansion coefficient : 2.87E-03 [1/K]
delT: temperature difference : 50 C
Kine.viscosity: 2.05E-05 [m^2/s]
Thermal diffusivity: 2.85E-05 [m^2/s]
therefore for L=H=0.02 [m] , the Ra No is: 1.92E+04
in CFX pre , I created material air with properties at 75 C and used laminar and thermal energy equations with Buoyancy ref temp of 50 C.
The convergence criteria for Momentum & continuity was 1E-4 and for energy 1E-6 with conservtion target as 0.01. Discretization scheme was high resolution with auto time scale.
The predicted nusselt number is about 100, whereas it should be around 2.5. and also the rayleigh no written in the out file is about 9E+01.
My question is:
1. why the rayleigh no. is coming different in the out file?
2. what may be the reason for overprediction of nusselt no.?
Attached Images
geom.jpg.jpg (22.4 KB, 27 views)
December 11, 2010, 06:11 #2 Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 14,326 Rep Power: 110 This is a standard benchmark simulation so you should be able to get very accurate answers. If you are referring to the Rayliegh and Nusselt numbers described in the output file then you should ignore these numbers. These numbers are in the output file so you can estimate what regime the flow is in to check your physics (eg laminar vs turbulent) is correct. The calculation of these numbers is based on an arbitrary length scale (the cube root of the total volume from memory), material properties (the mass average over the entire domain) and flow velocities (again I think it is the mass average over the whole domain). This means the numbers coming out from this calculation have little to do which traditional definitions of say, Rayliegh numbers, which should involve the distance the plates are apart and the temperature of the two plates. To get accurate Rayliegh and Nusselt numbers out of your simulation you need to: 1) Define a CEL expression which uses the correct definition of Rayliegh/Nusselt number and outputs that to a monitor point, AND/OR 2) Use CFD-Post to extract the quantities required to calculate the numbers with the definition you require.
September 24, 2017, 03:07
#3
New Member
Praphul.T
Join Date: Dec 2013
Location: Kochi, India
Posts: 6
Rep Power: 6
Quote:
Originally Posted by ghorrocks This is a standard benchmark simulation so you should be able to get very accurate answers. If you are referring to the Rayliegh and Nusselt numbers described in the output file then you should ignore these numbers. These numbers are in the output file so you can estimate what regime the flow is in to check your physics (eg laminar vs turbulent) is correct. The calculation of these numbers is based on an arbitrary length scale (the cube root of the total volume from memory), material properties (the mass average over the entire domain) and flow velocities (again I think it is the mass average over the whole domain). This means the numbers coming out from this calculation have little to do which traditional definitions of say, Rayliegh numbers, which should involve the distance the plates are apart and the temperature of the two plates. To get accurate Rayliegh and Nusselt numbers out of your simulation you need to: 1) Define a CEL expression which uses the correct definition of Rayliegh/Nusselt number and outputs that to a monitor point, AND/OR 2) Use CFD-Post to extract the quantities required to calculate the numbers with the definition you require.
So does this mean that the length scale used in Rayleigh number calculation according to the Fluent user manual is the cube root of total volume ?
September 25, 2017, 11:28 #4 Senior Member Join Date: Jun 2009 Posts: 732 Rep Power: 15 A bit confused. You are running ANSYS CFX, and you are using the ANSYS FLUENT documentation to understand the output? Keep in mind dimensionless numbers use reference values which can be defined differently for different audiences, i.e. there is no universal definition unless it is a material property such as the Prandtl number for example. Check their definitions for each case, i.e. read CFX documentation to understand their definition. If you do not feel comfortable with their definition, feel free to evaluate the quantity using what is most convenient for your simulation.
September 29, 2017, 09:23 #5 New Member Praphul.T Join Date: Dec 2013 Location: Kochi, India Posts: 6 Rep Power: 6 No no. Pavithran is some other guy who asked the question initially. While reading the reply of ghorrocks to pavithrans question , i got confused and thus asked the question. I use fluent and they have defined L as the characteristic length in Rayleigh number Ra calculation. I am pretty sure they have defined Ra in the same way in cfx. Well for square domains it isn't much of a problem as L=H. But for rectangular domains what can be L ? For a text book problem , normally we use the fluid layer depth as the characteristic length. What I didn't understand was that why the cfx solver takes in cube root of total volume as length. But thanks to you , i now understand that the dimensional numbers are calculated using the reference parameters that we specify in the solver. Sent from my Lenovo A2010-a using CFD Online Forum mobile app
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https://goprep.co/ex-23.6-q4-prove-that-the-lines-2x-3y-19-and-2x-3y-7-0-are-i-1nl7ht
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Q. 45.0( 3 Votes )
# Prove that the li
Given: lines A 2x + 3y = 19 and B 2x + 3y + 7 = 0 also a line C 2x + 3y = 6.
To prove:
Line A and B are equidistant from the line C
Proof:
Let d1 be the distance between lines 2x + 3y = 19 and 2x + 3y = 6,
While d2 is the distance between lines 2x + 3y + 7 = 0 and 2x + 3y = 6
Hence proved, the lines 2x + 3y = 19 and 2x + 3y + 7 = 0 are equidistant from the line 2x + 3y = 6
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# 31587 (number)
31,587 (thirty-one thousand five hundred eighty-seven) is an odd five-digits composite number following 31586 and preceding 31588. In scientific notation, it is written as 3.1587 × 104. The sum of its digits is 24. It has a total of 2 prime factors and 4 positive divisors. There are 21,056 positive integers (up to 31587) that are relatively prime to 31587.
## Basic properties
• Is Prime? No
• Number parity Odd
• Number length 5
• Sum of Digits 24
• Digital Root 6
## Name
Short name 31 thousand 587 thirty-one thousand five hundred eighty-seven
## Notation
Scientific notation 3.1587 × 104 31.587 × 103
## Prime Factorization of 31587
Prime Factorization 3 × 10529
Composite number
Distinct Factors Total Factors Radical ω(n) 2 Total number of distinct prime factors Ω(n) 2 Total number of prime factors rad(n) 31587 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 31,587 is 3 × 10529. Since it has a total of 2 prime factors, 31,587 is a composite number.
## Divisors of 31587
1, 3, 10529, 31587
4 divisors
Even divisors 0 4 2 2
Total Divisors Sum of Divisors Aliquot Sum τ(n) 4 Total number of the positive divisors of n σ(n) 42120 Sum of all the positive divisors of n s(n) 10533 Sum of the proper positive divisors of n A(n) 10530 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 177.727 Returns the nth root of the product of n divisors H(n) 2.99972 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 31,587 can be divided by 4 positive divisors (out of which 0 are even, and 4 are odd). The sum of these divisors (counting 31,587) is 42,120, the average is 10,530.
## Other Arithmetic Functions (n = 31587)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 21056 Total number of positive integers not greater than n that are coprime to n λ(n) 10528 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 3402 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 21,056 positive integers (less than 31,587) that are coprime with 31,587. And there are approximately 3,402 prime numbers less than or equal to 31,587.
## Divisibility of 31587
m n mod m 2 3 4 5 6 7 8 9 1 0 3 2 3 3 3 6
The number 31,587 is divisible by 3.
## Classification of 31587
• Arithmetic
• Semiprime
• Deficient
• Polite
• Square Free
### Other numbers
• LucasCarmichael
## Base conversion (31587)
Base System Value
2 Binary 111101101100011
3 Ternary 1121022220
4 Quaternary 13231203
5 Quinary 2002322
6 Senary 402123
8 Octal 75543
10 Decimal 31587
12 Duodecimal 16343
20 Vigesimal 3ij7
36 Base36 odf
## Basic calculations (n = 31587)
### Multiplication
n×y
n×2 63174 94761 126348 157935
### Division
n÷y
n÷2 15793.5 10529 7896.75 6317.4
### Exponentiation
ny
n2 997738569 31515568179003 995482252070167761 31444297896140389066707
### Nth Root
y√n
2√n 177.727 31.6108 13.3314 7.94148
## 31587 as geometric shapes
### Circle
Diameter 63174 198467 3.13449e+09
### Sphere
Volume 1.32012e+14 1.2538e+10 198467
### Square
Length = n
Perimeter 126348 9.97739e+08 44670.8
### Cube
Length = n
Surface area 5.98643e+09 3.15156e+13 54710.3
### Equilateral Triangle
Length = n
Perimeter 94761 4.32033e+08 27355.1
### Triangular Pyramid
Length = n
Surface area 1.72813e+09 3.71415e+12 25790.7
## Cryptographic Hash Functions
md5 dd87a43132f3ce443d1e50b29019de3b a5cc4021e4ea58d70a9429386bf829ab3038a5d9 ad00db91a8fa600bdd3a38cb0176f130991f464ef9a3bb6ce3519fb167c893ce 5491e109bd53f0f86326f9f7f2a384623b31bbd482e420d0305767c85b18d08397557dfe62ac55fa867399968f713f780c061b39091febce2a5ecc7b665e6ba6 ffa2e97b1b63c8bbae1d889005781a339dc0947b
| 1,446
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http://mr-mathematics.com/product/interpreting-pie-charts/
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# Interpreting Pie Charts
#### What's Included
• Smart Notebooks Presentation
• Interactive Excel File
• Activ Inspire Flipchart
• Lesson Plan
• Microsoft PowerPoint Presentation
• Differentiated Worksheet
# Interpreting Pie Charts
To interpret pie charts at GCSE students are taught to use equivalent ratios by identifying a common frequency and angle from the pie chart. As learning progresses they are challenged to compare sets of data by finding the frequencies from various pie charts.
##### Differentiated Learning Objectives
• All students should be able to recognise the limitations of representing data using pie charts.
• Most students should be able to calculate frequencies from a pie chart when given the sample size.
• Some students should be able to compare data distributions by comparing frequencies found from pie charts
Statistical Diagrams - Foundation
Representing Data - Higher
### Mr Mathematics Blog
#### Teaching Mathematics for a Growth Mindset
Inspiring students to enjoy maths and feel the success that comes with attempting a difficult challenge is why I teach. The feeling of success is addictive. The more students experience it the more they want it and the further out of their comfort zone they are willing to go to get more of it. Teaching […]
#### Equation of Straight Line Graphs
To find the equation of straight line graphs students need to calculate the gradient using two pairs of coordinates and the intercept which is the y value of where it crosses the vertical axis. Examiner’s reports of past exam questions show students are more able to find the intercept of a straight line than they […]
#### Arithmetic and Geometric Sequences
Students learn how to generate and describe arithmetic and geometric sequences on a position-to-term basis. Learning progresses from plotting and reading coordinates in the first quadrant to describing geometric sequences using the nth term. This unit takes place in Term 4 of Year 10 and is followed by the equations of straight line graphs. Arithmetic […]
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http://www.konradvoelkel.com/2009/10/classifying-riemann-surfaces/
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### Classifying Riemann surfaces
Wednesday, October 21st, 2009 | Author:
In this post, I will sketch a classification of Riemann surfaces.
For those who haven't heard about the subject before, there is an introduction. For the impatient, look at the bottom of the post, where I have written a very short summary.
### Introduction
At first, a definition: A Riemann surface is a connected complex manifold of (complex) dimension 1 (so real dimension 2, which qualifies it as a surface). A compact Riemann surface is a Riemann surface which is compact as a topological space.
At first, let's think only about orientable surfaces. Orientability means that the orientation double cover is trivial (not simply-connected), or equivalently, the tangent bundle (or sheaf, if you prefer) admits a global section. In simple terms, orientable means you can take an orientation with you, walk around the surface, return where you were first and the orientation is still the same.
It turns out that every complex manifold is orientable as real manifold, so a Riemann surface is always orientable as a real surface (and this is what we care about for the moment).
#### Some simple examples of Riemann surfaces:
• the complex plane $\mathbb{C}$ itself
• the upper half plane $\mathbb{H}$ (also called the hyperbolic disc; it's biholomorphic to the open unit disc)
• Complex projective space of one dimension $\mathbb{C}P^1$ which is topologically a sphere $S^2$, called Riemann sphere
• A complex torus $E_\tau$, that is the quotient of the complex plane $\mathbb{C}$ by a lattice $\Lambda_\tau = \mathbb{Z} + \mathbb{Z}\tau$ with some $\tau \in \mathbb{C}$, so we have $E_\tau = \mathbb{C}/\Lambda_\tau$
#### Some simple counter-examples:
• The moebius strip is not orientable (so it admits no complex structure).
• Complex projective space modulo action of $z \mapsto -z^{-1}$ is a real manifold, but no longer a complex one.
So we know what we're talking about. Now what kind of classification do we search? The "best" classification would be one up to biholomorphism, but let's see how far we can get. First, we can seperate different surfaces by their topology. This is a good approximation because each biholomorphism is a homeomorphism.
### Topological classification
Note that, topologically, all tori $E_\tau$ are homeomorphic. Their complex structure is different and depends on $\tau$ which can always be chosen to lie in $\mathbb{H}$, the complex upper half plane. This variable $\tau$ is called the modulus of $E_\tau$.
However, $\mathbb{C}P^1$ and $E_\tau$ are not homeomorphic, their genera are different. The genus is a topological invariant which completely classifies the compact (orientable real) surfaces up to homeomorphism. This can be shown by proving that each such surface admits a triangulation and then showing each triangulation is homeomorphic to a standard genus $g$ triangulation. Roughly speaking, the genus is "the number of holes" inside the surface. One can "mathematise" this definition by speaking about loops non-homotopic to the constant loop, which leads to a discussion of the fundamental group $\pi_1$. The study of fundamental groups is also necessary to understand holomorphic (branched) coverings, which are used in the biholomorphic classification theory.
### Biholomorphic classification
There are other surfaces than $\mathbb{C}P^1$ and tori $E_\tau$. The famous Riemann Mapping Theorem tells us, that the only simply connected Riemann surfaces are $\mathbb{C},\ \mathbb{H}$ and $\mathbb{C}P^1$.
#### Digression about algebraic field extensions
(You don't have to read this)
So the only compact surface without holes is $\mathbb{C}P^1$. This is interesting, because by definition a meromorphic function on a surface $X$ is a holomorphic map $X \rightarrow \mathbb{C}P^1$. The collection of all meromorphic functions on a surface $X$ is written $\mathcal{M}(X)$, it's always a field, called the function field of $X$. If there is an element $\eta$ in $\mathcal{M}(X)$, it is always a branched covering. There is a theorem, that shows each Riemann surface admits a non-constant meromorphic function. This leads to the conclusion, that the map $\eta^\ast : \mathcal{M}(\mathbb{C}P^1) \rightarrow \mathcal{M}(X)$ which sends each $f$ to $f \circ \eta$ is an algebraic field extension of degree $n$, where $n$ is the degree of the covering $\eta$. Since the meromorphic functions on $\mathbb{C}P^1$ are just the rational functions $\mathbb{C}(z)$ (a transcendence degree 1 extension of the complex numbers), each compact Riemann surface has a function field which is an algebraic field extension of $\mathbb{C}(z)$.
