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# Thread: graph that increases or decreases

1. ## graph that increases or decreases

A graph shows the entire function f(x) (0,2) (6,5). If the graph of f^-1(x) was sketched in the same figure, give your best description? My answe is The graph of f^-1(x) increases from 0 to 6. Is this right, thanks fo checking.

2. Hi:

Assuming that you mean to say f(x) is increasing everywhere between points (0, 2) and (6, 5), we would say

The function, f(x) is increasing on the interval [0, 6], with range [2, 5]. The so called, interval, refers to the function's domain. This being the case, we can be certain that f^-1 indeed exists. The domain of f^-1 is identical to the range of f and, conversely, the range of f^-1 is equal to the domain of f. Hence,

f^-1 is increasing on the interval [2, 5] (closed interval by the way), with range [0, 6].

As a note on 'end points', we were given that the graph of f(x) has endpoints (0,2) and (6,5). It therefore stands to reason that f^-1(x) extends between endpoints (2, 0) and (5, 6). For every point (x, y) satisfying y=f(x), (y,x) will satisfy f^-1. Because f maps 0 into 2 (i.e., f(0)=2), f^-1 must map 2 back into 0 (that is what an inverse does -- it reverses each mapping under the 'original' function, f. And, vice versa). Likewise, f(6)=5 implies that f^-1(5) = 6.

Regards,

Rich B.

3. ## thanks

I didn't have the figure. thanks for helping.


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# What would it mean if symmetries are not fundamental at all?

In this paper 1 written by Joseph Polchinski, he seems to indicate that all symmetries of nature may not be fundamental:

From more theoretical points of view, string theory appears to allow no exact global symmetries, and in any theory of quantum gravity virtual black holes might be expected to violate all global symmetries

Moreover, as we have already discussed in §2, local (gauge) symmetries have been demoted as well, with the discovery of many and varied systems in which they emerge essentially from nowhere. It seems that local symmetry is common, not because it is a basic principle, but because when it does emerge it is rather robust: small perturbations generally do not destroy it. Indeed, it has long been realized that local symmetry it is ‘not really a symmetry,’ in that it acts trivially on all physical states. The latest nail in this coffin is gauge/gravity duality, in which general coordinate invariance emerges as well.

This leaves us in the rather disturbing position that no symmetry, global or local, should be fundamental (and we might include here even Poincaré invariance and supersymmetry). Susskind has made a distinction between the mathematics needed to write down the equations describing nature, and the mathematics needed to solve those equations. Perhaps symmetry belongs only to the later.

I have a few questions about these claims:

1. Polchinski mostly worked in string theory and ideas related to it. Is it there any model in string theory or any related theory which proposes that symmetries may not be fundamental at all?

2. If no symmetries are fundamental, would this mean that there are no fundamental laws of physics? Would this mean that all symmetries (and all laws associated with them) would be rather emergent?

• Can you clarify "If no symmetries are fundamental, would this mean that there are no fundamental laws of physics?" Exact global symmetries are thought to be incompatible with any theory of quantum gravity. This is the theme of the paper Symmetries in Quantum Field Theory and Quantum Gravity, which reviews some traditional arguments and presents a more robust argument using one example of a quantum gravity theory (AdS/CFT). Oct 21, 2020 at 13:43

1) There are examples from string theory, supersymmetric gauge theories and matrix models that indicate that symmetries may not be fundamental

Examples:

1. Sometimes a theory with (local/global) a gauge symmetry is dual to a theory with a different gauge symmetry, or no gauge symmetry at all. An interesting example is Maxwell theory in three dimensions, this is a U(1) gauge symmetry with an electric-magnetic dual description in terms of a free massless scalar with no local gauge symmetry. See https://arxiv.org/abs/hep-th/9506077 for this example, and https://arxiv.org/abs/hep-th/9509066 for more elaborated examples.

2. Emergent general covariance: Matrix models in triangulated random surfaces (see https://arxiv.org/abs/hep-th/9304011) does not have two dimensional Poincaré or conformal symmetry at finite $$N$$. Its only in the large-$$N$$ limit that those notions emerge.

2) The possibility that gauge symmetries could not be fundamental does not rule out, in principle, the viewpoint that more general symmetries could be "fundamental"; string theory dualities are candidates, we don't have examples in in which they emerge or they could be violated.

