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# Problem coupling my code with OpenFOAM using preCICE
Hello,
I’m trying to couple OpenFOAM with my structural code using preCICE. I used the perpendicular-flap example as the benchmark. I set up the OpenFOAM as 3D problem, which is identical to the fluid participant in corresponding OpenFOAM-CalculiX example. On the solid part, I set up my code as 2D problem and perform coupling with force (read) and displacement (write). I think this set-up is sensible if the “dimensions” in precice-config.xml is 2.
When i run the simulation, OpenFOAM can run for 2 steps before failing, probably diverges:
``````PIMPLE: iteration 1
smoothSolver: Solving for cellDisplacementx, Initial residual = 1, Final residual = 2.47636e-17, No Iterations 2
smoothSolver: Solving for cellDisplacementy, Initial residual = 1, Final residual = 2.56708e-17, No Iterations 2
DICPCG: Solving for pcorr, Initial residual = 1, Final residual = 0.000990229, No Iterations 71
DICPCG: Solving for pcorr, Initial residual = 0.594785, Final residual = 7.88115e-09, No Iterations 92
time step continuity errors : sum local = 3.85436e-08, global = 9.07536e-09, cumulative = 2.94411e+08
#0 Foam::error::printStack(Foam::Ostream&) at ??:?
#1 Foam::sigFpe::sigHandler(int) at ??:?
#3 Foam::symGaussSeidelSmoother::smooth(Foam::word const&, Foam::Field<double>&, Foam::lduMatrix const&, Foam::Field<double> const&, Foam::FieldField<Foam::Field, double> const&, Foam::UPtrList<Foam::lduInterfaceField const> const&, unsigned char, int) at ??:?
#4 Foam::symGaussSeidelSmoother::smooth(Foam::Field<double>&, Foam::Field<double> const&, unsigned char, int) const at ??:?
#5 Foam::smoothSolver::solve(Foam::Field<double>&, Foam::Field<double> const&, unsigned char) const at ??:?
#6 Foam::fvMatrix<Foam::Vector<double> >::solveSegregated(Foam::dictionary const&) at ??:?
#7 Foam::fvMatrix<Foam::Vector<double> >::solveSegregatedOrCoupled(Foam::dictionary const&) at ??:?
#8 Foam::fvMesh::solve(Foam::fvMatrix<Foam::Vector<double> >&, Foam::dictionary const&) const at ??:?
#9 ? in ~/sw2/openfoam-OpenFOAM-v2012/platforms/linux64GccDPInt32Opt/bin/pimpleFoam
#10 __libc_start_main in /lib/x86_64-linux-gnu/libc.so.6
#11 ? in ~/sw2/openfoam-OpenFOAM-v2012/platforms/linux64GccDPInt32Opt/bin/pimpleFoam
Floating point exception (core dumped)
Looking for any time directories without results (e.g. stray functionObjectProperties files, see openfoam-adapter issue #26 on GitHub)...
``````
I think there may be the problem with the mapping but do not know how to track it. In the CalculiX adapter, the quasis2D3D mapping is used because CalculiX is a 3D code. In my case, I prefer to use 2D code specifically for this problem. Does it have any implication? Is it possible to dump the mapping description out from preCICE for the sake of check and comparison?
This is a problem we are currently working on. Could you try to use the `develop` version of the OpenFOAM adapter?
So, you copied the OpenFOAM case from the (`develop` version) of the tutorials and replaced CalculiX with your code? And OpenFOAM-CalculiX worked for you? Did you change anything on OpenFOAM side?
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# Periodicity of signals
1. $$x(t) = \cos(2 \pi t) \cdot u(t)$$ $$y(t) = x(t) + x(-t)$$Is $y(t)$ periodic. If so, what is the $T$?
2. $$x(t) = \sin(2 \pi t) \cdot u(t)$$ $$y(t)= x(t) + x(-t)$$ Is $y(t)$ periodic?
• Indeed, without showing any attempt, I don't really know how to help you. These are very basic homework problems, and I get the feeling that you should maybe go through your learning material again if you can't answer them by, for example, making a trivial drawing of the two $y(t)$s you describe. Mar 12, 2017 at 10:58
• By the way, hint, whether $y$ are periodic or not depend on the exact definition of $u$. So, if you want a solution, I think you should ask yourself what the value of $u(0)$ is. There's different common definitions of that. Mar 12, 2017 at 12:13
• Hint: Draw a picture of the signal. Another hint: To figure out if a signal is periodic, you should be able to find a constant $T$ such that $y(t-T) = y(t)$ for every $t$. Can you think of such a $T$? Mar 15, 2017 at 20:08
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# How to Calculate a Percentage in Python
To get a percentage of two numbers in Python, divide them using the division operator (`/`) then multiply the result by 100 using the Python multiplication operator (`*`).
To demonstrate this, let's get the percentage of 3 out of 9 using Python.
``````percent = 3 / 9 * 100
print(percent)
``````
``````33.33333333333333
``````
## Python Percentage Function
If you need to get percentages many times in your program, it may be worth creating a small helper function.
``````def getPercent(first, second, integer = False):
percent = first / second * 100
if integer:
return int(percent)
return percent
print(getPercent(3, 9))
``````
``````33.33333333333333
``````
With the above function, to get an integer back pass `True` as the third argument.
``````def getPercent(first, second, integer = False):
percent = first / second * 100
if integer:
return int(percent)
return percent
print(getPercent(3, 9, True))
``````
``````33
``````
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‘Impossible’ Logic Puzzle: Can You Tell How Many Liars Are at the Party?
July 6, 2020 Updated: July 6, 2020
Imagine you are at a party with 100 people, and those partygoers are one of either two types of people: either truth tellers who always tell the truth, or liars who always lie.
Now, imagine that before going home, some of them shake hands. Then you ask each person: “How many truth tellers did you shake hands with?” One person tells you 99, then next says 98, then 97, 96, 95 … and so on, all the way down to 0.
Remember: liars only lie, while truth tellers always tell the truth.
Can you determine how many liars there were at the party?
This may seem like an impossible problem, as we do not know how many of them shook hands with each other. However, using logic as a tool, there is way to determine how many are liars. Take a moment to figure out the solution, and when you think you have it, or if you’ve hit a dead end, scroll down to see how to unravel this logic problem.
Let’s take a closer look at each person who attended the party and see what logic tells us: first, label each person according to how many truth tellers they claimed to shake hands with:
Person 99: shook hands with 99 truth tellers
Person 98: shook hands with 98 truth tellers
Person 97: shook hands with 97 truth tellers
Person 1: shook hands with 1 truth teller
Person 0: shook hands with 0 truth tellers
Next, let’s take a closer look at Person 99 and see what we can deduce using logic. If Person 99 is a truth teller, then Person 99 shook hands with all other people at the party, AND all others at the party must also be truth tellers.
Which includes Person 0, who claims to have shaken hands with 0 truth tellers.
Therefore, it must be the case that either Person 99 and Person 0 did not shake hands with each other—which means Person 99 is a liar—OR it means Person 0 shook hands only with liars, which also means Person 99 is a liar.
From this, we can deduce that it’s not possible for Person 99 to be a truth teller.
So, Person 99 is a liar.
Next, if Person 98 is a truth teller, that means he must have shaken hands with Persons 0 to 97 (because we now know Person 99 is not a truth teller), AND that Persons 0 to 97 must be truth tellers.
And once again, we can deduce that either Person 98 and Person 0 did not shake hands with each other—which makes Person 98 a liar—OR that Person 0 shook hands only with liars, which also makes Person 98 a liar.
So, Person 98 is also a liar.
Now, following this pattern, we can make a similar deduction for Persons 97, 96, 95 … all the way to Person 1, and logically deduce the same conclusion: that they are all liars.
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Bivariate Data Notes
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1 Bivariate Data Notes Like all investigations, a Bivariate Data investigation should follow the statistical enquiry cycle or PPDAC. Each part of the PPDAC cycle plays an important part in the investigation and for the sake of convenience and assessment restrictions the starting point will be the first P, Problem. From here the rest of the investigation should follow ending with C, Conclusion, which should sum up the findings and give a response to the Problem identified at the start. Problem This section will define the investigative problem and lead the student to look into relationships between variables of choice. This is possibly the most important component of the investigation. Time spent on this component can determine the overall quality of the investigation. This component provides an opportunity to show justification (M) and statistical insight (E). Before writing this component of the investigation, some of the variables may need to be researched to find the precise meaning. When selecting the variables to investigate, careful consideration needs to be done to ensure you are looking for a potential causal relationship. An example of a problem for Achieved level responses could look like this: The purpose of this investigation is to investigate how well an athlete s BMI can be used to predict their percentage body fat. The data was supplied. When carrying out the investigation, the context of the problem should be well established and kept to the forefront of all discussion points. Some initial research could drive the production of the investigative problem. Comparisons can be alluded to and underlying variables could be discussed. All of these variations can lead to the above statement becoming suitable for a Merit or an Excellence investigation. An example of a problem for Merit level responses could look like this: The purpose of this investigation is to investigate if an athlete s BMI or their sum of skin folds is better used to predict their percentage body fat and to see if this is different depending
2 on the gender of the athlete. The data used in the investigation was supplied and it came from the Australian Institute of Sport. Here there is a definite look to compare two different control (independent) variables to see their effect on the response (dependent) variable. There is also a look to investigate subsets with in each control variable to see if this gives a different conclusion. It is worth noting at this point that the investigative question should be looking at variables that could potentially have a causal effect on each other. Asking if height was a good predictor of percentage body fat makes no sense as by making an athlete taller will not cause them to have a higher (or lower) percentage body fat reading. What might an excellence problem look like? It would be based on research that will be quoted throughout the investigation. It would look something like this: The purpose of this investigation is to look into a claim that was found in [insert reference 1 here]. This source stated that an athlete s BMI can be safely used to predict a person s percentage body fat. This report will look into whether this holds for athletes and it will also compare this to the sum of skin folds and its ability to predict an athlete s percentage body fat. Interestingly [insert reference 2 here] go on to say that BMI is a better predictor of percentage body fat in female subject, so this investigation will look to see if this is also true when looking at the gender of an athlete for both BMI and the sum of skin folds. The supplied data used in this investigation came from the Australian Institute of Sport. It includes data about 102 male athletes and 100 female athletes. Remember these are all just examples. So long as the purpose of the investigation is clear and the variables of interest have been clearly identified. Plan This section is where the process of the investigation is described. What will be done and what are the expected outcomes? This needs to be kept in
3 context and for this to count towards an M or an E grade then clear comparisons and research need to be linked into what is written. An example of a Plan for an Achieved level response could look like this: The computer software inzight is going to be used to produce the scatter plots for two different control variables against the same response variable. The equations will also be generated. The graphs will be used to choose the most valid model for predicting the response variable. The equation for this graph will then be used to make a prediction and a comment will be made to answer the investigative question. Data This section is where a description of the data is given. The extent of this description depends on whether the report is aimed at Achieved, Merit or Excellence. It is here that the data should be discussed including the use of correct units and a demonstration of understanding where the data has come from and what it means in terms of the context. Analysis A scatter plot is used to show how two variables are associated. If a population is being studied and in particular variable and are bing looked at, then each dot on the scatter plot represents the values and for an individual member of the population. The whole plot gives the visual representation of the entire sample.
4 A side note here, remember the names of variables are capital letters and a particular value of that variable is represented using the lower case version of the same letter. Unlike in a Time Series, the data points are not connected by line segments. Instead, when a pattern emerges in the placement of the data point, a line of best fit, or trend line is added. Usually you will fine ( ) on that line, where is the mean of the variable and is the mean of the variable. When analyzing a scatter plot, the mnemonic TARSOG will help to focus comments about specific features that are present. T A R S O G is for Trend, is it linear or something else? is for Association, is it positive or negative? is for Relationship, is it strong or weak? is for Scatter, is it constant or not? Fan shaped? is for Outliers, are any identifiable? is for Groups, are there any? This trend line (something inzight will produce) will be used later to make predictions of the response variable for particular values of the control variable. The fitting of a trend line initially is an arbitrary decision to choose it to be linear. The linear option is checked out first as it is the most simple and the easiest to interpret in context with any type of tangible meaning. The other options in inzight are quadratic (parabolic) and cubic. At this point it is a visual check as to the fit-ness of the model. Throughout the rest of this section, there are discussions that lead to evidence to support or reject the use of a linear trend line. The association of the data values looks at where there is a positive (as the control variable increases, so does the response variable) or a negative (as the control variable increases, the response variable decreases) association. When inzight gives the equation of this trend line it also produces another value it calls correlation. The correct name for this value is in fact the correlation coefficient and is often assigned the letter. The correlation coefficient can range in value from - 1 (a perfect negative association) through to 1 (a perfect positive association). This number allows the assignment of a description of the strength of the relationship.
5 As a general rule of thumb, these descriptions of the relationship present and values are acceptable: Strong Moderate Weak None None Weak Moderate Strong Outliers are a big source of variation and need to be looked into carefully. There must be good reason to remove a value from a data set as the process can dramatically alter the relationship. Also, 2-3 would be an absolute maximum to remove, and usually the removal of one outlier is sufficient to see a change. There are two distinct types of outliers, ones that do not fit the pattern of the rest of the data (the left hand graph below has it circled) and the ones that fit the pattern but are a long way from the main data set ( the right hand graph has one of these).
6 Outliers When trying to identify potential outliers of the first type, residuals help a lot. Residuals are the distance from the raw data to the predicted data (or trend line). These need to be calculated and graphed to back up the selection of type 1 outliers. In some cases, when graphing the residuals, a pattern will emerge, this suggests that perhaps a linear model was not the best choice. A visual check of the linear trend line on the raw data will confirm this. The programme inzight only has the option of trying a quadratic or a cubic as curved models. Other software allows the user to look at logarithmic, power and exponential models also. Sometimes when plotting bivariate data, groupings become apparent in the data. These groupings can usually be explained by looking at a third variable. This third variable is commonly a categorical variable, hence it has the ability to segregate groups of data. Conclusion Predictions form part of the conclusion as they are used to help answer the investigative question this report started with. There are two different types of predictions that should be looked into, interpolations and extrapolations. Interpolations look at predictions that are within the range of x-values present in the sample and an extrapolation looks outside that range, above or below.
7 An appropriate evaluation of these predictions is required and leads onto the answer of the investigative question. When summing up in the conclusion, great care must be taken when making causal relationship statements. Careful analysis of potential underlying variables must have been done in order to improve the strength of argument for or against such a claim. Have other variables that could potentially influence the response variable been considered, rather than just looking for a straight predictive relationship. To be continued
Quadratic Regressions Group Acitivity 2 Business Project Week #4 In activity 1 we created a scatter plot on the calculator using a table of values that were given. Some of you were able to create a linear
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Quantum nodes¶
Classical and quantum information¶
It is important to distinguish between classical and quantum forms of information. For our purposes, we will consider the value of a number stored within a conventional digital computer (say, a floating point binary representation of a real or complex number) as classical information. Many common functions — like addition, subtraction, multiplication, $$\sin,\cos,\exp,$$ etc. — can all be evaluated efficiently on a classical computer, e.g., using the NumPy library in Python. These functions map floating point numbers to floating point numbers. In other words, they are functions which process classical information.
On the other hand, quantum information will refer to the state of a complex-valued vector in a quantum Hilbert space. Gates in a quantum computer transform quantum states to quantum states, i.e., they process quantum information.
Classical information refers to the state of binary numbers stored on a conventional digital computer. Quantum information refers to the state of a complex-valued vector in a quantum Hilbert space.
Note
Quantum information processing can be simulated on a classical computer, but in general this cannot be done efficiently.
Interfacing the classical and quantum worlds¶
There are many schemes for loading classical information into quantum systems, but these can often get quite complex. To connect between the classical and quantum worlds, PennyLane uses two straightforward methods:
1. Gate parameters
The gates used in a quantum circuit often have classical parameters associated with them. This classical information determines how a quantum state is transformed — e.g., what angle we should rotate the quantum state by. Thus, gate arguments provide us a way to imprint classical data onto quantum states, converting classical information to quantum information [1].
2. Measurement of a quantum circuit
Measurements convert quantum information (the state of a quantum system) into classical information (the measurement value). Measurements often have a probability distribution of outcomes, with the pattern becoming clear only after a sufficient number of measurements are taken.
In PennyLane, we work with expectation values (i.e., averages) of measurement outcomes as our primary mechanism for obtaining classical information from quantum devices [2].
The quantum node abstraction¶
A quantum node is a computational encapsulation of a quantum function $$f(x;\mathbf{\theta})$$ which has different resolution for different computational devices.
• For a quantum computing device, a quantum node is a variational circuit whose gates are parameterized by $$x$$ and $$\mathbf{\theta}$$ and whose measurement outcomes are averaged to produce an expectation value.
• For a classical computing device, a quantum node is a callable function, taking the arguments $$(x,\mathbf{\theta})$$ and returning the value $$f(x;\mathbf{\theta})$$. The classical device cannot “zoom in” and see any intermediate state of the quantum circuit.
Quantum nodes are seen differently depending on the computational device. A classical device merely sees a callable function which transforms classical information. A quantum device sees a higher resolution version, with quantum gates and measurements.
Note
For a function $$f(x; \mathbf{\theta})$$, $$x$$ is considered to be the function’s input and $$\mathbf{\theta}$$ are parameters which determine the exact form of $$f$$.
So long as we provide some mechanism for evaluating quantum nodes (i.e., a quantum computing device or simulator), a classical computing device can treat it as it would any other callable function which manipulates classical data. We can thus connect quantum nodes with classical transformations to build complex multistage hybrid quantum-classical computations.
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# How Many Pages is 800 Words?
Looking to find 800 words is how many pages. If you are looking to write an essay, blog, or assignment. No problem, we have answered how many pages is 800 words.
Answer: 800 Words is 1.6 pages single spaced and 3.2 pages double spaced.
It also said as 800 words are 1 ⅗ page single spaced and 3 ⅕ pages double spaced.
This data is calculated using font size 12 and the Arial font family, which is one of the commonly used font sizes. We have provided enough paragraphs in the content to make it easily readable.
Now you have got the answer for how many pages is 800 and we have calculated other factors like character count, sentences, paragraphs, letters, read time, speak time, and handwritten.
## How Many Sentences in 800 words?
800 Words is 50 to 55 sentences. The number of sentences in the 800 words highly depends on various factors and the type of content you are writing.
So this is an approximate value.
## How many Pages is 800 Words Single spaced?
800 Words is 1.6 pages double spaced in font size 12 and Arial font family.
## How many Pages is 800 Words double spaced?
800 Words is 3.2 pages double spaced in Arial font and font size 12.
## What is the reading time for a page with 800 Words?
800 Words take 3 minutes and 13 seconds to read. It is calculated with an average reading speed of 250 words per minute.
It is common for an adult to read at that speed, but it could differ for each person.
## What is the Speaking Time for a Page with 800 Words?
800 Words takes 5 minutes 21 seconds to speak. When considering speech speed 150 words per minute is the normal speaking rate. At this, the listeners could easily understand the speaking.
## How Many Pages is 800 Words Handwritten?
800 Words handwritten is 3.2 pages. Handwritten takes the space as double spaced. So, 800 words take 3.2 pages in handwritten. Based on every person handwriting the pages required will change.
## How Many Paragraphs is 800 Words?
800 Words have 13 to 15 paragraphs. It is calculated by considering 4 sentences in each paragraph. Splitting the content into multiple paragraphs will helps readers to easily understand.
## How many characters in 800 words?
800 Words have approximately 5000 to 5500 characters. The character count includes spaces, letters, alphabets, numbers, and special characters present in the text content.
## How many letters in 800 words?
800 Words have approximately 4000 to 4500 letters. When calculating letters the spaces are not considered. The spaces between the words and paragraphs are not calculated.
So the letter count is always less than the character count.
## Time Taken to write 800 Words?
800 Words take 20 minutes to write. It is calculated with an average typing speed of 40 words per minute. A seasoned writer can write faster than this and also it varies based on the type of content you are writing.
## Pages Per Word Count?
If you have a target to write a certain number of pages, then we have derived a neat table that explains the number of pages required for different word counts.
## How Many Words Per Page?
If your target is to write a certain number of pages, then follow the below table to find the words required to fill each number of pages.
## How Many Pages is 800 Words: Summarize
• 800 Words is 1.6 pages single spaced
• 800 words is 3.2 pages double spaced
• 800 Words take 3 minutes 13 seconds to read
• 800 Words take 5 minutes 21 seconds to speak
• 800 Words have 5000 to 5500 characters
• 800 Words handwritten is 3.2 pages
• 800 Words take 20 minutes to write
This is the complete details about 800 Words is how many pages that including the character count, reading time, speech time, letter count, and a number of sentences are available in the 800 Words approximately.
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# How can I control the error bar colors to be the same as geom_point colors?
I wanted to make a point plot in ggplot and I used `geom_point` function to do it. To colorize the points, I used levels to fill them either in red or blue. However, now I’m adding the error bars to my point plot with `geom_errorbar` function, it seems I can’t give the colors I used in geom_points. In other words, I can only give them one color, which is by default black. Is there any way I can control the color of the error bars?
Let’s say we have the following data frame:
``````df <- data.frame (Xvalue=c(1.2, 1.3, 2.1, 2.4, 2.7),
Yvalue=c(12, 15, 17, 24, 27),
Kind=c('A', 'B', 'A', 'B', 'B'),
Ymax=c(13, 16, 19, 26, 29),
Ymin=c(11, 14, 15, 22, 25))
df\$Kind = factor(df\$Kind)
``````
Now I want to draw the plot with the error bars:
``````myplot <- ggplot (df, aes(Xvalue, Yvalue, fill=Kind)) +
geom_point( shape=21, size= 4, alpha= 0.7)+
geom_errorbar(aes(ymin=Ymin, ymax=Ymax, width=0.08))
myplot
``````
This results in a plot with error bars of black. How can I make sure this is the same color as the points?
Bonus question: Is this how you would usually make two colors in your points, I mean by putting the "levels" in the ggplot function as fill? Do you have an alternative way to where one doesn’t need to use Shape=21, where the outer pirameter of the circle is black?
Bonus qeustion 2: Is it generally easier to plot two kinds of points, when they are in 1 dataframe, or is it better to seperate the dataframes? For instance, I can have a smaller dataframe for the Kind A, and another one for dataframe B. Would that make the life easier? Why I’m asking is that, when I tried to plot with more than one levels (for instance once "Kind" and the other one "Original country"), it was quite confusing to plot points in different colors and sizes.
### >Solution :
You should add the `color` `aes` to your `geom_errorbar` like this (Please note: you could add `show.legend` FALSE to your `geom_errorbar` so there is no line in your elements of your legend):
``````library(ggplot2)
myplot <- ggplot (df, aes(Xvalue, Yvalue, fill=Kind)) +
geom_point( shape=21, size= 4, alpha= 0.7)+
geom_errorbar(aes(ymin=Ymin, ymax=Ymax, width=0.08, color = Kind), show.legend = FALSE)
myplot
``````
Created on 2023-01-12 with reprex v2.0.2
If you want the error bar behind your point, just swap the commands in order.
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# Geometry
posted by .
Given the points A(−2, 1) and B(3, 4), what are the coordinates of point C in the fourth
quadrant such that mCAB = 90 degrees and AB = AC? Express your answer as an ordered pair.
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The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195675 Round(Pi^(n+1)/(Pi^2 + 1)). 0
0, 1, 3, 9, 28, 88, 278, 873, 2742, 8616, 27067, 85032, 267137, 839237, 2636540, 8282934, 26021606, 81749286, 256822958, 806833117, 2534740992, 7963123679, 25016890851, 78592880513, 246906816043, 775680639401, 2436872598275, 7655661052475, 24050968520829 (list; graph; refs; listen; history; text; internal format)
OFFSET 0,3 COMMENTS a(n+1)/a(n) converges to Pi. LINKS Table of n, a(n) for n=0..28. FORMULA a(n) = round(Pi^(n+1)/(Pi^2 + 1)). EXAMPLE a(4) = 28 because (Pi^5)/(Pi^2 + 1) = 28.1537095089.... MATHEMATICA Table[Round[Pi^(n + 1)/(Pi^2 + 1)], {n, 0, 28}] PROG (PARI) for(n=0, 28, print1(round(Pi^(n+1)/(Pi^2+1)), ", ")) CROSSREFS Another version of A090426. Cf. A000796, A170953. Sequence in context: A095716 A124820 A022020 * A170953 A358092 A333504 Adjacent sequences: A195672 A195673 A195674 * A195676 A195677 A195678 KEYWORD nonn AUTHOR Arkadiusz Wesolowski, Apr 22 2012 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified May 31 22:36 EDT 2023. Contains 363068 sequences. (Running on oeis4.)
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# How to calculate a regression model with quadratic factors?
I'd appreciate your help. I want to obtain the equation shown in the image considering the quadratic factors of the approximation. Using lm() from the lmtest package
Cp<- c(0.4153, 0.4572, 0.26, 0.1446, 0.0749, 0.2778, 0.294, 0.4074, 0.0912, 0.2541, 0.0855, 0.444, 0.0983, 0.4263, 0.0712, 0.1286, 0.2951, 0.1389, 0.128, 0.3865, 0.5113, 0.5478, 0.2631, 0.4023, 0.2962, 0.2962, 0.2962)
L<- c(-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
p<- c(-1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0)
α<- c(-1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0)
Di/Do<- c(-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0)
Hi. I don't get your regression equation, but here is my attempt:
df <- data.frame(
Cp= c(0.4153, 0.4572, 0.26, 0.1446, 0.0749, 0.2778, 0.294, 0.4074, 0.0912, 0.2541, 0.0855, 0.444, 0.0983,
0.4263, 0.0712, 0.1286, 0.2951, 0.1389, 0.128, 0.3865, 0.5113, 0.5478, 0.2631, 0.4023, 0.2962, 0.2962, 0.2962),
L= c(-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0),
p= c(-1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0),
a= c(-1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0),
DiDo= c(-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0))
lm(Cp ~ L + p + a + DiDo + Lp + La + LDiDo + pa + p*DiDo + I(L^2) + I(p^2) + I(a^2) + I(DiDo^2), df)
Coefficients:
(Intercept) L p a DiDo I(L^2)
3.362e-01 5.519e-02 -7.222e-05 -1.872e-02 -3.293e-02 -1.391e-01
I(p^2) I(a^2) I(DiDo^2) L:p L:a L:DiDo
-9.888e-02 1.734e-01 -2.343e-02 -2.011e-02 1.586e-02 4.150e-02
p:a p:DiDo
1.923e-02 -1.338e-03
This topic was automatically closed 21 days after the last reply. New replies are no longer allowed.
If you have a query related to it or one of the replies, start a new topic and refer back with a link.
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Solved
# View Formula for Contract Expiry
Posted on 2004-10-20
Medium Priority
298 Views
Hi everyone,
I have 2 views, one of them should show contracts expiring next month, and the other view should show contracts expiring within 2 months. for example today is October 20, 2004. I need the first view to show contracts expiring before November 30, 2004. Second view should show contracts expiring before December 31, 2004.
How shall I write the formula for each view ?
Many thanks in advance.
Kindest Regards
0
Question by:Faraj1969
[X]
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LVL 14
Expert Comment
ID: 12361734
select form = "<formname>" & expirydate = @Adjust(@today;0;2;0;0;0;0)
But this will make the view very slow , especially when the database size is big
Partha
0
LVL 31
Assisted Solution
qwaletee earned 600 total points
ID: 12361736
Assume the contract expiration date field is name ContractExpires. The SELECT formula would be:
start := @Adjust(@Today; 0; 1; 1 - @Day(@Today); 0; 0; 0);
end := @Adjust(start; 0; 1; -1; 0; 0; 0);
ContractExpires >= start & ContractExpires < end;
start := @Adjust(@Today; 0; 2; 1 - @Day(@Today); 0; 0; 0);
end := @Adjust(start; 0; 1; -1; 0; 0; 0);
ContractExpires >= start & ContractExpires < end;
0
LVL 31
Expert Comment
ID: 12361763
Oh, wait, better...
dateToMatch := @Adjust(@Today; 0; 1; 1 - @Day(@Today); 0; 0; 0);
contractMonth := @Adjust(@Today; 0; 0; 1 - @Day(@Today); 0; 0; 0);
dateToMatch = contractMonth
dateToMatch := @Adjust(@Today; 0; 2; 1 - @Day(@Today); 0; 0; 0);
contractMonth := @Adjust(@Today; 0; 0; 1 - @Day(@Today); 0; 0; 0);
dateToMatch = contractMonth
0
Author Comment
ID: 12361963
Many Thanks p_partha and qwaletee, it worked very nicely.
Now, here in this company there's 2 types of contracts, Appointment and Assignment, each employee have both contracts, Appointment with HQ and Assignment with Branch. Expiry date field for appointment is dP1_Expire, and
Expiry date field for assignment is dP2_Expire.
The formula I have now is like this
start := @Adjust(@Today; 0; 2; 1 - @Day(@Today); 0; 0; 0);
end := @Adjust(start; 0; 1; -1; 0; 0; 0);
SELECT ( Form = "Staff Record" & tStatus = "On Board" & dP1_Expire >= start & dP1_Expire <= end )
How can I revise SELECT statement to show the Staff if the appointment or the assignment gonna expire within the same period ?
Cheers
0
LVL 15
Expert Comment
ID: 12362095
Is this R6 or R5 ? Because in R6, it's better to use the new 'editable' ViewSelection (use an agent to set the view selection), to avoid using @today in a view selection. This would improve performance somewhat, because @today prevents efficient view-indexing (the view index will always be recalculated)
cheers,
Tom
0
Author Comment
ID: 12362116
unfortunately we still use R5, since we have many applications and we need to revise them for compatibility before moving to R6.
Cheers
0
Author Comment
ID: 12362153
I believe my question now worth more.. so I increased the points... lol
0
LVL 15
Accepted Solution
Bozzie4 earned 400 total points
ID: 12362198
start := @Adjust(@Today; 0; 2; 1 - @Day(@Today); 0; 0; 0);
end := @Adjust(start; 0; 1; -1; 0; 0; 0);
SELECT ( Form = "Staff Record" & tStatus = "On Board" & ((dP1_Expire >= start & dP1_Expire <= end ) | (dP2_Expire >= Start & dP2_Expire <= End))
cheers,
tom
0
Author Comment
ID: 12362273
Many thanks everyone, I'll split the points.
Cheers.
0
LVL 46
Expert Comment
ID: 12367542
Just a suggestion: combine those views, and make the documents categorized by the number of months before expiration. Adding a view for 3 months would be simply reduced to adapting the select-statement.
0
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# Bessel potential space
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
fractional Sobolev space, Liouville space
A Banach space of integrable functions or distributions on the -dimensional Euclidean space , which generalizes the ordinary Sobolev space of functions whose derivatives belong to -classes, and their duals. If denotes the Laplace operator, the Bessel potential space , , , can be defined as the space of functions (or distributions) such that belongs to the Lebesgue space , normed by the corresponding Lebesgue norm. The operator , which for is a kind of fractional differentiation (cf. also Fractional integration and differentiation), is most easily defined by means of the Fourier transform. It corresponds, in fact, to multiplication of the Fourier transform of by . The operator clearly has the group properties , and .
It is a theorem of A.P. Calderón that for positive integers and the space coincides (with equivalence of norms) with the Sobolev space of functions all of whose derivatives (in the distributional, or weak sense) of order at most are functions in .
For the elements of are themselves -functions, which can be represented as Bessel potentials of -functions. In fact, the function is then the Fourier transform of an integrable function, the Bessel kernel , and the operator can be represented by a convolution with this kernel. In other words, , , , if and only if there is a such that , where the integral is taken over all of with respect to the Lebesgue measure.
The kernel can be expressed explicitly by means of a modified Bessel function of the third kind (cf. also Bessel functions), also known as a Macdonald function, and for this reason the Bessel potentials were given their name by N. Aronszajn and K.T. Smith in 1961. More important than the exact expression for the kernel is the fact that it is a suitable modification of the (Marcel) Riesz kernel , , whose Fourier transform is . The Bessel kernel has the same properties as the Riesz kernel for small , but thanks to the fact that its Fourier transform behaves nicely at , it decays exponentially at infinity. In contrast to the Riesz kernel it is therefore an integrable function, and this is its main advantage.
The spaces appear naturally as interpolation spaces that are obtained from Sobolev spaces by means of the complex interpolation method (cf. also Interpolation of operators). They are included in the more general scale of Lizorkin–Triebel spaces ; in fact, (with equivalence of norms) for and . This equivalence is a highly non-trivial result of so-called Littlewood–Paley type. Related to this are very useful representations by means of atoms.
The Hilbert space , also known as the Dirichlet space, and its generalizations are intimately related to classical potential theory. The study of more general non-Hilbert spaces and , motivated by investigations of non-linear partial differential equations, has lead to the creation of a new non-linear potential theory, and many of the results and concepts of the classical theory have been extended to the non-linear setting, sometimes in unexpected ways.
#### References
[a1] D.R. Adams, L.I. Hedberg, "Function spaces and potential theory" , Springer (1996) [a2] H. Triebel, "Theory of function spaces II" , Birkhäuser (1992)
How to Cite This Entry:
Bessel potential space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bessel_potential_space&oldid=16844
This article was adapted from an original article by L.I. Hedberg (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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# Discoverer 18
1966
Designer
Joseph V. Puccia
Builder
American Fiberglass Corp.
Associations
?
# Built
?
Hull
Monohull Dinghy
Keel
Centerboard
Rudder
?
Construction
FG
### Dimensions
Length Overall
17 7 / 5.4 m
Waterline Length
16 4 / 5 m
Beam
6 3 / 1.9 m
Draft
0 9 / 0.2 m 4 5 / 1.4 m
Displacement
650 lb / 295 kg
Ballast
?
• 1 / 1
### Rig and Sails
Type
Sloop
Reported Sail Area
165′² / 15.3 m²
Total Sail Area
?
Sail Area
?
P
?
E
?
Air Draft
?
Sail Area
?
I
?
J
?
Forestay Length
?
Make
?
Model
?
HP
?
Fuel Type
?
Fuel Capacity
?
### Accomodations
Water Capacity
?
Holding Tank Capacity
?
?
Cabins
?
Hull Speed
9.1 kn
Classic: 5.42 kn
### Hull Speed
The theoretical maximum speed that a displacement hull can move efficiently through the water is determined by it's waterline length and displacement. It may be unable to reach this speed if the boat is underpowered or heavily loaded, though it may exceed this speed given enough power. Read more.
Formula
Classic hull speed formula:
Hull Speed = 1.34 x √LWL
A more accurate formula devised by Dave Gerr in The Propeller Handbook replaces the Speed/Length ratio constant of 1.34 with a calculation based on the Displacement/Length ratio.
Max Speed/Length ratio = 8.26 ÷ Displacement/Length ratio.311
Hull Speed = Max Speed/Length ratio x √LWL
9.05 knots
Classic formula: 5.42 knots
Sail Area/Displacement
35.2
>20: high performance
### Sail Area / Displacement Ratio
A measure of the power of the sails relative to the weight of the boat. The higher the number, the higher the performance, but the harder the boat will be to handle. This ratio is a "non-dimensional" value that facilitates comparisons between boats of different types and sizes. Read more.
Formula
SA/D = SA ÷ (D ÷ 64)2/3
• SA: Sail area in square feet, derived by adding the mainsail area to 100% of the foretriangle area (the lateral area above the deck between the mast and the forestay).
• D: Displacement in pounds.
35.17
<16: under powered
16-20: good performance
>20: high performance
Ballast/Displacement
?
### Ballast / Displacement Ratio
A measure of the stability of a boat's hull that suggests how well a monohull will stand up to its sails. The ballast displacement ratio indicates how much of the weight of a boat is placed for maximum stability against capsizing and is an indicator of stiffness and resistance to capsize.
Formula
Ballast / Displacement * 100
?
<40: less stiff, less powerful
>40: stiffer, more powerful
Displacement/Length
66.6
<100: Ultralight
### Displacement / Length Ratio
A measure of the weight of the boat relative to it's length at the waterline. The higher a boat’s D/L ratio, the more easily it will carry a load and the more comfortable its motion will be. The lower a boat's ratio is, the less power it takes to drive the boat to its nominal hull speed or beyond. Read more.
Formula
D/L = (D ÷ 2240) ÷ (0.01 x LWL)³
• D: Displacement of the boat in pounds.
• LWL: Waterline length in feet
66.57
<100: ultralight
100-200: light
200-300: moderate
300-400: heavy
>400: very heavy
Comfort Ratio
5.2
<20: lightweight racing boat
### Comfort Ratio
This ratio assess how quickly and abruptly a boat’s hull reacts to waves in a significant seaway, these being the elements of a boat’s motion most likely to cause seasickness. Read more.
Formula
Comfort ratio = D ÷ (.65 x (.7 LWL + .3 LOA) x Beam1.33)
• D: Displacement of the boat in pounds
• LWL: Waterline length in feet
• LOA: Length overall in feet
• Beam: Width of boat at the widest point in feet
5.19
<20: lightweight racing boat
20-30: coastal cruiser
30-40: moderate bluewater cruising boat
40-50: heavy bluewater boat
>50: extremely heavy bluewater boat
Capsize Screening
2.9
>2.0: better suited for coastal cruising
### Capsize Screening Formula
This formula attempts to indicate whether a given boat might be too wide and light to readily right itself after being overturned in extreme conditions. Read more.
Formula
CSV = Beam ÷ ³√(D / 64)
• Beam: Width of boat at the widest point in feet
• D: Displacement of the boat in pounds
2.89
<2: better suited for ocean passages
>2: better suited for coastal cruising
### For Sale
Have a sailboat to sell?
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Rate of reaction Vs enzyme concentration: how does enzyme concentration affect the rate of reaction and how does the PH affect the rate of reaction.
Extracts from this document...
Introduction
Rate of reaction Vs enzyme concentration: how does enzyme concentration affect the rate of reaction and how does the PH affect the rate of reaction tools- take two test tubes, a test tube holder, a delivery tube, potatoes, cylindrical cutter, a ruler, water (PH 7 solution), a PH 9 and a PH 3 solutions- stop watch., H2O2 (perdoxide). Procedure- Six sets of results asking for 4 test tubes each were to be made. 2 sets for results of a neutral solution, 2 sets for a PH 9 solution, and 2 sets for a PH 3 solution. Each set had 4 test tubes ready to be used for it- one test tube to be filled with 1 potato piece, another with 4, and another with 7, and a last one with 10 potato pieces in it. ...read more.
Middle
These bubbles were counted for a minute which was started from the first bubble to be released. The bubble count was to give a rough idea of the energy released from the reaction. Hypothesis: the table with the highest results might be the one with the neutral solution, I also hypothesize that the more there will be potatoes the faster the reaction will be. The PH solutions will not yield high results. Results: TABLE 1 Neutral PH Amount of potatoes first try results Second try results 1 11 13 4 28 24 7 58 61 10 74 77 Table 2 10 ml of PH 9 solution mixed with 15 ml of water Amount of potatoes first try results Second try results 1 3 4 4 11 13 7 ...read more.
Conclusion
We also notice that the amount of bubbles oxygen do not increase geometrically. There is a reason for this and it is because there are too many molecules and not enough activation sites- thus they become saturated and some of the molecules do nothing (in regards of the reaction). The hypothesis was proven right. Discussion: The main problem was the precision in trying to get equal sized potato pieces. As ridiculous as it may sound it is necessary to obtain a greater accuracy. For future reference it would be easier to do the experiment with variable weights instead of variable amounts. Of course more than two sets of results would be more than good- but for that there'd be a need for more time. ...read more.
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Statics
If both the projection Pa and component Fb of the force F are 305 N, determine the magnitude F and the orientation è of the b-axis.
The angle between the negative y axis and the a- axis is 70 degrees.
The angle between the negative y axis and the force F is 108 degrees.
I found the Force F=305/cos38 = 387.05, but am having trouble with the angles. The answer requires a positive and negative angle theta.
1. 👍 0
2. 👎 0
3. 👁 395
1. The angles are not precisely specified.
It is not clear whether the a-axis makes an angle of -20 (340) with the x-axis, or -160 (200) with the x-axis.
Same problem for the force F.
Could you specify forces and axes using the following conventions:
1. All angles are measured from the positive x-axis.
2. Angles measured counterclockwise (CCW) are positive, angles measured clockwise (CW) are negative.
3. All forces (and axes) originate from the origin. Forces towards the origin may be converted to originate therefrom by adding 180 degrees.
After that, draw a diagram and make a table. Unknown quantities (force or orientation) should be denoted by a variable name.
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posted by MathMate
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# Cos2Pi/3, Cos2Pi 3 Cos 5Pi 3 Sin 2Pi 3 Brainly Co Id
Cos2Pi/3. And using the #color(blue) exact value triangle#. Pi/3 radians = 60 degrees, and cos is looking for the side adjacent to the 60 degree angle. 2pi is 360 degrees, which means a complete circle and thus same endpoint is startpoint. Online calculation with the function cos according to the cos(2*pi/3). Enter angle in degrees or radians since our angle is greater than π/2 and less than or equal to π radians, it is located in quadrant ii in the second quadrant, the values for sin are positive only. How do you show that #(costheta)(sectheta) = 1# if #theta=pi/4#? How do you know if #sin 30 = sin 150#? So only 1st and 4th quadrant answers are relevant. And we know $a = \frac{π}{3}$ so we replace and we see that this identity is true. This site might help you. In this video, we will learn to find the value of cos(2pi/3). The cosine calculator allows through the cos function to calculate online the cosine of an angle in radians, you must first select the desired unit by clicking on the options button calculation. Thus cos(2pi) is equal to cos(0) in magnitude, which is 1. See all questions in trigonometric functions of any angle. Cos ( 2 pi ) is equal to 1.
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## Cos2Pi/3 – What Is The Value Of Math Cos 2 Pi N Math Quora
Prove That Cos 3pi 2 X Cos 2pi X Cot 3pi 2 X Cot 2pi X 1 Mathematics Shaalaa Com. See all questions in trigonometric functions of any angle. So only 1st and 4th quadrant answers are relevant. The cosine calculator allows through the cos function to calculate online the cosine of an angle in radians, you must first select the desired unit by clicking on the options button calculation. Pi/3 radians = 60 degrees, and cos is looking for the side adjacent to the 60 degree angle. And using the #color(blue) exact value triangle#. How do you know if #sin 30 = sin 150#? Cos ( 2 pi ) is equal to 1. How do you show that #(costheta)(sectheta) = 1# if #theta=pi/4#? This site might help you. 2pi is 360 degrees, which means a complete circle and thus same endpoint is startpoint. Online calculation with the function cos according to the cos(2*pi/3). Thus cos(2pi) is equal to cos(0) in magnitude, which is 1. And we know $a = \frac{π}{3}$ so we replace and we see that this identity is true. In this video, we will learn to find the value of cos(2pi/3). Enter angle in degrees or radians since our angle is greater than π/2 and less than or equal to π radians, it is located in quadrant ii in the second quadrant, the values for sin are positive only.
Cos ( 2 pi ) is equal to 1. How do you show that #(costheta)(sectheta) = 1# if #theta=pi/4#? Pi/3 radians = 60 degrees, and cos is looking for the side adjacent to the 60 degree angle. Thus cos(2pi) is equal to cos(0) in magnitude, which is 1. And we know $a = \frac{π}{3}$ so we replace and we see that this identity is true. 2pi is 360 degrees, which means a complete circle and thus same endpoint is startpoint. Online calculation with the function cos according to the cos(2*pi/3).
## And using the #color(blue) exact value triangle#.
And we know $a = \frac{π}{3}$ so we replace and we see that this identity is true. 2pi is 360 degrees, which means a complete circle and thus same endpoint is startpoint. Online calculation with the function cos according to the cos(2*pi/3). So only 1st and 4th quadrant answers are relevant. Enter angle in degrees or radians since our angle is greater than π/2 and less than or equal to π radians, it is located in quadrant ii in the second quadrant, the values for sin are positive only. And we know $a = \frac{π}{3}$ so we replace and we see that this identity is true. How do you show that #(costheta)(sectheta) = 1# if #theta=pi/4#? Cos ( 2 pi ) is equal to 1. Pi/3 radians = 60 degrees, and cos is looking for the side adjacent to the 60 degree angle. The cosine calculator allows through the cos function to calculate online the cosine of an angle in radians, you must first select the desired unit by clicking on the options button calculation. How do you know if #sin 30 = sin 150#? See all questions in trigonometric functions of any angle. And using the #color(blue) exact value triangle#. Thus cos(2pi) is equal to cos(0) in magnitude, which is 1. In this video, we will learn to find the value of cos(2pi/3). This site might help you.