The other way works, too: To each algebraic field extension of $\mathbb{C}(z)$ we can define a corresponding compact Riemann surface.
Every compact Riemann surface can be embedded in complex projective space of at most dimension 3. With Chow's Theorem, we get the surprising statement that every compact Riemann surface is algebraic.
#### Universal coverings
We can understand a Riemann surface by it's coverings, since it will be a quotient of the covering. To be more specific: for each covering $p : Y \rightarrow X$, the space $X$ is biholomorphic to the quotient of $Y$ with respect to the transformation subgroup which commutes with the projection $p$. This transformation subgroup is called the group of deck transformations (it's similar to the Galois group of a field extension). There are some theorems about that:
A surface $X$ which is covered by $\mathbb{C}P^1$ is already biholomorphic to $\mathbb{C}P^1$.
A surface covered by $\mathbb{C}$ is biholomorphic either to $\mathbb{C},\ \mathbb{C}^\times$ or a torus. On the other hand, every torus is covered by $\mathbb{C}$. For surfaces with universal covering space $\mathbb{H}$, the situation is more complicated. For example, one can show that every hyper-elliptic surface is covered by $\mathbb{H}$.
#### Automorphisms of simply connected surfaces
Now we can realise every Riemann surface as quotient of the simply connected spaces, since every surface admits a universal covering, which is by definition a simply connected Riemann surface. In order to do the classification, we have to study the automorphism groups of the simply connected surfaces and their subgroups.
• $Aut(\mathbb{C}) = \{z \mapsto az+b \mid a,b \in \mathbb{C}\}$ (Affine translations)
• $Aut(\mathbb{C}P^1) = PSL_2(\mathbb{C})$ (Möbius transformations)
• $Aut(\mathbb{H}) = PSU_{1,1}(\mathbb{C})$ (Möbius transformations preserving the unit disc)
#### Curvature
One can show that each Riemann surface admits a Riemannian metric because they are all paracompact. Luckily, this metric is unique up to conformal equivalence for a given complex structure. Every such metric is equivalent to one with a constant Gaussian curvature either $-1,\ 0$ or $+1$.
### Short summary
Every Riemann surface is the quotient of a free, proper holomorphic group action on its universal covering, which is one of the simply connected surfaces $\mathbb{C},\ \mathbb{C}P^1,\ \mathbb{H}$. The complete list:
• Elliptic surfaces - constant Gauss curvature $+1$
• Genus 0: only the Riemann sphere $\mathbb{C}P^1$
• Genus 1 or higher: None.
• Parabolic surfaces - constant Gauss curvature $0$
• Genus 0: only the complex plane $\mathbb{C}$
• Genus 1: either $\mathbb{C}^\times$ or a torus $E_\tau$, where the tori biholomorphism classes are in one-to-one correspondence to the elements of their moduli space $\mathbb{H}$.
• Genus 2 or higher: None.
• Hyperbolic surfaces - constant Gauss curvature $-1$
• Genus 0: only the hyperbolic disc $\mathbb{H}$
• Genus 1 and higher: quotients of $\mathbb{H}$ by a Fuchsian group. Sadly, further classification is difficult (but at least for compact surfaces, we can apply the theory of field extensions sketched above)
• All genus > 1 and especially the so-called hyperelliptic surfaces belong to this class.
I wrote this because I couldn't find a quick overview of the classification, with enough but not too much detail, on the web. If you find mistakes or have any questions, don't hesitate to contact me and/or write a comment :-)
UPDATE: this is the conformal classification. There are various other classifications, see Solomentsevs explanations here and Krushkal's explanations here.
Category: English
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# Clojure Euler: Problem 016
2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.
What is the sum of the digits of the number 2^1000 ?
Are you kidding me?
• Find 1000th power of two
• Sum its digits
In Clojure Euler: Problem 008 we learned how to sum digits in the number. Just gentle reminder:
``````(defn sum-of-digits [n]
(reduce + (map #(- (int %) 48) (seq (str n)))))
``````
Now, let’s create sequence of powers of two:
``````(defn powers-of-2 []
(iterate (partial * 2) 1))
``````
Unfortunately, this sequence throws `integer overflow` on the `64th` element. We can fix that using long arithmetics, which known as `BigInteger` in Java. Change `1` to `1N`.
``````(iterate (partial * 2) 1N)
``````
Another way is to use automatic promotion operator (`+'`, `*'`). If result of some operation is not suitable for some type, instead of invalid computation and runtime exception, clojure automatically promotes the type to suitable one (for example `Long.MAX_VALUE +' 1` works fine and produces correct result with type of `BigInteger`):
``````(iterate (partial *' 2) 1)
``````
Choose `powers-of-2` that you prefer and final result will look like this:
``````(sum-of-digits (last (take 1001 (powers-of-2))))
``````
github
P.S. Automatic promotion is a beatiful thing. But be aware about losing in speed of calculations. Also, no way back. If promotion happened, depromotion won’t.
05 March 2013
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http://www.chegg.com/homework-help/questions-and-answers/yusef-pushes-chair-mass-m-550-across-carpeted-floor-force-magnitude-fp-148-directed-350-ho-q944344
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Yusef pushes a chair of mass m = 55.0 across a carpeted floor with a force of magnitude Fp = 148 directed at ? = 35.0 below the horizontal . The magnitude of the frictional force between the carpet and the floor is Ffr = 106 . What is the magnitude of the acceleration of the chair? What is the magnitude of the normal force acting on the chair?
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## Tuesday, 31 December 2013
### Strategy Design pattern - Implementation [Sort]
Click the below Image to Enlarge
Strategy Design pattern - Implementation [Sort]
Strategy Design pattern - Implementation [Sort] - Class Diagram
SortingStrategy.java
public interface SortingStrategy
{
int[] sort( int[] inputArray );
}
BubbleSort.java
public class BubbleSort implements SortingStrategy
{
public int[] sort( int[] inputArray )
{
int n = inputArray.length;
for( int i = 0; i < n; i++ )
{
for( int j = 1; j < (n - i); j++ )
{
if( inputArray[j - 1] > inputArray[j] )
{
swap(j - 1, j, inputArray);
}
}
}
System.out.println("Array is sorted using Bubble Sort Algorithm");
return inputArray;
}
private void swap( int k, int l, int[] inputArray )
{
int temp = inputArray[k];
inputArray[k] = inputArray[l];
inputArray[l] = temp;
}
}
InsertionSort.java
public class InsertionSort implements SortingStrategy
{
public int[] sort( int[] inputArray )
{
for( int i = 1; i < inputArray.length; i++ )
{
// a temporary copy of the current element
int tmp = inputArray[i];
int j;
// find the position for insertion
for( j = i; j > 0; j-- )
{
if( inputArray[j - 1] < tmp )
break;
// shift the sorted part to right
inputArray[j] = inputArray[j - 1];
}
// insert the current element
inputArray[j] = tmp;
}
System.out.println("Array is sorted using Insertion Sort Algorithm");
return inputArray;
}
}
SelectionSort.java
public class SelectionSort implements SortingStrategy
{
public int[] sort( int[] inputArray )
{
// find the smallest element starting from position i
for (int i = 0; i < inputArray.length - 1; i++)
{
int min = i; // record the position of the smallest
for (int j = i + 1; j < inputArray.length; j++)
{
// update min when finding a smaller element
if (inputArray[j] < inputArray[min])
min = j;
}
// put the smallest element at position i
swap(inputArray, i, min);
}
System.out.println("Array is sorted using Selection Sort Algorithm");
return inputArray;
}
private void swap( int[] inputArray,int k, int l )
{
int temp = inputArray[k];
inputArray[k] = inputArray[l];
inputArray[l] = temp;
}
}
SortContext.java
import java.util.Scanner;
public class SortContext
{
private SortingStrategy sortingStrategy;
public void setSortingStrategy( SortingStrategy sortingStrategy )
{
this.sortingStrategy = sortingStrategy;
}
private void printArray( int[] inputArray )
{
for( int i = 0; i < inputArray.length; i++ )
{
System.out.print(inputArray[i] + ",");
}
System.out.println("\n");
}
{
System.out.println("Enter array size : ");
Scanner scanner = new Scanner(System.in);
int n = scanner.nextInt();
System.out.println("Enter input array : ");
int[] inputArray = new int[n];
for( int i = 0; i < n; i++ )
{
inputArray[i] = scanner.nextInt();
}
return inputArray;
}
public void sort()
{
int[] inputArray = readUserInput();
inputArray = sortingStrategy.sort(inputArray);
printArray(inputArray);
}
}
StrategyClient.java
import java.util.Scanner;
public class StrategyClient
{
public static void main( String[] args )
{
System.out.println("Please enter Sort Algorithm : 'BubbleSort' or 'SelectionSort' or 'InsertionSort'");
Scanner scanner = new Scanner(System.in);
String sortAlgorithm = scanner.next();
System.out.println("Sort Algorithm is : " + sortAlgorithm);
SortContext context = new SortContext();
if( "BubbleSort".equalsIgnoreCase(sortAlgorithm) )
{
context.setSortingStrategy(new BubbleSort());
}
else if( "SelectionSort".equalsIgnoreCase(sortAlgorithm) )
{
context.setSortingStrategy(new SelectionSort());
}
else if( "InsertionSort".equalsIgnoreCase(sortAlgorithm) )
{
context.setSortingStrategy(new InsertionSort());
}
context.sort();
}
}
Output
Please enter Sort Algorithm : 'BubbleSort' or 'SelectionSort' or 'InsertionSort'
BubbleSort
Sort Algorithm is : BubbleSort
Enter array size :
5
Enter input array :
3 4 5 1 2
Array is sorted using Bubble Sort Algorithm
1,2,3,4,5,
Please enter Sort Algorithm : 'BubbleSort' or 'SelectionSort' or 'InsertionSort'
InsertionSort
Sort Algorithm is : InsertionSort
Enter array size :
5
Enter input array :
3 2 1 4 5
Array is sorted using Insertion Sort Algorithm
1,2,3,4,5,
• Strategy Design pattern - Introduction
• Strategy Design pattern - Real Time Example [Compress files]
• Strategy Design pattern - Real Time Example [Payment]
• Strategy Design pattern - Real Time Example [Travel]
• Strategy Design pattern - Real Time Example [Sorting]
• Strategy Design pattern - Real Time Example [Search]
• Strategy Design pattern - Class Diagram
• Strategy Design pattern - Sequence Diagram
• Strategy Design pattern - Implementation [Compress files]
• Strategy Design pattern - Implementation [Travel]
• Strategy Design pattern - Implementation [Payment]
• Strategy Design pattern - Implementation [Search]
• Strategy Design pattern - KeyPoints
• All Design Patterns Links
• ## Monday, 30 December 2013
### Strategy Design pattern - Implementation [Search]
Click the below Image to Enlarge
Strategy Design pattern - Implementation [Search]
Strategy Design pattern - Implementation [Search] - Class Diagram
SearchStrategy.java
public interface SearchStrategy
{
int search(int[] list, int elementToSearch);
}
BinarySearch.java
public class BinarySearch implements SearchStrategy
{
@Override
public int search( int[] list, int elementToSearch )
{
int position = 0;
for (int i = 0; i < list.length; i++)
{
if (list[i] == elementToSearch)
{
position = i;
break;
}
}
System.out.println("Position of the element has been found using BinarySearch Algorithm");
return position;
}
}
LinearSearch.java
public class LinearSearch implements SearchStrategy
{
@Override
public int search( int[] list, int elementToSearch )
{
int beg = 0;
int end = list.length - 1;
int mid = (int) ((beg + end) / 2);
int position = 0;
while( beg <= end && list[mid] != elementToSearch )
{
if( elementToSearch < list[mid] )
end = mid - 1;
else
beg = mid + 1;
mid = (int) ((beg + end) / 2);
}
if( list[mid] == elementToSearch )
position = mid;
else
position = 0;
System.out.println("Position of the element has been found using LinearSearch Algorithm");
return position;
}
}
SearchContext.java
public class SearchContext
{
private SearchStrategy searchStrategy;
public void setSearchStrategy( SearchStrategy searchStrategy )
{
this.searchStrategy = searchStrategy;
}
public int search( int[] list, int item )
{
return searchStrategy.search(list, item);
}
}
StrategyClient.java
import java.util.Scanner;
public class StrategyClient
{
public static void main( String[] args )
{
System.out.println("Please enter Search Algorithm : 'Linear' or 'Binary'");
Scanner scanner = new Scanner(System.in);
String searchAlgorithm = scanner.next();
System.out.println("Search Algorithm is : " + searchAlgorithm);
System.out.println("\nPlease enter element to be searched : ");
Scanner scanner1 = new Scanner(System.in);
int elementToSearch = scanner1.nextInt();
System.out.println("ElementToSearch is : " + elementToSearch);
SearchContext context = new SearchContext();
if( "Linear".equalsIgnoreCase(searchAlgorithm) )
{
context.setSearchStrategy(new LinearSearch());
}
else if( "Binary".equalsIgnoreCase(searchAlgorithm) )
{
context.setSearchStrategy(new BinarySearch());
}
int[] sortedList = { 1, 2, 3, 4, 5, 6, 7, 8 };
int position = context.search(sortedList,elementToSearch);
System.out.println("Position of the element is : "+ position);
}
}
Output
Please enter Search Algorithm : 'Linear' or 'Binary'
Linear
Search Algorithm is : Linear
Please enter element to be searched :
5
ElementToSearch is : 5
Position of the element has been found using LinearSearch Algorithm
Position of the element is : 4
Please enter Search Algorithm : 'Linear' or 'Binary'
Binary
Search Algorithm is : Binary
Please enter element to be searched :
7
ElementToSearch is : 7
Position of the element has been found using BinarySearch Algorithm
Position of the element is : 6
• Strategy Design pattern - Introduction
• Strategy Design pattern - Real Time Example [Compress files]
• Strategy Design pattern - Real Time Example [Payment]
• Strategy Design pattern - Real Time Example [Travel]
• Strategy Design pattern - Real Time Example [Sorting]
• Strategy Design pattern - Real Time Example [Search]
• Strategy Design pattern - Class Diagram
• Strategy Design pattern - Sequence Diagram