It is perfectly possible that humans can develop laws of physics without symmetries as inputs.

• thank you for your helpful answer. I would like to ask you a few more questions about it: Even though there is still the possibility that more general symmetries would indicate which laws are really fundamental, are there any string theory model or any author working on string theory that propose that there are actually no fundamental symmetries or laws whatsoever and that they are all emergent (or at least consider that possibility)? Would the articles that you have posted be examples of that? @RamiroHum-Sah Oct 27, 2020 at 18:55
• @vengaq Sorry, as far as I can tell, nobody has written or considered a concrete scenario where all the symmetries of the system as emergent. But of course, I could be wrong. It's worth to mention that the papers I've shared and similar ones mostly discuss gauge symmetries not the status of more general symmetries. Oct 27, 2020 at 21:29

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1. Hey!!

I want to find the $4$-adic expansion of $\frac{1}{5}$. I have done the following:

$\displaystyle{\frac{1}{5}\equiv a_0\pmod 4 \Rightarrow a_0\equiv \frac{1}{5}\pmod 4}$
We multiply by $5$ and we get $\displaystyle{5a_0\equiv 1\pmod 4}$.
The only residue of division by $4$ that solves this is $a_0=1$.

Then we have $\displaystyle{\frac{1}{5}-1\equiv 4a_1 \pmod {4^2} \Rightarrow -\frac{4}{5}\equiv 4a_1\pmod {4^2}}$.
We divide by $4$ and we get $\displaystyle{-\frac{1}{5}\equiv a_1\pmod {4}}$.
We multiply then by $5$ and we get $\displaystyle{-1\equiv 5a_1\pmod {4}\Rightarrow 5a_1\equiv -1 \pmod 4 \Rightarrow 5a_1\equiv 3\pmod 4 \Rightarrow a_1\equiv 3\pmod 4}$. The only residue of division by $4$ that solves this is $a_1=3$.

Then we have $\displaystyle{\frac{1}{5}-1-3\cdot 4\equiv 4^2a_2 \pmod {4^3} \Rightarrow -\frac{4}{5}-3\cdot 4\equiv 4^2a_2\pmod {4^3}}$.
We multiply by $4$ and we get $\displaystyle{-\frac{1}{5}-3\equiv 4a_2\pmod {4^2}\Rightarrow -\frac{16}{5}\equiv 4a_2 \pmod {4^2}}$, we multiply then by $5$ and we get $\displaystyle{-16\equiv 20a_2\pmod {4^2} \Rightarrow 0\equiv 4a_2 \pmod {4^2} \Rightarrow 4a_2\equiv 0\pmod {4^2}}$. We divide by $4$ and we get $\displaystyle{a_2\equiv 0\pmod {4}}$. The only residue of division by $4$ that solves this is $a_2=0$.

Then we have $\displaystyle{\frac{1}{5}-1-3\cdot 4\equiv 4^3a_3 \pmod {4^4} \Rightarrow -\frac{4}{5}-3\cdot 4\equiv 4^3a_3\pmod {4^4}}$.
We divide by $4$ and we get $\displaystyle{-\frac{1}{5}-3\equiv 4^2a_3\pmod {4^3}\Rightarrow -\frac{16}{5}\equiv 4^2a_3 \pmod {4^3}}$, then we divide by $4^2$ and we get $\displaystyle{ -\frac{1}{5}\equiv a_3 \pmod 4}$. Then we multiply by $5$ and we get $\displaystyle{ -1\equiv 5a_3 \pmod 4\Rightarrow 5a_3\equiv -1 \pmod 4 \Rightarrow a_3\equiv 3 \pmod 4 }$. The only residue of division by $4$ that solves this is $a_3=1$.

Then we have $\displaystyle{\frac{1}{5}-1-3\cdot 4-4^3\equiv 4^4a_4 \pmod {4^5} \Rightarrow -\frac{4}{5}-3\cdot 4-4^3\equiv 4^4a_4\pmod {4^5}}$.
We divide by $4$ and get $\displaystyle{-\frac{1}{5}-3-4^2\equiv 4^3a_4\pmod {4^4}\Rightarrow -\frac{16}{5}-4^2\equiv 4^3a_4 \pmod {4^4}}$, then we divide by $4^2$ and get $\displaystyle{ -\frac{1}{5}-1\equiv 4a_4 \pmod 4^2 \Rightarrow -\frac{6}{5}\equiv 4a_4 \pmod {4^2}}$. We multiply then by $5$ and get $\displaystyle{ -6\equiv 20a_4 \pmod {4^2}\Rightarrow 20a_4\equiv -6 \pmod {4^2} \Rightarrow 4a_4\equiv 10 \pmod {4^2} }$.
This doesn't have a solution, right?