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# How to assign up-values for Derivative?
I have defined several custom analytic functions. Here is the simplest example:
ln[x_, a_?NumericQ] := Piecewise[{{Log[x], Re[a] > 0}, {-Log[1/x], True}}]
Now I would like to let Mathematica know how to carry out derivatives on this: I need to make D and Series work on ln as if it were Log:
ln /: D[ln[f_, g_], x_] := D[Log[f], x];
Works wonderfully:
But Series doesn't work because it is using Derivative instead of D.
So, now I try TagSetDelayed on Derivative:
But as you can see, it doesn't work because ln is too deep. What can I do to make Series work?
• I'm not exactly sure I understood your question (though I answered already)... If you're just worried why the Series didn't simplify with your definition for D, then it's because you didn't define ln for symbolic a. That's why I used a numeric a in my answer in the series. – Jens Sep 10 '14 at 21:19
You don't need to use TagSetDelayed for the definition of the derivative because Derivative doesn't have attribute Protected.
I'll extend add the derivative definition to arbitrary order n:
ClearAll[ln];
Derivative[n_, 0][ln][x_, a_] := Derivative[n][Log][x]
ln[x_, a_?NumericQ] :=
Piecewise[{{Log[x], Re[a] > 0}, {-Log[1/x], True}}]
ln[x, -1/2]
$-\log \left(\frac{1}{x}\right)$
D[ln[x, a], x]
$\frac{1}{x}$
D[ln[Cos[x] + x, a], x]
$$\frac{1-\sin (x)}{x+\cos (x)}$$
Series[ln[Cos[x] + x, 1/2], {x, 0, 2}]
$x-x^2+O\left(x^3\right)$
Series[ln[Cos[x] + x, a], {x, 0, 2}]
$\ln (1,a)+x-x^2+O\left(x^3\right)$
The symbolic argument a also gives a result now because the definitions for the derivatives work for symbolic a, as well. Only the zeroth-order term is not simplified because it only knows what that evaluates to when a is numeric.
• Very nice! What I'm really trying to do is to define a function that works as seamlessly as possible with Mathematica's analytic functions like Integrate Limit Series etc.. do you know of a simple way to do this? Should I ask it as a separate question? – QuantumDot Sep 11 '14 at 11:35
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Cody
# Problem 10. Determine whether a vector is monotonically increasing
Solution 926188
Submitted on 22 Jul 2016 by Md Sumon
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### Test Suite
Test Status Code Input and Output
1 Pass
x = [0 1 2 3 4]; assert(isequal(mono_increase(x),true));
2 Pass
x = [0]; assert(isequal(mono_increase(x),true));
3 Pass
x = [0 0 0 0 0]; assert(isequal(mono_increase(x),false));
4 Pass
x = [0 1 2 3 -4]; assert(isequal(mono_increase(x),false));
5 Pass
x = [-3 -4 2 3 4]; assert(isequal(mono_increase(x),false));
6 Pass
x = 1:.1:10; assert(isequal(mono_increase(x),true));
7 Pass
x = cumsum(rand(1,100)); x(5) = -1; assert(isequal(mono_increase(x),false));
8 Pass
x = cumsum(rand(1,50)); assert(isequal(mono_increase(x),true));
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# Generalized Characteristic Polynomial with Unimodular Roots
Let us define a diagonal matrix $\mathbf{D}(z) = diag(z^{m_1}, \dots, z^{m_N})$ with $z\in\mathbb{C}$ and positive integers $m_1, \dots, m_N$.
The generalized characteristic polynomial of a matrix $\mathbf{A}$ is then: $$p(z) = det(\mathbf{D}(z) - \mathbf{A})$$
For which $\mathbf{A}$ are all roots of $p$ unimodular for all $m_1, \dots, m_N \geq 1$?
Known sufficient condition: $\mathbf{A}$ unitary. But it is also known that unitarity is not necessary.
Also, is there a name for the generalized characteristic polynomial (in literature as it seems that this term is not used for $p(z)$) ?
Examples:
• $p(z)$ with $\mathbf{A}= [3,2;-4,3]$ and $m_1 = 3, m_2 = 1$ has non-unimodular roots.
• $p(z)$ with $\mathbf{A}= [-0.5,1;0.75,0.5]$, which is non-unitary, has for all $m_1$ and $m_2$ unimodular roots.
• You mean that every product of unitary and upper triangular with unitary diagonal will do? Do you know whether this is the maximum set of matrices with this property? Thanks for the reference, I'll have a look. – Sebastian Schlecht Jul 21 '15 at 11:43
• [You mean that every product of unitary and upper triangular with unitary diagonal will do?]--> I am not sure, this should be checked. Please, have a look at Iwasawa decomposition (for example Bourbaki Integration Ch VII paragraph 3 Example 7) – Duchamp Gérard H. E. Jul 21 '15 at 15:52
• What's the reference for the unitary results? – Igor Rivin Jul 21 '15 at 18:33
• @IgorRivin: The reference for the unitary case can be found in Circulant and Elliptic Feedback Delay Networks for Artificial Reverberation by Davide Rocchesso and Julius O. Smith. Formula (18) gives the proof. Unfortunately, later in the paper there is a more general proof which is faulty. – Sebastian Schlecht Jul 21 '15 at 21:42
• @DuchampGérardH.E.: I've read the Bourbaki reference, though I'm not sure where you draw the connection to the generalized characteristic polynomial. I've added two examples, how can we separate these cases with the reference? – Sebastian Schlecht Jul 21 '15 at 21:51
Note that $p(z)$ is invariant under the conjugation by diagonal matrices (the proof is the same as for the usual characteristic polynomial). Thus if a matrix $A$ has the requisite property, the same property holds for all its diagonal conjugates. In particular, assuming that all unitary matrices yield $p(z)$ with "unimodular" (i.e. absolute value 1) roots, the same would hold for their diagonal conjugates, which are diagonalizable matrices with "unimodular" eigenvalues, but not necessarily unitary. This explains the second example (where the eigenvalues are $\pm 1$ and the matrix is diagonally conjugate to an orthogonal reflection).
• Great (+1 !). Did anybody check the assumption [all unitary matrices yield p(z) with "unimodular" (i.e. absolute value 1) roots] ? – Duchamp Gérard H. E. Jul 22 '15 at 8:11
• I don't know, but in the case $N=2$, the unitary matrices admit a simple parametrization: $A=(\begin{smallmatrix}a & b\\ -\overline{b} & \overline{a}\end{smallmatrix})$, where $|a|^2+|b|^2=1$. So the claim amounts to the following: for any $m,n>0$ and complex $a$ with $|a|\leq 1$, the polynomial $p(z)=z^{m+n}-az^m-\overline{a}z^n+1$ has only "unimodular" roots. – Victor Protsak Jul 22 '15 at 8:39
• Great! Do you have any idea whether this covers all possible matrices? – Sebastian Schlecht Jul 22 '15 at 11:33
• No, it does not. For example, any upper triangular matrix with "unimodular" diagonal has your property, and these are almost never diagonally conjugate to unitary matrices. I'll try to give more details later. – Victor Protsak Jul 22 '15 at 15:31
• @DuchampGérardH.E.: I thought, it's enough to work with $\mathbf{D}^{-1}(z) \mathbf{A}$ being para-unitary and therefore $|| \mathbf{D}^{-1}(z) \mathbf{A} \mathbf{v} ||_2 = || \mathbf{v} ||_2$ for any vector $\mathbf{v}$ and |z| = 1. – Sebastian Schlecht Jul 23 '15 at 8:09
This is a partial answer but too long for a comment.
Let us first prove the property stated i.e. $$\mathbf{A} \mbox{ unitary }\Longrightarrow \mbox{ all roots of }p(z) \mbox{ are of modulus } 1$$ Firsly $|p(0)|=|det(-\mathbf{A})|=1$, so $p$ has not zero as a root.
Second, if $z\not=0$, one can write $$det(\mathbf{D}(z)-\mathbf{A}) =det(\mathbf{D}(z))det(I-\mathbf{D}(z)^{-1}\mathbf{A})$$ so $p(z)=0$ is equivalent to $1\in sp(\mathbf{D}(z)^{-1}\mathbf{A})$ and to the existence of $\mathbf{v}\not=0$ such that $$\mathbf{D}(z)^{-1}\mathbf{A}\mathbf{v}=\mathbf{v}$$ for such $\mathbf{v}$ one has $\mathbf{A}\mathbf{v}=\mathbf{D}(z)\mathbf{v}$ and, writing $z=\rho e^{it}$ one gets $\mathbf{A}\mathbf{v}=\mathbf{D}(\rho)\mathbf{D}(e^{it})\mathbf{v}\ .$ Now, $\mathbf{D}(e^{it})$ being unitary, one gets finally $$||\mathbf{v}||_2=||\mathbf{D}(e^{-it})\mathbf{A}\mathbf{v}||_2=||\mathbf{D}(\rho)\mathbf{v}||_2\qquad \mbox{(*).}$$ As it is easy to check that for all $\mathbf{v}$ and $\rho>0$, $$||\mathbf{D}(\rho)\mathbf{v}||_2\geq \rho ||\mathbf{v}||_2 \mbox{ if } \rho>1\ ;\ ||\mathbf{D}(\rho)\mathbf{v}||_2\leq \rho ||\mathbf{v}||_2 \mbox{ if } \rho<1\ ,$$ the result follows from (*).
For $\alpha=(m_1,\cdots ,m_N)\in (\mathbb{N}_{\geq 1})^N$, let $$\mathbf{D}(\alpha,z)=diag(z^{m_1}, \dots, z^{m_N})$$ for $z$ fixed, one has $$\mathbf{D}(\alpha,z)\mathbf{D}(\beta,z)=\mathbf{D}(\alpha+\beta,z)$$ these matrices form a semigroup.
For $\alpha$ fixed
$$\mathbf{D}(\alpha,z_1)\mathbf{D}(\alpha,z_2)=\mathbf{D}(\alpha,z_1z_2)$$ for $z\not=0$ these matrices form a group. The set of all these matrices is normalised by the monomial matrices, i.e. the semi-direct product of the (Weyl) group of permutation matrices and of diagonal matrices as, if $W=W(\sigma)$ is a permutation matrix and if $D$ is a diagonal (regular) matrix, one has $$WD\mathbf{D}(\alpha,z)D^{-1}W^{-1}=\mathbf{D}(\alpha_\sigma,z)$$
As was remarked by Victor, matrices such as unitary (see above) and upper (or lower) triangular with unitary diagonal possess the property.
Their conjugates through the monomial group possess also the property.
How to test (algorithmically) that a matrix is conjugated of a unitary matrix through the monomial group ?
Firstly, as was remarked as the permutation matrices and as the diagonal ones with unitary spectrum are unitary, to be such is equivalent of being conjugated of a unitary matrix through the diagonal group of matrices with strictly positive eigenvalues i.e. for a matrix $B$ test whether it exists a unitary matrix and $R=diag(r_1,\cdots ,r_N)$ such that $$B=R^{-1}AR$$ (one can even restrict to the special group of them, but we will not use this)
(analysis) suppose it were the case, then $B^*R^2B=R^2$
(synthesis)
1. find all the diagonal matrices $D$ which fulfil $B^*DB=D$ (it is a linear system with $N$ variables, i.e. diagonal eigenvectors for the eigenvalue $1$ of the linear transformation $D\rightarrow B^*DB$).
2. among them select, if possible, a $D$ with strictly positive spectrum and set $R=\sqrt{D}$ then $A=R^{-1}AR$ is unitary.
Remark It can happen that the transformation $D\rightarrow B^*DB$ admit diagonal eigenvectors for the eigenvalue $1$ none of which is strictly positive. As the procedure provides a necessary and sufficient condition, the corresponding matrix is not diagonally conjugate to a unitary matrix.
(Counter)-example Set $$B= \begin{pmatrix} \sqrt{2} & 1\cr 1 & \sqrt{2} \end{pmatrix}$$ then, solving $$B^*\begin{pmatrix} x & 0\cr 0 & y \end{pmatrix} B = \begin{pmatrix} x & 0\cr 0 & y \end{pmatrix}$$ yields $x=-y$ so there are eigenvectors as $$\begin{pmatrix} 1 & 0\cr 0 & -1 \end{pmatrix}$$ but none of them is strictly positive.
• Right! Note, however, that permutation matrices are unitary, so you don't get anything new in that case. For the triangular subgroup, after conjugating with a permutation matrix, you get the corresponding subgroup triangular with respect to the permuted basis. – Victor Protsak Jul 28 '15 at 5:01
• Yes, of course. But in the triangular case, you gain a bit more in spite of the geometrical equivalence. However, I still do not see how to combine these results in order to get the most general answer. – Duchamp Gérard H. E. Jul 28 '15 at 8:19
• @VictorProtsak ... in the same vein, you do not gain anything when conjugating unitary matrices by all regular diagonal matrices, the group of those with strictly positive spectrum and determinant one suffices ... – Duchamp Gérard H. E. Jul 28 '15 at 15:31
• @DuchampGérardH.E.: The synthesis part could be replaced by the eigenvalue decomposition $B = T \Lambda T^{-1}$ $\rightarrow$ $B^* T^{-1*} T^{-1} B = T^{-1*} T^{-1}$. So, $B$ is a diagonally conjugated unitary, if $T^{-1*} T^{-1}$ is diagonal with positive spectrum. Does this help? – Sebastian Schlecht Jul 29 '15 at 10:52
• @SebastianSchlecht Yes, it might help. The problem is that, in general, you have several $T$, so one must study the stabilizer (I must think of it). In any case $\Lambda$ must be unitary (even if $T$ is not diagonal). – Duchamp Gérard H. E. Jul 29 '15 at 12:01
Also this is not an answer, but maybe a different path to tackle the problem.
The polynomial $p(z)=det(\mathbf{D}(z)−\mathbf{A})$ can be given explicitly as $$p(z) = \sum_{k = 0}^{M} z^k \sum_{I \in I_k} (-1)^{M-k} \det(\mathbf{A}_{I})$$ where $M = \sum_{k=0}^{N} m_k$ and $I_k = \{ I \subset \left\{ 1, \dots, N \} \middle| \sum_{i \in I} m_i = k \right\}$ is the set of index sets which sum up to $k$, $A_I$ is the sub-matrix of $A$ with the columns and rows with index $I$ deleted.
Theorem by Cohn, A. (1922). "Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise.": A polynomial p(z) has all its zeros on the unit circle if and only if it is self-inversive and its derivative p′(z) has all its zeros in the closed unit disk $|z| < 1.$
A polynomial $p(z)$ of degree $d$ is self-inversive if $p(z) = \epsilon z^d p(1/z)$ with $|\epsilon| = 1$.
As the original question requires it to be true for all $m_1, \dots, m_N$, there are also $m_1, \dots, m_N$ such that $|I_k| \leq 1$, consequently because of the necessary self-inversion: $$\det(\mathbf{A}_{I}) = \epsilon \det(\mathbf{A}_{\overline{I}}) \quad \textrm{for all } I \subset \{ 1, \dots, N \}$$ where $\overline{I}$ is the complement of $I$.
I don't know whether the condition on the derivation helps, but I believe that it might be possible to use the self-inversion to exclude some matrices in the original question.
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# diagonal
## Definitions
### Construction
• A straight structural member forming the hypotenuse of a right triangle, as in the diagonal bracing of a stud wall.
### Economics
• In a matrix, the elements on a straight line from the top left to the bottom right, or occasionally from the bottom left to the top right.
• In an Edgeworth box, the straight line from the bottom left corner to the top right. Along the diagonal, the ratios of allocations of the two agents (industries or consumers) are constant and equal.
• In an integrated world economy diagram, the straight line from the bottom left corner to the top right. Along the diagonal, the ratios of factor endowments of the two coutries are constant and equal.
## Origin & History of “diagonal”
Diagonal is commonly used simply as a synonym for oblique, but in strict mathematical terms it denotes a line joining two non-adjacent angles of a polygon. this reveals far more clearly its origins. It comes from diagōnālis, a Latin adjective derived from Greek diagṓnios. This was a compound formed from the prefix dia- ‘across’ and gōníā ‘angle’ (as in English polygon), meaning ‘from angle to angle’. Gōníā is related ultimately to English knee and genuine.
http://www.dictionarycentral.com/definition/diagonal.html
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# A passenger standing in a bus is thrown outward when the bus takes a sudden turn. This happens due to
A passenger standing in a bus is thrown outward when the bus takes a sudden turn. This happens due to
(1) Outward pull on him
(2) Inertia of motion
(3) Change in momentum
(4) Change in acceleration
Answer: (2) This is the inertia of direction. It is the ability of the body to be in a state of the direction of motion .for example sun holds planets in a fixed elliptical path .this is one of the examples of inertia of direction. The inertia of direction is non-existent however inertia only applies to a body at rest or moving with a constant velocity. It is the property possessed by a body to resist change. In another way, we can say that if a body moves in a particular direction under the action of a force and if the force is removed then the will continue to move in the same direction unless stopped under the action of another opposing force for a body at rest it under the inertia of rest whereas inertia of motion is for bodies in motion.
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https://www.bitsdiscover.com/calculate-the-execution-time-of-a-java-progam/
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# Calculate the Execution Time of a Java Progam
When we write an algorithm in any language, we must check the execution time of that algorithm. A bad code might eat a ginormous amount of resources that will result in slow execution of the program. There might be several ways to find the running time of an algorithm, but the simplest way is to get the start time (at the start of the program) and end time (at the end of the program) and then calculate the difference between end time and start time.
In Java program, use currentTimeMillis() at the start and end of the code to get the start and end time in milli seconds. Here is the sample Java code to find the Fibonacci series and I have used currentTimeMillis() to calculate the running time of the program.
``````
public class FibonacciCalculator{
public long fibonacci(long num){
if((num == 0) || (num == 1)){
return num;
}else{
return fibonacci(num-1) + fibonacci(num-2);
}
}
public void displayFibonacci(){
for(int i=0; i<=45; i++){
System.out.println("Fibo " + i + "= " + fibonacci(i));
}
}
}
import java.util.concurrent.TimeUnit;
public class FibonacciTest{
public static void main(String[] args){
long startMS = System.currentTimeMillis();
long startS = TimeUnit.MILLISECONDS.toSeconds(startMS); // convert to seconds
FibonacciCalculator fib = new FibonacciCalculator();
fib.displayFibonacci();
long endMS = System.currentTimeMillis();
long endS = TimeUnit.MILLISECONDS.toSeconds(endMS);
long diff = endS - startS;
System.out.println("Total Execution time: " + diff + "seconds");
}
}``````
The output of the code is as follows…
Fibo 0= 0
Fibo 1= 1
Fibo 2= 1
Fibo 3= 2
Fibo 4= 3
Fibo 5= 5
Fibo 6= 8
Fibo 7= 13
Fibo 8= 21
Fibo 9= 34
Fibo 10= 55
Fibo 11= 89
Fibo 12= 144
Fibo 13= 233
Fibo 14= 377
Fibo 15= 610
Fibo 16= 987
Fibo 17= 1597
Fibo 18= 2584
Fibo 19= 4181
Fibo 20= 6765
Fibo 21= 10946
Fibo 22= 17711
Fibo 23= 28657
Fibo 24= 46368
Fibo 25= 75025
Fibo 26= 121393
Fibo 27= 196418
Fibo 28= 317811
Fibo 29= 514229
Fibo 30= 832040
Fibo 31= 1346269
Fibo 32= 2178309
Fibo 33= 3524578
Fibo 34= 5702887
Fibo 35= 9227465
Fibo 36= 14930352
Fibo 37= 24157817
Fibo 38= 39088169
Fibo 39= 63245986
Fibo 40= 102334155
Fibo 41= 165580141
Fibo 42= 267914296
Fibo 43= 433494437
Fibo 44= 701408733
Fibo 45= 1134903170
Total Execution time: 15seconds
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https://www.studypool.com/discuss/1254299/Math-help-needed-with-slopes-and-y-intercepts?free
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##### Math help needed with slopes and y-intercepts
Mathematics Tutor: None Selected Time limit: 1 Day
what do you do when you are trying to find slopes and intercepts to solve equations? if I ask what is the slope and y- intercept of y=5/3 x +4 what would the answer be? Solve problem
Nov 5th, 2015
We have the equation as
y=(5x)/3 +4
It is the equation of the line in slope intercept form,y=mx+b
where m is the slope of the line and b is the y-intercept.
So on comparing the slope is m=5/3 and the y-intercept is b= 4.
---Thanks----
Nov 5th, 2015
...
Nov 5th, 2015
...
Nov 5th, 2015
May 30th, 2017
check_circle
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https://dreamworkandtravel.com/sky-diving/a-falling-skydiver-has-a-mass-of-110-kg/
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No Widgets found in the Sidebar
# A falling skydiver has a mass of 110 kg
#### Bydreamtravel
Nov 26, 2022
## A Falling Skydiver: Exploring the Physics of Freefall
### Introduction
Skydiving, an adrenaline-pumping adventure, involves jumping from an aircraft and experiencing the thrill of freefall. As the skydiver plummets towards the ground, their body undergoes significant physical changes due to the force of gravity. This article delves into the physics behind a falling skydiver, examining the forces involved and the intricate interplay that governs their descent.
## The Force of Gravity: The Driving Force
Gravity is the fundamental force that governs the motion of the skydiver. It acts directly downwards, pulling the skydiver towards the Earth’s center. The force of gravity is directly proportional to the skydiver’s mass, meaning the greater their mass, the stronger the gravitational pull.
### Air Resistance: The Counterforce
As the skydiver falls, they encounter air resistance. Air resistance arises due to the interaction between the skydiver’s body and the surrounding air molecules. It acts in the opposite direction of the skydiver’s motion, effectively slowing down their descent.
### Terminal Velocity: Achieving Equilibrium
When the force of gravity and air resistance become equal and opposite, the skydiver reaches a constant speed known as terminal velocity. At terminal velocity, the skydiver remains in a state of dynamic equilibrium, where the gravitational pull is exactly counterbalanced by air resistance.
### Factors Influencing Terminal Velocity
The terminal velocity of a skydiver depends on several factors:
– Mass: Higher mass means stronger gravitational pull, leading to higher terminal velocity.
– Surface Area: A larger surface area experiences greater air resistance, reducing terminal velocity.
– Body Position: A streamlined position minimizes air resistance, increasing terminal velocity, while a spread-out position increases resistance, decreasing it.
## Physiological Effects of Freefall
As the skydiver descends, various physiological changes occur:
– Increased Heart Rate: Gravity causes blood to rush to the lower body, leading to an increased heart rate.
– Blood Pressure Fluctuations: Changes in body position affect blood pressure, resulting in potential dizziness or fainting.
– Changes in Breathing: The increased air pressure in the lungs can cause shortness of breath or difficulty breathing.
## Safety Considerations
Skydiving is a highly regulated activity with strict safety protocols in place. These include:
– Parachute Training: Skydivers must undergo rigorous training to master parachute deployment techniques.
– Altitude Restrictions: Controlled altitudes ensure there is sufficient time for parachute deployment.
– Weather Monitoring: Favorable weather conditions are essential to minimize risks.
## Conclusion
A falling skydiver provides a fascinating example of physics in action. Gravity drives the descent, while air resistance acts as the opposing force. The interplay between these forces determines the skydiver’s terminal velocity. Understanding these principles is crucial for both the safety and enjoyment of this thrilling adventure sport.
Read Post How to get skydiving license malaysia
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# physics
posted by .
An airplane flies 200 km due west from city A to city B and then 340 km in the direction of 35.0° north of west from city B to city C.
(a) In straight-line distance, how far is city C from city A?
(b) Relative to city A, in what direction is city C?
° north of west
• physics-repost -
In case you did not see the response:
physics - bobpursley, Tuesday, September 21, 2010 at 6:45pm
Break up the vectors into N, W components, and add, then use the results to reform the vector.
• physics -
\frac{1}{2}
## Similar Questions
1. ### physics
An airplane flies 200 km due west from city A to city B and then 260 km in the direction of 32.0° north of west from city B to city C. (a) In straight-line distance, how far is city C from city A?
2. ### physics
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3. ### physics
an airplane flies 200 km due west from city A and then 350 km in the direction of 32.0 degrees north of west from city B to city C. a) in a straight-line distance, how far is city c from city a?
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an airplane flies 200 km due west from city A and then 350 km in the direction of 32.0 degrees north of west from city B to city C. a) in a straight-line distance, how far is city c from city a?
5. ### College Physics
An airplane flies 200 km due west from city A to city B and then 240 km in the direction of 31.0° north of west from city B to city C. (a) In straight-line distance, how far is city C from city A?
6. ### Physics
An airplane flies 200 km due west from city A to City B and them 300 km in the direction of 30.0 degrees north of west from city B to city C. In straight-line distance, how far is city C from city A?
7. ### physics
An airplane flies 200 km due west from city A to city B and then 305 km in the direction of 30.0° north of west from city B to city C. (a) In straight-line distance, how far is city C from city A?
8. ### physics
An airplane flies 200 km due west from city A to city B and then 245 km in the direction of 36.0° north of west from city B to city C. (a) In straight-line distance, how far is city C from city A?
9. ### physics
An airplane flies 200 km due west from city A to city B and then 245 km in the direction of 31.5° north of west from city B to city C. (a) In straight-line distance, how far is city C from city A?
10. ### physics
An airplane flies 200 km due west from city A to city B and then 270 km in the direction of 31.0° north of west from city B to city C. (a) In straight-line distance, how far is city C from city A?
More Similar Questions
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Home / Volume Conversion / Convert Megaliter to Gigaliter
# Convert Megaliter to Gigaliter
Please provide values below to convert megaliter [ML] to gigaliter [GL], or vice versa.
From: megaliter To: gigaliter
### Megaliter to Gigaliter Conversion Table
Megaliter [ML]Gigaliter [GL]
0.01 ML1.0E-5 GL
0.1 ML0.0001 GL
1 ML0.001 GL
2 ML0.002 GL
3 ML0.003 GL
5 ML0.005 GL
10 ML0.01 GL
20 ML0.02 GL
50 ML0.05 GL
100 ML0.1 GL
1000 ML1 GL
### How to Convert Megaliter to Gigaliter
1 ML = 0.001 GL
1 GL = 1000 ML
Example: convert 15 ML to GL:
15 ML = 15 × 0.001 GL = 0.015 GL
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# Download Today, Ch. 26 • The Electric Force • Coulomb`s Law • Insulators
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Transcript
```PHY132H1F
Introduction to Physics II
Lecture 9, October 7, 2009
Today, Ch. 26
• The Electric Force
• Coulomb’s Law
• Insulators, Conductors
• Charge Polarization
• The Electric Field
In-Class Question 1. Please write on the
same piece of paper as today’s mini-homework.
What is the SI unit of charge?
A. Coulomb
C. Ampere
D. Ohm
E. Volt
In SI units K = 8.99 × 109 N m2/C2.
In-class question 2.
Charges A and B exert repulsive forces on
each other. qA = 4qB. Which statement is
true?
A. FA on B > FB on A
B. FA on B < FB on A
C. FA on B = FB on A
1
Atoms and Electricity
• An atom consists of a very small and dense nucleus
surrounded by much less massive orbiting electrons.
• The nucleus is a composite structure consisting of
protons, positively charged particles, and neutral neutrons.
• A macroscopic object has net charge
• The atom is held together by the attractive electric force
between the positive nucleus and the negative electrons.
• Electrons and protons have charges of opposite sign but
exactly equal magnitude.
where Np and Ne are the number of protons and electrons
contained in the object.
• This atomic-level unit of charge, called the fundamental
unit of charge, is represented by the symbol e.
• The process of removing an electron from the electron
cloud of an atom is called ionization.
• An atom that is missing an electron is called a positive
ion. Its net charge is q = +e.
Insulators
• The electrons in the insulator
are all tightly bound to the
positive nuclei and not free to
move around.
• Charging an insulator by
friction leaves patches of
molecular ions on the surface,
but these patches are immobile.
Conductors
• In metals, the outer atomic
electrons are only weakly
bound to the nuclei.
• These outer electrons become
detached from their parent
nuclei and are free to wander
about through the entire solid.
• The solid as a whole remains
electrically neutral, but the
electrons are now like a
negatively charged liquid
permeating an array of
positively charged ion cores.
2
Getting zapped!
The Electric Field
We begin our investigation of electric fields by postulating
a field model that describes how charges interact:
1. Some charges, which we will call the source charges,
alter the space around them by creating an electric field.
2. A separate charge in the electric field experiences a
force exerted by the field.
Suppose probe charge q experiences an electric force Fon q
due to other charges.
Charge Polarization
The Electric Field of a Point
Charge
The electric field at distance r from a point charge q is
where the unit vector for r points away from the charge to
the point at which we want to know the field.
This unit vector expresses the idea “away from q”.
The units of the electric field are N/C. The magnitude E of
the electric field is called the electric field strength.
3
```
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# Properties of cubes of natural numbers
can anyone please give me whole list of properties of cubes of natural numbers Media URL: http://youtu.be/J_8xZmMqCRA
Description:
07:46 Thu 12th Apr 2012
1 to 9 of 9
http://youtu.be/J_8xZmMqCRA I'm reposting the link so we can look at it 07:46 Thu 12th Apr 2012 Your link lists quite a few for starters: (i) Cubes of all even natural numbers are even. (ii) Cubes of all odd natural numbers are odd. (iii) Cubes of numbers ending in digits 1, 4, 5, and 9 are the numbers ending in the same digit. (iii) Cubes of numbers ending in digits 2 ends in digit 8. (iv) Cubes of numbers ending in digits 8 ends in digit 2. (v) Cubes of numbers ending in digits 3 ends in digit 7. (vi) Cubes of numbers ending in digits 7 ends in digit 3. 07:50 Thu 12th Apr 2012 I had two number 3s in my list- there are 7 properties listed here. I'm sure a google search will throw up a longer list 07:51 Thu 12th Apr 2012 Cubes of numbers ending in 6 also end in 6. 07:54 Thu 12th Apr 2012 And of course that old favourite: for any integer n greater than or equal to 2, n³ can be represented as the sum of consecutive (positive) odd integers. 08:02 Thu 12th Apr 2012 cubes of all numbers ending in a zero will also end in a zero 08:03 Thu 12th Apr 2012 How old is your son and what level is he studying at? Maybe he is just expected to explore for himself by identifying some cube numbers and looking for patterns and properties. Here's an example. 1³ = 1 2³ = 8 = 3+5 3³ = 27 = 7+9+11 4³ = 64 = 13+15+17+19 5³ = 125 = 21+23+25+27+29 6³ = 216 = 31+33+35+37+39+41 13:34 Thu 12th Apr 2012 I must stop talking to myself online 07:06 Fri 13th Apr 2012 Well, I enjoyed working on this query but it'd be interesting to know whether our answers helped kpinky's son 18:45 Sun 15th Apr 2012
1 to 9 of 9
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## Properties of cubes of natural numbers
can anyone please give me whole list of properties of cubes of natural numbers http://youtu.be/J_8xZmMqCRA my child has got assignment for his academic year. can anyone please provide him a list of...
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# Tax System and Tax Policy: Taxation of High Incomes
Economic Issues 2D03
Tax System and Tax Policy: Taxation of High Incomes (A5)
macID:
Student number:
• Background:
In this section, draw on Statistics Canada’s public tables to cover the following:
Who are the top 1%?
• Top income cut-off, average income, share of income from labour & how much tax they pay
• Sex and age
• Province/Location
Compared to the bottom 50th percentile of tax filers, how has the income share and effective tax rate of the top 1% evolved over the data period?
By province, how has the income share and effective tax rate of the province-specific top 1% evolved over time?
• Policy evaluation.
Consider the following proposal to increase the top marginal tax rate on the top (province-specific) 1%:
Base Tax System, 2020 Fictitious System, +5 Top MTR threshold (\$) MTR (%) Top 1% MTR threshold (\$) MTR (%) NFLD 189,604 18.3 210,200 23.3 PEI 63,969 16.7 172,400 21.7 NS 150,000 21 191,900 26 NB 160,776 20.3 175,000 25.3 ON 220,000 13.16 260,600 18.16 MB 72,164 17.4 202,600 22.4 SK 129,214 14.5 209,800 19.5 AB 314,928 15 297,900 20 BC 157,747 16.8 244,800 21.8 Federal 214,368 33 244,800 33
Cover the following issues (by province) with this proposal (Assume a constant ETI of 0.664):
• What is the net revenue effect (by province) of this proposal? Comment on any noticeable provincial differences.
• How much of the mechanical revenue gain disappears because of a behavioural effect?
• What are the revenue and mechanical effects per tax filer?
• Why is the elasticity of taxable income important?
• What might explain these differences
• Think about skewness & revenue gain share of the mechanical effect
• What is the marginal cost of public funds?
• Explain and calculate the optimal province-specific top 1% marginal tax rate. How far off is it from the fictitious +5 marginal tax rate?
• Assuming no income shifting, what is the size of the vertical fiscal externality?
• What are the progressivity implications of this proposal?
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Question Video: Using Exact Trigonometric Values to Solve an Equation | Nagwa Question Video: Using Exact Trigonometric Values to Solve an Equation | Nagwa
# Question Video: Using Exact Trigonometric Values to Solve an Equation Mathematics • Third Year of Preparatory School
## Join Nagwa Classes
If cos ๐ฅ = 1/2, find the value of ๐ฅ, where 0 < ๐ฅ < 90ยฐ.
02:08
### Video Transcript
If cos ๐ฅ equals one-half, find the value of ๐ฅ, where ๐ฅ is greater than zero and less than 90 degrees.
Weโve been given information about the trigonometric ratio for cos of ๐ฅ. And we might recall that the cosine ratio tells us that, for a right triangle with angle ๐, the cos of ๐ is equal to the adjacent divided by the length of the hypotenuse. So, we need to find a right triangle such that the adjacent divided by the hypotenuse is equal to one-half. Now, in fact, the triangle that we used to generate this is an equilateral triangle of side length two units. The perpendicular bisector of one of the sides of this triangle will pass through the opposite vertex. So, we add the perpendicular bisector, creating a pair of congruent triangles of base length one unit.
So, what else do we know about this triangle? Well, we know the interior angles in an equilateral triangle are each 60 degrees. So, the angle at the vertex between the one-unit side and the two-unit side is 60 degrees. Then, since we bisected the angle at the other vertex, we have a 30-degree angle here. Since one-half is one divided by two, we need to find the angle ๐ฅ such that the adjacent side to this angle is the one-unit side and the hypotenuse is the two-unit side.
We might notice that the one-unit side is in fact adjacent to the angle of 60 degrees, whilst the hypotenuse lies directly opposite the right angle, so itโs the two-unit length. We can therefore say that cos of 60 must be equal to one-half. Therefore, ๐ฅ must be equal to 60 degrees. Now, whilst we derive this using the equilateral triangle of side length two units, this isnโt entirely necessary. In fact, we should learn that cos of 60 is equal to one-half, alongside the exact values for cos of zero, cos of 30, cos of 45, and cos of 90 degrees.
Using either method, we find that the value of ๐ฅ such that cos of ๐ฅ is equal to one-half and ๐ฅ is in the open interval from zero to 90 degrees is 60.
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An online community for showcasing R & Python tutorials. It operates as a networking platform for data scientists to promote their talent and get hired. Our mission is to empower data scientists by bridging the gap between talent and opportunity.
Basic Statistics
Cubic and Smoothing Splines in R
Splines are a smooth and flexible way of fitting Non linear Models and learning the Non linear interactions from the data.In most of the methods in which we fit Non linear Models to data and learn Non linearities is by transforming the data or the variables by applying a Non linear transformation.
Cubic Splines
Cubic Splines with knots(cutpoints) at $$\xi_K , \ K = 1,\ 2…\ k$$ is a piece-wise cubic polynomial with continious derivatives upto order 2 at each knot. They have continuous 1st and 2nd derivative. The order of continuity is = $$(d – 1)$$ , where $$d$$ is the degree of polynomial. Now we can represent the Model with truncated power Basis function $$b(x)$$. What happens is that we transform the variables $$X_i$$ by applying a Basis function $$b(x)$$ and fit a model using these transformed variables which adds non linearities to the model and enables the splines to fit smoother and flexible Non linear functions.
The Regression Equation Becomes —
$$f(x) = y_i = \alpha + \beta_1.b_1(x_i)\ + \beta_2.b_2(x_i)\ + \ …. \beta_{k+3}.b_{k+3}(x_i) \ + \epsilon_i$$
#loading the Splines Packages
require(splines)
#ISLR contains the Dataset
require(ISLR)
attach(Wage) #attaching Wage dataset
?Wage #for more details on the dataset
agelims<-range(age)
#Generating Test Data
age.grid<-seq(from=agelims[1], to = agelims[2])
Now let’s fit a Cubic Spline with 3 Knots (cutpoints)
The idea here is to transform the variables and add a linear combination of the variables using the Basis power function to the regression function f(x).The $$bs()$$ function is used in R to fit a Cubic Spline.
#3 cutpoints at ages 25 ,50 ,60
fit<-lm(wage ~ bs(age,knots = c(25,40,60)),data = Wage )
summary(fit)
##
## Call:
## lm(formula = wage ~ bs(age, knots = c(25, 40, 60)), data = Wage)
##
## Residuals:
## Min 1Q Median 3Q Max
## -98.832 -24.537 -5.049 15.209 203.207
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 60.494 9.460 6.394 1.86e-10 ***
## bs(age, knots = c(25, 40, 60))1 3.980 12.538 0.317 0.750899
## bs(age, knots = c(25, 40, 60))2 44.631 9.626 4.636 3.70e-06 ***
## bs(age, knots = c(25, 40, 60))3 62.839 10.755 5.843 5.69e-09 ***
## bs(age, knots = c(25, 40, 60))4 55.991 10.706 5.230 1.81e-07 ***
## bs(age, knots = c(25, 40, 60))5 50.688 14.402 3.520 0.000439 ***
## bs(age, knots = c(25, 40, 60))6 16.606 19.126 0.868 0.385338
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 39.92 on 2993 degrees of freedom
## Multiple R-squared: 0.08642, Adjusted R-squared: 0.08459
## F-statistic: 47.19 on 6 and 2993 DF, p-value: < 2.2e-16
Now plotting the Regression Line
#Plotting the Regression Line to the scatterplot
plot(age,wage,col="grey",xlab="Age",ylab="Wages")
points(age.grid,predict(fit,newdata = list(age=age.grid)),col="darkgreen",lwd=2,type="l")
abline(v=c(25,40,60),lty=2,col="darkgreen")
Gives this plot:
The Dashed Lines are the Cutpoints or the Knots. The above Plot shows the smoothing and local effect of Cubic Splines.
Smoothing Splines
These are mathematically more challenging but they are more smoother and flexible as well. But, it does not require the selection of the number of Knots, but require selection of only a Roughness Penalty which accounts for the wiggliness(fluctuations) and controls the roughness of the function and variance of the Model. Another important thing to remember in Smoothing Splines are that they have a Knot for every unique value of $$(x_i)$$.Our aim in Smoothing Splines is to minimize the Error function which is modified by adding a Roughness Penalty which penalizes it for Roughness(Wiggliness) and high variance.
$$minimize:{ g \in RSS} :\ \sum\limits_{i=1}^n ( \ y_i \ – \ g(x_i) \ )^2 + \lambda \ \int g”(t)^2 dt , \quad \lambda > 0$$ .
$$\lambda \ is \ the \ Tuning \ Parameter$$
#fitting smoothing splines using smooth.spline(X,Y,df=...)
fit1<-smooth.spline(age,wage,df=16) #16 degrees of freedom
#Plotting both cubic and Smoothing Splines
plot(age,wage,col="grey",xlab="Age",ylab="Wages")
points(age.grid,predict(fit,newdata = list(age=age.grid)),col="darkgreen",lwd=2,type="l")
abline(v=c(25,40,60),lty=2,col="darkgreen")
lines(fit1,col="red",lwd=2)
legend("topright",c("Smoothing Spline with 16 df","Cubic Spline"),col=c("red","darkgreen"),lwd=2)
Gives this plot:
Now as we can notice that the Red line i.e Smoothing Spline is more wiggly and fits data more flexibly.This is probably due to high degrees of freedom. The best way to select the value of $$\lambda$$ and df is Cross Validation . Now we have a direct method to implement cross validation in R using smooth.spline().
Implementing Cross Validation to select value of λ and Implement Smoothing Splines:
fit2<-smooth.spline(age,wage,cv = TRUE)
fit2
## Call:
## smooth.spline(x = age, y = wage, cv = TRUE)
##
## Smoothing Parameter spar= 0.6988943 lambda= 0.02792303 (12 iterations)
## Equivalent Degrees of Freedom (Df): 6.794596
## Penalized Criterion: 75215.9
## PRESS: 1593.383
#It selects $\lambda=0.0279$ and df = 6.794596 as it is a Heuristic and can take various values for how rough the #function is
plot(age,wage,col="grey")
#Plotting Regression Line
lines(fit2,lwd=2,col="purple")
legend("topright",("Smoothing Splines with 6.78 df selected by CV"),col="purple",lwd=2)
Gives this plot:
This Model is also very Smooth and Fits the data well.
Conclusion
Hence this was a simple overview of Cubic and Smoothing Splines and how they transform variables and add Non linearities to the Model and are more flexible and smoother than other techniques. It is better in terms of extrapolation and is more smoother.Other techniques such as Polynomial regression is very bad at extrapolation and oscillates a lot once it gets out of boundaries and it becomes very wiggly and fluctuating which shows the signs of High Variance and mostly Overfits at larger values of degree of polynomials. The main thing to remember while fitting Non linear Models to the data is that we need to do some transformations to data or the variables in order to make the model more flexible and stronger in learning Non linear Interactions between the Inputs $$X_i$$ and Output $$Y$$ variables.
Hope you guys liked the article and make sure to like and share it. Cheers!
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# Time dependent coefficients in R - how to do it?
Update: Sorry for another update but I've found some possible solutions with fractional polynomials and the competing risk-package that I need some help with.
## The problem
I can't find an easy way to do a time dependent coefficient analysis is in R. I want to be able to take my variables coefficient and do it into a time dependent coefficient (not variable) and then plot the variation against time:
$\beta_{my\_variable}=\beta_0+\beta_1*t+\beta_2*t^2...$
## Possible solutions
### 1) Splitting the dataset
I've looked at this example (Se part 2 of the lab session) but the creation of a separate dataset seems complicated, computationally costly and not very intuitive...
### 2) Reduced Rank models - The coxvc package
The coxvc package provides an elegant way of dealing with the problem - here's a manual. The problem is that the author is no longer developing the package (last version is since 05/23/2007), after some e-mail conversation I've gotten the package to work but one run took 5 hours on my dataset (140 000 entries) and gives extreme estimates at the end of the period. You can find a slightly updated package here - I've mostly just updated the plot function.
It might be just a question of tweaking but since the software doesn't easily provide confidence intervals and the process is so time consuming I'm looking right now at other solutions.
### 3) The timereg package
The impressive timereg package also addresses the problem but I'm not certain of how to use it and it doesn't give me a smooth plot.
### 4) Fractional Polynomial Time (FPT) model
I found Anika Buchholz' excellent dissertation on "Assessment of time–varying long–term effects of therapies and prognostic factors" that does an excellent job covering different models. She concludes that Sauerbrei et al's proposed FPT seems to be the most appropriate for time-dependent coefficients:
FPT is very good at detecting time-varying effects, while the Reduced Rank approach results in far too complex models, as it does not include selection of time-varying effects.
The research seems very complete but it's slightly out of reach for me. I'm also a little wondering since she happens to work with Sauerbrei. It seems sound though and I guess the analysis could be done with the mfp package but I'm not sure how.
### 5) The cmprsk package
I've been thinking of doing my competing risk analysis but the calculations have been to time-consuming so I switched to the regular cox regression. The crr has thoug an option for time dependent covariates:
....
cov2 matrix of covariates that will be multiplied
by functions of time; if used, often these
covariates would also appear in cov1 to give
a prop hazards effect plus a time interaction
....
There is the quadratic example but I'm don't quite follow where the time actually appears and I'm not sure of how to display it. I've also looked at the test.R file but the example there is basically the same...