• Strategy Design pattern - Implementation [Compress files]
• Strategy Design pattern - Implementation [Travel]
• Strategy Design pattern - Implementation [Payment]
• Strategy Design pattern - Implementation [Sort]
• Strategy Design pattern - KeyPoints
• All Design Patterns Links
• ### Strategy Design pattern - Implementation [Payment]
Click the below Image to Enlarge
Strategy Design pattern - Implementation [Payment]
Strategy Design pattern - Implementation [Payment] - Class Diagram
PaymentStrategy.java
public interface PaymentStrategy
{
public void pay(String amount);
}
DebitCardPaymentStrategy.java
public class DebitCardPaymentStrategy implements PaymentStrategy
{
public void pay(String amount)
{
System.out.println("Customer pays the money " +amount+ "Rs. using Debit Card");
}
}
CreditCardPaymentStrategy.java
public class CreditCardPaymentStrategy implements PaymentStrategy
{
public void pay( String amount )
{
System.out.println("Customer pays the money " + amount + "Rs. using Credit Card");
}
}
ByCashPaymentStrategy.java
public class ByCashPaymentStrategy implements PaymentStrategy
{
public void pay( String amount )
{
System.out.println("Customer pays the money " + amount + "Rs. as a Cash");
}
}
PaymentContext.java
public class PaymentContext
{
private PaymentStrategy paymentStrategy;
// Client will set what PaymentStrategy to use by calling this method
public void setPaymentStrategy(PaymentStrategy strategy)
{
this.paymentStrategy = strategy;
}
public PaymentStrategy getPaymentStrategy()
{
return paymentStrategy;
}
public void pay(String amount)
{
paymentStrategy.pay(amount);
}
}
Customer.java
import java.util.Scanner;
public class Customer
{
public static void main( String[] args )
{
System.out.println("Please enter Payment Type : 'CreditCard' or 'DebitCard' or 'ByCash'");
Scanner scanner = new Scanner(System.in);
String paymentType = scanner.next();
System.out.println("Payment type is : " + paymentType);
System.out.println("\nPlease enter Amount to Pay : ");
Scanner scanner1 = new Scanner(System.in);
String amount = scanner1.next();
System.out.println("amount is : " + amount);
PaymentContext ctx = null;
ctx = new PaymentContext();
if( "CreditCard".equalsIgnoreCase(paymentType) )
{
ctx.setPaymentStrategy(new CreditCardPaymentStrategy());
}
else if( "DebitCard".equalsIgnoreCase(paymentType) )
{
ctx.setPaymentStrategy(new DebitCardPaymentStrategy());
}
else if( "ByCash".equalsIgnoreCase(paymentType) )
{
ctx.setPaymentStrategy(new ByCashPaymentStrategy());
}
System.out.println("PaymentContext has :"+ctx.getPaymentStrategy());
ctx.pay(amount);
}
}
Output
Please enter Payment Type : 'CreditCard' or 'DebitCard' or 'ByCash'
CreditCard
Payment type is : CreditCard
Please enter Amount to Pay :
90000
amount is : 90000
PaymentContext has :CreditCardPaymentStrategy@1e4cbc4
Customer pays the money 90000Rs. using Credit Card
Please enter Payment Type : 'CreditCard' or 'DebitCard' or 'ByCash'
DebitCard
Payment type is : DebitCard
Please enter Amount to Pay :
90000
amount is : 90000
PaymentContext has :DebitCardPaymentStrategy@1e4cbc4
Customer pays the money 90000Rs. using Debit Card
• Strategy Design pattern - Introduction
• Strategy Design pattern - Real Time Example [Compress files]
• Strategy Design pattern - Real Time Example [Payment]
• Strategy Design pattern - Real Time Example [Travel]
• Strategy Design pattern - Real Time Example [Sorting]
• Strategy Design pattern - Real Time Example [Search]
• Strategy Design pattern - Class Diagram
• Strategy Design pattern - Sequence Diagram
• Strategy Design pattern - Implementation [Compress files]
• Strategy Design pattern - Implementation [Travel]
• Strategy Design pattern - Implementation [Search]
• Strategy Design pattern - Implementation [Sort]
• Strategy Design pattern - KeyPoints
• All Design Patterns Links
• ## Saturday, 28 December 2013
### Strategy Design pattern - Implementation [Travel]
Click the below Image to Enlarge
Strategy Design pattern - Implementation [Travel]
Strategy Design pattern - Implementation [Travel] - Class Diagram
TravelStrategy.java
public interface TravelStrategy
{
public void gotoAirport();
}
AutoTravelStrategy.java
public class AutoTravelStrategy implements TravelStrategy
{
public void gotoAirport()
{
System.out.println("Traveler is going to Airport by Auto and will be charged 600 Rs");
}
}
BusTravelStrategy.java
public class BusTravelStrategy implements TravelStrategy
{
public void gotoAirport()
{
System.out.println("Traveler is going to Airport by bus and will be charged 200 Rs");
}
}
TaxiTravelStrategy.java
public class TaxiTravelStrategy implements TravelStrategy
{
public void gotoAirport()
{
System.out.println("Traveler is going to Airport by Taxi and will be charged 1000 Rs");
}
}
TrainTravelStrategy.java
public class TrainTravelStrategy implements TravelStrategy
{
public void gotoAirport()
{
System.out.println("Traveler is going to Airport by Train and will be charged 300 Rs");
}
}
TravelContext.java
public class TravelContext
{
private TravelStrategy travelStrategy;
// Client will set what TravelStrategy to use by calling this method
public void setTravelStrategy(TravelStrategy strategy)
{
this.travelStrategy = strategy;
}
public TravelStrategy getTravelStrategy()
{
return travelStrategy;
}
public void gotoAirport()
{
travelStrategy.gotoAirport();
}
}
Traveler.java
import java.util.Scanner;
public class Traveler
{
public static void main( String[] args )
{
System.out.println("Please enter Travel Type : 'Bus' or 'Train' or 'Taxi' or 'Auto' ");
Scanner scanner = new Scanner(System.in);
String travelType = scanner.next();
System.out.println("Travel type is : " + travelType);
TravelContext ctx = null;
ctx = new TravelContext();
if( "Bus".equalsIgnoreCase(travelType) )
{
ctx.setTravelStrategy(new BusTravelStrategy());
}
else if("Train".equalsIgnoreCase(travelType))
{
ctx.setTravelStrategy(new TrainTravelStrategy());
}
else if("Taxi".equalsIgnoreCase(travelType))
{
ctx.setTravelStrategy(new TaxiTravelStrategy());
}
else if("Auto".equalsIgnoreCase(travelType))
{
ctx.setTravelStrategy(new AutoTravelStrategy());
}
System.out.println("Travel context has : "+ctx.getTravelStrategy());
ctx.gotoAirport();
}
}
Output
Please enter Travel Type : 'Bus' or 'Train' or 'Taxi' or 'Auto'
bus
Travel type is : bus
Travel context has : BusTravelStrategy@1e4cbc4
Traveler is going to Airport by bus and will be charged 200 Rs
Please enter Travel Type : 'Bus' or 'Train' or 'Taxi' or 'Auto'
train
Travel type is : train
Travel context has : TrainTravelStrategy@578ceb
Traveler is going to Airport by Train and will be charged 300 Rs
• Strategy Design pattern - Introduction
• Strategy Design pattern - Real Time Example [Compress files]
• Strategy Design pattern - Real Time Example [Payment]
• Strategy Design pattern - Real Time Example [Travel]
• Strategy Design pattern - Real Time Example [Sorting]
• Strategy Design pattern - Real Time Example [Search]
• Strategy Design pattern - Class Diagram
• Strategy Design pattern - Sequence Diagram
• Strategy Design pattern - Implementation [Compress files]
• Strategy Design pattern - Implementation [Payment]
• Strategy Design pattern - Implementation [Search]
• Strategy Design pattern - Implementation [Sort]
• Strategy Design pattern - KeyPoints
• All Design Patterns Links
• ## Friday, 27 December 2013
### Tablets,IPad,Mobile Devices or Android OS use Firefox/Google Chrome/Opera browser to view this blog
• All JavaEE viedos and code in Youtube | Facebook | Google plus | GitHub | BitBucket
• Design Pattern - Playlists
• Design Patterns - Introduction
• J2EE Design Patterns
• J2EE patterns
• Front Controller Design Pattern
• Intercepting Filter Design Pattern
• Business Delegate Design Pattern
• Service Locator Design Pattern
• Context Object Design Pattern
• Data Access Object Design Pattern
• Creational Design patterns
• Creational Design patterns
• Object Pool Design Pattern
• Singleton Design Pattern
• Factory Design Pattern
• Abstract Factory Design Pattern
• Prototype Design Pattern
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• Concurrency Design patterns
• Offline Concurrency Patterns
• Session State Design pattern
• Distribution Patterns
• Base Design Pattern
• Web Presentation Patterns
• Domain Logic Patterns
• Object Relational Structural Patterns
• Object Relational Behavioral Patterns
• Object Relational MetadataMapping Patterns
• Data Source Architectural Patterns
• More Design Patterns ...
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CC-MAIN-2017-26
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en
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https://math.stackexchange.com/questions/260021/convergence-of-fixed-point-iteration-for-convex-function
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# Convergence of fixed-point iteration for convex function
Let $f:[0,1]\to[0,1]$ be a smooth, convex (downward) function satisfying $$f(0)=f(1)=1,\quad \lim_{x\to 0}f'(x)=-\infty,\quad \lim_{x\to 1}f'(x)=+\infty.$$
I am confident to be able to argue that $f$ has exactly two fixed points in $[0,1]$ (one of them being $1$, of course.)
I would like to show that for any starting value $x\in (0,1)$, the sequence of function iterates $f(x), f(f(x)),\ldots$ converges to the fixed point which is not $1$.
I know from the convexity of $f$ that there exist $0<x_-<x_+<1$ such that $f'(x_\pm)=\pm1$ and that $f$ on the interval $(x_-,x_+)$ is non-expansive.
I was thinking to try and argue that for any starting value the iterates $f^i(x)$ would eventually lie in $(x_-,x_+)$ and to then apply Banach's fixed point theorem.
My questions are:
• Is it clear that the fixed point lies in the interval $(x_-,x_+)$? (I doubt it)
• In order to apply Banach's fixed-point theorem, would I have to show that $f((x_-,x_+))\subset (x_-,x_+)$?
• Is there a different approach that would guarantee convergence of the function iterates without checking additional conditions?
Thank you.
Edit:
Thanks to the efforts of richard and froggie it now seems that convergence of the iterates cannot be guaranteed under the conditions specified above.
I would therefore like to add the following assumptions: ($p$ denotes the fixed point which is not $1$)
• $-1<f'(p)<1$.
• If $c=\min_x f(x)$, then $-1<f'(c)<1$.
I think that with these additional assumptions it should be possible to prove convergence of the function iterates from every starting point.
• Do functions with these properties exist? – user108903 Dec 16 '12 at 15:30
• Yes, the maybe easiest example would be $f(x)=2-\sqrt{x}-\sqrt{1-x}$. – Eckhard Dec 16 '12 at 15:35
• Oops, I misread your question. Thanks for the example. – user108903 Dec 16 '12 at 15:41
• Do you assume that $f$ is differentiable on $(0,1)$? – 23rd Dec 16 '12 at 15:52
• Yes. In fact, I'm happy to assume the existence of as many derivatives as necessary. I added smoothness to the original question. – Eckhard Dec 16 '12 at 15:57
Since $f(1)=1$ and $\lim_{x\to 1}f'(x)=+\infty$, it is easy to see that there exists $a\in(0,1)$, such that $f(a)<a$. Define $g(x)=f(x)-x$ on $[0,1]$. Since $g(0)=1>0$ and $g(a)<0$, there exists $p\in[0,a]$, such that $g(p)=0$, i.e. $f(p)=p$. Since $g(p)=g(1)=0$ and $g$ is convex on $[p,1]$, either $g\equiv 0$ on $[p,1]$ or $g(x)<0$ on $(p,1)$. The former case cannot happen, because $\lim_{x\to 1}g'(x)=+\infty$. Therefore, $f$ has a unique fixed point $p$ in $[0,1)$.
Unfortunately, it could happen that $f'(p)<-1$. In this situation, the iteration of $f$ cannot converge to $p$.
When $-1<f'(p)<1$, note that the iteration of $f$ on $(p-\delta,p+\delta)$ converges to $p$ for some $\delta>0$. Then we can define $I=(l,r)$ to be the maximal interval containing $p$ such that the iteration of $f$ on $I$ converges to $p$. By definition, $f(I)\subset I$. Since $I$ is maximal, $f(l),f(r)\notin I$, i.e. $f(l),f(r)\in\{l,r\}$. Then there are two cases: $l=0$ and $r=1$ or $f(l)=r$ and $f(r)=l$. For the latter case, by the maximality of $I$, we can conclude that $f'(r)< 0$, and hence $f'(p)<0$. Moreover, due to $f(I)\subset I$, we know that $f'(l)f'(r)\ge 1$.
• Thank you for your answer, Richard. Would the condition $-1<f'(p)<1$ be sufficient for the iteration of $f$ to converge to $p$ for any starting value? In the notation of my original question this would mean $x_-<p<x_+$. – Eckhard Dec 16 '12 at 16:32
• @Eckhard: I have updated my answer for $-1<f'(p)<1$. I avoid to use your notations $x_\pm$, because the point $x$ for $f'(x)=\pm 1$ may not be unique. – 23rd Dec 16 '12 at 17:20
• Thanks again. I don't quite see yet why the maximal interval $I$ must be open, but otherwise the argument seems compelling. – Eckhard Dec 16 '12 at 17:28
• @Eckhard: It is because if $f^n(x)\to p$, then there exists a neighborhood of $x$ converging to $p$ under the iteration of $f$. – 23rd Dec 16 '12 at 17:33
• @Eckhard: I agree with you. Moreover, I think only $f'(c)\ge -1$ is sufficient to exclude the situation $f(l)=r,f(r)=l$. The reason is as follows. Letting $f(x)=c$, then $f'(x)=0$ and $f$ is decreasing on $[0,x]$. Therefore, $f'(x)>f'(r)\Rightarrow r\le x\Rightarrow l=f(r)\ge f(x)=c\Rightarrow f'(c)\le f'(l)<-1$. – 23rd Dec 17 '12 at 8:15
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| 3.421875
| 3
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CC-MAIN-2019-30
|
longest
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en
| 0.889727
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http://szybkiestrony.ga/qalyr/calculate-units-68.php
| 1,516,715,670,000,000,000
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| 332,722,420
| 5,002
|
# Calculate units
Schw artz Bedside GFR Calculator for Children IDMS-traceable; Conventional units (for use primarily in the U.S.) SI units (for use outside of the U.S.).Conversion and Calculation Center home page that contains links to our measurement conversion, currency exchange rate, world time zone, reference information, and.What makes the breakeven point so important is that every sale above your breakeven point generates a profit.
