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# complex-analytic structure on the generic fibre
Here's something that's probably well known to many here, and I'd like to have a suitable reference. I've got a map $f\colon X\to Y$ of complex spaces whose restriction to dense open subspaces $f\colon U\to V$ is the projection of a fibre bundle. Suppose also that $X$ and $Y$ are affine varieties, so that I can consider the fibres of the map $f$ in two different categories. That is, if $p\in V$ is a closed point, I could refine the Zariski topology on the fibre $f^{-1}(p)$ to the complex topology, and the result (I expect) must be homeomorphic to the same fibre in the category of complex spaces. (If true, I could probably learn this much from, say, Shafarevich's Basic Algebraic Geometry.)
This leads to my question. Instead of looking at fibres over closed points, I'd probably prefer handling the fibre of $f$ over the generic point of $Y$, which I'll call $f^{-1}(\eta)$. (Does the property that $f$ restricts to a fibre bundle translate to something nice about the variety $f^{-1}(\eta)$?) But I would want to compare the generic fibre, as a topological space, with the typical fibre of $f$ (as a complex space): I'd like to say that, suitably (re)topologized, the two notions of fibre are homeomorphic. However, I don't know how to refine the Zariski topology on the generic fibre, since my base field is now a function field (instead of $\mathbb C$). Does anyone know of some good reading that might sort me out?
-
You could use the Lefschetz principle to write the generic fiber as the base change of a variety defined over a finitely generated field extension $K$ of $\mathbb{Q}$, and then embed $K$ into $\mathbb{C}$ to "think of" the generic variety as a complex variety (which then has a corresponding complex analytic space). However, Serre's examples suggest the corresponding topological space may depend on the choice of embedding of $K$ into $\mathbb{C}$. – Jason Starr Jul 13 '12 at 20:16
Thanks, that's interesting. I should probably include a reference to mathoverflow.net/questions/90551/… -- it would be great if you would like to expand. Is that to say that obtaining a complex-analytic space from the generic fibre may be possible, but not functorially? – Graham Denham Jul 14 '12 at 2:00
Yes, I am saying that for any finite type variety over a characteristic $0$ field, there is non-canonically associated a complex analytic space. Non-surprisingly, these different complex analytic spaces will typically be non-biholomorphic. What was surprising when Serre first wrote down examples, is that these complex analytic spaces can also be non-homeomorphic. – Jason Starr Jul 14 '12 at 11:39
Sounds good -- if you wouldn't mind giving the reference to Serre as an answer, I'll accept it, although I'm not sure yet if my fibre bundle condition makes things any more special. – Graham Denham Jul 16 '12 at 20:27
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Natural logarithms
• Oct 4th 2012, 02:14 AM
charlesrussell
Natural logarithms
Hi,
I am doing a review on logarithms. When I reached my last question's solution I found something strange.
Question: Solve, Ln(y-1)=1+Ln(3y+2)
The solution gives:
Step 1. Ln(y-1)-Ln(3y+2)=1
Ln((y-1)/(3y+2))=1
Step 2. e^( Ln((y-1)/(3y+2))=e^1
(y-1)/(3y+2)=e
The solution then goes on:
y-1=e(3y+2)=3e*y+2e
(1-3e)y=1+2e
Finally,
y=(1+2e)/(1-3e)=-0.8996
Can you tell me what's wrong here and what does e mean without an index?
Or is there something I have failed to recognise?
• Oct 4th 2012, 02:18 AM
Prove It
Re: Natural logarithms
Quote:
Originally Posted by charlesrussell
Hi,
I am doing a review on logarithms. When I reached my last question's solution I found something strange.
Question: Solve, Ln(y-1)=1+Ln(3y+2)
The solution gives:
Step 1. Ln(y-1)-Ln(3y+2)=1
Ln((y-1)/(3y+2))=1
Step 2. e^( Ln((y-1)/(3y+2))=e^1
(y-1)/(3y+2)=e
The solution then goes on:
y-1=e(3y+2)=3e*y+2e
(1-3e)y=1+2e
Finally,
y=(1+2e)/(1+3e)=-0.8996
I found no solution and after graphing saw that there could be no solution for real numbers.
Can you tell me what's wrong here and what does e mean without an index?
How does e become -0.404273?
Or is there something I have failed to recognise?
e is Euler's number, which has the property of being the base of an exponential function so that its derivative is equal to the original function.
• Oct 4th 2012, 11:06 AM
ebaines
Re: Natural logarithms
You actually have the correct answer, with y = -0.8996 (one minor nit to pick - in the line right after "Finally" you should have y=(1+2e)/(1-3e)=-0.8996).
The issue is that the log of a negative number is a complex number, which has a real part consisting of the log of the absoulte value of that negative number plus an imaginary part equal to pi. This comes from: log(-a) = log(-1 x a) = log (-1) + log (a), and form e^(i pi) =-1 you get log(-1) = i pi. So your solution of -0.8996 when put back into the original equation yields:
ln(y-1) = 1 + ln(3y+2)
ln(-1.8996) = 1 + ln(-0.69883)
ln(1.8996)+i pi = 1 + ln(0.69883) + i pi
0.6416 + i pi = 1 + -0.3584 + i pi
0.6416 + i pi = 0.6416 + i pi
So it checks out.
• Oct 4th 2012, 11:23 AM
HallsofIvy
Re: Natural logarithms
Quote:
what does e mean without an index?
Since you are doing a problem involving "ln(x)", I presume you know what that means. It is the inverse function to " $e^x$". And that means just the number "e" to the x power. Saying that is "without an index" means it is $e^1$, just as "x", in a polynomial "without a coefficient" would be "1x".
• Oct 4th 2012, 12:10 PM
charlesrussell
Re: Natural logarithms
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# EK 1001 Physics Question #312
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#### OverlyNeurotic
2+ Year Member
Hey there!
Was going through a couple of EK 1001 Physics questions and came across this question that I couldn't quite figure out so hopefully someone here could lend some much needed clarification.
Here's a picture of the diagram and the question prompt:
My attempt at a solution:
a. Torque (CW) = Torque (CCW) --> 0.2mg = 0.2f where m = mass of the sign; I picked the rotation point to be at the attachment point of the rope to the sign which is 0.2m away from the wall and 0.2m away from the center of the sign; mg = f
b. Since the sign is at equilibrium, forces in the y direction cancel out so Tcos30 = mg + f --> T = (mg +f)/cos30
c. Since frictional force, f, <= uN where N = normal force and u = static coefficient;
d. Solving for f from (b), we get f = Tcos30 - mg, so Tcos30 - mg <= uN
e. Solving for T, and knowing that mg = f from (a), we get T = 2mg/cos30 from (b)
f. Plugging f and T into (d), we get mg < uN
This is where I get stuck. The book claims that since forces in the horizontal direction cancel out, N = Tsin30. Shouldn't the normal force always point in the vertical direction? From my understanding of the diagram, shouldn't N = Tcos30?
Hopefully someone can clarify this for me.
2+ Year Member
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Breaking News
# How Many Meters In One Inch
How Many Meters In One Inch. All in one units converter. 1 meter is equal to 39.37007874. How long is 1 meter? These small 16 units are.
According to 'inches to meters' conversion formula if you want to convert 1 (one) inches to meters you have to divide 1 by. Meters = (ft ÷ 3.28084) + (in ÷ 39.37) according to 'feet to meters' conversion formula if you want to convert 5 feet, 1 inch to meters you have to divide 5. How long is 1 meter?
## 1in = 1in × 0.0254 = 0.0254m.
A meter, or metre, is the fundamental unit of length in the metric system, from which all other length units are based. There are 12 inches in a foot and 36 inches in a yard. Value in meter = 1 × 0.0254 = 0.0254 meter definition of inch an inch is a unit of length or distance in a number of systems of measurement, including in the us customary units and.
## How Many Meters In A Inch?
How to convert 100 meters to inches to calculate a value in meters to the corresponding value in inches, just. So, 1 inch = 1 × 0.0254 = 0.0254 meter. Feet to meters conversion formula: A meter, or metre, is the fundamental unit of length in the metric system, from which all other length units are based.
### Explanation Of 1 Meters To Inches Conversion.
So, 1 inch = 1 × 0.0254 = 0.0254 meter.
### Kesimpulan dari How Many Meters In One Inch.
How far is 1 meter in inches? A meter, or metre, is the fundamental unit of length in the metric system, from which all other length units are based. Likewise the question how many meter in 1 inch has the answer of 0.0254 m in 1 in. How many inches is each line on a ruler?
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• 100% Satisfaction Guarantee
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# CheckPoint: Calculation of the Consumer Price Index (CPI) The
### Customer Question
CheckPoint: Calculation of the Consumer Price Index (CPI)
The Bureau of Labor Statistics follows five steps to calculate Consumer Price Index.
? Resource: Ch. 24 (pp. 520-522) of Principles of Economics and Appendix D
? Due Date: Day 5 [Individual] forum
? Review Appendix D. Using the chart provided, identify three strengths and three weaknesses of the calculation.
? Post a 200- to 300-word response that answers the following questions once your chart is complete:
o What are the characteristics of the items listed as strengths?
o What are the characteristics of the items listed as weaknesses?
o If the CPI is imperfect, why do we use it?
THE CONSUMER PRICE INDEX
The consumer price index (CPI) is a measure of the overall cost of the goods and
services bought by a typical consumer. Each month the Bureau of Labor Statistics,
which is part of the Department of Labor, computes and reports the consumer
price index. In this section we discuss how the consumer price index is calculated
and what problems arise in its measurement. We also consider how this index
compares to the GDP deflator, another measure of the overall level of prices, which
we examined in the preceding chapter.
How the Consumer Price Index Is Calculated
When the Bureau of Labor Statistics calculates the consumer price index and the
inflation rate, it uses data on the prices of thousands of goods and services. To see
exactly how these statistics are constructed, let’s consider a simple economy in
which consumers buy only two goods—hot dogs and hamburgers. Table 1 shows
the five steps that the Bureau of Labor Statistics follows.
1. Fix the basket. The first step in computing the consumer price index is to determine
which prices are most important to the typical consumer. If the typical
consumer buys more hot dogs than hamburgers, then the price of hot dogs is
more important than the price of hamburgers and, therefore, should be given
greater weight in measuring the cost of living. The Bureau of Labor Statistics
sets these weights by surveying consumers and finding the basket of goods and
services that the typical consumer buys. In the example in the table, the typical
2. Find the prices. The second step in computing the consumer price index is to find
the prices of each of the goods and services in the basket for each point in time.
The table shows the prices of hot dogs and hamburgers for three different years.
3. Compute the basket’s cost. The third step is to use the data on prices to calculate
the cost of the basket of goods and services at different times. The table shows
this calculation for each of the three years. Notice that only the prices in this calculation
change. By keeping the basket of goods the same (4 hot dogs and 2
520 PART 8 THE DATA OF MACROECONOMICS
consumer price index (CPI)
a measure of the overall cost of
the goods and services bought
by a typical consumer
Principles of Economics, 3e, Mankiw - © 2004 N. Gregory Mankiw
hamburgers), we are isolating the effects of price changes from the effect of any
quantity changes that might be occurring at the same time.
4. Choose a base year and compute the index. The fourth step is to designate one year
as the base year, which is the benchmark against which other years are compared.
To calculate the index, the price of the basket of goods and services in
each year is divided by the price of the basket in the base year, and this ratio is
then multiplied by 100. The resulting number is the consumer price index.
In the example in the table, the year 2001 is the base year. In this year, the basket
of hot dogs and hamburgers costs \$8. Therefore, the price of the basket in
all years is divided by \$8 and multiplied by 100. The consumer price index is
100 in 2001. (The index is always 100 in the base year.) The consumer price index
is 175 in 2002. This means that the price of the basket in 2002 is 175 percent
of its price in the base year. Put differently, a basket of goods that costs \$100 in
the base year costs \$175 in 2002. Similarly, the consumer price index is 250 in
2003, indicating that the price level in 2003 is 250 percent of the price level in the
base year.
CHAPTER 24 MEASURING THE COST OF LIVING 521
Calculating the
Consumer Price Index
and the Inflation Rate:
An Example
This table shows how to calculate
the consumer price index and the
inflation rate for a hypothetical
only hot dogs and hamburgers.
TABLE 1
Step 1: Survey Consumers to Determine a Fixed Basket of Goods
4 hot dogs, 2 hamburgers
Step 2: Find the Price of Each Good in Each Year
Year Price of Hot Dogs Price of Hamburgers
2001 \$1 \$2
2002 2 3
2003 3 4
Step 3: Compute the Cost of the Basket of Goods in Each Year
2001 (\$1 per hot dog 4 hot dogs) (\$2 per hamburger 2 hamburgers) \$8
2002 (\$2 per hot dog 4 hot dogs) (\$3 per hamburger 2 hamburgers) \$14
2003 (\$3 per hot dog 4 hot dogs) (\$4 per hamburger 2 hamburgers) \$20
Step 4: Choose One Year as a Base Year (2001) and Compute the Consumer Price Index
in Each Year
2001 (\$8/\$8) 100 100
2002 (\$14/\$8) 100 175
2003 (\$20/\$8) 100 250
Step 5: Use the Consumer Price Index to Compute the Inflation Rate from Previous Year
2002 (175 100)/100 100 75%
2003 (250 175)/175 100 43%
Principles of Economics, 3e, Mankiw - © 2004 N. Gregory Mankiw
5. Compute the inflation rate. The fifth and final step is to use the consumer price index
to calculate the inflation rate, which is the percentage change in the price
index from the preceding period. That is, the inflation rate between two consecutive
years is computed as follows:
Inflation rate in year 2 100.
In our example, the inflation rate is 75 percent in 2002 and 43 percent in 2003.
Although this example simplifies the real world by including only two goods, it
shows how the Bureau of Labor Statistics (BLS) computes the consumer price index
and the inflation rate. The BLS collects and processes data on the prices of
thousands of goods and services every month and, by following the five foregoing
steps, determines how quickly the cost of living for the typical consumer is rising.
When the BLS makes its monthly announcement of the consumer price index, you
CPI in year 2 CPI in year 1
CPI in year 1
522 PART 8 THE DATA OF MACROECONOMICS
When constructing the consumer price index, the Bureau of Labor
Statistics tries to include all the goods and services that the typical
consumer buys. Moreover, it tries to weight these goods and services
according to how much consumers buy of each item.
Figure 1 shows the breakdown of consumer spending into the major
categories of goods and services. By far the largest category is
housing, which makes up 41 percent of the typical consumer’s budget.
This category includes the cost of shelter (31 percent), fuel and
other utilities (5 percent), and household furnishings and operation (5
percent). The next largest category, at 17 percent, is transportation,
which includes spending on cars, gasoline, buses, subways, and so on.
The next category, at 16 percent, is food and beverages; this includes
food at home (9 percent), food away from home (6 percent), and alcoholic
beverages (1 percent). Next are medical care, recreation, and
education and communication, each at about 6 percent. This last category
includes, for example, college tuition and personal computers.
Apparel, which includes clothing, footwear, and jewelry, makes up 4
percent of the typical consumer’s budget.
Also included in the figure, at 4 percent of spending, is a category
for other goods and services. This is a catchall for things consumers
WHAT IS IN THE CPI’S BASKET?
buy that do not naturally fit into the other categories—such as cigarettes,
haircuts, and funeral expenses.
16%
Food and
beverages
17%
Transportation
Other goods
and services
Medical care
Recreation Apparel
6%
6% 4% 4%
6%
41%
Housing
Education and
communication
FIGURE 1
The Typical Basket of Goods and Services
This figure shows how the typical consumer divides his
spending among various categories of goods and services.
The Bureau of Labor Statistics calls each percentage the
“relative importance” of the category.
Source: Bureau of Labor Statistics.
inflation rate
the percentage change in the price
index from the preceding period
Principles of Economics, 3e, Mankiw - © 2004 N. Gregory Mankiw
can usually hear the number on the evening television news or see it in the next
day’s newspaper.
In addition to the consumer price index for the overall economy, the Bureau of
Labor Statistics calculates several other price indexes. It reports the index for specific
regions within the country (such as Boston, New York, and Los Angeles) and
for some narrow categories of goods and services (such as food, clothing, and energy).
It also calculates the producer price index, which measures the cost of a basket
of goods and services bought by firms rather than consumers. Because firms
eventually pass on their costs to consumers in the form of higher consumer prices,
changes in the producer price index are often thought to be useful in predicting
changes in the consumer price index.
Problems in Measuring the Cost of Living
The goal of the consumer price index is to measure changes in the cost of living. In
other words, the consumer price index tries to gauge how much incomes must rise
in order to maintain a constant standard of living. The consumer price index, however,
is not a perfect measure of the cost of living. Three problems with the index
are widely acknowledged but difficult to solve.
The first problem is called substitution bias. When prices change from one year
to the next, they do not all change proportionately: Some prices rise more than others.
Consumers respond to these differing price changes by buying less of the
goods whose prices have risen by large amounts and by buying more of the goods
whose prices have risen less or perhaps even have fallen. That is, consumers substitute
toward goods that have become relatively less expensive. If a price index is
computed assuming a fixed basket of goods, it ignores the possibility of consumer
substitution and, therefore, overstates the increase in the cost of living from one
year to the next.
Let’s consider a simple example. Imagine that in the base year, apples are
cheaper than pears, and so consumers buy more apples than pears. When the Bureau
of Labor Statistics constructs the basket of goods, it will include more apples
than pears. Suppose that next year pears are cheaper than apples. Consumers will
naturally respond to the price changes by buying more pears and fewer apples.
Yet, when computing the consumer price index, the Bureau of Labor Statistics uses
a fixed basket, which in essence assumes that consumers continue buying the now
expensive apples in the same quantities as before. For this reason, the index will
measure a much larger increase in the cost of living than consumers actually experience.
The second problem with the consumer price index is the introduction of new
goods. When a new good is introduced, consumers have more variety from which
to choose. Greater variety, in turn, makes each dollar more valuable, so consumers
need fewer dollars to maintain any given standard of living. Yet because the consumer
price index is based on a fixed basket of goods and services, it does not reflect
this change in the purchasing power of the dollar.
Again, let’s consider an example. When VCRs were introduced, consumers
were able to watch their favorite movies at home. Compared with going to a movie
theater, the convenience was greater and the cost was less. A perfect cost-of-living
index would have reflected the introduction of the VCR with a decrease in the cost
of living. The consumer price index, however, did not decrease in response to the
introduction of the VCR. Eventually, the Bureau of Labor Statistics did revise the
CHAPTER 24 MEASURING THE COST OF LIVING 523
producer price index
a measure of the cost of a basket of
goods and services bought by firms
Principles of
Submitted: 7 years ago.
Category: Homework
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ENG103 S08 MIDTERM PROB 2 KEY
# ENG103 S08 MIDTERM PROB 2 KEY - (REMINDER FOR FULL CREDIT...
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Unformatted text preview: (REMINDER: FOR FULL CREDIT, SHOW ALGEBRAIC DERNATION FIRST, THEN PLUG IN NUMBERS) 2. Air flows steadily through a section of circular pipe with diameter D. Flow conditions are provided in the sketch below. Assume ideal gas behavior (Rm-r = 287 J/kg/K). Clearly justify each assum tion made in su ort of our anal sis. P2 = 127 kPa P1 = 690kPa T2 = 252K T1 = 300K V2=320 m/s a. Pick and clearly draw on the sketch above a control volume that will allow the calculation of the frictional force, Rx, exerted by the pipe wall on the fluid b. Calculate the velocity of the air at 1, V1 in m/s. Mas/S Wok-M - (Slaw? b“ Fig”) BVIAZPL/lA —) VI: ELM; 17' P; " I27 : 1 2 L V - Pa L' 2 —— (532 (510 fl RH F2. RT; " ’5‘ TL 2 (670)51 5 c. Determine the frictional force, Rx , exerted by the pipe wall on the air flowing through pipe. 9L, (flow) 4"]; fl\7(\7’;)£; 23w I O L A‘;KDL Mzez‘/z,v4' L—L—VLQ ‘2? VT; 4 ...
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Re: Find a single solution to a system of equations
• To: mathgroup at smc.vnet.net
• Subject: [mg121852] Re: Find a single solution to a system of equations
• From: Peter Pein <petsie at dordos.net>
• Date: Wed, 5 Oct 2011 03:59:51 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j6e648\$kd6\$1@smc.vnet.net>
```Am 04.10.2011 07:38, schrieb jamievicary at NgOmSaPiAlM.com:
> Hi,
>
> I have a system of equations, and want to use Mathematica to find a
> single solution. It's no good using Solve, because then Mathematica
> tries to find all solutions, and that takes too long. It's no good
> containing FindInstance, because my equations contain unknowns.
>
> To illustrate this last point, consider the input
> FindInstance[a==b,a]
> {{a->b}}
> but it doesn't -- it fails, because FindInstance can't cope with
> independent variables in the expression.
>
> So, I either need a watered-down Solve, that doesn't try to find every
> solution, or a beefed-up FindInstance, that doesn't mind about the
> independent variables.
>
> Thanks!
> Jamie.
>
There is a trick in [1] (by Peter Valko).
Replace b by a constant not related to your problem, apply FindInstance
and substitute the chosen constant with b:
In[1]:= FindInstance[{a == b} /. b -> Catalan, a] /. Catalan -> b
Out[1]= {{a->b}}
Peter
[1] http://forums.wolfram.com/mathgroup/archive/2006/Sep/msg00207.html
```
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Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too!
A barometer is constructed with its tube having radius
Question:
A barometer is constructed with its tube having radius $1.0 \mathrm{~mm}$. Assume that the surface of mercury in the tube is spherical in shape. If the atmospheric pressure is equal to $76 \mathrm{~cm}$ of mercury, what will be the height raised in the barometer tube. The contact angle of mercury with glass $=135^{\circ}$ and surface tension of mercury $=0.465 \mathrm{~N} / \mathrm{m}$. Density of mercury = $13600 \mathrm{~kg} / \mathrm{m}^{3}$.
Solution:
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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22 Jan 2011, 02:33
I also want to apply for the LSE. There you probably have a disadvantage with your score. Maastricht University, I study there and I guess that you get accepted with 680.
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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22 Jan 2011, 08:25
1
KUDOS
Hello,
I am also applying to the same program except for HEC.
Here is the average acceptation for the master program that I got through my research :
1) LSE - around 700/730
3) Stockholm School of Economics in : 690
4) HEC Paris - around 700/720
Where do you come from ?
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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22 Jan 2011, 12:12
Assuming that the rest of your profile is good, then a 680 is probably enough for HEC and SSE. But also consider expanding your list of schools. Oxford, for example, has an MFE program, while IE has a MSc in Finance.
For LSE, the competition is hell and acceptance depends on much more than a GMAT score. That could be said, of course, for any program. But my 730 GMAT score, high GPA, and international exposure certainly wasn't enough. On the other hand, I read on these forums about someone who was accepted with a 660 (along with good recommendations and an internship). At this point, my advice to you is (1) get the best recommendations possible, and (2) answer the essay question perfectly. You need to make your application a work of art.
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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22 Jan 2011, 12:20
I think your 680 is already a great score and will help you get into many schools in Europe. From the schools you listed, I have only done some research on Warwick and LSE, as I would like to apply to those finance programmes as well.
- In the case of Warwick, your score seems be the minimum they expect, that means that it won't really strengthen your application, it will just be neutral.
- For LSE, a 680 score is low. This doesn't mean you shouldn't apply with a 680... but it will require other parts of your application to be above the average.
That said, I would re-take the GMAT if I was in your place. For all those schools that have a defined deadline, applying at the end of January or end of February won't make a huge difference. The case, however, would be different for schools that operate on a rolling admissions basis....
Good luck!
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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22 Jan 2011, 13:18
1
KUDOS
I just saw this post and wanted to react shortly.
You GMAT score is a good score, unless your really want to enter at LSE I wouldn't retake de test but focus on other area of the application. I also heard they are full.
For Maatrischt 680 is more than enough, I don't know for finance but for some master (business, mangement and other) they ask for a 500 or maybe 550. To be honnest I live in Belgium and know a lot of people studyng there, but with your potential I would aim higher.
I have a friend of mine who has been accepted with a 640, average academic record, but 2 summer internships in investment banking.
Get into a master program is not tough as an MBA and it this even more so for european (non UK, US) school. Don't forget those school want to have tuition fees and there are not so many people seeking for master degrees with high GMAT scores. Most of the people that want to study a master are young graduated (about 21-23 years) (bachelors), so GMAT score tend to be lower... I think; it is a really different profile.
I know for example other very good european business school that accept people with low GMAT where sometimes no GMAT but just an entrance exam (where they don't give you the score because they appreciate the results by their own).
eg: Vlerick School of Management 550
Good luck!
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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22 Jan 2011, 13:19
I have a friend of mine who has been accepted with a 640 AT WARWICK, average academic record, but 2 summer internships in investment banking
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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22 Jan 2011, 16:30
680 should be enough for SSE. Not a lot of people in Sweden do the GMAT, and I've heard from friends that people got in to the other specializations with 5-600.
However, you should note that the application deadline was 15 jan. 28 feb is the deadline for sending them your GMAT score.
In general, SSE is a really good school with tight connection to major players in the financial industry, both in Sweden and London. Lot of people go straight from BSc in finance to top banks in London.
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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23 Jan 2011, 01:52
Does anyone know whether passing CFA level 1 exam help in MSc Finance admission? If yes then how much?
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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23 Jan 2011, 10:53
For the Msc-Finance I am applying for, it is wether GMAT or CFA level 1. As I have no financial knowledge at all, neither strong quant knowledge I choosed the GMAT.
So I guess if you have a good GMAT and CFA you should be a very good candidate. I heard it is a non standardize test average required time of study 180h, 60% failure.
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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23 Jan 2011, 12:13
Do you guys know if it is necessary to submit the AWA as well to the b-schools mentioned.
And are you sure that 680 for HEC is enough? I did an internship with BCG as a consultant, is that considered as a good internship?
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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23 Jan 2011, 12:24
BCG yes it is one of the top consulting firm! Awa is automatically sent with your scores. I just know that with a 700 you will be directly accepted at hec.
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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23 Jan 2011, 12:35
Duke007 wrote:
BCG yes it is one of the top consulting firm! Awa is automatically sent with your scores. I just know that with a 700 you will be directly accepted at hec.
Posted from my mobile device
Sorry I was not clear enough. Is it necessary to do the AWA for the european b-schools? Otherwise I'd just skip the AWA and concentrate directly on quant and verbal.
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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23 Jan 2011, 14:51
If you have applied for SSE you will have a good shot at acceptance with a 680 score.
I have friends at CBS who got accepted at CBS most popular MSc Finance programme with just good grades, >3 GPA or so.
For the record, I'm going for SSE and CBS as well, with SSE as my 1st priority.
When is the last date for applying to HEC and LSE?
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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23 Jan 2011, 16:02
Sorry it is confusing because 2 people ara talking about 680 scores. Actually if you are in a rush of time to prepare for the gmat your chance to get a top score are thin!
AWA will take 2 days of preparation to get a somewhat decent score 3-5. So what is 2 days compared to several month of prep (at would say min 2 month for a topscore)
So it would be stupid to see a AWA 0 next to a top score. Otherwise if you have a toefl or ielts b school won t look that much at it.
Ps; I heard lse is already closed for this year. Can anyone confirm?
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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31 Jan 2011, 17:40
Duke007 wrote:
BCG yes it is one of the top consulting firm! Awa is automatically sent with your scores. I just know that with a 700 you will be directly accepted at hec.
Posted from my mobile device
Direct acceptance at HEC with a 700... is this correct? Where did you see this information?
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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23 Feb 2011, 16:44
Hi,
In case some might me interested, I just got accepted to the MSc in Finance programme at LSE.
My profile is as follows:
Nationality: Norwegian
GMAT: 720, 6 AWA
GPA: 3,688 (A Norwegian GPA of 3, or "B", is by LSE considered equal to an american GPA of 3,5)
WE: None what so ever.
References: At most average; we neither rank student nor have a close relationship with our professors.
The average GMAT score of the MSc in Finance students last year was around 690, so 680 should not be THAT big of a long shot.
I do believe the references are are very important. I have heard (from former alumni) that it is important for LSE to know that you are a top student from a top institution in your home country.
I am curious about where you are from, as you are applying for the same programmes as I did. Are you scandinavian?
Cheers
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Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink]
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23 Feb 2011, 16:54
And BTW,
Most of the LSE programmes are NOT closed yet, so the comment about LSE being closed is invalid
Re: is 680 enough for a MSc in Finance in a gdEuropean business [#permalink] 23 Feb 2011, 16:54
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# Extract camera position
Hi
Given a set of points in world coordinates lying around a field, how do i extract the POSITION in XYZ of the camera ?
Help thanks
EDIT: double cv::calibrateCamera gives me 90 error and my camera positions are wrong.
Position of camera 1 is [87.32213358065832; 31.93220642490884; 13.05887540297087]
I input the into the function following the tutorial http://docs.opencv.org/2.4/doc/tutori...
calibrateCamera(World_Coords, Image_Coords, Size(1920,1080), cameraMatrix, distCoeffs, rvecs, tvecs, CV_CALIB_FIX_K4 | CV_CALIB_FIX_K5);
The points in world_coords and Image_coords are arranged such that they correspond to each other.
Then i use rodrigues() to extract the 3x3 rot matrix then the camera position = - rot_matrix.transpose() * tvec.
But I am not getting the right camera position. Can i send the code and data to anyone ?
Camera positions
87.3212582849046; 31.93218648966307; 13.06565020386278]
[88.33600161820506; 36.45175643361132; 13.09339437945696]
[52.67469116679835; 32.05365845570439; 12.67307503062286]
[53.09438819350136; 36.17409639334836; 12.70318338140262]
[9.268389455871184; 35.52733695765274; 14.36430399165124]
[9.21543336317054; 38.71223919680707; 14.1736490348868]
EDIT: i changed to CV_CALIB_FIX_ASPECT_RATIO and the error has dropped to 19. how do i make it drop to ~1. help
edit retag close merge delete
3
If you have for each point the 3D coordinate in the world frame and the corresponding 2D coordinate in the image frame and you have the intrinsic parameters of the camera, you can use solvePnP to estimate the camera pose.
( 2016-01-15 03:29:55 -0500 )edit
Sort by ยป oldest newest most voted
Calm down. We can help.
The first question is how are you defining your world points? I will assume you can extract them from your imagery, and the labels you have in those images are those points. Does that top image accurately represent your coordinate system? That is, the bottom left corner of the field is (0,0,0) and the top left is (Positive X, Positive Y, 0)?
Secondly, what you are doing is two things in one. That function calculates camera parameters, distortion, rotation, and position. It seems what you need most is position and the camera parameters.
So. Use the function initCameraMatrix2D to find the camera matrix. Use all of the data you have, whether the camera is moving or rotating or not. Then save it, because you're going to re-use this over and over. I actually wrote this to a file to read in each time I use the camera.
Now. Use this, and each static scene as input to the solvePnP function. By static scene, I mean any time when the camera doesn't move, rotate, or zoom. If the camera can move, it probably means one frame. You now have output for the frame, that is rotation and translation vectors. The way you did it before seems to be correct, but to be sure, here is the code I use.
Rodrigues(rotation, R);
R = R.t();
t = -R * translation;
t now contains the position of the camera for that frame.
Now, to improve accuracy, there is one important step to take. Using the calibrateCamera function we are going to find the camera matrix and the distortion matrix. Split your worldPoints and cameraPoints vectors up by frame. vector<vector<point3f>> and vector<vector<point2f>> One outer vector, holding one vector per frame, which holds the points for that frame. This is important.
Now, make sure you pass the camera matrix you created earlier to the function and use the flag CV_CALIB_USE_INTRINSIC_GUESS. You have a guess, and it should help the accuracy.
Check the returned vector<mat> that is the rotation and translation. They may be good enough. If not, use the new camera matrix and distortion matrix in SolvePnP again, and use those.
If you post the world points named as the images you have above, I will be happy to double check the results.
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### Author Topic: tut0401 Quiz3 (Read 3573 times)
#### baixiaox
• Jr. Member
• Posts: 10
• Karma: 0
##### tut0401 Quiz3
« on: October 11, 2019, 01:59:16 PM »
Find the Wronskian of the given pair of functions:
$$cos^2(x),\,1+cos(2x)$$
$$W= \begin{vmatrix} cos^2(x)&1+cos(2x)\\ -2cos(x)sin(x)&-2sin(2x)\\ \end{vmatrix}\\ = \begin{vmatrix} cos^2(x)&1+cos(2x)\\ -sin(2x)&-2sin(2x)\\ \end{vmatrix}\\ cos(2x)=2cos^2(x)-1\\ sin(2x)=2sin(x)cos(x)\\ =-2cos^2(x)sin(2x)+sin(2x)+sin(2x)cos(2x)\\ =-sin(2x)[2cos^2(x)-1-cos(2x)]\\ =-sin(2x)[cos(2x)-cos(2x)]\\ =-sin(2x)\times0\\ =0\\ \$$
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https://discuss.codechef.com/t/cow203-editorial/61035
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# COW203 - Editorial
Author: shrivas7
Tester: sandeep1103
Editorialist: shrivas7
EASY
None
# EXPLANATION:
Our objective is to minimize the total problems to be solved in order to form N/2 teams.
This can we achieved if we try to minimize the no. of problems to be solved at individual
team level.Clearly if we want to do so we must make sure that the difference between the programming skills of the pair forming the team should be as minimum as possible.
Therefore we need to sort the array containing the programming skills of N students , and thereafter we can take pairs of students serially and form their team ,and the keep on calculating the minimum problems to be solved .
# SOLUTIONS:
Setter's Solution
``````#include<bits/stdc++.h>
using namespace std;
int main()
{
int t,n,i;
cin>>t;
while(t--)
{
cin>>n;
int a[n];
for(i=0;i<n;i++)
cin>>a[i];
sort(a,a+n);
int ans=0;
for(i=0;i<=n-2;i+=2)
ans += a[i+1]-a[i];
cout<<ans<<endl;
}
}
``````
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Christmas is an expensive time of year - and now it's over for another 12 months, many will be thinking of how they can rebuild their accounts.
Saving is one of the most common New Years resolutions for scores of people who may have goals at the end of it.
But taking huge sums out of the pay packet to do just this can have a noticeable impact.
There is a simple challenge which could see you turn your loose change into a decent amount in under a year.
Different versions of this have been around for a while, but this latest one from the parenting website PlayPennies has simplified it for us.
For those who want to save £667.95 in 365 days, you really have to start now.
### Here's how it works
The penny challenge - which starts in January, and runs for a full 12 months - asks you to put away a single copper a day.
This gradually grows to pounds as the year goes on - and by December 31 you'll have £667.95 to see you into the New Year.
To start with, you put in 1p on day one - you'll then put in the equivalent amount of pennies to the day of the year:
Day 1: Put in £0.01
Day 2: Put in £0.02
Day 3: Put in £0.03
Continue until...
Day 100: Put in £1.00
Day 101: Put in £1.01
Day 102: Put in £1.02
Double it on day 200...
Day 200: Put in £2.00
Day 201: Put in £2.01
Day 202: Put in £2.02
And continue until the 300th day, when you...
Day 300: Put in £3.00
Day 301: Put in £3.01
Day 302: Put in £3.02
On the final day Day 365 (December) drop in £3.65 and it's time to cash in your jar.
You should have £667.95 in it (if you've stuck to the plan).
And you could always do it the other way round and start off by saving £3.65 on day one, £3.64 on day two and so on.
### Money saving tips
Here are some other ways you could try to save money for next Christmas, from the experts at MoneySavingExpert.com
1. Look out for cash bonuses
Always be wary of offers that look too good to be true, but some banks offer good deals to switch accounts.
Switching accounts can be a hassle, but it could be worth it if you could earn a bonus of up to £200 that some banks reportedly offer from time to time.
Search online for bank account deals to see if any offers are available at the moment.
You could try getting rid of some of your old possessions you don’t need to bag some extra cash for other things.
Be honest with yourself about how much you really need or like your stuff - and how much you could fetch for it on eBay or Facebook.
3. Consider giving IOUs
Some things will be cheaper in the sales after Christmas, or may be easier for you to pay for a few weeks after the big day.
If there is anyone you know who you think won’t mind the wait - or if you are happy to make your children wait - then why not make your own IOU voucher or nicely wrapped IOU for something for them instead?
Then you could take your child, relative or friend out shopping in the sales - and they may even be more likely to find something they definitely like.
4. Look for deals
MoneySavingExpert.com has a special discount-finding tool that works with Amazon, that looks for reduced items for you.
Be wary of assuming discounted goods are always bargains - but you could certainly look on different sites for money off TVs, beauty products and other items.
5. Work out a budget
Money experts advise working out a budget in advance, rather than only asking how you will pay for everything when it is too late.
Budgeting may be a dull or even scary prospect, but it does not need to be - you can use MoneySavingExpert.com’s free online budget planner here, or call your local Citizens Advice Bureau for free advice.
### KentLive WhatsApp breaking news alerts
To receive KentLive breaking news and top stories alerts via WhatsApp, text NEWS to 07880 442229.
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# Find the solutions to $z^3 = 2 + 11i$.
Find the solutions to $z^3 = 2 + 11i$.