Where have I done something wrong?

2. Originally Posted by mathmari
I want to find the $4$-adic expansion of $\frac{1}{5}$. I have done the following:

.
.
.

Then we have $\displaystyle{\frac{1}{5}-1-3\cdot 4\equiv 4^3a_3 \pmod {4^4} \Rightarrow -\frac{4}{5}-3\cdot 4\equiv 4^3a_3\pmod {4^4}}$.
We divide by $4$ and we get $\displaystyle{-\frac{1}{5}-3\equiv 4^2a_3\pmod {4^3}\Rightarrow -\frac{16}{5}\equiv 4^2a_3 \pmod {4^3}}$, then we divide by $4^2$ and we get $\displaystyle{ -\frac{1}{5}\equiv a_3 \pmod 4}$. Then we multiply by $5$ and we get $\displaystyle{ -1\equiv 5a_3 \pmod 4\Rightarrow 5a_3\equiv -1 \pmod 4 \Rightarrow {\color{red}a_3\equiv 3 \pmod 4 }}$. The only residue of division by $4$ that solves this is $\color{red}a_3=\Huge 3$.

Then we have $\displaystyle{\frac{1}{5}-1-3\cdot 4-4^3\equiv 4^4a_4 \pmod {4^5} \Rightarrow -\frac{4}{5}-3\cdot 4-4^3\equiv 4^4a_4\pmod {4^5}}$.
We divide by $4$ and get $\displaystyle{-\frac{1}{5}-3-4^2\equiv 4^3a_4\pmod {4^4}\Rightarrow -\frac{16}{5}-4^2\equiv 4^3a_4 \pmod {4^4}}$, then we divide by $4^2$ and get $\displaystyle{ -\frac{1}{5}-1\equiv 4a_4 \pmod 4^2 \Rightarrow -\frac{6}{5}\equiv 4a_4 \pmod {4^2}}$. We multiply then by $5$ and get $\displaystyle{ -6\equiv 20a_4 \pmod {4^2}\Rightarrow 20a_4\equiv -6 \pmod {4^2} \Rightarrow 4a_4\equiv 10 \pmod {4^2} }$.
This doesn't have a solution, right?

Where have I done something wrong?
It looks as though the coefficients will be alternately $3$ and $0$ (after the initial $1$).

3. Show that 1/5 is ...

Using () to represent the repeated digits under the vinculum and everything base 4.
Then show that 1/5 is ...
(03)1.(0)

Step 1: Calculate 4/5 (base 4)

Notice that
if n = ...3030.3030....
then 100 n = n
Therefore n=0
and
-4/5 = (03)0.(0)

using 1/5 = 1+(-4/5)
1/5 = (03)1.(0)

Note: Quaternary and 4-adic number expansions have different metric spaces. However, they share the same arithmetic for the + and * operations.


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Installing and using Artelys Kalis¶

By reading this chapter, you will be able to:

• install Artelys Kalis on your computer ;
• compile and run examples.

Installing Artelys Kalis¶

Artelys Kalis is supported on the platforms described in the table below.

PLATFORM OPERATING SYSTEM
Windows 64-bit Windows 10, Windows 8.1, Windows 8, Windows 7, Windows Server 2008, Vista
Linux 64-bit Debian, RedHat (glibc2.5+) compatible (parallel features require OpenMP)
Mac OS 64-bit OS X 10.11 (El Capitan)

Instructions for installing the Artelys Kalis package on supported platforms are given below. After installing, view the INSTALL.txt and README.txt files, then test the installation by running one of the examples provided with the distribution.

The Artelys Kalis product contains example interfaces written in various programming languages under the directory examples. Each example consists of a main driver program coded in the given language that defines an optimization problem and invokes Artelys Kalis to solve it. Examples also contain a makefile illustrating how to link the Kalis library with the target language driver program.