### Glomerular Filtration Rate (GFR) Calculators
This tool will help you dynamically to calculate the Body Mass Index with units such as SI, US and UK.
Enter the desired value below in the Enter Quantity field and click the button to perform the metric.
### How to Calculate Cost of Goods Sold (CoGS) — Oblivious
Unit converter, Measurement conversion, Text tools and converters, Mathematical calculators, Date and time tools, sport calculators.
### Unit Conversion
Units of alcohol are used in the United Kingdom (UK) as a measure to quantify the actual alcoholic content within a given volume of an alcoholic beverage, in order to.
### How to Calculate Variable Cost per Unit | Double Entry
This article demonstrates how to calculate the dialog base unit for the dialog box using a font other than System Font in Windows 95.Collection of 77 free online unit converters for unit conversions between most of the units you can think of.But in most cases, the level of activity stays within the relevant range for fixed costs.Description Calcbot is an intelligent calculator and unit converter for the rest of us.You can calculate the unit costs of production by dividing the total amount of your fixed and variable costs by the total number of units you.
Tutoring guidance and examples on how to calculate the area plus an explanation on units of measurement for area.In order to scientifically calculate the right central air conditioner size, you can perform a Residential Load Calculation.Chemists use equivalent units, or equivalents, to express the contribution of an acid or base to the total acidity or alkalinity of a solution.Calculator You can use the calculator for any math problem you want to solve.Failing to get a grip on profit, loss, and breakeven point can be funny, at least on TV.Free calculator to convert between the common length, temperature, area, volume, weight, and time units.By Kenneth Boyd In cost accounting and management, cost-volume-profit analysis starts with the breakeven point.
### Retail Sales Math Formulas and Equations - The Balance
For convenience, this calculator allows you to select different volume and concentration units, and the necessary conversions are carried out for you to obtain the.Guidance and examples on how to calculate the volume of rectangular prisms, cones, cylinders, and spheres plus an explanation units of measurement.
Business Accounting Cost Accounting: How to Calculate the Breakeven Point.
### Dilution Calculator - Units per Volume - PhysiologyWeb
Calculate the average of numbers not in a contiguous row or column. This example calculates the average price paid for a unit across three purchases,.
Six Methods: Calculating the Volume of a Cube Calculating the Volume of a Rectangular Prism Calculating the Volume of a.
### Density, Specific Weight and Specific Gravity
Calculate unit rate, unit price or unit cost for a rate or ratio.
### Air Conditioning Sizing Calculator - AC Direct
Welcome to OnlineConversion.com. Convert just about anything to anything else.
### Unit Conversion Calculator
You can use this feature to calculate the unit price from the Unit Cost and the Profit % field.Convert kilowatt-hour to watt-hour. a counter display that counts units of kilowatt-hour (kWh).
Variable cost per unit example: To calculate the variable cost per unit divide the variable costs of the business by the number of units produced.Before you start selling a product, you need to know the fixed costs, the variable costs, and the sale price.Notes LMNO Engineering wrote the unit conversion computer program in the PHP computer language using double precision so that the maximum number of significant digits.
### Calculate the average of a group of numbers - Excel
Calculate the number of units sold by total valuation by dividing the amount of inventory sold off during the.
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| 2.9375
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https://poetsandquants.com/2016/04/25/things-buy-141k-cost-mba/?pq-category=videos&pq-category-2=pq-originals-videos
| 1,669,912,955,000,000,000
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| 497,729,866
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|
# Other Things You Could Buy For The \$141K Cost Of An MBA
An excerpt from “You Should Totally Get An MBA”
Does the MBA pay off?
Me: Hell yes it pays off.
You: Is that a guarantee?
Me: Yeah, man. Haven’t you been paying attention?
You: So it will absolutely, positively have a positive financial ROI?
Me: Well …
While attaining an MBA will move you down the road to enlightenment, getting an MBA is still really, really expensive. You might logically ask yourself, “What’s the ROI on enlightenment?”
Excellent question! Now you’re thinking like an MBA.
Let’s do the math. For our purposes here, we’ll assume that you are going to Harvard Business School (hey, you deserve it).
Investment:
• HBS first-year tuition for Class of 2017 = \$61,225
• HBS books, materials, fees = \$7,655
• Total for first year = \$68,8809
We will assume that tuition and fees increase 5% for year two, so that:
• Total tuition and fees for second year = \$72,324
• Two-year Total = \$141,204
And this does not include room, board and health insurance because you would have to pay for these whether or not you went to HBS.
Yikes! That’s a lot of dough. And like the guy selling knives on late night TV says, “But wait—there’s more!”
The average HBS grad walks out with about \$84,000 in student debt, and that debt costs money. The price is the interest that you pay until you pay it off. If you have the means, you can pay it off more quickly, but let’s assume it takes you a decade to knock it all out:
• Student loan interest: 6% * \$84,000 * 10 yrs = approx. \$27,908
• \$141k in tuition/fees + \$28k in interest = \$169,000
And we’re still not done. Because you won’t be working during your two years at HBS you have to factor in your lost wages in the calculation. Let’s say you make \$85,000/year at your good pre-MBA job. Including your foregone income of \$170,000, the total cost of getting a Harvard MBA (or one similar) is about \$339,000.
Holy crap. Enlightenment is expensive! Is it really worth \$339,000? Enlightenment is hard to put an exact number on, but wage growth isn’t. And this is where HBS has a dynamite return on average (we’ll get back to the assumptions we’re making a little later).
If you go to HBS, you will not only get a bunch of crazy smart friends and a closet full of crimson hoodies, you’ll also get on average a very juicy pay bump and an accelerated career path. Here’s what that might look like:
Return:
• Base pay bump from \$85,000 to \$140,000
• Signing bonus: \$25,000
• Summer internship income: \$20,000
• Career accelerator (4% raises v 2% raises)
Let’s take a look at what that pay bump and career accelerator look like in action. Your MBA begins paying off in the form of increased income in your first year out of school. You make \$55,000 more than you would have without it, and life is good.
But wait—there’s more!
Because HBS has put you on an accelerated career path (and the steeper income growth trajectory that comes with it), your pay grows at a faster rate than it would have sans-MBA.11 So that annual pay differential continues growing as you relish your MBA-ness and continue to kick business world ass.
It is in this stream of MBA-powered increased income that we answer the question, “Does an MBA pay off?” You can see that over your first 10 years out of HBS, your income will be \$750k more than it would have been had you never pursued that MBA.
Using our friend NPV (Net Present Value), we then measure how much that stream of income is worth today, relative to the \$369k that the MBA costs. While the NPV is less than the \$750k, and varies depending on your weighted average cost of capital, in both scenarios, an HBS MBA is a homerun, positive ROI fiesta de dinero!
By the way, weighted average cost-of-capital is one of those great things you’ll learn about at business school, along with NPV.
And this is just for the first 10 years out of HBS. You will likely work for another decade or two beyond this, and in those prime earning years, that pay differential will—theoretically—be even more pronounced.
ON THE OTHER HAND …
There are some really meaningful and impactful assumptions we’re making in the model above. And, to paraphrase the monetary philosopher Ol’ Dirty Bastard, assumptions’ll “bust yer ass.” So we should be aware of them, lest our assuming asses get busted.
First, remember that the average first year income for HBS alumni includes very non-average people making crazy money in consulting, investment banking, hedge funds and the like. If you are not committed to a career in one of these fields (or if you’re in these fields but below the mean earners in those fields), your income will likely be lower-to-much-lower. This doesn’t mean that your HBS degree will have a negative ROI over the long run, but it just might take longer to break even. That’s worth keeping in mind.
Second, these reported incomes are skewed way high by alumni living in New York, London, San Francisco and Hong Kong, i.e. the most expensive cities in the world. So while they may be making hundreds of thousands of dollars a year, they may also be paying \$4,000/month (or lots more) to rent a one-bedroom apartment. You shouldn’t look at these average incomes and think, “I am going to live like a king on \$175,000/year in Tulsa, OK!” ‘Cuz that’s probably not where you’re going to find these juicy pay packages.
Third, you are a growing and evolving human being. Your interests, desires and passions will change over time. The career you find intriguing right out of business school might not float your boat 5, 10 or 15 years later. Maybe you just decide that you’re not interested in doing [fill in the name of career] any more, and that you really want to [work with kids / do something for the developing world / become a stand-up comedian]. Or maybe the grind of an 80+ hour work week is something you can tolerate when you’re young and single but not when you’re older, married and raising children. Or maybe some heath issues present themselves and you need to hit “pause” on your career to deal with them. In any of these scenarios, the juicy comp packages and steepened earning curves pretty much fly out the window.
Fourth, the model above represents an uninterrupted, positive career trajectory. Due to the vicissitudes of the market, the economy and personal wackness, careers often do not maintain a smooth progression upward and to the right. If historical economic trends continue, you should expect some kind of ugly macroeconomic tornado to blow through seven years or so. Whether it’s dot-com bubbles busting, global mortgages imploding or Adam Smith’s invisible hand getting caught in the cookie jar, bad stuff that is way out of your control happens, and it’s going to affect your career.
And then, of course, you could just forget it. There are other things you could buy with \$141,000 (watch the video above to find out exactly what you could get for what that MBA will cost you).
Comedian & author Paul Ollinger
Author Paul Ollinger is a writer and stand-up comedian who has opened for some of the biggest names in the business. He also has an MBA from Dartmouth’s Tuck School and was one the first 250 employees of Facebook where he served as VP of Sales for the Western United States. When he’s not on the road speaking, doing stand-up and sharing his unique POV on business and life, he lives in Atlanta, GA, with his beautiful wife, two wonderful children and French bulldog, Colonel Tom Parker. This article is excerpted with his permission from his newly published book, You Should Totally Get An MBA: A Comedian’s Guide To Top U.S. Business Schools, now available on Amazon.
## ‘You Should Totally Get An MBA’ Video Series
So, You Want To Be An MBA: You Should Totally Do It!
Other Things You Could Buy For The \$141K Cost Of An MBA
Business School Vs. Law School: Why The MBA Totally Kills It
What You Should & Shouldn’t Say When Applying To B-School
My Story: From The Dartmouth Tuck Campus To The Improv Stage
Trending
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# If (cos α + cos β)
Question:
If $(\cos \alpha+\cos \beta)^{2}+(\sin \alpha+\sin \beta)^{2}=\lambda \cos ^{2}\left(\frac{\alpha-\beta}{2}\right)$, write the value of $\lambda$
Solution:
$(\cos \alpha+\cos \beta)^{2}+(\sin \alpha+\sin \beta)^{2}=\lambda \cos ^{2}\left(\frac{\alpha-\beta}{2}\right)$
Consider LHS:
(cos α + cos β)2 + (sin α + sin β)2
$=\left[2 \cos \left(\frac{\alpha+\beta}{2}\right) \cos \left(\frac{\alpha-\beta}{2}\right)\right]^{2}+\left[2 \sin \left(\frac{\alpha+\beta}{2}\right) \cos \left(\frac{\alpha-\beta}{2}\right)\right]^{2}$
$=4 \cos ^{2}\left(\frac{\alpha+\beta}{2}\right) \cos ^{2}\left(\frac{\alpha-\beta}{2}\right)+4 \sin ^{2}\left(\frac{\alpha+\beta}{2}\right) \cos ^{2}\left(\frac{\alpha-\beta}{2}\right)$
$=4 \cos ^{2}\left(\frac{\alpha-\beta}{2}\right)\left[\cos ^{2}\left(\frac{\alpha+\beta}{2}\right)+\sin ^{2}\left(\frac{\alpha+\beta}{2}\right)\right]$
$=4 \cos ^{2}\left(\frac{\alpha-\beta}{2}\right)$
= RHS
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# Lakerben's Single Digit Program P4 w/mods
Topic closed. 56 replies. Last post 3 years ago by Harve\$t Moon.
Page 4 of 4
GEORGIA
United States
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August 22, 2008
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Posted: December 30, 2012, 5:43 pm - IP Logged
Hey guys,
I took Lakerben's Single Digit Program and used it for P4 and modified it a bit. I hope you don't mind Lakerben.
Here it is:
Start by finding the second P3 number (eve drawing) drawn for the current month in your state (I will use NY) November 1st mid = 059 (I used midday instead of eve because the eve number was a double).
Taking your last 6 draws from your p4 game. Multiply each number by the number next to it for single digit and double digit number. Three digit numbers get added together.
1679>>>>this morning's draw.
3995
7330
8922
4658
9021
Starting with the 6th draw going upwards:9,4,8,7,3,1 >> to the last draw: the 5 from this morning's draw. This will give your pairs and picks for the next few draws.
Example: from left to right on the top row>(9 *4=36), (4*8=32), (8*7=56), (7*3=21),(3*1=3)
The third row is the result of multiplication of the second row from left to right: (36*32=1152),(32*56=1792), etc.
The fourth and fifth rows are the result of addition of the third and fourth rows from left to right: (1152+1792=2944) (each 4 digit number gets added to the number to its right) until you are left with just one or two 4 digit numbers (in this case the numbers are 5912 & 4207)
9 4 8 7 3 1 36 32 56 21 3 1152 1792 1176 63 2944 2968 1239 5912 4207
Now take the 5912 & 4207 and run them through a 1234 rundown
5 9 1 2 6 1 4 6 7 3 7 0 8 5 0 4 9 7 3 8 0 9 6 2 1 1 9 6 2 3 2 0 3 5 5 4 4 7 8 8 5 9 1 2
4 2 0 7 5 4 3 1 6 6 6 5 7 8 9 9 8 0 2 3 9 2 5 7 0 4 8 1 1 6 1 5 2 8 4 9 3 0 7 3 4 2 0 7
Now look for any numbers in this rundown that share pairs with the P3 number from the second draw of the month (059).
Now use the numbers that are highlighted in yellow as the fourth digit like so:
0598, 0594
0596, 0592
0597
9025 hit on Nov. 10th midday
Hello ranman I have 1 questions. After you run the last 2 p4 numbers (5912 & 4209) through the 1234 rundown, where did the yellow highlighted numbers 8,4,6,2 in the 5912 and the 2,7 in the 4207 come from? Athough those numbers appear several times, why those particular numbers?
Yesterday is behind us, tomorrow is not promised, today we move forward in JESUS name.