I wrote $z = x + iy$ to get $(x + iy)^3 = 2+ 11i$.
Expanding and equating the real and Imaginary parts I got,
$$x^3 - 3xy^2 = 2$$ $$y^3 - 3x^2y = 11$$
Let $tx = y$, Substituting this I got,
$$x^3 - 3t^2x^3 = 2$$ $$x^3(3t-t^3) = 11$$
Susbtituting for $x^3$ from first equation into second eaution I got,
$$2t^3 + -6t - 33t^2 + 11 = 0$$
I don't know how to solve this cubic, I tried finding roots by putting different numbers but I can't find any of them.
What are some other ways of solving without running into a cubic and how can I solve this cubic ?
your number has norm 125. The answer has norm 5. If they intended integers, that means either $\pm1 \pm 2 i$ or $\pm 2 \pm i.$ Try them.
As 11 is odd, we need $y = \pm 1,$ so $\pm 2 \pm i.$
• What is norm ? I see 5 wikipedia pages for norm. – A---B Feb 15 '17 at 1:26
• @A---B magnitude squared. $11^2 + 2^2 = 125 = 5^3$ – Will Jagy Feb 15 '17 at 1:27
• Yes got the answer. – A---B Feb 15 '17 at 1:31
• Nice! I suppose we could've also used rational roots theorem @A---B XD – Simply Beautiful Art Feb 15 '17 at 1:31
To avoid cubics, we use trig: $\theta=\arctan(11/2)$ and $r=\sqrt{11^2+2^2}=5\sqrt5$
The cube roots are then given as follows:
$$z^3=2+11i=r\operatorname{cis}(\theta)=re^{i\theta}$$
$$z=\sqrt[3]{r}\operatorname{cis}\left(\frac{\theta+2\pi k}3\right)=\sqrt[3]{r}e^{i\frac{\theta+2\pi k}3}$$
Where $\operatorname{cis}(\theta)=\cos(\theta)+i\sin(\theta)$ and $k\in\mathbb N$.
In general, the $n$th roots are:
$$z^n=2+11i$$
$$z=\sqrt[n]{r}\operatorname{cis}\left(\frac{\theta+2\pi k}n\right)$$
• why arctan(11/2) ? not something else. – A---B Feb 15 '17 at 1:22
• @A---B Since $2+11i$ lies in the 1st quadrant, it follows that the angle between that point and the real axis is given by $\arctan(11/2)$. Draw a picture to see this :D. It then follows amazingly that raising complex numbers to powers is equivalent to raising their magnitude by that power and appropriately multiplying or dividing the angles, accounting for $2\pi k$ modulus for rational powers like 1/3 (a.k.a. cube roots) – Simply Beautiful Art Feb 15 '17 at 1:25
• I would have selected your answer if using polar form was allowed. – A---B Feb 15 '17 at 1:31
• @A---B Lol, personally, spotting the rectangular form is almost always preferred. Polar is too easy :P – Simply Beautiful Art Feb 15 '17 at 1:32
• No doubt polar is easy. All hail to De Moivre. – A---B Feb 15 '17 at 1:34
Expanding and equating the real and Imaginary parts I got,
$$x^3 - 3xy^2 = 2 \tag{1}$$ $$y^3 - 3x^2y = 11$$
The second equation lost a sign along the way, it should be:
$$y^3 - 3x^2y = -11 \tag{2}$$
Subtracting $(1)-(2)$ and grouping:
$$x^3-y^3 - 3xy(y-x)=13 \;\iff\; (x-y)(x^2+4 xy+y^2) = 13$$
Looking for "nice" integer solutions leaves only $x-y=\pm 1,\pm 13$ to try.
• "Looking for "nice" integer solutions leaves only $x−y=±1,±13$ to try." reason for this ? why not $\pm 26, \pm 52$ etc ? – A---B Feb 15 '17 at 8:59
• @A---B $\pm1,\pm13$ are the only divisors of $13\,$. – dxiv Feb 15 '17 at 16:41
• Oh my question was vague. I want to know why we need divisors of 13 not multiples ? – A---B Feb 15 '17 at 18:03
• @A---B If $x,y$ are integers, then $x-y$ and $x^2+4xy+y^2$ are both integers, and they must both be divisors of $13$ since their product is $13$. But $13$ is a prime number, and its only divisors are $\pm1,\pm13$. The above does not prove that $x,y$ must be integers, only that if they are then they can be found by verifying a few simple cases. – dxiv Feb 16 '17 at 1:19
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# Metrics Essay Example
• Category:
Logic & Programming
• Document type:
Math Problem
• Level:
• Page:
1
• Words:
476
Requirement stability is what a company is expecting of its responsibilities to its clients at a particular time before the implementation of the actual plan. This metric requires that for a company to achieve stability, it must weigh between what it is expecting from the market and what is actually in the market. It is important for the software system to provide the company’s functions and capabilities as well as the rules by which it must stick to. This metric is important since it will provide issues such as the feedback to the customer. It is in simple language that the consumer understands to remove any ambiguity since what is expected has already been explored (Donn Le Vie, 2010).
This metric also decomposes any problem into different parts hence giving a simple understandable solution in an orderly manner. Such a metric also serves as the mother document that will be used as the standard for verifying any condition the company gives. This is because the metric is the initial development phase for the company’s products or services where everything the company requires or does not require is included. This is where all the information in regard to the customers’ needs is done. Interviews, fieldwork, questionnaires and surveys may be conducted to ensure that what is collected is the reality on the ground according to Donn Le Vie (2010).
Normally, the measure of a complexity of a scale is determined by two attributes which are internal and external. Internal attributes include those that are measured by observing the product and the process involved to produce it. External attributes are those that are measured in regard to how the product or its production process relate to its surroundings. The company to be scrutinized is classified in regard to its importance versus other similar companies in the measurement scale (Winston, 2008). The interviews, surveys, fieldwork and questionnaires will rate it. This is done before the above exercises are conducted so that an analysis of the feedback from the consumers show whether the company’s goals will be met or not. Compare it to other companies on the scale, give the general objectives of the company, come up with questions which you have answers to establish whether the company’s objectives are met, analyse the questions then calculate the average of the measurements given by the consumers to be. This will be a measure of the average of the complexity on this scale. This will provide the answers to what the consumers need and expects and what the company will offer. This poll is intended to ensure that the consumers are in agreement with the required details. This scale of 1-10 will give an average rating of the company (Winston, 2008).
References
Donn Le Vie, 2010, Writing Software Requirements Specifications, London: Inktopia.
Winston J, 2008, Meaningfulness in Measurement, New York: CaIU Education.
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# Running time Average of column values
조회 수: 7(최근 30일)
Yash Bhati 2021년 10월 19일
편집: Yash Bhati 2021년 10월 19일
I have to imported data form my simulation and made a table which is of Nx1 size.(N depends on number of output which i get from my simulation)
suppose my Table1 looks likes
1.10
2.20
3.20
4.40
......
now what i want is to create another Table2 which has running average of values from Table1, So my Table2 would look like
1.10
2.(10+20)/2
3.(10+20+20)/3
4.(10+20+20+40)/4
.....
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### 채택된 답변
KSSV 2021년 10월 19일
If A is your column array.
iwant = cumsum(A)./(1:numel(A))
##### 댓글 수: 2표시숨기기 이전 댓글 수: 1
Yash Bhati 2021년 10월 19일
t=length(A);
M = movmean(A,[t 0]);
Although script as mentioned by KSSV (iwant = cumsum(A)./(1:numel(A))) works well but had to exract data from diagonal matrix.
Thank you all.
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# NSTSE (National Science Talent Search Exam- Unified Council) Class 8: Questions 390 - 397 of 2028
Access detailed explanations (illustrated with images and videos) to 2028 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. Subscription can be renewed yearly absolutely FREE! View Sample Explanation or View Features.
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## Question number: 390
Edit
MCQ▾
________.
### Choices
Choice (4) Response
a.
0
b.
1
c.
d.
Question does not provide sufficient data or is vague
## Question number: 391
Edit
MCQ▾
### Question
The value of the product and when is:
### Choices
Choice (4) Response
a.
16
b.
10
c.
d.
0
## Question number: 392
Edit
MCQ▾
### Question
The least number which must be added to 2498 to make it a perfect square is:
### Choices
Choice (4) Response
a.
27
b.
2
c.
10
d.
6
## Question number: 393
Edit
MCQ▾
### Question
The value of an article which was purchased 2 years ago, depreciates at 5 % per annum. If its present value is Rs. 1805, the price at which it was purchased is:
### Choices
Choice (4) Response
a.
2000 Rs.
b.
3000 Rs.
c.
3600 Rs.
d.
2500 Rs.
## Question number: 394
Edit
MCQ▾
If then x is:
### Choices
Choice (4) Response
a.
b.
c.
d.
Question does not provide sufficient data or is vague
## Question number: 395
Edit
MCQ▾
### Question
One of the factors of is:
### Choices
Choice (4) Response
a.
b.
c.
d.
## Question number: 396
Edit
MCQ▾
### Question
An article when sold at a gain of 5 % yields Rs. 25 more than when sold at a loss of 5%. Its cost price would be:
### Choices
Choice (4) Response
a.
200 Rs.
b.
280 Rs.
c.
250 Rs.
d.
150 Rs.
## Question number: 397
Edit
MCQ▾
### Question
The length of diagonal of a square whose area is 15,625 is:
### Choices
Choice (4) Response
a.
m
b.
m
c.
m
d.
Question does not provide sufficient data or is vague
Developed by:
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rsenc
Reed-Solomon encoder
Syntax
```code = rsenc(msg,n,k) code = rsenc(msg,n,k,genpoly) code = rsenc(...,paritypos) ```
Description
`code = rsenc(msg,n,k)` encodes the message in `msg` using an [`n`,`k`] Reed-Solomon code with the narrow-sense generator polynomial. `msg` is a Galois array of symbols having m bits each. Each `k`-element row of `msg` represents a message word, where the leftmost symbol is the most significant symbol. `n` is at most 2m-1. If `n` is not exactly 2m-1, `rsenc` uses a shortened Reed-Solomon code. Parity symbols are at the end of each word in the output Galois array `code`.
`code = rsenc(msg,n,k,genpoly)` is the same as the syntax above, except that a nonempty value of `genpoly` specifies the generator polynomial for the code. In this case, `genpoly` is a Galois row vector that lists the coefficients, in order of descending powers, of the generator polynomial. The generator polynomial must have degree `n-k`. To use the default narrow-sense generator polynomial, set `genpoly` to `[]`.
`code = rsenc(...,paritypos)` specifies whether `rsenc` appends or prepends the parity symbols to the input message to form `code`. `paritypos` can be either `'end'` or `'beginning'`. The default is `'end'`.
Examples
collapse all
Set the code parameters.
```m = 3; % Number of bits per symbol n = 2^m - 1; % Codeword length k = 3; % Message length```
Create two messages based on GF(8).
`msg = gf([2 7 3; 4 0 6],m)`
``` msg = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal) Array elements = 2 7 3 4 0 6 ```
Generate RS (7,3) codewords.
`code = rsenc(msg,n,k)`
``` code = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal) Array elements = 2 7 3 3 6 7 6 4 0 6 4 2 2 0 ```
The codes are systematic so the first three symbols of each row match the rows of `msg`.
Limitations
`n` and `k` must differ by an integer. `n` between 7 and 65535.
Version History
Introduced before R2006a
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# onepointcom.com
## Sem Standard Error Of Means
Home > Standard Error > Sem Standard Error Of Means
# Sem Standard Error Of Means
## Contents
Boost Your Self-Esteem Self-Esteem Course Deal With Too Much Worry Worry Course How To Handle Social Anxiety Social Anxiety Course Handling Break-ups Separation Course Struggling With Arachnophobia? Detailed results are given in Table 1, where the four journals are listed in order of decreasing percentage misuse of sem. Repeating the sampling procedure as for the Cherry Blossom runners, take 20,000 samples of size n=16 from the age at first marriage population. This often leads to confusion about their interchangeability. http://onepointcom.com/standard-error/se-standard-error-standard-deviation.html
Thank you. 0 In my opinion Error is best represented by the Standard error!!!
-Pradeep Iyer- FROM BMJ The terms "standard error" and "standard deviation" are often confused.1 The contrast between In general, the use of the sem should be limited to inferential statistics where the author explicitly wants to inform the reader about the precision of the study, and how well The sample mean will very rarely be equal to the population mean. The ages in one such sample are 23, 27, 28, 29, 31, 31, 32, 33, 34, 38, 40, 40, 48, 53, 54, and 55. https://en.wikipedia.org/wiki/Standard_error
## Standard Error Of The Mean Formula
JSTOR2682923. ^ Sokal and Rohlf (1981) Biometry: Principles and Practice of Statistics in Biological Research , 2nd ed. It must be noted that in some of the articles that incorrectly used the sem, both parameters, sem and sd, were used. A natural way to describe the variation of these sample means around the true population mean is the standard deviation of the distribution of the sample means. Because the age of the runners have a larger standard deviation (9.27 years) than does the age at first marriage (4.72 years), the standard error of the mean is larger for
In each of these scenarios, a sample of observations is drawn from a large population. The standard error is also used to calculate P values in many circumstances. The term may also be used to refer to an estimate of that standard deviation, derived from a particular sample used to compute the estimate. Difference Between Standard Error And Standard Deviation Blackwell Publishing. 81 (1): 75–81.
Because the 5,534 women are the entire population, 23.44 years is the population mean, μ {\displaystyle \mu } , and 3.56 years is the population standard deviation, σ {\displaystyle \sigma } To estimate the standard error of a student t-distribution it is sufficient to use the sample standard deviation "s" instead of σ, and we could use this value to calculate confidence The sample mean will very rarely be equal to the population mean. It's going to be more normal, but it's going to have a tighter standard deviation.
If we magically knew the distribution, there's some true variance here. Standard Error Regression So 9.3 divided by the square root of 16-- n is 16-- so divided by the square root of 16, which is 4. If there is no change in the data points as experiments are repeated, then the standard error of mean is zero. . . For a value that is sampled with an unbiased normally distributed error, the above depicts the proportion of samples that would fall between 0, 1, 2, and 3 standard deviations above
## Standard Error Of The Mean Excel
Correction for finite population The formula given above for the standard error assumes that the sample size is much smaller than the population size, so that the population can be considered try this Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. Standard Error Of The Mean Formula Search this site: Leave this field blank: . Standard Error Of The Mean Definition Descriptive statistics aim to describe a given study sample without regard to the entire population; inferential statistics generalize about a population on the basis of data from a sample of this
In these articles, the sd was mostly found in the text and the sem in the figures. http://onepointcom.com/standard-error/see-standard-error.html So here, when n is 20, the standard deviation of the sampling distribution of the sample mean is going to be 1. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. Because the age of the runners have a larger standard deviation (9.27 years) than does the age at first marriage (4.72 years), the standard error of the mean is larger for Standard Error Vs Standard Deviation
The mean age was 33.88 years. It is the variance -- the SD squared -- that doesn't change predictably, but the change in SD is trivial and much much smaller than the change in the SEM.)Note that A medical research team tests a new drug to lower cholesterol. navigate here Previous Section References ↵ Glantz S.
So if I were to take 9.3-- so let me do this case. Standard Error Of Proportion For an upcoming national election, 2000 voters are chosen at random and asked if they will vote for candidate A or candidate B. doi:10.2307/2340569.
## E‐mail: [email protected] Next Section Abstract Background.
Conclusions. Let's see if I can remember it here. And sometimes this can get confusing, because you are taking samples of averages based on samples. Standard Error Symbol As the sem is always less than the sd, it misleads the reader into underestimating the variability between individuals within the study sample.
We may choose a different summary statistic, however, when data have a skewed distribution.3 When we calculate the sample mean we are usually interested not in the mean of this particular Using a sample to estimate the standard error In the examples so far, the population standard deviation σ was assumed to be known. When the sampling fraction is large (approximately at 5% or more) in an enumerative study, the estimate of the standard error must be corrected by multiplying by a "finite population correction"[9] his comment is here If values of the measured quantity A are not statistically independent but have been obtained from known locations in parameter space x, an unbiased estimate of the true standard error of
Let's see if it conforms to our formula. So we've seen multiple times, you take samples from this crazy distribution. So if I know the standard deviation, and I know n is going to change depending on how many samples I'm taking every time I do a sample mean. Because these 16 runners are a sample from the population of 9,732 runners, 37.25 is the sample mean, and 10.23 is the sample standard deviation, s.
They may be used to calculate confidence intervals. With standard error (unless you have a large enough sample size), typically if the error bars overlap or are close to each other, the differences are insignificant. Because the 5,534 women are the entire population, 23.44 years is the population mean, μ {\displaystyle \mu } , and 3.56 years is the population standard deviation, σ {\displaystyle \sigma } Despite the small difference in equations for the standard deviation and the standard error, this small difference changes the meaning of what is being reported from a description of the variation
Two data sets will be helpful to illustrate the concept of a sampling distribution and its use to calculate the standard error. ISBN 0-521-81099-X ^ Kenney, J.
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# physics
A rock is thrown off a vertical cliff at an angle of 58.6o above horizontal. The cliff is 84.6 m high and the ground extends horizontally from the base. The initial speed of the rock is 21.8 m/s. Neglect air resistance.
To what maximum height, in meters, does the rock rise above the edge of the cliff?
1. 👍
2. 👎
3. 👁
1. vertical speed initial :(Vi): 21.8*sin58
initial KE in vertical: 1/2 m (21.8*sin58)^2
final change in potential energy:
mgh=1/2 m (21.8*sin58)^2
solve for height h above the upper edge of the cliff.
1. 👍
2. 👎
👤
bobpursley
2. ok i got! what about these questions:
How high above the ground, in meters, is the rock 2.21 s before it hits the ground?
How far horizontally from the cliff, in meters, is the rock 2.21 s before it hits the ground?
using the same numbers given above
1. 👍
2. 👎
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Your Federal Quarterly Tax Payments are due April 15th
# Experiment CF Centripetal Force by sanmelody
VIEWS: 33 PAGES: 9
• pg 1
``` Experiment CF Centripetal Force
Note: You will need both of your LVPS for this experiment. So build your second LVPS if you
Introduction
This experiment is about centripetal force, the force that keeps objects moving in a circular path
at a constant velocity. This force is always at right angles to the motion and directed towards the
center of the circular orbit. By Newton’s Second Law when a centripetal force acts on a mass, the
force continually changes the direction of the velocity without changing its magnitude. This
change in the direction of the velocity is always towards the center and accounts for the
centripetal acceleration of the mass.
Examples of centripetal forces are tension in a string connected to a rotating mass; the
gravitation force between a planet and a rotating satellite; and magnetic forces on moving charged
particles in a magnetic field.
Experiment
In this experiment, the centripetal force is the restoring force of a stretched rubber band with one
end attached to the shaft of a dc permanent-magnet motor powered by your LVPS and the other
end attached to a # 6-32 nut. The nut has a mass 0.92 ± 0.01g and the rubber band has a mass
of 0.22 ± 0.02 g . The motor whirls the nut in a circular path at a rotational frequency f that you
will set using a stroboscopic method. You will measure the radius of the circular path, r, for
various rotation speeds. This will allow you to calculate the centripetal acceleration
a r = r 4 2 f 2 .
You will set the rotational frequency by using a light-emitting diode (LED) that flashes 60
times per second when connected to the wall transformer. (The wall transformer supplies a
nominal 12 Volts AC at 60 Hz). You can adjust the motor speed by adjusting the output voltage
of the LVPS. You can then set your motor speed by a stroboscopic method. You will place a
pattern of lines on the shaft of the motor. While the LED is directed downward onto the motor
shaft, you adjust the LVPS until you see a stationary pattern of lines. This will correspond to a
frequency that is some fraction of 60 Hz.
The rubber band stretches until the restoring force of the rubber band exerts the necessary
centripetal force on the nut to keep the nut spinning in a circular orbit. You calibrate the rubber
band by hanging pennies in a cup that stretch the rubber band and measure the stretched length of
the rubber band as a function of the hanging weight. Thus by measuring the stretched length of
the rotating rubber band (the radius of the circular orbit) you can use your calibration to
1
determine the centripetal force acting on the spinning nut. You can then verify that Newton's
Second Law is indeed correct, namely that
Fradial = m a radial = m r 4 2 f 2
Theory
When an object is moving in circular motion the direction of velocity is always tangent to
the circle. Therefore the direction of the velocity is always changing towards the center of the
circle. This means that there is a non-zero component of the acceleration directed radially inward.
This acceleration is called the centripetal acceleration. If our object is increasing its speed or
slowing down there is also a non-zero tangential acceleration. But when the object is moving at a
constant speed in a circle then only the centripetal acceleration is non-zero. Therefore there must
be a ‘centripetal force’, a radial force pointing inward, that produces this acceleration. Since
Newton’s Second Law is a vector equality, F = ma , can be applied to the radial direction yielding
(in magnitude)
Kinematics of Circular Motion
We choose the origin of our coordinate system as the fixed central point. We shall choose
coordinates for a point P in the plane as follows (Figure 1). One coordinate, r , measures the
radial distance from the origin to the point P. The coordinate r ranges in value from 0 r .
Our second coordinate measures an angular distance along the circle. We need to choose some
reference point to define the angle coordinate.
Figure 1: Polar Coordinate System
2
We choose a ‘reference ray’, a horizontal ray starting from the origin and extending to + along
the horizontal direction to the right. (In a typical Cartesian coordinate system, our reference ray
is the positive x-direction). We define the angle coordinate for the point P as follows. We draw a
ray from the origin to the point P. We define the angle as the angle in the counterclockwise
direction between our horizontal reference ray and the ray from the origin to the point P. All the
other points that lie on a ray from the origin to infinity passing through P have the same value
as . For any arbitrary point, our angle coordinate can take on values from 0 < 2 .
Velocity and Angular Velocity
The rate of change of angle with respect to time is called the angular velocity and is denoted by
the Greek letter ,
d
.
dt
Angular velocity has units [rad/sec]. The component of the velocity v for circular motion is given
by
d
v=r = r .
dt
Uniform Circular Motion
When the magnitude of the velocity (speed) remains constant, the object moves in uniform
circular motion. Since the speed v = r is constant, the amount of time that the mass takes to
complete one circular orbit of radius r is a constant. This time interval is called the period and is
denoted by T. In one period the object travels a distance s equal to the circumference, s = 2 r .
Since the distance traveled in one period is the product of speed and period, we have
s = 2 r = vT .
Thus the period T is given by
2 r 2 r 2
T= = = .
v r
The frequency f is defined to be the inverse of the period,
1
f = = ,
T 2
3
The units of frequency are [sec-1] = [hertz]= [Hz].
The magnitude of the component of radial acceleration (centripetal acceleration) is given by
a r = v .
The direction of the radial acceleration is towards the center of the circle.
The centripetal acceleration can be expressed in several equivalent forms since the
velocity and the angular velocity are related by v = r . Thus we have for the magnitude of the
centripetal acceleration two alternative forms:
ar = r 2 (6.1.1)
and
v2
ar = (6.1.2)
r
Recall that the angular velocity is related to the frequency by = 2 f . So we have a third
expression for the magnitude of the centripetal acceleration
ar = r 4 2 f 2 (6.1.3)
A fourth form commonly encountered uses the fact that the frequency is defined to be the inverse
of the period f = 1 / T . Thus we have the fourth expression for the centripetal acceleration
ar = r 4 2 f 2 (6.1.4)
Experiment: Building the Apparatus
Note: Do not plug in the wall transformer until you have completed the apparatus.
Clamping the motor
Take the 2-inch corner brace in the experiment kit and use the hose clamp to attach the motor to
it as shown. Handle the motor carefully to avoid damage to the terminals of the motor. The clamp
4
should be tight enough to keep the motor from wiggling around, but not so tight as to keep it
from turning freely. Use the ‘C-clamp’ to attach the assembly rigidly to your desk.
Attaching the nut
Attach the 6-32 nut to the rubber band and the rubber band to the motor shaft by looping the
rubber band over itself as shown. Loop it in the direction such that the rotation of the shaft tends
to tighten the loop. Try to keep the two strands the same length and not twisted up.
Figure 2: Clamping the motor and attaching the nut
Attaching the stroboscopic pattern
Cut out the four-line pattern (you can find it on the last page of this write-up), make a hole in the
center with a pushpin and press it onto the motor shaft above the rubber band.
Connecting the LED
The LED needs an alternating voltage in order to flash so you will connect it to the ac input
terminals of the rectifier in one of your partnerships’ LVPS (call this one LVPS-1). Split the
‘speaker wire’ (two conductor stranded wire in transparent plastic insulation) an inch or so at
each end of the 4 foot length provided in the experiment kit. Remove about 1/4 inch insulation
from each of the ends and tin the exposed wire. Solder the pair at one end to the LED without
twisting the wires. Use 1 1/2 inches of black tape folded lengthwise to protect the LED leads
from shorting each other. Solder the pair at the other end to the ac input terminals of the rectifier
in the LVPS-1. Again don’t twist the wires.
Connecting the two LVPS
5
Your LVPS only goes down to 1.5 volts, which is still to high to obtain the low rotational speeds
you will need for this experiment. You will your other LVPS (call this one LVPS-2) with the
voltage reversed to adjust the voltage down to zero voltage.
You only need one wall transformer to drive both LVPS. You will do this by connecting
the output of LVPS-1 rectifier to the 1000 µ F capacitor of LVPS-2. Use a red clip lead to
connect the positive sides of the 1000 µ F capacitors of LVPS-1 and LVPS-2 together. Use a
black clip lead to connect the negative sides of the 1000 µ F capacitors of LVPS-1 and LVPS-2
together.
Figure 3: Connecting the two LVPS
Connecting the 1157 lamp
You will use the 8-watt filament of your 1157 lamp for a current regulating effect that makes
settings less critical and more stable. As the current increases in the filament the resistance goes
up. This increased resistance tends to limit the increase in the current. Solder the leads of the 8 W
filament of the 1157 lamp to the output terminals of the LVPS-2.
Connecting the motor
Connect the motor leads to the plus terminals of the two LVPS with clip leads. By connecting
the motor to the two positive terminals you are effectively subtracting the differences between
the two voltage settings to get a net voltage across the motor between 0 and 1.5 volts. Connect
6
the input leads of the multimeter (MMM) at the 5 volt DC setting to the two positive output
terminals of the LVPS so that you can measure the voltage across the motor.
Doing the Spinning Nut Experiment
You will first measure the radius of the circular orbit of the spinning nut for various rotational
frequencies, 10 Hz (six stationary lines), 12 Hz (five stationary lines), 15 Hz (four stationary
lines), and 20 Hz (three stationary lines). Then you will calibrate the rubber band by stretching
the rubber band with pennies in a hanging cup.
Procedure:
• Unclip one motor lead and plug in the wall transformer. Adjust the voltage of LVPS-
2 to about 7.5 volts. This is enough to make the 8 W filament of the 1157 lamp glow
brightly. Turn down LVPS -1 all the way and then reconnect the motor.
• Hold the nut so the rubber band is slightly stretched; the band should not rub on the
motor housing. Turn up LVPS-1 so that there is 0.5 to 0.75 volts across the motor. You
will see the shaft start to turn; immediately launch the nut into orbit. Start all over if the
rubber band gets twisted up around the shaft.
• In order to see the stroboscopic pattern you will need to make the area immediately
around the experiment dark. One partner can hold the LED about 1 inch above the motor
and continually adjust the LVPS-1 until the 4-line pattern appears to be stationary. This
means that (the simplest case) the band is advancing 90 degrees = 1/4 of a revolution each
1/60 of a second, and therefore the shaft is turning at a rotational frequency f = 15 Hz.
• The other partner can measure the radius of the circular path of the spinning nut from the
center of the shaft to the center of the nut.
• Repeat these measurements for the various patterns corresponding to 10 Hz, 12
Hz, 15 Hz, and 20 Hz rotational frequencies.
Calibrating the Rubber Band
Clamp the corner brace on its edge with the motor shaft extended well out over the edge of your
table or desk so that the rubber band and nut hang freely. Bend a paper clip into an S-shaped
hook. Press one end through the paper cup just below its rim and hook the other end to the nut.
Now add pennies to the cup and measure the length, L, of the rubber band. Keep adding
pennies to cover the range of lengths you measured when spinning the nut. The mass of the
paper cup and the paper clip together is 5.8. ± 0.01g .
7
The weight required to stretch the rubber band to a length equal to the radius of the
circular path of the nut is approximately equal to the centripetal force needed to accelerate the
nut inward in its motion. We say "approximately", because the rubber band has mass and is
stretched by the rotation even when there's no nut at the end. This isn't too serious, as you can
see by spinning the rubber band by itself; it doesn't stretch much, and if it did, you could take
data to make an appropriate correction. You should also note that excessive stretching of the
rubber band could weaken it permanently; this could invalidate your results.
Figure 4: Calibrating the rubber band
Figure 5: Stroboscopic line patterns
8
PARTS LIST
1 permanent magnet DC motor
1 2" corner brace
1 hose clamp #12 SS
1 LED, wt. internal resistor
4' #22 speaker wire
2 nuts, 6-32 (5/16) steel
2 rubber bands, #18
1 paper clip, #1
1 pushpin
1 paper cup
100 pennies
9
```
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### Free Educational Resources
• > ACCT 504 Week 8 Final Exam Set 3
+
# ACCT 504 Week 8 Final Exam Set 3
##### Rating:
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Author: Christine Farr
##### Description:
http://www.devrygenius.com/product/acct-504-week-8-final-exam-set-3
1. (TCO A) An advantage of the corporate form of business is _____. (Points : 5)
2. (TCO A) Which one of the following statements is correct with regard to Dividends? (Points : 5)
3. (TCOs A, B) Below is a partial list of account balances for LBJ Company:
4. (TCOs B, E) Which of the following statements is incorrect with regard to accrual accounting? (Points : 5)
5. (TCO D) Three different companies each utilize a different inventory costing method. If the price of goods has increased during the period, then the company using _____. (Points : 5)
6. (TCOs A, E) Equipment was purchased for \$85,000. Freight charges amounted to \$2,550 and there was a cost of \$10,000 for building a foundation and installing the equipment. It is estimated that the equipment will have a \$5,000 salvage value at the end of its 6-year useful life. Depreciation expense each year using the straight-line method will be _____. (Points : 5)
7. (TCOs D, G) When the market rate of interest is equal to the stated rate of interest on the bond, the bond will require _____. (Points : 5)
8. (TCO C) Accounts receivable arising from sales to customers amounted to \$50,000 and \$45,000 at the beginning and end of the year, respectively. Income reported on the income statement for the year was \$150,000. Based on these transactions, the cash flows from operating activities to be reported on the statement of cash flows would be _____. (Points : 5)
9. (TCO F) Which one of the following tools uses the percentage change formula to make year-over-year comparisons of sales growth? (Points : 5)
10. (TCO F) When performing a common-size Income Statement, the 100% figure is _____. (Points : 5)
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Tutorial
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# hat decreases
by Karen
(Kalamazoo MI USA)
I am knitting a 2x2 ribbed hat. PATTERN CALLS FOR 100 cast on stitches. For decreases the beginning of round is moved up one stitch and markers are set every 24 stitches, always between two knit stitches.
I have cast o 90 stitches to get the proper head size and am having trouble with the math to place the stitch markers. It seems that the final group of stitches has 4 extra stitches in the written pattern.
Any help would be appreciated.
### Comments for hat decreases
Average Rating
Mar 26, 2019 Rating Hat decreases by: Ratchadawan The pattern decrease every 25 sts and that make 4 decreases for 100 sts. For your hat, you need to decreses 4 times out of 90 sts, so that would be 90/4 = 22 sts with extra 2 leftover. In this case, we can't decrease 4 times evenly unless we add or subtract 2 sts. alternatively, we can make decreases with slightly uneven at 22, 23, 22 and 23. so you'll be putting the markers at every 21, 22, 21, and 22 sts. The only problem with this is that two of the decreses won't be between the knit sts. If you ever decide to rib it all apart then you can make your cast on to be at 92 or 88. I wish you the best on your project! Thank you for the question. Ratcha
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Calculation of electrical loads is performed in order to choose the right wire size, which will be laid mains. If all network parameters (voltage, current and electrical resistance) will correspond to each other, it will last a long time, will not overheat, and therefore will not cause a fire.
Instruction
1
Calculate the maximum load on the electricity network. To do this, define the maximum capacity of consumers that can be simultaneously connected to it. Then define the material of the conductor, which will be done wiring. To do this, take a copper wire, it has a higher conductivity than aluminum and not so quickly burn out at higher load.
2
Calculate the wire size required for proper load distribution. To do this, the total power of all consumers, which can be found in the technical documentation on them, divide by the nominal voltage. The result is the maximum value of current which needs to flow (I=P/U). Domestic and industrial network are made so that the source voltage was the same on all connectors (sockets).
3
After determining the maximum flow in the power network, locate the wire cross section, from whence the network. Please note that the maximum current density for aluminum wire is 5 A/mm2 and for copper - 8 A/mm2. Install a fuse with a nominal value, minimum maximum circuit current, to avoid burnout of the conductors in the network in case of a short circuit.
4
Example If on a country site it is necessary to calculate electric load, add up the number of power appliances that may be included in the network. Lighting 10 lamps of 100 Watts (1 kW), boiler 4 kW, 0.5 kW refrigerator, microwave oven 2.5 kW, smaller household uses 2 kW. In sum, we obtain the capacity of 10 kW=10,000 watts. As in the home network, the effective voltage value is 220 V, calculate the maximum current in the network I=10000/220≈45,46 A. For network devices use the aluminum conductor section of at least 45,46/5≈10 mm2 or copper 45,46/8≈6 mm2. Install a fuse with a nominal value of at least 46 A.
# Advice 2: How to calculate electrical power
The powerconsumption of those or other electrical device, is measured by wattmeter. But it is not every DIY enthusiast. In its absence it is possible to measure other parameters of the circuit, which includes the consumer, and then based on these data to calculate the power consumption.
You will need
• One or two multimeter
• The meter
• Switch
Instruction
1
In most cases, at home worker, there is only one multimeter that can be switched in turns to the measuring mode current, mode voltage measurement. In this case, first switch the mode to measure voltage, selecting the right limit and type of current. Connecting the multimeter in parallel to the disconnected consumer (if it is powered by direct current - the polarity), plug it in, and then, measuring the voltage across it, remember or write down the result. Disconnect power from the load.
2
Switch the multimeter mode to measure the current, also selecting the right limit and type of current. Connect it in series with the consumer (when powered by direct current also observing polarity). If the starter load current significantly exceeds the worker, sexunderwate multimeter switch and lock it.Turn on the power load. If the multimeter is bridged by a switch, after the release of the consumer desktop mode, open it. Read the result, and then remember or write it down. Disconnect power from the load.
3
If you have two multimeter, inserting them appropriately, it is possible to measure the voltage across the load and current consumed her at the same time. Thus, working with the customer, starting current which is much higher than work, and do not forget to shunt multimeter, playing the role of the ammeter, the switch, opening it only after the load operation mode.
4
Multiplying the voltage to the current, calculate the power.
5
If the load is powered by the lighting network, to measure consumed her power by using the meter. Of course, the counter, which is located in a Cabinet in the stairwell, you will not do, because in order to use it as a power meter had to be turned off in the apartment all the other consumers such as a refrigerator, which is extremely inconvenient. You will have to use a separate meter, and not necessarily sealed and have passed the calibration, since for its intended purpose it will not be used.Enabling the user through the counter, count how many revolutions will it make the drive for a certain period of time. Looking at the front of the counter, how many revolutions of the disc corresponds to one kilowatt-hour, disconnect the load, and then calculate consumed her power according to the formula:P=(n/N)/(t/60) where n is the measured number of revolutions, N is the number of revolutions corresponding to one kilowatt-hour, t - duration of measurement in minutes.
Note
Instead of a multimeter, which plays the role of the ammeter, it is convenient to use a clamp on meter (clampmeter). This device allows you to measure current without breaking the circuit. Switch for protection against high inrush current is not required.
# Advice 3: How to calculate the lamp power
For proper illumination of rooms, corridors or free-standing object, such as aquarium, you need to determine the appropriate type of lamp: number, location and capacity of the installed lamps. There are a few rules, doing that, just to perform this task.
You will need
• roulette, sheet of paper, pen, calculator
Instruction
1
For the General calculation of the lamps use the following formula: P=pS/N, p –power, the specific lighting, measured in Watts per square meter (the average is 20 Watts per square meter), S is the area of the premises, for which this lamp is calculated in square meters and N is the number of lamps.
2
Example: calculate the room measure the length and width of the room. The results obtained (for example, 3.3 meters long and 4.5 meters wide) between multiply and get the area of this room (3,3 × 4,4 = 14,85 square meters). This figure multiply by 20 and divide by the expected number of bulbs in lamps. For example, take the 3 lamps on 2 lamps in each. In this case, 14,85 multiply by 20 and divide by 6 (3×2=6). Get the result, which means that in this case, you have 6 lamps at 49.5 Watts.
3
Can vary the wattage in each lamp, dividing the room into several zones with different lighting. The total power of all lamps in the room should not be less than 297 Watts.