## My example code
Here's an example that I use to test the different possibilities
library("survival")
library("timereg")
data(sTRACE)
# Basic cox regression
surv <- with(sTRACE, Surv(time/365,status==9))
fit1 <- coxph(surv~age+sex+diabetes+chf+vf, data=sTRACE)
check <- cox.zph(fit1)
print(check)
plot(check, resid=F)
# vf seems to be the most time varying
######################################
# Do the analysis with the code from #
# the example that I've found #
######################################
# Split the dataset according to the splitSurv() from prof. Wesley O. Johnson
# http://anson.ucdavis.edu/~johnson/st222/lab8/splitSurv.ssc
new_split_dataset = splitSuv(sTRACE$time/365, sTRACE$status==9, sTRACE[, grep("(age|sex|diabetes|chf|vf)", names(sTRACE))])
surv2 <- with(new_split_dataset, Surv(start, stop, event))
fit2 <- coxph(surv2~age+sex+diabetes+chf+I(pspline(stop)*vf), data=new_split_dataset)
print(fit2)
######################################
# Do the analysis by just straifying #
######################################
fit3 <- coxph(surv~age+sex+diabetes+chf+strata(vf), data=sTRACE)
print(fit3)
# High computational cost!
# The price for 259 events
sum((sTRACE$status==9)*1) # ~240 times larger dataset! NROW(new_split_dataset)/NROW(sTRACE) ######################################## # Do the analysis with the coxvc and # # the timecox from the timereg library # ######################################## Ft_1 <- cbind(rep(1,nrow(sTRACE)),bs(sTRACE$time/365,df=3))
fit_coxvc1 <- coxvc(surv~vf+sex, Ft_1, rank=2, data=sTRACE)
fit_coxvc2 <- coxvc(surv~vf+sex, Ft_1, rank=1, data=sTRACE)
Ft_3 <- cbind(rep(1,nrow(sTRACE)),bs(sTRACE$time/365,df=5)) fit_coxvc3 <- coxvc(surv~vf+sex, Ft_3, rank=2, data=sTRACE) layout(matrix(1:3, ncol=1)) my_plotcoxvc <- function(fit, fun="effects"){ plotcoxvc(fit,fun=fun,xlab='time in years', ylim=c(-1,1), legend_x=.010) abline(0,0, lty=2, col=rgb(.5,.5,.5,.5)) title(paste("B-spline =", NCOL(fit$Ftime)-1, "df and rank =", fit$rank)) } my_plotcoxvc(fit_coxvc1) my_plotcoxvc(fit_coxvc2) my_plotcoxvc(fit_coxvc3) # Next group my_plotcoxvc(fit_coxvc1) fit_timecox1<-timecox(surv~sex + vf, data=sTRACE) plot(fit_timecox1, xlab="time in years", specific.comps=c(2,3)) The code results in these graphs: Comparison of different settings for coxvc and of the coxvc and the timecox plots. I guess the results are ok but I don't think I'll be able to explain the timecox graph - it seems to complex... ## My (current) questions • How do I do the FPT analysis in R? • How do I use the time covariate in cmprsk? • How do I plot the result (preferably with confidence intervals)? • The example in the link is about time-varying covariates, not time varying coefficients. These are too different things. To get time varying parameters the way you described use interactions, i.e. instead of model$y=x\beta_{my}$, fit model$y=x\beta_0+x\cdot t\beta_1+x\cdot t^2\beta_2$. In R the formulas would look like y~x and y~x*(t+t^2)-t (also possible to write y~x+x:t+x:t^2 for the last one). – mpiktas Nov 18 '11 at 14:45 • I thought the second part: "2. Model Deterministic Time-dependent Covariates to Check the PH Assumption" would be the part dealing with my question. I was hoping to do something of the formula that you describe but when I tried it I either got an error or a separate time variable... I got a low p-value for time though :-D – Max Gordon Nov 18 '11 at 21:08 • @max-gordon, is your response variable a quantity, or the time elapsed until an even occurs? Because most of the methods you cite are specifically for time-to-event data. – f1r3br4nd Jul 10 '13 at 20:02 • @f1r3br4nd: It is a quantity (Age in my study) where the hazard is non-proportional, i.e. it varies over time in my time-to-event model. In the end I decided to split into two different time-frames as I was not thrilled by doing a 3-D graph - that would have never passed the reviewers... – Max Gordon Jul 11 '13 at 20:12 • There's a difference between time dependent/varying predictors and time interaction. Most variables are time dependent (sex is an exception). If you have one observation per person, then you'll have little or no chance to perform a time dependent/varying analysis. Anderson-Gill's method is the most frequently used for time- dependent survival analysis. The advantage of time dependent methods is that values during follow-up might be more predicitve of survival experience than baseline values. The second situation, time interacting predictors are simply tests of the PH assumption. – Adam Robinsson Aug 15 '15 at 6:31 ## 3 Answers @mpiktas came close in offering a feasible model, however the term that needs to be used for the quadratic in time=t would be I(t^2)) . This is so because in R the formula interpretation of "^" creates interactions and does not perform exponentiation, so the interaction of "t" with "t" is just "t". (Shouldn't this be migrated to SO with an [r] tag?) For alternatives to this process, which looks to me somewhat dubious for inference purposes, and one which probably fits your interest in using the supportive functions in Harrell's rms/Hmisc packages, see Harrell's "Regression Modeling Strategies". He mentions (but only in passing although he does cite some of his own papers) constructing spline fits to the time scale to model bathtub-shaped hazards. His chapter on parametric survival models describes a variety of plotting techniques for checking proportional hazards assumptions and for examining the linearity of estimated log-hazard effects on the time scale. Edit: An additional option is to use coxph's 'tt' parameter described as an "optional list of time-transform functions." • I agree that this should probably be moved to the SO [r] tag. – Zach Dec 11 '11 at 19:14 • +1 for for your answer, I wasn't aware that this would be so hard answering. It seems like a common problem, perhaps the question is more of a question of coding than and you might be right about SO being a better choice. I tried your formula it seems that vf+I(vflog(time)) has an excellent fit, I tried just vftime and vf*time^2 but the log gave by fare the lowest p-value. I tried to run it with the cph() function to get the AIC but it gave an error :( Do you have any idea of how to do a plot on the estimate? – Max Gordon Dec 11 '11 at 21:10 • I thought that check <- cox.zph(fit1); print(check); plot(check, resid=F) as in your set up gave informative plots of the time "effect". Did you mean cph() which is from the rms package or coxph from survival? – DWin Dec 11 '11 at 21:53 • Yes, the Schoenfeld residuals does give a nice idea of the time variation but I think people might have a hard time understanding it. The plot gives as I understand it the residual variation not explained by my model. I would like though a plot where I have the complete variable effect on the y-axis and time on the x-axis, I believe that this would be easier to interpret since you don't have to look at both the table and the plot to get the hazard at a specific point in time... Yes I meant cph() and not the coxph() since that one doesn't work with the AIC() – Max Gordon Dec 12 '11 at 5:37 • I'm also a little confused to why I've found all the complex methods described in my question while this I(variable*time) seems very straight forward and intuitive - as a non-statistician I'm thinking - what have I missed? – Max Gordon Dec 12 '11 at 5:41 I've changed the answer to this as neither @DWin's or @Zach's answers fully answers how to model time-varying coefficients. I've recently wrote a post about this. Here's the gist of it. The core concept in the Cox regression model is the hazard function,$h(t)$. It is defined as: $$h(t) = \frac{f(t)}{S(t)}$$ Where the$f(t)$is the risk of having an event at any given time while the$S(t)$is the probability of surviving that fare. The number is thus a fraction with a theoretical range from$0$to$\infty$. An interesting feature of the hazard function is that we can include observations at other points in time than$time_0$, e.g. if "Peter" is operated with a hip arthroplasty in England, arrives after 1 year to Sweden, he has been alive for 1 year when we choose to include him. Note that any patient that would have died prior to that would never have come to our attention and we can therefore not include Peter in the$S(t)\$ when looking at the hazard prior to 1 year. After 1 year we may include Peter.
When allowing subjects entering at other time points we must change the Surv from Surv(time, status) to Surv(start_time, end_time, status). While the end_time is strongly correlated with the outcome the start_time is now available as an interaction term (just as hinted in the original suggestions). In a regular setting the start_time is 0 except for a few subjects that appear later but is we split each observation into several periods we suddenly have plenty start times that are non-zero. The only difference is that each observation occurs multiple times where all but the last observation has the option of a non-censored outcome.
Time splitting in practice
I've just published on CRAN the Greg package that makes this time-split easy. First we start with some theoretical observations:
library(Greg)
test_data <- data.frame(
id = 1:4,
time = c(4, 3.5, 1, 5),
age = c(62.2, 55.3, 73.7, 46.3),
date = as.Date(
c("2003-01-01",
"2010-04-01",
"2013-09-20",
"2002-02-23"))
)
We can show this graphically with * being an indicator of event:
If we apply the timeSplitter as following:
library(dplyr)
split_data <-
test_data %>%
select(id, event, time, age, date) %>%
timeSplitter(by = 2, # The time that we want to split by
event_var = "event",
time_var = "time",
event_start_status = "alive",
time_related_vars = c("age", "date"))
We get the following:
As you can see each object has been split into multiple events where the last time span contains the actual event status. This allows us to now build models that have simple : interaction terms (do not use the * as this expands to time + var + time:var and we're not interested in the time per se). There is no need for using the I() function although if you want to check nonlinearity with time I often create a separate time-interaction variable that I add a spline to and then display using rms::contrast. Anyway, your regression call should now look like this:
coxp(Surv(start_time, end_time, event) ~ var1 + var2 + var2:time,
data = time_split_data)
Using the survival package's tt function
There is also a way to model time dependent coefficients directly in the survival package using the tt function. Prof. Therneau provides a thorough introduction to the subject in his vignette. Unfortunately in large datasets this is hard to do due to memory limitations. It seems that the tt function splits the time into very fine pieces generating in the process a huge matrix.
You can use the apply.rolling function in PerformanceAnalytics to run a linear regression through a rolling window, which will allow your coefficients to vary over time.
For example:
library(PerformanceAnalytics)
library(quantmod)
getSymbols(c('AAPL','SPY'), from='01-01-1900')
chart.RollingRegression(Cl(AAPL),Cl(SPY), width=252, attribute='Beta')
#Note: Alpha=y-intercept, Beta=regression coeffient
This works with other functions too.
• Thank you for your answer, I guess a moving time-window should work just as well as my approaches. I can't get your example to run though, could you please give an example based on my sTRACE example so that I know exactly how to implement it? – Max Gordon Dec 10 '11 at 13:43
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# Decision forest vs. Random woodland a€“ Which Algorithm in the event you make use of?
Decision forest vs. Random woodland a€“ Which Algorithm in the event you make use of?
## Straightforward Analogy to spell out Decision Tree vs. Random Woodland
Leta€™s focus on a believe test which will show the difference between a choice tree and a haphazard forest unit.
Assume a bank has to approve a tiny amount borrowed for a person and the lender must come to a decision easily. The financial institution checks the persona€™s credit score as well as their financial condition and discovers they havena€™t re-paid the old financing however. Thus, the financial institution rejects the application.
But right herea€™s the catch a€“ the borrowed funds amount got tiny for the banka€™s immense coffers in addition they may have effortlessly accepted they in an exceedingly low-risk move. Therefore, the financial institution lost the chance of making some money.
Today, another loan application comes in a couple of days later on but now the financial institution appears with an alternate method a€“ several decision-making procedures. Often it monitors for credit score initially, and sometimes they monitors for customera€™s economic disease and amount borrowed first. Then, the lender brings together results from these numerous decision making steps and decides to supply the loan towards the buyer.
In the event this process took more hours compared to the past one, the bank profited using this method. This will be a traditional sample where collective decision-making outperformed one decision-making techniques. Now, herea€™s my question to you a€“ are you aware what these two steps signify?
These are typically decision trees and an arbitrary woodland! Wea€™ll explore this concept thoroughly here, plunge inside biggest differences between these two practices, and address the important thing question a€“ which machine studying algorithm in the event you opt for?
## Brief Introduction to Decision Trees
A decision forest are a monitored maker training algorithm which can be used both for category and regression dilemmas. A little armenia prices decision tree is probably a number of sequential conclusion enabled to reach a particular consequences. Herea€™s an illustration of a choice forest for action (using all of our preceding sample):
Leta€™s understand how this tree operates.
1st, it monitors in the event that client possess an effective credit score. According to that, they categorizes the client into two groups, for example., consumers with a good credit score record and subscribers with poor credit record. After that, it checks the income of buyer and once again classifies him/her into two groups. Finally, they monitors the loan amount required by customer. Based on the outcomes from checking these three characteristics, the choice forest chooses when the customera€™s loan must be accepted or not.
The features/attributes and ailments can transform on the basis of the facts and complexity of the problem nevertheless as a whole concept continues to be the same. Very, a determination tree renders a number of conclusion centered on a collection of features/attributes within the information, that this example had been credit history, money, and amount borrowed.
Now, you may be questioning:
The reason why did the choice tree look at the credit history initially rather than the income?
This can be titled function advantages while the series of features to be examined is determined on the basis of standards like Gini Impurity directory or details earn. The explanation of these concepts try outside the scope of our own post here but you can make reference to either associated with the under tools to understand everything about decision woods:
Notice: the concept behind this information is to compare choice trees and arbitrary forests. Thus, i’ll perhaps not go into the specifics of the fundamental principles, but i’ll provide the appropriate website links in the event you desire to check out further.
## An Overview of Random Woodland
Your choice tree algorithm isn’t very difficult to know and understand. But typically, just one forest isn’t enough for creating successful outcomes. That is where the Random woodland formula makes the picture.
Random Forest was a tree-based device finding out formula that leverages the effectiveness of several decision woods in making choices. Since label indicates, it’s a a€?foresta€? of trees!
But why do we call it a a€?randoma€? forest? Thata€™s because it is a forest of arbitrarily produced decision woods. Each node inside choice tree works on a random subset of functions to assess the result. The haphazard forest next combines the output of individual decision woods to create the final production.
In quick statement:
The Random Forest formula combines the result of several (randomly developed) choice Trees to create the ultimate result.
This technique of mixing the production of numerous individual brands (also known as weak students) is known as Ensemble discovering. If you wish to read more exactly how the arbitrary forest also ensemble reading algorithms services, check out the soon after posts:
Today practical question are, how can we decide which formula to choose between a determination tree and an arbitrary forest? Leta€™s read them both in activity before we make any conclusions!
## Conflict of Random Forest and choice forest (in rule!)
Within area, we will be using Python to resolve a digital category challenge making use of both a choice forest and additionally a random woodland. We are going to next compare their success and find out which fitted our very own problem the number one.
Wea€™ll be concentrating on the mortgage forecast dataset from Analytics Vidhyaa€™s DataHack system. This is certainly a digital category issue where we will need to see whether you is provided that loan or otherwise not centered on a specific set of qualities.
Note: you can easily go directly to the DataHack program and contend with others in a variety of on-line device finding out contests and stand to be able to victory exciting prizes.
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### GMAT Challenge Problem Showdown: May 20, 2013
We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:
The octagon in the diagram above is regular: all of its sides are of equal length, and all of its angles are of equal measure. If the octagon’s perimeter is 8 inches, and every other vertex of the octagon is connected to create a square as shown above, what is the area of the square?
Discuss this week’s problem with like-minded GMAT takers on our Facebook page.
The weekly winner, drawn from among all the correct submissions, will receive One Year of Access to our Challenge Problem Archive, AND the GMAT Navigator, AND Our Six Computer Adaptive Tests (\$92 value).
1. Saif1khan October 1, 2013 at 7:46 pm
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If you're seeing this message, it means we're having trouble loading external resources on our website.
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## Algebra I (2018 edition)
### Course: Algebra I (2018 edition)>Unit 6
Lesson 5: Introduction to the domain and range of a function
# Worked example: domain and range from graph
Finding the domain and the range of a function that is given graphically. Created by Sal Khan.
## Want to join the conversation?
• What would I write if the function has arrows at the end of the line on both sides?
• The arrows simply mean that the function goes on forever.
• How do you find the domain of a parabola? Do you use the same process?
• A parabola should have a domain of all real numbers unless it is cut off and limited. Both the left side and the right side normally have arrows which mean it will go on forever to the left and forever to the right.
• So essentially we can interpret this as Domain being represented along the X-axis and Range along the Y-axis?
• -2<x<5 how can i write the inequalities?
• You would write your inequality in interval notation as:
(-2, 5)
The parentheses tell you that the inequalities do not include the end values of -2 and 5.
If the inequality is: -2≤x≤5, then the interval notation is:
[-2, 5]
The square brackets tells you that the end values are included in the interval.
If you have an inequality like: -2≤x<5, then the interval notation is:
[-2, 5)
A square bracket is on the -2 because it is included in the interval. The 5 gets a parentheses because it is not in the interval.
Hope this helps.
• I'm confused on what signs to use (greater than equal to, less than equal to, etc) I know that you use the greater than equal to and less than equal to, when it's included, but how do you know what sign to use when graphing? How do you know which way the graph is going? I'm not sure if I am making sense
• The "equal" part of the inequalities matches the line or curve of the function, so it would be solid just as if the inequality were not there. Without the "equal" part of the inequality, the line or curve does not count, so we draw it as a dashed line rather than a solid line
The < or > has to do with the shading of the graph, if it is >, shading is above the line, and < shading is below. The exception is a vertical line (x = #) where there is no above and below, so it changes to the left (<) or to the right (>)..
So lets say you have an equation y > 2x + 3 and you have graphed it and shaded. If you try points such as (0,0) and substitute in for x and y, you get 0 > 3 which is a false statement, and if you did it right, shading would not go through this point. If point is (1,5) you can do the same thing, 5 > 5, but this would be right on the line, so the line would have to be dashed because this statement is not true either. One more point (0,6) would give 6>3 which is a true statement, and shading should include this point.
• If we have f(x)=(1/3)^x, we can see that it approaches 0, but never touches it. Does that mean that the range is (∞,0)?
• Yes, but you should always right the range in numeric order: (0,∞).
• What is a function?
I keep confusing myself on what it is...
I know domain is x and range is y
• A function is a relation where every domain (x) value maps to only one range (y) value.
If you have the points (2, -3), (4, 6), (-1, 8), and (3, 7), that relation would be a function because there is only one y-value for each x. X-values don't repeat.
If you have the points (2, -3), (4, 6), (2, 8), and (3, 7), that relation would not be a function because 2 for the x-value repeats, meaning 2 maps to more than one y-value.
Repeating x-values mean the relation is not a function.
No repeating x-values mean the relation is a function.
You might want to check out https://www.khanacademy.org/math/algebra/algebra-functions/evaluating-functions/v/what-is-a-function
• how high is up
• what do I do if there are 2 points on one side of the domain and not a closed or open circle on the other side?
• How do you graph this domain? 0 is less than or equal to x, which is less than or equal to 20?
## Video transcript
The function f of x is graphed. What is its domain? So the way it's graphed right over here, we could assume that this is the entire function definition for f of x. So for example, if we say, well, what does f of x equal when x is equal to negative 9? Well, we go up here. We don't see it's graphed here. It's not defined for x equals negative 9 or x equals negative 8 and 1/2 or x equals negative 8. It's not defined for any of these values. It only starts getting defined at x equals negative 6. At x equals negative 6, f of x is equal to 5. And then it keeps getting defined. f of x is defined for x all the way from x equals negative 6 all the way to x equals 7. When x equals 7, f of x is equal to 5. You can take any x value between negative 6, including negative 6, and positive 7, including positive 7, and you just have to see-- you just have to move up above that number, wherever you are, to find out what the value of the function is at that point. So the domain of this function definition? Well, f of x is defined for any x that is greater than or equal to negative 6. Or we could say negative 6 is less than or equal to x, which is less than or equal to 7. If x satisfies this condition right over here, the function is defined. So that's its domain. So let's check our answer. Let's do a few more of these. The function f of x is graphed. What is its domain? Well, exact similar argument. This function is not defined for x is negative 9, negative 8, all the way down or all the way up I should say to negative 1. At negative 1, it starts getting defined. f of negative 1 is negative 5. So it's defined for negative 1 is less than or equal to x. And it's defined all the way up to x equals 7, including x equals 7. So this right over here, negative 1 is less than or equal to x is less than or equal to 7, the function is defined for any x that satisfies this double inequality right over here. Let's do a few more. The function f of x is graphed. What is its range? So now, we're not thinking about the x's for which this function is defined. We're thinking about the set of y values. Where do all of the y values fall into? Well, let's see. The lowest possible y value or the lowest possible value of f of x that we get here looks like it's 0. The function never goes below 0. So f of x-- so 0 is less than or equal to f of x. It does equal 0 right over here. f of negative 4 is 0. And then the highest y value or the highest value that f of x obtains in this function definition is 8. f of 7 is 8. It never gets above 8, but it does equal 8 right over here when x is equal to 7. So 0 is less than f of x, which is less than or equal to 8. So that's its range. Let's do a few more. This is kind of fun. The function f of x is graphed. What is its domain? So once again, this function is defined for negative 2. Negative 2 is less than or equal to x, which is less than or equal to 5. If you give me an x anywhere in between negative 2 and 5, I can look at this graph to see where the function is defined. f of negative 2 is negative 4. f of negative 1 is negative 3. So on and so forth, and I can even pick the values in between these integers. So negative 2 is less than or equal to x, which is less than or equal to 5.
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# NAG CL Interfacef08ahc (dgelqf)
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## 1Purpose
f08ahc computes the $LQ$ factorization of a real $m×n$ matrix.
## 2Specification
#include
void f08ahc (Nag_OrderType order, Integer m, Integer n, double a[], Integer pda, double tau[], NagError *fail)
The function may be called by the names: f08ahc, nag_lapackeig_dgelqf or nag_dgelqf.
## 3Description
f08ahc forms the $LQ$ factorization of an arbitrary rectangular real $m×n$ matrix. No pivoting is performed.
If $m\le n$, the factorization is given by:
$A = ( L 0 ) Q$
where $L$ is an $m×m$ lower triangular matrix and $Q$ is an $n×n$ orthogonal matrix. It is sometimes more convenient to write the factorization as
$A = ( L 0 ) ( Q1 Q2 )$
which reduces to
$A = LQ1 ,$
where ${Q}_{1}$ consists of the first $m$ rows of $Q$, and ${Q}_{2}$ the remaining $n-m$ rows.
If $m>n$, $L$ is trapezoidal, and the factorization can be written
$A = ( L1 L2 ) Q$
where ${L}_{1}$ is lower triangular and ${L}_{2}$ is rectangular.
The $LQ$ factorization of $A$ is essentially the same as the $QR$ factorization of ${A}^{\mathrm{T}}$, since
$A = ( L 0 ) Q⇔AT= QT ( LT 0 ) .$
The matrix $Q$ is not formed explicitly but is represented as a product of $\mathrm{min}\phantom{\rule{0.125em}{0ex}}\left(m,n\right)$ elementary reflectors (see the F08 Chapter Introduction for details). Functions are provided to work with $Q$ in this representation (see Section 9).
Note also that for any $k, the information returned in the first $k$ rows of the array a represents an $LQ$ factorization of the first $k$ rows of the original matrix $A$.
None.
## 5Arguments
1: $\mathbf{order}$Nag_OrderType Input
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by ${\mathbf{order}}=\mathrm{Nag_RowMajor}$. See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint: ${\mathbf{order}}=\mathrm{Nag_RowMajor}$ or $\mathrm{Nag_ColMajor}$.
2: $\mathbf{m}$Integer Input
On entry: $m$, the number of rows of the matrix $A$.
Constraint: ${\mathbf{m}}\ge 0$.
3: $\mathbf{n}$Integer Input
On entry: $n$, the number of columns of the matrix $A$.
Constraint: ${\mathbf{n}}\ge 0$.
4: $\mathbf{a}\left[\mathit{dim}\right]$double Input/Output
Note: the dimension, dim, of the array a must be at least
• $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{pda}}×{\mathbf{n}}\right)$ when ${\mathbf{order}}=\mathrm{Nag_ColMajor}$;
• $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}×{\mathbf{pda}}\right)$ when ${\mathbf{order}}=\mathrm{Nag_RowMajor}$.
The $\left(i,j\right)$th element of the matrix $A$ is stored in
• ${\mathbf{a}}\left[\left(j-1\right)×{\mathbf{pda}}+i-1\right]$ when ${\mathbf{order}}=\mathrm{Nag_ColMajor}$;
• ${\mathbf{a}}\left[\left(i-1\right)×{\mathbf{pda}}+j-1\right]$ when ${\mathbf{order}}=\mathrm{Nag_RowMajor}$.
On entry: the $m×n$ matrix $A$.
On exit: if $m\le n$, the elements above the diagonal are overwritten by details of the orthogonal matrix $Q$ and the lower triangle is overwritten by the corresponding elements of the $m×m$ lower triangular matrix $L$.
If $m>n$, the strictly upper triangular part is overwritten by details of the orthogonal matrix $Q$ and the remaining elements are overwritten by the corresponding elements of the $m×n$ lower trapezoidal matrix $L$.
5: $\mathbf{pda}$Integer Input
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
Constraints:
• if ${\mathbf{order}}=\mathrm{Nag_ColMajor}$, ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$;
• if ${\mathbf{order}}=\mathrm{Nag_RowMajor}$, ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
6: $\mathbf{tau}\left[\mathit{dim}\right]$double Output
Note: the dimension, dim, of the array tau must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,\mathrm{min}\phantom{\rule{0.125em}{0ex}}\left({\mathbf{m}},{\mathbf{n}}\right)\right)$.
On exit: further details of the orthogonal matrix $Q$.
7: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
## 6Error Indicators and Warnings
NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.
NE_INT
On entry, ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{m}}\ge 0$.
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 0$.
On entry, ${\mathbf{pda}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{pda}}>0$.
NE_INT_2
On entry, ${\mathbf{pda}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$.
On entry, ${\mathbf{pda}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
## 7Accuracy
The computed factorization is the exact factorization of a nearby matrix $\left(A+E\right)$, where
$‖E‖2 = O(ε) ‖A‖2 ,$
and $\epsilon$ is the machine precision.
## 8Parallelism and Performance
f08ahc makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
The total number of floating-point operations is approximately $\frac{2}{3}{m}^{2}\left(3n-m\right)$ if $m\le n$ or $\frac{2}{3}{n}^{2}\left(3m-n\right)$ if $m>n$.
To form the orthogonal matrix $Q$ f08ahc may be followed by a call to f08ajc :
`nag_lapackeig_dorglq(order,n,n,MIN(m,n),&a,pda,tau,&fail)`
but note that the first dimension of the array a must be at least n, which may be larger than was required by f08ahc.
When $m\le n$, it is often only the first $m$ rows of $Q$ that are required, and they may be formed by the call:
`nag_lapackeig_dorglq(order,m,n,m,&a,pda,tau,&fail)`
To apply $Q$ to an arbitrary $m×p$ real rectangular matrix $C$, f08ahc may be followed by a call to f08akc . For example,
```nag_lapackeig_dormlq(order,Nag_LeftSide,Nag_Trans,m,p,MIN(m,n),&a,pda,
tau,&c,pdc,&fail)```
forms the matrix product $C={Q}^{\mathrm{T}}C$.
The complex analogue of this function is f08avc.
## 10Example
This example finds the minimum norm solutions of the underdetermined systems of linear equations
$Ax1= b1 and Ax2= b2$
where ${b}_{1}$ and ${b}_{2}$ are the columns of the matrix $B$,
$A = ( -5.42 3.28 -3.68 0.27 2.06 0.46 -1.65 -3.40 -3.20 -1.03 -4.06 -0.01 -0.37 2.35 1.90 4.31 -1.76 1.13 -3.15 -0.11 1.99 -2.70 0.26 4.50 ) and B= ( -2.87 -5.23 1.63 0.29 -3.52 4.76 0.45 -8.41 ) .$
### 10.1Program Text
Program Text (f08ahce.c)
### 10.2Program Data
Program Data (f08ahce.d)
### 10.3Program Results
Program Results (f08ahce.r)
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#### Multiplying and Adding Rows of 2D and 1D Arrays
You are given a two dimensional array containing arrays of integers and a one dimensional array of integers as arguments. Return the largest sum that can be obtained by multiplying each element of one row of the 2D array by each corresponding element of the 1D array and adding them all together.
The 2D array will always have the same number of columns as there are elements in the 1D array.
### Requirements
• Must return an integer
#### Example #1
``````solve([
[1, 1, 1],
[-10, -2, 1000],
[-60, -50, -60]
],[-10, 30, -30])
> 900
``````
1. Start with the first row of the 2D array: (1 \ -10) + (1 \* 30) + (-30 \* 1) = -10*
2. Then try the second row: (-10 \ -10) + (-2 \* 30) + (-30 \* 1000) = -29,000*
3. Then finally the third row: (-60 \ -10) + (-50 \* 30) + (-30 \* -60) = 900*
4. Since the third row produced the largest integer, we return 900.
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Basics of Mechanical Engineering PDF: All the basic concepts of Mechanical Engineering which will be useful to you in the case of interviews will be presented in this article. Apart from that, it is also a subject in the field of Mechanical Engineering. As all the concepts will be furnished below and with the help of Tabular column you can navigate the concepts by clicking on the links in the Table.
Note: Download Basics of Mechanical Engineering at the end of the article.
## Tabular Column for Basics of Mechanical Engineering:
Principal Stresses, Principal planes, Maximum Shear stress, Maximum Shear Stress Planes with Formulas: When you are going for an interview or writing any competitive exam then a compulsory question will be asked on either of the above terms in terms of a Definition or a Numerical. If it is a numerical question, it generally carries 2 marks and if it is a theory question, it may be 1 mark or 2 marks. So, I am focussing on the definitions as well as formulas related to those terms. The Definitions and their Representation were presented below either in the form of text or in the form of Images. If you want formulas, then try to copy from the images. 1.Principal Stresses:
• The maximum or minimum normal stress is the principal stress.
• These principal stresses are used in the design.
2.Principal Planes:
• The plane on which principal stresses will be acting is called the principal plane.
• On the principal plane, shear stress must be zero.
• Any plane in the material without shear stress is by default principal plane.
• In a 2-D system, there are two principal planes separated by 90 degrees. On these planes, shear stress is zero.
3.Maximum Shear stress(in 2D Plane stress system): The Maximum Shear Stress in the 2D Plane stress system is presented below. 4.Maximum Shear Stress Planes: The plane on which maximum shear stress is acting called as maximum shear stress plane and the formula of Maximum Shear Stress Planes will be collected from the above image placed in the maximum shear stress section.
• In a 2D system, there are two (Tow max) planes separated by 90 degrees.
• The angle between any one principal plane and the nearest (Tow max) plane is 45°.
• On (Tow max) plane, there will be normal stress and which is in the middle of (Sigma 1) and (Sigma 2) by magnitude.
• The magnitude of shear stress on mutually perpendicular planes must be the same.
• The sum of normal stresses on mutually perpendicular planes must be constant.
This is the complete explanation of Principal Stresses, Principal planes, Maximum Shear stress, Maximum Shear Stress Planes with Formulas in a detailed manner. If you have any doubts, then you can ask us from the comments section.
7.Resilience: The ability of the material that can absorb energy without undergoing any shape change is called Resilience. Determination of Resilience:
• The resilience of the material will be determined by calculating the area under stress v/s strain curve up to an elastic point.
• Resilience says about the strength and ductility properties of the material.
• If a material possesses higher the resilience means it will absorb more energy against shape change.
Examples of Resilience are shown below.
• Steel
Retains the shape and does not fail immediately.
8.Punch Die Clearance in Design:
The die opening must be sufficiently larger than the punch to permit a clean fracture of metal. This difference in dimension between the mating members of die set is called clearance.
## Explanation about the Punch Die Clearance in Design:
• When the hole has to be held to size i.e.the hole in the sheet metal is to be accurate, the punch is made to the size of the hole and dies opening size is obtained by adding clearance to punch size.
• In blanking operation, where the size of the blank is to be maintained accurately, die opening size is exactly equal to blank size and clearance is to be subtracted from die opening size to get punch size.
9.Quasistatic Process: A system is made to undergo a series of change of states such that it is in thermodynamic equilibrium at each and every state. Then the locus of all these states is called a quasistatic process.
• It is an ideal and very slow process.
Example of Quasistatic Process: If sand grains are allowed to fall one after the other on a piston-cylinder mechanism, then the movement of such a piston is called a quasistatic process.
## Assumptions of Ideal gas:
• Molecular separation is very high.
• Molecules do not occupy any volume.
• The molecular collisions are elastic in nature.
• There are no inter-molecular forces of attraction are present.
The equation of Ideal gas is given as: P*V=m*R*T Where, P -Pressure(pascals) V -Volume(m^3) m -mass(Kg) R -Gas Constant(J/KgK) T -Temp(K)
10.SI Unit of Pressure: SI Unit of Pressure: The unit of pressure in the SI system is the pascal (Pa), defined as a force of one Newton per square meter. SI Unit of Pressure-Units of Pressure:
• 1 atm =101.325KPa
=760mm of Hg Column =10.33 m of H2O Column
• 1bar =10^5 Pascals
=100Kpa =751.6 mm of Hg Column
• 1torr =1mm of Hg
=133.33 Pascals
• For High Pressures, go for ‘Hg’ manometers
• For Low Pressures, go for ‘water’ manometers.
• Pabsolute=Patm+Pguage
• Pabsolute=Patm-Pvaccum
Note: For calculations part, Vaccum and Guage pressures are not used. Therefore, Absolute pressure comes into the picture.
Basics of Mechanical Engineering: 11. What is Strength? The definition of strength is as follows… The ability of the body to resist external loads without failure is called Strength.
• Strength is a material property.
• It is constant for the material.
• Any design is a strength-based design only.
This is the definition of strength with its features.
12.Mechanical Properties of Metals: When you want to apply any type of load on a particular member, you need to know its material properties, density, etc. For that, in this article, I am exploring the necessary properties of metals in a detailed manner. 11 Properties of Metals: The Properties of Metals which are essential for a mechanical engineer are as follows.
1. Bond: It possesses a metallic bond.
2. Strength: The strength of the metal is very high when compared to plastics and ceramics.
3. Binding Energy: The distance between the atoms is less and thereby the Binding energy is high.
4. Ductility: It possesses good ductility also.
5. Conductivity: The metals possess good electrical conductivity because of the presence of free electrons.
6. Thermal Conductivity: The metals possess good thermal conductivity.
7. Density: The metals possess high density which means that the weight of the metal is more and this is one of the disadvantages of metals.
8. Corrosiveness: The metals are highly corrosive to the environment.
9. Servicing Temperature: The servicing temperature of the metal is 800̊ C-1000̊ C.
• Hazardous: It is not hazardous and is environmentally friendly.
• Recyclability: The metals are partially recyclable in nature.
13.Properties of Ceramics: The mixture of metal oxide powders like the Powder of Aluminum oxide, Powder of Silicon Oxide and the Powder of Zirconium oxide are collectively called as ceramics. The various Properties of Ceramics are shown below in a detailed manner.
## Top 11 Properties of Ceramics:
The Properties of Ceramics which plays a crucial role in the field of mechanical engineering are as follows:
1. Bond: The ceramics possess both Ionic and Covalent bonds.
2. Strength: The strength of the metal is greater than the strength of Ceramics and that is greater than the strength of Polymer.
3. Distance between atoms: The distance between the atoms of metal is less than the Ceramics and is less than the Polymers.
4. Brittleness: The ceramics are brittle in nature.
5. Conductivity: The ceramics possess bad electrical conductivity because of the absence of free electrons.
6. Thermal Conductivity: The Ceramics possess bad thermal conductivity but they can sustain at high temperatures easily.
7. Density: The Density of Metal is greater than Density of Ceramics and that is greater than the Density of Polymers.
8. Corrosiveness: The Ceramics are Anti-Corrosive to the environment because they are already in corrosive form.
9. Servicing Temperature: The servicing temperature of the metal is 3000̊ C.
10. Hazardous: It is not hazardous to the environment.
11. Recyclability: The ceramics are non-recyclable in nature.
These are the top 11 Properties of Ceramics which are discussed in a detailed manner.
14.Compare Mass and Weight: Mass of the body:
• Mass of the body does not vary from place to place and it is not affected by the gravitational force.
• It is represented by “m”.
• Unit of mass “m”=Grams
Weight of the body:
• Weight of a body varies from place to place and depends on the acceleration due to gravity existing at that place.
• It is represented by “W”.
• The formula for weight of the body is
W=m/g
• If “g” is positive then the sign of “W” cannot changes whereas
• If “g” is negative then the sign of “W” changes.
So, this is the main difference between mass and weight of anybody. Unit of weight “W”=mg=Kg*(m/s2) Therefore, Unit if weight =Newton
15.The ratio of Specific heat at Constant Volume and Constant Pressure: The ratio of Specific heat: It is defined as the ratio of specific heat at Constant Pressure to Specific heat at Constant Volume. It is represented by Gamma(γ) (γ or Gamma) = Cp/Cv. A ratio of Specific heat at Constant Volume and Constant Pressure Specific heat at Constant Volume and Constant Pressure: The ‘γ‘ value is different for different gases and is as follows.
• γ = 1.63 for monoatomic gases.
• γ = 1.4 for Diatomic Gases.
• γ = 1.33 for Triatomic gases.
Specific heat at constant volume: It is defined as the ratio of change in Internal energy to Change in Temperature at Constant Volume. (Cv) = (du/dt)@Constant Volume Specific heat at Constant Pressure: It is defined as the ratio of Change in Enthalpy to Change in temperature at Constant Pressure. (Cp) = (dh/dt)@Constant Pressure.
16.Post Heating in Welding:
• Post-heating is done in order to relieve further residual stresses present in the weld pool after heat treatment process also.
• If post-heating is not done, then residual stresses develop as cracks and propagate throughout, resulting in the failure of the material.
• Therefore Preheating and Post heating must be done during welding.
17.Pre heating in Welding Process:
Need of Preheating in Welding process: Preheating in Welding involves heating the base metal, either in its entirety or just the region surrounding the joint, to a specific desired temperature called as preheating temperature, prior to welding. In this article, I am going to publish about, what is the need of Pre-heating in welding process in a detailed manner.
Heating may be continued during the welding process, but frequently the heat from welding is sufficient to maintain the desired temperature without a continuation of the external heat source.
WhyPre heating in Welding is necessary?
There are four primary reasons to utilize Preheating in Welding (1) It lowers the cooling rate in the weld metal and base metal, producing a more ductile metallurgical structure with greater resistance to cracking. (2) The slower cooling rate provides an opportunity for any hydrogen that may be present to diffuse out harmlessly without causing cracking. (3) It reduces the shrinkage stresses in the weld and adjacent base metal, which is especially important in highly restrained joints. (4) It raises some steels above the temperature at which brittle fracture would occur in fabrication. Additionally, preheat can be used to help ensure specific mechanical properties, such as notch and toughness.
18.Stepper Motor: Explanation of Stepper Motor along with its Importance: Stepper Motor is widely used in the field of Robotics where high precision is needed. In this article, I will be explaining about the stepper motor and its importance in a detailed way.
## Explanation of Stepper Motor:
The stepper motor is taking electrical energy input in the form of pulses and converting into mechanical energy in the form of revolutions. But, by changing no. of pulses of electrical energy to a motor (or) by changing the rate of pulses of electrical energy input to the motor, the speed of the stepper motor can be changed. Because of the presence of inertia effect of moving parts, even though the power supply is stopped to the motor, it is not possible to stop the motor axis immediately. Hence, the tool is traveling some more distance and therefore accuracy of the components produced is poor. i.e. The positional accuracy of the machine tool will become poor. This is the complete explanation of the stepper motor in detailed. There is an advanced of a stepper motor i.e. servo motor which will work much effectively than it and can be used in various installations. 19.Difference between Specific gravity and Specific Volume: Specific Volume: It is the reciprocal of Density which is defined as the ratio of Volume of the body to its unit mass. It is denoted by (ν)
• Specific Volume(ν)= Volume of the body/unit mass.
• Units = m3/Kg
Relative density or Specific Gravity: It is defined as the ratio of the Density of any substance to the Density of water. Specific Gravity = (Density of any substance/Density of Water). Units = No Units
20. What is Thermocouple? These are used to measure the temperature at a particular point. They are manufactured by using two dissimilar materials belonging to thermoelectric series.
• One is higher order element and another is a lower order element and 2 junctions are made.
• One junction is kept at Ice Point and Another junction is kept at the place whose temperature is to be measured.
• Due to the difference in temperature, an EMF is generated and this EMF is related to temperature.
21. What is the Seebeck Effect? Development of EMF due to the difference in temperature is called a Seebeck effect.
22. What are Pyrometers? They can function on the principle of radiation. They are used to measure the temperature’s from a distance.
23.What is Pressure?
It is defined as the ratio of Force acting per unit Area of the cross-section.
Pressure (P)=F/A
Measurement of pressure is done by the manometer.
Unit of Pressure in S.I. system is “Pascal”.
The eloborative units were presented above at Point No.10
24.What is Absolute Pressure?
The Sum of Atmospheric pressure and Gauge pressure is called Absolute Pressure. or
The Difference between Atmospheric pressure and Vaccum pressure is also called as Absolute Pressure
Absolute Pressure=Atmospheric pressure+Gauge pressure
Absolute Pressure=Atmospheric pressure-Vaccum Pressure.
25.What is Vaccum Pressure? It is defined as the difference between Atmospheric Pressure and the Absolute Pressure
Vaccum Pressure = Atmospheric Pressure-Absolute Pressure.
26.Numerical based on vaccum and atmosphere: Vaccum and Atmosphere are the two most popular terms used in the thermodynamics. So, let’s do a numerical on it. Therefore, In this article, I am going to explain about the simple Numerical based on vaccum and atmosphere in a detailed manner. Numerical based on Vaccum 1. A mass of 1Kg falls to a distance of 10m in Vaccum. What is Work done? Sol: Work done = Zero Numerical based on Atmosphere: 1. A mass of 100N falls through a distance of 10m overcoming drag resistance of 5N. What is the work done? Sol: W =F*S =FSCos(theta) = FCos(theta)*S =resisting force*distance =5*10 =50Nm
27.Difference between Engineering Mechanics and Strength of Materials: This type of questions will be asked in the interview point of view and the answer for this question is well explained in the next paragraph.
## Difference:
Engineering Mechanics deals with RIGID Bodies whereas Strength of materials deals with Deformable bodies. Rigid Body in the sense a body which cannot be deformed by the application of external force also called a Rigid body. It is also called as a real body. What Others are Reading:
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## Archive for May, 2014
### implicit function problem
From fakalin. If $$F(x, y, z)$$ is a function of 3 variables, and the relation $$F(x, y, z) = 0$$ defines each of the variables in terms of the other two, namely $$x = f(y, z)$$, $$y = g(x, z)$$, and $$z = h(x, y)$$, then show that:
$$\left(\frac{\partial x}{\partial y}\right) \left(\frac{\partial y}{\partial z}\right) \left(\frac{\partial z}{\partial x}\right) = -1$$.
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# Linea de Abonado Digital-Lock Out
## Linea de Abonado Digital-Lock Out
### Linea de Abonado Digital
Spanish name for DSL. See DSL.
### Linear Distortion
Amplitude distortion wherein the output signal envelope is not proportional to the input signal envelope. This distortion is often caused by part of the signal being bounced off something, while part arrives free and clear. Thus the receiver hears the same signal but bits of it arrive earlier and later than other bits, causing distortion. See Linearity for a better explanation.
See LFSR.
LPA.
### Linear Predictive Coding
A speech coding method that analyzes a speech waveform to produce a time-varying filter as a model of the human vocal tract . See also Digital Signal Processing.
### Linear Programming
Techniques in Operations Research (OR) to find an optimum solution to a linear function, given certain restrictions and typically expressed in many equations. A typical linear programming problem might be to find the least expensive, most efficient route between various pick-up and drop-off points in a transportation route.
### Linearly Polarized
A mode of operation of fiber optics for which the field components in the direction of propagation are small compared to components perpendicular to that direction.
### Lineman
A person who fixes the telephone company's outside aerial plant ” typically the wires hanging from poles dotted across the country-side. See also Lineman's Climbers.
### Lineman's Climbers
Telephone pole climbing irons which are strapped to the telephone lineman's legs, allowing him or her to climb a wooden telephone line. You can tell when a pole has been climbed by the holes left in it by the lineman's climbers.
### Lines
A computer imaging term. The line tool draws straight lines, typically from point to point. Most paint packages let you continue lines in a fashion that permits rapid creation of polygons.
### Lines Of Force
The directional lines of magnetic or static field which represent the stresses.
### Lines Per Minute
The way of measuring the speed of a line printer. Like any measure of speed, the speed you will get from your printer may be different from what the manufacturer says. Your speed will depend on how fast you feed the printer from your computer ” a function of how fast you're transmitting, what software you're running, how fast that software can get the information to be printed off your disk, etc.
### Line Side
See Lineside.
1. Another name for a communications channel or circuit. The ATM Forum defines link as an entity that defines a topological relationship (including available transport capacity) between two nodes in different subnetworks. Multiple links may exist between a pair of subnetworks. Synonymous with logical link.