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wisconsin
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Posted: December 30, 2012, 7:44 pm - IP Logged
Wisconsin 459 had it and scratched it out . Dang it was in minus colum
Wisconsin
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Posted: December 30, 2012, 10:19 pm - IP Logged
Yeah me too Picktowin. Ive been playing it for a week now three sets of it and decided not to play it tonight. Did you receive my email? I hope so, if you did give me a call soon and we will talk ok. I'm very anxious on this!
wisconsin
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Posted: December 31, 2012, 9:56 pm - IP Logged
Wisconson 434 I caught that box . It worked 12 times this month. Happy New Year To All
United States
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December 27, 2012
15 Posts
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Posted: January 8, 2013, 10:02 am - IP Logged
Wisconson 434 I caught that box . It worked 12 times this month. Happy New Year To All
INSTANT NEXT NUMBERS FOR P4 GAMES
EX: CA JAN 1 2013 NUMBERS 4539
4539 PLUS MIRROR
4539=9084
USING TOTAL IN P4 GAMES 9999 SUBTRACT BOTH THE WINNING AND MIRROR NUMBERS
9999 9999
- 4539 - 9084
5460 0915
NOW NUMBERS THAT ARE REPEAT SHOULD BE OUT
45 OF 4539 90 OF 9084
54 OF 5460 09 OF 0915
NOW I HAD 39 AND 60 84 AND 15 LEFT
SINCE 39 AND 84 ARE ON TOP OF BOTH 60 AND 15
3 OF 39 SHOULD BE WITH 6 OF 60
9 OF 39 WITH 0 OF 60
8 OF 84 WITH 1 OF 15
4 OF 84 WITH 5 OF 15
NOW I WILL HAD 3-6 9-0 8-1 4-5
SO WHAT I DO IS NOW SUBTRACT THE RIGHT NUMBERS TO THE LEFT NUMBERS
3-6 IS 6 MINUS 3= 3 SINCE 0 CANT SUBTRACT ABY NUMBERS I WILL CARRY 1 TO IT 0 + 1 = 10 NOW 10 MINUS 9= 1
IF ANY NUMBERS OF RIGHT SIDES IS SMALLER THAN LEFT SIDES JUST CARRY 1 TO IT
SO 11 MINUS 8= 3 AND 5 MINUS 4= 1
NOW I HAD THE NUMBERS 3131
SO WHAT I DO IS ADD THAT NUMBERS TO THE WINNING NUMBERS OF 4539 ON JAN 1 2013 OF CA
4539
+ 3131
7670 THIS JUST REGULAR MATH
NOW SINCE I HAD 3131 ALL I NEED IS A PAIR OF 2 NUMBERS AND ADD THEM TOGTHER SO 3 + 1 = 4
THE 7670 PLUS 4
I GET 7674 WHICH IS THE NEXT WINNING NUMBER IN CA
A STRAIGHT AUTOMATC WIN INSTANTLY
FINALLY I BEAT THE LOTTO SYSTEM OF CA
TAKE THAT SYSTEM AND THAT TOO LOL.
I THINK IT MAY WORK IN P3 TOO
I HAVENT TEST IT OUT YET ON P3 GAMES
SO THANKS ALOT
ANY SUGGESTIONS TO MAKE THIS SECRET TECHNIQUE MORE PERFECT IS ACCEPTED
THANKS
New Jersey
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November 27, 2009
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Posted: January 8, 2013, 11:33 am - IP Logged
Hello ranman I have 1 questions. After you run the last 2 p4 numbers (5912 & 4209) through the 1234 rundown, where did the yellow highlighted numbers 8,4,6,2 in the 5912 and the 2,7 in the 4207 come from? Athough those numbers appear several times, why those particular numbers?
Sorry it took so long for me to answer. The second P3 number of the month was 059. Under the 5912 rundown two numbers shared paires with the 059 they were: 8504 & 0962. The 4207 rundown produced one number that shared a pair with the 059 and that was 9257.
Now take the number that were not part of those pairs (meaning they are not the 0 or 5 or 9 from the 059) and use them to add to 059 to make your pick 4 numbers.
So, we would take 059 and add the 8 from 8504 to get 0598, then take the 4 from the 8504 and add it to the end of 059 to get 0594. Now do the same with the 0962 but only use the 6 & 2 toi add to the 059 giving you 0596 & 0592. Do the same with the 9257 which came from the 4207 rundown. you would use only the 2 and 7 from the 9257 and add them to the 059 to get 0592 & 0597. You already have 0592 as a playable number so you would scratch this one.
I hope that cleared it up.
Those who know don't tell and those who tell don't know...So I have a lot to tell you.
An Unfinished Work
What Must I Do?
Brooklyn, NY
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Posted: January 8, 2013, 1:33 pm - IP Logged
Sorry it took so long for me to answer. The second P3 number of the month was 059. Under the 5912 rundown two numbers shared paires with the 059 they were: 8504 & 0962. The 4207 rundown produced one number that shared a pair with the 059 and that was 9257.
Now take the number that were not part of those pairs (meaning they are not the 0 or 5 or 9 from the 059) and use them to add to 059 to make your pick 4 numbers.
So, we would take 059 and add the 8 from 8504 to get 0598, then take the 4 from the 8504 and add it to the end of 059 to get 0594. Now do the same with the 0962 but only use the 6 & 2 toi add to the 059 giving you 0596 & 0592. Do the same with the 9257 which came from the 4207 rundown. you would use only the 2 and 7 from the 9257 and add them to the 059 to get 0592 & 0597. You already have 0592 as a playable number so you would scratch this one.
I hope that cleared it up.
Hey Ranman. I like this because it gives you a definite target on what to add to your triplets for P4. I also like the fact that Picktowin's modification displayed a bunch of hits even though one still needed to decide which digits to play from each of the -111 +111 columns. I will backtest when I have a few spare minutes, but have you already back tested in NY to see if you're getting more than one hit? One hit is great because I've had cold spells.
Thanks Lakerben for the original method and thanks Picktowin for the modification. I will try them all!
New Jersey
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Posted: January 8, 2013, 1:43 pm - IP Logged
Hey Ranman. I like this because it gives you a definite target on what to add to your triplets for P4. I also like the fact that Picktowin's modification displayed a bunch of hits even though one still needed to decide which digits to play from each of the -111 +111 columns. I will backtest when I have a few spare minutes, but have you already back tested in NY to see if you're getting more than one hit? One hit is great because I've had cold spells.
Thanks Lakerben for the original method and thanks Picktowin for the modification. I will try them all!
I have not done extensive back testing. I am working on a few systems and I haven't had the time. If you do back test please be so kind as to share your findings.
Thanks
Those who know don't tell and those who tell don't know...So I have a lot to tell you.
An Unfinished Work
What Must I Do?
Brooklyn, NY
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Posted: January 8, 2013, 3:34 pm - IP Logged
I have not done extensive back testing. I am working on a few systems and I haven't had the time. If you do back test please be so kind as to share your findings.
Thanks
Will do. Another question. I did the method for New York January 2013, and I end up with one 4 digit and one 3 digit number:
2493 and 639
What do I do for the run down with the 3 digit? Do I add a leading, or perhaps a trailing zero?
New Jersey
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Posted: January 8, 2013, 3:36 pm - IP Logged
Forget the 3 digit number just use the 2493. Or, you could do what ever you like with it, i.e. add each of those 3 digits to the end of you P3 number (discarding any numbers already used) and play it that way.
Those who know don't tell and those who tell don't know...So I have a lot to tell you.
An Unfinished Work
What Must I Do?
New Jersey
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Posted: January 8, 2013, 3:40 pm - IP Logged
I ended up with 9174, 5917 & 7910 for this month.
Those who know don't tell and those who tell don't know...So I have a lot to tell you.
An Unfinished Work
What Must I Do?
United States
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7387 Posts
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Posted: January 29, 2013, 10:54 pm - IP Logged
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# There are m points on a straight line AB and n points on another straight line AC, none of them being A. How many triangles can be formed with these points as vertices?(a) $\dfrac{mn}{2}\left( m+n \right)$(b) $\dfrac{mn}{2}\left( m+n-2 \right)$(c) $\dfrac{mn}{2}\left( m+n-1 \right)$(d) None of these
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Hint: Consider two cases of counting triangles, one in which vertex A is included and the other one in which A is not included. Count all the possible ways of choosing other vertices. Sum up all the possible ways of choosing vertices to get the total number of ways in which triangles can be formed. Use the fact that ‘r’ objects can be chosen from a set of ‘n’ objects in ${}^{n}{{C}_{r}}$ ways.
We have two straight lines AB and AC such that AB has m points and AC has n points on it other than A. We have to count the number of triangles that can be formed with these vertices.
We will consider two cases to count the triangles – one in which vertex A is included and the other one in which A is not included. We will count all the possible ways to choose vertices in each of the cases and then sum up the values to get the total number of triangles that can be formed.
We know that ‘r’ objects can be chosen from a set of ‘n’ objects in ${}^{n}{{C}_{r}}$ ways.
Case 1: Vertex A is included in the triangle.
We already have 1 vertex. We have two choose two other vertices.
We know that more than two vertices on the same line can’t form a triangle. So, we must choose one vertex from each of the lines.
Thus, the number of ways to choose one vertex from m points $={}^{m}{{C}_{1}}=\dfrac{m!}{1!\left( m-1 \right)!}=m$.
Similarly, the number of ways to choose one vertex from n points $={}^{n}{{C}_{1}}=\dfrac{n!}{1!\left( n-1 \right)!}=n$.
Thus, the total number of ways to choose two vertices $={}^{m}{{C}_{1}}\times {}^{n}{{C}_{1}}=mn$.
Hence, we can form ‘mn’ triangles such that vertex A is included in the triangle.
Case 2: Vertex A is not included in the triangle.
We have to choose all the three vertices. So, we must choose two vertices from one line and one from the other one.
If we choose two vertices from line AB and one from AC, we need to choose 2 points out of m points and 1 point out of n points.
Number of ways to choose 2 vertices from m vertices $={}^{m}{{C}_{2}}=\dfrac{m!}{2!\left( m-2 \right)!}=\dfrac{m\left( m-1 \right)}{2}$.
Similarly, the number of ways to choose one vertex from n points $={}^{n}{{C}_{1}}=\dfrac{n!}{1!\left( n-1 \right)!}=n$.
Total number of ways to choose 2 vertices from AB and 1 from AC $={}^{m}{{C}_{2}}\times {}^{n}{{C}_{1}}=\dfrac{mn\left( m-1 \right)}{2}$.
Now, we will calculate the number of ways to choose two points from AC and one from AB.
Number of ways to choose 2 vertices from n vertices $={}^{n}{{C}_{2}}=\dfrac{n!}{2!\left( n-2 \right)!}=\dfrac{n\left( n-1 \right)}{2}$.
Similarly, the number of ways to choose one vertex from m points $={}^{m}{{C}_{1}}=\dfrac{m!}{1!\left( m-1 \right)!}=m$.
Total number of ways to choose 2 vertices from AC and 1 from AB $={}^{m}{{C}_{1}}\times {}^{n}{{C}_{2}}=\dfrac{mn\left( n-1 \right)}{2}$.
Total number of ways to choose 3 vertices is the sum of the number of ways of choosing 2 vertices from AB and 1 from AC with the number of ways of choosing 2 vertices from AC and 1 from AB.
Thus, total number of ways to choose 3 vertices $=\dfrac{mn\left( n-1 \right)}{2}+\dfrac{mn\left( m-1 \right)}{2}=\dfrac{mn\left( m+n-2 \right)}{2}$.
Total number of triangles that can be formed $=mn+\dfrac{mn\left( m+n-2 \right)}{2}=\dfrac{mn\left( 2+m+n-2 \right)}{2}=\dfrac{mn\left( m+n \right)}{2}$.
Hence, the number of triangles that can be formed is $\dfrac{mn\left( m+n \right)}{2}$, which is option (a).
Note: It’s necessary to consider each of the two cases separately. Also, we will get an incorrect answer if we don’t consider the fact that three points on the same line can’t form a triangle as they are collinear. We must know that ${}^{n}{{C}_{r}}=\dfrac{n!}{r!\left( n-r \right)!}$.
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Page 1 of 1
### Sensing 12v input using GPIO
Posted: Sun Mar 19, 2017 3:47 am
Hello guys
I'm doing quite a large project in which I'm planning to control a spa from the raspberry PI.
I've got most of the things figured out but i'm stuck at the following problem.
I've got 4 12vdc lines that I need to sense whether they are powered or not and read this into the pi by gpio.
I've found on the web that I should ideally use an optocoupler for each line so I refrain from frying the PI.
Unfortunately I wasn't able to find a clear how-to for connecting the whole, as I've only done a couple of projects I'm still a bit wary of calculating resistors and such.
From my current knowledge I should do the following:
-> The optocoupler has a forward voltage of 1.2 V at 0,02 A
-> This means the 12+ should be connected to a 560 ohm resistor and that should be connected to the anode, the cathode should be connected to the negative pin. (does the wattage of the resistor matter?)
-> The emitter should be connected to ground and the collector to the gpio pin and to the 3,3v rail with a 10k ohm resistor in between.
Is that correct?
As an extra question how much power would such a setup draw from the 3,3 pins? I think I'm getting very limited in available power there
### Re: Sensing 12v input using GPIO
Posted: Sun Mar 19, 2017 3:11 pm
12V=1.2V = 10.8V if R =560 then I = 10.8/560 = 0,0192 A or 19.2 mA close enough!
Wouldn't worry about the 0.33mA a 10K pullup would draw from the 3V3 device, when pulled low.
you are golden.
Two tips, a 100nF capacitor between the GPIO and GND would cure any glitches and most "key-bounce" problems that could occur, and a 560 Ohm resistor between the GPIO and the emitter of the optocouplers-isolator would prevent you could fry your GPIO if you accidentally program it to output 3V3, while the transistor of the optocouplers-isolator is open.
### Re: Sensing 12v input using GPIO
Posted: Sun Mar 19, 2017 5:39 pm
So this should be correct?
schama 12v sensing.PNG (9.74 KiB) Viewed 4424 times
### Re: Sensing 12v input using GPIO
Posted: Sun Mar 19, 2017 7:10 pm
Hi.
No you have R3 in the wrong place it needs to go between the GPIO and the point were R2 connects.
### Re: Sensing 12v input using GPIO
Posted: Sun Mar 19, 2017 7:14 pm
yeah, i meant collector not emitter.
### Re: Sensing 12v input using GPIO
Posted: Sun Mar 19, 2017 9:33 pm
Okay thanks for the correction, so this should be it?
schema 12v sensing.PNG (10.29 KiB) Viewed 4301 times
### Re: Sensing 12v input using GPIO
Posted: Mon Mar 20, 2017 9:52 am
Yes!
again, sorry for the confusion.