4
In some cases it is necessary to take into account the specifics of the premises, which make the calculation of the total power of the installed lamps. In this case, do the calculation, substituting the value of the coefficient p in the table below:property Type|incandescent Lamp|Halogen lamp|fluorescent svyatetsky room..............30-85....................70-85....................15-22
Living room.....................15-35....................25-35....................7-10
Bedroom......................10-25....................15-17....................4-7
Corridor......................10-20....................10-13....................3-5
Kitchen........................15-40....................30-37....................6-10
Bathroom...............15-30....................22-27....................6-9
Storage room, garage..............12-15....................11-14....................3-5Здесь, to calculate, for example, lighting in the kitchen (area 3 meters square) with the use of fluorescent lamps, take the coefficient of p (average 9) from table, multiply by the kitchen area and if you will be trehrozhkovye lamp, divide by three: 9×3/3 = 9 Watts in each of the three installed in the lamp bulb.
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# problem with list: how to count different elements?
Hello experts!
Im working with graphs.
My code is:
import numpy as np
import networkx as nx
M = np.zeros([6,6])
M[0,2]=1
M[2,0]=1
M[2,3]=1
M[3,2]=1
M[2,1]=1
M[1,2]=1
M[4,5]=1
M[5,4]=1
G=nx.Graph(M)
A=nx.node_connected_component(G,2)
Doing that, A is a list with all the nodes connected with the node 2, ie: A=[0, 1, 2, 3, 2]
1) Why the element '2' is repeated? 2) If, instead, we use A=nx.node_connected_component(G,0), we get A=[0, 1, 2, 3]. In this case: why now the element '0' is not repeated? 3) If we have a list K=[1,2,3,4,1,1,1], and we do P=list(set(K)), we get P=[1,2,3,4] (doing that we can eliminate the repeated elements in the list). But if I do the same with the list A obtained in my code, I get A=[0, 1, 2, 3, 2]. Why this doest work?
Thanks a lot
edit retag close merge delete
Sort by ยป oldest newest most voted
Hi,
This is a problem with Sage integers fighting with numpy integers
sage: A[2] == A[4]
False
sage: type(A[2])
<type 'sage.rings.integer.Integer'>
sage: type(A[4])
<type 'numpy.int64'>
You can solve the issue working only with Sage integers as follows
sage: M = matrix(6)
sage: M[0,2]=M[2,0]=M[2,3]=1
sage: M[3,2]=M[2,1]=M[1,2]=1
sage: M[4,5]=M[5,4]=1
sage: G = Graph(M)
sage: A = G.connected_component_containing_vertex(2)
sage: A
[0, 1, 2, 3]
(using networx is fine as well)
There is already an old ticket related to that problem on the Sage trac server: #13386: comparison of Sage integer with Numpy integer
EDIT: if you want to solve it on your example, use
sage: nx.node_connected_component(G, np.int(2))
[0, 1, 2, 3]
If you use only numpy and networkx, there is no need to use Sage. Just use the standard Ipython you will have less troubles.
Vincent
more
Thanks a lot Vincent. The problem is that in my full-code, 'M' is an numpy array with NxN element. How can I fix my problem keeping workin this this Numpy array? Thanks
( 2014-07-10 17:02:56 -0500 )edit
I updated my answer accordingly. But I do not see the point of using numpy and networkx inside Sage.
( 2014-07-12 14:42:02 -0500 )edit
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## 21.4.16
### Generating powers of k mod n
Previously I showed an algorithm for generating powers of 2 mod n without using multiplication or exponentiation. The algorithm can easily be modified to generate powers of any integer k mod n where the greatest common divisor of k and n is equal to 1.
The first part of the algorithm for generating powers of 2 mod n required listing all even integers smaller than n followed by all odd integers smaller than n, which is simply the 2nd row of the multiplication table of Zn since each entry at this row and a column j > 0 is equal to 2+aj mod n and if GCD(2, n) = 1 then there exists an integer k < n such that 2*k = 1 mod n
For example, below are a few multiplication tables of Zn for n = 5, 7, 11:
Each entry aij = i * j mod n
Note that in general for an entry aij at row i and column j, if aij == (n-i), then the end of the ith row has been reached and also if i+ aij-1> n then aij = (i+aij-1) - n
For example, below is the multiplication table of Zn for n = 35;
Let i = 3. Each entry aj at the 3rd row is generated as aj = 3 + aj-1 while aj is not equal to (35-3) since 32 is the last entry of the 3rd row. Furthermore, if (3 + aj-1) > 35 then aj = (3 + aj-1) - 35
The other function of the algorithm for generating powers of 2 mod n was the following. Given an array of the ith row of the multiplication table:
a. Look up the value at initial index;
b. Make that value the initial index;
c. Save and Repeat a and b until the value equals 1
This function can be applied in general for generating powers of any k mod n as long as GCD(k,n) = 1
With this in mind the generalized algorithm for generating powers of k mod n where GCD(k,n) = 1
becomes:
``````/* -------------------------------------------------
This content is released under the GNU License
http://www.gnu.org/copyleft/gpl.html
Author: Marina Ibrishimova
Version: 1.0
Purpose: Generate powers of k mod n,
generate the unique portion of row at k
of the exponentiation table of Z sub n
---------------------------------------------------- */
function powers_of_k_mod(n,k)
{
var index = 0;
var perm_slot = k;
var count = 1;
var perm = new Array(); var powers = new Array();
perm = generate_permutation(n, k);
powers.push(1);
powers.push(perm_slot);
while(perm_slot != 1)
{
index = perm_slot;
perm_slot = perm[index];
powers.push(perm_slot);
}
return powers;
}
/* -----------------------------------------------
generate kth row of the multiplication table
of Z sub n
-------------------------------------------------- */
function generate_permutation(n, k)
{
var index = 0;
var permutation = new Array();
permutation.push(0);
while(index!=(n-k))
{
index = index + k;
if (index > n) {
index = index - n;
}
permutation.push(index);
}
return permutation;
}
``````
Here's a point and click implementation of the algorithm above.
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×
# Transformer Exam Questions, NETA Level 2
1. Junior Member
Join Date
May 2017
Posts
6
Reputation
## Transformer Exam Questions, NETA Level 2
Can someone help me with these two questions:
What is the theoretical maximum symmetrical fault current that would be available at the secondary terminals of a 3-phase 12,470-480Y/277V, 1000kva, 7.0% impedance transformer?
A given 1000kva wye-wye transformer has a phase voltage of 277; what would you expect the full load line current to measure?
2. Member
Join Date
Jun 2015
Posts
25
Reputation
Originally Posted by adamstraub
Can someone help me with these two questions:
What is the theoretical maximum symmetrical fault current that would be available at the secondary terminals of a 3-phase 12,470-480Y/277V, 1000kva, 7.0% impedance transformer?
A given 1000kva wye-wye transformer has a phase voltage of 277; what would you expect the full load line current to measure?
i got the 1st question on my practice exam, and got it wrong also. waiting for answer too.....
3. Junior Member
Join Date
Jan 2019
Posts
1
Reputation
Originally Posted by adamstraub
Can someone help me with these two questions:
What is the theoretical maximum symmetrical fault current that would be available at the secondary terminals of a 3-phase 12,470-480Y/277V, 1000kva, 7.0% impedance transformer?
A given 1000kva wye-wye transformer has a phase voltage of 277; what would you expect the full load line current to measure?
This quick calculation can help you determine the fault current on the secondary of a transformer for the purpose of selecting the correct overcurrent protective devices that can interrupt the available fault current.
Fault Current = Full Load Amps / % Impedance (Z)
Example: Calculate the maximum fault current for a transformer rated 13.8kV-480Y/277V 1000kVA 5.75%Z
Step 1: Determine Full Load Amps (FLA)
You can determine the Full Load Amps of a transformer with the following formula: FLA = VA / L-L Voltage x 1.732, so using the example above we get FLA = 1000000 / 480 x 1.732 or 1000000 / 831.36 = 1202.84 (note the conversion from kVA to VA, 1000 x 1000 = 1000000).
FLA = 1203 amperes
Step 2: Divide FLA by Impedance
The next step is to simply divide the number obtained in step 1 by the transformer nameplate impedance. Using the example above we get: 1203 / 0.0575 = 20921.73 (REMEMBER TO CONVERT PERCENT TO DECIMAL, if 100% = 1.00 then 5.75% = 0.0575).
FC = 20,922 amperes
If a main breaker was to be installed in the circuit on the secondary of the transformer used in this example, it would have to have an Interrupting Rating greater than 21,000A.
### Help and Support
You are viewing the archives. Enjoy new features and join the conversation at wiki.testguy.net
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How to Keep Columns When Grouping/Summarizing - ITCodar
# How to Keep Columns When Grouping/Summarizing
## Applying group_by and summarise on data while keeping all the columns' info
Here are two options using a) `filter` and b) `slice` from dplyr. In this case there are no duplicated minimum values in column `c` for any of the groups and so the results of a) and b) are the same. If there were duplicated minima, approach a) would return each minima per group while b) would only return one minimum (the first) in each group.
a)
``> data %>% group_by(b) %>% filter(c == min(c))#Source: local data frame [4 x 4]#Groups: b## a b c d#1 1 a 1.2 small#2 4 b 1.7 larg#3 6 c 3.1 med#4 10 d 2.2 med``
Or similarly
``> data %>% group_by(b) %>% filter(min_rank(c) == 1L)#Source: local data frame [4 x 4]#Groups: b## a b c d#1 1 a 1.2 small#2 4 b 1.7 larg#3 6 c 3.1 med#4 10 d 2.2 med``
b)
``> data %>% group_by(b) %>% slice(which.min(c))#Source: local data frame [4 x 4]#Groups: b## a b c d#1 1 a 1.2 small#2 4 b 1.7 larg#3 6 c 3.1 med#4 10 d 2.2 med``
## How can I keep columns when grouping/summarizing?
You can do this using `base R`
``aggregate(data=df1,B~.,FUN = mean)``
## Grouping and summarizing by keeping other columns in R
Try
``summarize(MM_group, rank = which.max(Yield), Year_rank = Year[rank], County_rank = County[rank])``
## Applying group_by and summarise(sum) but keep columns with non-relevant conflicting data?
Here's the `data.table` solution, I'm assuming you want the `mean()` of Proportion, since these grouped proportions are likely not additive.
``setDT(df)df[, .(Type =paste(Type,collapse="_"), Proportion=mean(Proportion),N= sum(N),C=sum(C)), by=.(Label,Code)] [order(Label)] Label Code Type Proportion N C1: 203c c wholefish 1.000000 1 12: 203c a flesh 1.000000 2 23: 204a a flesh_formula 0.499995 8 84: 204a b fleshdelip_formuladelip 0.499995 10 105: 204a c formula_wholefish 0.499995 16 166: 204a d formuladelip_wholefishdelip 0.499995 18 18``
I'm not sure this is the cleanest `dplyr` solution, but it works:
``df %>% group_by(Label, Code) %>% mutate(Type = paste(Type,collapse="_")) %>% group_by(Label,Type,Code) %>% summarise(N=sum(N),C=sum(C),Proportion=mean(Proportion))``
Note the key here is to re-group once you create the combined `Type` column.
`` Label Type Code N C Proportion <fctr> <chr> <fctr> <int> <int> <dbl>1 203c flesh a 2 2 1.0000002 203c wholefish c 1 1 1.0000003 204a flesh_formula a 8 8 0.4999954 204a fleshdelip_formuladelip b 10 10 0.4999955 204a formula_wholefish c 16 16 0.4999956 204a formuladelip_wholefishdelip d 18 18 0.499995``
## Applying group_by and summarise(sum) but keep a large number of additional columns
We can create a column with `mutate` and then apply `distinct`
``library(dplyr)df %>% group_by(location) %>% mutate(count = sum(count)) %>% select(-date) %>% distinct(location, important_1, important_30, .keep_all = TRUE)``
If there are multiple column names, we can also use `syms` to convert to `symbol` and evaluate (`!!!`)
``df %>% group_by(location) %>% mutate(count = sum(count)) %>% select(-date) %>% distinct(location, !!! rlang::syms(names(.)[startsWith(names(.), 'important')]), .keep_all = TRUE)``
## keep columns after summarising using tidyverse in R
We can use `slice_max` to return the full row based on the `max` value of 'year' for each grouping block
``library(dplyr)dat %>% group_by(group, month) %>% slice_max(year)``
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BrainDen.com - Brain Teasers
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# Blind man's jigsaw puzzle
## Question
A blind old man loves jigsaw puzzles. He starts them by picking a piece at random and putting it down. He then picks another piece at random and tries to attach it to each side of the piece he started with (trying all four rotations and flipping it over) and repeats until the piece fits. Then he picks another piece at random and tries to attach it to the part of the puzzle he already has. He continues doing this until the puzzle is solved. What is the expected number of pieces he will try in order to solve an m by n puzzle?
## 7 answers to this question
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He will try m X n pieces as that is the number of pieces in the puzzle. Some pieces he will probably need to try more than once for other parts of the puzzle but that was not the question now was it?
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He will try m X n pieces as that is the number of pieces in the puzzle. Some pieces he will probably need to try more than once for other parts of the puzzle but that was not the question now was it?
Technically, you're right. What i mean to ask though is how many times will he pick up a piece.
Note: When a piece does not fit, he puts it back into the pile and may pick it up again immediately. If so, it still counts as picking up another piece.
The solution I found is recursive. I have closed forms for m=1 and m=2. I'm still working on generalizing it.
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the chances of success are determined by the perimeter. with 1 piece, you have a perimeter of 4. with 8 pieces, you could potentially have many different perimeters; ranging from 1 long perimeter of 18, or a more stout one of 12. so i don't really see any good way to analyze the problem other than running a bunch of simulations. even this may not be very helpful.
Edited by phil1882
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The solution would be straightforward, but...
From OP, each jigsaw puzzle piece can connect to four other pieces.
After picking the first bit at random, there may be 4 pieces out of mn - 1 that connect to it. With replacement, the average number of picks before getting one of those is (mn - 1)/4. Whereafter there are 6 exposed sides yielding the average of (mn - 2)/6.
Thus we get the series: (mn-1)/4 + (mn-2)/6 + (mn-3)/8 + ... + 1 for the average number of piece picking.
We could work with this series and try finding a closed-form expression for it.
However, not all pieces are equal. There are edge pieces, which connect to others only on 3 sides. (2m+2n-8 of those.) And there are 4 corner pieces, which connect with only 2 others.
So if the blind man happened to pick a corner piece first at the probability of 4/(mn), then the first term of the series would be (mn-1)/2. Also, the number of available sides would be increased by 1 instead of 2, when connecting an edge piece to the middle pieces build up.
To help us solving this problem, the blind man must first put aside all the edge and corner pieces by feeling straight edges with his fingers. Then he should start working on all the middle pieces.
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Actually, it's more complicated. Like Phil1882 noted.
Fitting another piece may increase or decrease the existing perimeter by anything from +2 to -4.
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A matrix showing the expected number of draws necessary to complete an
n by m (n,m<11) blind jigsaw using 1,000,000 iterations for each (n,m):
001.00 002.00 003.67 006.00 009.00 012.66 017.01 022.00 027.67 033.99
002.00 004.50 008.00 012.51 018.00 024.49 031.99 040.54 050.02 060.50
003.67 008.00 013.66 020.66 028.93 038.54 049.46 061.72 075.33 090.19
006.00 012.51 020.66 030.39 041.78 054.76 069.38 085.62 103.53 123.08
009.00 018.00 028.93 041.78 056.49 073.14 091.75 112.26 134.75 159.05
012.66 024.49 038.54 054.76 073.14 093.72 116.62 141.59 168.83 198.33
017.01 031.99 049.46 069.38 091.75 116.62 143.85 173.69 206.02 240.83
022.00 040.54 061.72 085.62 112.26 141.59 173.69 208.56 246.02 286.52
027.67 050.02 075.33 103.53 134.75 168.83 206.02 246.02 289.33 335.68
033.99 060.50 090.19 123.08 159.05 198.33 240.83 286.52 335.68 388.04
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Below are closed-form expressions for 1xn and 2xn cases
For 1xn, expected number of pieces is (n^2+2)/3
For 2xn, expected number of pieces is (n^2+2n+1)/2
I don't believe there is a polynomial for 3xn because I found the exact values for 3x3 and 3x4 and their denominators are huge. I could be wrong though.
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# 10 digit number puzzle
A 10 digit number has it first digit equals to the numbers of 1's, second digit equals to the numbers of 2's, 3rd digit equals to the numbers of 3's .4th equals number of 4’s…till 9th digit equals to the numbers of 9's and 10th digit equals to the number of 0's. what is the number?
This question is related to Infosys Interview
#### vidya sagar
• May 23rd, 2006
the no is 6000100012
#### aruna_sakhile Profile Answers by aruna_sakhile
• May 24th, 2006
Ans:
1 2 3 4 5 6 7 8 9 0
1 0 0 0 0 0 1 0 0 7 (The no of Zeros in 10th digit place)
#### k srujana Profile Answers by k srujana Questions by k srujana
• May 24th, 2006
i think the answer is 1000000008
#### dangerous Profile Answers by dangerous
• May 25th, 2006
the no is 6000100012.let me clear ur doubt
total no.of 1's in above no=2(in 1st digit );no.of 2's=1(in 2nd digit);no.of 3's,4's,5's=0;no.of 6's=1(6th digit);no.of 7's,8's nd 9's=0;in 10th digit no.of 0's=6;
vidya sagar.
#### CA Alpesh Tated
• Apr 19th, 2013
2100010006
#### Gowda Shivamurthy
• Oct 25th, 2014
6210001000
#### pranjay sagar
• Dec 24th, 2014
9000000000
#### soubhik
• Dec 29th, 2014
9000000000...only 10th digit contains no.of total zeros dats 9
#### soubhik
• Dec 29th, 2014
Sorry the no is 1000000008...coz 10th digit resembles unit place...
#### Sumit
• Dec 30th, 2014
2100010006
#### sumit
• Dec 30th, 2014
1st digit is last most digit
#### Dinesh
• Jan 8th, 2015
You can understand it as
1 2 3 4 5 6 7 8 9 10
2 1 0 0 0 1 0 0 0 6
Here total no. of 1s=2, total no. of 2s=1, total no. of 6s=1 & total no. of 3s,4s 5s,7s,8s,9s=0
#### Mano
• Aug 22nd, 2018
This is when first digit is number of zeros. The question for your answer is
Find a 10-digit number where the first digit is how many zeros in the number, the second digit is how many 1s in the number etc. until the tenth digit which is how many 9s in the number.
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# CIS 4360 Final
Alice and Bob use the Diffie-Hellman key exchange with common prime q = 11 and generator a = 2.
If the private key of Alice is X A = 6 what is her public key Y A?
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The ElGamal encryption scheme is based on the Diffie-Hellman key exchange. If q is the common modulus and a is a generator, then the public key of Alice is (Y A, q), where Y A = a^XA modq, XA backwards E Zq, and the private key is: (X A, q).
To encrypt a message m, 0 < m < q, Bob computers C1= a^k (modq), k backwards E Zq, and C2 = YA^k times m (modq),
Show how this is down for the special case: q = 11, a = 2, X A = 3, k = 2, m = 6. What is the public key Y A of Alice?
The ElGamal encryption scheme is based on the Diffie-Hellman key exchange. If q is the common modulus and a is a generator, then the public key of Alice is (Y A, q), where Y A = a^XA modq, XA backwards E Zq, and the private key is: (X A, q).
To encrypt a message m, 0 < m < q, Bob computers C1= a^k (modq), k backwards E Zq, and C2 = YA^k times m (modq),
Show how this is down for the special case: q = 11, a = 2, X A = 3, k = 2, m = 6. What is the encryption (C1,C2) of message m = 6?
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Questions tagged [j-invariant]
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Geometric interpretation of j-invariants of supersingular elliptic curves
In the classical theory of Complex Multiplication, one considers elliptic curves with an endomorphism ring larger than the integers. In this theory, it's possible to determine the j-invariants of all ...
146 views
Twisted modular equation
Let $\gamma_2(\tau)=j(\tau)^{1/3}$. The modular equation shows that the functions $$j\left(\frac{a\tau+b}{c\tau+d}\right),\qquad ad-bc=n$$ are integral over $\mathbf Z[j]$. Under what conditions is ...
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The degree of the cube root of the $j$-invariant
I have a question which is fairly elementary, but first I must provide relevant context. Without it, my question would seem rather arbitrary and scarcely interesting. Note also that my question can be ...
4k views
There's something strange about $\sqrt{\big(j(\tau)-1728\big)d}$
Given discriminant $d$ and j-function $j(\tau)$, I was looking at, $$F(\tau) = \sqrt{\big(j(\tau)-1728\big)d}$$ which appears in Ramanujan-type pi formulas. Let $C_d$ be the odd prime factors of the ...
239 views
Asymptotic Formula of the coefficients of the q-expansion of the J-Invariant
I'm currently writing my master thesis about the j-invariant and his q-expansion. Now i have the result that the growth of the coefficients is asymptotically c(n) \sim \frac{e^{4\pi \sqrt{n}}}{\...
144 views
From an eigenfom with $\mathbf{Q}$-coefficients to $j$-invariants
Given a cuspidal, classical eigenform $f\in S_2(\Gamma_0(N))$ of weight $2$ and with $\mathbf{Q}$-coefficients is there a way of describing the set $J_f$ of $j$-invariants of the elliptic curves lying ...
$j$-invariants of elliptic curves over finite fields
Let $K$ be a finite field, and $\overline{K}$ its algebraic closure. It is well known that two curves are isomorphic over $\overline{K}$ if and only if they have the same $j$-invariant. If two such ...
I learned of the following example in a recent seminar: if $j(\tau)$ denotes the usual $j$-invariant, and $\alpha = (-1+i\sqrt{163})/2$, then \begin{align*} \frac{j(i)}{1728} &= 1 \\ \frac{-j(\...
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# DIRECTIONS:FACTOR EACH OF THE FOLLOWING POLYNOMIALS.ANSWER THE QUESTIONS THAT FOLLOW.1.2x(squared)-8x2.-3s(squared) + 93.4x + 20x(squared)4.4x + 20x(squared)5.s(squared) + 8s + 126.x(squared) + 10x + 217.x(squared) + 5x -68.4r(squared) + 20r + 259.9t(squared) - 410. 2x(squared) + 3x + 14QUESTIONS:1. How did you factor each polynomial?2.what factoring technique did you use to come up with the factors of each polynomial? explain how you used this technique.3.how would you know if the factors you got are the correct ones?4.which of the polynomials did you find difficult to factor? why?
1
by DreiSky
#3 and #4 are the same?
2014-07-02T00:54:17+08:00
### 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.
1) Using the different factoring techniques
2) Items 1, 3. Factoring the greatest common factor
2, 9. Difference of two squares
5,6,7,8. Reverse FOIL method (looked for two binomials and used FOIL method to come up with the original expression)
3) To check if they are the right factors, use distribution or FOIL method.
4) #10 because it is not factorable.
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## Backpropagation from scratch in Julia (part II: derivation and implementation)
get the code from here
This is the second post of the series describing backpropagation algorithm applied to feed forward neural network training. In the last post we described what neural network is and we concluded it is a parametrized mathematical function. We implemented neural network initialization (meaning creating a proper entity representing the network – not weight initialization) and inference routine but we never made any connection to the data itself. In this post we will make such a connection and we will express meaning of parametrization “goodness” in terms of training data and network output.
---
## Solving logistic regression problem in Julia
In this post we will try to implement gradient descent approach to solve logistic regression problem.
Please note this is mainly for educational purpose and the aim here is to learn. If you want to “just apply” logistic regression in julia please check out this one
Logistic regression is a mathematical model serving to predict binary outcome (here we consider binary case) based on set of predictors. Binary outcome (meaning outcome with two possible values, like physiognomical gender spam/not spam email or fraud/legit transaction) is very often called target variable and predictors can be also called features. The latter name is much more intuitive as it is closer to Earth, so to say, it suggests we deal with some sort of objects with known features and we try to predict binary feature that is unknown at the time of prediction. The main idea is to predict the target given set of features based on some training data. Training data is a set of objects for which we know the true target.
So our task is to derive a function that will later serve as a 0/1 labelling machine – mechanism to produce (hopefully) correct target for given object described with features. The class of functions we choose to derive the target is called the model. Such a class is parametrized with set of parameters and the task of learning is in fact to derive these parameters to let our model perform well. Performing well is on the other hand measured with yet another function called goal function. The goal function is what we optimize when we learn parameters for a model. It involves model parameters and training data. It is a function of model parameters and training data with known labels. So the problem of machine learning can be (ignorantly of course) reduce to the problem of estimating set of parameters of given class of functions (model) to minimize given goal function.
---
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# GCSE Edexcel Statistics Coursework
Watch
Announcements
#1
Has anyone started the GCSE Statistics coursework? I think it's something about cars? I have no idea what to do? Can someone doing it or who's done it please help me by like providing a writing frame and what things to include, how to structure it? I'm aiming for A*. My teacher is giving us minimal support. I don't even know how to write coursework for Maths.
0
#2
anyone?
0
7 years ago
#3
Edexcel?
Posted from TSR Mobile
0
#4
(Original post by Some black lad)
Edexcel?
Posted from TSR Mobile
My exam board. I started my Planning today and still have no idea what to do.
The theme is cars. I chose: What factors affect the price of a used car?
My hypotheses are:
That the more mileage a car has will decrease its price
The spread of cars will be a normal distribution (Have no idea what to do with this, but was told I'd get high marks)
The distribution of diesel cars will be greater than that of petrol cars
Older cars will have a lower price
0
#5
Can someoen help?
0
7 years ago
#6
Are u doing edexcel or not
Posted from TSR Mobile
0
#7
(Original post by Some black lad)
Are u doing edexcel or not
Posted from TSR Mobile
I am
0
7 years ago
#8
There's a defined mark scheme for the plan alone, which counts for 25% (of the 25% coursework).
This will be done entirely in class and is important. You can message me if you like, but just for example You need to state
Hypotheses (maybe 2)
Populations
Variables -
How you will select sample data
What charts you will use
What analysis tools you will use
How you could extend your study
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https://community.intel.com/t5/Intel-Moderncode-for-Parallel/parallel-code-running-slower-than-serial-code/td-p/1116257
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Intel® Moderncode for Parallel Architectures
Support for developing parallel programming applications on Intel® Architecture.
parallel code running slower than serial code
Beginner
675 Views
I tried to write a simple code to repeatedly compute greek pi by simulation and then compare the performance of the serial vs parallelized version of the code. To my great surprise the parallel code was slower ! Since I am a beginner I suspect I am not grasping some key aspects of parallel programming. Below I report the whole code. I am working with a version of an Intel 6700 processor with 4 cores.
I don't know if this forum is for this kind of questions, but thanks in advance for any help youc an give me.
PROGRAM:
program pigreco
! This program computes the value of greek pi "n" times using simulation
! Each time the computation is performed using "m" draws
! The computation is carried out by the subroutine "montec"
! In the end the average of th n simulations is computed and printed on screen
implicit none
integer i,n,m
parameter(n=3200,m=250000)
double precision greekpi(n),outp,avpi,den
double precision start_time,end_time
parameter (chunk=400)
call CPU_TIME(start_time)
!\$omp parallel private(i)
!\$omp do schedule(dynamic,chunk)
do i = 1,n
call montec(m,outp)
greekpi(i) = outp
outp = 0.0d0
!print*, i,greekpi(i)
end do
!\$omp end do
!\$omp end parallel
call CPU_TIME(end_time)
print*, 'average value of greek pi'
den = n
avpi = sum(greekpi)/den
print*, avpi
print*, 'running time'
print*, end_time - start_time
end program
subroutine montec(ndr,sol)
implicit none
integer ndr
double precision sol
integer i
double precision xr1,xr2,yv(ndr),sumsq,totins,tot
totins = 0.0d0
do i = 1,ndr
call RANDOM_NUMBER(xr1)
call RANDOM_NUMBER(xr2)
sumsq = xr1**2.0d0 + xr2**2.0d0
if (sumsq.le.1.0d0) then
totins = totins + 1.0d0
end if
end do
tot = ndr
sol = totins/tot
sol = 4.0d0*sol
return
end subroutine
5 Replies
Employee
675 Views
Variable "outp" should be private.
Beginner
675 Views
I have tried both to make "outp" private and change "dynamic" to "static", in the latter case both letting the computer set the size of each chunk to pass to a thread and setting it myself. Neither worked: the code is still runs much slower than the serial version.
Black Belt
675 Views
Are you sure that the RANDOM_NUMBER function is thread-safe?
Most random number generators update some internal state after computing a new number. If this is protected by a lock, then the threads will have to process this function one at a time, and the overhead of handling the lock may be larger than the savings in any other parallel work.
Valued Contributor II
675 Views
>>...Most random number generators update some internal state after computing a new number. If this is protected by a lock, >>then the threads will have to process this function one at a time, and the overhead of handling the lock may be larger than >>the savings in any other parallel work. It could be easily verified and modify codes as follows: ... totins = 0.0d0 do i = 1,ndr ! call RANDOM_NUMBER(xr1) ! call RANDOM_NUMBER(xr2) xr1 = 1.0 xr2 = 2.0 sumsq = xr1**2.0d0 + xr2**2.0d0 if (sumsq.le.1.0d0) then totins = totins + 1.0d0 end if end do ... Even if the value of PI will be incorrect it should be faster then a single threaded processing.
Black Belt
675 Views
RANDOM_NUMBER is thread-safe, however, in order to be thread-safe, it uses a critical section (serializing section). In cases like this what you do is call RANDOM_NUMBER outside the parallel region with an argument that is an array (not scalar). The size of the array would typically be the iteration count of the parallel loop that follows. Then within the parallel loop, to get the random number, you index the array with the loop index. Using the array (harvest) format of RANDOM_NUMBER your program crosses the critical region once as opposed to on each iteration.
Note, in your case you would include:
```double precision harvest(ndr*2)
...
call RANDOM_NUMBER(harvest)
...
!\$omp parallel
...
!\$omp do
...
call montec(m,outp,harvest) ! add harvested array of random numbers
...
subroutine montec(ndr,sol,harvest)
...
double precision harvest(ndr*2)
...
do i = 1,ndr
xr1 = harvest((i-1)*2+1)
xr2 = harvest((i-1)*2+2)
```
Jim Dempsey
...
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# Operating Profit - definition & overview
Contents
## What is operating profit?
Operating Profit is the earnings from normal business activities before subtracting interest and taxes, also known as operating income.
Operating Profit, also known as operating income or operating earnings, is a crucial term in the world of small businesses. It's a key indicator of a company's profitability and financial health, and understanding it can be a game-changer for business owners. Operating Profit is the profit a company makes from its core business operations, excluding deductions of interest and taxes. It's a measure of the profits a company generates from its primary business activities, not including any income or expenses from non-operating activities.
Operating Profit is an essential metric because it directly reflects the efficiency of a company's operations. It's a clear indicator of how well a company's management is utilising resources to generate profits. For small businesses, this is particularly important as it can highlight areas of inefficiency that need to be addressed. Operating Profit is also a key factor in determining a company's net income, which is the final profit figure that appears on the bottom line of the income statement.
## Calculating Operating Profit
The calculation of Operating Profit is straightforward. It's derived from the gross profit of a company, which is the total revenue minus the cost of goods sold (COGS). From the gross profit, operating expenses are deducted. These expenses include rent, salaries, utilities, depreciation, and other costs associated with running the business. The resulting figure is the Operating Profit.
It's important to note that non-operating income and expenses, such as interest and taxes, are not included in the calculation of Operating Profit. This is because these items are not directly related to the core business operations. By excluding these items, Operating Profit provides a clearer picture of the profitability of the company's primary business activities.
### Formula for Operating Profit
The formula for calculating Operating Profit is as follows:
Operating Profit = Gross Profit - Operating Expenses
Or alternatively:
Operating Profit = Total Revenue - Cost of Goods Sold - Operating Expenses
### Example of Operating Profit Calculation
Let's consider a hypothetical small business in Australia. The business has total revenue of \$500,000. The cost of goods sold is \$200,000, and the operating expenses amount to \$150,000. Using the formula above, the Operating Profit would be calculated as follows:
Operating Profit = \$500,000 - \$200,000 - \$150,000 = \$150,000
## Importance of Operating Profit
Operating Profit is a vital measure of a company's profitability. It shows how much profit a company makes from its core business operations, before the deduction of interest and taxes. This makes it a more accurate indicator of a company's operational efficiency than net profit, which includes non-operating income and expenses.
For small businesses, understanding Operating Profit is particularly important. It can help business owners identify areas of inefficiency and make informed decisions about how to improve profitability. For example, if a company's Operating Profit is decreasing over time, it may indicate that the company's operating expenses are rising faster than its revenue. This could signal a need for cost-cutting measures or strategies to boost revenue.
### Operating Profit Margin
The Operating Profit Margin is a related metric that expresses Operating Profit as a percentage of total revenue. It's calculated by dividing Operating Profit by total revenue and multiplying by 100. The Operating Profit Margin provides a measure of a company's profitability per dollar of revenue, which can be useful for comparing the profitability of different companies or industries.
For small businesses, a high Operating Profit Margin can be a sign of strong operational efficiency. It indicates that a large portion of the revenue is being converted into profit, which can be reinvested in the business or distributed to shareholders. Conversely, a low Operating Profit Margin may suggest that a company's operating expenses are too high relative to its revenue.
## Operating Profit vs. Net Profit
While both Operating Profit and Net Profit are measures of a company's profitability, they are not the same. Operating Profit only considers income and expenses from core business operations, while Net Profit includes all income and expenses, including those from non-operating activities such as interest and taxes.
This distinction is important because it allows business owners to separate the performance of their core business operations from the effects of financing and tax strategies. For example, a company may have a high Operating Profit but a low Net Profit if it has high interest expenses or tax liabilities. Conversely, a company may have a low Operating Profit but a high Net Profit if it has significant non-operating income.
### Understanding the Difference
Understanding the difference between Operating Profit and Net Profit can help business owners make more informed decisions. For example, if a company's Operating Profit is strong but its Net Profit is weak, it may indicate that the company needs to review its financing or tax strategies. Conversely, if a company's Operating Profit is weak but its Net Profit is strong, it may suggest that the company is overly reliant on non-operating income and needs to improve its core business operations.
Furthermore, comparing Operating Profit and Net Profit can provide insights into a company's financial stability. A company with a high Operating Profit but a low Net Profit may be at risk if its non-operating income sources dry up. On the other hand, a company with a low Operating Profit but a high Net Profit may be more resilient to changes in market conditions, as it has multiple income streams.
## Improving Operating Profit
Improving Operating Profit is a key goal for many small businesses. There are two main ways to achieve this: increasing revenue or reducing operating expenses. Both strategies can be effective, but they require careful planning and execution.
Increasing revenue can be achieved through strategies such as expanding into new markets, launching new products or services, or improving marketing efforts. However, these strategies often require upfront investment and carry risks. Therefore, it's important for business owners to conduct thorough market research and financial analysis before pursuing these strategies.
### Reducing Operating Expenses
Reducing operating expenses is another effective strategy for improving Operating Profit. This can be achieved through cost-cutting measures such as negotiating better deals with suppliers, improving operational efficiency, or reducing waste. However, it's important for business owners to ensure that cost-cutting measures do not compromise the quality of their products or services, as this could negatively impact revenue.
Furthermore, reducing operating expenses can also involve making tough decisions, such as laying off staff or closing underperforming branches. These decisions should not be taken lightly, as they can have significant impacts on the business and its employees. Therefore, it's crucial for business owners to consider all options and seek professional advice before making these decisions.
## Conclusion
Operating Profit is a crucial metric for small businesses. It provides a clear picture of a company's operational efficiency and profitability, and can help business owners make informed decisions about how to improve their business. Whether it's through increasing revenue, reducing operating expenses, or a combination of both, improving Operating Profit can lead to increased financial stability and growth for small businesses.
Remember, the journey of improving your Operating Profit is a marathon, not a sprint. It requires patience, persistence, and a deep understanding of your business operations. But with the right approach and mindset, you can turn your small business into a profitable and sustainable enterprise. Here's to your success!
## Why waste time on financial admin when Thriday can do it for you?
Already have an account? Login here
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# If k is an integer such that 56 < k < 66, what is the value
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If k is an integer such that 56 < k < 66, what is the value [#permalink]
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If k is an integer such that 56 < k < 66, what is the value of k ?
(1) If k were divided by 2, the remainder would be 1.
(2) If k + 1 were divided by 3, the remainder would be 0.
[Reveal] Spoiler: OA
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Re: If k is an integer such that 56 < k < 66, what is the value [#permalink]
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If k is an integer such that 56 < k < 66, what is the value of k ?
(1) If k were divided by 2, the remainder would be 1 --> k is an odd number, thus it could be 57, 59, 61, 63, or 65. Not sufficient.
(2) If k + 1 were divided by 3, the remainder would be 0 --> k is 1 less than a multiple of 3, thus it could be 59, 62, or 65. Not sufficient.
(1)+(2) k could still take more than one value: 59 or 65. Not sufficient.
Answer: E.
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Re: If k is an integer such that 56 < k < 66, what is the value [#permalink]
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DivyanshuRohatgi wrote:
Bunuel wrote:
If k is an integer such that 56 < k < 66, what is the value of k ?