2. A Windows command that takes several programs and subprograms that were meant to be used together, but were written separately, and combines them into one. Usually used to create an executable program out of modules that were not themselves directly executable.
3. An element in an HTML document that points to a document or to a specific location in a document, using a URL. When the document is displayed in a browser, clicking on a link causes the browser to display the document and/or location that it points to. Links usually appear on-screen as underlined text and are usually in blue, although Web page designers can change how they look.
### Link Access Protocol
A version of HDLC in which the communication line has no single controller and either of the two connected stations may initiate a data transfer operation.
The grouping of multiple network links into one logical high bandwidth link. By grouping four 100 Mbps Ethernet connections into one logical link, you can create up to 800 Mbps of bidirectional throughput between the server and the switch.
### Link Aggregation Token
See Aggregation Token.
Describing devices that are connected to a network, a communications data link, or telecommunications circuit; compare with channel-attached.
A link state parameter that is considered individually to determine whether a given link is acceptable and/or desirable for carrying a given connection.
See LCAS.
An ATM term. A link connection (e.g., at the VP-level) is a connection capable of transferring information transparently across a link without adding any overhead, such as cells for purposes for monitoring. It is delineated by connection points at the boundary of the subnetwork.
A restriction on the use of links for path selection for a specific connection.
### Link Control Facility
A Fibre Channel hardware facility which attaches to the end of a link and manages the transmission and reception of data. The LCF is contained within each F Port (Fabric Port, i.e., switch port) and N Port (Node Port, i.e., device port). See Fibre Channel.
### Link Control Protocol
LCP. A Link Control Protocol is a protocol operating at Layer 2, the Data Link Layer, of the OSI Reference Model. Such a protocol is employed by circuit terminating equipment at each end of the link in order to communicate across it. The specifics of an LCP include packet format, packet size , compression mechanisms, link performance monitoring, handshake and authentication mechanisms, and error detection and correction. LCP examples include HDLC (High-level Data Link Control) and PPP (Point-to- Point Protocol). See also HDLC and PPP.
A device for an InteCom S/80 which connects distributed switching modules to the centralized switching equipment through a coaxial cable or a fiber optic cable.
LE. A function of the HiPPI Framing Protocol (FP) layer. LE encapsulates IEEE 802.2 Logical Link PDUs (Protocol Data Units) inside of HiPPI packets, thereby allowing IP traffic to travel over a HiPPI connection.
The logical second layer of the OSI Reference Model for Open Systems Interconnection, located between the Physical and Network layers . See OSI.
### Link Layer Access Method
The algorithm that determines when any given network interface in a PC/TCP local area network is allowed to transmit. It is also known as the access method. CSMA/CD is the access method for the Ethernet.
An ATM term. A link parameter that requires the values of the parameter for all links along a given path to be combined to determine whether the path is acceptable and/or desirable for carrying a given connection.
ISDN feature that prevents administration packet from opening the communications link and allows only user data to open the line. Link optimization ensures that remote connections are not kept open unnecessarily, which saves usage costs.
The set of rules by which a logical data link is set up and by which data transfers across the link. It includes formatting of the data.
A communication mechanism used in 10Base-T networks to indicate link status and, in auto-negotiation equipped devices, to communicate information about abilities and negotiate communication methods . 10Base-T uses Normal Link Pulses (NLPs) which indicate link status only. These are transmitted periodically while not transmitting packets. 10Base-T and 100Base-T nodes equipped with auto-negotiation exchange information using a Fast Link Pulse (FLP) mechanism which is compatible with NLP.
The process by which links on a Web page become obsolete because of changes in location or expiration of the sites to which they are connected. Link rot happens quickly.
A group of signaling links directly connecting two signaling points.
### Link State Parameter
Information that captures an aspect or property of a link.
### Link Status Signal Unit
LSSU. A packet sent between MTPs (Message Transfer Part of the SS7 Protocol) to provide SS7 information about the sending node and its links. This information is sent during the initial alignment of the links, when there is an associated processor outrage, or when link congestion is detected .
A test that is performed by the hardware to ensure the integrity of the cable in a local area network. The link test can be disabled to allow old style NICs incapable of performing a link test to connect to the repeater.
This is a specific time delay that allows access to PBX or Centrex features through a telephone system. Link Time is also referred to as a Hookswitch Flash or Recall.
A representation or place holder for an object that is inserted into a destination document. The object still exists in the source file and, when it is changed, the linked object is updated to reflect these changes.
1. The transmission portion of the local loop.
2. An affectionate name for Apple's electronic mail system, called AppleLink.
### LINX
London Internet Exchange. See IX.
### Linux
Linux (officially pronounced LINN-ucks) is the creation of Linus Torvalds, who started the Linux kernel as a research project at the University of Helsinki, Finland. Since then, Linux has evolved into a full-featured , powerful and robust open source, operating system based on Unix. While it is true that Linux is very closely modeled after Unix, and in most cases programs that run on Unix will run on Linux, Linux is not really Unix. Linux is among the most powerful and feature-packed operating systems available for the PC, offering a large base of hardware peripheral compatibility. Linux hosts an impressive array of compilers and development environments, including C/C++, Perl, Pascal, SmallTalk, and complete X-windows system that rivals many commercial offerings. For all its life, Linux has been free. But it is not shareware. Major parts of it are copyrighted . Linux has many script languages and parsers such as Awk, Sed, Yacc as well as all popular shells (Borne, Korn, C, BASH, etc.). The Linux kernel was originally written only for the Intel 80x86 microprocessor, i.e. the 386/486/Pentium family of chips. But it has been ported to Alphas, sparcs, 68k, and PowerPC. There are several companies selling pre-configured Alpha based systems as well as the standard 80x86 based systems. In many ways, Linux is a better performing UNIX than many of the commercial versions of UNIX. Here is the definition of Linux taken from the August, 1999 Linux Journal, the major Linux magazine. "Linux is a multi-user, multi-tasking operating system that runs on many platforms, including Intel, Motorola, MC68K, and DEC Alphas. It implements a superset of the POSIX standard. Linux works well with other operating systems, including Apple, Microsoft and Novell. It supports a wide range of software, including X Windows, Emacs, TCP/IP networking (including SLIP/PPP/ISDN), the works. A PC running Linux often makes an excellent and fast substitute for a conventional UNIX workstation. Linux (often pronounced with a short 'i' and with the first syllable stressed - LIH-nucks) is freely available ” it can be copied and redistributed without fees or royalties. The source code for Linux is available on the Internet to anyone who wants it." See www.linuxresources.com/what.html, www.redhat.com and www.rtems.com.
### LiIon
Lithium Ion. The Lithium Ion battery is lightweight and does not suffer from memory effect. It also delivers a higher run time average and about 80% more power per ounce. Similar to NiMH technology, LiIon batteries have a life expectancy of 500 charge and discharge cycles. LiIon batteries are typically used in mid- to high-priced portables.
### LIP
Loop Initialization Protocol. Part of the FC-AL (Fibre Channel Arbitrated Loop) standard for reconfiguring the system when nodes are added or removed from the loop.
### Lipstick
Over her lifetime, the average American woman will swallow four pounds of lipstick. The good news is that that's a lot less than the Coca Cola I drink.
### Lipstick Indicator
The tendency for lipstick sales to increase prior to and during a recession .
### Liquid Crystal Display
LCD. A low power display that aligns material suspended in a liquid under the influence of a low voltage so it reflects ambient light and displays alphanumeric characters . LCD displays are finding great use as methods of displaying information on new electronic telephones, especially those positioned behind PBXs. The advantage of putting such displays on telephones is that the power to drive the display is very small. The display can be line powered ” i.e. powered by the one or two pairs coming from the PBX. This avoids the necessity and cost of a transformer/ rectifier ” the little black box you plug into the wall to run your answering machine or to power up your rechargeable calculator/laptop computer. Such LCD displays on electronic phones can perform many functions. The most useful is that of "walking" the user through the phone call ” showing him/her how to transfer a call, to make a conference call, to split a conference, etc. An LCD can also alert you as to who's calling you.
### LIRC
Long Run Incremental Cost.
### LIS
1. Link Interface Shelf.
2. Local Interconnection Service. A local interconnection service arrangement with an ILEC (Incumbent Local Exchange Carrier) to provide trunking, E911, SS7 requirements for LNP (Local Number Portability).
### LISP
An interpretive language developed for manipulation of symbolic strings and recursive data; while the language has been developed to aid in the handling of symbolic lists, it can be and has been used successfully in the manipulation of mathematical and arithmetic logic.
### List Box
A Windows term. In a dialog box, a box that lists available choices, for example, a list of all files in a directory. If all the choices do not fit in the list box, there is a scroll bar.
### List Host
A host computer, in the form of a server, that is used to support e-mail list services, usually on an outsourced basis. The service provider will place your e-mail list on its host computer, and associate it with an e-mail that you want to send to many e-mail addresses. You just send the e-mail to a special target mailbox, and the list host server forwards it to everyone on your list. If people want to be removed from the list, they so indicate with a return e-mail, and the list host server takes care of it. At least that's the theory.
### List Server
An automated mailing list distribution system.
### Listed Directory Number
LDN. Incoming exchange network calls to the PBX via assigned listed local telephone directory number are directed to the attendant.
### Listen Before Talk
LBT. Same as carrier sense multiple access (CSMA). Compare with Listen While Talk.
### Listen While Talk
LWT. Same as carrier sense multiple access with collision detection (CSMA /CD). Compare with Listen Before Talk.
### LIT
See Line Insulation Test.
### Lit Fiber
Let's start with optical fiber. When a carrier initially installs an optical fiber in the ground (sub-terrestrial), under the ocean ( submarine ), or through the air (hung on poles), it's called "dark" fiber. That means he hasn't put any electronics on it, so he's not sending any light down the fiber and thus he's not transmitting any information. Usually a dark fiber is one of many dark fibers in a cable containing a great many fibers, commonly 432 in sub-terrestrial cabling systems. The carrier deploys such a large cabling system because the incremental cost of pulling one large cable is much less than the incremental cost of pulling fibers one at a time, as needed. The dark fibers are designated for future use, or for backup purposes in the event that a fiber fails for some reason. Sometimes dark fiber is sold or leased by a carrier without the accompanying transmission service, e.g., SONET. The customer is expected to put his own electronics and photonics on the fiber and thus be able to make transmissions. This process is calling "lighting" the fiber, since light now moves down the fiber. And the fiber is now called "lit" since that's the past participle of the verb "to light." If a given optical fiber system supports WDM (Wavelength Division Multiplexing) or DWDM (Dense WDM), multiple wavelengths of light can be transmitted across the system simultaneously . If not all of the available wavelengths are active (e.g., only 10 of a possible 32), the fiber is said to be "dim," i.e., neither dark nor fully lit. See also Dark Fiber, Dim Fiber, DWDM, SONET, and WDM.
### Lithium Ion
Type of highly efficient rechargeable battery, often used in computer lap- tops and cellular portables. Here's an explanation from 1-800-BATTERIES, a seller of rechargeable batteries:
NiCad: Nickel Cadmium is the most popular and durable type of rechargeable battery. It is quick to charge, lasts about 700 charge and discharge cycles, and works well in extreme temperatures . Unfortunately, NiCads suffer from "memory effect" if they are not completely discharged during each cycle. The memory effect reduces the overall capacity and run time of the battery.
Nickel Metal Hydride (NiMH) batteries do not suffer from memory effect. Compared to a NiCad battery of equal size, NiMH batteries run for 30% longer on each charge. They are also made from non-toxic metals so they are environmentally friendly. The downside to NiMH technology is overall battery life. These batteries last for 400 charge and discharge cycles.
Lithium Ion (LiON) is the latest development in portable battery technology. These batteries do not suffer from memory effect. Compared to a NiMH of equal size, a LiON will deliver twice the run time from each charge. Unfortunately, these batteries are only available for a limited number of models and are expensive. Similar to NiMH technology, LiON batteries have a life expectancy of 400 charge and discharge cycles.
### Little Endian
A format for storage or transmission of binary data in which the least significant byte (bit) comes first. See Little-endian.
### Little LEO
Relatively small and inexpensive low earth orbiting satellites that provide low-cost, low-data rate, two-way digital communications, and location positioning to small handheld terminals. The frequency allocations are in the VHF band below 400 MHz. Systems include Leosat, Orbcomm, Starnet, and Vitasat. For example, the Orbcomm system requires 34 satellites for reliable full-world coverage. See Big LEO.
See Big-endian.
### LIU
Line Interface Unit. Essentially a digital transceiver, an LIU is a generic term for a type of Circuit Terminating Equipment (CTE) used to terminate a T-1/E-1 circuit or ISDN PRI (Primary Rate Interface) circuit. In an optical environment, an OLIU (Optical Line Interface Unit) serves the same function for interfacing with a SONET/SDH OC-1, or better, optical circuit. Generally speaking, an LIU provides CSU (Channel Service Unit) and DSU (Digital Service Unit) functionality, supports a variety of framing formats, provides loopback test capability, and offers performance monitoring and diagnostics. The term LIU also sometimes is used to describe a PBX line card, which serves to interface PBX extensions to the switch, as opposed to trunk cards, which serve to interface the PBX switch to a CO (Central Office) switch. See also CSU, DSU, E-1, Loopback Test, SONET, SDH, and T-1.
### LIU7
Line Interface Unit for CCS7.
### Live Bug
Colloquialism used to refer to a leaded integrated circuit package when the leads are down, like a bug that is alive and standing upright.
See LCS.
### Livelock
A request for an exclusive lock that is repeatedly denied because a series of overlapping shared locks in a shared database keeps interfering. A SQL server will detect the situation after several denials, and refuse further shared locks.
### Liver
The human liver stretches across almost the width of the body, occupying a space about the size of a football. It weighs more than 3lbs. I have no idea why anyone other than me would be interested in this trivia.
People.
Long Lines.
### LLB
Line LoopBack. A maintenance and/or diagnostic mode of operation whereby a CSU regenerates a signal received from a span line and retransmits that signal back onto the span towards its point of origin.
### LLC
Logical Link Control. A protocol developed by the IEEE 802.2 committee for data-link- level transmission control. It is the upper sublayer of the IEEE Layer 2 (OSI) protocol that complements the MAC protocol. IEEE standard 802.2 includes end-system addressing and error checking. It also provides a common access control standard and governs the assembly of data packets and their exchange between data stations independent of how the packets are transmitted on the LAN. See 802 Standards.
### LLC2
Logical Link Control 2. The frame format used to carry 3270 traffic on Token Ring LANs.
### LLDP
Local Loop Demarcation Point. See MPOE.
### LLF
1. Line Link Frame. See Crossbar Switching.
2. Low Layer Functions.
### LLPOFYNILTATW
Liar, Liar Pants On Fire, Your Nose Is Longer Than A Telephone Wire.
### LLWAS
Low Level Wind Shear Alert System.
### LM
Long distance Marketer.
### LMCS
Local Multipoint Communication Service. The Canadian equivalent of LMDS (Local Multipoint Communications Service). Using frequencies above 25 GHz, LMCS produces a wireless broadband digital network capable of delivering high-bandwidth signals over the air. Industry Canada has allocated the frequency band 25.35 to 28.35 GHz for LMCS networks. Some observers believe LMCS may represent a form of fiber to the curb. See also LMDS.
### LMEI
Layer Management Entity Identifier.
### LMHost
LMHhost is a text file which contains the NetBIOS name and IP addresses of other computers on a network. Microsoft Windows Network is a NetBIOS-based network where each computer is given a unique name, the NetBIOS name. In a traditional NetBIOS name, each machine sends a NetBIOS broadcast that announces its name as it boots. If another host already exists with that name, it will send a message to the new client saying that that name is in use. If it doesn't get a message back, the client assumes that the name is available. One of the ways to get around this broadcast problem is to create a text file named LMHost on every computer. Not a recommended course of action.
### LMI
1. Local Management Interface. A specification for the use of frame-relay products that define a method of exchanging status information between devices such as routers.
2. Logical Modem Interface. The core of the Microsoft Fax interface. LMI lets third-party licensed vendors write plug-in modules to provide instant and transparent access to diverse underlying systems. An easy analogy for the LMI is to consider the Windows print manager. To the user, simply installing the printer driver suited to their printer is all that is required. According to Microsoft, "The LMI interface provides a similar layer between the internal fax components of Windows 95 and the fax hardware or, in our case, the fax server."
### LML
Lineup Maintenance Level.
### LMOS
Loop Maintenance Operations System.
### LMP
A Bluetooth term. Link Manager Protocol. The LMP is used for peer-to-peer communication.
Lmp Authentication A Bluetooth term. An LMP level procedure for verifying the identity of a remote device. The procedure is based on a challenge-response mechanism using a random number, a secret key and the BD_ADDR of the non-initiating device. The secret key used can be a previously exchanged link key or an initialization key created based on a PIN (as used when pairing ).
Lmp Pairing A Bluetooth term. A LMP procedure that authenticates two devices based on a PIN and subsequently creates a common link key that can be used as a basis for a trusted relationship or a (single) secure connection. The procedure consists of the steps: creation of an initialization key (based on a random number and a PIN), lmp authentication based on the initialization key and creation of a common link key.
### LMS
1. Local Message Switch.
2. Loop Monitoring System.
### LMSS
Land Mobile Satellite Service.
### LMU
Line Monitor Unit.
### LNA
Low Noise Amplifier.
### LNB
Low Noise Block converter. The device at the focal point of the satellite dish that gathers the signal reflected by the dish to the system's low-noise block amplifier.
### LNC
Low Noise Converter.
### LND
Last Number dialed .
### LNNI
LANE Network-to-Network Interface. An ATM term for the standardized interface protocol between LANE (LAN Emulation) servers (LES-LES, BUS-BUS, LECS-LECS and LECSLES). See also LANE and LUNI.
### LNP
Local Number Portability. Similar in concept to 800/888 and other toll-free number portability, LNP was mandated by the Telecommunications Act of 1996 to level the playing field between the ILECs (Incumbent Local Exchange Carriers) and the CLECs (Competitive Local Exchange Carriers ). In July 1996, the FCC issued a ruling that LNP must be in place nationwide by January 1, 1998. Since each state is responsible for implementation of LNP, timetables vary; the specifics of the implementations vary, as well.
In some states, the implementation approach is exactly like that for 800 (toll-free) number portability. In other words, the originating central office "dips" into a centralized database of numbers via an signaling system 7 (SS7) data link. The database, known as a SCP (Service Control Point) in IN (Intelligent Network) terms, identifies the LEC (local exchange carrier) providing service to the target telephone number in order that the originating carrier can hand the call off to the terminating carrier.
In other states, such as Illinois, which is the first to implement LNP, a totally different approach is taken. This implementation involves the use of a new 10-digit telephone number, known as a LRN (Local Routing Number). When the originating CO switch consults the SCP, the new 10-digit number is provided along with the identification of the CLEC to which the service has been ported. The originating carrier then hands off the call to the CLEC. While this approach is claimed to be faster, clearly two telephone numbers are required, thereby placing additional pressure on the North American Numbering Plan (NANP).
To implement LNP, the FCC has mandated a system of regional databases, which will store master copies of all porting information. These databases will be maintained by regional Number Portability Administration Centers (NPACs) that will serve as number portability clearinghouses for all local operators. Originally, the deal was that Lockheed Martin would maintain the databases in four regions and Perot Systems in three regions . After Perot had some problems getting going on time, Lockheed Martin was selected to run all seven. That responsibility now rests with NeuStar, which was an independent business unit within Lockheed Martin before being spun off.
In either case, LNP will require the SCPs be established by LECs, CLECs, IXCs (inter- exchange carriers) and wireless carriers. Further, the SCPs must be synchronized in order that the databases are consistent across them all. The concept is simple, but its implementation is complex and expensive. MNP (Mobile Number Portability) is the LNP version intended for eventual use in certain mobile networks. See also Number Portability and Trigger. www.NeuStar.com
### LNRU
Like New Repair and Update. A term in the industry which repairs telecom equipment. It means all equipment is repaired and updated to the current manufacturer's specifications. New plastic is used to refurbish to a "like new" status. Also added are a new coil cord, line cord and address tray. Included is a full diagnostic test with a burn-in (if required) and an operational system test. Definition courtesy Nitsuko America. See also Repair And Quick Clean and Repair, Update And Refurbish.
### LO
Local Operator. In the PCS sense, a functional entity providing local wireless service to customers in a geographical region. The LO (Local Operator) is serviced by the National Services Organization in the PCN (Personal Communications Network) for long-distance communications and for marketing/sales.
### LOA
Letter Of Agency. A letter that you give to someone whom you allow to represent you and act on your behalf. For example, a letter of agency is used when your interconnect company orders lines from your local phone company on your behalf . Letters of Agency are also used when companies switch their long distance service from one carrier to another. A blanket LOA can mean everything from a group of numbers belonging to one customer at multiple sites or multiple customers at multiple sites.
1. The act of taking a program or data from external storage ” a cassette, a floppy or hard disk, etc. and storing it in the computer's main RAM memory.
2. The load is any electric or electronic appliance or gadget plugged into an AC electrical outlet. It completes the circuit from the transformer through the hot conductor, to the load, through the neutral conductor and back to the utility transformer. See AC, AC Power, Ground and Grounding.
A telephone company term. Load Balance is the even distribution of customer traffic volume across all loading units in a switching entity. Load Balance is not related to the absolute level of load, but only to how well the existing load is distributed. See also Load Balancing.
### Load Balance Index
LBI. A telephone company term. Indicates trends, identifies superior performances and points up opportunities for improvement in load balance administration of dial Central Office line equipment.
In server farms, a load balancer accepts IP packets and then distributes them among identical web servers. This enables the manager to add web servers as loads grow, or to take a server out of service and not have the clients notice. This definition contributed by Alan Simmons. See also Load Balancing.
The practice of splitting communication into two (or more) routes. By balancing the traffic on each route, communication is made faster and more reliable. In telephone systems, you can change phone and trunk terminations in order to even out traffic on the network. An example: You have a PBX of three separate cabinets, each of which are joined by tie lines. Instead of having each cabinet serve anyone in the building, you might figure which groups talk to each other the most and concentrate them into specific cabinets. The objective is to maximize the number of calls that can be handled inside each cabinet and reduce the number of calls that need to travel between the cabinets . This makes the calls go faster and reduces the need for inter- cabinet lines.
In data internetworking, bridges and routers perform load balancing by splitting LAN-to- LAN traffic among two or more WAN links. This allows for the combination of several lower speed lines to transmit higher speed LAN data simultaneously. In local area networking, load balancing is a function performed by token ring routers. In data networking, load balancing can also be a form of inverse multiplexing where data packets are alternated over all available circuits. At the receiving end, the packets are reassembled in their proper order.
In disk arrays, load balancing means using multiple power supplies within a disk array so that power usage is spread equally across all the power supplies . The failure of one supply will not cause the entire array to fail. See also Load Balancer.
Load coils are also known as impedance matching transformers . Load coils are used by the telephone companies on long analog POTS (Plain Old Telephone Service) lines to filter out frequencies above 4 kHz, using the energy of the higher frequency elements of the signal to improve the quality of the lower frequencies in the 4 kHz voice range. Load coils are great for analog voice grade local loops, but must be removed for digital circuits to function. Load coils must be removed for DSL loops , as the frequencies required are well above 4 kHz.
### Load Coil Detector
A device use to detect unseen load coils on a wire pair. See Load Coil.
Ratio of the Peak to Average ratio over a designated time period; has meaning in both traffic engineering and in transmission technology, particularly for data transmission.
Load can apply to telecommunications traffic or electricity (AC or DC). Load leveling in telecom typically means distributing traffic over more than one route. Load leveling in electricity typically means
Load number is the Canadian equivalent of the U.S. concept of Ringer Equivalence. The idea is that each phone or "phone thing" you buy (e.g. answering machine) comes with a number. You add the numbers together and if you get above a certain number, you are drawing too much current and none of the bells on the phones will ring. In Canada, single line phones are typically rated at 10 for the newer ones with electronic "bells" or 20 for the older electro-mechanical ones with real metal bells. In Canada, the rule is not more than 100 points on a line. In the U.S., phones are typically one and the rule is not more than five points on a line.
### Load Service Curves
The output from load and stress testing on a computer telephony system is a set of load service curves. Load service curves identify how individual areas of the system respond under various load amounts. Traffic is provided to the computer telephony system at defined steps (perhaps at 1,000 call per hour increments ) until the system design threshold is reached. Measurements are taken at each step, and usually shown graphically, in a "curve". Most computer telephony systems are designed to handle up to a specified number of busy hour calls with specific response times. For example, the time that passes between the point in time a caller enters a DTMF digit and the point the computer telephony system speaks a response should usually be no more than 1 second 97% of the time, nor more than 3 seconds 99% of the time. A load service curve would be used to illustrate the response time at each step of increasing load. When the load curve shows the response time is slower than the above parameters, the system has reached its capacity. Of course, the load placed on the system must accurately mimic the real world load the system will experience or it is largely meaningless. This definition from Steve Gladstone, president, Hammer Technologies, makers of fine computer telephony testing systems, 508-694-9959.
In data processing, load sharing is the technique of using two computers to balance the processing normally assigned to one of them. In local area networking, load sharing is performed by token ring routers when connecting remote LANs. It allows combining Ethernet and Token Ring traffic over a common WAN (Wide Area Network) link such as T-1 or 56 Kbps circuit. Loads sharing eliminates the need for duplicate WAN links (and bridges or routers) each serving a different type of LAN.
Twisted wire pair into which inductors have been inserted at periodic intervals to approximate the optimum ratios of the primary cable constants for minimum loss. A loaded cable acts like a lowpass filter. Transmission loss below the cutoff frequency is reduced below that for the nonleaded cable and is nearly flat. Above the cutoff frequency, loss increases very rapidly . See Loading.
Also called a Loaded Pair (loaded twisted pair); a loop that contains series inductors, typically spaced every 6000 feet for the purpose of improving the voice- band performance of long loops. However, high bandwidth DSL operation over loaded loops is not possible because of excessive loss at higher frequencies. See Loading.
A method of improving the voice quality of a phone line. Telephone companies put load coils on local lines. What this loading does is to insert inductance in a local loop circuit to offset the effect of capacitance in the cable. Loading "tunes" the circuit to the voice frequency band (500 to 2500 Hz) and thus improves the quality at the expense of overall bandwidth. You usually have to ask that the loading coils be removed if you're planning to transmit high-speed data exclusively on that circuit. See Loading Coil.
A telephone company term. A group of the same type of equipment designed to be loaded similarly by both usage and classes of service.
A memory management verb for loading a device driver or TSR (Terminate and Stay Resident) program into upper memory, out of conventional memory. Under DOS, the loading high commands are DEVICEHIGH for device drivers and LOADHIGH (or LH) for TSRs. Third party memory managers use their own routines to load high, though they can sometimes borrow DOS commands.
A telephone company term. A Loading Plan is a systematic scheme for fully utilizing all existing capacity in a given switching entity; Utilizing and coordinating the capabilities and capacity limitations of various entities in a multi-entity wire center and maintaining objective service levels at all times. A Loading Plan is the basis for achieving and retaining good Load Balance.
### LOC
An ATM term. Loss of Cell Delineation: A condition at the receiver or a maintenance signal transmitted in the PHY overhead indicating that the receiving equipment has lost cell delineation. Used to monitor the performance of the PHY layer.
### Local
Pertaining to a system or device that resides within a subject device's switching domain.
### Local Access
The connection between a customer's premises and a point of presence of the Exchange Carrier.
### Local Access and Transport Area
LATA. The MFJ (Modified Final Judgement), which broke up the Bell System, also defined 196 distinct geographical areas known as LATAs. The LATA boundaries generally were drawn in consideration of SMSAs (Standard Metropolitan Statistical Areas), which were defined by the Census Bureau to identify "communities of interest" in economic terms. Generally speaking, the LATA boundaries also were coterminous with state lines and existing area code boundaries, and generally included the territory served by only a single RBOC. The basic purpose of the LATA concept was to delineate the serving areas reserved for LEC (Local Exchange Carrier) activity. In other words, IntraLATA traffic (i.e., local and local long distance) became the sole right and responsibility of the LECs. InterLATA traffic, on the other hand, became the sole right and responsibility of the IXCs. Over time, a number of state PUCs allowed the IXCs to compete for IntraLATA long distance; they also allowed CAPs (Competitive Access Providers) to provided limited local service in competition with the LECs. The Telecommunications Act of 1996 (The Act) opened the floodgates for competition with the LATA boundaries. The Act also allows the RBOCs to provide InterLATA service outside the states in which they provide local service. Additionally, The Act contains provisions for the RBOCs to offer InterLATA service within the state in which they provide local service, once they have satisfied a 14-point checklist, the most significant conditions of which relate to significant, demonstrated levels of competition within their respective local exchange serving areas. California is divided into 11 LATAs. Sparsely populated states such as South Dakota comprise only a single LATA.
### Local Airtime Detail
This cellular telephone carrier option (which means it costs money) provides a line-itemized, detailed billing of all calls, including call attempts and incoming calls to the mobile. What you get for free is generally a non-detailed, total summary of all calls.
See LATA.
### Local Area Data Transport
LADT. A service of your local phone company which provides you, the user, with synchronous data communications.
### Local Area Network
LAN. A short distance data communications network (typically within a building or campus) used to link computers and peripheral devices (such as printers, CD-ROMs, modems) under some form of standard control. Older data communications networks used dumb terminals (devices with no computing power) to talk to distant computers. But the economics of computing changed with the invention of the personal computer which had "intelligence" and which was cheap. LANs were invented as an afterthought ” after PCs ” and were originally designed to let cheap PCs share peripherals ” like laser printers ” which were too expensive to dedicate to individual PCs. And as time went on, what LANs were used for got broader and broader. Today, LANs have four main advantages:
1. Anyone on the LAN can use any of the peripheral devices connected to the LAN.
2. Anyone on the LAN can access databases and programs running on client servers (super powerful PCs) attached to the LAN; and
3. Anyone on the LAN can send messages to and work jointly with others on the LAN.
4. While a LAN does not use common carrier circuits, it may have gateways and/or bridges to public telecommunications networks. See LAN Manager, Token Ring and Ethernet.
### Local Area Signaling Services
LASS is a group of central office features provided now by virtually all central office switch makers that uses existing customer lines to provide some extra features to the end user (typically a business user). They are based on delivery of calling party number via the local signaling network. LASS can be implemented on a standalone single central office basis for intra office calls or on a multiple central office grouping in a LATA (what the local phone companies are allowed to serve) for interoffice calls. Local CCS7 (Common Channel Signaling Seven) is required for all configurations. The following features typically make up LASS:
Automatic Callback: Lets the customer automatically call the last incoming call directory number associated with the customer's phone when both phones become idle. This feature gives the customer the ability to camp-on to a line.
Automatic Recall: Lets the customer automatically call the last outgoing call currently associated with the customer's station when both stations become idle. This feature gives the customer the ability to camp-on to a line.
Customer-Originated Trace: Lets the terminating party request an automatic trace of the last call received. The trace includes the calling line directory number and time and date of the call. This information is transmitted via an AM IOP channel to a designated agency, such as the telephone company or law enforcement agency.
Individual Calling Line Identification: Consists of two distinct features: 1. Calling Number Delivery which transmits data on an incoming call to the terminating phone. 1. Directory Number Privacy which prevents delivery of the directory number to the terminating phone.
Also, LASS has some selective features:
Selective Call Acceptance: Allows users to restrict which incoming voice calls can terminate, based on the identity attribute of the calling party. Only calls from parties identified on a screening lists are allowed to terminate. Calls from parties not specified on a screening list are rerouted to an appropriate announcement or forwarded to an alternate directory number.
Selective Call Forwarding: Allows a customer to pre-select which calls are forwarded based on the identity attribute of the calling party.
Selective Call Rejection: Allows a customer to reject incoming voice calls from identity attributes which are on the customer's rejection list. Call attempts from parties specified on the rejection list are prevented from terminating to the customer and are routed to an announcement which informs the caller that his/her call is not presently being accepted by the called party.
Selective Distinctive Alert: Allows a customer to pre-select which voice calls are to be provided distinctive alerting treatment based on the identify attributes of the calling party.
Users can, at their convenience, activate or modify any of these features by sending commands to the central switch from their existing touchtone telephones.
### Local Attack
A network security term. An attack that targets the machine on which the attacker is interactively logged on.
### Local Automatic Message Accounting
LAMA. A combination of automatic message accounting equipment and automatic number identification equipment in your telephone company's central office and used by them to bill your local phone calls.
### Local Battery
Having "local battery" means the telecom equipment ” the telephone, the PBX, the key system, etc. ” has its own source of power and does not draw from the power coming down the phone line. The term came from telegraphy and was used to distinguish the battery which provided power to the telegraphic station as against the power that went to drive the line and the signal traveling down it. See Battery.
### Local Bridge
A bridge between two or more similar networks on a local site (within same building).
### Local Bus
A microprocessor inside a PC must communicate with certain integral devices, including memory, video controllers, hard disks. This is typically called an internal bus. That is to distinguish it from the "external" bus, such as the AT, ISA, EISA, MCA buses, which define the communications between the motherboard and the various peripheral devices, such as the I/O cards like those handling modems and LAN connections. As microprocessors have gotten faster, so they have begun to outpace the speed of their computer's internal bus, which has tended to narrow the stream of data in and out of the CPU, slowing the computer. A Local Bus is a new type of internal bus. It is a faster bus. The idea is to get a broader path between your critical components ” memory, video and disk controller ” and your microprocessor. The idea is to get the data in and out of the microprocessor at the same speed as the microprocessor's system clock. Local Bus is an emerging standard. See also EISA, PCI and VESA.
### Local Call
Any call within the local service area of the calling phone. Individual local calls may or may not cost money. In many parts of the US, the phone company bills its local service as a "flat" monthly fee. This means you can make as many local calls per month as you wish and not pay extra. Increasingly this luxury is dying and local calls are costing money.
### Local Call Accounting
Computes the dollar amount for local calls based on the total message units stored for each phone.
### Local Call Billing
Computes the dollar amount for local calls placed by guests based on total message units.
### Local Central Office
Switching office in which a subscriber's lines terminate.
### Local Channel Controller
An AT&T name for its family of 3270 compatible cluster controllers.
### Local Composite Loopback
In network management systems. Composite loopback test that forms the loop at the output of the local multiplexer that returns transmitted signals to their source. See loopback.
### Local Dataset
Signal converter that conditions the digital signal transmitted by an RS-232 interface to ensure reliable transmission over a dc continuous metallic circuit without interfering with adjacent pairs in the same telephone cable. Normally conforms with Bell 43401. Also called baseband modem, limited distance modem, local modem, or short- haul modem. See line driver.
### Local Digital Services
LDS. LDS is a term used by long distance companies to describe "last mile" services provided by local phone companies. LDS is generic word to describe any digital services, including T-1, T-3, OC-12, Frame Relay and dedicated Internet services.
### Local Distribution Frame
LDF. Another word for an Intermediate Distribution Frame. It's a device for cross connecting cables ” from one thing to another. On one side of the LDF are the pairs from individual phones in that part of the building or area. On the other side are trunks coming in from a central office or cables coming in from the central, larger PBX. LDFs typically help with the organization of cables in a building or area. See also Intermediate Distribution Frame.
### Local Echo
A modem feature that enables the modem to send copies of keyboard commands and transmitted data to the screen. When the modem is in Command mode (not online to another system) the local echo is invoked through the ATE1 command. The command causes the modem to display your typed commands. When the modem is online to another system, the local echo is invoked through the ATFO command. This command causes the modem to display the data it transmits to the remote system.
### Local Exchange
The telephone company exchange where subscribers lines are terminated . Also called an "End Office."
### Local Exchange Carrier
A local phone company. See also LEC. As defined by the Telecommunications Act of 1996, a local exchange carrier means any person that is engaged in the provision of telephone exchange service or exchange access. Such term does not include a person insofar as such person is engaged in the provision of a commercial mobile service under section 332(c), except to the extent that the Commission (the Federal Communications Commission) finds that such service should be included in the definition of such term.
### Local Explorer Packet
Packet generated by an end system in an SRB network to find a host connected to the local ring. If the local explorer packet fails to find a local host, the end system produces either a spanning explorer packet or an all-routes explorer packet.
### Local Heap
A memory storage area limited to 64K in size.
### Local IP
A telephone company AIN term. The Internet Protocol (IP) indicated when an SCP or Adjunct requests a local AIN switch to make a connection to an IP to which the SSP or ASC switch has a direct ISDN connection.
### Local Long Distance
IntraLATA long distance. A marketing term invented by the LECs (local exchange carriers) to distinguish intraLATA from interLATA toll calling. Specifically, the term was invented by the RHCs (Regional Holding Companies), which currently are limited to providing "long distance" calls only within the intraLATA toll market in their home states.
### Local Loop
The physical connection from the subscriber's premise to the carrier's POP (Point of Presence). The local loop can be provided over any suitable transmission medium, including twisted pair, fiber optic, coax, or microwave. Traditionally and most commonly, the local loop comprises twisted pair or pairs between the telephone set, PBX or key telephone system, and the LEC (Local Exchange Carrier) CO (Central Office). As a result of the deregulation of inside wire and cable in the United States, the local loop typically goes from the demarc (demarcation point) in the phone room closet, in the basement or garage, or on the outside of the house, to the CO. The subscriber or building owner is responsible for extending the connection from the demarc to the phone, PBX, key system, router, or other CPE device. See also Demarc and Subloop.
### Local Management Interface
LMI. The specification for a polling protocol for use in Frame Relay networks between the user equipment in the form of a FRAD (Frame Relay Access Device) and the network equipment in the form of a FRND (Frame Relay Network Device). The LMI verifies the existence of the UNI (User Network Interface) and the Permanent Virtual Circuit (PVC).
### Local Measured Service
LMS. Years ago virtually all phone lines in the United States were FLAT RATE. That meant that for a fixed amount of money each month, you, the customer (a.k.a. subscriber) were allowed to make as many local calls as you wanted. For many reasons, the U.S. phone industry has progressively moved to LOCAL MEASURED SERVICE for local calls. Typically this means that for a fixed amount of money each month, you, the customer, can receive as many calls as you want and can make a finite number of outgoing local calls ” typically 50. Each additional call beyond the 50 (or whatever the number is) costs extra. How much that call costs depends on the distant the call travels, the time of day, the day of the week, and the local company's tariffs.
See LMCS.
See LMDS.
### Local Net
The broadband architecture used in Sytek's work. Also the product name of their network. Sytek is in Sunnyvale, CA.
### Local Number Portability
LNP. Imagine a town in which there are many local phone companies. You have service from one company. But another comes along offering better service, lower price and more features. You want to switch. But you don't want to change your phone number. That's what LNP is all about ” the ability to change your phone company and still keep your phone number.
Regardless of the local provider selected, consumers will continue to have access to Emergency 911 service; operator and directory assistance services; advanced services such as voice mail, Caller ID and Call Forwarding; and other customized local area and signaling capabilities, including equal access to all 800 and 888 toll-free telephone numbers.
On November 15, 1997 I received a press release from Lockheed Martin saying that they had successfully developed and tested Local Number Portability (LNP) in the Midwest, the FCC's mandated national test region. The implementation was mandated by the Federal government as part of the Telecommunications Act of 1996, which required this process be completed by October, 1997. In the press release, Lockheed Martin explain that in 1994, amidst concern over the need for fair, open telecommunications markets, the MCI Telecommunications Corporation initiated a Gallup Poll to investigate the demand for a Local Number Portability system. The poll randomly surveyed approximately 2000 businesses and consumers across the country in September and October 1994. The study assessed whether business or consumers would switch local telephone service providers under various market scenarios. The results of the poll indicated that 83 percent of business customers and 80 percent of residential customers would not change local service providers if changing service providers meant changing phone numbers. The study helped articulate the need for LNP in order to facilitate fair and open market competition in the local telecommunications industry. The LNP system developed in response to that survey and completed by Lockheed Martin in October, 1997, represents a substantial benefit to consumers: They now can choose local service from a variety of providers without changing their phone numbers. The system works for voice, data, and video lines, residential and business lines.
Here is what Lockheed wrote about local number portability technology in that press release: The database that facilitates Local Number Portability is a technological marvel in its complexity and the speed with which it operates. Each phone number has a network address. The LNP database keeps track of these addresses. When a customer places a call, the database records the caller's network address, locates the dialed number's network address, and notifies all telecommunications companies involved where to route the call and which companies to credit for the call.
Simplified, the process works like this:
• Call placed
• Network address of caller identified
• Network address of call recipient identified
• Telecommunications companies told how to route the call and which companies to credit.
All of this happens within nano-seconds of the customer placing the call ” an imperceptible lapse of time. The LNP system also records the appropriate information whenever a customer changes local carriers, updating account information and ensuring that no interruption in service occurs.
In developing LNP, Lockheed Martin IMS drew on two types of existing technology. In 1993, Lockheed Martin IMS developed a portability system for 800 numbers that was used by 140 telecommunications companies in the United States at the request of Bellcore, the research and engineering division of the Regional Bell Operating Companies. This database allowed customers to handpick 800 numbers (such as 1-800-FLOWERS) and keep those numbers regardless of the long-distance carrier used. That experience laid the groundwork for developing LNP.
Lockheed Martin IMS also used existing infrastructure to run LNP. Twenty years ago, each local phone company installed computerized databases for their own internal use. LNP is an incremental application of this network, the Advanced Intelligent Network (AIN), and was made possible by the investment that local service providers made years ago. See also LNP and Location Portability.
### Local Order Wire
A communications circuit between a technical control center and selected terminal or repeater locations.
### Local Oscillator
LO. A device which generates a specific single wave frequency. A local oscillators is used to reduce a high microwave frequency to a low intermediate frequency, so that it can be processed .
### Local Phone
A phone attached to your computer. See also Handset Management.
### Local Phone Service
When I dial the pizza store on the corner, I'm making a local phone call. But when I'm calling the pizza store 50 blocks away, is that a local phone call? Answer, it could be. It depends. What's local phone service? What do you charge for it? Once upon a time, most Americans didn't pay for local phone service. They paid a flat monthly fee. Then the phone companies needed money, so they started charging for local service. A few cents per call. Then the phone companies timed the call and charged more the longer you talked. Then they started charging for longer local calls ” maybe for calls of ten miles and further. In short, the definition and pricing of local phone calls is changing. Now local calls are looking increasingly like long distance calls ” charged by time, distance, and day of the week.
### Local Printer
A printer that is directly connected to one of the ports on your computer.
### Local Redirector
A local redirector is a shim that redirects HTTP requests to a local proxy server. A local redirector is also known as a load balancer, a local redirector is a piece of software that receives a server request (e.g., HTTP, FTP or NFS) and reroutes it to one of a cluster of Web servers to be actioned. The distribution function may be based on which machine in the cluster has the lowest current level of utilization, the proximity of the server to the client, or which machine has the resources necessary to carry out the request. This definition courtesy of Mark Gibbs.
### Local Service Area
The geographic area that telephones may call without incurring toll charges. A flat rate calling area. Increasingly rare.
See LSMS.
### Local Service Ordering Guidelines
LSOG. A manual that describes and provides examples of the LSR (Local Service Request) forms that are used by a CLEC to communicate with an ILEC for the purpose of ordering changes, additions, deletions, or enhancements in service. For example, LSRs are used to order various types of local loops, to port telephone numbers. The LSOG is printed and distributed by Telcordia Technologies (nee Bellcore) under the auspices of the Ordering and Billing Forum (OBF) of the Carrier Liaison Committee of the Alliance for Telecommunications Industry Solutions (ATIS). See also ATIS, CLEC, ILEC, LSR, OBF, and Telcordia Technologies.
### Local Service Request
A form used by a CLEC (Competitive Local Exchange Carrier) to request local service from an ILEC (Incumbent LEC). See LSR for a full explanation.
### Local Switch
The term local switch refers to the switch (PBX, ACD, dumb) to which the computer telephony system is directly connected. Usually, the local switch will provide better integration with the computer telephony system (more comprehensive call data) than connections that take place over the network. Additionally, the local switch will have both line and trunk side connections and will also support connection to whatever agents or desktop users that may use the computer telephony application.
### Local Switching Center
The switching center where telephone exchange service customer station channels are terminated for purposes of interconnection to each other and to interoffice trunks.
### Local Tandem
A central office, usually in large metropolitan areas, serving as a transit switch between noncontiguous class 5 exchanges. It connects end office trunks.
### Local Test Desk
A testing system that is used to test local loops and central office subscriber line equipment from a central point, typically a central office.