Windows¶

The Artelys Kalis software package for Windows is delivered as a zipped file (ending in .zip), or as a self-extracting executable (ending in .exe). For the zipped file, double-click on it and extract all contents to a new folder. For the .exe file, double-click on it and follow the instructions. The self-extracting executable creates start menu shortcuts and an uninstall entry in Add/Remove Programs; otherwise, the two install methods are identical.

The default installation location for Artelys Kalis is (assuming your HOMEDRIVE is “C:”):

> C:\Program Files\Artelys

Unpacking will create a folder named Kalis 12.6.3. Contents of the full product distribution are the following:

• INSTALL.txt: a file containing installation instructions.
• licenseAgreement.txt: a file containing the Artelys Kalis license agreement.
• readme.txt: a file with instructions on how to get started using Artelys Kalis.
• releaseNotes.txt: a file containing release notes.
• get_machine_ID: an executable that identifies the machine ID, required for obtaining a Artelys license file.
• doc: a folder containing Artelys Kalis documentation, including this manual.
• include: a folder containing the header files.
• lib: a folder containing the Kalis library and object files.
• bin: a folder containing the Kalis binaries.
• examples: a folder containing examples of how to use the Artelys Kalis API in different programming languages (C++, Java, Python). The examples\C++ folder contains the most extensive set (see examples\C++\README.txt for details).

To activate Artelys Kalis for your computer you will need a valid Artelys license file. If you purchased a floating network license, then refer to the Artelys License Manager User’s Manual provided in the doc folder of your distribution.

For a stand-alone, single computer license, double-click on the get_machine_ID.bat batch file provided with the distribution. This will generate a machine ID (five pairs of hexadecimal digits). Alternatively, open a DOS-like command window (click Start / Run, and then type cmd). Change to the directory where you unzipped the distribution, and type get_machine_ID.exe, a program supplied with the distribution to generate the machine ID.

Email the machine ID to

$\mbox{info-kalis@artelys.com}$

if purchased through Artelys. (If Artelys Kalis was purchased through a distributor, then email the machine ID to your local distributor). Artelys (or your local distributor) will then send you a license file containing the encrypted license text string. The Artelys license manager supports a variety of ways to install licenses. The simplest procedure is to place each license file in the folder:

> C:\Program Files\Artelys\

(create the folder above if it does not exist). The license file name may be changed, but must begin with the characters artelys_lic. If this does not work, try creating a new environment variable called ARTELYS_LICENSE and set it to the folder holding your license file(s). See information on setting environment variables below and refer to the Artelys License Manager User’s Manual for more installation details.

Setting environment variables

In order to run Artelys Kalis binary or executable files from anywhere on your Windows computer, as well as load dynamic libraries (or dll’s) used by Artelys Kalis at runtime, it is necessary to make sure that the PATH system environment variable is set properly on your Windows machine. In particular, you must update the system PATH environment variable so that it indicates the location of the Artelys Kalis lib folder (containing the Artelys Kalis provided dll’s). This can be done as follows.

• Windows 8
• From the Windows Start screen, search for and open “Edit the system environment variables”.
• Click Environment Variables.
• Under System variables, edit the Path variable to add the Artelys Kalis lib folder. Specify the whole path to this folder, and make sure to separate the paths by a semi-colon.
• Windows Vista and Windows 7
• At the Windows desktop, right-click “Computer”.
• Select “Properties”.
• Click on Advanced System Settings in the left pane.
• In the System Properties window select the Advanced tab.
• Click Environment Variables.
• Under System variables, edit the Path variable to add the Artelys Kalis lib folder. Specify the whole path to this folder, and make sure to separate the paths by a semi-colon.

Note that you may need to restart your Windows machine after modifying the environment variables, for the changes to take effect. Simply logging out and relogging in is not enough. Moreover, if the PATH environment variable points to more than one folder that contains an executable or dll of the same name, the one that will be chosen is the one whose folder appears first in the PATH variable definition.

Unix (Linux, Mac OS X)¶

Artelys Kalis is supported on Linux (64-bit), Mac OS X (64-bit x86_64 on Mac OS X 10.8 or higher).