(1) If k were divided by 2, the remainder would be 1 --> k is an odd number, thus it could be 57, 59, 61, 63, or 65. Not sufficient.
(2) If k + 1 were divided by 3, the remainder would be 0 --> k is 1 less than a multiple of 3, thus it could be 59, 62, or 65. Not sufficient.
(1)+(2) k could still take more than one value: 59 or 65. Not sufficient.
Answer: E.
Hi Bunuel
Could you please explain the last part , I am still not able to figure out how E is the answer
Regards
From (1) k can be: 57, 59, 61, 63, or 65.
From (2) k can be: 59, 62, or 65.
Thus k can be 59, or 65. Two different answers. Hence not sufficient.
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k is an integer such that 56 < k < 66 which means k=(57,58,59,60,61,62,63,64,65)
Now
Statement 1
If k were divided by 2, the remainder would be 1. which means k is odd so possible values of k=(57,59,61,63,65), not sufficient
Statement 2
If k + 1 were divided by 3, the remainder would be 0 so the possible values of k+1 are 60,63,66 so possible values of k=(59,62,65), insufficient
Combining 1 and 2
we still get 2 values 59 and 65 so insufficient
Answer is E
Please consider a kudos if you get the explanation
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21 Oct 2013, 19:53
Bunuel wrote:
If k is an integer such that 56 < k < 66, what is the value of k ?
(1) If k were divided by 2, the remainder would be 1 --> k is an odd number, thus it could be 57, 59, 61, 63, or 65. Not sufficient.
(2) If k + 1 were divided by 3, the remainder would be 0 --> k is 1 less than a multiple of 3, thus it could be 59, 62, or 65. Not sufficient.
(1)+(2) k could still take more than one value: 59 or 65. Not sufficient.
Answer: E.
Hi Bunuel
Could you please explain the last part , I am still not able to figure out how E is the answer
Regards
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
If k is an integer such that 56 < k < 66, what is the value of k ?
(1) If k were divided by 2, the remainder would be 1.
(2) If k + 1 were divided by 3, the remainder would be 0.
In the original condition, there is 1 variable(k), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), k=2t+1=57,59,61...., which is not unique and not sufficient.
For 2), k+1=3m, k=3m-1=59, 62, 65, which is not unique and not sufficient.
When 1) & 2), n=59,65, which is not unique and not sufficient. Therefore, the answer is E.
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: If k is an integer such that 56 < k < 66, what is the value [#permalink]
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11 May 2016, 02:53
the most common mistake while solving this question is -
frm stat 1 and stat 2
people will compare the values of k = 57 59 61 63 65 (from stat 1 )
to the values of k+1 = 60 63 66 (from stat 2 )
and will end up choosing 63 as the value of K which is WRONG
but from stat 2
the values of k will be 59 62 and 65.
so from 1 and 2 the values will be 59 and 65...not sufficient.
answer - E
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14 May 2016, 05:59
Walkabout wrote:
If k is an integer such that 56 < k < 66, what is the value of k ?
(1) If k were divided by 2, the remainder would be 1.
(2) If k + 1 were divided by 3, the remainder would be 0.
Solution:
We are given that k is between 56 and 66. We must determine the value of k.
Statement One Alone:
If k were divided by 2, the remainder would be 1.
This means k must be an odd number. However, since 56 < k < 66, k can be any odd integer between 56 and 66, which means that k could be 57, 59, 61, 63, or 65. Statement one is not sufficient to determine a value of k. We can eliminate answer choices A and D.
Statement Two Alone:
If k + 1 were divided by 3 the remainder would be 0.
This means k + 1 is a multiple of 3. However, since 56 < k < 66, there is more than one value between 56 and 66 that, when increased by 1, will be a multiple of 3. For example, since 60, 63 and 66 are all multiples of 3, we see that k could be 59, 62 or 65. Since we have three possible values for k, statement two is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
From statement one we know that k can be 57, 59, 61, 63, or 65, and from statement two we know that k could be 59, 62 or 65. From the combined statements, then, k could be either 59 or 65; thus, we can’t determine a unique value for k. Statements one and two together are not sufficient to answer the question.
The answer is E.
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Re: If k is an integer such that 56 < k < 66, what is the value [#permalink]
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01 Apr 2017, 10:50
Walkabout wrote:
If k is an integer such that 56 < k < 66, what is the value of k ?
(1) If k were divided by 2, the remainder would be 1.
(2) If k + 1 were divided by 3, the remainder would be 0.
k can be 57, 58,...........65
(1) K is odd because on division with 2, the remainder is 1.
So k is of the form 2n+1.
K can be 57, 59, 61, 63, or 65
Not sufficient
BCE
(2) That means k is not divisible by 3.
k can be 59, 62, or 65
Not sufficient
Both statement together:
Statement 1: k=57, 59, 61, 63, or 65
Statement 2: k= 59,62, or 65
No unique value for k.
E
Re: If k is an integer such that 56 < k < 66, what is the value [#permalink] 01 Apr 2017, 10:50
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Shhhhh!
Rationale: This lesson can be used to help students recognize the digraph
/sh/. Students will become aware that when certain letters are put together in a word, and they are said with a single mouth move. This lesson is designed to help students to read, write, spell and speak words with /sh/ in them.
Materials: Chart paper with the riddle: "Should Ashley share her slushy with her sister Shelly?" on it, Class set of the book by Dr. Seuss, One Fish, Two Fish, Red Fish, Blue Fish, Class set of Elkonian boxes, with the letters (a, b, c, e, f, h, i, l, l, o, r, s, u), overhead, Primary paper, and pencils for each student, Work sheet with pictures on one side and on the other side a blank for them to write the word that would match the picture.
Procedure:
1. Ask students when we want someone to be quiet, what do we say? "Shhh!" Ask them to put their hand in front of their mouth when you say it. Ask what do they feel? "Air." The /sh/ sound is made by putting your teeth together and blowing out of your mouth. Ask if anyone knows what letters are put together to make the /sh/ sound? "An S and an H." When these to letter are together in a word they make that special sound, this sound is called a digraph.
2. Tell students: I am going to say a sentence, listen hard for words that have /sh/ in them. Should Ashley share her slushy with her sister Shelly? Let's say that sentence a few times together. Does everyone here /sh/ in that sentence? Now lets say it, but stretch out the /sh/ in the sentence. Shhhould Ashhhley Shhhare her Slushhhy with her sister Shhhelly? Can someone raise their hand and tell me how many words in that sentence have /sh/ in them? "5."
3. We already know that /sh/ is made from the letters S and H. Can anyone think of any words that were not in our sentence that has that sound in it? Get out your paper and pencil and write as many words that you can think of. (Have several of the students write one or two of their words on the board to discuss as a class.)
4. Erase the words on the board after discussing them, and then begin the letterbox lesson. I would like everyone to start by spelling she with their letters. (Continue with ship, shell, she, fish, cash, flesh, brush, flush.)
5. After the kids have spelled all the words, use your own letters to spell the words on the overhead and have them read them as a class.
6. We are now going to read One Fish, Two Fish, Red Fish, Blue Fish by Dr. Seuss, ask if any of the students have ever read this book? Give the students a short book talk and then pass out the class set, have the children get into groups and take turns reading pages. This will be review, because the children will practice reading /sh/.
Assessment: Pass out the worksheets to the students explaining that they write the word of what the picture is in the blank across from it. If they are not able to tell what the picture is they may ask the teacher for a hint.
References:
Seuss, Dr. (1960). One Fish, Two Fish, Red Fish, Blue Fish. Random House, Inc: New York, NY. 1960.
Eldredge, J. Lloyd (1995) Teaching Decoding in the Holistic Classroom. Englewood Cliffs, New Jersey, Prentice Hall, p.67.
http://www.auburn.edu/rdggenie/insights. I used several of the /sh/ lessons as a guide.
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# When a person is under intense psychological stress, his or
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When a person is under intense psychological stress, his or [#permalink]
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11. When a person is under intense psychological stress,
his or her cardiovascular response is the same as it is
during vigorous physical exercise. Psychological
stress, then, must be beneficial for the heart as is
vigorous physical exercise.
The argument above relies on which of the following
assumptions?
(A) Exercise is an effective means of relieving
psychological stress.
(B) The body's short-term cardiovascular response
to any activity indicates that activity's long-
term effect on the body.
(C) Cardiovascular response during an activity is an
adequate measure of how beneficial the activ-
ity is for the heart.
(D) Psychological stress can have a positive effect
on the body.
(E) Vigorous exercise is the most reliable method of
maintaining a healthy heart.
If you have any questions
you can ask an expert
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# TensorFlow Variance Scaling Initializer – What You Need to Know
If you’re looking to get started with TensorFlow, you’ll need to know about the Variance Scaling Initializer. This guide will explain what it is and how it works.
Check out this video:
## What is the TensorFlow variance scaling initializer?
The TensorFlow variance scaling initializer is a type of initializer that is used to help improve the performance of neural networks. This initializer helps to scale the weights of the network so that they are better able to learn from data. The initializer is based on the idea of variance scaling, which is a technique used in statistics to help improve the accuracy of predictions.
## How does the TensorFlow variance scaling initializer work?
In order to understand how the TensorFlow variance scaling initializer works, we need to first understand what a variance is. Variance is a measure of how spread out a set of data is. In other words, it measures how much each data point varies from the mean. The higher the variance, the more spread out the data will be.
The TensorFlow variance scaling initializer calculates the variance of the input data and then scales it by a factor. This scale factor is a hyperparameter that you can tune. The goal is to have a scaled variance that is close to 1.0. This allows the model to learn faster and converge to a good solution more quickly.
The TensorFlow variance scaling initializer has two parameters: scale and mode. The scale parameter controls how much the input data will be scaled by. The mode parameter controls how the input data will be scaled. There are three possible values for this parameter: fan_in, fan_out, and fan_avg.
If you are using the TensorFlow variance scaling initializer with a fully-connected layer, then you should use mode=”fan_in”. This will scale the input data by 1/sqrt(fan_in). If you are using the TensorFlow variance scaling initializer with a convolutional layer, then you should use mode=”fan_out”. This will scale the input data by 1/sqrt(fan_out). If you are using the TensorFlow variance scaling initializer with either a fully-connected or convolutional layer, then you can use mode=”fan_avg”. This will scale the input data by 1/sqrt( (fan_in + fan_out)/2 ).
## Why is the TensorFlow variance scaling initializer important?
The TensorFlow variance scaling initializer is a tool that is used to help scale the weights of a neural network. This is important because it can help improve the accuracy of the network. The initializer is used to scale the weights so that they are better able to be used by the network. This can help improve the accuracy of the network by making sure that the weights are better able to be used.
## What are some benefits of using the TensorFlow variance scaling initializer?
There are many benefits of using the TensorFlow variance scaling initializer. It is designed to help improve the performance of deep learning models by scaling the weights so that they have equal variance. This can help to reduce the amount of overfitting and improve generalization. The initializer is also easy to use and can be integrated into existing models with minimal effort.
## How can the TensorFlow variance scaling initializer be used in practice?
The TensorFlow variance scaling initializer can be used to help improve the performance of your neural networks. This initializer is based on the paper “Efficient Backprop” by Yann LeCun, et al. which was published in 1998.
The variance scaling initializer can be used to initialize the weights of your neural network in a way that is designed to reduce the overfitting of your model. This initializer scales the weights of each layer in your neural network according to the layer’s input dimensionality.
This initializer can be used by specifying the “variance_scaling_initializer” argument when you create a new layer in your TensorFlow model. For example, if you wanted to use this initializer for a dense layer with an input dimensionality of 100, you would specify the following:
layer = tf.layers.dense(inputs, 100,kernel_initializer=tf.variance_scaling_initializer())
You can also specify other parameters such as the scale factor and mode when creating a new instance of this initializer. The scale factor is used to scale the variance of the weights and is typically set to 1.0 or 2.0. The mode can be set to “fan_in” or “fan_out” and determines how the variance is scaled according to the input or output dimensionality respectively.
## What are some potential drawbacks of using the TensorFlow variance scaling initializer?
There are a few potential drawbacks to using the TensorFlow variance scaling initializer. First, it can be slow to initialize large number of parameters. Second, it can be less stable than other initializers when training very deep networks. Finally, the variance scaling initializer does not always produce the best results on all tasks.
## How does the TensorFlow variance scaling initializer compare to other initialization methods?
There are many different ways to initialize the weights of a neural network, and each has its own advantages and disadvantages. One popular method is the TensorFlow variance scaling initializer, which is well-suited for use with ReLU neurons. In this article, we’ll take a look at how the TensorFlow variance scaling initializer works and how it compares to other initialization methods.
The TensorFlow variance scaling initializer is a good choice for use with ReLU neurons because it helps to prevent the “dead neuron” problem. This problem can occur when all of the weights for a given neuron are initialized to the same value, resulting in the neuron outputting a constant value regardless of the input.
The TensorFlow variance scaling initializer helps to prevent this problem by initializing the weights with a small amount of noise. This noise is generated from a normal distribution with a mean of 0 and a standard deviation that is inversely proportional to the square root of the number of input units. This standard deviation ensures that the noise is small enough to not cause too much disruption, but large enough to break symmetry and prevent dead neurons.
One advantage of the TensorFlow variance scaling initializer over other methods is that it does not require special handling for biases. Other methods, such as Xavier initialization, require that the biases be initialized differently in order to maintain symmetry between the weights and biases. With TensorFlow variance scaling initialization, however, there is no need to worry about this; simply initialize all weights and biases using the same method.
Another advantage of using TensorFlow variance scaling initialization is that it typically leads to faster convergence than other methods. This speed-up is due to the fact that noisy weights tend to break symmetry more effectively than non-noisy weights, leading to faster learning.
Despite its advantages, there are some situations where TensorFlow variance scaling initialization may not be ideal. One such situation is when you have very few training examples; in this case, noisy weights can actually lead to slower convergence. Additionally, if your data is already very symmetric (for example, if you are training on images that have been pre-processed so that all pixels have values between 0 and 1), then noisy weights may not be necessary or beneficial.
Overall, the TensorFlow variance scaling initializer is a good choice for most applications where you are using ReLU neurons. It is simple to use and does not require special handling for biases, plus it often leads to faster convergence than other initialization methods. However, there are some situations where it may not be ideal; in these cases, you may want to experiment with other methods such as Xavier initialization or He normalization
## What are some possible future directions for the TensorFlow variance scaling initializer?
There has been a lot of recent interest in the TensorFlow variance scaling initializer, which is a tool that can help improve the performance of deep learning models. However, there is still a lot of work to be done in this area, and there are a few possible future directions that could be explored.
One possible direction is to further investigate how the variance scaling initializer can be used in different types of models, such as recurrent neural networks or convolutional neural networks. Additionally, it would be interesting to see how the initializer performs on more challenging datasets. Finally, it would be helpful to develop more user-friendly tools that make it easier to use the variance scaling initializer in practice.
## Conclusion: Is the TensorFlow variance scaling initializer right for you?
Yes, the TensorFlow variance scaling initializer is right for you if you want to use a variance scaling initializer.
## References
There are many ways to initialize the weights of a deep neural network; one popular method is known as Xavier initialization, or Xavier Glorot initialization. This technique was first proposed in the paper “Understanding the difficulty of training deep feedforward neural networks” by Xavier Glorot and Yoshua Bengio. The idea behind Xavier initialization is to keep the variance of the inputs to each hidden layer constant, so that the gradient signal is not diluted as it propagates back through the network.
One issue with Xavier initialization is that it can lead to vanishing gradients when used with ReLU neurons (as opposed to neurons with a linear activation function). To address this issue, He et al. proposed a variant of Xavier initialization known as “variance scaling.” In their paper “Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification,” He et al. show that variance scaling outperforms Xavier initialization on a wide range of tasks.
Variance scaling can be used with any activation function, not just ReLU. However, it works best with activation functions that have a mean output of zero (such as ReLU). To initialize the weights using variance scaling, you simply need to scale the weights by a factor of 1/sqrt(n), where n is the number of inputs to the neuron. For example, if a neuron has 100 inputs, you would multiply each weight by 0.1/sqrt(100), or 0.31622776601683794.
There are many other ways to initialize the weights of a neural network; for more information, see “Weight Initialization in Neural Networks: A Survey” by LeCun et al.
Keyword: TensorFlow Variance Scaling Initializer – What You Need to Know
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Mobile Robot Control 2021 Group 6
(Difference between revisions)
Revision as of 11:25, 20 May 2021 (view source)20194019 (Talk | contribs) (→Entrance Detection)← Older edit Revision as of 11:25, 20 May 2021 (view source)20194019 (Talk | contribs) (→Entrance Detection)Newer edit → Line 69: Line 69: If there are more segments located, it will iterate through each segment and compares its slope with the following 2 segments. If there are 2 segments located, the algorithm will check if the system is parallel. If so, the system detects it as a hallway. Based on if a hallway is detected or an interance, a entrance point is calculated between the lines. If there are more segments located, it will iterate through each segment and compares its slope with the following 2 segments. If there are 2 segments located, the algorithm will check if the system is parallel. If so, the system detects it as a hallway. Based on if a hallway is detected or an interance, a entrance point is calculated between the lines. - A picture: [[File:Final 60a642b090fb0d0053beef86 136379.gif|600 px|]] + A picture: [[File:Final 60a642b090fb0d0053beef86 136379.gif|1000 px|]] = Hospital Competition = = Hospital Competition =
Group Members
Stefan van der Palen - 1501054
Paul Munns - 1522795
Saray Bakker - 1002248
Liang Oei - 1522779
Boudewijn Kempers - 1398164
Walter MacAulay - 1632817
Design Document
The Design Document: media:MRC_Design_Document_Group6.pdf
Escape Room Competition
For the Escape room competition two version were build, a smarter robot and a back-up version were the robot follows the wall. For both cases a 20 Hz execution rate is used.
The general structure of the smarter robot is given below. First, an initial scan is performed to find the entrance of the hallway. If an entrance is found, PICO will receive a point where it can move towards via the states 'Move entrance rotation' and 'Move entrance forward'. How the exit is determined is explained in the section 'Line segments and entrance detection'. If no entrance is detected, PICO will perform a partial rotation of 30 degrees and start scanning again for an exit. When no entrance is found after performing a full scan of the room, it is likely that the entrance is not visible from the current position of the robot. In the state 'No entrance - move to free space', PICO will move forward towards a new spot and try to locate the entrance at the new position.
If an entrance is detected, PICO will rotate until it faces the entrance and move forward. Since it should be taken into account that PICO might indicate an exit where there is none, an evaluation is performed after a few steps. If the entrance is still in front of the robot, PICO keeps moving forward. If the entrance is not directly in front of PICO due to drift, a rotation is performed before moving forward again. It could be possible that a false exit was detected before or PICO has drifted too much to still find the exit. Then a new full room scan is performed.
PICO should avoid running into obstacles including static and dynamic objects. Therefore a function is designed that maintains a certain distance from all obstacles which is called 'bubbleRobot'. When PICO is too close to an obstacle, it will stop and move in the opposite direction. To avoid running into the obstacle again, the movement away from the obstacle is more than the distance to leave the bubble. When the robot has moved away from the obstacle, it will reevaluate its position.
Line Segmentation
Line detection from data points is a fundamental task in many fields of science and engineering. In the case of the mobile robot, line detection algorithm is the underlying cornerstone for feature extraction, such as wall, corner and entrance detection.
PICO acquires its data points via the laser range finder (LRF). The LRF outputs in one sweep 1000 data points, consisting of the distances (r) corresponding to particular angles (θ), as shown in Figure 1. The first data point is at -2 rad and the last data point is at +2 rad. Invalid data points above 10 m and below 0.01 m are filtered out. The data points are then converted from polar coordinates to cartesian coordinates using the following geometric relations:
x = r cos(-2 + Δθ)
and
y = r sin(-2 + Δθ)
Failed to parse (PNG conversion failed; check for correct installation of latex, dvips, gs, and convert): =
The line segmentation algorithm is based on the iterative end-point fit (IEPF) algorithm. The algorithm works as follows:
1. A line is first drawn from the first data point (i_begin) to the last data point (i_end). This corresponds to -2 rad and +2 rad respectively when all data is valid, i.e. not filtered out.
2. The perpendicular distances from the line are calculated for each data point between i_begin and i_end.
3. The line is split at the point with the largest perpendicular distance from the line if it is above a certain threshold.
4. If it is below the threshold, a line is found and the segment is stored. The algorithm goes back to point 2, but sets i_begin equal to one index further from the end of the last segment found.
This is also called the split-and-merge algorithm, but merging is not done.
Figure 1: The coordinate system used with the angular limits of the LRF.
Entrance Detection
Laser data can be quite noisy, which can result in a false detection of the entrance when just using one scan as input. Therefore a few scans after each other are performed. The median of the estimated angle and distance towards the entrance is used to plan the motion.
The entrance detection algorithm uses the slopes of the walls to detect the entrance. Firstly the walls are detected via line segmentation of which the slopes can be calculated. For each segment (wall), the slope is compared to the slope of wall that follows next and also the slope of the wall that follows the next wall. So in total 3 segments are used for the algorithm. The following are compared; - The slopes are compared to each other if they are parallel/perpendicular in a certain bound. These bounds are introduced since the walls can be not perfectly parallel or perpedicular. These bounds also determine the robustness of the algorithm. - If the end-point of a segment is in a certain bound of the begin-point of the next segment. If these points differ a lot, this most likely will be an entrance and an entrance point is calculated.
If there are more segments located, it will iterate through each segment and compares its slope with the following 2 segments. If there are 2 segments located, the algorithm will check if the system is parallel. If so, the system detects it as a hallway. Based on if a hallway is detected or an interance, a entrance point is calculated between the lines.
A picture:
Meeting Schedule
Date Chairman Secretary Summary
26-4-2021 - - Introduction meeting
28-4-2021 Boudewijn Kempers Paul Munns First tutor meeting, dividing tasks for Design document
3-5-2021 Boudewijn Kempers Paul Munns Divide coding tasks: Perception (Liang and Paul), Path planning (Saray and Stefan), Initial/Main (Boudewijn and Walter)
10-5-2021 Paul Munns Stefan van der Palen Show functionality of wall following robot (dumb robot), show status smart robot which uses perception to find the entrance.
17-5-2021 Stefan van der Palen Walter MacAulay ..
26-5-2021 Walter MacAulay Saray Bakker ..
31-5-2021 Saray Bakker Boudewijn Kempers ..
7-6-2021 Boudewijn Kempers Paul Munns ..
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https://calculate.plus/en/categories/density/atomic-mass-unit-per-cubic-foot-to-troy-ounce-per-cubic-millimeter
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# atomic mass unit/cubic foot to troy ounce/cubic millimeter
## Density
1 u/ft3
atomic mass unit/cubic foot
1.0e+00
#### Engineering notation
0.1e1
1.8853655531086482267474355149904013303104429791591658974922057588108606559379e-33* oz.tr/mm3
troy ounce/cubic millimeter
#### Standard notation
0.000000000000000000000000000000001885365553108648226747435514990401330310442979159165897492205758810860655937988257313
#### Engineering notation
0.1885365553108648226747435514990401330310442979159165897492205758810860655937988257313e-32
## Free online Density conversion. Convert atomic mass unit/cubic foot to troy ounce/cubic millimeter (u/ft3 to oz.tr/mm3). How much is atomic mass unit/cubic foot to troy ounce/cubic millimeter? Made for you with much by CalculatePlus.
### Conversion table
u/ft3oz.tr/mm3
11.8853655531086482267474355149904013303104429791591658974922057588108606559379e-33*
23.7707311062172964534948710299808026606208859583183317949844115176217213118759e-33*
35.6560966593259446802423065449712039909313289374774976924766172764325819678139e-33*
47.5414622124345929069897420599616053212417719166366635899688230352434426237519e-33*
59.4268277655432411337371775749520066515522148957958294874610287940543032796899e-33*
61.1312193318651889360484613089942407981862657874954995384953234552865163935627e-32*
71.3197558871760537587232048604932809312173100854114161282445440311676024591565e-32*
81.5082924424869185813979484119923210642483543833273327179937646070486885247503e-32*
91.6968289977977834040726919634913611972793986812432493077429851829297745903441e-32*
101.8853655531086482267474355149904013303104429791591658974922057588108606559379e-32*
1001.8853655531086482267474355149904013303104429791591658974922057588108606559379e-31*
10001.8853655531086482267474355149904013303104429791591658974922057588108606559379e-30*
* This value is an approximation to the real value.
* This value is an approximation to the real value.
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https://www.mytutor.co.uk/answers/6573/11-plus/Maths/What-is-the-difference-between-ratios-and-fractions
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# What is the difference between ratios and fractions?
• 584 views
Both are different ways to represent an amount of something. Fractions show how much of a whole item there is for example 2/10 2 parts out of a total of 10. On the other hand, a ratio describes one amount relative to another, for example 1:3 meaning 1 part of one amount corresponds to 3 parts of another amount, a good way to think about this is when making squash, you take an amount of squash, such as 10ml and add another amount of water, for example 100ml, the ratio would be 10:100, which can be simplified as 1:10, since there is 10 times more water as squash.
Still stuck? Get one-to-one help from a personally interviewed subject specialist.
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https://blog.myrank.co.in/volume-or-cubical-expansion/
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# Volume or Cubical Expansion
## Volume or Cubical Expansion
When a solid is heated and its volume increases, then the expansion is called volume expansion (or) cubical expansion.
Consider a rectangular parallel piped of slides l₁, l₂ and l₃.
Its initial volume (V₀) = l₁ x l₂ x l₃.
Differentiating both sides with respect to T, we get:
$$\frac{dV}{dT}={{l}_{2}}{{l}_{3}}\frac{d{{l}_{1}}}{dT}+{{l}_{1}}{{l}_{3}}\frac{d{{l}_{2}}}{dT}+{{l}_{1}}{{l}_{2}}\frac{d{{l}_{3}}}{dT}$$.
dV/ dT = l₂l₃ (αl₁) + l₁l₃ (αl₂) + l₁l₂ (αl₃) = 3 αl₁l₂l₃
dV = 3 αV₀dT … (1)
If γ is constant over the temperature range of under consideration, then equation (1) can be interchanged.
$$\int\limits_{{{V}_{i}}}^{{{V}_{f}}}{dV}=3\alpha {{V}_{0}}\int\limits_{{{T}_{i}}}^{{{T}_{f}}}{dT}$$.
ΔV = 3αV₀ΔT (or) γV₀ΔT
Where,
γ = Coefficient of superficial expansion.
Thrice the coefficient of linear expansion α.
Final area of the parallel piped, V = V₀ (1 + γΔT).
The average coefficient of superficial expansion, $$\gamma =\frac{\Delta V}{{{V}_{0}}\Delta T}$$ and unit is same as α i.e., °C⁻¹ or K⁻¹.
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https://numberworld.info/32674
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# Number 32674
### Properties of number 32674
Cross Sum:
Factorization:
2 * 17 * 31 * 31
Divisors:
1, 2, 17, 31, 34, 62, 527, 961, 1054, 1922, 16337, 32674
Count of divisors:
Sum of divisors:
Prime number?
No
Fibonacci number?
No
Bell Number?
No
Catalan Number?
No
Base 2 (Binary):
Base 3 (Ternary):
Base 4 (Quaternary):
Base 5 (Quintal):
Base 8 (Octal):
7fa2
Base 32:
vt2
sin(32674)
0.99098275645082
cos(32674)
0.13398946382882
tan(32674)
7.3959752366562
ln(32674)
10.394334933586
lg(32674)
4.5142023047108
sqrt(32674)
180.7595087402
Square(32674)
### Number Look Up
Look Up
32674 which is pronounced (thirty-two thousand six hundred seventy-four) is a very great figure. The cross sum of 32674 is 22. If you factorisate the number 32674 you will get these result 2 * 17 * 31 * 31. 32674 has 12 divisors ( 1, 2, 17, 31, 34, 62, 527, 961, 1054, 1922, 16337, 32674 ) whith a sum of 53622. The figure 32674 is not a prime number. The figure 32674 is not a fibonacci number. 32674 is not a Bell Number. The figure 32674 is not a Catalan Number. The convertion of 32674 to base 2 (Binary) is 111111110100010. The convertion of 32674 to base 3 (Ternary) is 1122211011. The convertion of 32674 to base 4 (Quaternary) is 13332202. The convertion of 32674 to base 5 (Quintal) is 2021144. The convertion of 32674 to base 8 (Octal) is 77642. The convertion of 32674 to base 16 (Hexadecimal) is 7fa2. The convertion of 32674 to base 32 is vt2. The sine of the figure 32674 is 0.99098275645082. The cosine of 32674 is 0.13398946382882. The tangent of 32674 is 7.3959752366562. The root of 32674 is 180.7595087402.
If you square 32674 you will get the following result 1067590276. The natural logarithm of 32674 is 10.394334933586 and the decimal logarithm is 4.5142023047108. that 32674 is unique figure!
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https://whatisconvert.com/16-long-tons-in-kilograms
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Convert 16 Long Tons to Kilograms
To calculate 16 Long Tons to the corresponding value in Kilograms, multiply the quantity in Long Tons by 1016.0469088 (conversion factor). In this case we should multiply 16 Long Tons by 1016.0469088 to get the equivalent result in Kilograms:
16 Long Tons x 1016.0469088 = 16256.7505408 Kilograms
16 Long Tons is equivalent to 16256.7505408 Kilograms.
How to convert from Long Tons to Kilograms
The conversion factor from Long Tons to Kilograms is 1016.0469088. To find out how many Long Tons in Kilograms, multiply by the conversion factor or use the Mass converter above. Sixteen Long Tons is equivalent to sixteen thousand two hundred fifty-six point seven five one Kilograms.
Definition of Long Ton
A long ton is defined as exactly 2,240 pounds. The long ton arises from the traditional British measurement system: A long ton is 20 cwt, each of which is 8 stone (1 stone = 14 pounds). Thus a long ton is 20 × 8 × 14 lb = 2,240 lb. Long ton, also known as the imperial ton or displacement ton is the name for the unit called the "ton" in the avoirdupois or Imperial system of measurements standardised in the thirteenth century that is used in the United Kingdom
Definition of Kilogram
The kilogram (or kilogramme, SI symbol: kg), also known as the kilo, is the fundamental unit of mass in the International System of Units. Defined as being equal to the mass of the International Prototype Kilogram (IPK), that is almost exactly equal to the mass of one liter of water. The kilogram is the only SI base unit using an SI prefix ("kilo", symbol "k") as part of its name. The stability of kilogram is really important, for four of the seven fundamental units in the SI system are defined relative to it.
Using the Long Tons to Kilograms converter you can get answers to questions like the following:
• How many Kilograms are in 16 Long Tons?
• 16 Long Tons is equal to how many Kilograms?
• How to convert 16 Long Tons to Kilograms?
• How many is 16 Long Tons in Kilograms?
• What is 16 Long Tons in Kilograms?
• How much is 16 Long Tons in Kilograms?
• How many kg are in 16 uk ton?
• 16 uk ton is equal to how many kg?
• How to convert 16 uk ton to kg?
• How many is 16 uk ton in kg?
• What is 16 uk ton in kg?
• How much is 16 uk ton in kg?
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# The volume that a gas occupies at 343K if its volume at -25^(0)C is 7.5 litre is (The process is isobaric)
15 views
in Physics
The volume that a gas occupies at 343K if its volume at -25^(0)C is 7.5 litre is (The process is isobaric)
A. 10.29 lit
B. 102.9 lit
C. 1.029 lit
D. 1029 lit
by (91.0k points)
V prop T, (V_(1))/(V_(2)) = (T_(1))/(T_(2))
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Now you are in the subtree of Special Topics in Many-Body Theory, Spring 2016 project.
# BCS theory
Around 1957, Bardeen, Cooper, and Schrieffer developed an insightful model for how superconductivity can arise when the interaction between electrons in a metal has an attractive piece. A retarded phonon-mediated attraction between electrons, for example, can induce superconductivity, a qualitative change in the electrical conductivity and other properties. We now want to understand how that happens microscopically, using a variational approach and the second quantization formalism. Our starting point will be the interacting electron Hamiltonian
$$$$H = \sum_{{\bf k}\sigma} \epsilon_{\bf k} c^\dagger_{{\bf k} \sigma} c_{{\bf k} \sigma} + \sum_{{\bf k},{\bf k}^\prime,{\bf q}; \sigma,\sigma^\prime} V({\bf k},{\bf k}^\prime,{\bf q}) c^\dagger_{{\bf k}^\prime-{\bf q},\sigma^\prime} c_{{\bf k}^\prime,\sigma^\prime} c^\dagger_{{\bf k}+{\bf q},\sigma} c_{{\bf k}; \sigma}$$$$
As a simplifying approximation, we keep only one part of the full interaction term.
First introduce the pair creation and annihilation operators
$$$$b^\dagger_{\bf k} = c^\dagger_{k\uparrow} c^\dagger_{-k \downarrow},\quad b_{\bf k} = c_{-k \downarrow} c_{k \uparrow}.$$$$
Note that these are not quite bosons: they commute with each other at different $k$, as expected for bosons, but fail to have the correct commutation relation at the same $k$, where they behave more like fermions (one cannot create two pairs or annihilate two pairs at one value of $k$).
What we will keep is only the "pairing interaction" for zero total momentum pairs:
$$H_{reduced} = \sum_{{\bf k}\sigma} \epsilon_{\bf k} c^\dagger_{{\bf k} \sigma} c_{{\bf k} \sigma} + \sum_{{\bf k},{\bf k}^\prime} V_{{\bf k},{\bf k}^\prime} b^\dagger_{{\bf k}^\prime} b_{\bf k}.$$
(Some justification is that this part of the interaction gives the leading instability of the Fermi liquid; taking into account the pairing interaction gives a new state, the superconducting state, that is stable to the neglected parts of the interaction.)
Now assume that the pairing interaction is always attractive. Then the ground state of $H_{red}$ turns out to have only empty or occupied pairs: i.e., for no value of ${\bf k}$ should there be exactly one total electron in the states ${\bf k},\uparrow$ and $-{\bf k},\downarrow$. Then
$$$$H_{red} = \sum_{{\bf k}\sigma} 2 \epsilon_{\bf k} b^\dagger_{\bf k} b_{\bf k} + \sum_{{\bf k},{\bf k}^\prime} V_{{\bf k},{\bf k}^\prime} b^\dagger_{{\bf k}^\prime} b_{\bf k}.$$$$
(The factor of 2 appears because there are two electrons per pair.)
Now we have a quadratic Hamiltonian in terms of the boson operators.
The main challenge in the variational technique is to select a sufficiently general class of variational wavefunctions that capture the physics of the new state. BCS had the idea to try wavefunctions of the form
$$$$|\psi_0\rangle = \prod_{\bf k} (1 + g_{\bf k} b^\dagger_{\bf k}) |0\rangle.$$$$
The normalization of this state is
$$$$\langle \psi_0 | \psi_0 \rangle = \prod_{\bf k} (1 + |g_{\bf k}|^2)$$$$
so henceforth let
$$$$|\psi_0\rangle = \prod_{\bf k} {1 + g_{\bf k} b^\dagger_{\bf k} \over (1 + |g_{\bf k}|^2)^{1/2}} |0\rangle.$$$$
We want to constrain the total number of electrons to be some constant $N_0$, which
means looking for a stationary point (here $\mu$ is the chemical potential)
$$$$\delta W = \delta \langle \psi_0 | H_{red} - \mu N_0 | \psi_0 \rangle = 0.$$$$
Then substituting the wavefunction gives, for the expectation value $W$,
$$$$W = \sum_{\bf k} 2(\epsilon_{\bf k} -\mu) {v_{\bf k}}^2 + \sum_{{\bf k},{\bf k}^\prime} V_{{\bf k},{\bf k}^\prime} u_{\bf k} v_{\bf k} u_{{\bf k}^\prime} v_{{\bf k}^\prime}$$$$
Here we have introduced a shorthand (henceforth assuming spherical symmetry and
$g_k$ real)
$$$$u_k = {1 \over (1+{g_k}^2)^{1/2}},\quad v_k = {g_k \over (1+{g_k}^2)^{1/2}}.$$$$
Note that ${u_k}^2 + {v_k}^2 = 1$.
Let us assume that there is a self-consistent solution of the famous "gap equation":
$$$$\Delta_k = - \sum_{k^\prime} V_{k k^\prime} {\Delta_{k^\prime} \over 2 E_{k^\prime}},$$$$
where $E_k = \sqrt{(\epsilon_k - \mu)^2 + {\Delta_k}^2}$. This $E_k$ will turn out to be the energy required to create a "quasiparticle" at momentum $k$. We will choose
$$$$u_k v_k = {\Delta_k \over 2 E_k}.$$$$
Now the variational equation (from varying $W$ with respect to the $g_k$) can be written simply: (note that variations of $u_k$ and of $v_k$ are not independent: $\delta u_k = - {u_k}^2 v_k \delta g_k$, $\delta v_k = {u_k}^3 \delta g_k$)
$$$$\delta W = {u_k}^2 \delta g_k \left( 4 (\epsilon_k - \mu) {v_k} {u_k} + 2 (\sum_{k^\prime} {V_{k k^\prime} \Delta_{k^\prime} \over 2 E_{k^\prime}}) ({u_k}^2 - {v_k}^2) \right) = 0.$$$$
Then substituting in the gap equation gives
$$$${u_k}^2 - {v_k}^2 = {\epsilon_k - \mu \over E_k},$$$$
which combined with the constraint ${u_k}^2 + {v_k}^2 = 1$ gives
$$$${u_k}^2 = \frac{1}{2}\left(1 + {\epsilon_k - \mu \over E_k}\right),\quad {v_k}^2 = \frac{1}{2}\left(1 - {\epsilon_k - \mu \over E_k}\right).$$$$
We can think of this wavefunction as describing a large number $N/2$ of "Cooper pairs", all in the zero-momentum and zero-spin state. However, note that there is still a hint of the fermionic nature of the underlying electrons, since we had to use all the electron states up to the Fermi level in order to make these Cooper pairs. The connection to the Ginzburg-Landau equation is, in words, that the LG equation describes the wavefunction of Cooper pairs, which in the absence of an external potential are all in the same center-of-mass state.