### Local Traffic
Telephone calling traffic that is classified as "local" in the tariff on file with the appropriate state regulatory body. This term includes single and multimessage unit traffic. See Toll Traffic.
### Local Trunk
Trunks between Class 5 local central offices, also called switching centers.
### LocDev
Local Device. A Bluetooth device which initiates a SDP procedure. A Local Device is typically a master device on the piconet. However, a Local Device may not always have a master connection relationship to other devices. See also RemDev.
### Locality
A measure of how close commonly-accessed files are to one another on a hard disk. "High locality" means the files reside on sectors or tracks which are close to each other. When this is the case, seek times during operation are shorter than average.
### LocalTalk
Apple Computer's proprietary Local Area Network (LAN) for linking Macintosh computers and peripherals, especially LaserWriter printers is called Appletalk. AppleShare is the company's networking software, and the LAN hardware is called LocalTalk. Appletalk is a CSMA/CA network that runs at 230.4 Kbps and is therefore incompatible with any other LAN. It is also a lot slower than the present top speeds of Ethernet (100 Mbps) and Token Ring (16 Mbps). Outside manufacturers, however, make gateways which will connect an Appletalk LAN to other local area and telecommunications networks ” LANs, WANs and MANs. See also AppleTalk, Ethernet, and CSMA/CA.
### Location
One definition is the place where a telephone jack is located. This location is given a number. The wire going to that location is given a number. All this in hope of being organized for installation, moves, changes and maintenance.
### Location Based Services
Location based services enable personalised (customised) services to be offered based on a person's (item's) location. Services include areas of security, fleet and resource management, location based information, vehicle tracking, person-to-person location and messaging applications. To enable these services, there are a number of different technology layers that need to be co-ordinated on a network. These technologies include Applications, Middleware, Determination technologies and associated Silicon and Intellectual Property (IP). See Location Services.
### Location ID
A feature of the IS-136 standards for digital cellular networks employing TDMA (Time Division Multiple Access). A capable telephone set will display the name of the cellular carrier providing service. In a wireless office system application, the phone can display the name of the company. When you are at home, connected to your PBS (Personal Base Station), the phone can display "cordless."
### Location Interoperability Forum
LIF. Open standards forum announced in September of 2000 to develop and promote a simple, ubiquitous interoperable location service solution necessary for mass consumer acceptance of mobile location services. Motorola, Nokia, and Ericsson were the charter members . See also LIF and Location Services.
### Location Portability
The ability of an end user to retain the same geographic or non-geographic telephone number (NANP numbers) as he/she moves from one permanent physical location to another. Location Portability will involve either of the following scenarios: 1) new location is within the same central office area, or 2) new location is within a different central office area. See also Local Number Portability.
### Location Services
Cellphone carriers will soon be able to figure out, within 100 metres (or less), where you, a cellphone user, are. The first application of this technology is called Emergency Location Services (or E911). What this means is that if you dial 911 in the United States on your cellphone, the operator will know where you are and be able to send help. There are two technologies currently being adopted; E-OTD (Enhanced Observed Time Difference) uses a software-enabled cellphone handset and cell sites to calculate your location. GPS (Global Positioning Systems) relies on a chip being installed in the cellular phone and orbiting satellites to determine position. From October 1, 2001, the FCC mandated 50% of all the new cellphone activations in the United States should be equipped with location services. See E-OTD, GPS and Location Based Services.
### Location Tracking
Vehicle Location Tracking Devices (VLD) are products targeted at the mobile fleet/ vehicle management space. Weighing less than eight ounces, they can be installed in almost any vehicle including: automobiles; construction equipment; trucks ; buses; motorcycles or even boats. When used with a carrier-grade server, it allows users to track the locations of specific vehicles equipped with these devices, via the Internet. I first heard about this from a company called Paradigm Advanced Technologies, Inc., which provides wireless location-based electronic commerce (L-Commerce) solutions. Paradigm has licensing rights to a wireless location patent (US Patent #B1 5,043,736) covering the apparatus and method of transmitting position information from satellite navigational signals (like GPS) over cellular systems to a base unit, and displaying the location of a person or object so equipped. Paradigm owns PowerLOC Technologies Inc. , which anticipates providing a comprehensive range of L-Commerce and L-Business products and services including a family of proprietary wireless-location devices for this industry and for location- based service providers (LSPs) in particular.
### Location Transparency
More professionals are working from home, customer sites or from the road. Location transparency means that your communications system ” faxing, email, voice mail, etc ” works as well for you, the user, whether you're in the office or in the field, or where in the field you are.
### Locator
A term used in the secondary telecom equipment business. A locator is a company that assists both a buyer and seller to quickly find each other. A locator contracts with dealers to provide them with daily lists of potential customers. The list develops from phone calls to an 800-number asking for a specific component.
### Lock And Load
Originally a military term. Then it became software speak for freezing code on a program in development. Then it became "Let's make a decision and get on with it."
### Lock Code
The lock code locks a cellular telephone to prevent unauthorized use. The lock code is programmed into the NAM (Numerical Assignment Module) and is frequently factory set to either 1234 or 00004.
### Lock On
The process by which an earth station initially acquires the signal from a satellite.
### Lock Out
In a satellite telephone circuit controlled by an echo suppressor , one or both subscribers can't get through because of excessive noise at one end. You get this also with speakerphones. The person with the speakerphone can simply hog the conversation because his speakerphone keeps transmitting his voice. There are weird variations on this. Sometimes you might call someone on your speakerphone and wait for them to pick up. They do. They shout into the phone "I'm here." All they can hear is you at the other end talking or typing. The sound at your end is hogging the channel and thus locking out the person at the other end. The solution? Turn the "mute" button on your speakerphone. This will stop your end transmitting and allow the other end to say "Hello, I'm here." See also Lockout.
Newton[ap]s Telecom Dictionary
ISBN: 979387345
EAN: N/A
Year: 2004
Pages: 133
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# 9.6 Binomial theorem (Page 3/6)
Page 3 / 6
## Key equations
Binomial Theorem ${\left(x+y\right)}^{n}=\sum _{k-0}^{n}\left(\begin{array}{c}n\\ k\end{array}\right){x}^{n-k}{y}^{k}$ $\left(r+1\right)th\text{\hspace{0.17em}}$ term of a binomial expansion $\left(\begin{array}{c}n\\ r\end{array}\right){x}^{n-r}{y}^{r}$
## Key concepts
• $\left(\begin{array}{c}n\\ r\end{array}\right)\text{\hspace{0.17em}}$ is called a binomial coefficient and is equal to $C\left(n,r\right).\text{\hspace{0.17em}}$ See [link] .
• The Binomial Theorem allows us to expand binomials without multiplying. See [link] .
• We can find a given term of a binomial expansion without fully expanding the binomial. See [link] .
## Verbal
What is a binomial coefficient, and how it is calculated?
A binomial coefficient is an alternative way of denoting the combination $\text{\hspace{0.17em}}C\left(n,r\right).\text{\hspace{0.17em}}$ It is defined as $\text{\hspace{0.17em}}\left(\begin{array}{c}n\\ r\end{array}\right)=\text{\hspace{0.17em}}C\left(n,r\right)\text{\hspace{0.17em}}=\frac{n!}{r!\left(n-r\right)!}.$
What role do binomial coefficients play in a binomial expansion? Are they restricted to any type of number?
What is the Binomial Theorem and what is its use?
The Binomial Theorem is defined as $\text{\hspace{0.17em}}{\left(x+y\right)}^{n}=\sum _{k=0}^{n}\left(\begin{array}{c}n\\ k\end{array}\right){x}^{n-k}{y}^{k}\text{\hspace{0.17em}}$ and can be used to expand any binomial.
When is it an advantage to use the Binomial Theorem? Explain.
## Algebraic
For the following exercises, evaluate the binomial coefficient.
$\left(\begin{array}{c}6\\ 2\end{array}\right)$
15
$\left(\begin{array}{c}5\\ 3\end{array}\right)$
$\left(\begin{array}{c}7\\ 4\end{array}\right)$
35
$\left(\begin{array}{c}9\\ 7\end{array}\right)$
$\left(\begin{array}{c}10\\ 9\end{array}\right)$
10
$\left(\begin{array}{c}25\\ 11\end{array}\right)$
$\left(\begin{array}{c}17\\ 6\end{array}\right)$
12,376
$\left(\begin{array}{c}200\\ 199\end{array}\right)$
For the following exercises, use the Binomial Theorem to expand each binomial.
${\left(4a-b\right)}^{3}$
$64{a}^{3}-48{a}^{2}b+12a{b}^{2}-{b}^{3}$
${\left(5a+2\right)}^{3}$
${\left(3a+2b\right)}^{3}$
$27{a}^{3}+54{a}^{2}b+36a{b}^{2}+8{b}^{3}$
${\left(2x+3y\right)}^{4}$
${\left(4x+2y\right)}^{5}$
$1024{x}^{5}+2560{x}^{4}y+2560{x}^{3}{y}^{2}+1280{x}^{2}{y}^{3}+320x{y}^{4}+32{y}^{5}$
${\left(3x-2y\right)}^{4}$
${\left(4x-3y\right)}^{5}$
$1024{x}^{5}-3840{x}^{4}y+5760{x}^{3}{y}^{2}-4320{x}^{2}{y}^{3}+1620x{y}^{4}-243{y}^{5}$
${\left(\frac{1}{x}+3y\right)}^{5}$
${\left({x}^{-1}+2{y}^{-1}\right)}^{4}$
$\frac{1}{{x}^{4}}+\frac{8}{{x}^{3}y}+\frac{24}{{x}^{2}{y}^{2}}+\frac{32}{x{y}^{3}}+\frac{16}{{y}^{4}}$
${\left(\sqrt{x}-\sqrt{y}\right)}^{5}$
For the following exercises, use the Binomial Theorem to write the first three terms of each binomial.
${\left(a+b\right)}^{17}$
${a}^{17}+17{a}^{16}b+136{a}^{15}{b}^{2}$
${\left(x-1\right)}^{18}$
${\left(a-2b\right)}^{15}$
${a}^{15}-30{a}^{14}b+420{a}^{13}{b}^{2}$
${\left(x-2y\right)}^{8}$
${\left(3a+b\right)}^{20}$
$3,486,784,401{a}^{20}+23,245,229,340{a}^{19}b+73,609,892,910{a}^{18}{b}^{2}$
${\left(2a+4b\right)}^{7}$
${\left({x}^{3}-\sqrt{y}\right)}^{8}$
${x}^{24}-8{x}^{21}\sqrt{y}+28{x}^{18}y$
For the following exercises, find the indicated term of each binomial without fully expanding the binomial.
The fourth term of $\text{\hspace{0.17em}}{\left(2x-3y\right)}^{4}$
The fourth term of $\text{\hspace{0.17em}}{\left(3x-2y\right)}^{5}$
$-720{x}^{2}{y}^{3}$
The third term of $\text{\hspace{0.17em}}{\left(6x-3y\right)}^{7}$
The eighth term of $\text{\hspace{0.17em}}{\left(7+5y\right)}^{14}$
$220,812,466,875,000{y}^{7}$
The seventh term of $\text{\hspace{0.17em}}{\left(a+b\right)}^{11}$
The fifth term of $\text{\hspace{0.17em}}{\left(x-y\right)}^{7}$
$35{x}^{3}{y}^{4}$
The tenth term of $\text{\hspace{0.17em}}{\left(x-1\right)}^{12}$
The ninth term of $\text{\hspace{0.17em}}{\left(a-3{b}^{2}\right)}^{11}$
$1,082,565{a}^{3}{b}^{16}$
The fourth term of $\text{\hspace{0.17em}}{\left({x}^{3}-\frac{1}{2}\right)}^{10}$
The eighth term of $\text{\hspace{0.17em}}{\left(\frac{y}{2}+\frac{2}{x}\right)}^{9}$
$\frac{1152{y}^{2}}{{x}^{7}}$
## Graphical
For the following exercises, use the Binomial Theorem to expand the binomial $f\left(x\right)={\left(x+3\right)}^{4}.$ Then find and graph each indicated sum on one set of axes.
Find and graph $\text{\hspace{0.17em}}{f}_{1}\left(x\right),\text{\hspace{0.17em}}$ such that $\text{\hspace{0.17em}}{f}_{1}\left(x\right)\text{\hspace{0.17em}}$ is the first term of the expansion.
Find and graph $\text{\hspace{0.17em}}{f}_{2}\left(x\right),\text{\hspace{0.17em}}$ such that $\text{\hspace{0.17em}}{f}_{2}\left(x\right)\text{\hspace{0.17em}}$ is the sum of the first two terms of the expansion.
${f}_{2}\left(x\right)={x}^{4}+12{x}^{3}$
Find and graph $\text{\hspace{0.17em}}{f}_{3}\left(x\right),\text{\hspace{0.17em}}$ such that $\text{\hspace{0.17em}}{f}_{3}\left(x\right)\text{\hspace{0.17em}}$ is the sum of the first three terms of the expansion.
Find and graph $\text{\hspace{0.17em}}{f}_{4}\left(x\right),\text{\hspace{0.17em}}$ such that $\text{\hspace{0.17em}}{f}_{4}\left(x\right)\text{\hspace{0.17em}}$ is the sum of the first four terms of the expansion.
${f}_{4}\left(x\right)={x}^{4}+12{x}^{3}+54{x}^{2}+108x$
Find and graph $\text{\hspace{0.17em}}{f}_{5}\left(x\right),\text{\hspace{0.17em}}$ such that $\text{\hspace{0.17em}}{f}_{5}\left(x\right)\text{\hspace{0.17em}}$ is the sum of the first five terms of the expansion.
## Extensions
In the expansion of $\text{\hspace{0.17em}}{\left(5x+3y\right)}^{n},\text{\hspace{0.17em}}$ each term has the form successively takes on the value $\text{\hspace{0.17em}}0,1,2,\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}n.$ If $\text{\hspace{0.17em}}\left(\begin{array}{c}n\\ k\end{array}\right)=\left(\begin{array}{c}7\\ 2\end{array}\right),\text{\hspace{0.17em}}$ what is the corresponding term?
$590,625{x}^{5}{y}^{2}$
In the expansion of $\text{\hspace{0.17em}}{\left(a+b\right)}^{n},\text{\hspace{0.17em}}$ the coefficient of $\text{\hspace{0.17em}}{a}^{n-k}{b}^{k}\text{\hspace{0.17em}}$ is the same as the coefficient of which other term?
Consider the expansion of $\text{\hspace{0.17em}}{\left(x+b\right)}^{40}.\text{\hspace{0.17em}}$ What is the exponent of $b$ in the $k\text{th}$ term?
$k-1$
Find $\text{\hspace{0.17em}}\left(\begin{array}{c}n\\ k-1\end{array}\right)+\left(\begin{array}{c}n\\ k\end{array}\right)\text{\hspace{0.17em}}$ and write the answer as a binomial coefficient in the form $\text{\hspace{0.17em}}\left(\begin{array}{c}n\\ k\end{array}\right).\text{\hspace{0.17em}}$ Prove it. Hint: Use the fact that, for any integer $\text{\hspace{0.17em}}p,\text{\hspace{0.17em}}$ such that $\text{\hspace{0.17em}}p\ge 1,\text{\hspace{0.17em}}p!=p\left(p-1\right)!\text{.}$
$\left(\begin{array}{c}n\\ k-1\end{array}\right)+\left(\begin{array}{l}n\\ k\end{array}\right)=\left(\begin{array}{c}n+1\\ k\end{array}\right);\text{\hspace{0.17em}}$ Proof:
$\begin{array}{}\\ \\ \\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\begin{array}{c}n\\ k-1\end{array}\right)+\left(\begin{array}{l}n\\ k\end{array}\right)\\ =\frac{n!}{k!\left(n-k\right)!}+\frac{n!}{\left(k-1\right)!\left(n-\left(k-1\right)\right)!}\\ =\frac{n!}{k!\left(n-k\right)!}+\frac{n!}{\left(k-1\right)!\left(n-k+1\right)!}\\ =\frac{\left(n-k+1\right)n!}{\left(n-k+1\right)k!\left(n-k\right)!}+\frac{kn!}{k\left(k-1\right)!\left(n-k+1\right)!}\\ =\frac{\left(n-k+1\right)n!+kn!}{k!\left(n-k+1\right)!}\\ =\frac{\left(n+1\right)n!}{k!\left(\left(n+1\right)-k\right)!}\\ =\frac{\left(n+1\right)!}{k!\left(\left(n+1\right)-k\right)!}\\ =\left(\begin{array}{c}n+1\\ k\end{array}\right)\end{array}$
Which expression cannot be expanded using the Binomial Theorem? Explain.
• $\left({x}^{2}-2x+1\right)$
• ${\left(\sqrt{a}+4\sqrt{a}-5\right)}^{8}$
• ${\left({x}^{3}+2{y}^{2}-z\right)}^{5}$
• ${\left(3{x}^{2}-\sqrt{2{y}^{3}}\right)}^{12}$
The expression $\text{\hspace{0.17em}}{\left({x}^{3}+2{y}^{2}-z\right)}^{5}\text{\hspace{0.17em}}$ cannot be expanded using the Binomial Theorem because it cannot be rewritten as a binomial.
#### Questions & Answers
how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
please can go further on polynomials quadratic
Abdullahi
hi mam
Mark
I need quadratic equation link to Alpa Beta
find the value of 2x=32
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
yes i wantt to review
Mark
use the y -intercept and slope to sketch the graph of the equation y=6x
how do we prove the quadratic formular
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
x+2y-z=7
Sidiki
what is the coefficient of -4×
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
An investment account was opened with an initial deposit of \$9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
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# Proving the inequality $\sup_{s\in{[0,1]}}\int_0^1|(1-\cos(st^2))s| \, dt<1$
I want to show this:
$$S=\sup_{s\in{[0,1]}}\int_0^1|(1-\cos(st^2))s| \, dt<1$$
1. Since $1-\cos(st^2)$ is decreasing (fixed a $s$) for $t \in[0,1]$ so we have this: $$\sup_{s\in{[0,1]}}s\int_0^11-\cos(st^2) \, dt$$
2. So if I prove $\int_0^1 1-\cos(st^2) \, dt< 1$ then we have $S<1$.
Setting $x=st^2$ $$1-\cos(st^2)=1-\cos(x)$$
Since $$\cos(x)>\frac{x}{2}\quad \forall x\in[0,1]$$
we have $$1-\cos(x)<1-\frac{x}{2}$$ then$$\int_0^11-\cos(st^2) dt<\int_0^1 1-\frac{s t^2}{2}dt= 1-\frac{s}{6}=\frac{6-s}{6}$$
so $$\sup_{s\in[0,1]} s\left(\frac{6-s}{6}\right)<1$$
Is this correct? Please let me know if some point is wrong, thanks1!
I could see one wrong, in point 1 of your solution, you said $1-cos(st^2)$ is decreasing on the interval for $s$ being constant, and $t\in [0,1]$ whereas the function should be increasing. If you think properly you surely can get that. In other parts I could not find any problem. If there is any retrospective effect of the mistake after considering the error I pointed out and then check out the places and see the solution.
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## SUMIFS criteria: INDEX MATCH or XLOOKUP criteria
Using the SUMIFS function, we can sum all of the values in a defined column (or row) that meet one or more criteria. SUMIFS criteria can reference cells, contain values or text, contain logical tests, or contain formulas and functions. By nesting the INDEX MATCH combination or the XLOOKUP function as SUMIFS criteria, we can return values based on criteria that are not present in the table we are returning values from. Consider the following example: This table contains (repeating)
## Combining SUMIFS with XLOOKUP
Using the SUMIFS function, we can sum all of the values in a defined column (or row) that meet one or more criteria. When SUMIFS is combined with XLOOKUP, that sum range doesn’t have to be defined anymore; it is now rather specified in the function arguments. By combining SUMIFS with XLOOKUP, we can then sum all of the values that meet multiple criteria in different rows and columns and do this in a simple way, avoiding complex and resource-intensive
## Combining SUMIFS with INDEX MATCH
Using the SUMIFS function, we can sum all of the values in a defined column (or row) that meet one or more criteria. When SUMIFS is combined with INDEX MATCH, that sum range doesn’t have to be defined anymore; it is now rather specified in the function arguments. By combining SUMIFS with INDEX MATCH, we can then sum all of the values that meet multiple criteria in different rows and columns and do this in a simple way, avoiding complex and
## Conditional calculations
IF functions for cell ranges Using conditional statements, i.e., the IF function, we can test conditions and perform actions if conditions are met. This IF-THEN-ELSE conditional processing is useful when we want to add something new to our rows. However, it is not really appropriate for retrieving data from or about whole ranges of cells, sometimes containing thousands of rows and columns. For example, in order to sum the incentive paid out to “green” team members, we had to
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A269790 Primes p such that 2*p + 79 is a square. 1
73, 181, 2341, 4861, 6121, 9901, 12601, 18973, 20161, 26641, 47701, 51481, 59473, 61561, 68041, 79561, 81973, 84421, 94573, 110881, 157321, 185401, 192781, 207973, 231841, 244261, 248473, 270073, 292573, 335341, 365473, 440821, 446473, 452161, 475273 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 COMMENTS Primes of the form 2*k^2 + 2*k - 39. 2*p + h is not verified if h is an odd prime that belongs to A055025 because (2*h-1)/2 is a multiple of 2. LINKS EXAMPLE a(1) = 73 because 2*73 + 79 = 225, which is a square. MATHEMATICA Select[Prime[Range[50000]], IntegerQ[Sqrt[2 # + 79]] &] PROG (MAGMA) [p: p in PrimesUpTo(600000) | IsSquare(2*p+79)]; (PARI) lista(nn) = {forprime(p=2, nn, if(issquare(2*p + 79), print1(p, ", "))); } \\ Altug Alkan, Mar 24 2016 (Python) from sympy import isprime from gmpy2 import is_square for p in xrange(0, 1000000): if(is_square(2*p+79) and isprime(p)):print(p) # Soumil Mandal, Apr 03 2016 CROSSREFS Cf. A000040. Subsequence of A002144, A045433, A061237, A068228. Cf. similar sequences listed in A269784. Sequence in context: A044786 A244774 A142550 * A142741 A088199 A140010 Adjacent sequences: A269787 A269788 A269789 * A269791 A269792 A269793 KEYWORD nonn AUTHOR Vincenzo Librandi, Mar 24 2016 STATUS approved
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linsolve
Solve symbolic linear equations in matrix form
Syntax
``X = linsolve(A,B)``
``````[X,R] = linsolve(A,B)``````
Description
example
````X = linsolve(A,B)` solves the matrix equation AX = B, where `A` is a symbolic matrix and `B` is a symbolic column vector.```
example
``````[X,R] = linsolve(A,B)``` also returns the reciprocal of the condition number of `A` if `A` is a square matrix. Otherwise, `linsolve` returns the rank of `A`.```
Examples
collapse all
Solve this system of linear equations in matrix form by using `linsolve`.
`$\left[\begin{array}{ccc}2& 1& 1\\ -1& 1& -1\\ 1& 2& 3\end{array}\right]\left[\begin{array}{c}\mathit{x}\\ \mathit{y}\\ \mathit{z}\end{array}\right]=\left[\begin{array}{c}2\\ 3\\ -10\end{array}\right]$`
```A = [ 2 1 1; -1 1 -1; 1 2 3]; B = [2; 3; -10]; X = linsolve(A,B)```
```X = 3×1 3 1 -5 ```
The solutions are $\mathit{x}=3$, $\mathit{y}=1$, and $\mathit{z}=-5$.
Compute the reciprocal of the condition number of the square coefficient matrix by using two output arguments.
```syms a x y z A = [a 0 0; 0 a 0; 0 0 1]; B = [x; y; z]; [X, R] = linsolve(A, B)```
```X = $\left(\begin{array}{c}\frac{x}{a}\\ \frac{y}{a}\\ z\end{array}\right)$```
```R = $\frac{1}{\mathrm{max}\left(|a|,1\right) \mathrm{max}\left(\frac{1}{|a|},1\right)}$```
If the coefficient matrix is rectangular, `linsolve` returns the rank of the coefficient matrix as the second output argument. Show this behavior.
```syms a b x y A = [a 0 1; 1 b 0]; B = [x; y]; [X,R] = linsolve(A,B)```
```Warning: Solution is not unique because the system is rank-deficient. ```
```X = $\left(\begin{array}{c}\frac{x}{a}\\ -\frac{x-a y}{a b}\\ 0\end{array}\right)$```
`R = $2$`
Input Arguments
collapse all
Coefficient matrix, specified as a symbolic matrix.
Right side of equations, specified as a symbolic vector or matrix.
Output Arguments
collapse all
Solution, returned as a symbolic vector or matrix.
Reciprocal condition number or rank, returned as a symbolic number of expression. If `A` is a square matrix, `linsolve` returns the condition number of `A`. Otherwise, `linsolve` returns the rank of `A`.
collapse all
Matrix Representation of System of Linear Equations
A system of linear equations is as follows.
`$\begin{array}{l}{a}_{11}{x}_{1}+{a}_{12}{x}_{2}+\dots +{a}_{1n}{x}_{n}={b}_{1}\\ {a}_{21}{x}_{1}+{a}_{22}{x}_{2}+\dots +{a}_{2n}{x}_{n}={b}_{2}\\ \cdots \\ {a}_{m1}{x}_{1}+{a}_{m2}{x}_{2}+\dots +{a}_{mn}{x}_{n}={b}_{m}\end{array}$`
This system can be represented as the matrix equation $A\cdot \stackrel{\to }{x}=\stackrel{\to }{b}$, where A is the coefficient matrix.
`$A=\left(\begin{array}{ccc}{a}_{11}& \dots & {a}_{1n}\\ ⋮& \ddots & ⋮\\ {a}_{m1}& \cdots & {a}_{mn}\end{array}\right)$`
$\stackrel{\to }{b}$ is the vector containing the right sides of equations.
`$\stackrel{\to }{b}=\left(\begin{array}{c}{b}_{1}\\ ⋮\\ {b}_{m}\end{array}\right)$`
Tips
• If the solution is not unique, `linsolve` issues a warning, chooses one solution, and returns it.
• If the system does not have a solution, `linsolve` issues a warning and returns `X` with all elements set to `Inf`.
• Calling `linsolve` for numeric matrices that are not symbolic objects invokes the MATLAB® `linsolve` function. This function accepts real arguments only. If your system of equations uses complex numbers, use `sym` to convert at least one matrix to a symbolic matrix, and then call `linsolve`.
Version History
Introduced in R2012b
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# expand calculator
Calculator is able to expand an algebraic expression online and remove unnecessary brackets.
Here somes examples of using the computer to expand algebraic expression:
### Expand, online calculus
#### Summary :
Calculator is able to expand an algebraic expression online and remove unnecessary brackets.
expand online
# Expand calculator
In mathematics, to expand an expression or to expand a product that is transformed into algebraic sum. This calculator allows to expand all forms of algebraic expressions online, it also helps to calculate special expansions online (the difference of squares, the identitiy for the square of a sum and the identity for the square of a difference). For simple expansions, the calculator gives the calculation steps.
## Expand algebraic expressions
the expansion calculator allows to expand online all forms of mathematical expressions, the expression can be alphanumeric, ie it can contain numbers and letters :
• Expand the following product (3 x+ 1) (2 x+ 4) (3x+1)(2x+4) returns 3*x*2*x+3*x*4+2*x+4
• Expand this algebraic expression (x+2)^3 returns 2^3+3*x*2^2+3*2*x^2+x^3
Note that the result is not returned as the simplest expression in order to be able to follow the steps of calculations. To simplify the results, simply use the reduce function.
## Special expansions online
The expansion calculator makes it possible to expand a product, it applies to all mathematical expressions, especially the following identities :
• the identitiy for the square of a sum : It allows to expand online expressions of the form (a+b)^2
• the identity for the square of a difference : It allows to expand online expressions of the form (a-b)^2
• the difference of squares : It allows to expand online expressions of the form (a-b)(a+b)
## Use of Newton's binomial formula
Newton's binomial formula is written : (a+b)^n=sum_(k=0)^{n} ((n),(k)) a^k*b^(n-k). The numbers ((n),(k)) are the binomial coefficients, they are calculated using the following formula : ((n),(k))=(n!)/(k!(n-k)!).
We note, that by replacing n by 2, we can find remarkable identities.
The calculator uses Newton's formula to develop expressions of the form (a+b)^n.
## Expand and simplify an expression
The calculator allows you to expand and collapse an expression online, to achieve this, the calculator combines the functions collapse and expand. For example it is possible to expand and reduce the expression following (3x+1)(2x+4), The calculator will returns the expression in two forms :
• expanded expression 3*x*2*x+3*x*4+2*x+4
• expanded and reduced expression 4+14*x+6*x^2.
#### Syntax :
expand(expression), expression is expression algebraic to expand.
#### Examples :
Here somes examples of using the computer to expand algebraic expression:
Calculate online with expand (expand calculator)
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# Parallel Universes
### By Paul Hughes-Barlow
We all live in our own parallel universe. Everyone sees you from a slightly different angle to everyone else. Each angle is unique since each person occupies their own space.
Back in 1852 Bernhard Riemann created a new geometry that did away with the Euclidean geometry. Riemannian geometry is all about space, curved surfaces and multiple dimensions. But he was way ahead of his time and it's only recently that the significance of his insights have been realized.
In 1904, Einstein was working on his Special Theory of Relativity, but he had a problem. He did not have the mathematical formulae to make his theory work, and it was not until someone showed him Riemann's theorems that he had the answer. Space-time geometry is Riemannian. Einstein's theories held sway until until the beginning of the 1930s when Quantum Mechanics was king. Quantum Mechanics was so accurate that science thought it could answer the ultimate questions about the universe.
In 1988, Stephen Hawking in his 'A Brief History of Time' was able to dismiss theories that had multiple dimensions, but at the start of the 21st century, physicists are scrambling to learn Riemannian geometry as it is at the heart of Superstring Theory and M Theory. M Theory is the latest mathematical and geometrical model that not only unites the four forces of nature (Electromagnetism, Strong Force, Weak Force and Gravity), but allows physicists to see before the Big Bang 15 billion years ago. These theories postulate that we have an infinite number of parallel universes all slightly different.
I first came across the Hegelian Dialect, a concept over 2,000 years old, when I was researching the Golden Dawn Opening of the Key Tarot spread. The system of Elemental Dignities is based upon the Hegelian Dialect. The Hegelian Dialect looks at objects as either similar or different, thesis or antithesis, and then we can create the synthesis or relationship between the two. In Elemental Dignities, we see that Fire and Water are opposites, so they weaken each other, and create either Air or Earth. The Father and Mother unite to create the child, which is either a boy or a girl. Air and Earth are also opposites, and they cancel each other out. Fire and Air are active and friendly, while Water and Earth are passive and friendly. In other words, Elemental Dignities are a form of the Hegelian Dialect.
It is characteristic of all high spiritual vision that the formulation of any idea is immediately destroyed or cancelled out by the arising of the contradictory. So, we have the uniting energy of love separating chaos from order – it is a paradox. "Love is the Law, Love under Will" is an inspiration from this insight.
We are now in a position to understand what might be happening in a tarot reading. The parallel universe of the Tarot reader (thesis) and the parallel universe of the client (antithesis) meet at the synthesis of the tarot spread. Significantly, Crowley discusses the individual tarot cards has having their own universe.
Hegel did not invent the Dialect; he took the idea from the Kabbalah, in particular the Sepher Yetsirah, while 2,000 years ago the Greeks understood the concept. It is now time to reclaim a fundamental principal that drives not only the creation of our Universe but is the basis of the Tree of Life, the Golden Dawn teachings and the Tarot.
At the level of Wisdom (on the Kabbalah's Tree of Life), the duality is not present, so it is only on levels below Wisdom that people are separated into different individuals. Only on lower levels does the division between good and evil exist. According to Kaplan, "Wisdom is the pure mind force that transcends time. On the level of Wisdom, past, present and future have not yet been separated. Hence, on this level, one can see the future just like the past and present."
Further research has shown that Crowley was looking for a mathematical model of consciousness as early as 1900, but this has been obscured by his notoriety as magician. An early influence was the Theosophical Society founded by Mme Blavatsky. She quotes Hegel in terms of the Vedantic philosophy, and her own vision is of an infinite number of universes manifesting and disappearing using the Vedantic model. A follower of Theosophy, Rudolf Steiner, founded the Anthroposophical Society. Steiner was deeply influenced by geometry, and he developed the system of Projective Synthetic Geometry, the geometrical designs of which were incorporated into the Thoth Tarot under the tutelage of Olive Whicher. A colleague of Olive Whicher was George Adams who was a student of Bertrand Russell, philosopher and mathematician, who was a friend of Albert Einstein. Crowley quotes Russell in the Book of Thoth. In order to understand the ideas in the Book of Thoth, we have to study a vast range of sources in addition to the magical writings of Aleister Crowley.
Research with my colleague, Tim Rifat, suggests that Aleister Crowley hid a magical system using Riemannian and Projective Synthetic Geometry as a model of consciousness in the text and designs of the Thoth Tarot. This magical system was used by Crowley in a magical war against the Nazis in World War II. The first public unveiling of the Thoth Tarot cards in London, July 1st 1942 was at a pivotal moment in the war when the Allies began to have victories against Germany.
In a letter on July 5th 1942, Dion Fortune, magician and colleague of Aleister Crowley, wrote that now the War had been won on the Inner Planes, her attention was now turning to events after the war.
Paul's web site: Supertarot
More Esoteric History & Philosophy articles
Good info on many topics:
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### Welcome Back,
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• 0
Teacher
# The next number in the series 20 23 28 14 17 22 11
The next number in the series 20 23 28 14 17 22 11
### Related Questions
1. 20,23,28,14,17,22,11,
2. Beginning with the 20, the set of rules to get the next 3 terms is:
Add 3 . . . . . 23
Add 5 . . . . . 28
Take half. . . 14
Add 3 . . . . . 17
Add 5 . . . . . 22
Take half. . . 11
Next comes:
Add 3 . . . . . 14
Add 5 . . . . . 19
• 0
Pundit
# The next number in the series 20 23 28 14 17 22 11?
The next number in the series 20 23 28 14 17 22 11?
### Related Questions
1. 14 and then 19 are the next two numbers in the sequence
Beginning with the 20, the set of rules to get the next 3 terms is:
```Add 3 . . . . . 23
Add 5 . . . . . 28
Take half. . . 14
Add 3 . . . . . 17
Add 5 . . . . . 22
Take half. . . 11
Next comes:
Add 3 . . . . . 14
Add 5 . . . . . 19```
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The Learning Point > Mathematics >
Calculus - Differential Calculus - Problem Set III - Outline of Contents (Also try out the MCQ Quiz at the end):
This tutorial contains examples and solved problems - related to increasing and decreasing functions; maxima, minima and extreme values; Rolle's Theorem ; inspection of polynomials and trigonometric expressions.
Here's a quick look at the kind of problems which have been solved in this tutorial. We will try to sketch some curves and inspect them visually as well.
• Verify Rolle’s theorem for (i)x2 in [−1, 1]. (ii)x(x + 3)e−x/2 in [−3, 0].
• Learning to apply Leibnitz formula for differentiation.
• Seperate the intervals in which the polynomial 2x3 − 15x2 + 36x + 1 is increasing or decreasing. Also draw the graph of the function.
• Show that x2 > (1 + x)[log (1 + x)]2 for x > 0.
• Find the greatest and the least values of 3x4 − 2x3 − 6x2 + 6x + 1 in the interval [0, 2].
• Examine the polynomial 10x6 − 24x5 + 15x4 − 40x3 + 108 for maximum and minimum values.
• Find the extreme values of x4 − 8x3 + 22x2 − 24x + 1 and distinguish between them.
• Find the maximum and minimum values of the polynomial 8x5 − 15x4 + 10x2 .
• Find the maximum and the minimum values of the function sin x + cos 2x.
• Find the slope and concavity of the graph of x2 y + y 4 = 4 + 2x at the point (−1, 1).
• Consider the equation x2 + xy + y 2 = 1. Find equations for y and y in terms of x and y only.
This way, you will gain an understanding of maxima and minima; be familiar with what it means for a function to be monotonically increasing or monotonically decreasing or have zeros, in a particular range. The process of finding and identifying a maxima or minima is known as optimization.
To gain a good understanding of maxima/minima, it is important to visualize and draw curves or figures. Looking at a function, one should intuitively be able to identify its zeros or the points where dy/dx = 0, in-flexion points, points of continuity and dis-continuity; points where the curve may not be differentiable.
MCQ Quiz- Differential Calculus and Mean Value Theorems
Companion MCQ Quiz for Differential Calculus and Mean Value Theorems: test how much you know about the topic. Your score will be e-mailed to you at the address you provide.
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# If the value of g suddenly becomes twice its value, it will become two times more difficult to pull a heavy object along the floor. Why?
S. Giri
63 Points
6 years ago
To pull object on the floor we should apply force on it. In this case force is equals to product of mass of that object (m) and g. That is F=gm .Here force is directly proportional to g.. And. m....hence if g becomes double without any change in mass then force also become double. Hence it will become two times more difficult to pull the object on the floor. Rather than for extra information if we thrice the g and twice the mass then required force will be (i.e. F = 3g ✖ 2m = 6 gm =6 F. ) sixth time more.
SR Roy
128 Points
6 years ago
To pull object on the floor we should apply force on it. In this case force is equals to product of mass of that object (m) and g. That is F=gm .Here force is directly proportional to g.. And. m....hence if g becomes double without any change in mass then force also become double. Hence it will become two times more difficult to pull the object on the floor. Rather than for extra information if we thrice the g and twice the mass then required force will be (i.e. F = 3g ✖ 2m = 6 gm =6 F. ) sixth time more.
S. Giri
63 Points
6 years ago
One of the two . answer i.e. first response is given by me but someone copied it and gave same answer after some time, what is this going this is wrong stop it and give your own answer.
Subhash Kumar Mehta
100 Points
6 years ago
when we pull the heavy object only friction force opposes the motion of object and we know that friction force is proportional to the vertical contact force and vertical force is given by Fv=mg which further depends on g so whem g is twice Fv is twice
Subhash Kumar Mehta
100 Points
6 years ago
........carried forward when g becomes twice then Fv will become twice which will further double the frictional force so twice force is needed to move the object»REGARDS»Subhash Kumar»St. Xavier`s College, Ranchi
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# Lernkarten
Karten 30 Karten 2 Lernende English Universität 24.09.2020 / 27.09.2020 Keine Angabe
0 Exakte Antworten 30 Text Antworten 0 Multiple Choice Antworten
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
e. Third Quartile
e. Using the QUARTILE command in Excel (as per the lecture), we find the third quartile (Q3) value to be 183.75. Three-quarters (75%) of the families in our sample paid $183.75 or less to have their taxes prepared. 9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics: f. 90 Percentile f. Using the PERCENTILE command in Excel (as per the lecture), we find the 90th Percentile (P90) value to be 237. 90% of the families in our sample paid$237 or less to have their taxes prepared.
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
g. Five-Number Summary
g. Using the MIN and MAX commands in Excel, we find the lowest value is 100 and the highest value is 360. So the Five Number Summary is: 100, 115, 135, 183.75, 360
10. The following data measure the price of a stock at the end of six consecutive quarters. 182 168 184 190 170 174 Use your calculator (not Excel) to calculate the following statistic values.
a. Mean
b. Variance
c. Standard Deviation
Lizenzierung: Keine Angabe
11. The cost of renting a car for one month in Switzerland varies depending on location and the type of car being rented. Suppose this cost has a mean of 3,100 CHF and a standard deviation of 1,200 CHF. Calculate the standardized value for each of the following costs. Then interpret each of these Z-score values. Finally, explain why each value either would or would not be considered an outlier here.
a. 2,300 CHF
b. 4,900 CHF
c. 13,000 CHF
Lizenzierung: Keine Angabe
Lizenzierung: Keine Angabe
12.
Lizenzierung: Keine Angabe
b. Examining the graph in part “a” we see that there appears to be a positive linear relationship. (The variables tend to move in the same direction; e.g., as one goes up, the other also tends to go up.)
c. Using the CORREL command in Excel (as per the lecture), we find the correlation value to be 0.69.
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1. Given the following number line, place an x where 324 is approximately |300——————————-400| Explain with words how you determined where the x should be placed.
2. Mrs. B. left school at 3:25. She had to stop at the Dr’s office, that was 15 minutes from school. Then, she went to the grocery store. It took her 30 minutes to buy what she needed for dinner. After going to the store she drove home. What time could Mrs. B. have gotten home? Explain how you got your answer with words or pictures.
3. Dan had some money, all dollar bills larger than \$1. He bought a movie for \$16.50 and spent \$6.50 on candy. Explain how much money Dan could have started with.
4. Look at a page of a story book that has both text and picture. Which area is greater? The area for the text or the area for the picture?
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Understanding through Discussion
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Possibility Order of Magnetude Metric (POMM)
Author Topic: Possibility Order of Magnetude Metric (POMM)
RAZD
Member (Idle past 519 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004
Message 1 of 5 (722198) 03-18-2014 7:10 AM
We see any number of arguments that "X" is possible when dealing with YEC arguments.
Example: speed of movement of tectonic plates -- to get from one continent just after the flood (so the animals can disperse to their current locations) the blocks must move at a pretty fantastic clip ... is it possible?
Technically anything is "possible" but a critical analysis says that it is not very possible ...
To get a handle on this I propose a metric to deal with this issue: The POMM, the "Possibility Order of Magnitude Metric."
Take the current known maximum rate (CKMR)-- any proposal that uses this rate is assigned a POMM value of 1 (highly possible)
Double that rate is assigned a POMM of 0.5 (fairly possible)
The rest is an exponential curve:
POMM = (1/2)r
where r = proposed rate / CKMR
So if one proposes that continents move at 1 foot per day when the CKMR is 1 inch per year the POMM would be (1/2)(12x365) = 3.080484244×10⁻¹³¹⁹
Edited by Admin, : Remove unnecessary and possibly confusing "^" characters.
we are limited in our ability to understand
by our ability to understand
Rebel American Zen Deist
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Replies to this message: Message 3 by Stile, posted 03-18-2014 9:24 AM RAZD has responded
RAZD
Member (Idle past 519 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004
Message 5 of 5 (722231) 03-18-2014 10:46 PM Reply to: Message 3 by Stile03-18-2014 9:24 AM
My first question was "why an exponential curve?" ...
Well, I saw it as including scientific tentativity, that the possibility could not be absolutely ruled out, never reach zero ... just get very close to zero fairly rapidly the more outrageous the claims.
Taking that sort of position into account... I don't see this "additional rational exercise" being helpful in trying to show a creationist the error of their ways. It seems like the rebuttal would just be another "tree rings worked differently then!!!" kind of denial...
YEC 6,000 year old earth vs current known maximum age 4.55 billion years ... meaning an average apparent aging rate of
4.55x10^9/6x10^3 = 7.58x^5 years per year
so POMM = (1/2)^7.58x^5 = 1.8×10^-228181
Near zero yes?
we are limited in our ability to understand
by our ability to understand
Rebel American Zen Deist
... to learn ... to think ... to live ... to laugh ...
to share.
• • • Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click) • • •
This message is a reply to: Message 3 by Stile, posted 03-18-2014 9:24 AM Stile has acknowledged this reply
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# AHSEC - Class 12 Question Papers: CMST' 2019
2019
COMMERCIAL MATHEMATICS AND STATISTICS
Full Marks: 100
Pass Marks: 30
Time: Three hours
The figures in the margin indicate full marks for the questions
1. Answer the following questions as directed: 1x8=8
1. Is the set a null set?
2. Find the co-factor ofin the following determinant.
1. What is the difference between simple interest and compound interest?
2. Write True or False: ‘Every null matrix is a square matrix’
3. Fill in the gap: A.M. x H.M. = _____
4. What is the arithmetic mean of first n natural numbers?
5. What is the minimum value that the probability of an event can take?
6. Fill in the gap: Standard deviation is always _____.
2. Answer the following questions in brief: 2x5=10
1. What is the difference between and?
2. For what value of x the matrixwill be singular?
3. What is perpetual annuity?
4. Iffind n.
5. If, show that, a and b are constants.
3. Find the simple interest on Rs. 6000 from 4th March, 2017 to 28th July, 2017 @ 5% p.a. 3
4. If, find n. 3
Or
Ifand, find n and r.
5. Without expanding show that: 3
Or
If 3
what is the value of x and y?