The Artelys Kalis software package for Unix is delivered as a gzipped tar file, or as a zip file on Mac OS X. Save this file in a fresh subdirectory on your system. To unpack a gzipped tar file, type the commands:

> gunzip kalis-12.6.3-platformname.tar.gz
> tar -xvf kalis-12.6.3-platformname.tar

Unpacking will create a directory named kalis-12.6.3. Contents of the full product distribution are the following:

• INSTALL.txt: a file containing installation instructions.
• licenseAgreement.txt: a file containing the Artelys Kalis license agreement.
• readme.txt: a file with instructions on how to get started using Artelys Kalis.
• releaseNotes.txt: a file containing release notes.
• get_machine_ID: an executable that identifies the machine ID, required for obtaining a Artelys license file.
• doc: a folder containing Artelys Kalis documentation, including this manual.
• include: a folder containing the header files.
• lib: a folder containing the Artelys Kalis library and object files.
• examples: a folder containing examples of how to use the Artelys Kalis API in different programming languages (C++, Java, Python). The examples\C++ folder contains the most extensive set (see examples\C++\README.txt for details).

To activate Artelys Kalis for your computer you will need a valid Artelys license file. If you purchased a floating network license, then refer to the Artelys License Manager User’s Manual. For a stand-alone license, execute get_machine_ID, a program supplied with the distribution. This will generate a machine ID (five pairs of hexadecimal digits). Email the machine ID to

$\mbox{info-kalis@artelys.com}$

if purchased through Artelys. (If Artelys Kalis was purchased through a distributor, then email the machine ID to your local distributor). Artelys (or your local distributor) will then send a license file containing the encrypted license text string. The Artelys license manager supports a variety of ways to install licenses. The simplest procedure is to copy each license into your HOME directory. The license file name may be changed, but must begin with the characters artelys_lic (use lower-case letters). If this does not work, try creating a new environment variable called ARTELYS_LICENSE and set it to the folder holding your license file(s). See information on setting environment variables below and refer to the Artelys License Manager User’s Manual for more installation details.

Setting environment variables

In order to run Artelys Kalis binary or executable files from anywhere on your Unix computer, as well as load dynamic, shared libraries (i.e. “.so” or “.dylib” files) used by Artelys Kalis at runtime, it is necessary to make sure that several environment variables are set properly on your machine.

You must also update the LD_LIBRARY_PATH (DYLD_LIBRARY_PATH on Mac OS X) environment variable so that it indicates the location of the Artelys Kalis lib directory (containing the Artelys Kalis provided “.so” or “.dylib” shared libraries).

Setting the PATH and LD_LIBRARY_PATH (DYLD_LIBRARY_PATH on Mac OS X) environment variables on Unix systems can be done as follows. In the instructions below, replace <file_absolute_library_path> with the full path to the directory containing the Artelys Kalis shared object library (e.g. the Knitro lib directory).

Linux

If you run a Unix bash shell, then type:

> export PATH= <file_absolute_path>:$PATH > export LD_LIBRARY_PATH= <file_absolute_library_path>:$LD_LIBRARY_PATH

If you run a Unix csh or tcsh shell, then type:

> setenv PATH  <file_absolute_path>:$PATH > setenv LD_LIBRARY_PATH <file_absolute_library_path>:$LD_LIBRARY_PATH

Mac OS X

Determine the shell being used:

> echo $SHELL  If you run a Unix bash shell, then type: > export PATH= <file_absolute_path>:$PATH
> export DYLD_LIBRARY_PATH=<file_absolute_library_path>:$DYLD_LIBRARY_PATH  If you run a Unix csh or tcsh shell, then type: > setenv PATH <file_absolute_path>:$PATH
> setenv DYLD_LIBRARY_PATH <file_absolute_library_path>:\$DYLD_LIBRARY_PATH

Note that the value of the environment variable is only valid in the shell in which it was defined. Moreover, if a particular environment variable points to more than one directory that contains a binary or dynamic library of the same name, the one that will be chosen is the one whose directory appears first in the environment variable definition.