For now, we are going to make a simple step-function choice for the interaction $V$ that will give a so-called "s-wave" superconductor:
$$$$V_{{\bf k},{\bf k}^\prime} = -V < 0$$$$
if both ${\bf k}$ and ${\bf k}^\prime$ are within some small distance $\delta k$ of the Fermi level, and 0 otherwise. We will see later how other potentials can give exotic superconductors of other symmetries.
Note that the fractional number variations in the BCS state are statistically very small ($\sim N^{1/2}$, where $N$ is the total number of electrons). We could choose a similar state of well-defined number, but would find that then the phase appearing in the Ginzburg-Landau equation is not well-defined: in this sense number and phase are conjugate variables in a superconductor.
It is amazing that the small attractive residual interaction, which only changes the electron interaction energy by a factor of about $10^{-8}$, can so dramatically change the physical properties.
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# Lagrane vs Hamilton
1. Jul 11, 2013
### Sami Ullah
if lagrangian mechanics is available the why we needed hamiltonian mechanics. where they differ from each other?
2. Jul 11, 2013
### Joey21
If natural sciences only studied what was neccesary I believe two things would happen:
- Things would get boring,
- Human knowledge would lose a hell of a load of insight.
I reckon if you're going to ask that question, there is one that should go before it: why do we need Lagrangian mechanics when Newtonian mechanics is available? Lagrangian mechanics, for all the power it has, is really limited to a handful of situations: non-holonomic constraints blow Lagrangian mechanics put of the water 1. Newtonian vector mechanics, however has not problem with them. So why do we use Lagrangian mechanics? It turns out that the equations of motion both methods supply are identical, but arriving at those equations, while relativly easy in Lagrangian mechanics, can be quite a pain in the backside if one uses vector mechanics ( forces, reactions, etc). And, apart from the practical issues, which I believe are what would interest an engineer when he or she has to finish a project, from a theoretical point of view Lagrangian mechanics offers a lot of insight into the structure of mechanics as a theory, gives a neat explanation for conservation laws (based of symmetries in the Lagrangian), and builds up concepts which are used all throughout physics.
Back to your question, why use hamiltonian mechanics if Lagrangian mechanics is available? Like in the Lagrangian vs Newtonian case, Hamiltonian mechanics has a characteristic that from a practical point of view : while Lagrangian Mechanics spits out a second order ordinary differential equations (ODE), Hamiltonian mechanics gives us two first order ODE's, which in a lot of cases are easier to solve, and offers new ways to calculate conserved quantities of motion. Also, Hamiltonian mechanics presents new theoretical concepts, such as Poisson Brackets, which is used in any branches of physics to study the time evolution of a system, canonical transforations, phase space, Liouville's theorem, etc. Even the Hamiltonian, which a lot of the time can be thought of as the mechanical energy of the system ( if certain conditions are met) becomes an important concept in Modern Physics ( I believe, I still have to trust my prof on that one).
During my still short time in college I have studied Newtonian Mechanics, Lagrangian Mechanics and Hamltonian Mechanics. We learnt about Lagrangian Mechanics from the point of view of virtual work and D'Alembert's principle, and from the point of view of the principle of least action. In the first, you use Newton's laws as a starting point. In the later, you can recover Newton's laws very quickly. Hamiltonian mechanics can be formulated by using a partial legendre transform on the Lagrangian ( changing the generalized velocities for the canconical momenta) or from a modified action principle. And there are more formulations, such as the Hamilton-Jacobi equation.
What I am trying to say with this overgrown response is that looking at things from different points of view often reveals information which was hidden behind the curtains. And the fact is that if we want to understand the way the universe works, we have to look behind all of them. Especially when it comes to the basics, like classical mechanics. Because really, if you come to think about it, a lot of the results of physics are concepts that you can later plug into equations of motion from mechanics to learn how things move and work, so the better we understand mechanics (classical, quantum, statistical...) the better the basis we will have to study branches like EM, optics, thermodynamics, solid state, etc.
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# Blank screen after calling glm::perspective
Hi there!
This code works fine:
``````glm::mat4 proj = glm:: perspective(45.0f, 4.0f / 3.0f, 1.0f, 100.0f);
glm::mat4 translate = glm::translate(glm::mat4(1.0f), glm::vec3(0.0f, 0.0f, 1.0f));
glm::mat4 rotate = glm::rotate(glm::mat4(1.0f), i / (2 * glm:: pi<float>()), glm::vec3(0.0f, 1.0f, 0.0f));
glm::mat4 scale = glm::scale(glm::mat4(1.0f), glm::vec3(0.3f));
glm::mat4 model = translate * rotate * scale;
``````
But when I multiply by the proj matrix:
``````glm::mat4 proj = glm:: perspective(45.0f, 4.0f / 3.0f, 1.0f, 100.0f);
glm::mat4 translate = glm::translate(glm::mat4(1.0f), glm::vec3(0.0f, 0.0f, [b]5.0f[/b]));
glm::mat4 rotate = glm::rotate(glm::mat4(1.0f), i / (2 * glm:: pi<float>()), glm::vec3(0.0f, 1.0f, 0.0f));
glm::mat4 scale = glm::scale(glm::mat4(1.0f), glm::vec3(0.3f));
glm::mat4 model = [b]proj[/b] * translate * rotate * scale;
``````
it turns into a black screen. What could have possible gone wrong?
45 radians is a bit wide. Try:
``````
glm::mat4 proj = glm:: perspective(glm::radians(45.0f), 4.0f / 3.0f, 1.0f, 100.0f);
``````
GLM uses radians for angles, whereas OpenGL (and GLU) use degrees.
still blank
Try translating by (0,0,-5).
Conventional projection matrices (those generated by glOrtho, glFrustum, gluOrtho2D and gluPerspective, and their GLM counterparts) negate the Z direction. For a perspective projection, the near and far planes are always in front of the viewpoint, so only points with negative eye-space Z will be visible.
Bingo!!!
And is there a way to get rid of the negative sign? It feels a bit awkward to me having to enter -5.0f when my near and farZ are between 1.0 and 100f
You can rotate by 180 degrees about the Y axis, but then the positive X axis will point to the left.
Or you could add a scale(1,1,-1) after the perspective, but that’s going to give you a left-handed coordinate system, so any objects will be mirrored (e.g. a character holding something in their left hand will end up with it in their right hand), clockwise-ordered faces will become counter-clockwise, etc.
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# MATH-direct variation
posted by .
Which of the following represents a direct variation function?
A)d=2r
B)y=9x+1
C)y=-3
D)a=1/2h(b1+b2)
• MATH-direct variation -
A direct variation should
1. be a linear function of one variable
2. passes through the origin (0,0), i.e. if the independent variable is set to zero, the dependent variable should also be zero.
If you examine the four choices according to the above criteria, you will be able to eliminate all but the required function.
• MATH-direct variation -
-4 + 7x + 4 = 3y
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# Definitions for ascendedas·cend·ed
### WikipediaRate this definition:0.0 / 0 votes
1. ascended
Ascendency or ascendancy is a quantitative attribute of an ecosystem, defined as a function of the ecosystem's trophic network. Ascendency is derived using mathematical tools from information theory. It is intended to capture in a single index the ability of an ecosystem to prevail against disturbance by virtue of its combined organization and size. One way of depicting ascendency is to regard it as "organized power", because the index represents the magnitude of the power that is flowing within the system towards particular ends, as distinct from power that is dissipated naturally. Almost half a century earlier, Alfred J. Lotka (1922) had suggested that a system's capacity to prevail in evolution was related to its ability to capture useful power. Ascendency can thus be regarded as a refinement of Lotka's supposition that also takes into account how power is actually being channeled within a system. In mathematical terms, ascendency is the product of the aggregate amount of material or energy being transferred in an ecosystem times the coherency with which the outputs from the members of the system relate to the set of inputs to the same components (Ulanowicz 1986). Coherence is gauged by the average mutual information shared between inputs and outputs (Rutledge et al. 1976). Originally, it was thought that ecosystems increase uniformly in ascendency as they developed, but subsequent empirical observation has suggested that all sustainable ecosystems are confined to a narrow "window of vitality" (Ulanowicz 2002). Systems with relative values of ascendency plotting below the window tend to fall apart due to lack of significant internal constraints, whereas systems above the window tend to be so "brittle" that they become vulnerable to external perturbations. Sensitivity analysis on the components of the ascendency reveals the controlling transfers within the system in the sense of Liebig (Ulanowicz and Baird 1999). That is, ascendency can be used to identify which resource is limiting the functioning of each component of the ecosystem. It is thought that autocatalytic feedback is the primary route by which systems increase and maintain their ascendencies (Ulanowicz 1997.)
1. Ascended
of Ascend
### Numerology
1. Chaldean Numerology
The numerical value of ascended in Chaldean Numerology is: 3
2. Pythagorean Numerology
The numerical value of ascended in Pythagorean Numerology is: 1
### Examples of ascended in a Sentence
1. False positive killings amount to one of the worst episodes of mass atrocity in the Western Hemisphere in recent years, and there is mounting evidence that many senior army officers bear responsibility, yet the army officials in charge at the time of the killings have escaped justice and even ascended to the top of the military command, including the current heads of the army and armed forces.
2. This day before dawn I ascended a hill and looked at the crowded heaven.
3. Home prices are continuing to move upward, but the rate at which they ascended slowed in the third quarter.
4. [ T ] Charles Krauthammer idea that the court should decree that it’s a Constitutional right, something that had been hidden in the Constitution for over a hundred years and that nobody had ever discerned, is simply a way of saying that it has been removed from the democratic arena. It can no longer be debated, all the laws are cancelled, and we are now in a new place, ironically, Ruth Bader Ginsburg who is on the court today once said, before she ascended to the court, that the abortion decision had prevented a stable social settlement of the abortion issue that was headed in the reform direction because it took it out of the political arena.
5. Born Into Reality Towards Heaven this is your birth right because we were all born from the same source and because we were born into our bodies. Therefore everyone is ascended equally.
### Popularity rank by frequency of use
ascended#10000#32891#100000
## Translations for ascended
### From our Multilingual Translation Dictionary
• صعد
• aufgestiegen
• ανέβηκε
• supreniris
• ylosnousseet
• monté
• ascended
• चढ़ा
• felemelkedett
• վերելք
• naik
• 上昇
• besteg
• ascendeu
• అధిరోహించాడు
### Translation
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##### the official who holds an office
A incumbent
B ultimo
C appellative
D aculeate
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When studying the CSS framework Bluma, I found that it use a very smart way to determine the text color based on the bg color, utiliizing the color luminance to decide to use black text or white text, which is interesting and I found some interesting facts to note it down.
### Color Luminance
Steven Bradley wrote an great article about color luminance, and here are some details:
1. Our eyes have rods（视杆细胞）and cones（视锥细胞）to perceive light/dark as well as different color information; rods are responsible for seeing in low light and are sensitive to light/dark, while cones are responsible for distinguishing different colors. Moreover we have S-cones (blue), M-cones (green) and L-cones (red) for short, medium and long wavelength. – three primary colors.
2. Luminance is the measurement of the intensity of light that reaches our eye, while brightness and value are only the perception of an object’s luminance. Lightness is the brightness relative to the brightness of a similarly illuminated white.
3. Our perception of lightness (or brightness) don’t scale linearly with luminance. The perceived luminance is dependent on both light intensity and the specific wavelength of that light (a.k.a type of color).
4. Every color has its own natural luminance levels.
5. Saturation also affects luminance. If you reduce the saturation of a pure color to 0% the result is a 50% grey with a 50% value for luminance.
6. differences between HSL, HSB, and HSV:
• HSB/V is measuring the amount of light
• HSL is measuring the amount of white
#### Quantitive Implementation
From WCAG’s Definition, the relative luminance is:
the relative brightness of any point in a colorspace, normalized to 0 for darkest black and 1 for lightest white.
WCAG also provides the formula for luminance:
For the sRGB colorspace, the relative luminance of a color is defined as L = 0.2126 * R + 0.7152 * G + 0.0722 * B where R, G and B are defined.
as:
• if RsRGB <= 0.03928 then R = RsRGB/12.92 else R = ((RsRGB+0.055)/1.055) ^ 2.4
• if GsRGB <= 0.03928 then G = GsRGB/12.92 else G = ((GsRGB+0.055)/1.055) ^ 2.4
• if BsRGB <= 0.03928 then B = BsRGB/12.92 else B = ((BsRGB+0.055)/1.055) ^ 2.4
and RsRGB, GsRGB, and BsRGB are defined as:
• RsRGB = R8bit / 255
• GsRGB = G8bit / 255
• BsRGB = B8bit / 255
Bluma strictly implements the spec above by having such Sass function:
Another similar implementation is documented here
Work With Color says:
Luminance on the other hand is a measure to describe the perceived brightness of a color
Contrast as in the distance of luminance between two colors
Color decisions need to consider luminance / contrast because it is key to usability.
HSL Color Picker
To put it simply, the luminance of a color defines whether its brightness. A luminance of 1 means the color is white. On the opposite, a luminance score of 0 means the color is black.
NOTE: WCAG = Web Content Accessibility Guidelines
### This video blows my mind
Notice 3:50 – that is crazy. Remember that our eyes could be cheated.
### Color Models
Colorizer have listed all common color models.
#### RGB
From Wikipedia:
The RGB color model is an addictive color model in which red, green and blue light are added together in various ways to reproduce a broad array of colors.
The RGB color model is addictive in the sense that the three light beams are added together, and their light spectra add, wavelength by wavelength, to make the final color’s spectrum. This is essentially opposite to the subtractive color model that applies to paints, inks, dyes and other substances whose colors depends on reflecting the light under which we see them.
##### why R,G,B
The choice of primary colors (red, green, blue) is related to the physiology of the human eye; good primaries are stimuli that maximize the difference between the responses of the cone cells of the human retina to light of different wavelengths, and that thereby make a large color triangle.
The difference in the signals received from the three kinds allows the brain to differentiate a wide gamut of different colors.
The color triangle represents the range of colors which could be reproduced by additive mixing of non-negative amounts of three primary colors.
“原色”的指定并没有唯一的选法，因为就理论上而言，凡是彼此之间无法替代的颜色都可以被选为“原色”，只是目前普遍认定“光的三原色”为红绿蓝。
##### numeric representations
• float
• percentage
• integer range (0,255) - decimal / hexadecimal
• larger integer ranges for each primary color (High-end digital image equipment)
[Concept] illuminant
From Wikipedia Standard Illuminant:
The International Commission on Illumination (usually abbreviated CIE for its French name) is th body responsible for publishing all of the well-known standard illuminants.
There are many standards like Illuminant A, B, C … The most common used one is called Illuminant D, which:
… represents phases of daylight, … the D series of illuminants are constructed to represent natural daylight. They are difficult to produce artificially, but are easy to characterized mathematically.
##### What is white?
White Point
A white point is a set of tristimulus values (a set of values of 3 primary colors) or chromaticity coordinates that serve to define the color “white” in image capture, encoding, or reproduction. Depending on the application, different definitions of white are needed to give acceptable results.
SPD = Spectral Power Distribution (光谱能量分布??)
色度(Colorfulness/Chroma/Saturation), 色相(Hue)
#### CMYK
CMYK - Wikipedia
The CMYK color model (process color, four color) is a subtractive color model, used in color printing, and is also used to describe the printing process itself.
• C - Cyan
• M - Magenta
• Y - Yellow
• K - Key (black)
#### HSL
HSL和HSV色彩空间
HSL和HSV都是一种将RGB色彩模型中的点在圆柱坐标系中的表示法。这两种表示法试图做到比RGB基于笛卡尔坐标系的几何结构更加直观。
Colorizer 使用了圆锥表示 HSL：
• Hue（H），色相，是色彩的基本属性，即平时所说的颜色名称
• Saturation（S），饱和度，是指色彩的纯度，越高色彩越纯，低则逐渐变灰，取 0~100% 的数值
• Lightness（L），亮度，取 0~100%
#### RGB => HSL
Algorithm in CSS3 Specification
An JS implementation based on the spec:
### Color Meaning
http://vanseodesign.com/web-design/color-meaning/
… there is no substantive evidence that support a universal system of color meaning. It’s not that colors themselves have specific meaning, but rather that we have culturally assigned meanings to them.
… it’s important to understand who your target audience is and how your audience attaches meaning to color.
• warm colors: red, orange, yellow – passion, energy, impulsiveness, happiness, coziness and comfort
• cool colors: green, blue, violet – calm, trust, professionalism, also sadness and melancholy
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# Evaluating Excel formulae (formulas if you prefer)
Anyone know how to do this ?
Given an Excel formula like
=SUM(D4:H12,A14-B15*2,100-(A19+B19*2))
how can I parse it and evaluate it???
There are expression evaluators at
http://swiss.torry.net/expressions.htm
but none specifically mention Excel.
Is there some formal definition of the Excel formula language? If so, one might expect that something like Lex and Yacc could be used. But that is a bit too much heavy lifting for me.
What about tweaking one of the existing expression evaluators ? Anyone have experience/suggestions. And yes I do want to parse AND evaluate, because I want to be able to identify cells that have been referenced in formulae
###### Who is Participating?
Commented:
The attached link deals with the parsing half of the problem:-
http://www.mcs.vuw.ac.nz/~db/FishBrainWiki?Excel
0
Commented:
i think you can try to use "Excel.Application" object
FExcel := CreateOleObject('Excel.Application');
info below is from MSDN about "Excel.Application" object
Visual Studio Tools for the Microsoft Office System
How to: Run Excel Calculations Programmatically
The Calculate method runs all calculations in the specified object. Use the method of the object that limits the calculation range to the smallest number of cells that you want to recalculate. The recalculation engine in Microsoft Office Excel 2003 is very fast, but if you can limit the number of cells involved, you can optimize the operation.
To run calculations in a range
Call the Calculate method of the specified range. The following example requires a range named "SomeNamedRange" in the worksheet:
' Visual Basic
ThisApplication.Range("SomeNamedRange").Calculate()
// C#
ThisApplication.get_Range("SomeNamedRange",Type.Missing).Calculate();
To run calculations in all open workbooks
Call the Calculate method of the Application object:
' Visual Basic
ThisApplication.Calculate()
// C#
ThisApplication.Calculate();
0
Author Commented:
moorhouselondon --the fishbrain stuff is cool .. a good link, thanks.
vadim - not quite what I had in mind, but there are some good ideas there.
0
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Play Video
### Part - 1
In this lecture, I am discussing how to find the rate of change (rate of increasing and rate of decreasing) of any object with respect to another object and questions based on rate of change application of derivatives from NCERT Exercise 6.1
Questions discussed in this lecture:
## NCERT EXERCISE 6.1 (Rate of Change)
Question 1. Find the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm
(b) r = 4 cm
Question 2. The volume of a cube is increasing at the rate of 8 cm3/s. How fast is the surface area increasing when the length of an edge is 12 cm?
Question 3. The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.
Question 4. An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?
Question 5. A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?
Question 6. The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?
Question 7. The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8cm and y = 6cm, find the rates of change of (a) the perimeter, and (b) the area of the rectangle.
Question 8. A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimeters of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.
Play Video
### Part - 2
Question 9. A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.
Question 10. A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?
Question 11. A particle moves along the curve 6y = x3 +2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.
Question 12. The radius of an air bubble is increasing at the rate of $\frac{1}{2}$ cm/s. At what rate is the volume of the bubble increasing when the radius is 1 cm?
Question 13. A balloon, which always remains spherical, has a variable diameter $\frac{3}{2}(2x + 1)$. Find the rate of change of its volume with respect to x.
Question 14. Sand is pouring from a pipe at the rate of 12 cm3/s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?
Question 15. The total cost C (x) in Rupees associated with the production of x units of an item is given by $$C(x) = 0.007x^3 – 0.003x^2 + 15x + 4000$$ Find the marginal cost when 17 units are produced.
Question 16. The total revenue in Rupees received from the sale of x units of a product is given by $$R(x) = 13x^2 + 26x + 15$$ Find the marginal revenue when x = 7.
Choose the correct answer for questions 17 and 18.
Question 17. The rate of change of the area of a circle with respect to its radius r at r = 6 cm is
(A) 10π
(B) 12π
(C) 8π
(D) 11π
Question 18. The total revenue in Rupees received from the sale of x units of a product is given by $R(x) = 3x^2 + 36x + 5$. The marginal revenue, when x = 15 is
(A) 116
(B) 96
(C) 90
(D) 126
आये हो निभाने को जब, किरदार ज़मीं पर,
कुछ ऐसा कर चलो कि ज़माना मिसाल दे।
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# 4 3 Slope Slope of a Line Slope
• Slides: 11
4. 3 Slope
Slope of a Line Slope • steepness of a line • compares the vertical change to the horizontal change • also used for rate of change, grade, pitch Formula: The slope of the line through the points (x 1, y 1) and (x 2, y 2) is where x 1≠x 2
Ex. Find the slope of the line through the points (1, -2) and (-3, -7). (1, -2) (-3, -7) (x 1, y 1) (x 2, y 2) (-3, -7) (1, -2) (x 1, y 1) (x 2, y 2) It doesn’t matter which pt you call (x 1, y 1) & (x 2, y 2)
Ex. Find the slope of the line run= 2 y 3 rise = 4 2 1 -3 -2 -1 1 -1 -2 -3 2 3 x
Ex. Find the slope (a) using the line and (b) using points y (a) 3 2 1 rise = -2 -3 (b) (-2, 1) (1, -1) (x 1, y 1) (x 2, y 2) -2 -1 1 -1 rise = 3 -2 -3 2 3 x
Slope of Horizontal Lines y Ex. Find the slope of the line through (0, 2) and (2, 2). 3 2 1 -3 -2 -1 1 2 3 x (0, 2) (2, 2) (x 1, y 1) (x 2, y 2) -1 -2 -3 Slope of any horizontal line is 0!
Slope of Vertical Lines Ex. Find the slope of the line through (3, 2) and (3, 0). y 3 (3, 2) (3, 0) (x 1, y 1) (x 2, y 2) 2 1 -3 -2 -1 1 2 3 x -1 -2 -3 Slope of any vertical line is undefined!
Slopes of Lines y m is neg if line falls from left to right m is pos if line rises from left to right 3 m is undefined if line is vertical 2 1 -3 -2 -1 1 2 3 x -1 -2 -3 m is 0 if line is horizontal
Parallel and Perpendicular Lines Parallel Lines Perpendicular Lines slopes are the same slopes are negative reciprocals (mult. to -1) (or hor. & vert)
Ex. Determine whether the lines through the points are parallel, perpendicular, or neither. (-2, -15) and (0, -3); (-12, 6) and (6, 3) Slope of the first line is 6 and the slope of the second line is -1/6, so slopes are negative reciprocals; therefore, the lines are perpendicular
Groups Page 254: 37, 39, 41
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# Coordinate systems
Back to PastelMath
A coordinate system in ${\mathbb{R}}^{n}$ is a function $f : S \subset {\mathbb{R}}^{n} \to {\mathbb{R}}^{n}$ such that the restriction of $f$ to some cofinite set is a homeomorphism.
## Theory
Some commonly used coordinate systems include:
### Cartesian ${\mathbb{R}}^{n}$
${f}_{\textrm{c a r t e s i a n}} : {\mathbb{R}}^{n} \to {\mathbb{R}}^{n} : {f}_{\textrm{c a r t e s i a n}} \left({x}_{1} , \ldots , {x}_{n}\right) = \left(\begin{matrix}{x}_{1} \\ \setminus \vdots \\ {x}_{n}\end{matrix}\right)$
${f}_{\textrm{c a r t e s i a n}}^{-} 1 : {\mathbb{R}}^{n} \to {\mathbb{R}}^{n} : {f}_{\textrm{c a r t e s i a n}}^{-} 1 \left({x}_{1} , \ldots , {x}_{n}\right) = \left(\begin{matrix}{x}_{1} \\ \setminus \vdots \\ {x}_{n}\end{matrix}\right)$
### Spherical ${\mathbb{R}}^{n}$
The polar and spherical coordinate systems are simply special cases of the spherical coordinate system in ${\mathbb{R}}^{n}$:
Spherical coordinate systems are only defined for $n \ge 2$. To see where the spherical coordinate system gets its name, notice that $| {f}_{\textrm{h y p e r s p h e r i c a l}} \left(r , {\alpha}_{1} , \setminus \cdots , {\alpha}_{n - 1}\right) | = r$, where the norm is Euclidean.
### Generalized cylinder ${\mathbb{R}}^{n}$
All of the mentioned coordinate systems can be united under a single generalization. This is done by computing spherical coordinates only for the $k \le n$ first components of $v \in {\mathbb{R}}^{n}$, and leaving the other $n - k$ components as they were. This is called the generalized cylinder coordinate system. The spherical coordinate system is obtained by setting $k = n$. The cylinder coordinate system is obtained by setting $k = n - 1$. The Cartesian coordinate system is obtained by setting $k = 0$ (this is of course interesting only theoretically, since for $k = 0$, the conversion is just the identity function).
## Practice
Pastel implements coordinate conversions so that the Cartesian coordinate system is thought of as the most natural coordinate system. For all other coordinate system Pastel offers functions to convert to Cartesian coordinates and back. This way, if there are $n$ coordinate systems, only $O \left(n\right)$ conversion functions are needed instead of $O \left({n}^{2}\right)$ for conversions between all systems. Pastel offers conversion functions for the generalized cylinder coordinate system, as well as specialized functions for spherical and cylinder coordinate systems.
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- Monevator - https://monevator.com -
# Weekend reading: The exceptional mathematics of average returns
Good reads from around the Web.
The clever bods at The Value Perspective have been doing a sterling job recently in tackling the weird world of the average and what it means for returns [1].
From writing here on Monevator, I know a lot of people get confused when it comes to how average returns work in practice – or more specifically about the different kinds of average – and what it implies for our investment decisions, whether it’s asset allocation [2] or investing a lump sum [3] or confronting sequence of returns risk [4].
And when I say “a lot of people get confused”, I’ll admit that can include me!
So most people could do with a refresher on the maths.
Start with this Value Perspective article on the law of averages [5], which begins:
Let’s play a game we will call ‘Russian dice’, the rules of which were invented by a physicist/economist called Ole Peters. They are pretty simple – roll a dice and, if it comes up ‘one’, I will shoot you.
Do you fancy playing? It does not sound very appealing but, if you were a nihilistic mathematician, you might be tempted because – in the very strictest terms – on average you will be absolutely fine.
The word ‘average’, however, can be somewhat misleading if not defined very precisely. If 100 people roll the dice instantaneously, the average result is ‘three and a half’ – that is, (1 + 2 + 3 + 4 + 5 + 6) ÷ 6 – so, if you are judging the game on the average result, everyone survives.
However, if I asked you to roll the dice 100 times in a row, it is extremely unlikely you could do so without at some point seeing a ‘one’ come up. Bang. You do not get a chance to see the result of the 100-roll average over time.
Intuitively, we all know there is a difference between these scenarios without any complicated maths or concepts. Mathematically speaking, it is known as the difference between an ‘ensemble average’ (the average of an event happening many times concurrently) and a ‘time average’ (what happens when you do something a lot of times consecutively).
However, this concept and its implications are not well understood in investment.
After that first article provoked a fair bit of debate and confusion, their follow-up [6] tried to explain it with a diagram:
[This time] you simply start off with a stake of, say, £100 in the pot and we toss a coin. Every time the coin comes up heads, you increase what is in the pot by 50%; every time it comes up tails, you lose 40% of whatever is in the pot.
The coin is a fair one – so it is always a straight 50/50 chance – and there is not a firearm in sight.
Would you like to play?
At first sight, there appears to be no reason not to play – after all, if on each coin toss the only two possibilities are going up 50% or falling 40%, then surely, on average, it is a winning game. And indeed it is. No matter how long you play it for, on average, the expected return is positive – but, as we argued in the previous article, the word ‘average’, if not defined very precisely, can be misleading.
In this particular example, the average obscures a pattern where the majority of people who play the game actually end up losing.
Here’s the pattern:
[7]
Would you play the Value Perspective’s counter-intuitive game?
It reveals:
In the above example, 11 of the 16 possible sequences of coin tosses are losing permutations and, the longer the game goes on, the more money is lost.
In a game where the only possible outcome each time is a 50% upside or a 40% downside, that would appear counter-intuitive so what is complicating matters?
It is that difference between time and ensemble averages.
Read the whole article [6] for a deeper explanation.
Go on – you’ve got Sunday to recover from the headache!
p.s. I was struck by the latest article by Carl Richards for the New York Times [8] on the difficulties of investing in real estate. It’s aimed at US readers, and argues that most property investors will make a low return unless they have special skills and insights. How different from the UK, where almost anyone who bought a buy-to-let 5-10 years ago is an investing genius! Now it’s true that the US is a very different market when it comes to property. Still, I think the big divergence isn’t so much to do with the asset class as because their bubble burst and ours hasn’t. Would Richards have published this piece in the still-roaring US property market of 2006? I doubt it. (I wonder if he will be able to re-purpose his piece for a UK publication come 2016?)
### From the blogs
Making good use of the things that we find…
#### Other articles
Product of the week: Investing in alternative energy has an obvious appeal if you believe we’re not moving fast enough on climate change [21]. So I’d expect the latest share offer from long-established Tridos Renewables [22] to do well, especially since you can now put in as little as £50. With my hard-headed capitalist hat on though, I’d question whether the 5.8% return that The Guardian [23] estimates an investor who is cashing out would have achieved over the past nine years is enough for the risk. The 9-10% touted by the company is more like it, but is it realistic? I suppose there’s also a good vibes dividend to take into account.
### Mainstream media money
Some links are Google search results – in PC/desktop view these enable you to click through to read the piece without being a paid subscriber of that site.1 [24]
#### Passive investing
• Farewell to the fund manager [No plug for us 🙁 ] [Search result]FT [25]
• New ideas about asset allocation in retirement – WSJ [26] [w/ Mike [27]]
• Targeting the liquidity return premium – Swedroe / ETF.com [28]
#### Active investing
• Buy experiences, not things – The Atlantic [32]
• How to be rich with less money – Alan Roth/AARP [33]
• The optimal age to buy National Trust lifetime membership – Telegraph [34]
• The downsides of Scotland’s 12% stamp duty property tax – Telegraph [35]
• Beware this sophisticated Airbnb fraud – The Guardian [36]
• Author economics: The brutal truth [Search result]FT [37]
• Coming soon: (Happily) working until you die – CNBC [38]
Book of the week: The Education of a Value Investor [39] by hedge fund manager Guy Spiers is my new favourite book on active investing. It’s all about mindset rather than metrics and every active investor should read it. Prepare for regular plugs here.
Like these links? Subscribe [40] to get them every week!
1. Reader Ken notes that: “FT articles can only be accessed through the search results if you’re using PC/desktop view (from mobile/tablet view they bring up the firewall/subscription page). To circumvent, switch your mobile browser to use the desktop view. On Chrome for Android: press the menu button followed by “Request Desktop Site”.” [ [42]]
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# List (or set) of matrices
Hi, I am trying to write a function that will put all the 2x2 matrices over a finite field Z_p into a list or set. I am just switching from Mathematica to Sage, so this might be way off, but could you please help me go in the right direction?
def ListM(p):
var('UT')
UT=[]
for i1 in range(0,p):
for i2 in range(0,p):
for i3 in range(0,p):
for i4 in range(0,p):
UT=UT+[matrix([[i1,i2],[i3,i4]])]
I am trying to create a dummy list UT, and recursively add to it. I want it to serve as a variable though. The output gives me some error as well. I've been on it for a few hours and cant seem to figure it out.
edit retag close merge delete
Sort by » oldest newest most voted
You should mention what error you got. For creating all the 2x2 matrices over some finite field use the MatrixSpace class.
sage: M = MatrixSpace(GF(3), 2, 2)
sage: M
Full MatrixSpace of 2 by 2 dense matrices over Finite Field of size 3
sage: Mlist = M.list() # List containing all the matrices
sage: len(Mlist)
81
As for your function, it is also not correct, unless you have copy-pasted incorrectly.
1. First, the indentation in the function is wrong.
2. Secondly, you need not define UT to be a symbolic variable because you are redefining UT to be a list.
3. Thirdly, you are not returning anything from the function, so I don't know whether your function is incomplete, or this is what you intended.
more
def ListM(p):
UT=[]
for i1 in range(p):
for i2 in range(p):
for i3 in range(p):
for i4 in range(p):
UT=UT+[matrix([[i1,i2],[i3,i4]])]
return UT
Note that output of ListM(3) looks ugly, but this is a formatting "bug" when you display such a list, output is correct.
Python has very nice syntax for "list comprehensions", you may write:
def rows(p):
return [[x,y] for x in range(p) for y in range(p)]
def ListM(p):
return [matrix([r1,r2]) for r1 in rows(p) for r2 in rows(p)]
Of course in this case using MatrixSpace(GF(p),2,2) is definitely the right solution. Good luck with Sage !
more
## Stats
Seen: 589 times
Last updated: Mar 24 '13
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https://it.mathworks.com/matlabcentral/cody/problems/44652-draw-a-x/solutions/3306988
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Cody
# Problem 44652. Draw a 'X'!
Solution 3306988
Submitted on 21 Oct 2020 by Alex
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
n=3; y=[1 0 1 0 1 0 1 0 1]; assert(isequal(X(n),y))
2 Pass
n=4; y=[1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1]; assert(isequal(X(n),y))
3 Pass
n=1; y=[1] assert(isequal(X(n),y))
y = 1
4 Pass
n=2; y=[1 1;1 1] assert(isequal(X(n),y))
y = 1 1 1 1
5 Pass
n=5; y=[1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1]; assert(isequal(X(n),y))
### Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
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https://365financialanalyst.com/question/please-could-you-comment-on-my-p-value-understanding-below/
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02 Dec 2022
Posted on:
11 Apr 2022
0
# Please could you comment on my P-value understanding below?
Dear Author,
First of all, thank you very much for such a nice video presentation. But I have doubt below on exercise file.
So, the p-value is 0.038, right? we rejected the H0 "= program does not work" at all SL's, but 1%. So is the "1%" mean the following idea?:
"1% of those who employ the weight-loss program may not lose weight" - is, this correct?
Posted on:
02 Dec 2022
0
Hi, Timur.
Fellow student here. I think that's one way to put it. I would personally prefer to say that "There is 3.8% chance that those who do the training program may not lose weight." 3.8% for a more accurate number, the p-value.
Dominus vobiscum,
Julián
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# Weekly Challenge
Solve the challenge, share your solution and summit the ranks of our Community!
###### IDEAS WANTED
We're actively looking for ideas on how to improve Weekly Challenges and would love to hear what you think!
Submit Feedback
We've recently made an accessibility improvement to the community and therefore posts without any content are no longer allowed. Please use the spoiler feature or add a short message in the message body in order to submit your weekly challenge.
## Challenge #213: Optimized Flower Arrangements
Highlighted
7 - Meteor
So much work/ trial and error, for three tools. That took a while to figure out.
Highlighted
11 - Bolide
This was a great challenge - a simple problem to practice an infrequently-used tool. I have to spend quality time with Tool Mastery and help for some of these!
I solved this one with the Optimization tool (variables in rows) and with Python (PuLP). The output from the Python method is valid but slightly different (57 white daisies / 40 red roses, while the Optimization tool produced 40 white daisies / 57 red roses; still the same total of 417). I didn't want to mess with installing GLPK right now, so I used the PuLP default CBC solver.