6. Find the Mean Deviation from median from the given marks of 7 students. 3
18, 26, 15, 20, 17, 12, 25
7. Write any two algebraic properties of Arithmetic Mean. 3
Or
Calculate the Harmonic Mean of 4, 8 and 12. 3
8. The value of a machine at the end of a year becomes 90% of its value at the beginning of that year. The machine was bought at Rs. 4800 and after using it for some years it was sold at Rs. 1800. How many years was the machine in use? 5
9. A committee of 6 is to be formed out of 7 gentleman and 4 ladies. In how many ways can the committee be formed, if at least 2 ladies are to be included? 5
10. Mr. Roy borrows Rs. 20,000 at 4% compound interest and agrees to pay both principal and interest in 10 equal annual installment at the end of each year. Find the amount of each installment.
Given
11. Show that there will be no term containingin the expansion of 5
Or
If the coefficients ofandin the expansion ofare equal, find the value of k. 5
12. Prove by mathematical induction that the sum of first n odd natural numbers is
Or
Using mathematical induction prove that 5
for all
13. Draw the graph of: (any one) 5
14. Calculate the missing frequency, you are given that arithmetic mean is 50.9.
Marks: 0-20 20-40 40-60 60-80 80-100 Frequency: 5 - 30 12 8
Or
Iffind 4
15. (a) Prove that: 4
(b) Solve: 4
Or
If and, show that 4
16. (a) Calculate Standard Deviation from the following data: 4
Class: 10-19 20-29 30-39 40-49 50-59 60-69 70-79 Frequency: 3 61 223 137 53 19 4
(b) Calculate coefficient of variation from the data given in Question 16. (a). 4
17. (a) Two dice are thrown simultaneously. Find the probability of getting even number on both the dice. 4
(b) A bag contains 4 red, 3 blue and 3 white balls. 2 balls are drawn at random from it. Find the probability of getting
1. 2 red and 1 blue ball.
2. 2 balls of the same colour. 4
Or
Define and give one example of each: 2+2=4
1. Mutually exclusive events.
2. Positive correlation.
18. (a) Find out Karl Person’s coefficient of correlation. 6
X: 2 2 4 5 5 Y: 6 3 2 6 4
(b) Karl Person’s coefficient of correlation between two variables x and y is 0.28 and their covariance is 7.6. If the variance of x is 9, find the standard deviation of y. 2
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ADOBE AFTER EFFECTS: Forum Expressions Tutorials Creative Cloud
# Animate position in isometric 2D space
FAQ • VIEW ALL
Animate position in isometric 2D space by Chris Voon Aug 20, 2015 at 9:08:11 pm
Hi All,
I have an isometric project that will require a lot of position animation -- is there a technique to quickly and accurately animate my position movements along my isometric grid? For example when you hold shift, it constrains your movement linear x and y -- can you do something similar along 30degrees/150degrees (any degree).
Currently I've overlaid my isometric grid in my comp and eyeballing it but I'm curious if there's a more precise/systematic way of doing it.
Thanks,
Re: Animate position in isometric 2D spaceon Aug 21, 2015 at 7:56:17 amLast Edited By Kalle Kannisto on Aug 21, 2015 at 7:57:45 am
Here's how you could do it for 30 degree isometric:
Make a precomp that is a square, about 1.5 times the longer dimension of your final comp. Put your isometric elements inside the precomp and scale each of your original elements to 173,2% (square root of 3 times 100%) on the y axis, then rotate them 45%.
In your main comp, add two separate Transform effects to your precomp, the first one to rotate the comp -45 degrees, the second one to scale the height to 57,7% (1 divided by square root of 3 times 100%).
Now you can drag anything inside the precomp x and y axis and it will become the 30/150 degree isometric axis in main comp.
Re: Animate position in isometric 2D spaceon Aug 21, 2015 at 10:57:10 am
Position a 2D layer which you'd like to move over the isometric grid in the center of your origin tile.
Add a Point Control effect to the layer and name it "Grid Position".
Add a Slider Control effect and name it "Tile Width". Measure the width of your isometric tile in pixels and adjust this slider accordingly.
Add a Slider Control effect and name it "Tile Height". Measure the height of your isometric tile in pixels and adjust this slider accordingly.
Alt+click the position stopwatch and enter the following expression:
```xGrid = effect("Grid Position")("Point")[0]; yGrid = effect("Grid Position")("Point")[1]; x = (xGrid - yGrid) * effect("Tile Width")("Slider")/2; y = (xGrid + yGrid) * effect("Tile Height")("Slider")/2; value + [x,y]```
You can now use the Grid Position effect to address the screen in tile units.
Re: Animate position in isometric 2D spaceon Aug 21, 2015 at 12:58:03 pm
@Walter: Nice!
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# Find the slope and the y-interept of the line y=-3/2x+6
###### Question:
Find the slope and the y-interept of the line
y=-3/2x+6
### At intersections with no stop or yield signs, you should slow down and be ready to stop. a. true b. false
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### Which quadrilateral with side lengths shown will have a perimeter of 20 meters? 3 m, 7 m, 3 m, 7 m 6 m, 5 m, 4 m, 6 m 6 m, 3 m, 5 m, 5 m 7 m, 4 m, 4 m, 6 m
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### (PLEASE HELP I WILL GIVE BRAINLIEST IF CORRECT (40 POINTS) Estimate the range of the product 43 x 77. Enter a hyphen (-) between the two numbers.
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### The San Andreas Fault in California exists along a _____ plate boundary.
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### Claire tried to evaluate 30x8 step by step
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### Why is it important to understand the audience for your cover letter ? A. So you can provide an explanation of why you left your previous jobs B. So you can provide information that relates directly to the audiences needs C. So you can provide references that your audience will be impressed by D. So you can provide a short summary of your future goals aspirations
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### Which rays are part of line BE? E O Ac and E O AR and Ac and AB OAB and A
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### Can any one give me answer plz?
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### Point B(6, −3) is translated using the rule (x−5, y+9). What is the y-coordinate of B′ ?
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### PLEASE NEED HELP REALLY FAST. I WILL GIVE 30 POINTS!!! Imagine you are an Acadian man or woman living in Canada at the time of the deportation. Write a letter to a relative in France to describe your experience. Include details from the lesson and the passages you read in your response.
PLEASE NEED HELP REALLY FAST. I WILL GIVE 30 POINTS!!! Imagine you are an Acadian man or woman living in Canada at the time of the deportation. Write a letter to a relative in France to describe your experience. Include details from the lesson and the passages you read in your response....
### Math troubles :/ greatly appreciated if you can helpThe volume of a sphere with a radius of 5 cm is approximately _[blank]_ cm.Enter the value that correctly fills in the blank in the previous sentence.Use 3.14 for π, and round your answer to the nearest hundredths place if necessary.
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### There are three factors that determine the elasticity of demand for goods and service. select all of the factors that determine the elasticity of demand?A) technology,B) market size, C) proportion of income, D) time, E)substitute goods and services,F) luxuries vs. necessities
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## (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
14 Lesson(s)
### Manufacturing Cat Toys (Day 1 of 2)
12th Grade Math » Unit: Matrices and Systems
12th Grade Math » Unit: Matrices and Systems
Troy, MI
Environment: Suburban
Big Idea:
Standards:
Favorites (3)
Resources (13)
Reflections (1)
### Manufacturing Cat Toys (Day 2 of 2)
12th Grade Math » Unit: Matrices and Systems
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Troy, MI
Environment: Suburban
Big Idea:
#### We can set up matrix equations - now it is time to solve them!
Standards:
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12th Grade Math » Unit: Review
Phoenix, AZ
Environment: Urban
Big Idea:
#### Students review by working through various stations at their own pace and receive immediate feedback on their work.
Standards:
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12th Grade Math » Unit: Matrices
Phoenix, AZ
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Big Idea:
#### Students use matrices to decode messages that lead to a hidden treasure in the classroom.
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12th Grade Math » Unit: Matrices and Systems
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### Matrices Test Review
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Phoenix, AZ
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#### Students answer questions on their personal response systems to guide the review for the test.
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#### Students find their love (if they didn’t find it yesterday) for matrices when they learn how much easier solving systems of equations can be.
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### Inverses of Matrices
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### Unit Review and Cryptography
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### Hop on the Carousel
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Big Idea:
#### Use a group activity to help students make sense of solving systems with matrices.
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12th Grade Math » Unit: Matrices
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### Inverses and Determinants
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### Matrices Exam
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Common Core Math
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1. /
2. CBSE
3. /
4. Class 08
5. /
6. Playing with Numbers worksheet...
Playing with Numbers worksheet for class 8
Table of Contents
myCBSEguide App
Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.
CBSE worksheets for Playing with Numbers worksheet for class 8 in PDF for free download. Maths worksheets for class 8 CBSE includes worksheets on Playing with Numbers as per NCERT syllabus. CBSE class 8 worksheets as PDF for free download Playing with Numbers worksheets. Users can download and print the worksheets on class 8 Mathematics Playing with Numbers for free.
Download Playing with Numbers worksheet for class 8
Playing with Numbers worksheet for class 8 Important Topics
• Introduction
• Numbers in General Form
• Games with Numbers
• Letters for Digits
• Tests of Divisibility
Some important Facts about Playing with Numbers worksheet for class 8
1. Numbers can be written in general form. Thus, a two digit number ab will be written as ab = 10a + b.
2. The general form of numbers are helpful in solving puzzles or number games.
3. The reasons for the divisibility of numbers by 10, 5, 2, 9 or 3 can be given when numbers are written in general form
NCERT Class 8 Mathematics Solved Worksheets
• Chapter 1: Rational Numbers
• Chapter 2: Linear Equations in One Variable
• Chapter 3: Understanding Quadrilaterals
• Chapter 4: Practical Geometry
• Chapter 5: Data Handling
• Chapter 6: Squares and Square Roots
• Chapter 7: Cubes and Cube Roots
• Chapter 8: Comparing Quantities
• Chapter 9: Algebraic Expressions and Identities
• Chapter 10: Visualising Solid Shapes
• Chapter 11: Mensuration
• Chapter 12: Exponents and Powers
• Chapter 13: Direct and Inverse Proportions
• Chapter 14: Factorisation
• Chapter 15: Introduction to Graphs
• Chapter 16: Playing with Numbers
Letters for Digits
Here we have puzzles in which letters take the place of digits in an arithmetic ‘sum’, and the problem is to find out which letter represents which digit; so it is like cracking a code. Here we stick to problems of addition and multiplication.
Here are two rules we follow while doing such puzzles.
1. Each letter in the puzzle must stand for just one digit. Each digit must be represented by just one letter.
2. The first digit of a number cannot be zero. Thus, we write the number “sixty three” as 63, and not as 063, or 0063
To download Printable worksheets for class 8 Mathematics and Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through the best app for CBSE students and myCBSEguide website.
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# Math
posted by .
A dog kennel owner needs to build a dog run (rectangular area) adjacent to a kennel cage (so that it is in the shape of a rectangle, but only three sides need to be built- one long side is already there). The short side walls of the run are to be cinder block (costs \$0.50 per square foot) and the outer walls are to be chain link fence (\$2.75 per square foot). Local regulations require the walls to be at least seven feet high and the are to measure no fewer than 120 square feet.
Any help would be greatly appericiated! I can't seem to find an equation with only one variable.
• Math -
uuuhu
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If you're seeing this message, it means we're having trouble loading external resources on our website.
# 方程简介
## 什么是等式?
$5+3=6+2$
$6-2=3+1$
$7-4=3$
## 方程
$\phantom{\rule{2em}{0ex}}$ $\begin{array}{rl}x+2& =6\\ 4+2& \stackrel{?}{=}6\\ 6& =6\end{array}$$\phantom{\rule{2em}{0ex}}$ $\begin{array}{rl}x+2& =6\\ 3+2& \stackrel{?}{=}6\\ 5& \ne 6\end{array}$
## 试试解一些问题
$3+g=10$
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# What is the rate, in cubic feet per minute, at which water
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What is the rate, in cubic feet per minute, at which water is flowing into a certain rectangular tank?
(1) The height of the water in the tank is increasing at the rate of 2 feet per minute.
(2) The capacity of the tank is 216 cubic feet.
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banksy wrote:
What is the rate, in cubic feet per minute, at which water is flowing into a certain rectangular tank?
(1) The height of the water in the tank is increasing at the rate of 2 feet per minute.
(2) The capacity of the tank is 216 cubic feet.
Clear E. Rate=volume/time and even when we combine the statements all we know is one dimension (2 feet) of the volume which flows into the tank per minute (we still need the width and length of the tank to calculate volume=2lw but from the second statement length*width*height=216 we can not get these values).
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26 Feb 2011, 23:08
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From 1 we have :
2 * l * b/min
From 2 we have :
h * l * b = 216
But we still can't get h ( or l*b), so answer is E.
l - length of base
h - height of base
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# Which transformations have been performed on the graph of f(x)= 3 √x to obtain the graph of g(x)=1/4x+ 3 √x+3+6?
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Which transformations have been performed on the graph of f(x)=3√x to obtain the graph of g(x)=1/4x+3√x+3+6?
translate the graph down
translate the graph to the right
stretch the graph away from the x-axis
reflect the graph over the x-axis
translate the graph to the left
compress the graph closer to the x-axis
translate the graph up
Mar 23, 2018
#1
+10357
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stretch the graph away from the x-axis
translate the graph to the left
translate the graph up
Mar 23, 2018
#1
+10357
+1
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## CatapultTrevor and Addison
vertex form- Y=a(x-h)2+K
Where (h,k) is the coordinate of the vertex
Is your catapult launching consistently every time? It is with in 2 1/2 feet each time.
What can you change to make the launch consistent? The launcher because sometimes sometimes she gets scared (Janessa) and doesn't pull the catapult all the way back.
What revisions can you make to your catapult to get a launch that goes farther? Have another bar to stop the bucket earlier.
Where do you need to place your target to hit a bullseye every time? Place the target right by where the vertex would be.
Where does your projectile hit the ground according to the equation you found? After roughly 28 feet.
What is the maximum height of the ball? When did the maximum height occur? Roughly 2.45 feet
How could you make the maximum height higher and what effect would it have on the path of the projectile? We could make a stopper that would stop the bar so that the initial is earlier and there for starts out at a higher distance. The new path or parabola would travel higher overall, but would not cover as much distance. We would also change maybe the person launching the catapult due to the fact that the launcher wasn't exerting the same type of force each time and wasn't launching it from the same spot. We could also make the arm longer and the base more sturdy.
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Lemma 77.29.2. Let $B \to S$ be as in Section 77.3. Let $(U, R, s, t, c)$ be a groupoid in algebraic spaces over $B$. Let $G \to U$ be the stabilizer group algebraic space.
1. The following are equivalent
1. $j : R \to U \times _ B U$ is separated,
2. $G \to U$ is separated, and
3. $e : U \to G$ is a closed immersion.
2. The following are equivalent
1. $j : R \to U \times _ B U$ is locally separated,
2. $G \to U$ is locally separated, and
3. $e : U \to G$ is an immersion.
3. The following are equivalent
1. $j : R \to U \times _ B U$ is quasi-separated,
2. $G \to U$ is quasi-separated, and
3. $e : U \to G$ is quasi-compact.
Proof. The group algebraic space $G \to U$ is the base change of $R \to U \times _ B U$ by the diagonal morphism $U \to U \times _ B U$, see Lemma 77.16.1. Hence if $j$ is separated (resp. locally separated, resp. quasi-separated), then $G \to U$ is separated (resp. locally separated, resp. quasi-separated). See Morphisms of Spaces, Lemma 66.4.4. Thus (a) $\Rightarrow$ (b) in (1), (2), and (3).
Conversely, if $G \to U$ is separated (resp. locally separated, resp. quasi-separated), then the morphism $e : U \to G$, as a section of the structure morphism $G \to U$ is a closed immersion (resp. an immersion, resp. quasi-compact), see Morphisms of Spaces, Lemma 66.4.7. Thus (b) $\Rightarrow$ (c) in (1), (2), and (3).
If $e$ is a closed immersion (resp. an immersion, resp. quasi-compact) then by the result of Lemma 77.29.1 (and Spaces, Lemma 64.12.3, and Morphisms of Spaces, Lemma 66.8.4) we see that $\Delta _{R/U \times _ B U}$ is a closed immersion (resp. an immersion, resp. quasi-compact). Thus (c) $\Rightarrow$ (a) in (1), (2), and (3). $\square$
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
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# Oh go dear! again… we Here
What is the missing one?
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$
[Some colours look alike, sorry about that, but then again you don't really need to be able to make a visual difference between them, do you? Oh and sorry for being slightly inconsistent just there - not a native speaker.]
Hint:
Should same colour digits be read from top to bottom or from left to right?
Here is a google sheet required by OmegaKrypton to make any analysis easier.
• the answer is given in the puzzle. “what is the missing ONE” – Omega Krypton Aug 4 '19 at 9:48
• @OmegaKrypton This doesn't explain a lot. – Arnaud Mortier Aug 4 '19 at 12:20
• @ArnaudMortier Rot13(Fgngvfgvpnyyl V jbhyq tb sbe 1) – Ak19 Aug 4 '19 at 12:24
• @Ak19 That's one of the hints :) keep it up! – Arnaud Mortier Aug 4 '19 at 12:26
• @Alto It is not by accident. I think that on PSE people usually rot13 this kind of questions though. – Arnaud Mortier Aug 4 '19 at 22:25
It's E!
Reasoning:
Using the RGB hex values for the colors given results in:
.
,
.
where the rows are, top to bottom, in the order of the first row by color. The colors in the rows in the original image are always in the same order from left to right, just shifted for each row. Reading the values by color from left to right, and arranging the rows in the same way, we get:
.
.
which happens to be the same. In summary, the numbers/letters associated with each color are, from left to right, the same as the RGB hex values for the associated color.
EDIT: Formatting
• You got the right answer! Can you also explain the different hints (such as the title and how the numbers in the grid were chosen)? – Arnaud Mortier Aug 9 '19 at 21:36
• @ArnaudMortier - I'm not sure... Is the title rot13(Onfrq ba gur iregvpny cbfvgvba bs gur erq nf lbh tb sebz yrsg gb evtug)? I am also stumped as to how Ak19's find fits in... Perhaps someone else has an idea? – IronEagle Aug 9 '19 at 22:13
• Yes, but not only that. What @Ak19 found is a hint to find the meaning of the numbers. – Arnaud Mortier Aug 9 '19 at 22:26
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QA-Tf4: QA-Möbius Conjugate
A Möbius Transformation transforms generalized circles into generalized circles. A generalized circle is either a circle or a line, the latter being considered as a circle through the point at infinity. Even if it maps a circle to another circle, it does not necessarily map the first circle's center to the second circle's center.
However it preserves the angles between the intersection of circles. See Ref-35.
In a strictly geometric way we define here the Möbius Conjugate as follows.
Given a circle Ci and an axis Ax through the center of Ci. The Möbius Conjugate is defined here as the Reflection in Ax of the Inverse wrt Ci of some point P.
It also could be defined as the Inverse wrt Ci of the Reflection in Ax of that same point P, since it gives the same result. Applying the Möbius Conjugate twice results in the point of origin.
This Möbius Conjugate occurs also in Quadrangle Geometry and Quadrilateral Geometry.
In Quadrilateral Geometry we have QL-Tf1, the Clawson-Schmidt Conjugate with QL-P1 as the circle center.
In Quadrangle Geometry we here have QA-Tf4, which is called the QA-Möbius Conjugate.
It comes forward from a property from QA-P4 that the angle bisectors of Pi.QA-P4.Oi (i=1,2,3,4) coincide, where Oi = Circumcenter (Pj,Pk,Pl) and where (i,j,k,l) (1,2,3,4).
This Angle bisector is the Axis of the QA-Möbius Conjugate. The circle of this QA-Möbius Conjugate is the circle with center QA-P4 and squared radius = |QA-P4.Pi|.|QA-P4.Oi|, which has the same values for i=1,2,3,4.
The QA-Möbius Conjugate was discovered and mentioned as "T-Inversion" with a simple construction method in a not published paper of Eckart Schmidt in 2000.
Seperately about at the same time the QA-Möbius Conjugate also was discovered by Benedetto Scimemi. Later on he published it. See Ref-36, page 341.
The coordinates of the image are not very simple and of the second degree.
However somehow this conjugate relates quite a lot of Quadri-points.
Here is a way of constructing the QA-Möbius Conjugate:
There is another surprisingly simple construction described by Eckart Schmidt (unpublished paper, 2000) without the use of QA-P4, its circle and its axis.
Transformation:
1st CT-Coordinate of the QA-Tf4 image of P(x:y:z):
-b2 c2 p (c2 q2 - a2 q r + b2 q r + c2 q r + b2 r2) (-a2 p2 + b2 p2 + c2 p2 - a2 p q + b2 p q - c2 p q - a2 p r - b2 p r + c2 p r - 2 a2 q r) x2
+c2 q (c2 p2 + a2 p r - b2 p r + c2 p r + a2 r2) (a4 p q - a2 b2 p q - 2 a2 c2 p q - b2 c2 p q + c4 p q + a4 q2 - a2 b2 q2 - a2 c2 q2 - a2 b2 p r - b4 p r + b2 c2 p r - 2 a2 b2 q r) y2
+b2 r (b2 p2 + a2 p q + b2 p q - c2 p q + a2 q2) (-a2 c2 p q + b2 c2 p q - c4 p q + a4 p r - 2 a2 b2 p r + b4 p r - a2 c2 p r - b2 c2 p r - 2 a2 c2 q r + a4 r2 - a2 b2 r2 - a2 c2 r2) z2
+(a4 c4 p3 q2 - a2 b2 c4 p3 q2 - 2 a2 c6 p3 q2 - b2 c6 p3 q2 + c8 p3 q2 + a4 c4 p2 q3 - a2 b2 c4 p2 q3 - a2 c6 p2 q3 - a8 p3 q r + 3 a6 b2 p3 q r - 3 a4 b4 p3 q r + a2 b6 p3 q r + 3 a6 c2 p3 q r - 2 a4 b2 c2 p3 q r - 2 a2 b4 c2 p3 q r + b6 c2 p3 q r - 3 a4 c4 p3 q r - 2 a2 b2 c4 p3 q r - 2 b4 c4 p3 q r + a2 c6 p3 q r + b2 c6 p3 q r - 2 a8 p2 q2 r + 6 a6 b2 p2 q2 r - 6 a4 b4 p2 q2 r + 2 a2 b6 p2 q2 r + 6 a6 c2 p2 q2 r - 5 a4 b2 c2 p2 q2 r - 2 a2 b4 c2 p2 q2 r + b6 c2 p2 q2 r - 5 a4 c4 p2 q2 r - 2 a2 b2 c4 p2 q2 r - b4 c4 p2 q2 r - b2 c6 p2 q2 r + c8 p2 q2 r - a8 p q3 r + 3 a6 b2 p q3 r - 3 a4 b4 p q3 r + a2 b6 p q3 r + 3 a6 c2 p q3 r - 3 a4 b2 c2 p q3 r - a4 c4 p q3 r - a2 c6 p q3 r + a4 b4 p3 r2 - 2 a2 b6 p3 r2 + b8 p3 r2 - a2 b4 c2 p3 r2 - b6 c2 p3 r2 - 2 a8 p2 q r2 + 6 a6 b2 p2 q r2 - 5 a4 b4 p2 q r2 + b8 p2 q r2 + 6 a6 c2 p2 q r2 - 5 a4 b2 c2 p2 q r2 - 2 a2 b4 c2 p2 q r2 - b6 c2 p2 q r2 - 6 a4 c4 p2 q r2 - 2 a2 b2 c4 p2 q r2 - b4 c4 p2 q r2 + 2 a2 c6 p2 q r2 + b2 c6 p2 q r2 - 3 a8 p q2 r2 + 8 a6 b2 p q2 r2 - 7 a4 b4 p q2 r2 + 2 a2 b6 p q2 r2 + 8 a6 c2 p q2 r2 - 4 a4 b2 c2 p q2 r2 - 2 a2 b4 c2 p q2 r2 - 7 a4 c4 p q2 r2 - 2 a2 b2 c4 p q2 r2 + 2 a2 c6 p q2 r2 - a8 q3 r2 + 2 a6 b2 q3 r2 - a4 b4 q3 r2 + 3 a6 c2 q3 r2 - a4 b2 c2 q3 r2 - 2 a4 c4 q3 r2 + a4 b4 p2 r3 - a2 b6 p2 r3 - a2 b4 c2 p2 r3 - a8 p q r3 + 3 a6 b2 p q r3 - a4 b4 p q r3 - a2 b6 p q r3 + 3 a6 c2 p q r3 - 3 a4 b2 c2 p q r3 - 3 a4 c4 p q r3 + a2 c6 p q r3 - a8 q2 r3 + 3 a6 b2 q2 r3 - 2 a4 b4 q2 r3 + 2 a6 c2 q2 r3 - a4 b2 c2 q2 r3 - a4 c4 q2 r3) y z
+c2 (a4 c2 p3 q2 - b4 c2 p3 q2 - 2 a2 c4 p3 q2 - 2 b2 c4 p3 q2 + c6 p3 q2 + a4 c2 p2 q3 - b4 c2 p2 q3 - a2 c4 p2 q3 + b2 c4 p2 q3 - a6 p3 q r + 2 a4 b2 p3 q r - a2 b4 p3 q r + 3 a4 c2 p3 q r - a2 b2 c2 p3 q r - 4 b4 c2 p3 q r - 3 a2 c4 p3 q r - b2 c4 p3 q r + c6 p3 q r - a6 p2 q2 r + 3 a4 b2 p2 q2 r - 3 a2 b4 p2 q2 r + b6 p2 q2 r + 4 a4 c2 p2 q2 r - 3 a2 b2 c2 p2 q2 r - b4 c2 p2 q2 r - 5 a2 c4 p2 q2 r - 2 b2 c4 p2 q2 r + 2 c6 p2 q2 r + a4 b2 p q3 r - 2 a2 b4 p q3 r + b6 p q3 r + 2 a4 c2 p q3 r + 2 a2 b2 c2 p q3 r - 2 b4 c2 p q3 r - 2 a2 c4 p q3 r + b2 c4 p q3 r + a2 b4 p3 r2 - b6 p3 r2 - b4 c2 p3 r2 - 2 a6 p2 q r2 + 3 a4 b2 p2 q r2 - 3 a2 b4 p2 q r2 + 2 b6 p2 q r2 + 6 a4 c2 p2 q r2 - b4 c2 p2 q r2 - 6 a2 c4 p2 q r2 - 3 b2 c4 p2 q r2 + 2 c6 p2 q r2 - 2 a6 p q2 r2 + 2 a4 b2 p q2 r2 - a2 b4 p q2 r2 + b6 p q2 r2 + 5 a4 c2 p q2 r2 + a2 b2 c2 p q2 r2 - b4 c2 p q2 r2 - 4 a2 c4 p q2 r2 - b2 c4 p q2 r2 + c6 p q2 r2 + a4 b2 q3 r2 - a2 b4 q3 r2 + a4 c2 q3 r2 + 2 a2 b2 c2 q3 r2 - a2 c4 q3 r2 + a2 b4 p2 r3 + b6 p2 r3 - b4 c2 p2 r3 - a6 p q r3 + a4 b2 p q r3 + 3 a4 c2 p q r3 + a2 b2 c2 p q r3 + b4 c2 p q r3 - 3 a2 c4 p q r3 - 2 b2 c4 p q r3 + c6 p q r3 - a6 q2 r3 - a2 b4 q2 r3 + 2 a4 c2 q2 r3 + 2 a2 b2 c2 q2 r3 - a2 c4 q2 r3) x y
+b2 (a2 c4 p3 q2 - b2 c4 p3 q2 - c6 p3 q2 + a2 c4 p2 q3 - b2 c4 p2 q3 + c6 p2 q3 - a6 p3 q r + 3 a4 b2 p3 q r - 3 a2 b4 p3 q r + b6 p3 q r + 2 a4 c2 p3 q r - a2 b2 c2 p3 q r - b4 c2 p3 q r - a2 c4 p3 q r - 4 b2 c4 p3 q r - 2 a6 p2 q2 r + 6 a4 b2 p2 q2 r - 6 a2 b4 p2 q2 r + 2 b6 p2 q2 r + 3 a4 c2 p2 q2 r - 3 b4 c2 p2 q2 r - 3 a2 c4 p2 q2 r - b2 c4 p2 q2 r + 2 c6 p2 q2 r - a6 p q3 r + 3 a4 b2 p q3 r - 3 a2 b4 p q3 r + b6 p q3 r + a4 c2 p q3 r + a2 b2 c2 p q3 r - 2 b4 c2 p q3 r + b2 c4 p q3 r + a4 b2 p3 r2 - 2 a2 b4 p3 r2 + b6 p3 r2 - 2 b4 c2 p3 r2 - b2 c4 p3 r2 - a6 p2 q r2 + 4 a4 b2 p2 q r2 - 5 a2 b4 p2 q r2 + 2 b6 p2 q r2 + 3 a4 c2 p2 q r2 - 3 a2 b2 c2 p2 q r2 - 2 b4 c2 p2 q r2 - 3 a2 c4 p2 q r2 - b2 c4 p2 q r2 + c6 p2 q r2 - 2 a6 p q2 r2 + 5 a4 b2 p q2 r2 - 4 a2 b4 p q2 r2 + b6 p q2 r2 + 2 a4 c2 p q2 r2 + a2 b2 c2 p q2 r2 - b4 c2 p q2 r2 - a2 c4 p q2 r2 - b2 c4 p q2 r2 + c6 p q2 r2 - a6 q3 r2 + 2 a4 b2 q3 r2 - a2 b4 q3 r2 + 2 a2 b2 c2 q3 r2 - a2 c4 q3 r2 + a4 b2 p2 r3 - a2 b4 p2 r3 + b4 c2 p2 r3 - b2 c4 p2 r3 + 2 a4 b2 p q r3 - 2 a2 b4 p q r3 + a4 c2 p q r3 + 2 a2 b2 c2 p q r3 + b4 c2 p q r3 - 2 a2 c4 p q r3 - 2 b2 c4 p q r3 + c6 p q r3 + a4 b2 q2 r3 - a2 b4 q2 r3 + a4 c2 q2 r3 + 2 a2 b2 c2 q2 r3 - a2 c4 q2 r3) x z
Examples of QA-Möbius Conjugates:
Point/Line/Curve QA-Tf4 - image GENERAL Defining Quadrangle Points: P1,P2,P3,P4 Circumcenters O1, O2, O3, O4 of the corresponding QA-Component Triangle The vertices of the Diagonal Triangle QA-Tr1 of the Reference Quadrangle The vertices of the Miquel Triangle QA-Tr2 of the Quadrangle O1.O2.O3.O4 (Eckart Schmidt, 2000) A line not through QA-P4 A circle through QA-P4 A line through QA-P4 A line through QA-P4 A circle with QA-P4 as center Another circle with QA-P4 as center A circle not through QA-P4 Another circle not through QA-P4 A circle through QA-P4 A line not through QA-P4 SPECIFIC QA-P4: Isogonal Center Some (undefined) point at infinity QA-P2: Euler-Poncelet Point Midpoint (QA-P4,QA-P6*) (suffix * means “QA-Möbius Conjugate of”) QA-P3: Gergonne-Steiner Point QA-P9: QA-Miquel Center QA-P41: Involutary Conjugate of QA-P4 Reflection of QA-P3 in QA-P32 QL-P1: Miquel Point QG-P5: 1st QG-Quasi Circumcenter
Collinearities:
(suffix * means “QA-Möbius Conjugate of”)
QA-P10*. QA-P28*. QA-P4 (1 : 3)
Other Properties:
• The Reflection Axis of the Conjugate is:
the internal bisector of Angle QA-P3.QA-P4.QA-P9
the external bisector of Angle QA-P2.QA-P4.QA-P41.
• Let Q1 and Q2 be two points collinear with QA-P4. Let Q1* and Q2* be their respective QA-Möbius Conjugate. Now Q1.Q2* // Q2.Q1*.
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http://www.ficgs.com/shortest-possible-bigchess-checkmates-q6924.html
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shortest possible bigchess checkmates
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Normajean Yates (2009-04-15)
shortest possible bigchess checkmates?
What are the shortest checkmates in bigchess, for white and for black (e.g. in 'normal' 8x8 chess they are the "fool's mates" - 3 moves = 5 half-moves for white; 2 moves = 4-half-moves for black..)
So which are the bigchess "fool's mates" (shortest mates)?
Thibault de Vassal (2009-04-15 13:48:07)
shortest possible bigchess checkmates
Good question & good idea to develop the bigchess theory :)
I don't know, no time to think about it today but it may be not so easy to do it in less than the obvious 11 half-moves checkmate for White.
William Taylor (2009-04-15 15:24:11)
shortest possible bigchess checkmates
I like the 13 half-move mate where black pushes an edge pawn or something while white hops his knight all the way over to l15. :) May have a lookk for other ones later.
Normajean Yates (2009-04-15 21:22:03)
11 half-moves: decent uper bound..
Thanks for the posts so far - So, we made progress (in the pure math sense) - we have a 'small enough' upper bound now - 11 half-moves for white, so by symmetry 12 (or 10?) half moves for black...
I can't say 12 or 10 (above) because I havent though about the answer at all - the question came to mind; I posted it; went to sleep... will think later..
Normajean Yates (2009-04-26 18:11:42)
I think Thib's IS the shortest...
To spell it out, white moves Nh2-j4-h6-j8-h10-j12, while black helps by g15-g14,Nj15-h13-g15,Ng16-j15, (and one irrelevant move e.g. moving an edge pawn). That is 5 moves ['half-moves'] by each side, and the 11th half-move is white's Nj12xh14 mate (the black K is smothered and the h14-pawn is unprotected).
You need five [half-]moves for a N to reach the opposite king; so: black can mate white (helpmate ie white co-operates) in 10 half-moves.
Philip Roe (2009-04-27 20:32:11)
Nine half-moves
1. e2-e4 m15-m13 2. Bf1-a6 Bl16-n14 3. Nj2-h4 j14-j13 4. Qh1-k3 helps 5. Qk3xk13 mate
with many minor variations.
Normajean Yates (2009-04-28 12:25:12)
PhilipRoe+SophieLeClerc - wonderful!
PhilipRoe+SophieLeClerc (Sophie should get joint credit I think because she first posted in 'international chat' (2009-04-16 08:31:15-25) that a Q+N mate would be even shorter) - that's wonderful - congratulations!
But Sophie had posted that 'it can be done in 8 half-moves with the Q and N' (she didn't give the line). Philip's line, if reversed so that *black* checkmates white, will need 10 half-moves because the mating side in this process needs to free the f-Bishop, free the Q, move the f-bishop once and move the Q twice - a total of 5 [half-]moves. So if black mates by Roe's method it on black's 5th move - which means 10 half-moves.
So, is there a shorter way [specially, with *black* mating]?
Philip Roe (2009-04-28 19:50:26)
Thanks for the appreciation, Normajean
I hadn't seen Sophies post. Do you have a line, Sophie? The knight looks awfully slow! Perhaps Big Chess needs Big Knights.
Normajean Yates (2009-04-29 00:53:19)
Philip, Sophie posted in the chat..
not the forums - I am not sure she has noticed this thread. Perhaps we should send a message to her and/or post in the international chat - ok, I'll do the latter.
Normajean Yates (2009-04-29 13:39:24)
sorry: correction: sophie said Q+B!
I typed Q+N but I was thinking of Q+B which is what Sophie leclerc had posted: I was slightly puzzled by Philip's reference to Knights in this context and I just realised I must have mistyped 'N' for 'B'; saw that I *had* ! :(
Sorry for the confusion, the misquotation and the inconvenience...
Sophie Leclerc (2009-05-01 01:23:07)
Thanks
While I thanks for the credits, I'll tell you that I am not a woman, ( why i have that name, you doN,t want to know kay. I got a wrong name, but I like it. )
I saw to real way for black to check mate white. But to get a queen take the weak pawn. And white does it faster.
1 e4 j13 2.Ba6 h14 3. Nh4 m14 4. Qk3 Bm15 5. Qxk5 mate. was the lines I poster in the internationnal chat. ( I am not a girl. )
Normajean Yates (2009-05-01 04:06:00)
sorry+thanks Sophie - but: its still 9..
but it is still 9 [half-]moves because the mate is on white's 5th move, so 5 white-moves + 4 black-moves, = 9 [half-]moves.
If you see, yours and Philip's solutions are essentially minor variants of each other...
In Sophie's solution, 2..h14 is of couse an easily repaired mistype [2..h14 is not possible, you see]- one can just replace it by say 2..a14.
Normajean Yates (2009-05-01 04:18:45)
Sphie's soln is a tad more interesting..
arguably. Because, the L16-B instead of moving away, comes to k15 to be captured..
Interestingly, (very minor point) both Philip and Sophie mistype the checkmating move 5.Q(k3)xk15 mate: Philip gives 5.Qk3xk13, Sophie gives 5.Qxk5... (I just noticed it because I was reading what was meant, not what was written..)
Finally, by 'she' I meant 'she or he': I sometimes do...
Philip Roe (2009-05-01 04:49:32)
We should all be so lucky..
to have readers who read what we mean and not what we write!
Sophie Leclerc (2009-05-01 05:09:37)
8 moves
I am man....
The presence of knight around the king protect him from worst idiocy, I don,t think a lone queen can mate sooner
Normajean Yates (2009-05-01 07:10:41)
yes this (9 [half-]moves seems shortest.
I agree, doesnt look like it can be done sooner..
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# Tensorflow.js tf.metrics.meanAbsoluteError() Function
• Last Updated : 25 May, 2021
Tensorflow.js is an open-source library developed by Google for running machine learning models and deep learning neural networks in the browser or node environment.
The tf.metrics.meanAbsoluteError() is used to calculate mean absolute error. The mean absolute error is defined as the mean of absolute difference of two tensors. Where, the mean is applied over feature dimensions. It takes two tensors as a parameter.
Hey geek! The constant emerging technologies in the world of web development always keeps the excitement for this subject through the roof. But before you tackle the big projects, we suggest you start by learning the basics. Kickstart your web development journey by learning JS concepts with our JavaScript Course. Now at it's lowest price ever!
`mean(abs(Prediction - True))`
Syntax:
`tf.metrics.meanAbsoluteError(Tensor1, Tensor2);`
Parameters:
• Tensor1: It is the truth tensor.
• Tensor2: It is the Prediction tensor.
Return Value: It returns the tensor of the mean absolute errors.
Example 1: In this example, we are giving two 1d tensors as a parameter, and the metrics.meanAbsoluteError function will calculate the mean absolute error and return a tensor.
## Javascript
`// Importing the tensorflow library``import * as tf from ``"@tensorflow/tfjs"`` ` `// Defining the value of the tensors``const True = tf.tensor([1,2,3]);``const Prediction = tf.tensor([3,2,1]);`` ` `// Calculating mean absolute error``const error = tf.metrics.meanAbsoluteError(True, Prediction);`` ` `// Printing the tensor``error.print();`
Output:
```Tensor
1.3333333730697632```
Example 2: In this example, we are giving two 2d tensors as a parameter, and the metrics.meanAbsoluteError function will calculate the mean absolute error and return a tensor.
## Javascript
`// Importing the tensorflow library``import * as tf from ``"@tensorflow/tfjs"`` ` `// Defining the value of the tensors``const True = tf.tensor([[1,2,3],[2,4,1]]);``const Prediction = tf.tensor([[3,2,1],[5,2,1]]);`` ` `// Calculating mean absolute error``const error = tf.metrics.meanAbsoluteError(True, Prediction);`` ` `// Printing the tensor``error.print();`
Output:
```Tensor
[1.3333334, 1.6666667]```
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# How precisely can particle position be measured in a laboratory?
If we have any given particle, such as a photon or an electron (it doesn't really matter what for the sake of the question), how precisely can modern physics devices measure their position? Specifically, assuming that the wave function collapse is a real, physical process (which is of course not certain yet), how 'tight' can we make the wave function (from end-to-end of the biggest 'spike'). Given the existence of the Heisenberg Uncertainty Principle, can we measure the position of a particle precisely enough (make the wave packet 'tight' enough) to invoke an increase in the 'spread' of possible position values using current technology? Given how incredibly small the values in the formula for the Heisenberg Uncertainty Principle are, measuring a particle to the point where the uncertainty in position is low enough to warrant an increase in uncertainty in momentum must be incredibly small. Can modern measurement devices decrease the uncertainty in position to such an amount?
## 1 Answer
There is a basic misunderstanding in this question:
how 'tight' can we make the wave function (from end-to-end of the biggest 'spike').
The wave function controls the probability of interaction, probabilities are about the accumulation of data for many particles in the same boundary conditions and cannot constrain a track/footprint of a particle, except probabilistically.
Look at this double slit experiment one photon at a time, to understand the difference between particle and wave function describing a particle. This is the de facto solution of a "scattering a photon on double slits, a given width, a given distance apart"
. Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.
The dimensions of the footprint of the individual photon have to do with the accuracy of the screen in microns, the wavefunction describing the system appears in the interference pattern. The same is true for single electrons.
Can modern measurement devices decrease the uncertainty in position to such an amount?
Modern devices have not reached that precision yet for individual particles, as Plancks constant is very small, $$4.135667696×10^{−15}$$ eVs.
In bubble chambers the accuracy is in microns and the momenta too low . The detectors in the high energy labs are not much better, so the detector measurements obey the HUP .
Given the existence of the Heisenberg Uncertainty Principle, can we measure the position of a particle precisely enough
Yes, because with our detectors up to now the HUP holds.
(make the wave packet 'tight' enough)
The wavepacket representation of free particles comes again quantum mechanically, we cannot make it "tight". It will depend on its momentum and the particular detector, we can only affect the momentum, the space depends on the detector choice and as a said above, at present the HUP holds
• While the wave function of a system does work in probabilities as you described up until measurement, I was under the impression that each individual particle has its own wave function that describes where it is likely to be measured. Once the measurement is made, if the particle is measured again, the same particle will almost certainly be measured in approximately the same place. I interpret this as meaning that the wave packet is now 'tighter' as the position will now be measured to be in a smaller variety of places for an individual particle. Commented Feb 3, 2021 at 23:04
• Furthermore, I find your wording in the section describing measurement devices in bubble chambers and such unclear. Can such measurement devices measure the position of these particles to a point where its position is known to a small enough range of locations to invoke the HUP? Finally, why does it matter if their momentum is small? 1) The HUP deals with UNCERTAINTY in momentum, to the difference between minimum and maximum momentum would be similar regardless of their values relative to the origin, and 2) momentum, being a function of velocity, is relative anyway, and not objectively 'low'. Commented Feb 3, 2021 at 23:08
• @Sciencemaster "if the particle is measured again, the same particle will almost certainly be measured in approximately the same place. " The same particle cannot be measured again, measurement is interaction, and new wave functions are obeyed. If the measurement is a spot on a screen, as above, for example. Same boundary condition particles will show the probability of interaction. The HUP of uncertainty in momentum, means that the larger the momentum the smaller the position can be defined [dp,dx]>h Commented Feb 4, 2021 at 5:05
• .the momenta we can reach and the location of position in detectors is such that the HUP is always obeyed Commented Feb 4, 2021 at 5:05
• Okay, it took me a moment to realize what you meant by 'the wave function is destroyed'. You and I think of the wave function post-collapse differently. I imagine it as the same wave function instantly having its properties changed to have a smaller standard deviation and such, because it can be measured again, and when that happens, it will be seen in approximately the same location if enough time has not passed for it to spread back out. However, you seem to view observation as the initial particle being destroyed and a new particle with a new wave function replacing the old one. Commented Feb 9, 2021 at 21:11
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# Exercise 4: Using Minisat
## Overview
In this exercise you will use a real sat-solver, MiniSat, to test some propositions to see if they are tautologies. If a proposition is not a tautology you will extract a counter-example. You will download and install the system on your computer, create files that MiniSat can use as input, run the system on your files, and extract answers from the output of running the system.
## Learning Objectives
As you work through this exercise we expect you to learn the following:
• The format of DIMACS CNF files
• How to invoke MiniSat
• How to use the negation of a formula to test for tautology-hood.
• How to use MiniSat to find another find additional solutions (or counter examples).
## Getting Started
• Recall what we have learned about SAT-solvers. A perfect understanding of this material is not necessary to work through this exercise, as we are more concerned with using a SAT solver here, than in how they work.
## Directions
Study the problems below. We will try and prove that each is a tautology. Each problem has several parts.
1. Formed a proposition by moving formula from the left of the turnstyle into an implication on the right.
For example: p,q |- r leads to the proposition p -> (q -> r).