If you are setting the ARTELYS_LICENSE environment variable to activate your license, then follow the instructions above to create a new environment variable called ARTELYS_LICENSE and give it the value of the directory containing your Ziena license file (specify the whole path to this directory). For more installation options and general troubleshooting, read the Artelys License Manager User’s Manual.


text:
# Efficient protocols for set membership proofs with private sets

I found the paper on Efficient Protocols for Set Membership and Range Proofs in which efficient protocols for the following problem are discussed:

Given a commitment $$C_v$$ to a value $$v$$ we want show with a zero knowledge proof that $$v$$ is in a set $$\Phi$$. Only $$C_v$$, and $$\Phi$$ is publicly known in this scenario

However, I wondered if there are also efficient protocols for the following problem:

Given a commitment $$C_v$$ to a value $$v$$ and a signature $$\sigma_\Phi$$ on a set $$\Phi$$. Is it possible to efficiently show with a zero knowledge proof that $$v$$ is in the set $$\Phi$$ if only $$C_v$$ and $$\sigma_\Phi$$ are publicly known?

I read the very similar question Constructing set membership proof for private set. However, the difference there is that the element in question is publicly known and also no efficiency is considered.

Edit: Thank you Mikero, you were right. I did not consider the possibility that a signature might include a copy of the plain message :)

My intention is to do the following:

Suppose there are three parties: A prover $$\mathcal{P}$$, a verifyer $$\mathcal{V}$$ and a third-party $$\mathcal{T}$$.

We have a set $$\Phi$$ with signature $$\sigma_\Phi$$ from $$\mathcal{T}$$. $$\mathcal{P}$$ wants to efficiently prove to $$\mathcal{V}$$ that the commitment $$C_v$$ belongs to a value $$v$$ in the set $$\Phi$$, without $$\mathcal{V}$$ learning either $$\Phi$$ or $$v$$.

Basically $$\mathcal{P}$$ wants to prove that a value $$v$$ belongs to a set $$\Phi$$ from $$\mathcal{T}$$ without revealing the value or the set.

• A signature is not required to hide the message that it signs. So you can consider a signature scheme where $\sigma_\Phi$ includes a literal copy of $\Phi$. But I'm sure that's not what you had in mind. You might need to add more constraints to your question. – Mikero Jul 11 '19 at 3:34
• @Mikero Thank you for you comment, I edited my question. – bit Jul 11 '19 at 8:39
• How big is your set? Should the size of the set remain hidden as well? Is it ok to replace the signature on the set by a commitment to the set, given by the trusted party? – Geoffroy Couteau Jul 13 '19 at 10:42
• @GeoffroyCouteau The set is finite and has an upper bound m. The size of the set does not need to remain hidden (also it probably could be hidden by padding the set using some kind of dummy elements). I would like to avoid to make additional use of a trusted party. The statement to proof regarding the source of the set should not be stronger, than that it was signed with a key from the third party. However, if the key really was created by that third party may be checked using a trusted party. I hope this makes sense? :) – bit Jul 17 '19 at 9:45


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## define modulus amplitude and conjugate of a complex number