### Re: Sensing 12v input using GPIO
Posted: Mon Mar 20, 2017 10:30 am
I think you also meant to say "while the transistor of the optocouplers-isolator is closed", or even better conducting, not open.
### Re: Sensing 12v input using GPIO
Posted: Mon Mar 20, 2017 12:06 pm
No! I don't think I made a lapsus here..
I was learned that you can "steer a transistor open", that is you steer (send) current into it's base and the transistor "opens", meaning it starts to conduct current. But yes its a bit confusing because an "open switch" means that the switch does not conduct current.
But IMHO a transistor that is "open" is conducting, in normal parlor.
But I could be wrong... I guess its open to two interpretations.
### Re: Sensing 12v input using GPIO
Posted: Mon Mar 20, 2017 12:30 pm
I've always used open/closed for a transistor in the switch sense ie on=conducting=closed and off=non-conducting=open. But there again I'm a self-taught hobbyist of 40 years, not the electronics pro I suspect you are... also that's why i suggested "conducting" may be less ambiguous.
### Re: Sensing 12v input using GPIO
Posted: Tue Mar 21, 2017 12:58 am
yeah conducting would have been better.
By the way I have been "into electronics" for about 50 years, and a professional for about 40 years.
Also English isn't my native language, and so maybe I learned "steering open" in my native language, and it might not apply well to English.
Still I think you shouldn't apply terminology meant for switches to transistors, or things like Opamps, or for that matter Tubes.
When I think about it, I think I picked up "steering open" in relation to tubes where the grid is used to "open or close a path for the electrons" so steering open means leaving a conductive path open for the electrons.
### Re: Sensing 12v input using GPIO
Posted: Tue Mar 21, 2017 6:56 am
The use of open/closed & my misunderstanding/its ambiguity seems to stem from whichever crude model you relate to: the plumbing model with a valve controlling the flow of water (open=on), or the electrical model of a mechanical switch (open=off).
### Re: Sensing 12v input using GPIO
Posted: Tue Mar 21, 2017 7:16 am
@mahjongg
Your use of '[steering] open' is definitely not something a native English speaker would understand; the phrase conveys the opposite of what you intend.
You're right that 'Conducting' would make your meaning clear. It's also common to refer to a conducting transistor as 'on', but that is less intuitive to a beginner.
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# When an int is cast to a short and truncated, how is the new value determined?
Can someone clarify what happens when an integer is cast to a `short` in C? I'm using Raspberry Pi, so I'm aware that an `int` is 32 bits, and therefore a `short` must be 16 bits.
Let's say I use the following C code for example:
``````int x = 0x1248642;
short sx = (short)x;
int y = sx;
``````
I get that `x` would be truncated, but can someone explain how exactly? Are shifts used? How exactly is a number truncated from 32 bits to 16 bits?
-
Note that the cast (like most casts) is unnecessary. You can declare `short sx = x;`, and the value of `x` will be implicitly converted to `short`. – Keith Thompson Jan 19 at 20:12
The actual size of "int" and "short" can and will vary from platform to platform. But yes, let's say "int" is 32 bit and "short" is 16 bit: 1) Yes, the cast will truncate the value from 32 to 16 bits, 2) Yes, the upper 16 bits are "lost", 3) No, there's no "shift". PS: Did you know that your Raspberry Pi probably has a full-fledged copy of Mathematica? Definitely worth checking out :) – paulsm4 Jan 19 at 20:13
Not exactly a duplicate, but closely related: stackoverflow.com/q/19273658/4996248 – John Coleman Jan 19 at 20:13
An aside: you can remove bit-width guesswork with `#include <stdint.h>` to bring in `int32_t`, `int16_t`, etc. – rubicks Jan 20 at 1:13
According to the ISO C standard, when you convert an integer to a signed type, and the value is outside the range of the target type, the result is implementation-defined. (Or an implementation-defined signal can be raised, but I don't know of any compilers that do this.)
In practice, the most common behavior is that the high-order bits are discarded. So assuming `int` is 32 bits and `short` is 16 bits, converting the value `0x1248642` will probably yield a bit pattern that looks like `0x8642`. And assuming a two's-complement representation for signed types (which is used on almost all systems), the high-order bit is the sign bit, so the numeric value of the result will be `-31166`.
``````int y = sx;
``````
This also involves an implicit conversion, from `short` to `int`. Since the range of `int` is guaranteed to cover at least the entire range of `short`, the value is unchanged. (Since, in your example, the value of `sx` happens to be negative, this change of representation is likely to involve sign extension, propagating the `1` sign bit to all 16 high-order bits of the result.)
As I indicated, none of these details are required by the language standard. If you really want to truncate values to a narrower type, it's probably best to use unsigned types (which have language-specified wraparound behavior) and perhaps explicit masking operations, like this:
``````unsigned int x = 0x1248642;
unsigned short sx = x & 0xFFFF;
``````
If you have a 32-bit quantity that you want to shove into a 16-bit variable, the first thing you should do is decide how you want your code to behave if the value doesn't fit. Once you've decided that, you can figure out how to write C code that does what you want. Sometimes truncation happens to be what you want, in which case your task is going to be easy, especially if you're using unsigned types. Sometimes an out-of-range value is an error, in which case you need to check for it and decide how to handle the error. Sometimes you might want the value to saturate, rather than truncate, so you'll need to write code to do that.
Knowing how conversions work in C is important, but if you start with that question you just might be approaching your problem from the wrong direction.
-
If your code assumes `x` will fit in a short, instead of masking you can `assert( x <= USHRT_MAX )` to enforce that assumption. – Schwern Jan 19 at 20:13
Notice `x & 0xFFF` != `(short) x` if `CHAR_BIT != 8`. – black Jan 19 at 20:16
@black: Or, more precisely, if `CHAR_BIT * sizeof (short) != 16`. (I've worked on systems with `CHAR_BIT==8` where `sizeof (short)` is 4 or even 8. – Keith Thompson Jan 19 at 20:18
Unless you are programming for a very esoteric platform (and then you probably know), you can safely assume that the truncating behaviour takes place. – FUZxxl Jan 19 at 20:20
Very useful answer, in particular the last two paragraphs. – CompuChip Jan 20 at 12:59
The 32 bit value is truncated to 16 bits in the same way a 32cm long banana bread would be cut if you jam it into a 16cm long pan. Half of it would fit in and still be a banana bread, and the rest will be "gone".
-
Not the best analogy. I can fit a 32-cm banana into a 16-cm pan by smashing it or by cutting it into two side-by-side pieces. Bits in a word have much tighter constraints than bananas bits in a pan. And you say nothing about which half you end up with, or why. – Keith Thompson Jan 19 at 20:25
@KeithThompson - you could slice and dice 32 bits as well (you need a knife for the bread, or buy manipulation operations for the bits though) but the analogy calls for shoving the cake into the pan, not slicing it. Regarding the part that goes in or three part that goes away, yes, I didn't manage to include that detail – Amit Jan 19 at 20:32
That is one long banana. – PC Luddite Jan 19 at 20:51
size matters `;-)` – chqrlie Jan 19 at 23:13
if and only if your banana bread is `unsigned` :) – Ciprian Tomoiaga Jan 20 at 11:20
Simply the high 16 bits are cut off from the integer. Therefore your short will become `0x8642` which is actually negative number `-31166`.
-
Although I believe it's implementation specific whether high or low bits are used? – Link Jan 19 at 20:11
@Link The result is entirely implementation-defined according to the language standard, but I don't believe there are any compilers that will give you the high-order bits. – Keith Thompson Jan 19 at 20:12
@Link: No, it's not implementation specific. Any cast to narrower type will always cut off the most significant bits. If would be different for unions of types of different widths - here the big endian/little endian would make the difference. But for the above it's everywhere the same. – Zbynek Vyskovsky - kvr000 Jan 19 at 20:12
@ZbynekVyskovsky-kvr000: No, the result of converting an out-of-range value to a signed type is implementation-defined. See N1570 section 6.3.1.3. (Discarding the high-order bits is certainly the most common behavior.) – Keith Thompson Jan 19 at 20:20
@KeithThompson: Weird, I always assumed the compilers are consistent here for unsigned and signed types. Fortunately all of them do the same as for unsigned values, otherwise lot of software would stop working... – Zbynek Vyskovsky - kvr000 Jan 19 at 20:26
Truncation happens in CPU registers. These have different sizes: 8/16/32/64 bits. Now, you can imagine a register like:
``````<--rax----------------------------------------------------------------> (64-bit)
<--eax----------------------------> (32-bit)
<--ax-----------> (16-bit)
<--ah--> <--al--> (8-bit high & low)
01100011 01100001 01110010 01110010 01111001 00100000 01101111 01101110
``````
`x` is first given the 32 bit value `0x1248642`. In memory*, it'll look like:
``````-----------------------------
| 01 | 24 | 86 | 42 |
-----------------------------
31..24 23..16 15..8 7..0
``````
Now, the compiler loads `x` in a register. From it, it can simply load the least significant 16 bits (namely, `ax`) and store them into `sx`.
*Endianness is not taken into account for the sake of simplicity
-
I believe the OP wants to know how that discarding happens. What 16 bits of the original 32 are retained? – Schwern Jan 19 at 20:16
@Schwern Thanks, added more explanation -- does that clarify? – black Jan 19 at 20:25
Yeah. Will it always be the least significant 16 bits? – Schwern Jan 19 at 20:31
@black I submitted an edit to fix a typo in the result, but there weren't enough characters so I improved (IMO) the register illustration as well. Feel free to improve it further if you disagree with my interpretation. – Dan Jan 20 at 14:42
@Dan Thanks Dan, I took some of the suggestions you proposed. It should look much better now. – black Jan 20 at 16:35
Perhaps let the code speak for itself:
``````#include <stdio.h>
#define BYTETOBINARYPATTERN "%d%d%d%d%d%d%d%d"
#define BYTETOBINARY(byte) \
((byte) & 0x80 ? 1 : 0), \
((byte) & 0x40 ? 1 : 0), \
((byte) & 0x20 ? 1 : 0), \
((byte) & 0x10 ? 1 : 0), \
((byte) & 0x08 ? 1 : 0), \
((byte) & 0x04 ? 1 : 0), \
((byte) & 0x02 ? 1 : 0), \
((byte) & 0x01 ? 1 : 0)
int main()
{
int x = 0x1248642;
short sx = (short) x;
int y = sx;
printf("%d\n", x);
printf("%hu\n", sx);
printf("%d\n", y);
printf("x: "BYTETOBINARYPATTERN" "BYTETOBINARYPATTERN" "BYTETOBINARYPATTERN" "BYTETOBINARYPATTERN"\n",
BYTETOBINARY(x>>24), BYTETOBINARY(x>>16), BYTETOBINARY(x>>8), BYTETOBINARY(x));
printf("sx: "BYTETOBINARYPATTERN" "BYTETOBINARYPATTERN"\n",
BYTETOBINARY(y>>8), BYTETOBINARY(y));
printf("y: "BYTETOBINARYPATTERN" "BYTETOBINARYPATTERN" "BYTETOBINARYPATTERN" "BYTETOBINARYPATTERN"\n",
BYTETOBINARY(y>>24), BYTETOBINARY(y>>16), BYTETOBINARY(y>>8), BYTETOBINARY(y));
return 0;
}
``````
Output:
``````19170882
34370
-31166
x: 00000001 00100100 10000110 01000010
sx: 10000110 01000010
y: 11111111 11111111 10000110 01000010
``````
As you can see, `int` -> `short` yields the lower 16 bits, as expected.
Casting `short` to `int` yields the `short` with the 16 high bits set. However, I suspect this is implementation specific and undefined behavior. You're essentially interpreting 16 bits of memory as an integer, which reads 16 extra bits of whatever rubbish happens to be there (or 1's if the compiler is nice and wants to help you find bugs quicker).
I think it should be safe to do the following:
``````int y = 0x0000FFFF & sx;
``````
Obviously you won't get back the lost bits, but this will guarantee that the high bits are properly zeroed.
If anyone can verify the short -> int high bit behavior with an authoritative reference, that would be appreciated.
`sx` value will be the same as 2 least significant bytes of `x`, in this case it will be 0x8642 which (if interpreted as 16 bit signed integer) gives -31166 in decimal.
`0x8642` is not `-31166` in decimal. `0x8642` is `34370` in decimal. That value, when converted to a 16-bit signed type, typically yields `-31166`, but that's a different value. – Keith Thompson Jan 19 at 20:28
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# How do you play these ukelele tabs?
## How do you play ukulele tabs?
The third line down represents the third string. The second line down represents. The second string. And the first line of tab or the top line represents the first string or the top string.
## How do I read ukulele sheet music?
But just know that key of C for learning how to read sheet music and play sheet music is definitely the easiest key to be learning and mastering these skills on. Okay. Alright so we have oh three to
## What does H mean in ukulele tabs?
half note
(Shown above each fret number.) W – whole note. H – half note. Q – quarter note.
## What does 0 mean in ukulele tabs?
A tab is always read from left to right and each number refers to the fret number. In this example you would: pluck the 3rd fret of the bottom string (A). Then you would pluck the open E string (open string = 0), followed by the open C string.
## How do you read a chord tab?
So as i mentioned earlier on guitar tab the bottom line represented the thickest string and the top line represented the thinnest string. And when our guitar was on our lap it was the same.
## How do you read fingerpicking tabs?
Then second fret third fret. And then the same for each successive string on the a play open 2nd. And 3rd fret open 2nd 3rd fret open 2nd fret and so forth and so on so whenever.
## How do I learn ukulele notes?
So if that was e open the next note the first fret would be f then the next one will be f sharp next one will be g next one will be g sharp. Next one will be a next one after that would be a sharp.
## What are the notes on a uke?
The standard tuning for a ukulele (from the bottom string to the top string) is G-C-E-A. This means that each open string produces the associate note, from the bottom G string to the C string, E string, and A string. On a concert ukulele, these notes are specifically G4-C4-E4-A4.
## How do you read a ukulele strumming pattern?
Strumming Notation
1. d : down strum.
2. u : up strum.
3. – : pause or missed strum i.e. moving your hand either up or down but not hitting the strings. …
4. x : indicates a chnk. …
5. (d) or (u) : A muted down/up strum. …
6. D or U: capitalised letters mean the strum is emphasized (i.e. give it a bit more welly).
## What does l mean in tabs?
Hold the preceding note for the indicated duration of the preceding note, plus the indicated duration of the tied note (L). For example, if the preceding note is a quarter note and the tied note is an eighth note, play the note for a quarter beat plus an eighth beat.
## How do you read a ukulele chord chart?
So the way to read that is to imagine that the neck is going up and down like this and the top line is the nut is this part right here and then the lines below that are the frets.