Python version:
Spoiler
Code:
Spoiler
``````#################################
from ayx import Alteryx
Alteryx.installPackages(['pulp'])
from pandas import concat, DataFrame, Series
from pulp import GLPK, LpMaximize, LpProblem, LpStatus, lpSum, LpVariable
#################################
# read in the flower costs from the workflow and update the name
df.index = df['Flower'].str.replace(' ', '_').str.lower()
df.index.name = 'index'
#################################
# create a dictionary of cost for each flower name
costs = Series(data=df['Price']).to_dict()
costs
#################################
# define the model
model = LpProblem(name="flower-arrangements", sense=LpMaximize)
#################################
# define the decision variables
# this creates a dictionary of LpVariables with the same keys as costs
counts = {}
for k in costs.keys():
if k == 'filler_greens':
lb = 30
ub = 40
else:
lb = 40
ub = 80
counts[k] = LpVariable(name=k, lowBound=lb, upBound=ub, cat='Integer')
#################################
model += lpSum(costs[i] * counts[i] for i in costs.keys()) <= 950, \
'Total cost constraint'
#################################
# Set the objective (maximize the total number of flowers)
model += lpSum(counts[i] for i in counts.keys()), \
'Total number of flowers'
#################################
# Solve the optimization problem
status = model.solve()
# Get the results
print('--- status ---')
print(f"status: {model.status}, {LpStatus[model.status]}")
print('\n--- objective value ---')
print(f"objective: {model.objective.value()}")
print('\n--- variable values ---')
for v in counts.values():
print(f"{v.name}: {v.value()}")
print('\n--- constraints ---')
for name, constraint in model.constraints.items():
print(f"{name}: {constraint.value()}")
model.solver
#################################
# add the variables to a dataframe for output
df_vars = DataFrame({ 'value': [v.value() for v in counts.values()] },
index = [v.name for v in counts.values()])
df_vars.index.name = 'index'
#################################
# format the dataframe for output to the workflow
# with the original flower name
df_out = df[['Flower']].merge(df_vars, on='index')
df_out.columns = ['name', 'value']
#################################
# add a row for the objective value
df_out = concat([df_out, DataFrame({ 'name' : 'Objective Value',
'value' : model.objective.value() },
index=[0])] )
#################################
Alteryx.write(df_out, 1)``````
Alteryx version (variables in rows):
Spoiler
Highlighted
12 - Quasar
Spoiler
The optimization tool always gets me. Little options here and there that throw me off. Once I looked at old challenges using this tool it all clicked again.
Highlighted
Alteryx Certified Partner
Challenge Completed
Highlighted
12 - Quasar
really interesting tool to learn about. My solution enclosed.
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# What Is The Definition Of Two Dimensional?
## What is meant by 3 dimensional?
Having three dimensions (such as height, width and depth), like any object in the real world.
Also known as “3D”..
## What is the difference between two dimensional and three dimensional shapes?
A two-dimensional (2D) shape has only two measurements, such as length and height. … However, a three-dimensional (3D) shape has three measurements, such as length, width, and height. One example of a 3D shape is a rectangular prism, which is made up of four rectangles and two squares.
## Is a ray one dimensional?
A ray starts at a given point and goes off in a certain direction forever, to infinity. The point where the ray starts is called (confusingly) the endpoint. … A ray is one-dimensional. It has zero width.
## Are humans three dimensional?
Therefore, although a person (or any other object) occupies only a 3-dimensional volume in space, its path through spacetime would look like a 4-dimensional volume. … If you include time as a dimension, then people are 4 dimensional entities. (Three spacial dimensions, plus time equals spacetime).
## Is a cone 2 or 3 dimensional?
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
## What is a two dimensional shape with 4 sides?
A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides.
## What is meant by dimensional?
A measurement of length in one direction. Examples: width, depth and height are dimensions. … a square has two dimensions (2D), and a cube has three dimensions (3D). In Physics it can also mean any physical measurement such as length, time, mass, etc.
## What is an example of two dimensional?
A two-dimensional shape is a shape that has length and width but no depth. In mathematics, shapes (mathematical models) are derived from objects in the real world that have common geometric attributes. A circle is one example of a two-dimensional shape. A rectangle is another example of a two-dimensional shape.
## What is a 2 dimensional art?
Two-dimensional art processes and techniques are those that are created on a flat plane. They have height and width, but not significant depth. These include drawing, printmaking, painting, photography, and some mixed media.
## What are 2d shell elements?
• 2D shell—A 2D shell is a one-dimensional element that has constant thickness and represents a shell in one of the following models: ◦ 2D plane strain. ◦ 2D axisymmetric. 2D shell elements are linear but can be curved or straight, much as a beam element would be in a 3D model.
## Is drawing two dimensional?
When a work of art is classified as being 2-dimensional, it means that the composition possesses the dimensions of length and width but does not possess depth. All 2-dimensional pieces of art, such as drawings, paintings, and prints, are made up of shapes.
## Is a line two dimensional?
A line is one-dimensional. … So we have two dimensions, or “2D”. Circles, triangles, squares and more are plane shapes. Now we let that point move in another completely different direction and we have three dimensions.
## What are three dimensions?
A three dimensional universe is made up of three dimensions, width, breadth, and height.
## What is the meaning of 2 dimensional?
adjective. having the dimensions of height and width only: a two-dimensional surface. (of a work of art) having its elements organized in terms of a flat surface, especially emphasizing the vertical and horizontal character of the picture plane: the two-dimensional structure of a painting.
## What is a two dimensional figure called?
A two-dimensional figure, also called a plane or planar figure, is a set of line segments or sides and curve segments or arcs, all lying in a single plane. The sides and arcs are called the edges of the figure. The edges are one-dimensional, but they lie in the plane, which is two-dimensional.
## What are the attributes of 2 dimensional shapes?
In geometry, a two-dimensional shape can be defined as a flat plane figure or a shape that has two dimensions – length and width. Two-dimensional or 2-D shapes do not have any thickness and can be measured in only two faces.
## What are three dimensional shapes examples?
A cube, rectangular prism, sphere, cone and cylinder are the basic 3-dimensional shapes we see around us.
## What are 1d/2d 3d elements in FEM?
1D element is used for long and slender structure such as javelins, poles, etc. 2D element is used for plate or shell like structure while 3D element is used for structure with complex geometry which cannot be simplified for analysis.
## How do you define two dimensional elements?
In a two-dimensional model the elements are defined in one flat surface and deformations and loadings are restricted to act in the plane of this surface. Three different configurations of a two-dimensional model can be distinguished: Plane stress or membrane elements.
## What is meant by node or joint?
A node is a coordinate location in space where the degrees of freedom (DOFs) are defined. The DOFs for this point represent the possible movement of this point due to the loading of the structure. The DOFs also represent which forces and moments are transferred from one element to the next.
## What shape has no sides or corners?
sphereA sphere is a solid figure that has no faces, edges, or vertices. This is because it is completely round; it has no flat sides or corners.
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# Purchasing Power Parity Converted GDP Chain per worker for Sierra Leone
2010: 2,422.45013 2005 International Dollars per Worker (+ see more)
Annual, Not Seasonally Adjusted, RGDPWOSLA627NUPN, Updated: 2012-09-17 9:55 AM CDT
Click and drag in the plot area or select dates: Select date: 1yr | 5yr | 10yr | Max to
Worker for this variable is usually a census definition based of economically active population. More information is available at http://pwt.econ.upenn.edu/Documentation/append61.pdf.
For proper citation, see http://pwt.econ.upenn.edu/php_site/pwt_index.php
Source Indicator: rgdpwok
Source: University of Pennsylvania
Release: Penn World Table 7.1
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w h
Graph Background: Plot Background: Text:
Color:
(a) Purchasing Power Parity Converted GDP Chain per worker for Sierra Leone, 2005 International Dollars per Worker, Not Seasonally Adjusted (RGDPWOSLA627NUPN)
Worker for this variable is usually a census definition based of economically active population. More information is available at http://pwt.econ.upenn.edu/Documentation/append61.pdf.
For proper citation, see http://pwt.econ.upenn.edu/php_site/pwt_index.php
Source Indicator: rgdpwok
Purchasing Power Parity Converted GDP Chain per worker for Sierra Leone
Integer Period Range: to copy to all
Create your own data transformation: [+]
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Use a formula to modify and combine data series into a single line. For example, invert an exchange rate a by using formula 1/a, or calculate the spread between 2 interest rates a and b by using formula a - b.
Use the assigned data series variables above (e.g. a, b, ...) together with operators {+, -, *, /, ^}, braces {(,)}, and constants {e.g. 2, 1.5} to create your own formula {e.g. 1/a, a-b, (a+b)/2, (a/(a+b+c))*100}. The default formula 'a' displays only the first data series added to this line. You may also add data series to this line before entering a formula.
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``` University of Pennsylvania, Purchasing Power Parity Converted GDP Chain per worker for Sierra Leone [RGDPWOSLA627NUPN], retrieved from FRED, Federal Reserve Bank of St. Louis https://research.stlouisfed.org/fred2/series/RGDPWOSLA627NUPN/, April 18, 2015. ```
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Name: Email:
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+ -
## GK Trick
### Reasoning Quiz For IBPS Clerk Mains: 2019
Directions (1-5): Study the following information and answer the questions given below:
Eight persons are sitting around a circular table such that four of them are facing towards the center and the rest outside. They work in different ministries i.e. A, B, C, D, E, F, G, H but not necessarily in the same order. They have their breaks in different time slots i.e. 8-9, 9-10 and 10-11. Not more than three persons have break in the same slot. The one who works in G sits opposite to the one who works in E. N sits opposite to S, who works in A. N neither works in D nor B. T is not neighbor of P. The ones who work in G, works with only the one who works in C. N sits 3rd right to Q. N faces towards the center. The immediate neighbors of S have break in same slot. Two persons sit between N and O.T, who works in E sits 3rd right to O. The one who sits opposite to M has break in the same slot as M. The one who works in E has break before the one who sits immediate right to T. Immediate neighbors of P faces center. P sits 2nd right to M and has break in 8-9 time slot. The one who works in H sits opposite to the one who works in F. Neither M nor O works in H. The one who works in E is not neighbor of the persons who work in F and B. S and T do not face same direction as O. The one who works in D has break in the time slot just after P. R does not works in A.
Q1. Who among the following works in B?
P
N
S
T
none of these
Q2. How many persons are sitting between the one who works in D and G (in clockwise direction from the one from D)?
four
three
two
one
none of these
Q3. Who among the following has break in last shift?
N, R
S, P
M, T
O, P
none of these
Q4. Which of the following combination is true?
S-A-(8-9)
P- C-(10-11)
Q- E-(9-10)
M- B-(9-10)
none of these
Q5. Four of the five are alike in a certain way and hence form a group, which among the following does not belong to the group?
Q
S
M
P
O
Directions (6-10): Study the following information carefully to answer the given questions:
A number arrangement machine when given an input line of numbers rearranges them following a particular rule. The following is an illustration of input and rearrangement.
Input: 10 51 18 47 26 65 61 32
Step I: 12 51 18 47 26 61 32 63
Step II: 22 12 51 47 26 32 63 57
Step III: 34 22 12 47 32 63 57 43
Step IV: 48 34 22 12 47 57 43 31
Step IV, is the last step of the rearrangement. As per the rules followed in the above steps, find out in each of the following questions the appropriate steps for the given input.
Input: 81 8 22 73 34 97 44 57
Q6. Which of the following is the last step of the following Input?
34 22 12 47 32 63 57 43
32 63 57 4360 42 26 10
60 42 26 10 95 77 65 41
95 77 65 4160 42 26 10
None of these
Q7. What will be the addition of the numbers which is forth from the right end in step II and 4th from the right end in step IV?
139
100
97
107
None of these
Q8. Which of the following would be the difference of the numbers which is 2nd from right end in step IV and 1st from right end in Step II?
12
14
17
10
None of these
Q9. Which of the following element will be 2nd to the left of 4th from the right end in step III?
10
26
44
57
None of these
Q10. How many steps will be required for the following machine input-output?
6
3
5
4
None of these
Directions (11-15): Answer these questions based on the following information.
In a certain code:
“choice question section update” is coded as - “lt mx tr ce”
“aspirant everyday update bank” is coded as - “ro iy ce nh”
“question section similar aspirant” is coded as - “mx tr qc ro”
“everyday similar update choice” is coded as – “iy qc ce lt”
Q11. What will be the code for “everyday”?
ce
ro
qc
can’t be determined
iy
Q12. What may be the code for “choice bank monsoon”?
lt nh kl
tr nh kl
ce mx iy
either (a) or (b)
None of these
Q13. What will be the code for “aspirant”?
mx
iy
ro
qc
tr
Q14. What may be the code for “update software”?
ce tr
iy mx
tr ro
ce gh
None of these
Q15. “nh” is the code for?
bank
question
section
update
None of these
SOLUTIONS
1.E
2.C
3.A
4.A
5.B
6.C
7.A
8.A
9.A
10.D
11.E
12.A
13.C
14.D
15.A
5 Banking and SSC : Reasoning Quiz For IBPS Clerk Mains: 2019 Directions (1-5): Study the following information and answer the questions given below: Eight persons are sitting around a circular table...
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## Worksheet #2 On Histograms And Box And Whisker Plots - Free Download PDF
29d ago
4 Views
518.25 KB
11 Pages
Transcription
9852 - 1 - Page 1Name:Chapter 16 Worksheet #2 and Notes on Histograms and Box and Whisker Plots Algebra, Mrs. SlackJoles1)Using the data below, complete the frequency table.DATA: 30, 32, 11, 14, 40, 37, 16, 26, 12, 33, 13, 19, 38, 12, 28, 15, 39, 11, 37, 17, 27, 14, 362)The test scores for 10 students in Ms. Sampson's homeroom were 61, 67, 81, 83, 87, 88, 89, 90,98, and 100. Which frequency table is accurate for this set of data?A)C)B)D)
9852 - 1 - Page 23)The graph below shows the distribution of scores of 30 students on a mathematics test.Complete the frequency table below using the data in the frequency histogram shown.4)The scores on a mathematics test were 70, 55, 61, 80, 85, 72, 65, 40, 74, 68, and 84. Completethe accompanying table, and use the table to construct a frequency histogram for these scores.
9852 - 1 - Page 35)6)Which one of the following histograms represents the data in the table below?A)C)B)D)The following data consists of the weights, in pounds, of 24 high school students: 195, 206, 100,98, 150, 210, 195, 106, 195, 108, 180, 212, 104, 195, 100, 216, 99, 206, 116, 142, 100, 135,98, 160.Using this data, complete the accompanying cumulative frequency table and construct a cumulativefrequency histogram on the grid below.
9852 - 1 - Page 47)The accompanying table shows the weights, in pounds, for the students in an algebra class. Usingthe data, complete the cumulative frequency table and construct a cumulative frequency histogramon the grid below.8)The accompanying diagram is an example of which type of graph?A) bar graphB) histogram9)C) box-and-whisker plotD) stem-and-leaf plotGiven the following data:10, 8, 9, 16, 19, 15, 20, 16, 21, 22, 19Which of the following is the box-and-whisker graph for this data?A)C)B)D)
9852 - 1 - Page 510)Construct a box-and-whisker graph using the following data:16, 12, 13, 14, 16, 18, 15, 17, 20, 12, 14, 15, 15Questions 11 through 14 refer to the following:The accompanying box-and-whisker plot represents the scores earned on a science test.11)12)According to the diagram shown, what is the median score?A) 75B) 70C) 85D) 77According to the diagram shown, what score represents the first quartile?A) 55B) 70C) 100D) 7513)What statement is not true about the box and whisker plot shown?A) 75 represents the mean scoreC) 85 represents the 3rd quartileB) 100 represents the maximum scoreD) 55 represents the minimum score14)A score of an 85 on the box-and-whisker plot shown refers toA) the third quartileC) the medianB) the maximum scoreD) the mean15)(a) Arrange the following data from least to greatest and find the median.20, 25, 24, 17, 18, 19, 21, 27(b) Find the median of the upper half of the data. What is this called?(c) Find the median of the lower half of the data. What is this called?(d) Draw a box-and-whisker graph using the above information.
9852 - 1 - Page 616)The accompanying histogram shows the heights of the students in Kyra's health class.What is the total number of students in the class?A) 15B) 20917)D) 5The accompanying histogram shows the height distribution for students in a high schoolmathematics class.What is the total number of students in the class?A) 28B) 2618)C) 16C) 49D) 11Using the cumulative frequency table below, how many students received a test score betweena 70-79?A) 0B) 80C) 12D) 26
9852 - 1 - Page 7Questions 19 through 21 refer to the following:The test scores for 20 students in a Spanish class are shown in the frequency table below.19)According to the information shown, how many students received a score greater than a 69?20)The median lies in which interval of the frequency table shown?21)The upper quartile lies in which interval of the frequency table shown?22)Which of the following sets of data values could represent the box-and-whisker plot below?A) 3, 10, 11, 13, 21B) 3, 6, 9, 12, 15, 18, 21C) 3, 9, 10, 12,16, 18, 21D) 3, 9, 10, 11, 13, 15, 18, 21
9852 - 1 - Page 823)The USA Track and Field Committee published the following report illustrating the comparison oflap speed and finishing placement of several top relay teams.Based on the bar graph above, which of the following conclusions is most accurate?A) The first-place team was twice as fast as the fourth-place team.B) The fastest time for the 200-meter relay is 7 meters per second.C) The first-place and second-place teams were closest in time to one another.D) Every runner on the first-place team ran faster than the runners on the second-place team.24)A television network wants to pilot a new series in a city with 25,000 residents. They decided tochoose a random sample of 1,000 people to determine the best time to run the series. The surveyasked participants to state what time of day they watched the most television. The table belowshows the results.Based on these results, approximately how many people in the city watch television between 4 pmand 7 pm?A) 8,050 peopleC) 14,500 peopleB) 1,450 peopleD) 580 people
9852 - 1 - Page 925)The Statistical Data Bureau published an analysis of incomes and expenditures of 100 averagefamilies throughout the United States. The circle graph below represents the Rosen family'smonthly budget.If their total monthly income is 1,820, how much money do they spend each month on food?A) 546B) 728C) 606D) 18226)The accompanying graph shows the amount of water left in Rover's water dish over a period oftime.How long did Rover wait from the end of his first drink to the start of his second drink of water?A) 60 secB) 30 secC) 10 secD) 75 sec27)Janae's first seven French grades for the year are 91, 87, 80, 99, 85, 78, and 90. What grade is atthe 75th percentile?A) 90B) 78C) 90.5D) 91
9852 - 1 - Page 1028)Terri waitressed 10 days out of the last two weeks. The amount of money she earned each day intips are 32, 58, 17, 27, 69, 73, 42, 38, 24, and 52. How much money is at the50th percentile?A) 42B) 69C) 38D) 4029)The median of any set of data always represents theA) upper quartileC) mean of the dataB) 50th percentileD) 1st quartile30)Ms. Michalson drew a box-and-whisker plot to represent her students' scores on a recent math test.If Jennifer scored a 85 on the test, explain how her grade compares with the rest of her class.Questions 31 through 34 refer to the following:The number of text messages 10 different students sent in 1 day is shown in the box-and-whisker plotbelow.31)What is the minimum number of text messages sent according to the plot shown?A) 0B) 2C) 20D) 832)What number is at the 50th percentile according to the plot shown?A) 12B) 8C) 14D) 1033)According to the plot shown, between what two numbers does half of the data lie?A) 10 and 12B) 8 and 12C) 8 and 14D) 2 and 2034)According to the plot shown, how many text messages are at the 75th percentile (upper quartile)?A) 15B) 12C) 13.5D) 14
9852 - 1 - Page 11Questions 35 through 37 refer to the following:In order to pass a driver's safety course, a person must answer at least 45 out 50 questions correctly.The cumulative histogram below gives the scores of a group of people who passed the exam.35)According to the table shown, how many total people passed the driver's safety exam?A) 25B) 57C) 50D) 2036)According to the table shown, how many people answered 49 questions correctly?A) 5B) 9C) 14D) 4137)According to the table shown, how many people received a score of 48 or less?A) 23B) 9C) 11D) 25
B) The fastest time for the 200-meter relay is 7 meters per second. C) The first-place and second-place teams were closest in time to one another. D) Every runner on the first-place team ran faster than the runners on the second-place team. 24) A television network wants to pilot a new series in a city with 25,000 residents. They decided to
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Enable contrast version
# Tutor profile: Elena T.
Inactive
Elena T.
Math&Physics Educator | Hydraulic Numerical Modeler
Tutor Satisfaction Guarantee
## Questions
### Subject:Physics (Waves and Optics)
TutorMe
Question:
An observer standing by the edge of a pond perceives it as 1 m deep near the shoreline. A refractive index of water is $$n=1.33$$. What is the true depth of the pond?
Inactive
Elena T.
Let $$A$$ be a point on the bottom of the pond; $$B$$ be a point on the surface directly above $$A$$; and $$C$$ be a point on the surface at a small distance from $$B$$. Think of a light ray directed from $$A$$ to $$C$$. This ray makes an angle $$\theta_i$$ with the vertical in water, and then refracts at $$C$$ as it transitions into the air, and continues at angle $$\theta_r$$ with the vertical. From the Snell's law, $$\sin{\theta_r}=n\sin{\theta_i}$$ (1) (refractive index of an air is approximately unity). Let us extend the airborne segment of the ray back into the water, where it intersects line $$AB$$ at point $$D$$. As follows from the Snell's law, $$\theta_r > \theta_i$$, so point $$D$$ is positioned above point $$A$$. Above the water, the ray appears coming from point $$D$$ (please make the drawing, if you are actually working through this solution). Distance $$DB$$ is the perceived water depth. Distance $$AB$$ is the true water depth. From trigonometric relations for triangles $$ABC$$ and $$DBC$$, $$\tan {\theta_i}=BC/AB$$, (2) and $$\tan {\theta_r}=BC/DB$$. (3) Neglecting difference between $$\sin{\theta}$$ and $$\tan{\theta}$$ for small angles $$\theta$$, and substituting (2) and (3) into (1), we obtain from Snell's law: $$AB=n \cdot DC$$. That is, the true depth of the pond is $$n$$ times its perceived depth, 1.33 m in our case.
### Subject:Physics (Newtonian Mechanics)
TutorMe
Question:
A bucket is suspended above a well from a cord winding around a drum. The drum weights $$M=15$$ kg. It is a uniform wooden cylinder of radius $$r=0.1$$ m which can rotate with negligible friction around the horizontal axis. The bucket weights $$m=5$$ kg. The bucket is released from the rest and falls into the well. Neglecting the weight of the cord, find the tension force in the cord while the bucket is falling.
Inactive
Elena T.
Motion of three bodies has to be considered — that of the bucket, the drum, and the cord. (1) The bucket is in translational motion (when all its points move along parallel trajectories) along the vertical axis, which is fully determined by a trajectory of a single point — its centre of mass. The Newton’s 2-d law of motion for the bucket’s centre of mass states: $$m \cdot \vec{a_b} = \vec{T_b} + m \vec{g}$$, where $$\vec{a_b}$$ is the bucket’s acceleration (we won’t differentiate anymore between the bucket and its centre of mass); $$\vec{T_b}$$ is the force exerted by cord directed up; $$\vec{g}$$ is the gravity acceleration directed down. (2) The drum rotates about a horizontal axis coming through its centre of mass. The only uncompensated force acting on the drum is that exerted by the cord $$\vec{T_c}$$, applied at a horizontal distance $$r$$ from the axis and directed down. This force creates a torque with a magnitude $$rT_c$$ (hereafter, $$a$$ stands for a vertical projection of the vector $$\vec{a}$$), which is equal to the rate of change of the drum's angular momentum $$I \gamma$$, where $$I$$ is the drum's moment of inertia about the rotation axis, and $$\gamma$$ is the angular acceleration: $$I \gamma = rT_c$$. (3) By the Newton’s 3-d law, the vertical segment of the cord is pulled on the ends by oppositely directed forces $$-\vec{T_b}$$ and $$-\vec{T_c}$$. It would experience an infinitely large acceleration, if these forces were not in balance. Hence, $$\vec{T_b}+\vec{T_c}=0$$. (4) And finally, the bucket's acceleration must be equal to the tangential acceleration of a point on the rim of the drum directly above the bucket (which follows from the assumption that the cord does not stretch, so all points in its vertical segment, from the bucket to the rim of the drum, have the same velocity and the same acceleration). Combing (1)-(4), expressing the vector equations in the vertical projection, positive down, and using $$T=T_c=-T_b$$ for the tension in the cord, yields: $$m \cdot a_b = - T + m g$$ (2-nd law for the bucket) $$I \gamma = rT$$ (moment equation for the drum) $$a_b =r \gamma$$ (kinematic condition (4) ) Solving for $$T$$ yields: $$T=mgI/(I+mr^2)$$. The moment of inertia of the drum (a uniform cylinder) is $$I=Mr^2/2$$, so $$T= g mM/(M+2m)$$. Substituting numbers in units of SI gives $$T=3 g$$ ($$kg \cdot m/s^2$$).
### Subject:Calculus
TutorMe
Question:
A shape in $$xy$$-plane is given by $$x^2+y^2+9 \le 6x+2y$$. Find the volume of the solid obtained by revolving the shape about the $$y$$-axis.
Inactive
Elena T.
Let us re-write the inequality as $$(x^2-6x+9)+(y^2-2y) \le 0$$, or $$(x-3)^2+(y-1)^2 \le 1$$. We see, that the shape is a disk of a unit radius centered at $$(3,1)$$. The sought solid of revolution is, therefore, a torus. Its volume is composed of very thin rings, swept by the shape’s elementary sub-areas $$dA=dxdy$$ rotating about $$y$$-axis. The sub-areal $$x$$-coordinate is the radius of the ring which the sub-area generates. Each sub-area sweeps a volume $$dV=2 \pi x \cdot dA$$, which is the volume of a very thin rod of a length $$2 \pi x$$ and a base area $$dA$$, bent to form a circle of radius $$x$$. The total volume can be found by integration over the shape $$V=\int \int {dV} = \int \int {2 \pi x dA} = 2 \pi x_c A$$, where $$x_c=(1/A) \int \int {x dA}$$ is the x-coordinate of the shape’s centroid, as well as the centroid’s distance to the axis of rotation. (We just proved Pappus's theorem for the volume generated by a revolving shape: this volume is the product of the shape’s area and the circumference of the circle traveled by the shape’s centroid. The axis of rotation should be outside the shape, though.) For our disk, its centroid coincides with its center: $$x_c=3$$. Revolving about $$y$$-axis, the centroid makes a circle with a circumference $$6 \pi$$. The disk’s area $$A=\pi$$, since the radius is a unit. The sought volume is then: $$V=6 \pi^2$$.
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# HW8 - 3 Find the shear flow for the three-stringer section...
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EAS4200C Aerospace Structures Homework #8 (Due: Nov. 6th) 1 Find the flexural shear flow produced by the transverse shear force V z = 1,000N in the beam with the thin-walled section given in the figure. Sketch the shear flow on the cross-section. Assume that V z is applied at the shear center. 2. Find the shear center of the cross-section above.
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Unformatted text preview: 3. Find the shear flow for the three-stringer section shown in the figure for V z = 5,000N and V y = 0. Given shear modulus G = 27GPa, find the twist angle per unit length. Also determine the shear center. Is the shear flow statically determinate?...
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Indicate the life of a lamp from the new process with .Y. The mean of Y is and the standard deviation of Y is Y 200 hours. The manager accepts the alternative hypothesis as Y 2100 hours. a) The magnitude of a test is the probability of falsely rejecting a valid null hypothesis. We first calculate the probability that the manager falsely accepts the null hypothesis when it is invalid:.
## Linear Regression with One Regressor
Solutions to Odd Number End-of-Chapter Exercises 17. a) ui represents factors other than time that affect the student's performance on the exam, including amount of time to study, aptitude for the material, and so on. Some students will have studied more than average, others less; some students will have higher than average aptitude for the subject, others lower, and so on. The expectation of ˆ0 is obtained by taking expectations from both sides of Equation (4.8): YiY for all i, which implies thatˆ10, or that Xi is constant for all i.
Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals
## Linear Regression with Multiple Regressors
Note that the estimator for 1 is identical to the OLS estimator from the regression of Y on X1, omitting X2. In other words, when (X1iX1)(X2iX2) 0 , the estimated coefficient on X1 in the OLS regression of Y on X1 and X2 is equal to the estimated coefficient in the OLS regression of Y on X1.
## Hypothesis Tests and Confidence Intervals in Multiple Regression
The BDR coefficient measures the partial effect of the number of bedrooms, holding the house size (Hsize) constant. If lot size were measured in thousand square feet, the rating coefficient would be 2 instead of 0.002. a) Treatment (allocation into small sections) was not randomly distributed in the population (continuing students and newly enrolled students) due to the difference in the proportion of treated continuing students and newly enrolled students. Solutions to end-of-chapter exercises 25. b) Since the treatment was randomly assigned based on enrollment status (continuing or newly enrolled), E(u | X1, X2) will not depend on X1.
## Nonlinear Regression Functions
However, since X2 was not randomly assigned (newly enrolled students may, on average, have attributes other than being newly enrolled that affect test scores), E(u | X1, X2) may depend on X2, so that ˆ2 can be biased and inconsistent. With all three binary class size variables included in the regression, it is impossible to calculate OLS estimates because the intercept is a perfect linear function of the three class size regressors. a) (1) Demand for older journals is less elastic than for younger journals because the interaction term between the log of journal age and price per citation is positive. As described in Equation (8.8) and Note on page 303, the standard error can be found by dividing 0.28, the absolute value of the estimate, by the square root of .
The signs will not change and the constant (intercept) will change. ii) The error term has a standard deviation of 2.65 (measured in logarithmic points). However, the regression does not control for many factors (firm size, industry, profitability, experience, and so on). Discrimination on the basis of gender means that two workers who are the same in all respects except gender receive different wages.
It is therefore also important to check for employee characteristics that can influence their productivity (education, number of years of experience, etc.). These are potentially important omitted variables in the regression that will lead to bias in the OLS coefficient estimator for women. Since these characteristics were not controlled for in the statistical analysis, it is premature to draw conclusions about gender discrimination. ii) Female is correlated with the two new variables included and at least one of the variables is important for explaining ln(Income).
Solutions to End-of-Chapter Exercises 27. c) Neglecting the effect or return, whose effects appear to be small and statistically insignificant, the formula for the omitted variable bias (see equation (6.1)) suggests that female is negatively related to ln(market value) .
## Assessing Studies Based on Multiple Regression
Both regressions suffer from omitted variable bias, so they will not provide reliable estimates of the causal effect of income on test scores. However, the non-linear regression in (8.18) fits the data well enough that it could be used for forecasting. Internal consistency: To the extent that price is affected by demand, there may be simultaneous equation bias.
External consistency: The Internet and the introduction of "e-journals" may cause significant changes in the academic journal market, so results for the year 2000 may not be relevant to today's market. Since all Xi are used (although some are used for incorrect values of Yj), X X and. As elsewhere in the book, we interpret n 300 as a large sample, so we use an approximation of n that tends to infinity.
Solutions for Odd Number End of Chapter Exercises 31. where the last result follows because Xi X. i for the shuffled observations and Xj is independent of Xi for i j. c) Yes, the estimator based on the first 240 observations is better than the adjusted estimator from part (b). Equation (4.21) in Key Concept 4.4 (page 171) implies that the estimator based on the first 240 observations has a variance, ie From part (a), the OLS estimator based on all the observations has two sources of sampling.
## Regression with Panel Data
To check the robustness of the linear specification, it would be useful to consider a log or a quadratic specification. Measurement error does not appear to be a problem, as variables such as traffic fatalities and taxes are accurately measured. Similarly, sample selection is not a problem because data are used from all states.
Expert knowledge is required to determine if this is a problem. a) Average snowfall does not change over time, and so will be perfectly aligned with the state fixed effect. In this case T is small (T 4), so the normal approximation by CLT is unlikely to be very good.
## Regression with a Binary Dependent Variable
Solutions to odd-numbered end-of-chapter exercises 37. b) With the P/I ratio reduced to 0.30, the probability of rejection is. For a white applicant who has a P/I ratio of 0.35, the probability that the application is the probability of being denied is 2.519. the probability of denial is 2.08 percentage points lower. In the functional form of logit regression, the marginal effect depends on the probability level which in turn depends on the race of the applicant.
The coefficient on black is 0.084, indicating an estimated rejection probability that is 8.4 percentage points higher for the black applicant. Such variables must be related to race and also be related to the probability of default on the mortgage (which in turn would lead to denial of the mortgage application). Standard measures of default probability (past credit history and employment variables) are included in the regressions shown in Table 9.2, so these omitted variables are unlikely to affect the answer in (a).
Other variables such as education, marital status, and occupation may also be related to the probability of default, and these variables are omitted from the regression in the column. Adding these variables (see columns (4)-(6)) has little effect on the estimated effect of black on the probability of mortgage rejection. one).
## Instrumental Variables Regression
The response of demand to a fall in income will be less in the short run than in the long run. There are other factors that can influence both the choice to serve in the military and the annual earnings. Another variable is "ability", which is difficult to measure, and thus difficult to control for in the regression.
The draft was determined by a national lottery, so the choice of military service was random. Because it affects the probability of serving in the military, the lottery number is important. For students in kindergarten, the estimated effect of small class treatment compared to being in a regular class is an increase of 13.90 test points with a standard error of 2.45.
For students in Grade 1, the estimated effect of small class treatment compared to being in a regular class is an increase of 29.78 test scores with a standard error of 2.83. The local network is a failure to follow the treatment protocol, and this leads to bias in the OLS estimator of the average causal effect. The treatment is to make connections available in the room; the treatment is not using the internet.
Following the notation used in Chapter 13, let 1i denote the coefficient on the state sales tax in the first stage” IV regression, and let 1i denote the cigarette demand elasticity.
## Introduction to Time Series Regression and Forecasting
Solutions for the exercises at the end of the odd numbered chapter 45. d) The conditional expectation of YT1 given YT is.
## Estimation of Dynamic Causal Effects
The dynamic causal effects are for Experiment A. The regression in Exercise 15.1 does not control for interest rates, so interest rates are assumed to evolve in their "normal pattern" given changes in oil prices.
Additional Topics in Time Series Regression
The Theory of Linear Regression with One Regressor
## ˆ 1 RLS ,
Combining the results on the numerator and denominator and applying Slutsky's theorem leads to Using the conditional mean and conditional variance of ˆ1RLS derived in parts (c) and (d), respectively, the sampling distribution of ˆ1RLS, conditional on X1,, Xn. The inequality follows by applying the Cauchy-Schwartz inequality, and the second inequality follows due to the finite fourth moments of (Xi, ui).
The finite variance together with the fact that we have the mean zero (by assumption 1 in Key Concept 15.1) and we are i.i.d. by assumption 2) implies that the sample mean v satisfies the requirements of the central limit theorem. satisfies the central limit theorem. The conditional probability distribution function of ui and Xi given uj and Xj is f (ui, Xi|uj, Xj). The second equality used the conclusion from part (a) and the independence between Xi and Xj.
In this case, the result follows directly if the nonzero exponent (r or s) is less than 4. Note: In early printing of the third edition, there was a typographical error in the expression for Y|X. The result was also shown in Exercise 13.10, and the procedure used in the exercise is discussed in part (b).
## The Theory of Multiple Regression
Solutions to the odd end-of-chapter exercises 71. where the second equality uses the fact that Q is a scalar and the third equality uses the fact that Q cw. b) Since the covariance matrix W is positive definite, we have cwc 0 for every non-zero vector from the definition.
The second equality used assumption (ii) that (,X Wi i, Y)i are i.i.d., and the third equality enforced assumption of conditional mean independence (i). e) n1X M X W converges in probability to a finite irreducible matrix, and n1X M U W converges in probability to a zero vector.
Fever is a common issue in neurological intensive care unit and is associated with a poor neurological outcome in traumatic brain injury.. Hospital treatment of patient with traumatic
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# PracticalApproachToYose/Problem 1 Solution
Path: <= Endgame =>
### Black's continuation
tenuki
Second line hane connect: 3 points.
First line hane into 12 point: 3 points.
### White's continuation
tenuki
Second line hane connect: 3 points.
First line hane connect depth 2: 4 points.
3 + 3 + 3 + 4 = 13 points
The yose here worth 13 points gote.
Iago Why is tenuki ? since the value of the sente follow up is bigger than the initial play, shouldnt Black play 4 now, maybe at 9 ?
Path: <= Endgame =>
PracticalApproachToYose/Problem 1 Solution last edited by 2a01:0e34:ec97:49d0 on August 27, 2022 - 01:08
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The OEIS is supported by the many generous donors to the OEIS Foundation.
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A373461 a(n) = s - t where s = ceiling(sqrt(n*i)), t = sqrt(m), and m = s^2 mod n, for the smallest positive integer i for which m is square. 1
1, 2, 1, 2, 1, 2, 3, 2, 3, 4, 5, 2, 7, 8, 3, 4, 9, 6, 11, 4, 3, 14, 15, 4, 5, 16, 3, 6, 19, 6, 21, 4, 9, 24, 5, 6, 25, 26, 9, 4, 29, 6, 31, 12, 5, 34, 35, 6, 7, 10, 9, 14, 39, 12, 5, 8, 9, 44, 45, 6, 47, 48, 7, 8, 5, 12, 51, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,2 COMMENTS This is "s - t" in Hart's factoring algorithm. The quantities found have s^2 - t^2 = (s-t)*(s+t) = n*i when n >= 3 and Hart notes that g = gcd(s-t, n) is a nontrivial factor of n (when n is composite). REFERENCES S. S. Wagstaff, Jr., The Joy of Factoring, AMS, 2013, pages 119-120. LINKS Table of n, a(n) for n=1..68. William B. Hart, A One Line Factoring Algorithm, J. Aust. Math. Soc. 92 (2012), 61-69. EXAMPLE For n=9, i=1, s=ceiling(sqrt(9*1))=3 and m=0 then s-floor(sqrt(m))=3-0=3, so a(9)=3. Also gcd(9, 3) gives a divisor of 3. PROG (Python) from sympy.ntheory.primetest import is_square from sympy.core.power import isqrt A003059 = lambda n: isqrt((n)-1)+1 def a(n): i = 1 while True: s = A003059(n*i) if is_square(m:=pow(s, 2, n)): return s-isqrt(m) i+=1 print([a(n) for n in range(1, 69)]) (PARI) a(n) = my(i=1, s, t); while(!issquare((s=sqrtint((n*i)-1)+1)^2 % n, &t), i++); s-t; CROSSREFS Cf. A003059, A362502. Sequence in context: A325622 A060145 A358997 * A257806 A035391 A242552 Adjacent sequences: A373458 A373459 A373460 * A373462 A373464 A373465 KEYWORD nonn AUTHOR Darío Clavijo, Jun 06 2024 STATUS approved
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Last modified August 5 04:43 EDT 2024. Contains 374935 sequences. (Running on oeis4.)