2. Negated the formula.
3. Turn the negated formula into CNF.
1. Sequent p \/ q, ~q \/ r |- (p \/ r)
2. Formula p \/ q => ~q \/ r => (p \/ r)
3. Negated ~(p \/ q => ~q \/ r => (p \/ r)
4. CNF Negated (p \/ q) /\ (~q \/ r) /\ ~p /\ ~r
1. Sequent (p /\ ~p) |- ~(r => q) /\ (r => q)
2. Formula (p /\ ~p) => (~(r => q) /\ (r => q))
3. Negated ~((p /\ ~p) => (~(r => q) /\ (r => q)))
4. CNF Negated p /\ (~r \/ q \/ r) /\ (~r \/ q \/ ~q) /\ ~p
1. Sequent (p => q), (s => t) |- (p \/ s) => (q /\ t)
2. Formula (p => q) => (s => t) => p \/ s => (q /\ t)
3. Negated ~((p => q) => (s => t) => p \/ s => (q /\ t))
4. CNF Negated (~p \/ q) /\ (~s \/ t) /\ (p \/ s) /\ (~q \/ ~t)
## What To Do
• Create a DIMACS CNF file to encode each negated CNF formula.
• Run MiniSat.
• Determine if the formula is a tautology. If it is not, find two counter examples. (See How to use the MiniSAT SAT Solver for strategies for finding more than one solution).
• You should discover at least on tautology, and one-non tautology.
## What To Turn In
• Write up a simple report about what you discovered.
• Create a small directory with the *.cnf files and your report.
• Drop it in the Ex4 folder in the class drop box
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0
# How do you get three different ways to get 10 only using the number 9?
Wiki User
2009-12-21 16:01:37
9 + (9/9) = 10
(99/9) - (9/9) = 10
[ (9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9) / 9 ] + (9/9) = 10
Wiki User
2009-12-21 16:01:37
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# Thread: How do you multiply double exponents?
1. ## How do you multiply double exponents?
I've been having an issue with Wikipedia; I need to somehow explain to Joe Public in layman's terms what the number 10^10^10^122 means. Well, I can say that it is 1 followed by 10^10^122 zeroes. I know that 10^10^100 is a googolplex, but how many times a googolplex is 10^10^122? I initially thought that it was 10^22 times a googolplex, but I think it might be 10^10^22 times a googolplex. Er, help?
2. You could test it with smaller numbers ...
2^2^3 = 256.
2^2^5 = 4,294,967,296.
The ratio is: 2^24 ~= 2^2^4.7
So I think the answer is that 10^10^122 is almost 10^10^122 times bigger than a Googolplex.
3. 10^10^10^122 may be easier to sort out with some parentheses:
((10^10)^10)^122
Expanding the innermost parentheses:
(10 000 000 000^10)^122
Repeat as needed, but I think you'll end up with 1 followed by 10^244 zeroes.
In math, parentheses are your friends
eta
Parentheses are, indeed, your friends. If the correct way to parse something like this is from the top down:
10^10^10^122 should be parsed as
10^10^(1 followed by 122 zeroes)
10^(1 followed by 10^122 zeroes)
I've probably messed this one up, too.
I will now, officially, give up until I dig up a text book that describes the rules instead of relying on a memory that's increasing like a steel sieve.
Last edited by swampyankee; 2012-Apr-16 at 10:39 PM.
4. Established Member
Join Date
Mar 2005
Posts
1,235
Originally Posted by antoniseb
2^2^3 = 256.
Originally Posted by swampyankee
10^10^10^122 may be easier to sort out with some parentheses:
((10^10)^10)^122
By this logic, antoniseb should have got 64 instead of 256.
256 requires
2^(2^3)
My TI-84 says that 2^2^3 = 64, as does writing a short computer program in Visual Basic:
Code:
```x=2^2^3
print x```
gives 64. But Google calculator says 2^2^3 = 256
Only parenthesis can get you beyond this ambiguity
5. If exponentiation is indicated by stacked symbols, the rule is to work from the top down, thus:
...
Special cases
6. Originally Posted by tony873004
By this logic, antoniseb should have got 64 instead of 256.
256 requires
2^(2^3)
My TI-84 says that 2^2^3 = 64, as does writing a short computer program in Visual Basic:
Code:
```x=2^2^3
print x```
gives 64. But Google calculator says 2^2^3 = 256
Only parenthesis can get you beyond this ambiguity
I think that is because of the way you enter the equation into your TI-84
typing 2 ^2 ^3 your doing left to right which is not the correct order of precedence.
223 is 256
You'd have to do 2^(2^3) for your calculator.
7. Originally Posted by parallaxicality
I know that 10^10^100 is a googolplex, but how many times a googolplex is 10^10^122? I initially thought that it was 10^22 times a googolplex, but I think it might be 10^10^22 times a googolplex. Er, help?
Originally Posted by antoniseb
So I think the answer is that 10^10^122 is almost 10^10^122 times bigger than a Googolplex.
In a way, I think that's right.
But that tells us nothing at all about how big 10^10^122 is.
Another way of putting it is, 10^10^122 is googolplex^(10^22):
googolplex^(10^22) =
(10^10^100)^(10^22) =
10^(10^100 * 10^22) =
10^(10^122)
So, 10^10^122 equals a googolplex times itself 10,000,000,000,000,000,000,000 times
8. When you raise a power to a power, don't you multiply the powers? If so, then ((10^10)^10)^122 gives 10^12200?
9. Originally Posted by Bogie
When you raise a power to a power, don't you multiply the powers? If so, then ((10^10)^10)^122 gives 10^12200?
Yes and no. ((A^x)^y)^z equals A^(xyz) but when you see A^x^y^z it typically means A^(x^(y^z)), which might be a much larger number. As the OP says, a googol is 10^100, and a googolplex is 10^googol, so a googolplex is 10^(10^100) which is 1 followed by 10,000,000,000,000,000,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000,000,000,000 zeroes, whereas (10^10)^100 has only 1000 zeroes.
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Join Date
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I thought exponents were associative.
(2^2)^2=4^2=16
2^(2^2)=2^4=16
11. Banned
Join Date
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Posts
211
(10^10)^10 = 10000000000^10 = 10^100
10^(10^10) = 10^10000000000
12. Originally Posted by tony873004
By this logic, antoniseb should have got 64 instead of 256.
256 requires
2^(2^3)
My TI-84 says that 2^2^3 = 64, as does writing a short computer program in Visual Basic:
Code:
```x=2^2^3
print x```
gives 64. But Google calculator says 2^2^3 = 256
Only parenthesis can get you beyond this ambiguity
Most programming languages parse arithmetic statements with the same operator -- like 1*2*3*4*5.... from left to right. They parse exponents from right to left, so 2^3^4 is parsed as 2^(3^4), or 2^81. The way I parenthesized it would be (2^3)^4, which is 8^4, which is not the same. I think the right-to-left method is right, and I erred above.
13. the right to left rule is correct for order of precedence and another way to think about it is like this
2^3^4^5
is since exponents are done first 2^3 can't be done because 3 is raised to the power of 4 and well 4 has a power but 5 doesn't....
actually Right to Left rule is more simple to remember.
The exception being when there is parentheses involved. IE (2^3)^4 is not the same as 2^3^4
The former is only 4096 where the later is 2,417,851,639,229,258,349,412,352
2^3^4 and 2^(3^4) are the same. I hate useless parentheses
14. OK, I have to admit to a mental block here .
To make it simple, we are raising x to three levels of power as follows"
x^2^3^4
For x=2:
x^2^3^4=x^24=((X^2)^3)^4=(x^6)^4=(x2)^12=(x^8)^3=
16,777,216
My mental block, if it is a mental block is about raising a power to a power to a power which I think is accomplished by multiplying the powers. *It doesn't matter which order you do the multiplying, does it?
x^24=2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 *2=16,777,216
((x^2)^3)^4=*
2*2=4 *
4*4*4=64 *
64*64*64*64=16,777,216
(x^6)^4=
2*2*2*2*2*2=64
64*64*64*64=16,777,216
(x^2)^12=
2*2=4
4*4*4*4*4*4*4*4*4*4*4*4=16,777,216
(x^8)^3=
2*2*2*2*2*2*2*2=256
256*256*256=16,777,216
15. X^2^3^4 is not x^24, it's X^(2^(3^4)), which is X^(2^81), which is X^2417851639229258349412352
16. Can you show me the steps using x=2? And maybe a link to the rule?
17. That would be 2^2417851639229258349412352. The rule was linked by a1call in post #5, labeled "special cases"
18. So x^2^3^4 is not ((x^2)^3)^4, it is x^(2^(3^4) then?
And if I could only figure it out from there I would be happy.
So let's see ... how do you get X^(2^81) from that. I other words, can you show me the steps instead of saying that would be 2^2417851639229258349412352?
19. 3^4 is 81
20. Oh, so it is, lol. I was still trying to do 3*4. From there is see ... 2^81 must be 241785163922925834941235, and so then when x=2, it comes out 2^2417851639229258349412352. Slightly higher than what I get by failing to follow the "special cases" rule. Thanks.
21. You're welcome!
Now, where's parallaxacality?
22. Over at
http://en.wikipedia.org/wiki/Orders_...e_%28length%29
Hope I managed to make sense of all this...
23. 10^10^10^122 metres = 10^10^10^122 yottameters? That's gonna get you in the tabloids!
24. Now there is a rule that will help, lol. The "unitless" rule should be a big boost when sorting out units of measure. Just multiply your answer by 10^10^10^122 and use any units of measure you like. Where was that when I was in school?
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# FAQ: How Many Calories Does Two Slices Of Pizza Have?
## How many calories are in 2 large slices of pizza?
From Pepperoni to Margherita, This Is How Many Calories Are in That Slice of Pizza
1 slice Calories Protein (g)
Cheese 272 12.3
Extra cheese 310 14
Hawaiian 294 14
Margherita 250 9
## Is 2 slices of pizza bad?
Will 2 slices of pizza ruin my diet? Consider this: The average slice of cheese pizza packs about 285 calories, according to the USDA. If you’re trying to lose weight and your goal is to consume around 1,500 calories a day, eating two slices is over a third of your daily caloric intake.
## How many calories are in a regular slice of pizza?
Some more pizza math: The average slice of cheese is around 250 calories (and around 400 for a heaping pile of meat atop that cheese, which, of course, is how God intended). The average person eats roughly three pieces per sitting. That’s between 750 to 1,200 calories before decrusting.
You might be interested: FAQ: How To Build A Wood Fire Pizza Oven?
## How many calories are in 2 slices of cheese pizza?
There are 475 calories in 2 pieces of Cheese Pizza.
## Which pizza has the least calories?
The lowest calorie Domino’s pizza is the chain’s Thin Crust Veggie Pizza. The lowest calorie Domino’s pizza option is their Thin Crust Veggie Pizza with light cheese. Each slice has 135 calories, 250 milligrams of sodium, two grams of sugar, and two grams of saturated fat.
## How many calories is 3 slices of thin crust pizza?
There are 575 calories in 3 slices of 14″ Cheese Pizza (Thin Crust).
## Is it OK to eat pizza on a diet?
You should only choose pizza toppings, which are good for your diet. Make sure that you do not add too much cheese and bread. A thin crust is best, and vegetables and protein-rich toppings are a great way to go. You will need to eat less to lose weight, which is why the size of the pizza you make is important.
## How many slices of pizza does an average person eat?
How Many Slices of Pizza Does the Average American Eat in a Lifetime? According to a poll, the average American eats more than 6,000 slices of pizza in his or her lifetime. No matter how you slice it, we Americans love our pizza.
## Can I eat pizza once a week and still lose weight?
If you love pizza, you can work around your calorie goals so that you can still indulge in a slice or two once a week. You can also continue toward your weight loss goals by choosing healthier pizza options. For example, a large slice of cheese pizza from Hungry Howie’s has 200 calories.
You might be interested: Question: What Does Carryout Mean Pizza Hut?
## Why is pizza so high in calories?
Most types of pizzas are high in calories and sodium, as they’re usually topped with cheese, salty meats and other high – calorie toppings. Plus, some pizzas contain added sugar in the crust, certain toppings and sauces.
## Is one slice of pizza healthy?
They get a bad rap but you can make them work in a healthy diet. Regardless, one slice of regular crust pizza has about 285 calories, which, with a side salad and a piece of fruit is a pretty decent lunch — especially since it also delivers about 20% of your daily value for calcium and a healthy dose of protein.
## How do I burn off the pizza I just ate?
If you eat a quarter slice of a large pizza containing 449 calories, you need to walk for 1 hour and 23 minutes or run for 43 minutes to burn it off. If you eat a 420-calorie cinnamon roll, you need to walk for 1 hour and 17 minutes or run for 40 minutes to offset the calorie intake.
## How many calories are in 2 slices of thin crust pizza?
There are 383 calories in 2 slices of 14 ” Cheese Pizza (Thin Crust).
## How many calories should I eat to lose weight?
When trying to lose weight, a general rule of thumb is to reduce your calorie intake to 500 fewer calories than your body needs to maintain your current weight. This will help you lose about 1 pound (0.45 kg) of body weight per week.
## How many calories are in 2 slices of Little Caesars Pizza?
Nutrition Facts
You might be interested: Question: How To Build A Woodfire Pizza Oven?
Calories 280 (1170 kJ)
Cholesterol 25 mg 8%
Sodium 560 mg 23%
Total Carbohydrate 32 g 11%
Dietary Fiber 2 g 8%
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InfluentialPoints.com
Biology, images, analysis, design...
Use/Abuse Principles How To Related
"It has long been an axiom of mine that the little things are infinitely the most important" (Sherlock Holmes)
Just a note
(0.05 × 0.95)/1000 = 0.0000475; 2.58 × sqrt(0.0000475) = 0.0178
or p = 0.05 +/- 0.018
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# ifft
Inverse fast Fourier transform
## Description
example
X = ifft(Y) computes the inverse discrete Fourier transform of Y using a fast Fourier transform algorithm. X is the same size as Y.
• If Y is a vector, then ifft(Y) returns the inverse transform of the vector.
• If Y is a matrix, then ifft(Y) returns the inverse transform of each column of the matrix.
• If Y is a multidimensional array, then ifft(Y) treats the values along the first dimension whose size does not equal 1 as vectors and returns the inverse transform of each vector.
example
X = ifft(Y,n) returns the n-point inverse Fourier transform of Y by padding Y with trailing zeros to length n.
example
X = ifft(Y,n,dim) returns the inverse Fourier transform along the dimension dim. For example, if Y is a matrix, then ifft(Y,n,2) returns the n-point inverse transform of each row.
example
X = ifft(___,symflag) specifies the symmetry of Y in addition to any of the input argument combinations in previous syntaxes. For example, ifft(Y,'symmetric') treats Y as conjugate symmetric.
## Examples
collapse all
The Fourier transform and its inverse convert between data sampled in time and space and data sampled in frequency.
Create a vector and compute its Fourier transform.
X = [1 2 3 4 5];
Y = fft(X)
Y = 1×5 complex
15.0000 + 0.0000i -2.5000 + 3.4410i -2.5000 + 0.8123i -2.5000 - 0.8123i -2.5000 - 3.4410i
Compute the inverse transform of Y, which is the same as the original vector X.
ifft(Y)
ans = 1×5
1 2 3 4 5
Find the inverse Fourier transform of the single-sided spectrum that is the Fourier transform of a real signal.
Load the single-sided spectrum in the frequency domain. Show the sampling frequency and the sampling period of this spectrum.
Fs
Fs = 1000
T
T = 1.0000e-03
Plot the complex magnitude of the single-sided spectrum.
L1 = length(Y1);
f = Fs/(2*L1-1)*(0:L1-1);
plot(f,abs(Y1))
xlabel("f (Hz)")
ylabel("|Y1(f)|")
The discrete Fourier transform of a time-domain signal has a periodic nature, where the first half of its spectrum is in positive frequencies and the second half is in negative frequencies, with the first element reserved for the zero frequency. For real signals, the discrete Fourier transform in the frequency domain is a two-sided spectrum, where the spectrum in the positive frequencies is the complex conjugate of the spectrum in the negative frequencies with half the peak amplitudes of the real signal in the time domain. To find the inverse Fourier transform of a single-sided spectrum, convert the single-sided spectrum to a two-sided spectrum.
Y2 = [Y1(1) Y1(2:end)/2 fliplr(conj(Y1(2:end)))/2];
Find the inverse Fourier transform of the two-sided spectrum to recover the real signal in the time domain.
X = ifft(Y2);
Plot the signal.
t = (0:length(X)-1)*T;
plot(t,X)
xlabel("t (seconds)")
ylabel("X(t)")
The ifft function allows you to control the size of the transform.
Create a random 3-by-5 matrix and compute the 8-point inverse Fourier transform of each row. Each row of the result has length 8.
Y = rand(3,5);
n = 8;
X = ifft(Y,n,2);
size(X)
ans = 1×2
3 8
For nearly conjugate symmetric vectors, you can compute the inverse Fourier transform faster by specifying the 'symmetric' option, which also ensures that the output is real. Nearly conjugate symmetric data can arise when computations introduce round-off error.
Create a vector Y that is nearly conjugate symmetric and compute its inverse Fourier transform. Then, compute the inverse transform specifying the 'symmetric' option, which eliminates the nearly 0 imaginary parts.
Y = [1 2:4+eps(4) 4:-1:2]
Y = 1×7
1 2 3 4 4 3 2
X = ifft(Y)
X = 1×7
2.7143 -0.7213 -0.0440 -0.0919 -0.0919 -0.0440 -0.7213
Xsym = ifft(Y,'symmetric')
Xsym = 1×7
2.7143 -0.7213 -0.0440 -0.0919 -0.0919 -0.0440 -0.7213
## Input Arguments
collapse all
Input array, specified as a vector, a matrix, or a multidimensional array. If Y is of type single, then ifft natively computes in single precision, and X is also of type single. Otherwise, X is returned as type double.
Data Types: double | single | int8 | int16 | int32 | uint8 | uint16 | uint32 | logical
Complex Number Support: Yes
Inverse transform length, specified as [] or a nonnegative integer scalar. Padding Y with zeros by specifying a transform length larger than the length of Y can improve the performance of ifft. The length is typically specified as a power of 2 or a product of small prime numbers. If n is less than the length of the signal, then ifft ignores the remaining signal values past the nth entry and returns the truncated result. If n is 0, then ifft returns an empty matrix.
Data Types: double | single | int8 | int16 | int32 | uint8 | uint16 | uint32 | logical
Dimension to operate along, specified as a positive integer scalar. By default, dim is the first array dimension whose size does not equal 1. For example, consider a matrix Y.
• ifft(Y,[],1) returns the inverse Fourier transform of each column.
• ifft(Y,[],2) returns the inverse Fourier transform of each row.
Data Types: double | single | int8 | int16 | int32 | uint8 | uint16 | uint32 | logical
Symmetry type, specified as 'nonsymmetric' or 'symmetric'. When Y is not exactly conjugate symmetric due to round-off error, ifft(Y,'symmetric') treats Y as if it were conjugate symmetric by ignoring the second half of its elements (that are in the negative frequency spectrum). For more information on conjugate symmetry, see Algorithms.
collapse all
### Discrete Fourier Transform of Vector
Y = fft(X) and X = ifft(Y) implement the Fourier transform and inverse Fourier transform, respectively. For X and Y of length n, these transforms are defined as follows:
$\begin{array}{l}Y\left(k\right)=\sum _{j=1}^{n}X\left(j\right)\text{\hspace{0.17em}}{W}_{n}^{\left(j-1\right)\text{}\left(k-1\right)}\\ X\left(j\right)=\frac{1}{n}\sum _{k=1}^{n}Y\left(k\right)\text{\hspace{0.17em}}{W}_{n}{}^{-\left(j-1\right)\text{}\left(k-1\right)},\end{array}$
where
${W}_{n}={e}^{\left(-2\pi i\right)/n}$
is one of n roots of unity.
## Algorithms
• The ifft function tests whether the vectors in Y are conjugate symmetric. If the vectors in Y are conjugate symmetric, then the inverse transform computation is faster and the output is real.
A function $g\left(a\right)$ is conjugate symmetric if $g\left(a\right)={g}^{*}\left(-a\right)$. However, the fast Fourier transform of a time-domain signal has one half of its spectrum in positive frequencies and the other half in negative frequencies, with the first element reserved for the zero frequency. For this reason, a vector v is conjugate symmetric when v(2:end) is equal to conj(v(end:-1:2)).
## Version History
Introduced before R2006a
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# The inverse
The inverse matrix for matrix A has a determinant value of 0.333. What value has a determinant of the matrix A?
Correct result:
d = 3.003
#### Solution:
$d=1\mathrm{/}0.333=\frac{1000}{333}=3.003$
We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!
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Revision d73e4a2afcfbd6402c11716877e8f7466f309ef4 authored by Dominique Makowski on 22 October 2020, 13:40:02 UTC, committed by cran-robot on 22 October 2020, 13:40:02 UTC
1 parent 1b89ec8
estimate_density.Rd
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/estimate_density.R
\name{estimate_density}
\alias{estimate_density}
\alias{estimate_density.data.frame}
\title{Density Estimation}
\usage{
estimate_density(
x,
method = "kernel",
precision = 2^10,
extend = FALSE,
extend_scale = 0.1,
bw = "SJ",
...
)
\method{estimate_density}{data.frame}(
x,
method = "kernel",
precision = 2^10,
extend = FALSE,
extend_scale = 0.1,
bw = "SJ",
group_by = NULL,
...
)
}
\arguments{
\item{x}{Vector representing a posterior distribution, or a data frame of such
vectors. Can also be a Bayesian model (\code{stanreg}, \code{brmsfit},
\code{MCMCglmm}, \code{mcmc} or \code{bcplm}) or a \code{BayesFactor} model.}
\item{method}{Density estimation method. Can be \code{"kernel"} (default), \code{"logspline"} or \code{"KernSmooth"}.}
\item{precision}{Number of points of density data. See the \code{n} parameter in \code{density}.}
\item{extend}{Extend the range of the x axis by a factor of \code{extend_scale}.}
\item{extend_scale}{Ratio of range by which to extend the x axis. A value of \code{0.1} means that the x axis will be extended by \code{1/10} of the range of the data.}
\item{bw}{See the eponymous argument in \code{density}. Here, the default has been changed for \code{"SJ"}, which is recommended.}
\item{...}{Currently not used.}
\item{group_by}{Optional character vector. If not \code{NULL} and \code{x} is a data frame, density estimation is performed for each group (subset) indicated by \code{group_by}.}
}
\description{
This function is a wrapper over different methods of density estimation. By default, it uses the base R \code{density} with by default uses a different smoothing bandwidth (\code{"SJ"}) from the legacy default implemented the base R \code{density} function (\code{"nrd0"}). However, Deng \& Wickham suggest that \code{method = "KernSmooth"} is the fastest and the most accurate.
}
\note{
There is also a \href{https://easystats.github.io/see/articles/bayestestR.html}{\code{plot()}-method} implemented in the \href{https://easystats.github.io/see/}{\pkg{see}-package}.
}
\examples{
library(bayestestR)
set.seed(1)
x <- rnorm(250, 1)
# Methods
density_kernel <- estimate_density(x, method = "kernel")
density_logspline <- estimate_density(x, method = "logspline")
density_KernSmooth <- estimate_density(x, method = "KernSmooth")
density_mixture <- estimate_density(x, method = "mixture")
hist(x, prob = TRUE)
lines(density_kernel$x, density_kernel$y, col = "black", lwd = 2)
lines(density_logspline$x, density_logspline$y, col = "red", lwd = 2)
lines(density_KernSmooth$x, density_KernSmooth$y, col = "blue", lwd = 2)
lines(density_mixture$x, density_mixture$y, col = "green", lwd = 2)
# Extension
density_extended <- estimate_density(x, extend = TRUE)
density_default <- estimate_density(x, extend = FALSE)
hist(x, prob = TRUE)
lines(density_extended$x, density_extended$y, col = "red", lwd = 3)
lines(density_default$x, density_default$y, col = "black", lwd = 3)
df <- data.frame(replicate(4, rnorm(100)))
\dontrun{
# rstanarm models
# -----------------------------------------------
library(rstanarm)
model <- stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200, refresh = 0)
library(emmeans)
# brms models
# -----------------------------------------------
library(brms)
model <- brms::brm(mpg ~ wt + cyl, data = mtcars)
estimate_density(model)
}
}
\references{
Deng, H., & Wickham, H. (2011). Density estimation in R. Electronic publication.
}
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# Why are 2m and 70cm the common frequencies on HTs?
Why do most HTs have 2m and 70cm as the two bands? Is it just out of history or tradition, licensing restrictions, or is there something in the transceiver or antenna design that would make these the two obvious frequency bands of choice?
Worthy of mention is that 432MHz is a harmonic of 144MHz, meaning that the antenna can be much simpler; if it's (electrically) an odd number of half-waves on 2m, it's also an odd number of half-waves on 432MHz.
• Oh this is good! Didn't realize that relationship had such a practical effect. Commented May 14, 2018 at 2:22
• Circuit-wise too, Scott. Same reason that the HF bands are harmonically related. Back in the day, frequency multiplier circuits were used extensively. Commented May 14, 2018 at 3:05
• Yes, of course. Another reason why 40m antennas are some of the most commonly-sold, as they can also be used on 15m (3 x 7.000-7.200 works well on 21.000-21.450) Commented May 14, 2018 at 3:16
• @MikeWaters that and it made it more likely that if a ham was putting out harmonics it would only bother other hams. Long ago, 5m and 2.5m bands even occupied their natural places between 10m and 1.25m (but eventually they morphed into 6m and 2m instead). Commented May 14, 2018 at 6:59
• Note that 440mhz is not an exact 3rd harmonic of 146mhz but it's very close, which means that your antenna has to have a bit of extra bandwidth for it to work on both bands. Luckily, this isn't hard. Commented May 17, 2018 at 11:18
History and tradition are good choices of words, yes. Historically, they have been the most popular bands for mobile work; the antennas are small enough for a vehicle and many repeaters have been constructed for that reason.
6 meters used to be a popular mobile band back in the 50s and 60s. (For that matter, so were 80 and even 160.) All those bands required a larger antenna, and back in those days many hams made their own. And since 2m and 440 were so popular, 220 never caught on except in some terrestrial and EME circles.
• 80 for a mobile band? How did that work, antenna-wise? (I remember a Field Day where the club I belonged to took advantage of a loophole and strung a full size 80m quad between two really tall telephone poles on our site on the top of a hill. We were "mobile" but you know, not really mobile.) Commented May 14, 2018 at 2:24
• @davidbak Loaded verticals. Same as for 160m, which BTW have about a 1% efficiency on a truck (according to W8JI. :-) Commented May 14, 2018 at 15:17
• How do long wavelengths work as mobile bands? The HF equivalent of the rubber duck -- broadside helical. Modern commercial examples are the hamstick, iron horse, superantenna. Commented May 17, 2018 at 11:20
One reason 1.25m / 220MHz is not too popular is that not many other countries than the US have allocations in it, just like we (the US) do not have the 4m band.
Other reasons including what was previously said, could be size/practicality of antennas and useful RF distance. 6m has better propagation and bigger antennas, 23cm smaller antenna/more manageable but quite a bit line of sight propagation. Everything is a trade off in RF.
Virtually any HF antenna on a mobile is a compromised antenna by using coils to make it electrically longer than it physically is, which reduces its effectiveness, but there are those that do it because they can.
• United Parcel Service bought some of that band from the US Government. IIRC, UPS never even used it. Did that affect the amateur use of 220? Commented May 14, 2018 at 15:13
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August 28 2013, 11:59 PM #1126 cbspock Rear Admiral Location: San Antonio, TX Re: Starship Size Argument™ thread I guess you guys didn't read the article in Cinefex where they said they cheated the size of both ships in various shots. Just like in Trek 3 with the BoP. -Chris __________________ "It's important to give it all you have while you have the chance."-Shania
August 29 2013, 07:40 AM #1127
Crazy Eddie
CorporalCaptain wrote:
Crazy Eddie wrote:
WarpFactorZ wrote: At 300,000km from Earth, the gravitation field from the Earth is effectively 0.
What exactly is 55 millimeters per second? That's a speed. What does it indicate?
Acceleration due to gravity. At sea level, it's 9.8m/s^2. At 200,000km, it's about 55mm/s^2.
Though I might have missed a decimal somewhere since I was typing this on my iPad over lunch.
At an altitude of 300,000 km above the Earth, I get an acceleration, due to the Earth's gravitation, of about 4.2 millimeters per second per second, or 4.2mm/s^2 using abbreviations.
So I either missed a decimal or I rounded something too low. That's what I get for doing physics equations over a ham sandwich.
__________________
The Complete Illustrated Guide to Starfleet - Online Now!
August 29 2013, 11:09 AM #1128
Belz...
Commodore
Location: In a finely-crafted cosmos... of my own making.
WarpFactorZ wrote: If you watch the scene, the Enterprise is always pointed toward the Moon while the imuplse engines are "on." That wouldn't push them toward the Earth (and moreover doesn't really push them at all).
Aren't we over-analysing this ? And how is this about the Enterprise's size ?
__________________
And that's my opinion.
August 29 2013, 02:50 PM #1129
cbspock
Location: San Antonio, TX
Belz... wrote:
WarpFactorZ wrote: If you watch the scene, the Enterprise is always pointed toward the Moon while the imuplse engines are "on." That wouldn't push them toward the Earth (and moreover doesn't really push them at all).
Aren't we over-analysing this ? And how is this about the Enterprise's size ?
That Shatner bit makes a lot of sense
-Chris
__________________
"It's important to give it all you have while you have the chance."-Shania
August 29 2013, 06:50 PM #1130
trevanian
cbspock wrote: I guess you guys didn't read the article in Cinefex where they said they cheated the size of both ships in various shots. Just like in Trek 3 with the BoP. -Chris
Did they say WHY? That's the real question. Is this just another 'to look good/to look cool' type rationalization or is it 'director told us to,' like a lot of ILM's more problematic MUMMY 2 shots?
Man, GRAVITY is going to be so refreshing. No cheating on the scale, no sound effects in space, and they don't swing the sun around 90 or 180 degrees to get it in a convenient position for the next shot.
And the lens flares come from a real source, instead of being pulled out of a director's ass along with a ton of flashlights.
August 29 2013, 10:23 PM #1131
Kruezerman
Commodore
Location: ButtHerFace, SnooSnoo
trevanian wrote: Man, GRAVITY is going to be so refreshing. No cheating on the scale, no sound effects in space, and they don't swing the sun around 90 or 180 degrees to get it in a convenient position for the next shot.
Then you're gonna hate EVERY Star Trek episode, movie, video game, book, anything. Period.
Because few, if any, follow the laws of physics in such a tight fashion.
__________________
Lifting to make a Klingon feel inadequate.
August 29 2013, 11:01 PM #1132
BillJ
Location: alt.nerd.obsessive.pic
Kruezerman wrote:
trevanian wrote: Man, GRAVITY is going to be so refreshing. No cheating on the scale, no sound effects in space, and they don't swing the sun around 90 or 180 degrees to get it in a convenient position for the next shot.
Then you're gonna hate EVERY Star Trek episode, movie, video game, book, anything. Period.
Because few, if any, follow the laws of physics in such a tight fashion.
That and there's no guarantee that the story and characters will be worth a damn until we see the actual movie.
__________________
"If we're going to be damned, let's be damned for what we really are." - Jean-Luc Picard, "Encounter at Farpoint"
August 29 2013, 11:10 PM #1133
SeerSGB
Location: RIP Leonard Nimoy
BillJ wrote:
Kruezerman wrote:
trevanian wrote: Man, GRAVITY is going to be so refreshing. No cheating on the scale, no sound effects in space, and they don't swing the sun around 90 or 180 degrees to get it in a convenient position for the next shot.
Then you're gonna hate EVERY Star Trek episode, movie, video game, book, anything. Period.
Because few, if any, follow the laws of physics in such a tight fashion.
That and there's no guarantee that the story and characters will be worth a damn until we see the actual movie.
For the visuals I'm interested in Gravity. For the story, that slots in the rent / borrow from friend pile. What I've read out there about the movie, none of it makes me really want to see the movie in theaters.
__________________
- SeerSGB -
August 30 2013, 12:14 AM #1134 Locutus of Bored I Don't Need Your Civil War Location: Huntington Beach, California Re: Starship Size Argument™ thread I'm looking forward to Gravity because I admire Cuarón's work, Clooney is a great actor, the few reviews we've had from film festival screenings have universally praised it so far, and it makes an effort to show a more realistic take on space travel/catastrophes. That being said, I'm not looking forward to the armchair physics professors who are likely going to hold this up as an example of flawless physics and total realism when it's going to no doubt have plenty of physics flaws and questionable logic and realism, just fewer than your average science fiction film. It'll probably be like the people who call the Nolan Dark Knight trilogy "realistic" when what it actually is would be more accurately described as "more realistic than most other comic book movies." All I've seen is the trailers (including the teaser where some goofballs editing the trailer thought we needed sound in space to make it more exciting even though it's not in the actual film), so I can't make too much out of it, but it seems to me in the trailers and clips below that there's an awful lot of pinballing around back and forth in different directions between the non-existent space shuttle and the ISS where their motion should have been arrested once they grabbed on to the station. Plus they seem to fluctuate between being in a way higher orbit than the ISS actually is to being on the verge of burning up in the atmosphere in no time despite not having any source of propulsion, and there's (very) slow moving satellite debris hitting from multiple vectors before the main explosion happens when it should all come from one direction. http://www.youtube.com/watch?v=H4coTNta-YA http://www.youtube.com/watch?v=n6L0sYP-1YM Plus, Bullock seems to be playing the female astronaut who went on the cross country stalking fest in Depends given her hysterics rather than the kind of calm, cool, collected professional astronaut (male or female) one would expect given their extensive training. I get that she's a first time astronaut and this is the worst of the worst case scenarios, but they basically have her repeating the same kind of nervous jittery unsure of herself dialog she gave in Speed and every other movie she's ever done. I'm not saying she shouldn't be scared, but maybe she shouldn't be "oohing! and aahing!" so much that Clooney can barely communicate with her. Anyway, despite all that, I'm sure it will be a great, enjoyable movie, I just hope people don't get too insufferable about it and overlook the flaws in a film trying to seek greater realism while playing up the flaws in scifi movies that are seeking to give a more fantastic portrayal of space travel, like Star Trek or Star Wars. __________________ - There are stories about what happened. - It's true. All of it. TNZ, Hulk, ModMan. They're real.
August 30 2013, 01:25 AM #1135
Set Harth
Location: Angmar
they seem to fluctuate between being in a way higher orbit than the ISS actually is to being on the verge of burning up in the atmosphere in no time despite not having any source of propulsion
That kind of thing seems to be going around.
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August 30 2013, 02:07 AM #1136
trevanian
Kruezerman wrote:
trevanian wrote: Man, GRAVITY is going to be so refreshing. No cheating on the scale, no sound effects in space, and they don't swing the sun around 90 or 180 degrees to get it in a convenient position for the next shot.
Then you're gonna hate EVERY Star Trek episode, movie, video game, book, anything. Period.
Because few, if any, follow the laws of physics in such a tight fashion.
Because I like something that tries to play things honestly, I should hate all of STAR TREK? Does that include TMP, where they try to keep the lighting for space realistic much of the time?
Or Duane's THE WOUNDED SKY, which informed me about 'creative physics' in a way that made me go out and study up on all the stuff I did NOT get to hear about in school?
If you want to try applying absolutes, do so about things that ARE absolutes, or close to them. Like absolute zero.
August 30 2013, 02:20 AM #1137
trevanian
Locutus of Bored wrote: Iit seems to me in the trailers and clips below that there's an awful lot of pinballing around back and forth in different directions between the non-existent space shuttle and the ISS where their motion should have been arrested once they grabbed on to the station. Plus they seem to fluctuate between being in a way higher orbit than the ISS actually is to being on the verge of burning up in the atmosphere in no time despite not having any source of propulsion, and there's (very) slow moving satellite debris hitting from multiple vectors before the main explosion happens when it should all come from one direction.
The VFX guys ran dynamic simulations to give the animators a physics-based set of actions and movements, so the tumbling mass issues and how cables behave should be pretty damn accurate. The cinematographer got the movie's consultants to figure out the size of the Earth from the ISS altitude in order to build a bounce light source that would match accordingly.
They did their due diligence here, like 2001 did, and if they chose to deviate, they didn't do so by having the ISS built intact on Earth and lifted into orbit by Dumbo. In my book that is commendable and honorable. Add to that it's Cuaron, who is describing his style on this as trying to deliver a thriller that looks like an IMAX doc, and it may well fulfill all the expectations I once had for Fincher as The One, and I seriously doubt it is going to disappoint me on many levels.
EDIT ADDON: I can tell you that my rough cut on this article (not counting Cuaron who is a separate piece) ran to about 7000 words, even though I had to cut it by two-thirds for publication length. And I barely scratched the surface on what they did on this movie, talking to the DP, VFX super, 3D guy and asset mgr/workflow guy. It might be folks won't really even know just what all went into this till they go through the blu ray supplements (which to a certain degree was true with CHILDREN OF MEN as well ... I was utterly fooled by the baby, and for me that just doesn't ever happen anymore - so it was a pleasant shock-surprise.)
August 30 2013, 02:35 AM #1138 SeerSGB Admiral Location: RIP Leonard Nimoy Re: Starship Size Argument™ thread People are talking about the visuals of Gravity, but not many seem to be talking about the story of the movie. And to me, that's a red flag. And really the old complaint about starships being built on Earth? With a culture that can control gravity, deconstruct and reconstruct living being with ease, has various forcefields to keep a ship intact and / or safe, and warps space to travel faster than light, building a ship on the surface of a planet is a bridge to far? __________________ - SeerSGB -
August 30 2013, 02:37 AM #1139 Set Harth Rear Admiral Location: Angmar Re: Starship Size Argument™ thread They also can't go underwater. __________________ You get hurt, hurt 'em back. You get killed, walk it off.
August 30 2013, 02:57 AM #1140
Locutus of Bored
I Don't Need Your Civil War
Location: Huntington Beach, California
trevanian wrote: They did their due diligence here, like 2001 did, and if they chose to deviate, they didn't do so by having the ISS built intact on Earth and lifted into orbit by Dumbo.
That would be a cute remark if the ISS was a heavily armed FTL starship using fantastic technology being built 250 years in the future in a fictional universe that's never been all that concerned with accurate physics. But since it's not...
SeerSGB wrote: People are talking about the visuals of Gravity, but not many seem to be talking about the story of the movie. And to me, that's a red flag.
Well, that's because --as you can see from the trailers-- the story is pretty straightforward and bare bones. Disaster in space leaves two astronauts stranded and trying to survive. It's basically Open Water or 127 Hours in space. And I'm fine with that. It doesn't need a complex plot, as long as there's gripping suspense and beautiful visuals, which this seems to have in abundance.
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# ICSE Board Exam 2016 : Physics
7 pages, 73 questions, 73 questions with responses, 504 total responses, 0 0
Srujan Deshpande Sri Chaitanya Techno School, Bangalore XI-XII PCM, IP, English
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PHYSICS SCIENCE Paper -I (Two hours) Answers to this Paper must be writlen on the paper provided separately. l'ou will not be allowed to write during the first I5 minutes. This time is to be spent in reading the Question Poper. The time given at the head of this Paper is the time allowed Section I is compulsory. Attempt any The intended marl<s four questions for writing the answers. from Section II. for questions or parts of questions are given in brockets I J. SECTION I (40 Marks) Attempt all questions from this Section. Question (a) (i) (ii) I Give an example of a-non contact force which is always of attractive nature. tzl How does the magnitude oittrls non contactJbrceon the two bodies depend on the distance of separation between them? (b) A boy'weighing and a (i) 40kgf climbs up a stair of 30 steps each 20cm high in 4 minute 121 girl weighing 30kgf does the same in 3 minutes. Compare:- The work done by them. (ii) The power developed (c) by them. With reference to the terms Mechanical Advantage, Velocity Ratio and t2) efficiency of a machine, name and define the term that will not change for a machine of a given design. (d) Calculate the mass of ice required to lower the temperature of 3009 of water at 40oC to water at 0oC. (Specific latent heat of ice:336 J/g, Specific heat capacity of water:4.2 llg"C) 521 This Paper consists of 7 printed pages and T16 O Copyright reserved. I blank page. Turn over tzl
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Using numbers and handling data
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# 3.5 Line graphs
To illustrate how to create and use line graphs, we will use the example of a calibration curve.
A calibration curve is a type of line graph in which the response of a measuring device to a series of known concentrations of a substance is plotted. You can then make a measurement of an unknown sample - in the case we're about to examine, blood serum samples from new-born infants - and use the calibration curve to work out what concentration of substance is present.
## SAQ 6
Think of a type of machine that can perform measurements to give readings that can then be used to make a standard curve.
A spectrophotometer provides these types of measurement data, which can be used to produce standard curves.
## Box 5 Spectrophotometers explained
A spectrophotometer is an instrument that determines how much light of a particular colour is absorbed by a liquid sample. The more there is of a coloured substance in the solution, the more light will be absorbed (i.e. the less light passes through the solution). After measuring how much light is absorbed by a series of solutions containing known concentrations of the coloured substance, you can draw a graph of this data and use it to calculate the concentration of that substance in an unknown sample from a measurement of how much light it absorbs.
Here's how a spectrophotometer works:
1. White light from a bulb (source) is focused into a narrow beam by passing it through a thin slit.
2. A prism is used to split the beam of white light into its component colours, in the same way that water droplets can split sunlight into its component colours to make a rainbow. Different colours of light have a different wavelength: the distance between the peaks of the light waves, measured in nanometres (where 1 nanometre is 10-9 metres). For an idea of scale, individual virus particles range in size from about 20-300 nm).
3. A second thin slit, just after the prism, can be moved from side to side to select just one colour of light to pass through to the sample.
4. The light passes through a container with the liquid sample inside (usually the light passes through 1 cm thickness of the liquid).
5. A light detector measures how much light is transmitted through the sample, and compares this with how much light was emitted by the source. The difference between these values gives a measure of how much light was absorbed by the sample: i.e. the absorbance (A), often also called the optical density (OD). The absorbance varies with wavelength, so measurements of this type always specify the wavelength of light that was shone through the sample. In the following example with C-reactive protein, the wavelength was 450 nm, so this would be quoted as A450 or OD450.
This process is summarised below in Figure 10, which also gives an indication of the wavelengths of different parts of the visible light spectrum.
Figure 10 A spectrophotometer measures how much light of a certain wavelength is absorbed by a liquid
In this particular example, we are looking at how the concentration of C-reactive protein (CRP: a blood component produced in response to infection) changes the intensity of a blue-coloured test solution: the more CRP present, the more intense the blue colour becomes. The intensity of the blue colour is determined using a spectrophotometer to measure the Optical Density at 450 nm (O.D. 450 nm). More specifically, this is a measure of the amount of a blue light with a wavelength of 450 nanometres (450 nm) that is absorbed by a known thickness of the solution before the light reaches a detector.
When making a calibration curve, the following points need to be considered:
1. What is the expected range of concentrations?
• The range of blood serum CRP concentrations that might be encountered in infants, and the level of infection that this correlates with, are as follows:
• normal: <2 μg/ml
• sepsis: >22 μg/ml
• dying: >120 μg/ml
• Where < means 'less than' and > means 'more than'.
• (Romagnoli et al., 2001)
• From these values, a range of known standards containing between 0-100 μg/ml CRP should cover the most likely range of infant serum CRP concentrations.
2. Am I within the working range of the instrument?
• Many instruments are only accurate over a specific range of values. As we continue to increase the CRP concentration, the blue dye will become more and more intense. However, this can't continue forever and after a point the solution will be saturated with blue dye. Beyond that the solution can't get any more intense, no matter how much CRP we add. As we begin to reach this saturation point, the measurements will plateau out to the maximum value as CRP is increased. The most reliable part of the calibration curve covers the middle range of concentrations, where it is closest to being a straight line. For this reason, it is called the linear part of the graph.
3. How random or 'noisy' is the assay and the measuring device?
• Depending on the precision of the measuring device you may not get the same reading every time from the same sample. To compensate for this it is a good idea to repeat the sample measurement two or three times and then calculate the average or mean value. For example, if you repeated the measurement of the same sample once, then you'd add both results together and then divide the resulting figure by 2 to find the average value.
With these points in mind, Figure 11 shows a table and graph of OD450 values measured using a series of known concentrations of CRP.
Figure 11 Calibration curve for CRP
In general, the x-axis is used to represent a variable that changes in a consistent way, or in a way that you can control (here, it's the known concentrations of CRP that you have measured out). The y-axis is normally used to represent a variable that you measure but may not be able to affect directly (in this case the optical density of the CRP test solutions that you read from the measuring device).
The small circular symbols on the graph mark the measured data points and they are joined by a curved line.