## What is E7 on ukulele?
To play the E7 chord, place the index finger on the 1st fret of the top g-string, middle finger on the 2nd fret of the C-string, and ring finger on the 2nd fret of the bottom A-string.
## How do you play tabs?
Tabs are read like sentences in a book – read them from left to right, across the page, dropping down to the next line only when you’ve reached the end of the previous. Play the notes and chords in sequence as you read them from left to right.
## How do you memorize tabs?
Play that a few times then put them together see if you can play all eight measures the second aspect. Look over what you're trying to work on and see if there are any patterns that you can learn.
## What is the difference between tabs and chords?
A chord is a collection of tones which is sounded together all at once. Tabs or tablature is a musical notation that indicates the fingering of the instrument rather than the musical pitches. In a tab, there are six line grids, and each of them represent the guitar strings.
## Are tabs good for beginners?
This comes in handy, especially since the guitar has many different places to play the same notes. For this reason, understanding guitar tablature is particularly useful for beginners, and allows students to learn how to play the guitar without ever having to learn how to read traditional musical notation.
## Should I learn tabs or chords first?
Chords are easier to learn at first and you’ll definitely have an easier time playing songs you enjoy by figuring out chords, first.
## Is it better to learn tabs or notes?
Guitar tablature has unique benefits that music notation does not have. Tab can be used to guide the learner in playing a musical part exactly how it was originally played. Tab can show you which frets to play on what strings, and how to pluck the notes. This is very helpful when learning guitar.
## Are tabs the same as sheet music?
The main difference between tab vs sheet music notation is that tabs display fret numbers in lieu of notes on a staff. This means that tabs are idiomatic to the guitar, while sheet music is used for any instrument. The key similarity is that both systems notate every single note of the composition.
## What does tab stand for in music?
Tablature (or tabulature, or tab for short) is a form of musical notation indicating instrument fingering rather than musical pitches.
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Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.
QUESTION
# Homework #4F (Bond Yield to Call. YTM and Price after original Issue)
Homework #4F (Bond Yield to Call. YTM and Price after original Issue)
Finance
Question 1 (1 point)
What is the yield to call of a 30-year to maturity bond that pays a coupon rate of 14.81 percent per year, has a \$1,000 par value, and is currently priced at \$915? The bond can be called back in 6 years at a call price \$1,076. Assume annual coupon payments.
Round the answer to two decimal places in percentage form. (Write the percentage sign in the "units" box)
You should use Excel or financial calculator.
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# Scale Factor
I’m trying to create a tapered tower mass by assigning a predetermined gross square foot value 11,000 square feet to the top floor. This will be slightly smaller than the base of the tower which is approx. 11,916 square feet.
I’ve divided the 2 values and returned a scale factor of 0.923, however when I use the scale component and apply it to the base curve it doesn’t scale the top floor as expected. It seems to need the scale of 0.9608 to return the desired result, but I can trace back the logic.
I’m sure some basic principle I’m missing…so thanks in advance for any nudge in the right direction
Area varies as the square of linear dimensions.
Linear dimensions varies as the square root of area.
Scale factors in Rhino are for linear dimensions, not area.
Example:
A square with an area of 16 feet has sides 4 feet long.
A square with an area of 25 feet has sides 5 feet long.
Square root (16/25) = 4/5
The needed scale factor is the square root (11,000 / 11,916) = square root (0.92312) = 0.96080
2 Likes
Thank you
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# How can we explain the fact that "Bagging reduces the variance while retaining the bias" mathematically?
I am able to understand the intution behind saying that "Bagging reduces the variance while retaining the bias".
What is the mathematically principle behind this intution? I checked with few experts and they are not able to explain the math well.
Quite surprising that the experts couldn't help you out, the chapter on random forests in "The Elements of Statistical Learning" explains it very well.
Basically, given n i.d.d. random variables each with variance sigma², the variance of the mean of this variables will be sigma²/n.
Since the random forest is build on bootstrap samples of the data, the outputs of the individual trees can be viewed as identically distributed random variables.
Thus, by averaging the outputs of B trees, the variance of the final prediction is given by p*sigma² + (1 - p)sigma² / B, where p is the pairwise correlation between trees. For large B the right term vanishes and the variance is reduced to p*sigma².
This works not only for decision trees but every model that's baggable. The reason why it works particularly well for decision trees is that they inherently have a low bias (no assumptions are made, such as e.g linear relation between features and response) but a very high variance.
Since only the variance can be reduced, decision trees are build to node purity in context of random forest and tree bagging. (Building to node purity maximizes the variance of the individual trees, i.e. they fit the data perfectly, while minimizing the bias.)
• You can use mathjax to do math typeseting. math.meta.stackexchange.com/questions/5020/…
– Sycorax
Sep 12, 2020 at 23:11
• Bagging does not work if the cross-correlation (p in the answer) is close to 1. I think the answer is incomplete without an explanation of how random forests keep the cross-correlation low. It does so by sampling the features also, not only the data set. Oct 7, 2022 at 16:19
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# Why Is Area Squared And Perimeter Is Not?
## What is area and perimeter?
Perimeter is the distance around the outside of a shape.
Area measures the space inside a shape..
## What is the formula of area?
A = lw (rectangle). That is, the area of the rectangle is the length multiplied by the width. As a special case, as l = w in the case of a square, the area of a square with side length s is given by the formula: A = s2 (square).
## What is area and perimeter Grade 4?
This distance is the perimeter of the figure. … The perimeter is 18 feet. Finding area is another way to measure a figure. Area is the number of square units needed to cover a figure. To find the area of a rectangle, count the number of square units or use a formula.
## How do you find the perimeter with the area?
Perimeter of a RectangleRemember the formula for perimeter and area of a rectangle. The area of a rectangle is a = length * width, while the perimeter is p = (2 * length) + (2 * width)Substitute the known values into the area formula. 36 = 4 * w. … Substitute values for length and width into the perimeter formula.
## How do you explain cm squared?
Find the area of a rectangle in square centimeters by measuring the length and width of the rectangle in centimeters. Multiply the length of the rectangle by its width. If the rectangle has a length of 10 cm and a width of 5 cm, the equation is: 10 cm x 5 cm = 50 cm2.
## What cm3 means?
A cubic centimetre (or cubic centimeter in US English) (SI unit symbol: cm3; non-SI abbreviations: cc and ccm) is a commonly used unit of volume that corresponds to the volume of a cube that measures 1 cm x 1 cm × 1 cm. One cubic centimetre corresponds to a volume of one millilitre.
## Why is it squared for area?
Area is measured in “square” units. The area of a figure is the number of squares required to cover it completely, like tiles on a floor. Area of a square = side times side. Since each side of a square is the same, it can simply be the length of one side squared.
## Is area a perimeter or square?
There are different units for perimeter and area The perimeter has the same units as the length of the sides of rectangle or square whereas the area’s unit is squared.
## Why do we calculate area and perimeter?
They help you to quantify physical space and also provide a foundation for more advanced mathematics found in algebra, trigonometry, and calculus. Perimeter is a measurement of the distance around a shape and area gives us an idea of how much surface the shape covers.
## Why is area cm squared?
Each side of this square measures one centimeter, so it’s a square centimeter. The square centimeter is perfect for measuring the area of smaller objects like this rectangle. … The cm is an abbreviation for centimeter and the two represents squared.
## What is perimeter in math definition?
Perimeter is the distance around a two-dimensional shape. Add the side lengths to find the perimeter of regular polygons.
## Why do we say cm2?
Square Centimeters, abbreviated cm², is defined as 1 cm x 1 cm. It is a unit of area. So let us look at an example: You have a rectangular bedroom that is 400 cm long ang and 300 cm wide. … The last amount, 120,000 cm², is a unit of area; it tells you how much room you have on the floor.
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Courses
# Test: Graphical Representations
## 5 Questions MCQ Test Mathematics (Maths) Class 9 | Test: Graphical Representations
Description
This mock test of Test: Graphical Representations for Class 9 helps you for every Class 9 entrance exam. This contains 5 Multiple Choice Questions for Class 9 Test: Graphical Representations (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Graphical Representations quiz give you a good mix of easy questions and tough questions. Class 9 students definitely take this Test: Graphical Representations exercise for a better result in the exam. You can find other Test: Graphical Representations extra questions, long questions & short questions for Class 9 on EduRev as well by searching above.
QUESTION: 1
### 2x + 4 = 3x + 1 will represent a.
Solution: 2x+4=3x+1 2x-3x=1-4 -x=-3 x=3 Here x is positive.So it is in the right side and value of x is 3.So it is 3unit in right of y axis.
QUESTION: 2
### The line x = 3 is
Solution:
Line x=3 has special form - it is not from the same family of lines in the form y=mx+b.
Slope is not defined for a line x=3 because it represents vertical line.
Remember the definition of slope. In common words, it is the value that tells us how much is line increasing/decreasing as we move from left to right on the graph. That is why horizontal lines have zero slope - no increase nor decrease on horizontal line.
Now, imagine vertical line. In only 1 point it increases in infinity. Thus, we cannot use any real value of m to describe this behaviour.
QUESTION: 3
### A line intercepts the x axis at (-7, 0), so its x intercept is
Solution:
QUESTION: 4
An equation of the type ————- represents a line passing through the origin.
Solution:
QUESTION: 5
——————- is the equation of y-axis.
Solution:
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## ◂Math Worksheets and Study Guides Second Grade. Comparing Objects
### The resources above correspond to the standards listed below:
#### New York State Learning Standards and Core Curriculum
NY-2.MD. Measurement & Data
Measure and estimate lengths in standard units.
NY-2.MD.1. Measure the length of an object to the nearest whole by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
NY-2.MD.4. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard “length unit.”
Represent and interpret data.
NY-2.MD.9. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Present the measurement data in a line plot, where the horizontal scale is marked off in whole-number units.
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Enter the total volume (ft^3) into the Calculator. The calculator will evaluate the Dehumidifier Capacity.
## Dehumidifier Capacity Formula
DHC = V / 60 * 3
Variables:
• DHC is the Dehumidifier Capacity (SCFM)
• V is the total volume (ft^3)
To calculate Dehumidifier Capacity, divide the total volume by 60, then multiply by 3.
## How to Calculate Dehumidifier Capacity?
The following steps outline how to calculate the Dehumidifier Capacity.
1. First, determine the total volume (ft^3).
2. Next, gather the formula from above = DHC = V / 60 * 3.
3. Finally, calculate the Dehumidifier Capacity.
4. After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
total volume (ft^3) = 300,000
## Frequently Asked Questions
What is Dehumidifier Capacity?
Dehumidifier Capacity, measured in Standard Cubic Feet per Minute (SCFM), refers to the amount of air a dehumidifier can treat by removing moisture within a minute.
Why is it important to calculate the correct Dehumidifier Capacity?
Calculating the correct Dehumidifier Capacity ensures efficient moisture removal, prevents mold and mildew growth, and maintains a comfortable indoor humidity level.
Can I use the same formula for any room size?
Yes, the formula DHC = V / 60 * 3 can be used for any room size. However, it’s important to accurately measure the room’s total volume (ft^3) for precise calculations.
How often should I check or replace my dehumidifier to maintain its capacity?
Regular maintenance, such as cleaning filters and checking for leaks, should be performed every few months. Replacement depends on the dehumidifier’s performance and age, but typically, a dehumidifier can last 3-5 years with proper care.
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# Homework Help: Very easy proportions question
1. Aug 3, 2008
### iamthewalrus
hey its been a while since i had to do proportions so i was wondering if someone could show me how to solve a problem like this: if x increases by a factor of square root of 2, y decreases by 2, how are x and y related. just by looking at it, i can see that y = 1/x^2 but can someone show me a formal solution, i cant seem to come up with one!
ty.
Last edited: Aug 3, 2008
2. Aug 3, 2008
### symbolipoint
Best translation seems to be, directly as:
x*(2^(1/2))=y*(1/2)
But your provided wording may not exactly fit the proportion idea. Anyway, you should transcribe into conventional notation that you can more easily recognize (lack of typesetting here).
3. Aug 3, 2008
### iamthewalrus
hi i tried the approach you suggested but when you solve for y in terms of x using that equation, you get
y = sqrt(2)/x which basically tells me y is inversely proportional to x whereas it is clear y is inversely proportional the square of x...
4. Aug 4, 2008
### symbolipoint
iamthewalrus, possibly I mishandled the original translation. I will rethink this but someone else will probably respond before I do.
5. Aug 4, 2008
### Varnick
IamtheWalrus, if you use Symbolipont's relationship, you should find that
$$y = 2\sqrt{2} x$$
6. Aug 4, 2008
### iamthewalrus
hi Varnick, thanks for your reply and you're right that's what symbolipoint's equation implies but it's not the correct answer. firstly, if y goes down when x goes up, wouldn't that suggest already some type of inverse relationship? the right answer is supposed to be y = 1/x^2 which seems to be more consistent with the conditions I initially stated.
7. Aug 4, 2008
### Varnick
Where have you got this answer from? It does not appear to be consistent with your initial post (your first post would describe a relationship between y and x, not y and x squared).
V
8. Aug 4, 2008
### nothing123
its from an MCAT question that asked about the relationship between intensity and f-stop of a camera. i just replaced the variables with y and x. and it seems plausible that if x increased by the square root of 2, y would decrease by 2 would describe a relationship where y = 1/x^2. that is, if x increases by sqrt(2), y decreases by [sqrt(2)]^2 = 2. anyways, that was the answer and it appears correct but it did not provide a formal proof for it.
9. Aug 5, 2008
### nothing123
sorry posted on a friends account.
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# Aperiodic lattices and beamwidth of reflectarray antenna
This question is about reflectarray antennas. In the paper below, it is mentioned that:
"A second useful property of aperiodic arrays is the possibility to reduce the number of elements in one assigned aperture without major impact on the beamwidth."
Viganó, M. C., Toso, G., Caille, G., Mangenot, C., & Lager, I. E. (2009). Sunflower Array Antenna with Adjustable Density Taper. International Journal of Antennas and Propagation, 2009, 1-10.
I understand that aperiodic lattices are able to reduce sidelobe levels by suppressing grating lobe formation. However, why does the periodicity of the lattice affect the beamwidth of the antenna? I am hoping to get an answer on this that includes a qualitative explanation in addition to any math that is required. Thank you!