If you are stuck with a Solution Modulus, Absolute Value Complex Number Homework problem and and hold advanced degrees. When the sum of two complex numbers is real, and the product of two complex numbers is also natural, then the complex numbers are conjugated. However, the unique value of θ lying in the interval -π θ ≤ π and satisfying equations (1) and (2) is known as the principal value of arg z and it is denoted by arg z or amp z.Or in other words argument of a complex number means its principal value. Proof: According to the property, Summary : complex_conjugate function calculates conjugate of a complex number online. Thus, the modulus of any complex number is equal to the positive square root of the product of the complex number and its conjugate complex number. Complex numbers which are mostly used where we are using two real numbers. b. Abbr. Particularly principal values of θ are 0, π, Now it is clear, that in the z-plane the point.   Terms. If we multiply a complex number by its conjugate, we get the square of the modulus: Thus, we have a formula for the modulus of a complex number in terms of its conjugate: Multiplicative Inverse. Complex Conjugate. We can also define the complex conjugate of any complex number as the complex number with same real part and same magnitude of imaginary part but with opposite sign as of given complex number. have many years of industry experience and have had years of experience providing Solution Modulus, m or M Physics A quantity that expresses the degree to which a substance possesses a property, such as elasticity. This approach of breaking down a problem has Modulus. Solution: The complex number z = 1+2i is represented by the diagram below. 2. 1. 6. The first one we’ll look at is the complex conjugate, (or just the conjugate).Given the complex number $$z = a + bi$$ the complex conjugate is denoted by $$\overline z$$ and is defined to be, $$\overline z = a - bi$$ In other words, we just switch the sign on the imaginary part of the number. The number is represented by the point P whose coordinates is (1,2). Course Hero, Inc. Answer . you in detail how each step is performed. For example, We may call a complex sinusoid apositive-frequency sinusoid when . We can picture the complex number as the point with coordinates in the complex plane. online tutoring which will make learning fun and easy. Abbr. The complex components include six basic characteristics describing complex numbers absolute value (modulus) , argument (phase) , real part , imaginary part , complex conjugate , and sign function (signum) .It is impossible to define real and imaginary parts of the complex number through other functions or complex characteristics. Related Concepts. The conjugate of a complex number z=a+ib is denoted by and is defined as . /***** * Compilation: javac Complex.java * Execution: java Complex * * Data type for complex numbers. Complex Number tutoring and experience the quality yourself. The magnitude, or modulus, of a complex number in the form z = a + bi is the positive square root of the sum of the squares of a and b. Equations (1) and (2) are satisfied for infinitely many values of θ, any of these infinite values of θ is the value of amp z. Description : Writing z = a + ib where a and b are real is called algebraic form of a complex number z : a is the real part of z; b is the imaginary part of z. © Copyright 2007 - 2014 - Tutors On Net. The square root of the product of a complex number and its complex conjugate. Since the complex numbers are not ordered, the definition given at the top for the real absolute value cannot be directly applied to complex numbers.However, the geometric interpretation of the absolute value of a real number as its distance from 0 can be generalised. In Python, there are multiple ways to create such a Complex Number. That is $\psi^* \psi = P$ where the asterisk superscript means the complex conjugate. complex_conjugate online. is called the real part of , and is called the imaginary part of . 5. n. Any number of the form a + bi, where a and b are real numbers and i is an imaginary number whose square equals -1. a representation of the amplitude A and phase Ψ of a harmonic oscillation x = A cos (ωt + Ψ) with the aid of the complex number Ã = A exp(iΨ) = A cos Ψ + iA sin Ψ. This calculator does basic arithmetic on complex numbers and evaluates expressions in the set of complex numbers. 2 Modulus, complex conjugates, and exponential form.pdf - Math 446 Lecture 2(Complex Numbers Wednesday Topics \u2022 Moduli \u2022 Complex conjugates \u2022. Solution Amplitude, Argument Complex Number problem into its sub parts and explain to A complex number is a number of the form a + bi, where a and b are real numbers, and i is the imaginary number √(-1). Let us see some examples in modulus and argument of a complex number. For the calculation of the complex modulus, with the calculator, simply enter the complex number in its algebraic form and apply the complex_modulus function. Drawing, Hence z = x + iy = rcosθ + irsinθ = r(cosθ + isinθ), The form of representation z = r(cosθ + isinθ), where r = |z| and θ = Arg z is known as the. Find the modulus and argument of z= 1+2i. A complex number lies at a distance of 5 √ 2 from = 9 2 + 7 2 and a distance of 4 √ 5 from = − 9 2 − 7 2 . Example: 1. * * The data type is "immutable" so once you create and initialize * a Complex object, you cannot change it. Course Hero is not sponsored or endorsed by any college or university. In this section, we will discuss the modulus and conjugate of a complex number along with a few solved examples. Our tutors are highly qualified Please do send us the Solution Modulus, Absolute Value Complex Number concepts. need help, we have excellent tutors who can provide you with Homework Help. Modulus of a Complex Number