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## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.
A polynomial is an expression of power n where n= 0, 1, 2, 3… n
Where n is a positive integer.
Degree of a polynomial in one variable: -
In case of a polynomial in one variable, the highest power of the variable is called the degree of polynomial.
Polynomial of various degrees
♦ Linear polynomial: - a polynomial of degree 1 is called a linear polynomial.
♦ Quadratic polynomial: - A polynomial of degree 2 is called a quadratic polynomial.
♦ Cubic polynomial: - A polynomial of degree 3 is called a cubic polynomial.
♦ Biquadratic polynomial: - A polynomial of degree 4 is called a biquadratic polynomial.
Number of terms in a polynomial: -
♦ Monomial: - A polynomial containing one nonzero term is called a monomial.
♦ Binomial: - A polynomial containing two nonzero terms is called a binomial.
♦ Trinomial: - A polynomial containing three nonzero terms is called a trinomial.
Example of adding and subtracting polynomials: -
Question1: - Add the following polynomials
y^4 + 2y^2 + 3y + 5 and 5y^4 + 4y^3 + 3y^2 + 5y
Solution: -
(y^4 + 2y^2 + 3y + 5) + (5y^4 + 4y^3 + 3y^2 + 5y)
=(y^4 + 5y^4) + 4y^3 + (2y^2 + 3y^2) + (3y + 5y) + 5
=6y^4 + 4y^3 + 5y^2 + 8y + 5
Question2: - Subtract the following polynomials:
Z^3 + 2z + 1 and z^2 + 3z + 5
Solution: -
(z^3 + 2z + 1) - (z^2 + 3z + 5)
=z^3 + 2z + 1 – z^2 -3z -5
=z^3 – z^2 –z -4
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# Question: The Eastern Shuttle Inc is a regional airline providing shuttle
The Eastern Shuttle, Inc., is a regional airline providing shuttle service between New York and Washington, D.C. An analysis of the monthly demand for service has revealed the following demand relation:
Q = 26,000 - 500P - 250POG + 200IB - 5,000S,
where Q is quantity measured by the number of passengers per month, P is price (\$), POG is a regional price index for other consumer goods (1967 = 1.00), IB is an index of business activity, and S, a binary or dummy variable, equals 1 in summer months and 0 otherwise.
A. Determine the demand curve facing the airline during the winter month of January if POG = 4 and IB = 250.
B. Determine the demand curve facing the airline, quantity demanded, and total revenues during the summer month of July if P = \$100 and all other price-related and business activity variables are as specified previously.
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Magnetic Flux Video Lessons
Concept
# Problem: The metal equilateral triangle in the diagram above, 22.8 cm on a side, is halfway into a 0.574 T magnetic field. What is the magnetic flux (in Wb) through the triangle?
###### FREE Expert Solution
Magnetic flux:
$\overline{){{\mathbf{\varphi }}}_{{\mathbf{B}}}{\mathbf{=}}{\mathbf{B}}{\mathbf{A}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\theta }}}$
A is the area of half the triangle, which is:
A = (1/2)[(1/2)(22.8 × 10-2)][sin (60°) (22.8 × 10-2)] = 0.1125 m2
98% (361 ratings)
###### Problem Details
The metal equilateral triangle in the diagram above, 22.8 cm on a side, is halfway into a 0.574 T magnetic field. What is the magnetic flux (in Wb) through the triangle?
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# Find the Inverse operator
Find $A^{-1}$ if $Af(x)=f(x)+\int\limits_{0}^{1}\cos(x+y)f(y)dy$.
Any ideas? I am not sure how to approach it...
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$\def\l{\lambda}$ We assume the integral is over $[0,\pi]$ and not $[0,1]$. If $[0,1]$ is the intended interval the method below will work but the eigenfunctions and eigevalues will be different. We use the standard shorthand $(K f)(x) = \int_0^\pi dy\, K(x,y) f(y)$ and $\langle f,g\rangle = \int_0^\pi dx f(x)^* g(x)$. The norm of $f$ is $\sqrt{\langle f,f\rangle}$.
Let $A f = g$. We wish to solve $g = f + K f$, for $f$, that is, to solve the inhomogeneous integral equation $$\begin{equation*} f = g + \l K f,\tag{1} \end{equation*}$$ where $\l = -1$. The kernel $K(x,y) = \cos(x+y)$ is that of a degenerate Hilbert-Schmidt integral operator. We expect there to be a finite number of orthogonal eigenfunctions.
A standard technique involves first examining the homogeneous eigenvalue equation $$u_i = \l_i K u_i.$$ This is straightforward to solve. In detail $$\begin{eqnarray*} u_i(x) &=& \l_i \int_0^\pi dy\, \cos(x+y) u_i(y) \\ &=& \l_i \left( \cos x \int_0^\pi dy\, \cos(y) u_i(y) -\sin x \int_0^\pi dy\, \sin(y) u_i(y)\right). \end{eqnarray*}$$ The eigenfunctions must be of the form $A \cos x + B \sin x$. Plugging this into the equation above allows us to find the eigenfunctions (up to an overall constant) and eigenvalues. We find the normalized eigenfunctions are $\sqrt{\frac{2}{\pi}}\cos x$ and $\sqrt{\frac{2}{\pi}}\sin x$, with eigenvalues $2/\pi$ and $-2/\pi$, respectively.
Having the eigenfunctions, one can show that the solution to (1) is $$f = g + \l \sum_i \frac{u_i}{\l_i-\l} \langle u_i,g\rangle,$$ that is, $$\begin{equation*} A^{-1}f = f + \l \sum_i \frac{u_i}{\l_i-\l} \langle u_i,f\rangle.\tag{2} \end{equation*}$$
Addendum: For the interval $[0,1]$, the eigenfunctions are $$\begin{eqnarray*} u_1(x) &=& c_1(\cos x - \alpha \sin x) \\ u_2(x) &=& c_2(\sin x - \alpha \cos x), \end{eqnarray*}$$ where $\alpha = \frac{1}{2} \left(2-\sqrt{6-2\cos2} \, \cos1\right)\csc^2 1$. It it straightforward to verify the $u_i$ are orthogonal. The eigenvalues are $$\begin{eqnarray*} \lambda_1 &=& (\sqrt{6-2\cos 2} - 2\sin 1)\sec 1\\ \lambda_2 &=& -(\sqrt{6-2\cos 2} + 2\sin 1)\sec 1. \end{eqnarray*}$$ The $c_i$ are got by imposing $\langle u_i,u_i\rangle = 1$, $$\begin{eqnarray*} c_1 &=& \frac{2}{\sqrt{(2-\sin 2) \alpha^2-4 \alpha\sin ^2 1 +\sin 2+2}} \\ c_2 &=& \frac{2}{\sqrt{(2+\sin 2) \alpha^2-4 \alpha\sin ^2 1 -\sin 2+2}}. \end{eqnarray*}$$
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Thank you all, I solved it myself last night. Here is my solution: $g(x)=f(x)-\int\limits_{0}^{1}\cos(x+y)f(y)dy=f(x)-\cos{x}\int\limits_{0}^{1}\cos{y}f(y)dy+\sin{x}\int\limits_{0}^{1}\sin{y}f(y)dy=\\$ $f(x)-\cos{x}c_f+\sin{x}d_f$, where $c_f=\int\limits_{0}^{1}\cos{y}f(y)dy$ and $d_f=\int\limits_{0}^{1}\sin{y}f(y)dy$. Now: $f(x)=g(x)+\cos{x}c_f-\sin{x}d_f$ and if we substitute $f(x)$ in expressions for $c_f$ and $d_f$ we get: $c_f=\int\limits_{0}^{1}\cos{x}f(x)dx=\int\limits_{0}^{1}\cos{x}(g(x)+\cos{x}c_f-\sin{x}d_f)=c_g+c_f\int\limits_{0}^{1}\cos^2{x}-d_f\int\limits_{0}^{1}\sin{x}\cos{x}dx.$ We can easily calculate these integrals and obtain first equation (we get another equation by doing the same thing, only starting with $d_f$). At the end we get a 2x2 system, where $c_g$ and $d_g$ are "constants" and $c_f$ and $d_f$ are unknown. By doing this we get $f(x)=g(x)+$something that depends only of $g(x)$ and some trigonometric functions and constants.
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Hints:
1. Define notation $c:=\cos$ and $s:=\sin$.
2. Define inner product $\langle f, g \rangle := \int_0^1 \overline{f(x)} g(x) dx$.
3. Then $(Af)(x)~=~f(x) + c(x) \langle c, f \rangle - s(x)\langle s, f \rangle .$
4. Guess that the inverse is of the form $$(A^{-1}f)(x)~=~f(x) + [c(x)~s(x)] M \left[\begin{array}{c} \langle c, f \rangle \cr \langle s, f \rangle \end{array}\right] ,$$ where $M$ is a constant $2\times 2$ matrix independent of the function $f$ and the argument $x$.
5. Determine $M$ by checking either $A^{-1}A=id$ or $AA^{-1}=id$.
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Actually, your method, i.e. determine $M$, helped me solve a similar exercise I had to deal with. Would you have any textbook references to get more familiar with these kind of tricks? – johnny Jul 5 '12 at 14:44
No, unfortunately I don't have a reference. I just guessed the Ansatz. – Qmechanic Jul 5 '12 at 15:04
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# SOLUTION: word problem. please use a table and the 5 step method to solve this problem. thank you. marcus invested a sum of money at 5%. he invested an amount of money \$250 more than the
Algebra -> Polynomials-and-rational-expressions -> SOLUTION: word problem. please use a table and the 5 step method to solve this problem. thank you. marcus invested a sum of money at 5%. he invested an amount of money \$250 more than the Log On
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Algebra: Polynomials, rational expressions and equations Solvers Lessons Answers archive Quiz In Depth
Click here to see ALL problems on Polynomials-and-rational-expressions Question 389727: word problem. please use a table and the 5 step method to solve this problem. thank you. marcus invested a sum of money at 5%. he invested an amount of money \$250 more than the first amount at 6%. if the annual income from both investments totaled \$59, how much did he invest at each rate. Answer by ewatrrr(11176) (Show Source): You can put this solution on YOUR website! Hi, Let x represent the first amount invested at 5% Therefore, (x+ \$250) would be the amount invested at 6% question States*** .05x + .06(x + \$250) = \$59 solving for x .05x + .06x + .06*\$250 = %59 .11x = \$59 - .06*\$250 .11x = \$59 - \$15 .11x = \$44 x = \$44/.11 = \$400, amount invested at 5% the amount invested at 6% would be \$650 (\$400+ \$250) IV. CHECKING Our Answer*** .05*\$400 + .06*\$650 = \$20 + \$39 = \$59
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# How to solve any problem
Do you need help with your math homework? Are you struggling to understand concepts How to solve any problem? Our website can help me with math work.
## How can we solve any problem
These can be very helpful when you're stuck on a problem and don't know How to solve any problem. Then, we can use the characteristics and properties of the triangle after the filling line to solve the relevant line segments and angles, which we need to understand in this process. Walking based on conditions is the real solution, and it must not be carried out indiscriminately? Even if the line is complemented. It conforms to the types of triangles we commonly use, but it is not suitable for the application of conditions in the subject. So this supplementary law is actually a failure.
Pay attention to the connection between mathematics and real life, and through a variety of methods, highlight the cultivation of students' ability to understand and analyze, operate and explore, express, and flexibly apply knowledge to solve problems, so as to develop students' mathematical literacy. This test paper is based on the mathematics curriculum standards and the current teaching materials, focusing on the key points of knowledge learned in the first half of the four volumes: Division of the remainder, recognition of numbers, decimeters and millimeters, addition, recognition of directions, and a small part of the content of the previous semester. The examination paper is examined by questions such as directly write the number, fill in the blanks, measure the quantity, draw a picture, and solve the problem by vertical calculation and by means of combination of pictures and text. The overall structure of the examination paper is reasonable, close to the presentation mode of the textbook, and the level is clear. The examination paper attaches importance to the examination of students' mastery of the core concepts of mathematics, the establishment of the sense of numbers, symbols, space, and the application consciousness and reasoning ability.
Exclusion is a method of finding inconsistent options by excluding options that are consistent with the question stem, or finding options that are consistent with the question stem by excluding inconsistent options, and then solving the answer. The essence of the exclusion method is to find the options that are not involved in the question stem as the answer by excluding the options that are already involved in the question stem, or to find the options that are consistent with the question stem as the answer by excluding the options that are not involved in the question stem. In fact, you can try to use the exclusion method when solving every logic test. Problem d is an integer 0-1 programming problem.
Search housing loan reverse calculation calculator on Baidu by yourself, and enter the value of the maximum monthly payment to reverse the total amount of housing loans; Taking the total amount of housing loans as the starting point, calculate the red line of the total purchasing power of the city: the red line of the total purchasing power = the total amount of housing loans / 0.7..
Think back, is solving equations the main thing? Students show their answers, and other students are invited to evaluate, supplement and improve them. Teachers will evaluate, ask questions, emphasize and focus on their answers. (the presupposition should focus on the nature of the equation, how to solve the equation using the nature of the equation, and the importance of testing the equation) If we put these questions together, we can see that the difficulty of the college entrance examination is slowly increasing. In the triangle problem in 2015, the final result can be obtained by solving the equation; In this problem, after solving the equation, we need to take two more steps to get the final result.
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# Arc length
An arc is a part of a circle. The arc length is the distance along the portion of the circle that forms the arc.
The circumference can be calculated as follows. It is necessary to calculate the circumference, and then multiply by the measure of the arc and divide the result by 360 degrees.
.
Arc length through radius and angle
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ViolinPlot - Maple Help
Statistics
ViolinPlot
create violin plots from data
Calling Sequence ViolinPlot(X, Y, options, plotoptions)
Parameters
X - data Y - (optional) data to be plotted in conjunction with X. When Y is specified, the command will draw half a violin plot for each individual sample in X and Y respectively. This can make it easier to directly compare the the distributions. options - (optional) equation(s) of the form option=value where option is one of datasetlabels, offset, distance, width, mean, symbol, quantiles, interval, divider, orientation, color, filled, scale, method, range, kernel, bins, left, right, or bandwidth; specify options for generating the violin plot plotoptions - options to be passed to the plots[display] command
Description
• The ViolinPlot command generates a violin plot for the specified data. A violin plot is a visualization of the distribution of data consisting of a rotated kernel density plot and markers for the quartiles and the mean.
• The parameter X is either a single data sample - given as e.g. a Vector - or a list of data samples. Note that the individual samples may be of variable size.
• The optional parameter Y is either a single data sample - given as e.g. a Vector - or a list of data samples. Note that the individual samples may be of variable size but the number of individual samples must be equal to the number samples specified in X.
Options
The options argument can contain one or more of the options shown below. All unrecognized options will be passed to the plots[display] command. See plot/options for details.
• datasetlabels=default or list
Data set labels for the individual violin plots. The labels appear along the axes. By default, the labels are set to 1, 2, 3, etc.
• offset=realcons
Initial offset along the x-axis. The default value is 0.
Note: By default, the view wraps tightly around all visible plot objects and the horizontal axis is marked by data set labels, not regular coordinates, so this option will have no (visual) effect. It is meant for the case where this plot is combined with other plot elements.
• distance=nonnegative
This option controls the distance between the violin plots. The default value is 0.25.
• width=realcons
This option controls the width of the violin plots. The default value is 0.75.
The following plot illustrates how the options offset, distance, and width are interpreted.
– Note the lengths of the arrows labeled "offset", "width" and "distance" correspond to values for the offset, width and distance options respectively.
• mean=true or false
If this option is set to true then the mean is included in the plot. The default value is true.
• symbol=name or list
This option specifies the symbol type for the points representing the mean. By default, the symbol type is diamond. When two data sets are given, X and Y, you can specify one symbol type or a list of two symbol types. Providing a list of two names specifies the symbol types for for plotting the points corresponding to the means of X and Y.
• quantiles=list of lists
This option can be used to mark specific quantiles. Quantiles are represented by horizontal lines of specified length. Each sublist is a list containing two elements where the first element specifies the quantile to be marked and the second element specifies the length of the horizontal line. The default value is [ [3/4,.5], [1/2, .75], [1/4, .5] ]
• interval=realcons
This option controls the amount of space inserted between the two halves of a violin plot. The default value is set to 0.
• divider=true or false
If divider is set to true then a vertical line is drawn to separate the halves of a violin plot. By default divider=false in which case no such line is drawn.
• orientation=horizontal or vertical
Indicate the orientation of the violin plots. The default is vertical. The option descriptions in this help page assume the orientation is set to vertical as well.
• color=name, list, or range
This option specifies colors for the individual data sets. If a range of colors is given, the colors are generated by selecting an appropriate number of equally spaced points in the corresponding hue range. For a list of colors, the behavior depends on whether the optional data Y is specified. In the case where Y is specified, the list can have at most two colors where the halves corresponding to the first data are colored using the first value in the list and the halves corresponding to the optional data are colored using the second value. Otherwise each of the violin plots is colored with the corresponding color in the list.
• filled=true or false
If the filled option is set to true, the area inside each of the violin plots is filled with a solid color. The color value of a filled area is set to the color of the adjacent curve. The default value is set to true.
• scale=value
The option specifies the method used to scale the width of violin plots. The option can be specified in the following ways:
• scale=width(scalelistX, scalelistY) or scale=width
In the case where the scaling method is specified as width or width(scalelistX, scalelistY), the violin plots are scaled so that their widths are proportional to the values specified in scalelistX and optionally scalelistY, where the value 1 represents the width that makes the violin plot fill the bounding box defined by the width option exactly.
In all cases, scalelistX and scalelistY are specified as lists of numeric values.
The default value for a scalelist is a list of all ones.
Note scale=width is used as default.
• scale=area(scaletype, scalelistX, scalelistY) or scale=area
When the scaling method is specified as area, by default the violin plots are scaled such that their areas are proportional to the values specified in scalelistX and optionally scalelistY, and the maximal width among all of them is given by the width option. Then if scaletype is setwise, the proportional comparison is only within the X data set and within the Y data set. Finally, if scaletype is pairwise, the proportional comparison is within each pair of (X, Y)-data sets plotted next to each other. See the Examples section for a specific example using this option.
• scale=count(scaletype) or scale=count
In the case where scaling method specified to be count, by default the violin plots are scaled such that the area of a particular violin plot is proportional to number of observations in the associated data sample, and the maximal width among all of them is given by the width option. Then if scaletype=setwise, the proportional comparison is only within the X data set and within the Y data set. Finally, if scaletype=pairwise, the proportional comparison is within each pair of (X, Y)-data sets plotted next to each other.
If Y data is specified but only one list of scales is provided, then the specified list of scales is used to scale both sets of Violin Plots. However this generates an error if scaletype is set to pairwise.
Note that the number of elements in scalelistX and scalelistY when specified, must at least be equal to the number of elements in X and Y respectively.
• method=exact or piecewise
This parameter specifies the method of plotting the kernel density estimate (by default this is piecewise). For more information, see Statistics[KernelDensity].
• range=deduce or realrange
By default this is deduce. This option is used to specify the vertical range in the violin plot.
• kernel=gaussian, biweight, epanechnikov, triangular, or rectangular
The default value is gaussian. This option allows a non-Gaussian kernel to be used in developing the estimate. For more information, see Statistics[KernelDensity].
• bins=posint
The number of bins in which to categorize data points (128 by default). This value must be a power of 2 and is equal to the size of the array returned by KernelDensity when the option method=piecewise is specified. This parameter is ignored if method=exact.
• left=realcons
This option specifies the lower boundary on valid data values. Any data values that are smaller than this value are discarded. By default, this procedure will impose boundary conditions consistent with the specified range rng.
• right=realcons
This option specifies the upper boundary on valid data values. Any data values that are smaller than this value are discarded. By default, this procedure will impose boundary conditions consistent with the specified range rng.
• bandwidth=realcons
The bandwidth is a positive quantity that specifies the width of the kernel (the amount each data point affects distant portions of the probability density estimate). Each kernel is scaled such that the bandwidth is equal to the standard deviation of the kernel.
Notes
• Note that the labels for the data sets are placed on the axes, and should not be confused for coordinates.
Examples
> $\mathrm{with}\left(\mathrm{Statistics}\right):$
> $A≔\mathrm{Array}\left(\left[-1.,-0.4,-0.2,0.,0.,0.1,0.2,0.7,0.9\right]\right):$
> $\mathrm{ViolinPlot}\left(A,\mathrm{range}=-5..5,\mathrm{bins}=256,\mathrm{bandwidth}=\frac{1}{4},\mathrm{method}=\mathrm{exact}\right)$
The commands to create the plot from the Plotting Guide are
> $N≔\mathrm{RandomVariable}\left(\mathrm{Normal}\left(0,1\right)\right):$
> $\mathrm{PDF}\left(N,0.\right):$
> $S≔\mathrm{Sample}\left(N,16\right):$
> $\mathrm{ViolinPlot}\left(S,\mathrm{bins}=512,\mathrm{kernel}=\mathrm{epanechnikov},\mathrm{color}="Niagara Green",\mathrm{left}=-6,\mathrm{right}=6,\mathrm{method}=\mathrm{piecewise}\right)$
> $\mathrm{ViolinPlot}\left(\left[S\right],\left[A\right],\mathrm{scale}=\mathrm{count}\right)$
> $C≔\left[\mathrm{seq}\left(\mathrm{Sample}\left(\mathrm{Normal}\left(\mathrm{ln}\left(i\right),3\right),60\right),i=1..20\right)\right]:$
> $F≔\left[\mathrm{seq}\left(\mathrm{Sample}\left(\mathrm{Normal}\left(\mathrm{sin}\left(i\mathrm{Pi}\right),3\right),120\right),i=1..20\right)\right]:$
> $\mathrm{ViolinPlot}\left({C}_{1..3},{F}_{1..3},\mathrm{size}=\left[1000,500\right],\mathrm{color}="LightBlue".."red",\mathrm{scale}=\mathrm{area}\left(\mathrm{pairwise},\left[1,1,2\right],\left[2,3,1\right]\right)\right)$
The ViolinPlot command also accepts a Matrix. The columns are understood as individual data samples.
> $R≔\left[\mathrm{seq}\left(\mathrm{Sample}\left(\mathrm{Normal}\left(\mathrm{ln}\left(i\right),3\right),10\right),i=1..3\right)\right]:$
> $M≔{\mathrm{Matrix}\left(R,\mathrm{scan}=\mathrm{columns}\right)}^{\mathrm{%T}}:$
Plot options such as title are passed to the plots:-display command:
> $\mathrm{ViolinPlot}\left(M,\mathrm{color}="Niagara Blue",\mathrm{title}="Violin Plots"\right)$
Compatibility
• The Statistics[ViolinPlot] command was introduced in Maple 2017.
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# Here are ten of the most difficult math problems that remain largely unsolved.
Math isn’t for the faint of minds, obviously. Think of it, what was the difficult math problem you feared at school. From algebra to calculus to geometry to quadratics to let us stop freaking you out in this article, huh? Well…, buckle up and get ready for more arithmophobia (the fear of math). Some math problems seem not to have a solution, at all. Or not yet. These are brain-busters that seem impossible to crunch, but maybe not for long. Here are ten of the most difficult math problems yet unsolved.
### #1. Birch And Swinnerton-Dyer Conjecture
This conjecture describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory, meaning anyone can have a go at it. An elliptic curve is a special kind of function which takes the form of something like y²=x³+ax+b. Weird, huh?
### #2. Collatz Conjecture
The infamous Collatz conjecture says that if you start with any positive integer, you’ll always end up in this loop. However, the conjecture isn’t infamous for only that reason. Although every number ever tried ends up in that loop, we’re still not certain if that’s accurate. Thence cometh the problem.
### #3. Euler’s Number (𝜋+e)
Euler’s number, name after mathematician Leonhard Eulere is the base of the natural logarithms. This is the ratio of the circumference of any circle to the diameter of that circle. And no matter the size, it’s ratio will always equal pi (𝜋). Spoiler, it wasn’t invented by Euler, it was rather invented by John Napier.
### #4. Gamma’s Rationality
Is γ a number? Sounds not, but it is. However, the number γ has not been proven to be an algebraic or transcendental number, yet. And as a matter of fact, it is not known whether it is even irrational. In 1997, the Greek physician Georgios Papanikolaou proved with a continued fraction analysis that if γ is rational, its denominator must be greater than 10^244663.
### #5. Goldbach’s Conjecture
This is the oldest unsolved math problem in number theory and in all of mathematics. It simply states that every even whole number greater than 2 is the sum of two prime numbers. Is every even number greater than 2 the sum of 2 primes? Goldbach says, yes. For instance, 4=2+2, 6=3+3, 8=3+5, and so on.
### #6. Kissing Number Problem
This problem isn’t romantic if you think it is. It seeks to ask the maximal number k(n) of equal size non-overlapping spheres in n-dimensional space that can touch another sphere of the same size. It became the subject of a famous discussion between Isaac Newton and David Gregory in 1694.
### #7. Riemann Hypothesis
Mathematically, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 12. Many mathematicians consider this to be the most important yet unsolved problem left in pure mathematics.
### #8. The Large Cardinal Project
This project is about the large cardinal axiom which states that there exists a cardinal (perhaps many of them) with some specified large cardinal property. Most set theorists believe that the large cardinal axioms that are currently being considered are consistent with Zermelo-Fraenkel set theory (ZFC).
### #9. Twin Prime Conjecture
Also known as Polignac’s conjecture, in number theory, is an assertion that there are infinitely many twin primes, or pairs of primes that differ by 2. For instance, 3 and 5, 5 and 7, 11 and 13, and 17 and 19 are twin primes. By contrast, the sum of the reciprocal of the primes diverges to infinity.
### #10. Unknotting Problem
The unknotting problem, in mathematics, is just as its name says. It is the problem of algorithmically unknotting a knot. In one word, untie. For example, a representation of knots in a knot diagram. There are several types of unknotting algorithms.
Let us know which problem you think we left out.
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Re: Is a Person One or Many?
From: Stathis Papaioannou (stathisp@gmail.com)
Date: Sun Mar 09 2008 - 23:10:21 MDT
On 10/03/2008, Mike Dougherty <msd001@gmail.com> wrote:
> > - If 1000 copies of you are made in London lacking 50% of your
> > memories and 10 copies are made in Paris lacking 5% of your memories,
> > are you more likely to find yourself waking up in London or Paris?
> >
> I guess it depends on what part of your memories you use to identify your
> Self :)
Let's say many memories, aspects of personality etc. are involved in
sense of self, and these are lacking in the proportions as above. Is
your subjective probability of ending up as a particular copy
proportional to the degree of fidelity of that copy? What if the
copying is low in quality but high in quantity? You would expect
*something* since you might expect something after a head injury with
partial memory loss. But what, exactly, if there are multiple copies
involved? I don't think there is a clear answer because the notion of
subjective probability is based on the idea that you are a single
person who persists through time.
> > - You are offered two choices:
> > (a) 100 copies of you are made in London and one copy is made in
> > Paris. The Paris copy is tortured while the London copies are not
> > tortured.
> > (b) 100 copies of you are made in London and one copy is made in
> > Paris. After an hour, the 100 copies in London are tortured while the
> > copy in Paris is duplicated 100,000 times and none of these copies are
> > tortured.
> > Is your subjective probability of being tortured at the moment of the
> > original copying greater in (a) or (b)?
>
> How do we even measure the _degree_ of torture? If I am to identify with
> every copy as myself: scenario A divides my identity 101 ways and only one
> is tortured (resulting in <1% subjective torture, assuming the 100 London
> copies are blissfully happy) Scenario B has a division of my identity into
> 100,100 parts, with 100 being tortured (<0.1% subjective torture) So it
> doesn't seem to matter that scenario B has 100 times as much torture in my
> future because it is statistically overwhelmed by the greater number of
> copies experiencing the Not-torture option.
That's one way to look at it. The other way to look at it is that if
you choose (b) you have a 100-fold greater chance of finding yourself
in London, where torture is certain in an hour, as compared to finding
yourself in Paris, where you will notice nothing at all when you are
duplicated in an hour. To change the example a little, nothing makes a
difference to the subjective probability of being tortured to either
the London copies or the Paris copy if they are able to decide on
finding themselves at either city whether the Paris duplication takes
place, so why should it make a difference at an earlier point?
> > Note that there is no problem *objectively* describing what happens in
> > any of these cases. Lee tries to take the objective point of view and
> > translate it into the subjective point of view as well. But to do this
> > would require a complete overthrow of our notions of anticipation and
> > subjective probability, and I don't think this is possible without
> > rewiring our brains.
> >
>
> I believe the rewiring our brains is part of the assumptions for this
> thought experiment. I assumed the greater "run-time" offered by many copies
> was only really possible in either an uploaded consciousness situation or
> some massively expanded awareness of multiple worlds. In either case,
> rewiring a brain would seem to be the easy part. :)
I am assuming that, though our brains might be rewired, they are
functionally identical, including beliefs about personal identity and
subjective probabilities. Of course if the uploads are designed, for
example, to desire a greater total runtime regardless of subjective
probabilities and anticipation of the future that would change things.
```--
Stathis Papaioannou
```
This archive was generated by hypermail 2.1.5 : Wed Jul 17 2013 - 04:01:02 MDT
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Follow
# Calculating using vectors: Velocity^2 vs. DOT(Velocity,Velocity)
Same caution needs to be used when implementing in the calculator equations containing the square of a vector field: what the equation is exactly indicating can indeed be not so clear from the mathematical formulation.
Let's assume for example that you want to calculate the the dynamic pressure as a scalar:
dynamic_pressure = 0.5 * Density * Velocity^2 (eqn #1)
where velocity is a vector [vx,vy,vz] and Density is a scalar.
If you simply use the expression Velocity^2 in the calculator, you are actually using a vector with components [vx*vx, vy*vy, vz*vz] and with magnitude = sqrt(vx^4+vy^4+vz^4), and therefore the expression above in equation #1 would become:
dynamic_pressure = 0.5*Density*sqrt(vx^4+vy^4+vz^4)
and return a vector field instead of a scalar. The correct way to calculate this quantity is to use the expression:
dynamic_pressure = 0.5*Density*DOT(Velocity,Velocity) (eqn #2)
which will return a scalar of magnitude 0.5*Density*(vx^2+vy^2+vz^2)
The difference between the vector magnitude in equation #1 and the scalar in equation #2 becomes more pronounced as velocity gets larger.
On a more general note, please keep in mind:
Scalars that are equivalent to each other
• DOT(velocity,velocity)
• RMS(velocity) * RMS(velocity)
• (Velocity[x]*Velocity[x] + Velocity[y]*Velocity[y]+Velocity[z]*Velocity[z])
Vectors that are equivalent to each other.
• Velocity^2
• Velocity * Velocity. They both give you a vector of magnitude sqrt(vx^4+vy^4+vz^4)
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# Unit 1 Review – Science
```Name:_________________________________________________________Date:___________________Period:______
Unit 1 Review – Physical Science
Show work and units:
1. What is the density of an object with a mass of 60 g and a volume of 2 cm3?
2. If you have a rectangular gold brick that is 2 cm by 3 cm by 4 cm and has a mass of 48 g,
what is its density?
3. If a block of wood has a density of 0.6 g/ cm3 and a mass of 120 g, what is its volume?
4. What is the mass of an object that has a volume of 34 cm3 and a density of 6 g/ cm3?
5. Observation or Inference: Place an O for Observation or I for Inference on the space.
_______ The sandwich smells nasty.
_______ The girls looks 14 years old.
_______ Mr. Yancey is the principal of Westerville North High school.
_______The school is on County Line Road in Westerville, Ohio.
_______A dog is the best pet to have.
6. Three items you use for safety in this science lab are:
a) _______________________________________________________
b) _______________________________________________________
c) _______________________________________________________
7. To smell a chemical in a science lab, you _______________ the odor toward your nose.
8. What are the two types of observations a person can make?
a.) ________________________________
b.) ________________________________
9. In what format do you write a title on a graph? __________________________________________
10. The density of water is equal to __________________________ (don’t forget to include your units!)
11. One cubic centimeter equals _________________________ mL.
12. What is the base unit for measuring each of the following?
Volume _____________________ Mass _______________________ Length ____________________
13. What is the area of an office that is 15 meters by 12 meters?
14. Draw an example of a line graph showing each of the following:
Direct relationship
between two variables
Indirect relationship
between two variables
No relationship
between two variables
15. What is the volume of box that is 5 cm by 8 cm by 2 cm?
16. What does DRY MIX stand for?
17. What is the metric ladder? Write it below.
18. Name a tool to measure the mass of a paperclip. ___________________________________________
19. Name a tool used to measure the length of the hallway. ______________________________________
20. Name a tool used to measure the volume of a bottle of Gatorade. ______________________________
22. In the following scenarios identify the independent variable, dependent variable, control, and one
constant.
A researcher is curious to find out what effect classical music has on people’s level of relaxation (as
measured by heart rate). He suspects that listening to classical music will make people feel more calm
and relaxed. He lets one group listen to classical music for one hour. He lets another group sit in a
quiet room for one hour (i.e they hear no music). After one hour, he monitors the heart rate of each
participant to measure their level of relaxation.
Independent Variable:
Dependent Variable:
Control:
Constants:
A psychology teacher allowed his third period class to eat snacks while taking an exam. His fourth
period class was not allowed to eat snacks while taking the same exam. He compared the test averages
from both classes. Prior to this, both classes averaged comparable exam scores.
Independent Variable:
Dependent Variable:
Control:
Constants:
The leading producer of paper products wants to increase their sales of paper cups. They set up a test
program in local supermarkets. Identical 8 ounce paper cups were packaged in two ways—half of the
stock was packaged in the present plain boxes, while the other half of the stock was packaged in
bright, cheery, pastel-colored boxes. Sales volumes for each type of package were recorded over a
period of six months.
Independent Variable:
Dependent Variable:
Control:
Constants:
Question: Does the mass of a wooden block affect the density?
Design an experimental procedure to test the question above. Assume you have multiple size blocks made of
the same type of wood to use in your experiment.
Now use the following rubric to grade your own procedure. On a scale of 1 -5, how well did you write your
experiment?
Characteristic of a Good Procedure
Is it reproducible?
Is only one independent variable being changed at a
time while all other variable are held constant?
Is it clear how the dependent variable will be measured?
Are there a sufficient number of trials?
Is there a control trial?
Score (1 point each)
```
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# BubbleSort random integers in array list question
Page 1 of 1
## 0 Replies - 306 Views - Last Post: 06 February 2013 - 09:38 AMRate Topic: 1 Votes //<![CDATA[ rating = new ipb.rating( 'topic_rate_', { url: 'http://www.dreamincode.net/forums/index.php?app=forums&module=ajax§ion=topics&do=rateTopic&t=311370&s=b0a3250fce214ed7f94c63cdc053f6d2&md5check=' + ipb.vars['secure_hash'], cur_rating: 5, rated: 0, allow_rate: 0, multi_rate: 1, show_rate_text: true } ); //]]>
### #1 iridebmxnj
Reputation: 0
• Posts: 15
• Joined: 15-December 12
# BubbleSort random integers in array list question
Posted 06 February 2013 - 09:38 AM
I was given the following code to use to start my project, the project is to first create an array of random integers from 0-1000 and then sort them from least to greatest.