Notice that the graph shows a positive correlation between the two variables: the more CRP that is present, the larger the optical density reading. Other types of data may show a negative correlation between the variables, whereby one of the measured entities decreases as the other increases, e.g. the further you drive your car, the less petrol you have in the petrol tank.
S110_1
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Freedmans survey showed that people living in small towns
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Re: Freedman's survey showed that people living in small towns [#permalink]
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15 Feb 2016, 13:37
tonebeeze wrote:
Freedman's survey showed that people living in small towns and rural areas consider themselves no happier than do people living in big cities.
a. no happier than do people living
b. not any happier than do people living
c. not any happier than do people who live
d. no happier than are people who are living
e. not as happy as are people who live
In D and E we have wrong comparison (happiness vs people). In C and B "not any happier" is wordy, i think. Hence correct choice is A
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Re: Freedman's survey showed that people living in small towns [#permalink]
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16 Feb 2016, 02:41
Konstantin1983 wrote:
tonebeeze wrote:
Freedman's survey showed that people living in small towns and rural areas consider themselves no happier than do people living in big cities.
a. no happier than do people living
b. not any happier than do people living
c. not any happier than do people who live
d. no happier than are people who are living
e. not as happy as are people who live
In D and E we have wrong comparison (happiness vs people). In C and B "not any happier" is wordy, i think. Hence correct choice is A
Konstantin1983
The simplified structure of the sentence is as follows:
X consider themselves happier than Y consider themselves.
The comparison is between how happy X consider themselves and how happy Y consider themselves.
You may replace the second verb consider with do, but not with are.
If you use are instead of do, the comparison would be between how happy X consider themselves and how happy Y actually are. This meaning is not intended.
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Re: Freedman's survey showed that people living in small towns [#permalink]
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16 Feb 2016, 14:05
It is also interesting to note that E changes the meaning. “Not as happy” is not the same as “no happier”. Eliminate E. “No happier” is better than “not any happier”. Eliminate B and C. The simplified sentence structure is “people A consider themselves happier than people B consider themselves”. To eliminate repetition of “consider” you can use the auxiliary verb “do”. Eliminate D. A is the answer. To simplify the sentence by breaking it down to its essential structure is a very valuable tool in sentence correction.
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Re: Freedmans survey showed that people living in small towns [#permalink]
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12 Mar 2016, 21:56
ugimba wrote:
317. Freedman’s survey showed that people living in small towns and rural areas consider themselves no happier than do people living in big cities.
(A) no happier than do people living
(B) not any happier than do people living
(C) not any happier than do people who live
(D) no happier than are people who are living
(E) not as happy as are people who live
and explain 'no happier' versus 'not any happier' also....
no +er is idomatic
not any+er is not idiomatic. end of story.
in d and e, "are" need a form of to be in previous part.
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Re: Freedmans survey showed that people living in small towns [#permalink]
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25 Aug 2017, 00:54
Merged topics. Please, search before posting questions!
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# Calculation Of Prospective Short-Circuit Currents On T&D Systems (Practical Guidance)
Home / Download Center / Electrical Engineering Books, Technical Guides and Publications / Electricity generation, transmission and distribution guides / Calculation Of Prospective Short-Circuit Currents On T&D Systems (Practical Guidance)
## Faults In T&D Systems
When a fault occurs on the transmission or distribution system, the current which flows into the fault will be derived from a combination of three sources: (1) Major generating stations via the T&D networks, (2) Embedded generators connected to the local network and (3) Conversion of the mechanical inertia of rotating plant equipment.
### Calculation Of Fault Levels
#### Fault Level Calculation Fundamentals
The management of prospective fault level conditions in terms of circuit breaker make and break duties requires an assessment of the fault current contributions from all potential sources.
This section addresses the procedures for the development of network and load models to enable the assessment of the interaction of the various sources of fault current contributions.
The methodology described in IEC 60909 allows for the calculation of short circuit currents using sequence components.
The methodology makes certain assumptions about the nature of the fault for the purposes of defining the network impedance conditions.
1. For the duration of the short circuit there is no change in the type of short circuit involved, that is a three phase short circuit remains three phase and a line-to-earth short circuit remains line-to-earth fault for the duration of the fault.
2. For the duration of the short circuit, there are no other changes in the network.
3. The impedance of the transformers is referred to the tap-changer in nominal position. This is admissible because an impedance correction factor KT for network transformers is introduced.
4. Arc Resistances are not taken into account.
5. All line capacitances and shunt admittances and non-rotating loads, except those of the zero sequence system, are neglected.
### Simple Fault Level Calculations
The method of calculating system fault levels are covered in detail in many text books and it is not the intention of this document to reproduce that material. However, some practical guidance may be of assistance.
The basis of fault level calculations can be either:
1. Ohms at a chosen Standard Voltage
2. Percentage impedance drop at a chosen standard MVA base
3. Per unit method (an adaptation of (b))
Many planners prefer option (b) and the most convenient and normal standard base is 100MVA.
Title: Calculation Of Prospective Short-Circuit Currents On T&D Systems (Practical Guidance) by SP Power Systems Format: PDF Size: 710 KB Pages: 32 Download: Right here | Get Download Updates | Get Technical articles
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# LeetCode 332. Reconstruct Itinerary
Problem:
Given a list of airline tickets represented by pairs of departure and arrival airports [from, to], reconstruct the itinerary in order. All of the tickets belong to a man who departs from JFK. Thus, the itinerary must begin with JFK.
Note:
1. If there are multiple valid itineraries, you should return the itinerary that has the smallest lexical order when read as a single string. For example, the itinerary ["JFK", "LGA"] has a smaller lexical order than ["JFK", "LGB"].
2. All airports are represented by three capital letters (IATA code).
3. You may assume all tickets form at least one valid itinerary.
Example 1:
tickets = [["MUC", "LHR"], ["JFK", "MUC"], ["SFO", "SJC"], ["LHR", "SFO"]]
Return ["JFK", "MUC", "LHR", "SFO", "SJC"].
Example 2:
tickets = [["JFK","SFO"],["JFK","ATL"],["SFO","ATL"],["ATL","JFK"],["ATL","SFO"]]
Return ["JFK","ATL","JFK","SFO","ATL","SFO"].
Another possible reconstruction is ["JFK","SFO","ATL","JFK","ATL","SFO"]. But it is larger in lexical order.
Solution:
DFS+backtracking. At first I did not realize all tickets have to be used. Reading the question thoroughly is very important.
public class Solution {
Map<String, List<String>> g = new HashMap<String, List<String>>();
List<String> sol = new ArrayList<String>();
int size;
public List<String> findItinerary(String[][] tickets) {
for (int i = 0; i < tickets.length; i++) {
String from = tickets[i][0];
String to = tickets[i][1];
if (!g.containsKey(from)) {
List<String> opts = new ArrayList<String>();
g.put(from, opts);
}
else {
List<String> opts = g.get(from);
g.put(from, opts);
}
}
size = tickets.length + 1;
find(sol);
return sol;
}
private boolean find(List<String> current) {
if (current.size() == size) return true;
String start = current.get(current.size() - 1);
List<String> opts = g.get(start);
if (opts == null || opts.size() == 0) {
return false;
}
Collections.sort(opts);
for (int i = 0; i < opts.size(); i++) {
String opt = opts.get(i);
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https://www.futurestarr.com/blog/mathematics/6-out-of-25-as-a-percentage-or
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FutureStarr
6 Out of 25 As a Percentage OR
## 6 Out of 25 As a Percentage
Miles and miles of cliffs lie between my two homes. To be honest, I barely noticed the blackish canyon wall looming in the distance until my brother video called me from the cabin. Now, as I look at it from a boat, it’s as familiar to me as my own backyard.
### Decimal
Percentages are sometimes better at expressing various quantities than decimal fractions in chemistry or physics. For example, it is much convenient to say that percentage concentration of a specific substance is 15.7% than that there are 18.66 grams of substance in 118.66 grams of solution (like in an example in percentage concentration calculator). Another example is efficiency (or its special case - Carnot efficiency). Is it better to say that a car engine works with an efficiency of 20% or that it produces an energy output of 0.2 kWh from the input energy of 1 kWh? What do you think? We are sure that you're already well aware that knowing how to get a percentage of a number is a valuable ability.
Although Ancient Romans used Roman numerals I, V, X, L, and so on, calculations were often performed in fractions that were divided by 100. It was equivalent to the computing of percentages that we know today. Computations with a denominator of 100 became more standard after the introduction of the decimal system. Many medieval arithmetic texts applied this method to describe finances, e.g., interest rates. However, the percent sign % we know today only became popular a little while ago, in the 20th century, after years of constant evolution. (Source: www.omnicalculator.com)
### Divide
Percentage increase and decrease are calculated by computing the difference between two values and comparing that difference to the initial value. Mathematically, this involves using the absolute value of the difference between two values, and dividing the result by the initial value, essentially calculating how much the initial value has changed.
Let's give ourselves a little bit of practice with percentages. So let's ask ourselves, what percent of-- I don't know, let's say what percent of 16 is 4? And I encourage you to pause this video and to try it out yourself. So when you're saying what percent of 16 is 4, percent is another way of saying, what fraction of 16 is 4? And we just need to write it as a percent, as per 100. So if you said what fraction of 16 is 4, you would say, well, look, this is the same thing as 4/16, which is the same thing as 1/4. But this is saying what fraction 4 is of 16. You'd say, well, 4 is 1/4 of 16. But that still doesn't answer our question. What percent? So in order to write this as a percent, we literally have to write it as something over 100. Percent literally means "per cent." The word "cent" you know from cents and century. It relates to the number 100. So it's per 100. So you could say, well, this is going to be equal to question mark over 100, the part of 100. And there's a bunch of ways that you could think about this. You could say, well, look, if in the denominator to go from 4 to 100, I have to multiply by 25. In the numerator to go from-- I need to also multiply by 25 in order to have an equivalent fraction. So I'm also going to multiply by 25. So 1/4 is the same thing as 25/100. And another way of saying 25/100 is this is 25 per 100, or 25%. So this is equal to 25%. Now, there's a couple of other ways you could have thought about it. You could have said well, 4/16, this is literally 4 divided by 16. Well, let me just do the division and convert to a decimal, which is very easy to convert to a percentage. So let's try to actually do this division right over here. So we're going to literally divide 4 by 16. Now, 16 goes into 4 zero times. 0 times 16 is 0. You subtract, and you get a 4. And we're not satisfied just having this remainder. We want to keep adding zeroes to get a decimal answer right over here. So let's put a decimal right over here. We're going into the tenths place. And let's throw some zeroes right over here. The decimal makes sure we keep track of the fact that we are now in the tenths, and in the hundredths, and in the thousandths place if we have to go that far. But let's bring another 0 down. 16 goes into 40 two times. 2 times 16 is 32. If you subtract, you get 8. And you could bring down another 0. And we have 16 goes into 80. Let's see, 16 goes into 80 five times. 5 times 16 is 80. You subtract, you have no remainder, and you're done. 4/16 is the same thing as 0.25. Now, 0.25 is the same thing as twenty-five hundredths. Or, this is the same thing as 25/100, which is the same thing as 25%. (Source: www.khanacademy.org)
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http://www.education.com/reference/article/mechanical-motion/?page=3
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Education.com
# Mechanical Comprehension Study Guide 2 for McGraw-Hill's ASVAB (page 3)
By Dr. Janet E. Wall
McGraw-Hill Professional
### Cams and Cam Followers
Camsare lobes attached to rotating shafts to push separate pieces, called cam followers. Cams are often found in engines, where they push intake and exhaust valves open when the engine turns. For every complete rotation of the camshaft, the cam follower will move away from and then back to its original position. A spring pushes the follower tight to the cam.
### Cranks and Pistons
Cranksare used to change motion in a straight line to motion in a circle. You'll find cranks connected to pedals on a bike, and to pistons in a car engine. When a crank makes one complete revolution, the piston must go up and down and return to its original position.
### Fluid Dynamics
Fluidsare substances that take the shape of their container. Gases and liquids are both fluids. The behavior of fluids is called fluid dynamics, and it can get rather complicated, but not on the ASVAB. Let's start with air, and move on to hydraulics—the engineering of liquids.
### Air Pressure
Air pressure is measured in pounds per square inch. Atmospheric pressure at sea level is 14.7 lb/in2, which is actually quite a bit of pressure. Since it's present all around us, we don't notice it. However, if you create a vacuum inside a weak container, the container will be crushed by all that pressure.
Pneumatics and the Gas LawsSystems that use compressed air to do work are called pneumatic systems. Air is easily compressed, and the calculations are more complicated than they are with liquids, which usually can't be compressed. The larger the driven cylinder, the more air pressure it is exposed to, and the greater the force it can exert.
The "gas laws" apply to air as it is compressed and expanded.
• When a gas is compressed, it gains thermal energy—it warms up. The gas also gains potential energy, which is why compressed air can be used to drive nail guns and pneumatic hammers.
• When a given amount of gas expands, its pressure drops and the gas cools.
• When a gas cools without a change in outside pressure, it loses volume.
What happens when you increase the air pressure outside a balloon? The balloon shrinks until the pressure inside becomes great enough to balance the pressure outside.
Air pressure is also what keeps airplanes aloft. The bulge on the top of an airplane wing increases the speed of air passing over the wing, and that causes a reduction in pressure. Because air pressure does not change below the wing, the result is an unbalanced upward force. This force lifts the airplane.
RefrigeratorsRefrigerators and air conditioners provide interesting applications of the gas laws. A compressor compresses a fluid, called a refrigerant. The refrigerant warms up, as predicted by the gas laws. Then the refrigerant loses heat (but not pressure) in the condenser. The refrigerant is piped into an evaporator, where it goes through a small hole and evaporates under reduced pressure. Expansion causes the temperature to drop, and the cold refrigerant can pick up heat from the surroundings. This is why the evaporator is placed in the area to be cooled. The condenser is placed where it's easy to get rid of excess heat—in the backyard for an air conditioner, or in back for a refrigerator.
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posted by .
Miss B. built a vegetable garden in her backyard. Her rectangular garden was 11m by 9m.
Every morning she would notice carrots missing from her garden! In order to keep Bugs Bunny from eating all her carrots, she built a fence surrounding them. This fence had a total perimeter of 8m.
Bugs Bunny had a big appetite; he also liked to eat her lettuce from the garden as well. Miss B. placed toy snakes in her garden to scare Bugs Bunny. These snakes surrounded the lettuce, stretching 3m wide by 5m long.
1. What is the total area of Miss B. garden NOT including the carrot and lettuce patches?
1. Total area of garden:
A= lxw (11m x 9m)= 99m sq.
2. Area of Carrot patch
A= LxW (2m x 2m) = 4m sq.
3. Area of lettuce patch
A= LxW (3m x 5m) = 15m sq.
Area of garden not including carrots/lettuce:
99m - 4m - 15m = 80m sq.
is this correct?
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Physics
posted by .
An airplane takes off at a constant speed of 331 m/s at an angle of 45 degrees. What is the airplane's horizontal velocity
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https://metanumbers.com/31745
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# 31745 (number)
31,745 (thirty-one thousand seven hundred forty-five) is an odd five-digits composite number following 31744 and preceding 31746. In scientific notation, it is written as 3.1745 × 104. The sum of its digits is 20. It has a total of 3 prime factors and 8 positive divisors. There are 21,744 positive integers (up to 31745) that are relatively prime to 31745.
## Basic properties
• Is Prime? No
• Number parity Odd
• Number length 5
• Sum of Digits 20
• Digital Root 2
## Name
Short name 31 thousand 745 thirty-one thousand seven hundred forty-five
## Notation
Scientific notation 3.1745 × 104 31.745 × 103
## Prime Factorization of 31745
Prime Factorization 5 × 7 × 907
Composite number
Distinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 3 Total number of prime factors rad(n) 31745 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 31,745 is 5 × 7 × 907. Since it has a total of 3 prime factors, 31,745 is a composite number.
## Divisors of 31745
1, 5, 7, 35, 907, 4535, 6349, 31745
8 divisors
Even divisors 0 8 4 4
Total Divisors Sum of Divisors Aliquot Sum τ(n) 8 Total number of the positive divisors of n σ(n) 43584 Sum of all the positive divisors of n s(n) 11839 Sum of the proper positive divisors of n A(n) 5448 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 178.171 Returns the nth root of the product of n divisors H(n) 5.82691 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 31,745 can be divided by 8 positive divisors (out of which 0 are even, and 8 are odd). The sum of these divisors (counting 31,745) is 43,584, the average is 5,448.
## Other Arithmetic Functions (n = 31745)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 21744 Total number of positive integers not greater than n that are coprime to n λ(n) 1812 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 3417 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 21,744 positive integers (less than 31,745) that are coprime with 31,745. And there are approximately 3,417 prime numbers less than or equal to 31,745.
## Divisibility of 31745
m n mod m 2 3 4 5 6 7 8 9 1 2 1 0 5 0 1 2
The number 31,745 is divisible by 5 and 7.
## Classification of 31745
• Arithmetic
• Deficient
• Polite
• Square Free
### Other numbers
• LucasCarmichael
• Sphenic
## Base conversion (31745)
Base System Value
2 Binary 111110000000001
3 Ternary 1121112202
4 Quaternary 13300001
5 Quinary 2003440
6 Senary 402545
8 Octal 76001
10 Decimal 31745
12 Duodecimal 16455
20 Vigesimal 3j75
36 Base36 oht
## Basic calculations (n = 31745)
### Multiplication
n×y
n×2 63490 95235 126980 158725
### Division
n÷y
n÷2 15872.5 10581.7 7936.25 6349
### Exponentiation
ny
n2 1007745025 31990865818625 1015550035412250625 32238635874161896090625
### Nth Root
y√n
2√n 178.171 31.6635 13.3481 7.94941
## 31745 as geometric shapes
### Circle
Diameter 63490 199460 3.16592e+09
### Sphere
Volume 1.34003e+14 1.26637e+10 199460
### Square
Length = n
Perimeter 126980 1.00775e+09 44894.2
### Cube
Length = n
Surface area 6.04647e+09 3.19909e+13 54984
### Equilateral Triangle
Length = n
Perimeter 95235 4.36366e+08 27492
### Triangular Pyramid
Length = n
Surface area 1.74547e+09 3.77016e+12 25919.7
## Cryptographic Hash Functions
md5 ed21b54c417d6d8638aef8efc652fe37 9e19d36b52369878634b9cd2d4d3aa31d1e3f311 d3837082b79219df8ee07e5e96c9fd21299d5e2fb6bd01de7b2299b4a0f5b088 f660eeb2fb1e460181d8b32ac38662b3e40dd3a85b88c2df4e1d818799505f8df1bfea0e2f78e27a516619dc4f71fa24ffddc936c227e21ce59b90684edc6af9 448b387f940feefc562024aed075bb6101db7db3
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https://functions.wolfram.com/Bessel-TypeFunctions/AiryBi/06/02/03/02/0006/
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html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }
AiryBi
http://functions.wolfram.com/03.06.06.0054.01
Input Form
AiryBi[z] \[Proportional] Piecewise[ {{(-((-1)^(3/4)/(Sqrt[2 Pi] z^(1/4)))) (Cosh[(2 z^(3/2))/3] + I Sinh[(2 z^(3/2))/3]), Arg[z] <= -((2 Pi)/3)}, {(-(I/(2 Sqrt[Pi] z^(1/4)))) ((1 + 2 I) Cosh[(2 z^(3/2))/3] - (1 - 2 I) Sinh[(2 z^(3/2))/3]), Inequality[-((2 Pi)/3), Less, Arg[z], LessEqual, 0]}, {(I/(2 Sqrt[Pi] z^(1/4))) ((1 - 2 I) Cosh[(2 z^(3/2))/3] - (1 + 2 I) Sinh[(2 z^(3/2))/3]), Inequality[0, Less, Arg[z], LessEqual, (2 Pi)/3]}}, ((-1)^(1/4)/(Sqrt[2 Pi] z^(1/4))) (Cosh[(2 z^(3/2))/3] - I Sinh[(2 z^(3/2))/3])] /; (Abs[z] -> Infinity)
Standard Form
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["AiryBi", "[", "z", "]"]], "\[Proportional]", RowBox[List["Piecewise", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " "]], RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]]]], ")"]]]], ",", RowBox[List[RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", RowBox[List["-", FractionBox[RowBox[List["2", "\[Pi]"]], "3"]]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " "]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]]]], ")"]]]], ",", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", "\[Pi]"]], "3"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " "]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]]]], ")"]]]], ",", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox[RowBox[List["2", "\[Pi]"]], "3"]]]]], "}"]]]], "}"]], ",", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " "]], RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]]]], ")"]]]]]], "]"]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]
MathML Form
Bi ( z ) - ( - 1 ) 3 / 4 2 π z 4 ( cosh ( 2 z 3 / 2 3 ) + sinh ( 2 z 3 / 2 3 ) ) arg ( z ) - 2 π 3 - 2 π z 4 ( ( 1 + 2 ) cosh ( 2 z 3 / 2 3 ) - ( 1 - 2 ) sinh ( 2 z 3 / 2 3 ) ) - 2 π 3 < arg ( z ) 0 2 π z 4 ( ( 1 - 2 ) cosh ( 2 z 3 / 2 3 ) - ( 1 + 2 ) sinh ( 2 z 3 / 2 3 ) ) 0 < arg ( z ) 2 π 3 - 1 4 2 π z 4 ( cosh ( 2 z 3 / 2 3 ) - sinh ( 2 z 3 / 2 3 ) ) True TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional AiryBi z -1 -1 3 4 2 1 2 z 1 4 -1 2 z 3 2 3 -1 2 z 3 2 3 -1 z -1 2 3 -1 -1 2 1 2 z 1 4 -1 1 2 2 z 3 2 3 -1 -1 1 -2 2 z 3 2 3 -1 Inequality -1 2 3 -1 z 0 2 1 2 z 1 4 -1 1 -2 2 z 3 2 3 -1 -1 1 2 2 z 3 2 3 -1 Inequality 0 z 2 3 -1 -1 1 4 2 1 2 z 1 4 -1 2 z 3 2 3 -1 -1 2 z 3 2 3 -1 Rule z [/itex]
Rule Form
Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryBi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Piecewise]", GridBox[List[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]]]], ")"]]]], RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], RowBox[List[RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["(", RowBox[List["2", " ", "\[Pi]"]], ")"]]]]]]], List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]]]], ")"]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]]]], RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["(", RowBox[List["2", " ", "\[Pi]"]], ")"]]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]], List[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]]]], ")"]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox[RowBox[List["2", " ", "\[Pi]"]], "3"]]]], List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"], "]"]]]]]], ")"]]]], RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]
Date Added to functions.wolfram.com (modification date)
2007-05-02
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# sine rule
• Nov 19th 2006, 03:39 AM
jim49990
sine rule
using the sine rule solve the following triangles DEF and find their areas
d=17cm f=22cm F=26*
could anyone please show me how to do this example so i could do the others
tha
:confused: nks
• Nov 19th 2006, 04:10 AM
topsquark
Quote:
Originally Posted by jim49990
using the sine rule solve the following triangles DEF and find their areas
d=17cm f=22cm F=26*
could anyone please show me how to do this example so i could do the others
tha
:confused: nks
The Law of Sines is:
$\frac{d}{sin(D)} = \frac{e}{sin(E)} = \frac{f}{sin(F)}$
So for sides d and f:
$\frac{17}{sin(D)} = \frac{22}{sin(26)}$
$sin(D) = \frac{17 \cdot sin(26)}{22} = 0.338741$
So $D = 19.8^o$. Now, D could merely be the reference angle, so it is possible that $D = 180^o - 19.8^o = 160.2^o$ except that the sum of the interior angles in any triangle is 180 degrees. If D were 160.2 degrees then angle D plus angle F accounts for more than 180 degrees not even counting angle E. So angle D must be 19.8 degrees.
So we know two angles in the triangle and as I said above we know that the sum of the interior angles of a triangle is 180 degrees. So for angle E:
$E = 180 - D - F = 180^o - 19.8^o - 26^o = 134.2^o$
Employing the Law of Sines for e and f:
$\frac{e}{sin(134.2)} = \frac{22}{sin(26)}$
$e = \frac{22 \cdot sin(134.2)}{sin(26)} = 35.9788$
So side e is about 36.0 cm in length.
There are various ways to get the area of the triangle. This is Heron's formula:
$A = \sqrt{s(s-d)(s-e)(s-f)}$ where $s = \frac{d+e+f}{2}$ (Called the "semi-perimeter.")
So
$s = \frac{17 + 36 + 22}{2} = 37.4894$ (I am using the unrounded expression for e.)
$A = \sqrt{37.4894 (37.4894 - 17)(37.4894 - 36)(37.4894 - 22)} = 134.063$
So the area of the triangle is about $134.1 \, cm^2$.
-Dan
• Nov 19th 2006, 05:30 AM
Soroban
Hello, Jim!
Quote:
Using the Sine Rule, solve triangle $D{E}F$ and find its area.
. . $d = 17\text{ cm, } f = 22\text{ cm, }F = 26^o$
Dan did an excellent job in solving the triangle.
Here's another way to find its area.
. . $\text{Area } = \:\frac{1}{2}bc\sin A$
One-half the product of two sides and the sine of the included angle.
Since we know: . $d = 17,\:f = 22,\:E = 134.2^o$
. . we have: . $A \:=\:\frac{1}{2}(17)(22)\sin134.2^o \:=\:134.0622836 \:\approx\:134.1$ cm².
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https://math.stackexchange.com/questions/linked/1334832
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5 questions linked to/from Prove limit converges in definition of $e.$
1k views
### Prove that $a_n = \{\left(1+\frac{1}{n}\right)^n\}$ is bounded sequence, $n\in\mathbb{N}$
How to prove the following: $a_n = \left\{\left(1+\frac{1}{n}\right)^n\right\}$ is bounded sequence, $n\in\mathbb{N}$
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http://www.algebra.com/cgi-bin/show-question-source.mpl?solution=348501
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```Question 526246
Since angle 1 and angle 2 are equal, name each angle "x." The sum of angle 1 and angle 2 is 2x, which is equal to 180 degrees (since BD is a straight line). Hence 2x = 180, x = 90, so the angles are right angles. This implies that AC and BD are perpendicular.
Use this to write out your proof.```
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https://oeis.org/A319586
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The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A319586 Number of n-digit base-10 palindromes (A002113) that cannot be written as the sum of two positive base-10 palindromes. 1
2, 0, 8, 7, 95, 94, 975, 971, 9810, 9805, 98288, 98272 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 LINKS Table of n, a(n) for n=1..12. EXAMPLE a(1) = 2, because 0 and 1 are not sums of two positive 1-digit integers, all of which are palindromes. a(3) = 8, because the 8 3-digit palindromes 111, 131, 141, 151, 161, 171, 181, and 191 (A213879(2) ... A213879(9)) cannot be written as sum of two nonzero palindromes. PROG (PARI) \\ calculates a(2)...a(8) using M. F. Hasler's functions in A002113 A002113(n)={my(L=logint(n, 10)); (n-=L=10^max(L-(n<11*10^(L-1)), 0))*L+fromdigits(Vecrev(digits(if(nP/2, break); if(is_A002113(P-PP), issum=1; break)); if(issum==0, j++)); print1(j, ", ", )) (Python) from sympy import isprime from itertools import product def pals(d, base=10): # all d-digit palindromes digits = "".join(str(i) for i in range(base)) for p in product(digits, repeat=d//2): if d > 1 and p[0] == "0": continue left = "".join(p); right = left[::-1] for mid in [[""], digits][d%2]: yield int(left + mid + right) def a(n): palslst = [p for d in range(1, n+1) for p in pals(d)][1:] palsset = set(palslst) cs = ctot = 0 for p in pals(n): ctot += 1 for p1 in palslst: if p - p1 in palsset: cs += 1; break if p1 > p//2: break return ctot - cs print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Jul 12 2021 CROSSREFS Cf. A002113, A035137, A213879, A319477. Sequence in context: A366164 A021483 A011015 * A287467 A288015 A288438 Adjacent sequences: A319583 A319584 A319585 * A319587 A319588 A319589 KEYWORD nonn,base,hard,more AUTHOR Hugo Pfoertner, Sep 23 2018 EXTENSIONS a(12) from Giovanni Resta, Oct 01 2018 STATUS approved
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Last modified May 24 05:24 EDT 2024. Contains 372772 sequences. (Running on oeis4.)
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https://www.itl.nist.gov/div898/handbook/pri/section3/eqns/2to6m2.txt
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THIS IS DATAPLOT DESIGN-OF-EXPERIMENT FILE 2TO6M2.DAT 2**(6-2) FRACTIONAL FACTORIAL DESIGN NUMBER OF LEVELS FOR EACH FACTOR = 2 NUMBER OF FACTORS = 6 NUMBER OF OBSERVATIONS = 16 RESOLUTION = 4 (THEREFORE NO MAIN EFFECTS ARE CONFOUNDED WITH ANY 2-FACTOR INTERACTIONS; MAIN EFFECTS ARE CONFOUNDED WITH 3-FACTOR INTERACTIONS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FACTOR DEFINITION CONFOUNDING STRUCTURE 1 1 1 + 235 + 456 + 12346 2 2 2 + 135 + 346 + 12456 3 3 3 + 125 + 246 + 13456 4 4 4 + 156 + 236 + 12345 5 123 5 + 123 + 146 + 23456 6 234 6 + 145 + 234 + 12356 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 12 + 35 + 1346 + 2456 13 13 + 25 + 1246 + 3456 14 14 + 56 + 1236 + 2345 15 15 + 23 + 46 + 123456 16 16 + 45 + 1234 + 2356 23 23 + 15 + 46 + 123456 24 24 + 36 + 1256 + 1345 25 25 + 13 + 1246 + 3456 26 26 + 34 + 1245 + 1356 34 34 + 26 + 1245 + 1356 35 35 + 12 + 1346 + 2456 36 36 + 24 + 1256 + 1345 45 45 + 16 + 1234 + 2356 46 46 + 15 + 23 + 123456 56 56 + 14 + 1236 + 2345 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DEFINING RELATION = I = 1235 = 2346 = 1456 REFERENCE--BOX, HUNTER & HUNTER, STAT. FOR EXP., PAGE 410, NOTE--IF POSSIBLE, THIS (AS WITH ALL EXPERIMENT DESIGNS) SHOULD BE RUN IN RANDOM ORDER (SEE DATAPLOT'S RANDOM PERMUTATION FILES). NOTE--TO READ THIS FILE INTO DATAPLOT-- SKIP 50 READ 2TO6M2.DAT X1 TO X6 DATE--DECEMBER 1988 NOTE--IN THE DESIGN BELOW, "-1" REPRESENTS THE "LOW" SETTING OF A FACTOR "+1" REPRESENTS THE "HIGH" SETTING OF A FACTOR NOTE--ALL FACTOR EFFECT ESTIMATES WILL BE OF THE FORM AVERAGE OF THE "HIGH" - AVERAGE OF THE "LOW" X1 X2 X3 X4 X5 X6 ---------------------- -1 -1 -1 -1 -1 -1 +1 -1 -1 -1 +1 -1 -1 +1 -1 -1 +1 +1 +1 +1 -1 -1 -1 +1 -1 -1 +1 -1 +1 +1 +1 -1 +1 -1 -1 +1 -1 +1 +1 -1 -1 -1 +1 +1 +1 -1 +1 -1 -1 -1 -1 +1 -1 +1 +1 -1 -1 +1 +1 +1 -1 +1 -1 +1 +1 -1 +1 +1 -1 +1 -1 -1 -1 -1 +1 +1 +1 -1 +1 -1 +1 +1 -1 -1 -1 +1 +1 +1 -1 +1 +1 +1 +1 +1 +1 +1
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# Search 7th Grade Common Core Lesson Plans
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Informational Essay: Revising
Lesson Plan
Informational Essay: Revising
Students will have the opportunity to fine-tune their writing by adding, deleting, or reworking content in their informational essay drafts. They’ll use a checklist to guide this critical step in the writing process.
7th grade
Reading & Writing
Lesson Plan
Informational Essay: Creating an Outline for a Draft
Lesson Plan
Informational Essay: Creating an Outline for a Draft
Students will continue their informational writing project by creating an essay outline prior to drafting.
7th grade
Reading & Writing
Lesson Plan
Informational Essay: Getting Organized Before Writing
Lesson Plan
Informational Essay: Getting Organized Before Writing
Students will continue their informational writing project by organizing the information they gathered through research. They will use a graphic organizer to organize their ideas and sort their research notes into meaningful sections.
7th grade
Reading & Writing
Lesson Plan
Informational Essay: Prewriting With Research
Lesson Plan
Informational Essay: Prewriting With Research
Students begin their informational writing process by gathering information through research. They will use a graphic organizer to record important information and sources and reflect on how to present the information.
7th grade
Reading & Writing
Lesson Plan
Compound Probability
Lesson Plan
Compound Probability
Use this math lesson to introduce compound events! Students will build on their understanding of probability as they learn how to find the sample space and probability of compound events given real-world examples.
7th grade
Math
Lesson Plan
Informational Essay: Editing
Lesson Plan
Informational Essay: Editing
Students will have the opportunity to strengthen their informational essay drafts by correcting errors in conventions and mechanics. They’ll use a checklist to guide this critical step in the writing process.
7th grade
Reading & Writing
Lesson Plan
Solving One-Step Inequalities
Lesson Plan
Solving One-Step Inequalities
This lesson will help students understand how to solve one-step addition, subtraction, multiplication, and division inequalities using inverse operations, as well as how to graph inequalities on a number line.
7th grade
Math
Lesson Plan
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https://couryes.com/%E6%95%B0%E5%AD%A6%E4%BB%A3%E5%86%99%E7%A6%BB%E6%95%A3%E6%95%B0%E5%AD%A6%E4%BD%9C%E4%B8%9A%E4%BB%A3%E5%86%99discrete-mathematics%E4%BB%A3%E8%80%83mpcs50103/
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# 数学代写|离散数学作业代写discrete mathematics代考|MPCS50103
#### Doug I. Jones
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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
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## 数学代写|离散数学作业代写discrete mathematics代考|Cyclic Groups
These examples suggest that a periodical structure, which we observed in this particular case, should exist in general when we deal with the comparison of the integers. This periodicity is explored in more detail now. It is clear that an order of any element in a finite group cannot be bigger than the order of the group itself. Group elements having this largest possible order $\operatorname{ord}(G)=|G|$ are called primitive elements or generators of the group. Thus, as we saw above, the group $\mathbb{Z}{7}^{}$ has two generators 3 and 5 . since both these elements have the largest possible order $6=7-1$. We also see that the powers of both these elements, 3 and 5 , – of course, modulo 7 , are $3,2,6,4,5,1$ and $5,4,6,2,3,1$, that is, each sequence is the entire group $\mathbb{Z}{7}^{}$; the elements with the maximal order are called generators of a group, and these groups are called cyclic groups.
Problem 132. Are $\mathbb{Z}{11}^{}$ and $\mathbb{Z}{13}^{}$ cyclic groups? Compute the orders of elements of these groups and find, if any, their generators.
Problem 133. The additive group of all the integers is an infinite cyclic group.
We omit a proof of the next statement, important in cryptography.
Theorem 10. (1) If d is prime, then $\mathbb{Z}_{d}^{*}$ with a congruence as a group operation, is a commutative cyclic group.
(2) If $|G|$ is prime, then all elements $a \in G, a \neq 1$, are primitive.
The next property says that all cyclic groups of a given order are, in a sense, the same.
(3) All the finite cyclic groups of the given order n are isomorphic to each other. All infinite cyclic groups are isomorphic to one another.
## 数学代写|离散数学作业代写discrete mathematics代考|THE DISCRETE LOGARITHM PROBLEM
While developing the Affine Ciphers, we had to find the inverse elements of some group elements. It is ensy if we work with renl numbers, since $x^{-1}$ exists for every real $x \neq 0$. However, in cryptography $x$ is supposed to be integer, and its reciprocal must be also integer; hence the problem of finding the reciprocal may have no solution. Moreover, the exponent does not have to be – 1. Again, solving an equation $a^{x}=b$, when $a>0$ and $b$ is a real number, straightforwardly leads to logarithms. Therefore, we have to extend that notion to a discrete setting.
Consider the finite cyclic group $\mathbb{Z}{p}^{}$ with prime $p$, its order is $p-1$, and let $g \in \mathbb{Z}{p}^{}$ be a generator of this group. Let also another element be $h \in \mathbb{Z}_{p}^{*}$. The Discrete Logarithm Problem (DLP) requires finding the integer $x, 1 \leq x \leq p-1$, such that $g^{x}=h(\bmod p)$. We denote the solution of this congruence, if it exists, as $x=\log h(\bmod p)$.
For example, computations in Example 11 tell that $5^{\circ 4}(\bmod 7)=2$, therefore, we set $g=5, h=2$, and get $x=\log _{5} 2(\bmod 7)=2$, which has nothing in common with $\ln 2 / \ln 5 \approx 0.43$. We can straightforwardly check that $5^{* 4}=625$ and $625=7 \times 89+2$.
This example shows why DLP is used in cryptography. We deal with a one-way function – see Def. 68 (p. 167). Given the value of the discrete logarithm, the verification is straightforward and fast. But the computations for finding this value currently, for really large parameters, are infeasible. For more about the DLP, the reader can consult, for example, [40] and the references therein.
## 数学代写|离散数学作业代写discrete mathematics代考| Cyclic Groups
（2）如果 $|G|$ 是栍数，则所有元溸 $a \in G, a \neq 1$ ，是原始的。
（3）给定阶 $n$ 的所有有限旿环群彼此同构。所有无限楿环群彼此同构。
## 有限元方法代写
tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。
## MATLAB代写
MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。
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# Analytical expression of the dependence of the multi-lattice truss deflection on the number of panels
Автор: Buka-Vaivade Karina, Kirsanov Mikhail Nikolaevich, Serdjuks Dmitrijs
Статья в выпуске: 5 (90), 2020 года.
Бесплатный доступ
The object of research is a flat statically determinate trapezoidal truss with a rectilinear lower chord and four supports, one of which is a pinned, and three are roller. The purpose of this work is to analyze the dependence of the deflection of the truss and the shift of the movable support on the size, load, and number of panels. The load concentrated in the middle of the span, the load uniformly distributed over the nodes of the upper or lower belt are considered. Method. The initial forces in the elements are determined in analytical form by method of joints in the Maple computer mathematics system. The dependence of the truss performance characteristics on the number of panels is derived by induction based on analytical calculations of the sequence of trusses with different numbers of panels. External static uncertainty is revealed by adding five reactions of supports to the number of unknown components of the equilibrium system of the structure. The deflection of the truss and the displacement of the support are based on the Maxwell-Mohr formula. Results. By solving a number of problems for trusses with a different number of panels, it is found that for trusses whose number of panels is a multiple of three, the determinant of the system of equilibrium equations of nodes turns to zero, which corresponds to the instantaneous kinematic variability of the truss. The corresponding scheme of possible node speeds was found. For kinematically unchangeable trusses, formulas for deflection depending on the number of panels are obtained. The coefficients in the formula are polynomial type. The solution graphs show an abrupt increase in deflection as the number of panels increases.
Еще
Truss, maple, deflection, symbolic solution, induction
IDR: 143172529 | DOI: 10.18720/CUBS.90.3
## Список литературы Analytical expression of the dependence of the multi-lattice truss deflection on the number of panels
• Vatin, N.L., Havula, J., Martikainen, L., Sinelnikov, A.S., Orlova, A. V., Salamakhin, S. V. Thin- walled cross-sections and their joints: Tests and FEM-modelling (2014) Advanced Materials Research, 945-949, pp. 1211-1215. DOI: 10.4028/www.scientific.net/AMR.945-949.1211
• Gusakova, N.V., Filyushina, K.E., Gusakov A.M., Minaev, N.N. Selection criteria of space planning and structural solutions of low-rise buildings (2017) Magazine of Civil Engineering, 75 (7), pp. 84-93. DOI: 10.18720/MCE.75.8
• Travush, V.I., Fedorova, N. V. Survivability of structural systems of buildings with special effects (2018) Magazine of Civil Engineering, 81 (5), pp. 73-80. DOI: 10.18720/MCE.81.8
• Chiriki, S.S., Harsha, G.S. Finite element analysis of RC deep beams strengthened with I- section and truss reinforcement (2020) Materials Today: Proceedings. DOI: 10.1016/j.matpr.2020.03.579
• Li, S., Jiang, W., Tu, S.T. Life prediction model of creep-rupture and creep-buckling of a pyramidal lattice truss panel structure by analytical and finite element study (2018) International Journal of Mechanical Sciences, 141, pp. 502-511. DOI: 10.1016/j.ijmecsci.2018.04.026
• Kamiński, M., Solecka, M. Optimization of the truss-type structures using the generalized perturbation-based Stochastic Finite Element Method (2013) Finite Elements in Analysis and Design, 63, pp. 69-79.
• DOI: 10.1016/j.finel.2012.08.002
• Arndt, M., Machado, R.D., Scremin, A. An adaptive generalized finite element method applied to free vibration analysis of straight bars and trusses (2010) Journal of Sound and Vibration, 329 (6), pp. 659-672.
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• Goloskokov, D.P., Matrosov, A. V. Comparison of two analytical approaches to the analysis of grillages (2015) International Conference on "Stability and Control Processes" in Memory of V.I. Zubov, SCP 2015 - Proceedings. 2015, pp. 382-385.
• DOI: 10.1109/SCP.2015.7342169
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• Rybakov, L. S. Lineynaya teoriya ploskogo prizmaticheskogo karkasa [Linear theory of a flat prismatic frame] (2001) Bulletin of the Russian Academy of Sciences. Ser. Solid mechanics, (4), pp. 106-118.
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• Kirsanov, M. Planar Trusses: Schemes and Formulas (2019) Newcastle upon Tyne, United Kingdom, Cambridge Scholars Publishing, 198 p.
• Astakhov, S. The derivation of formula for deflection of statically indeterminate externally flat truss under load at midspan (2017) Construction and Architecture, 5 (2), pp. 50-54.
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• Voropay R.A., Domanov E.V. The formula for the dependence of the deflection of a truss with an asymmetric lattice on the number of panels (2018) Postulat, (6). http://e- postulat.ru/index.php/Postulat/article/view/1653/1687.
• Domanov E.V. An analytical solution of the problem of the externally statically indeterminate truss deflection with an arbitrary number of panels (2018) Postulat, (7). http://e- postulat.ru/index.php/Postulat/article/view/1739/1773
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Статья научная
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# Bra-ket notation, Bits, & Superposition
I am a quantum computing enthusiast, and recently I stumbled upon this the following two propositions:
$$\alpha|1\rangle + \beta|0\rangle$$
What does this mean?
My understanding of this is that: the two bits, 1 and 0 are represented in a state of superposition, hence the bra-ket notation (which is commonly used for quantum mechanics), i.e., this is a qubit.
Or is there a more concise explanation of this?
Also:
$$(\alpha|1\rangle + \beta|0\rangle)^N$$
What does it mean to raise this quantity (of superimposed bits, i.e., qubit) to the $N$th degree? If we take $2^N$ where $N$ is the number of qubits then this tells us the number of bits in the desired number of qubits.
Is what I have stated in this post, generally correct?
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The expression \begin{align} \alpha|1\rangle+\beta|0\rangle \end{align} is the state of a single qubit written as a linear combination of the state $|1\rangle$ and the state $|0\rangle$. If you were to make a measurement on this qubit, then you would either return $1$ or $0$ with probabilities $|\alpha|^2$ and $|\beta|^2$ respectively.
The expression \begin{align} (\alpha|1\rangle + \beta|0\rangle)^N \end{align} is probably a shorthand for \begin{align} \underbrace{(\alpha|1\rangle + \beta|1\rangle)\otimes\cdots \otimes(\alpha|1\rangle + \beta|0\rangle)}_{N\,\text{factors}},{}{} \end{align} namely the $N$-fold tensor product of the state $\alpha|1\rangle + \beta|1\rangle$ with itself. This represents the state of $N$ qubits.
If you make a measurement on a system of $N$ such qubits, then you will obtain one of $2^N$ possibilities, namely the $2^N$ distinct sequences of $1$'s and $0$'s obtained by expanding out the product. The probability of obtaining such a sequence is its associated coefficient. In fact, in this case, the probability of measuring a single such sequence is $|\alpha|^n|\beta|^{N-n}$ where $n$ is the number of $1$'s in the sequence, and therefore $N-n$ is the number of $0$'s in the sequence. So, for example, the state \begin{align} |1\rangle|1\rangle\underbrace{|0\rangle\cdots |0\rangle}_{N-2\,\text{factors}} \end{align} has associated probability $|\alpha|^2|\beta|^{N-2}$ of measurement.
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CC-MAIN-2016-30
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latest
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