• Please don't repost the same question under a different title, edit your original question. Mar 4, 2018 at 4:21
• This is a different question. This question is on beamwidth while the previous one was on bandwidth Mar 4, 2018 at 6:17
• My apologies, much of the wording and formatting was the same. Mar 4, 2018 at 7:19
• Yupz I have a science fair next week and I realised I still don't understand some concepts that I used in my report... that's why so many questions asked by me on reflectarray antennas Mar 4, 2018 at 12:51
The beam width of the main lobe is rather insensitive to changes of the element positions and to the total number of elements; it depends primarily on the total length of the array. Unless the excitations of the elements are strongly tapered, and the inter element spacing vary wildly, the following formula can be used with reasonable accuracy for determining the total length $$\L\$$ of a broadside array required to produce a 3-dB beam width, $$\\Delta\theta\$$, where it is assumed that $$\\Delta\theta\ll1\$$ radian $$\frac{L}{\lambda}\approx\frac{1}{\Delta\theta}$$
Here $$\\lambda\$$ is the the wavelength and the expression can be solved for the beam width: $$\Delta\theta \approx \frac{\lambda}{L}$$
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Calculation For Jaw Crusher Capacity Jaw Crusher
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Home solutions crusher capacity calculation formula 150tph andesite crushing and reshaping production line material andesite output size 05102030mm capacity 150tph jc series jaw crusher message get price ci5x series impact crusher
• ### Calculation Of Production Capacity Of Stone Crushingjaw
Crusher production capacity calculation estimate jaw crusher capacity nov 21 2018 the first step in understanding production capacity is to calculate the machinehour capacity of the factory or manufacturing plant for example say that a plant has 50 machines and workers can use the machines from 6 am until 10 pm or for 16 hours a day
• ### How To Determine The Capacity Of A Stone Crusher Farmine
Crusher capacity calculation jaw crusher capacity calculation calculating circulating load around screen and crusher kenya crushers the formula for this ow to determine the capacity of a crusheretailed calculation of capacity and power of a roll crusher calculate belt conveyor capacity in stone crusherrusher capacity aw crusher jaw get more
• ### How To Calculate Jaw Crusher Capacity
Jaw crusher capacity calculation bargentino be cone crusher capacity crusher mills cone crusher jaw cone crusher capacity cone crusher specification and advantagescalculate home faqs cone crusher cone crusher more jaw crushers mining and construction the jaw crusher is a single toggle jaw crusher character ized by attention to detail mizes feed size capacity and reduction
• ### Volumetric Capacity Of Jaw Crushers Formulari
Crushing machine production capacity calculation formula jaw crusher capacity formula iie mexico get price capacity of gyratory crusher and size snmarketing the optimum volumetric capacity of a gyratory crusher is given by the expression the feed size to a gyratory crusher
• ### Calculations On Jaw Crusher Caesarmachinerycom
Calculation of rpm of roller crusher answerscom rpm is used to calculate horsepower linear velocity gear ratios and tangential of crushers used depending chapter 4 jaw crusher scribd 19 apr 2010 jaw crusher capacity the capacity of jaw crushers is a measure of mathematically the capacity can be expressed by
• ### How To Calculate The Capacity Of A Jaw Crusher Rock
How to calculate jaw crusher capacity calculate the capacity of a jaw crusher the available data are rpm of the main drive shaft is 170 width of swing jaw is 12 meter estimate jaw crusher capacity 911 metallurgist mar 19 2017 capacities and horsepower of jaw crusher tonshr capacities of a example capacity calculation of read more
• ### How Calculate Coal Crusher Capacity
How to calculate crusher production capacity jaw crusher calculate capacity of crusher cleveland bb holiday calculate the strength of the jaw crusher s eccentric shaft jaw crusher is composed of 4 the double cavity jaw crushers production capacity is bigger get price and support online calculation of capacity of cone crusher
• ### Capacity Calculation Formula For Jaw Crusher
Calculation for jaw crusher capacity comparison between bond crushing energy and fracture saimm crushing energy and work done by the jaw crusher for rocks it appears that the bond inputted microparameters were changed until the calculated dataelasticity consumption product size and capacity of jaw crushers
• ### Power Calculation For Jaw Crusher Pdf
Venting volume calculation for jaw crusher youtube 13 aug 2013 power calculation of jaw crusherpower calculation for jaw crusher pdf crusher south africa belt feeder power calculation in bellingham us instead of the onestage reduction the capacity of the jaw crusher with theory or equation has long been used to
• ### Calculation Theoretical Capacity In Roll Crusher
Calculate theoretical capacity of crushing rollroll crusher capacity accgroup calculate theoretical capacity of crushing roll assakkaf mali is an rising african market and a lot of customers need crusher and grinding mill from gulin everylive chat jaw crusher capacity calculation parkingproeuview all
• ### Calculation Theoretical Capacity In Roll Crusher
Jaw crusher theoretical calculation theoretical capacity in roll crusher roll crusher capacity calculation roll l erow to calculate the roll crusher capacity using a the theoretical capacity of crushing rolls is arrived at simply ating the volume of the ribbon whose cross section is the area of rge opening and whose length is the peripheral
• ### Jaw Mobile Crusher Capacity Calculation
Jaw mobile crusher capacity calculation metallurgical contentcapacities and horsepower of jaw crusher tonshrcapacities of a gyratory crushers tonshrtypical capacities of twinroll crushers tonshrtypical capacities of cone crusherstypical capacities of hammermills example capacity calculation of a 10 x 20 250 mm x 500 mm pp 2800 28 sg e 02 halfway between dolomite and
• ### Power Calculation For Jaw Crusher Pdf Russian Federation
Kleemann mobicat mc r evo used crusher for sale how to calculate clamping force in fixture design carr lane kleemann mobicat mc 100 evo 2019 kleemann mobicat mr evo used jaw crusher with remote control magnetic separator vibrating feeder with up to 330 tons per hour feed capacity hydraulic crusher gap adjustment touch control panel and lockable control cabinet
• ### Jaw Crusher Calculation Of Capacity
Formula of capacity of jaw crusher seshadrivaradhanin for the production capacity of jaw crusher can be calculated as a result of the increase from 20 to 30 coal hhv calculation formula crusher
• ### Jaw Crusher Capacity Formula
Tph formula of crusher formula of crushing efficiency crusher usa crusher efficiency calculations a jaw crusher like 2036 in the jaw crusher table here above would be able to take the maximum 12 in size quarry stone but it would not have the required 70 tph capacity needed to have the needed capacity a jaw crusher like the 2042 or 2436 sizes will have to be
• ### Solutions To Improve The Production Capacity Of Jaw Crusher
Dec 03 2020 the production capacity of jaw crusher directly affects the economic profits of investors and the production capacity of jaw crusher is affected by many factors such as the properties of raw material hardness size and bulk density typeamp size of jaw crusher operation condition of jaw crusher and so on
• ### How To Calculate Jaw Crusher Size And Capacity
How to calculate jaw crusher rpm s calculate the capacity of a jaw crusher the available data are rpm of the main drive shaft is 170 width of swing jaw is 12 meter estimate jaw crusher capacity 911 metallurgist mar 19 2017 capacities and horsepower of jaw crusher tonshr capacities of a exa
• ### Volumetric Capacity Of Jaw Crushers Formulari
Crushing machine production capacity calculation formula jaw crusher capacity formula iie mexico get price capacity of gyratory crusher and size snmarketing the optimum volumetric capacity of a gyratory crusher is given by the expression the feed size to a gyratory crusher
• ### Crusher Production Capacity Calculation
Crusher capacity calculation lutherfestbornarusher capacity calculation formula ethesis the capacity of the crusher is determined by its size to calculate capacity of double roll crusher 102 capacity of nline price list engineered to be the highest capacity jaw crusher on the market our portable pioneer jaw crushing plant will deliver up to 25
• ### How To Calculate The Capacity Of A Jaw Crusher Rock
How to calculate jaw crusher capacity calculate the capacity of a jaw crusher the available data are rpm of the main drive shaft is 170 width of swing jaw is 12 meter estimate jaw crusher capacity 911 metallurgist mar 19 2017 capacities and horsepower of jaw crusher tonshr capacities of a example capacity calculation of read more
• ### Tips To Maximize Crushing Efficiency Pit Amp Quarry Pit
May 13 2019 additionally jaw crusher feed should be prescreened using a grizzly screen prior to crushing to remove material finer than the closedside setting setting jaw crushers ideally the reduction ratio of a jaw crusher should be 6to1 there are different ways to calculate reduction ratio but the best way is something called the p80 factor
• ### Jaw Crusher Capacity Calculation Xls
Jaw crusher capacity calculation xls protable plant primary crushing plant is equipped with highefficiency jaw crusher and impact crusher and millions of crushers have been installed worldwide since the end of the 20th century there are 8 types of jaw crushers and 4 types of impact crushers you can choose for mobile crushing
• ### Taggart Formula For Jaw Crusher Capacity Binq Mining
Apr 17 2013 gyratory crushers capacity onemine mining and minerals library matches 1 10 of 787 search results search results for gyratory crushers capacity panu h and popa e method of calculation of the capacity of jaw crusher has been an invaluable author taggart arthur f published 1943 more detailed
• ### Jaw Crusher Sizing Calculations Free Software Excel
Belt conveyor excel calculation stone crusher machine free online chat jaw crusher capacity calculation request quotation free conveyor calculation software downloads ce calc the design and calculation of jaw crusher amp the size of screw conveyor depends on request quotation wheeled jaw crusher palm calculator
• ### About Us Cpc Crushing And Screening Equipment
Cpc primary jaw crusher with vibrating grizzly at a stone crusher plant of 200 tph capacity we are the only manufacturer of preengineered stone crusher plant in a jawjaw combination our plants offer the lowest cost per ton for the production of aggregates from 040mm we design and manufacture crushing and screening plants upto 200 tph
• ### Calculate Theoretical Capacity Of Crushing Roll
Jaw crusher capacity calculation xls 2020714crusher capacity calculation lutherfestbornarusher capacity calculation formula ethesis the capacity of the crusher is determined by its sie to calculate capacity of double roll crusher 102 capacity of nline price list engineered to be the highest capacity jaw crusher on the market our portable
• ### Power Calculation For Jaw Crusher Pdf
Venting volume calculation for jaw crusher youtube 13 aug 2013 power calculation of jaw crusherpower calculation for jaw crusher pdf crusher south africa belt feeder power calculation in bellingham us instead of the onestage reduction the capacity of the jaw crusher with theory or equation has long been used to
• ### Estimate Jaw Crusher Capacity 911 Metallurgist
8 rows feb 17 2016 jaw crusher production capacity example capacity calculation of a 10 x 20 250 mm x 500
• ### Jaw Crusher Calculation Of Capacity
Formula of capacity of jaw crusher seshadrivaradhanin for the production capacity of jaw crusher can be calculated as a result of the increase from 20 to 30 coal hhv calculation formula crusher
• ### Determination Of Capacity Of Singletoggle Jaw Crusher
Denegin v v 1993 to the question of the capacity of the jaw crusher journal of mining institute 138 2931 machines for mineral dressing their theory calculation and design jan 1933
• ### Jaw Crusher An Overview Sciencedirect Topics
frequency cyclemin w width of jaw plates m lmin closed set r machine reduction ratio gapeset and qs capacity slow frequency in terms of volume of material product per hour equation 412 indicates that the capacity qs is directly proportional to frequency
• ### Jaw Crusher Sciencedirect
5 rows jan 01 2016 in order to calculate the capacity of crushers taggart considered the size reduction r 80
• ### Capacity Calculation For Single Impact Crusher
Jaw crushers capacity calculations 2020618crusher efficiency calculations it must be at least 36 in wide for an 18 x 36 jaw crusher so a 4ft by 8ft screen would be acceptable the 1in screen is a second deck for the 38 tph from the jaw crusher so the deck correction factor is
• ### Technical Notes 5 Crushers Mineral Tech
The capacity of the crusher is determined by its size the gape determines the maximum size of material that can be accepted maximum size that can be accepted into the crusher is approximately 80 of the gape jaw crushers are operated to produce a size reduction ratio between 41 and 91 gyratory crushers
• ### Amit 135 Lesson 5 Crushing Mining Mill Operator Training
Rose and hill 1967 considered crusher capacity by determining the amount of time and distance a particle takes between two jaw plates particles in the ab zone discharges at the next reverse movement of the jaw the maximum size of a particle dropping out of the crusher d max is determined by the open size setting l max
• ### Calculation For Jaw Crusher Capacity Pochirajucoin
Nov 19 2014 and voids in aggregate is used in the calculations capacity sensitive and readable to 001 pound 5 grams and a balance of at least 216 jaw crusher an electricpowered mechanical jaw crusher having a minimum
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# Autoscout.be visualized
update
Visualize traffic of autoscout.be. Can you realise a group of 140,242 people? The answer is no. Our brain can't visualize a group of 140,242 people. If you read 140,242, it has just the meaning of a number. To put the number of visitors autoscout.be has in a perspective we can visualize better how much people 140,242 really are.
### Currently Autoscout.be has 140,242 daily visitors and 4,207,260 monthly visitors. let's put them in a perspective!
Daily 140,242 of the 7,017,846,922 internet users are visiting autoscout.be. 140,242 daily visitors,
let's see what happens if they all come together.
### If Autoscout.be where a country, it will be bigger than Saint Vincent and the Grenadines with a population of 109,000 people.
Below here you find a list where autoscout.be would be ranked on the list of country populations if autoscout.be where a country
Nr Country Population Percentage
1 São Tomé and PrÃÂncipe 165,000 0.002%
2 Curaçao 142,180 0.002%
3 Autoscout.be 140,242 0.002%
4 U.S. Virgin Islands 109,000 0.002%
5 Saint Vincent and the Grenadines 109,000 0.002%
6 Federated States of Micronesia 107,839 0.002%
7 Aruba 107,000 0.002%
There are at least 2 stadium(s) required to provide all 140,242 visitors of autoscout.be a seat.
The stadium of FC Barcelona is one of the largest stadiums in the world. It offers a seat for over 100.000 people.
### If we count how many water the 140,242 visitors of Autoscout.be consume it will be 17,950,976 gallon every day.
The average water consumption a person is 123 liter. Big spender of water is taking a shower, using the toilet or doing the dishes.
### If all 140,242 daily visitors of Autoscout.be take each other by hand we will have a straight line with a length of 238,411.4 km.
The average span width of a human is 1.79 meter
### What is the electricity usage by Autoscout.be in a year with 140,242 visitors a day.
Before a visitor leaves autoscout.be, the average page views of a visitor is 11. This means the server of autoscout.be generates 1,586,137 page view a day. We estimate that autoscout.be uses 28 web server(s). The average of electricity use by a internet server is 2.400 kWh a year. With this info we can calucalte how much the server(s) of autoscout.be will consume 48,384 kWh a year. Looking at the average cost of 1 kWh with a price of 0,23 cent per kWh, the cost for using electricity will be €11,128.32 a year.
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