I have created the array of random integers but I am not sure how to implement the bubble sort class that was included.
here is the code I have written so far
```class bubbleDriver
{
public static void main(String args[])
{
int capacity = Integer.parseInt(args[0]);
SortableArrayList<Integer> integerList = new bubbleSorting<Integer>(capacity);
int j = 10;
int myarray[] = new int [j];
for (int i = 0 ; i < j ; i++)
{
myarray [i] = (int) (Math.random () * 1000);
System.out.println(myarray[i]);
}
System.out.println("Array length is " + myarray.length);
// Sort and print in numerical order
integerList.sort();
System.out.println("Contents of NumberList sorted : " );
} // main
}
```
This was the code I was given to work with
bubble sorting class
```class bubbleSorting<T extends Comparable<T>>
extends SortableArrayList<T>
{
public bubbleSorting(int capacity)
{
super(capacity);
}
// Sorts the sublist from lowIndex to highIndex using Bubble Sort
// Uses recursion to sort smaller sublists
protected void sortSublist(int lowIndex, int highIndex)
{
if(lowIndex < highIndex)
{
// The sublist has more than one element, so sort it
/* "Bubble" largest value in listItem[lowIndex]...listItem[i]
to position i by swapping adjacent items that are out of order
*/
for (int i = lowIndex; i < highIndex; i++)
{
if (listItem[i].compareTo(listItem[i+1]) > 0)
{
// swap items
T temp = listItem[i];
listItem[i] = listItem[i+1];
listItem[i+1] = temp;
}
} //for loop
// Use bubble sort to sort the rest of the list
sortSublist(lowIndex,highIndex-1);
} //if statement
}
}
```
SortableArrayList Class
```abstract class SortableArrayList<T extends Comparable<T>>
{
protected T[] listItem;
protected int itemCount;
private static int DEFAULT_CAPACITY = 50;
private boolean isSorted;
// Constructs a list with the specified capacity
public SortableArrayList(int capacity)
{
@SuppressWarnings("unchecked")
T[] tempList = (T[]) new Comparable[DEFAULT_CAPACITY];
listItem = tempList;
itemCount = 0;
isSorted = false;
}
// Constructs a list with the default capacity
public SortableArrayList()
{
this(DEFAULT_CAPACITY);
}
/* Adds item to end of list
pre-contition: itemCount < listItem.length() - 1
post-contition: itemCount == itemCount@pre + 1
item added to end of list
*/
public void append(T newItem)
{
listItem[itemCount] = newItem;
itemCount++;
isSorted = false; //List may no longer be sorted
}
/* Return item in given position
If position is out of range, return null
*/
public T getItem(int position)
{
if (0 <= position && position < itemCount)
return listItem[position];//position
else
return null;
}
// Return length of list
public int getLength()
{
return itemCount;
}
// Sort list
public void sort()
{
sortSublist(0,itemCount-1);
}
// Sort sublist from lowIndex to highIndex
abstract protected void sortSublist(int lowIndex, int highIndex); // method does not get implemented in class
// only used in this class, or a subclass
/*
Returns the position of the item with the given value.
If the item is not in the list, returns -1.
*/
public int search(T searchValue)
{
if (isSorted)
{
return binarySearch(searchValue,0,itemCount-1);
}
else
{
return linearSearch(searchValue);
}
}
/*
Searches for the index of the given value using the binary search algorithm
*/
private int binarySearch(T searchValue, int lowIndex, int highIndex)
{
if (highIndex < lowIndex)
{
return -1; // not in list
}
else
{
int midIndex = lowIndex + (highIndex-lowIndex)/2;
if (listItem[midIndex].equals(searchValue))
{
return midIndex; //found it -- position is one more than index
}
else if (listItem[midIndex].compareTo(searchValue) > 0)
{
// searchValue comes before midIndex in array
return binarySearch(searchValue,lowIndex,midIndex-1);
}
else
{
// listItem[midIndex] comes after midIndex in array
return binarySearch(searchValue,midIndex+1,highIndex);
}
}
}
// Searches for the index of the given value using linear search
private int linearSearch(T searchValue)
{
int index = itemCount-1;
while (index >= 0 && !listItem[index].equals(searchValue))
{
index--;
}
return index;
}
// Returns a string of the items in the list --
public String toString()
{
StringBuilder returnStringBuilder = new StringBuilder();
for (int i = 0; i < itemCount; i++)
{
returnStringBuilder.append(listItem[i].toString() + "\n");
}
return returnStringBuilder.toString();
}
}
```
Is This A Good Question/Topic? 0
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# Homework Help: Monatomic gas, Isochoric Process.
1. Dec 16, 2012
### yaylee
1. The problem statement, all variables and given/known data
n = 1.46 moles of ideal gas are heated isochorically (at constant volume) from tepmerature To = 649 oC to temperature Tf = 1184 oC. Find:
a) Work done on the system.
b) Change in Internal Energy of the system.
c) The total heat, Q, added or removed from the system.
2. Relevant equations
Change in I.E. = Q + W
KE (avg) = T = 3/2kT, where k = 1.38 x 10^-26 kJ/K
3. The attempt at a solution
a) Since this is an isochoric system, work done is ZERO! (No issues here.)
b,c) Change in Internal Energy, therefore is equal to Q, by the first equation, Change in IE = Q + W.
So, we can calculate change in IE, by change in KE.
KE = (3/2kT) for a monatomic gas.
so, change in KE = 3/2(k)(Tfinal - Tinitial), = (3/2)(1.38E-26)(1500 K - 704K) = change in IE = Q = 1.65 x 10^-23.
Am I reading the problem incorrectly? Many thanks in advance once again!
2. Dec 16, 2012
### TSny
(3/2)kT is the average translational KE of just one molecule.
3. Dec 16, 2012
### SteamKing
Staff Emeritus
It appears you have calculated the change in KE for a single molecule of the gas.
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Next: Node Priority Queues ( Up: Graphs and Related Data Previous: Lists of Nodes ( Contents Index
# Node Partitions ( node_partition )
Definition
An instance P of the data type nodepartition is a partition of the nodes of a graph G .
#include < LEDA/graph/node_partition.h >
Creation
node_partition P(const graph& G) creates a node_partition P containing for every node v in G a block {v} .
Operations
int P.same_block(node v, node w) returns true if v and w belong to the same block of P, false otherwise. void P.union_blocks(node v, node w) unites the blocks of P containing nodes v and w . void P.split(const list< node> & L) makes all nodes in L to singleton blocks. Precondition L is a union of blocks. node P.find(node v) returns a canonical representative node of the block that contains node v . void P.make_rep(node v) makes v the canonical representative of the block containing v . int P.size(node v) returns the size of the block that contains node v . int P.number_of_blocks() returns the number of blocks of P. node P(node v) returns P.find(v ).
Implementation
A node partition for a graph G is implemented by a combination of a partition P and a node array of partitionitem associating with each node in G a partition item in P . Initialization takes linear time, union_blocks takes time O(1) (worst-case), and same_block and find take time O((n)) (amortized). The cost of a split is proportional to the cost of the blocks dismantled. The space requirement is O(n) , where n is the number of nodes of G .
Next: Node Priority Queues ( Up: Graphs and Related Data Previous: Lists of Nodes ( Contents Index
Christian Uhrig 2017-04-07
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http://math.stackexchange.com/questions/6988/is-the-scalar-curvature-the-only-isometric-invariant-of-a-riemannian-2-manifold
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# Is the scalar curvature the only isometric invariant of a Riemannian 2-manifold?
Given two Riemannian Manifolds of dimension 2, and a point on each. If the scalar curvatures are isomorphic (as functions) in some neighbourhoods of these points, are then the manifolds necessarily locally isometric?
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The answer is 'no' for simple reasons: If the two Riemannian surfaces $(M_1,g_1)$ and $(M_2,g_2)$ have Gauss curvatures $K_1:M_1\to\mathbb{R}$ and $K_2:M_2\to\mathbb{R}$ respectively and there happen to be points $p_i\in M_i$ such that $K_1(p_1) = K_2(p_2)$ and such that $dK_i$ is nonvanishing at $p_i$, then there will always be $p_i$-neighborhoods $U_i\subset M_i$ and a local diffeomorphism $\phi:U_1\to U_2$ with $\phi(p_1)=p_2$ such that $K_1 = K_2\circ\phi$ on $U_1$. This is just basic calculus. Of course, there is no reason for $\phi$ to be a local isometry.
However, now set $L_i = |dK_i|^2_{g_i}$ and suppose, in addition, that $L_1(p_1)=L_2(p_2)$ and that $dK_i\wedge dL_i$ is nonvanishing in a neighborhood of $p_i$ for $i=1,2$. Then there will be $p_i$-neighborhoods $U_i\subset M_i$ and a unique local diffeomorphism $\phi:U_1\to U_2$ with $\phi(p_1)=p_2$ such that $K_1 = K_2\circ\phi$ and $L_1 = L_2\circ\phi$ on $U_1$. Using $\phi$, you can now compare $g_1$ with $\phi^*(g_2)$. If these are equal on $U_1$, then the two metrics are (obviously) locally isometric. If these are not equal, then there is no local isometry between the two metrics that carries $p_1$ to $p_2$.
If you happen to have the bad luck that $dK_i\wedge dL_i$ vanishes identically on a neighborhood of $p_i$ (while, still $dK_i$ is nonvanishing), then, locally, one can write $L_i = f_i\circ K_i$ for some (essentially unique) functions $f_i$, and these will have to be equal in a neighborhood of $K_i(p_i)$ or there is no isometry. However, even if this does hold, there might still be no isometry, you have to go to higher order.
For example, if $K_1(p_1) = K_2(p_2)$, each $dK_i$ is nonvanishing on a neighborhood of $p_i$, and there exists a function $f$ on a neighborhood of $K_i(p_1)$ such that $L_i = f\circ K_i$ on some neighborhood of $p_i$, then you might consider the function $J_i = \Delta K_i$ and hope that this is independent of $K_i$, and, if so, ask whether the map $\phi$ that satisfies $(K_1,J_1) = (K_2\circ\phi, J_2\circ\phi)$ is an isometry. Etc.
The point is, though, that, after a finite number of tests of this kind (assuming that some mild nondegeneracy conditions hold), you will be able to completely determine whether the metrics are locally isometric in neighborhoods of the points $p_i$.
-
Welcome to math.SE, and thanks for the answer! It's much clearer than my own flailing attempt, anyways... – Aaron Mazel-Gee May 10 '11 at 16:52
This is true if the curvatures are constant (Minding's theorem), but not in general. I actually don't know a counterexample, but (edit: I think that) Stillwell points out on page 344 of Mathematics and its history that Strubecker's Differentialgeometrie gives such an a related example in Volume III on page 124, but I'm not 100% sure if that is a counterexample of what you're asking, and I don't currently have access to it.
Update: Okay, here's an example I can access. In Audin's Geometry, after the Theorema egregium, there is a remark that the "converse is wrong; a classical counter-example will be found in Exercise VIII.24." Thankfully Exercise VIII.24 is available on Google Books, at least to me. There is a section with hints and solutions, too, but I can't see whether it includes that exercise.
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The section with hints and solutions is not available to me. So how do you prove that the two surfaces in that exercise are non-isometric? – Anirbit Dec 13 '10 at 20:01
@Anirbit: I'm sorry, I did not try the exercise, and I don't think I have access to the solutions either at present. If I find something I'll let you know, but I have no plans to do so soon. – Jonas Meyer Dec 14 '10 at 0:05
I'm a little rusty on this stuff, but here's a sketch of a general answer. Basically the idea is that for any differential-geometric structure on a manifold (Riemannian metric, almost-complex structure, Finsler structure, symplectic structure, jet structure, web structure, etc.) you define the "frame bundle" to be the space of ways of identifying the structure with the canonical one on $\mathbb{R}^n$. So in the case of a Riemannian metric, point by point you choose an identification of the tangent space with $\mathbb{R}^n$ so that the inner product agrees with the usual one on $\mathbb{R}^n$, and then you allow yourself to post-compose with any element of the orthogonal group $O(n)$ in order to allow for differences in the original choices. (This is because the orthogonal group is exactly the space of linear maps that preserves the inner product.) This gives you what is known as a G-structure on the manifold (here $G=O(n)$). This is a bundle over the manifold where every fiber is a $G$-torsor, i.e. a space which is topologically the same as $G$ but there's no choice of which point is the identity because there was no canonical choice of how to identify $T_pM$ with $\mathbb{R}^n$. (So e.g. a real line is a torsor for the group $\mathbb{R}$.) The next step is to try and make a connection for this bundle, and if I remember correctly, this is the place where we tease out geometric invariants. There's a Lie-algebra-valued 1-form (with values in $Lie(G)$) that measures the failure of the connection to be trivial(izable), I think, and then you calculate something called the "Spencer cohomology". The main point is that this gives all the invariants, so for example it falls out as an immediate consequence that two manifolds are locally isomorphic if and only if there's a local diffeomorphism that lines up their Gaussian curvatures. (Something else really cool is that this perspective tells you exactly why we can have the Riemann mapping theorem in dimension 2, but then in all higher dimensions the only conformal maps are Möbius transformations. Also this can be used to prove Darboux's theorem, and the same method gives the Nijenhaus tensor.)
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And the answer to your question is that I don't remember, but it will be yes if and only if scalar curvature determines Gaussian curvature. Embarrassingly, even though I remember the story I just told you, I don't remember whether that's true. I suspect not, though? – Aaron Mazel-Gee Oct 16 '10 at 22:47
I'm rusty on my Riemannian geometry, too, but scalar curvature is a constant multiple of the Gaussian curvature in the 2-dimensional case. – Jonas Meyer Oct 16 '10 at 23:00
... the constant being exactly two. – Willie Wong Oct 17 '10 at 0:17
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Lesson Plans (4)
## ALEX Lesson Plans
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Subject: Mathematics (9 - 12)
Title: Polynomial Subtraction
Description: Students will review the meaning of vocabulary relevant to subtracting polynomials such as opposites and the definition of subtract. They will be presented with examples of subtracting polynomials both vertically and horizontally. They will also be given ample opportunities to apply this new skill through game play.
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Subject: Mathematics (9 - 12)
Title: Conquering Polynomials
Description: In this lesson, students will be introduced to polynomials. A polynomial is a made up of terms, which are algebraic expressions combined by addition or subtraction. In a polynomial, there is no expressions that involve dividing by the variable or taking any root of a variable.
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Title: Polynomials Divided by Monomials
Description: Investigation of division of polynomials by mononials. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
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Title: What's The Real Cost of That Car?
Description: This is a Commerce and Information Technology lesson plan. A project requiring research, critical thinking and complex decision-making about factoring all the costs of purchasing a large ticket item... a car.
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Title: A Geometric Investigation of (a + b)2
Description: This student interactive, from Illuminations, allows students to explore a geometric explanation of why (A + B) squared = A squared + 2AB + B squared. The page includes directions for using the interactive as well as hints to help students understand this demonstration.
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https://www.ijert.org/economic-load-dispatch-of-a-three-unit-thermal-system-using-both-analytical-method-and-fuzzy-logic
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# Economic Load Dispatch of a Three Unit Thermal System : Using Both Analytical Method and Fuzzy Logic
DOI : 10.17577/IJERTV5IS060063
Text Only Version
#### Economic Load Dispatch of a Three Unit Thermal System : Using Both Analytical Method and Fuzzy Logic
Suranjana Bharadwaj1 Bipul Kumar Talukdar2
Department of Electrical Engineering
Girijananda Chowdhury Institute of Management and Technology Guwahati, India
Abstract This paper gives a theoretical analysis of the economic load dispatch problem by taking a three unit thermal system as the reference. Load allocation to each unit is determined using analytical method keeping in mind that it serves the total system load and satisfies the generation constraints. A MATLAB program is developed which gives the load allocation as output when the system load is varied step by step. Results are shown with the help of both tables and graphs. In the second phase system is again analyzed using a fuzzy controller and a comparative analysis is done in terms of the fuel costs obtained from conventional method and the fuzzy controller. The whole analysis is done without considering the transmission losses.
KeywordsLoad, Demad, Lambda, Fuzzy Controller, Membership Function, Fuel Cost
1. INTRODUCTION
Economic Load Dispatch (ELD) problem is one of the major concerns for power engineers as it is directly related to the reliability, stability and economy of the system. The prime concern of ELD scheme is to allocate the total system load among all the generators of the system in such a way that the fuel cost is minimized and at the same time the generation constraints are also satisfied.
The total cost of generation can be divided into two parts
i.e. fixed cost and variable cost. The fixed cost comprises largely of the capital investment and some other miscellaneous expenses which do not have any relation with the load demand or the generator loadings. The variable cost mainly comprises of the generator loadings, system losses and purchase or sale of power.
The cost minimization using ELD scheme is thereby refers only to the variable cost. The fixed cost is indifferent of the system generation or load demand.
2. THE INCREMENTAL FUEL COST
The incremental fuel cost, mostly referred to as lambda() is one of the key terms in economic load dispatch. It is the minimum value of the operating cost that is obtained after equalizing all the partial derivatives of the cost functions of all the plants and also satisfying the load demand.
=dCi/dPi, i=1,2,.n
Where Ci is the cost function of the ith unit, Pi is the generation of the ith unit and n is the total number of units.
III CONSTRAINTS OF ECONOMIC DISPATCH
The first constraint is the equality constraint i.e. the total generation must be equal to the total system load provided losses are neglected.
The second constraint is the inequality constraint. It ensures that the load allocated to each generator lies between the minimum and maximum limits of generation of that particular unit.
Pimin Pi Pimax
IV SYSTEM UNDER INVESTIGATION
The system considered here is a three unit thermal system whose cost functions and constraints are as given below:
Unit1:
C1=300+1.6P1+0.005P12 Rs/MW 80 P1250
Unit2:
C2=250+2.02P2+0.001P22 Rs/MW 300 P1 700
Unit3:
C3=160+2.03P3+0.025P32 Rs/MW 60P1 550
The system is solved using analytical method with the help of a MATLAB program which takes load demand as the input and gives out power generation as the output for all the three units while satisfying all the constraints mentioned earlier.
The algorithm for analytical solution is mentioned below:
step1: Start
step2: Input the system load demand step3: Calculate P1, P2, P3,
step4: Check if any of the generation constraints are violated.
If they are within limit then go to step6
step5: If limit is violated for the ith unit then fix it at the margin value i.e. Pi=Pmax and Pload=Pload-Pi
step6: Again reschedule the remaining units with the new load demand.
step6: Display P1, P2, P3, step7: Stop
V ANALYTICAL SOLUTION METHOD
Using the analytical method load allocations to the units have, incremental fuel cost and total fuel cost been found for different values of load demand(Pd) as input which can be observed from the following table. It is observed that on increasing the load, both incremental cost and fuel cost rises and the pattern has been shown with graphs. All the graphs show an increasing pattern.
TABLE I: RESULTS OF ANALYTICAL METHOD
Pd P1 P2 P3 FC(total) 450 100 290 60 2.6 1801.7 480 105 315 60 2.65 1880.45 500 108.3 331.67 60 2.68 1933.78 550 116.67 373.33 60 2.76 2070.03 600 125 415 60 2.85 2210.45 650 133 456 60 2.93 2355.03 700 141 498 60 3.01 2503.78 720 145 515 60 3.05 2564.45 750 150 540 60 3.10 2656.7 780 155 565 60 3.15 2750.45 800 158 581 60 3.18 2813.78 850 166.67 623 60 3.26 2975
The different responses obtained are as shown below:
Fig1: Generation vs. incremental cost curve for 3 units
Fig2: Generation vs. load demand curve for 3 units
Fig3: Total fuel cost vs. load demand curve for 3 units
Fig4: Total fuel cost vs. incremental cost curve for 3 units
1. IMPLEMENTATION OF FUZZY LOGIC CONTROLLER
The fuzzy logic controller provides an alternate way to solve the economic dispatch problem. The fuzzy controller implemented here is a two input one output system. The designing and tuning of the controller is done manually on the basis of understanding the behavior of the output in response to the change of input quantities. The input quantities are demand Pd and incremental cost . The output quantity is power generation of respective units. Three separate but similar type of controllers are used for the three units. The input output relation is given by the following rule table:
TABLE II: RULE TABLE FOR P1, P2, P3
Pd / L M H L L L L M L L L H M M M
The terms L, M, H stands for Low, Medium and High respectively. Hence the rules will be depicted as: If Pd is Low and isLow then P is Low. The Membership functions for the Pd, and P1 are shown below. Triangular membership functions are used. For defuzzification, Centroid method has been used.
Fig 5: Membership function for
Fig 6: Membership function for Pd
Fig 7: Membership function for P1
2. RESPONSES OF FUZZY LOGIC CONTROLLER
The following table lists out the generation scheduling given by the fuzzy logic controller in response to a wide variation of system load and also gives a comparison between the total fuel costs between analytical solution method and fuzzy controller method.
TABLE III: FUZZY CONTROLLER OUTPUT
Pd Fuel Cost (Analytical) Fuel Cost (Fuzzy) 450 2.6 1801.7 2750 480 2.65 1880.45 2750 500 2.68 1933.78 2750 550 2.76 2070.03 2760 600 2.85 2210.45 2750 650 2.93 2355.03 2750.05 700 3.01 2503.78 2750 720 3.05 2564.45 2823.6 750 3.10 2656.7 3035.6 780 3.15 2750.45 3180.9 800 3.18 2813.78 3170.7 850 3.26 2975 3409.8
Fig 8: Comparison Between Fuel Costs
V CONCLUSION
This paper finally does a comparison between the economic load dispatch solution with analytical method and using a fuzzy controller. In Fig 8, the cost comparison curve is shown. By adjusting the MFs of the input and output quantities it was possible to bring down the fuel cost significantly but doing it leads to mismatch of the power equation. Hereby we can conclude that the analytical solution is showing better result in comparison to fuzzy method.
REFERENCES
1. Assad Abu-Jasser1, Mohammed M. Hijjo2 ,Fuzzy-Logic-Based Approach to Solve the Unit-Commitment Problem, International Journal of Engineering Research and Development ISSN: 2278-067X,
Volume 2, Issue 1 (July 2012), PP. 22-29 www.ijerd.com
2. Assad Abu-Jasser, Solving the Unit Commitment Problem Using Fuzzy Logic, International Journal of Computer and Electrical Engineering,
Vol. 3, No. 6, December 2011
3. Vijay Kumar ,Jagdev Singh ,Yaduvir Singh, Sanjay Sood, "Optimal Economic Load Dispatch Using Fuzzy Logic & Genetic Algorithms, International Journal of Computer Engineering & Technology (IJCET),
Volume 7, Issue 1, Jan-Feb 2016
4. Prof. Vikrant Sharma*, 2Navpreet Singh Tung, 3Rashmi Rana, 4Vivek Guleria, Fuzzy Logic Controller Modelling for Economic Dispatch and Unit Commitment in Electrical Power System, International Journal of Emerging Research in Management &Technology ISSN: 2278-9359 (Volume-2, Issue-10)
5. Mr.Rudresh.B.Magadum, Smt.G.Suchitra, Dr.S.H.Jangamshetti, Fuzzy Logic solution for Unit Commitment, International Journal Of Scientific & Engineering Research Volume 3, Issue 4, April-2012
6. Abhijit Chakrabarti, Sunita Halder, Power System AnalysisOperation and Control, Third Edition, PHI
7. Allen J. Wood, Bruce F. Wollenberg, Power Generation, Operation and Control, 2nd Edition, Wiley
8. D P Kothari, I.J.Nagrath, Modern Power System Analysis, 3rd Edition, Tata McGraw Hill
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# Class 11 Physics Model Paper 2018 MCQs Test
FBISE Federal Board Class 11 Physics Model Paper 2018 MCQs Test. Do as much practice as you can so that you get good marks in the final exams.
Class 11 Physics MCQs Tests
### Model Paper 2018 MCQs Test
/17
507
Class 11 Physics
Model Paper 2018
Practice MCQs Test
1 / 17
If momentum is increased by 20% then K.E increases by:
2 / 17
What is to ratio 1μm/1Gm ?
3 / 17
For which angle the equation $$\left| \bar{A}.\bar{B}\right| = \left| \bar{A}\times\bar{B}\right|$$ is correct ?
4 / 17
Which one of the following factors has no effect on the speed of sound in a gas?
5 / 17
The angular speed in rad/hrs for the daily rotation of our earth is:Â
6 / 17
In an isothermal change, internal energy of a system:
7 / 17
What does NOT change when force is applied on a body?
8 / 17
The atmosphere is held to the earth by:
9 / 17
The tip of a needle does NOT give a sharp image. It is due to:
10 / 17
Artificial satellite moves around:
11 / 17
Triple point of water is:
12 / 17
The pressure will be low where the speed of the fluid is:
13 / 17
Which one of the following properties is NOT exhibited by the longitudinal waves?
14 / 17
The periods of the pendulum at Karachi (Tk) and at Murree (Tm) are related as:Â
15 / 17
What is the angle between $$\bar{A}$$ and $$\bar{B}$$ for which $$\left| \bar{A}+\bar{B}\right| = \left| \bar{A} - \bar{B}\right|$$ ?
16 / 17
The Principle of Michelson Interferometer is based on the division of:
17 / 17
A projectile is thrown so that it travels a maximum range of 1000m. How high will it rise?
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Overload Function Selection Algorithm Example in C++
```//Overloading functions
const int BIG = 100;
class rational{
public:
rational(int n = 0) : a(n),q(1){}
rational(int i, int j) : a(i), q(j){}
rational(double r) : q(BIG), a(r * BIG){}
void print() const { cout << a << " / " << q ; }
operator double() { return static_cast<double>(a)/q; }
private:
long a, q;
};
inline int greater(int i, int j){
return ( i > j ? i : j);
}
inline double greater(double x, double y){
return ( x > y ? x : y);
}
inline rational greater(rational w, rational z) {
return ( w > z ? w : z);
}
int main(){
int i = 10, j = 5;
float x = 7.0;
double y = 14.5;
rational w(10), z(3.5), zmax;
cout << "\ngreater(" << i << ", " << j << ") = "
<< greater(i, j);
cout << "\ngreater(" << x << ", " << y << ") = "
<< greater(x, y);
cout << "\ngreater(" << i << ", " ;
z.print();
cout << ") = " << greater(static_cast<rational>(i), z);
zmax = greater(w, z);
cout << "\ngreater(";
w.print();
cout << ", ";
z.print();
cout << ") = ";
zmax.print();
}
```
```rational(double r) : q(BIG), a(r * BIG){}
```
This constructor converts from double to rational .
```operator double(){ return static_cast<double>(a)/q; }
```
This member function converts from rational to double.
```inline int greater(int i, int j)
{ return ( i > j ? i : j); }
inline double greater(double x, double y)
{ return ( x > y ? x : y); }
inline rational greater(rational w, rational z)
{ return ( w > z ? w : z); }
```
Three distinct functions are overloaded. The most interesting has rational type for its argument list variables and its return type. The conversion member function operator double is required to evaluate w > z. Later, we'll show how to overload operator>() to take rational types directly.
```cout << "\ngreater(" << i << ", " << j << ") = "
<< greater(i, j);
cout << "\ngreater(" << x << ", " << y << ") = "
<< greater(x, y);
```
The first statement selects the first definition of greater because of the exact match rule. The second statement selects the second definition of greater because of the use of a standard promotion conversion float to double. The value of variable x is promoted to double.
```<< greater(static_cast<rational>(i), z);
```
The third definition of greater is selected because the required cast coerces i to be type rational. The explicit conversion of i to a rational is necessary to avoid ambiguity. The function call greater(i, z) would have to have two available conversions to achieve a match. The user-defined conversion of int to rational for the argument i matches the third definition. The user-defined conversion from rational to double for the argument z matches the second definition. This violates the uniqueness provision for matching when user-specified conversions are involved. This is an exact match for definition three.
```zmax = greater(w, z);
```
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1. ## recurrence equations
Hey, I need a little help:
Solve this with recurrence equations: One string with decade digits is valid only if the string consists even number of zeros. How many valid words with length n are there?
Thank you.
2. ## Re: recurrence equations
neat problem.
Suppose you've got a $k$ digit string
There are $v_k$ valid strings and $10^k-v_k$ invalid strings.
We select the $k+1$th digit, $d_{k+1}$
If $d_{k+1}=0$ then adding this to all the currently invalid strings makes them valid.
Similarly if $d_{k+1}\neq 0$ then adding this to all the currently valid strings keeps them valid.
so we have
$v_{k+1} = 9 v_k + (10^k-v_k) = 8v_k + 10^k$
there are $9$ valid strings of length $1$ so $v_1 = 9$
and this completes the recursion equation.
a bit of toying with this reveals
$v_n = 9 \cdot 8^{n-1} + \displaystyle \sum_{k=2}^n 8^{n-k}\cdot 10^{k-1} = 9\cdot 8^{n-1}-2^{n-3} \left(5\cdot 2^{2 n}-4\cdot 5^n\right)$
3. ## Re: recurrence equations
Decade digits are $\{0,1,2,...,9\}$?
If you wish to find $c(n)$ the count of words length $n$, you can consider how such words can be made from those of length $(n-1)$ (you must add a non-zero digit) and from those of length $(n-2)$ (by adding two zeros). You thus get an expression of the form
$c(n) = A c(n-1) + Bc(n-2)$
where $A$ and $B$ are either constants or expressions in $n$
The trick is to avoid double counting. This is why from words of length $(n-2)$ we only look at adding two zeros, because if we add two non-zeros, we pass through the $(n-1)$ case on the way to words of length $n$.
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http://www.acmerblog.com/hdu-3731-god-of-number-theory-6711.html
| 1,501,268,135,000,000,000
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2015
02-21
# God of Number Theory
In ACM_DIY, there is one master called “AekdyCoin”. As we know, he is the god of “Number Theory”. He always kills the problem about “Number Theory” in seconds! But of course we do not have any idea about these problems~ One day in ACM_DIY, AekdyCoin asks us one problem:
You are given three non-negative integers A, B and K, you are expected to find how many X that satisfy.
X^A = B( mod (2K + 1) )
X is in the ranger [0, 2K];
Of course we have no idea about this problem, so could you help us?
The first line is one integer T indicates the number of the test cases. (T <= 1000)
Then for every case, only one line contains three integers A, B and K. (1 <= A, B <= 10^9, 1 <= K <= 5 * 10^8)
The first line is one integer T indicates the number of the test cases. (T <= 1000)
Then for every case, only one line contains three integers A, B and K. (1 <= A, B <= 10^9, 1 <= K <= 5 * 10^8)
3
1 1 1
11 11 11
111 111 111
1
0
0
1. 问题3是不是应该为1/4 .因为截取的三段，无论是否能组成三角形， x， y-x ，1-y,都应大于0，所以 x<y,基础应该是一个大三角形。小三角是大三角的 1/4.
2. simple, however efficient. A lot of instances it is difficult to get that a??perfect balancea?? among usability and appearance. I must say that youa??ve done a exceptional task with this. Also, the blog masses quite fast for me on Web explore.
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https://fr.scribd.com/document/390254835/courseoutline-EQT221-STUDENTversion
| 1,582,169,793,000,000,000
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Vous êtes sur la page 1sur 2
# UNIVERSITI MALAYSIA PERLIS
## Institut Matematik Kejuruteraan
Course Schedule for Statistics for Discrete Mathematics & Linear Algebra / EQT 221
Subject and Code: Discrete Mathematics & Linear Algebra / EQT 221
Total Lecture Hours: 3 Hours (lecture) x 14 weeks and 1 Hours (tutorial) x 14 weeks
Synopsis: This course introduces the definition and concepts in discrete mathematics
and linear algebra which is an essential tools in almost all subareas of
computer science and communication systems. The topics discuss
includes sets and functions, logic, theory number and cryptography,
matrices and linear transformation, vector spaces and inner product
spaces.
Course Outcomes : At the end of this course, students should be able to:
CO1: Ability to identify and choose the suitable concepts of discrete
mathematics in solving engineering problems.
CO2: Ability to apply the concept of linear algebra in solving engineering
problems
CO3: Ability to relate and solve engineering problems using discrete
mathematics and linear algebra
## CHAPTER 1 : Propositional Logic
1.1 Introduction Lecture (3 hrs)
1.2 Proposition Tutorial (1 hrs)
1-2 1.3 Compound Statement
1.4 Formal Proposition Quiz 1
1.5 Conditional Statement (Week 3)
1.6 Propositional Equivalence
## CHAPTER 2 : A Primer Of Mathematical Writing
Lecture (3 hrs)
2.1 Number System
3-4 Tutorial (1 hrs)
2.2 Number Theory
2.3 Introduction to Cryptography
## CHAPTER 3 : Sets & Boolean Algebra Lecture (3 hrs)
3.1 Sets Tutorial (1 hrs)
5-6
3.2 Boolean Algebra Quiz 2
3.3 Logic Circuits (Week 7)
Lecture (3 hrs)
CHAPTER 4 : Functions & Relations
Tutorial (1 hrs)
7 4.1 Definition, Diagrams & Inverse
MIDTERM EXAM
4.2 The Composition Operations
(10 OCTOBER 2017)
Mid-term break
Lecture (3 hrs)
CHAPTER 5 : Vector Space
Tutorial (1 hrs)
8-10 5.1 Vectors In R2, R3 & Rn
Quiz 3
5.2 Norm & Dot Product
(Week 10)
5.3 Matrix Transformations from Rn to Rm
1
CHAPTER 6 : Inner Product Space
6.1 Inner Product
Lecture (3 hrs)
6.2 Angle & Orthogonality In Inner Product
11-12 Tutorial (1 hrs)
6.3 Gram Schmidt Process : QR-Decomposition
Quiz 4
6.4 Best Approximation: Least Squares
(Week 13)
6.5 Least Squares Fitting to Data
## CHAPTER 7 : Linear Transformation Lecture (3 hrs)
13-14 6.1 General Linear Transformations Tutorial (1 hrs)
6.1 Matrices for General Linear Transformations
15 Revision Week
16-18 Final Exam
Evaluation:
(i) Peperiksaan/ Examination: 70%
Final Examination = 50%
Mid Term Examination = 20%
## (ii) Penilaian Berterusan/ Continual Assessment: 30%
Quizzes = 30%
Quiz 1 – 5 %; Quiz 2 – 10%; Quiz 3 – 5 %; Quiz 4 – 10 %
References:
(i) Rosen, H. Kenneth. 2007. Discrete Mathematics and Its Application (6th Edition).McGraw-
Hill, New York.
(ii) Ross, A. Kenneth & Wright, R. B. Charles. 1999. Discrete Mathematics (4th Edition).
Prentice Hall, Inc, New Jersey
(iii) Kolman, Bernard & Hill, R. David. 2004. Elementery Linear Algebra ( 8th Edition). Pearson
Education, Inc, New Jersey
(iv) Buchmann, J.A. 2004. Introduction to Cryptography (2nd Edition). Springer-Verlag, New
York
(v) Kolblizt, N. 1994. A course in Number Theory and Crytpgraphy (2nd Edition). Springer-
Verlag, New York.
(vi) Ma Siu Lun, Victor Tan. 2006. Linear Algebra I. Pearson Prentice Hall, Inc, New Jersey.
(vii) Larson, R & Falvo, D. 2010. Elementary Linear Algebra, Brooks/Cole Cengage Learning.
Lecturer Details:
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# Tagged Questions
The tag has no usage guidance.
1k views
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If an interest rate model with the following $P$-dynamics for the short rate. $$dr(t)=\mu(t,r(t))dt+\sigma(t,r(t))d\bar{W}(t)$$ Now consider a $T$-claim of the form $\chi = \Phi(r(T))$ with ...
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How can I calculate the sum of square deviations between two normalized price series according to (Gatev et. co 2006)? My normalized price series of stocks $X$ and $Y$ consist of the cumulative total ...
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# Nonlinear theory of elasticity : applications in by Larry A Taber
By Larry A Taber
“This booklet can be utilized as a textbook for a path in nonlinear elasticity, as a reference e-book for a path in biomechanics, or as a reference booklet for researchers attempting to study the topic on their own.” Zentralblatt Math smooth organic tissues frequently endure huge (nearly) elastic deformations that may be analyzed utilizing the nonlinear conception of elasticity. as a result of different ways to nonlinear elasticity within the literature, a few features of the topic might be tough to understand. This booklet makes an attempt to elucidate and unify these remedies, illustrating the benefits and downsides of every via quite a few examples within the mechanics of soppy tissues. purposes contain muscle, arteries, the guts, and embryonic tissues.
Read or Download Nonlinear theory of elasticity : applications in biomechanics PDF
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Sample text
52) Substituting Eqs. ) The tensor B can be found from Eq. 47) or Eq. 50). 2). 3. For instance, using Eq. 44)i, we can transform g2 = gy to g2 = Se by gs = A'gy — A*e y ~ —rsin# r cos# 0 cos( smt 0 —r sin 9 0 r cos 9 0 0 1 = - r sin 6 ex + r cos 9 ey which agrees with gg in Eq. 10). Components of the Coordinate Transformation Tensors In practice, the components of the transformation tensors usually are computed from the equations that relate the unbarred and barred curvilinear coordinates. For a unique mapping of one system to the other, we can write xl = xl(xj), xl = xl(xj).
Solution. With (a; 1 ,^ 2 ,^ 3 ) = (r,9,z), Eqs. 136) and the nonzero components of the metric tensor (gtj = gigj, g1J = g'-g J ) are 9n = 1, 922 =r2, 311 = 1, g22 = r-\ 333 = 1 ff33 = l. 137) As the only nonzero derivative of the g^ is 522,1 = 2r, the only nonzero Christoffel symbols given by Eq. 138) Vector and Tensor Calculus and from T^- = 47 Tijkgkl, T\2 2 T 2 = T221gn = = -r 2 T 21=Yl22g22=Y2l2g22=r~l. 139) As a check, we now compute gr,e = gi,2 = ri2fcgfc = rj2gfc as given by Eqs. 127). Substituting Eqs.
6 Since each of the vectors in a dyad is geometrically invariant in a given frame 6 Some authors use the notation a g> b for the tensor product. Vectors, Dyadics, and Tensors 18 of reference, it follows that the dyad also is invariant. , a b / ba. The same is true of higher-order polyads, such as abc or abed, which also are useful in some applications. Here, we are concerned primarily with dyads and linear combinations of dyads, which are called dyadics. , f = ma) are said to be written in direct notation.
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