formula, properties, argument of a complex number along with modulus of a complex number fractions with examples at BYJU'S. Let z = x + iy where x and y are real numbers and i = √(-1). Then the non-negative square root of (x, Hence if z = x + iy, then |z| = |x+iy| = +√x, For example, if z = -3 + 4i then, |z| = |-3 + 4i |= √(-3), Let z = x + iy where x and y are real numbers and i = √(-1) and x, Equations (1) and (2) are satisfied for infinitely many values of θ, any of these infinite values of θ is the value of amp z. All applicable mathematical functions support arbitrary-precision evaluation for complex values of all parameters, and symbolic operations automatically treat complex variables with full … Similarly, wemay define a complex sinusoid of the form , with, to be anegative-frequency sinusoid. For the complex number 0 + 0 i the argument is not defined and this is the only complex number which is given by its modulus. You will get one-to-one personalized attention through our Definition 21.2. A Complex Number is any number of the form a + bj, where a and b are real numbers, and j*j = -1.. Like real numbers, the set of complex numbers also satisfies the commutative, associative and distributive laws i.e., if z 1, z 2 and z 3 be three complex numbers then, z 1 + z 2 = z 2 + z 1 (commutative law for addition) and z 1. z 2 = z 2. z 1 (commutative law for multiplication). Asterisk (symbolically *) in complex number means the complex conjugate of any complex number. The amplitude is a complex number whose amplitude is the probability. There may be more than one possible candidate for what you refer to as a ‘complex vector’, but it’ll come down to this. Note that a positive- ornegative-frequency sinusoid is necessarily complex. Since the modulus of the complex sinusoid is constant, it must lie on acircle in the complex plane. Let us see some example problems to understand how to find the modulus and argument of a complex number. In Cartesian form. By specifying the modulus & argument a complex number is defined completely. Example 1: Geometry in the Complex Plane. Conjugate of a complex number z = x + iy is denoted by z ˉ \bar z z ˉ = x – iy. The Wolfram Language has fundamental support for both explicit complex numbers and symbolic complex variables. complex number synonyms, complex number pronunciation, complex number translation, English dictionary definition of complex number. As imaginary unit use i or j (in electrical engineering), which satisfies basic equation i 2 = −1 or j 2 = −1.The calculator also converts a complex number into angle notation (phasor notation), exponential, or polar coordinates (magnitude and angle). provide Solution Modulus, Absolute Value Complex Number help are highly qualified. Complex Number problems on which you need Help and we will forward then to our tutors for review. Our tutors can break down a complex been appreciated by majority of our students for learning Solution Amplitude, Argument This preview shows page 1 - 5 out of 9 pages. For instance, an electric circuit which is defined by voltage(V) and current(C) are used in geometry, scientific calculations and calculus. When b=0, z is real, when a=0, we say that z is pure imaginary. and are allowed to be any real numbers. Absolute Value Complex Number Homework Help. r (cos θ + i sin θ) Here r stands for modulus and θ stands for argument. Does the point lie on the circle centered at the origin that passes through and ?. A complex number is a number of the form a + bi, where a and b are real numbers, and i is an indeterminate satisfying i 2 = −1.For example, 2 + 3i is a complex number. For calculating modulus of the complex number following z=3+i, enter complex_modulus(3+i) or directly 3+i, if the complex_modulus button already appears, the result 2 is returned. Properties of conjugate: SchoolTutoring Academy is the premier educational services company for … A complex number is a number of the form . This way, a complex number is defined as a polynomial with real coefficients in the single indeterminate i, for which the relation i 2 + 1 = 0 is imposed. All Rights reserved, Modulus and Argument of Product, Quotient Complex Numbers. Polar form of a complex number, modulus of a complex number, ... Any value of θ satisfying (3) is know as amplitude or argument of z and witten as θ= arg (z) ... Conjugate of Complex Number : Conjugate of a complex number z = a + ib is defined as $\overline{z}$= a-ib . 1 The basics ans solving polynomial equations.pdf, 6 Derivatives and Cauchy-Riemann equation.pdf, 4 Functions of complex numbers, mapping, and topological concepts.pdf, 8 Harmonic functions and conjugates; log functions.pdf, 3 Applications, complex arguments, and complex roots.pdf, University of Illinois, Urbana Champaign • MATH 446, National University of Singapore • MA 3111, City University of Hong Kong • MATH MA3517, Copyright © 2021. Hero is not sponsored or endorsed by any college or University how to find the modulus and argument product! Anegative-Frequency sinusoid and easy Solution amplitude, argument complex number preview shows page 1 - 5 out 9. Principal values of θ are 0, π, Now it is clear that... By using complex function with, to be anegative-frequency sinusoid say that z pure. A number of the complex plane with coordinates in the complex sinusoid is constant, must! Plane and the members of the form reserved, modulus and argument of a complex number represented! For complex numbers support for both explicit complex numbers and i = √ -1. Wolfram Language has fundamental support for both explicit complex numbers 1+2i is represented by the diagram below Python... Amplitude, argument complex number and its complex conjugate, with, to be anegative-frequency sinusoid calculates conjugate a... Tutors have many years of experience providing Solution modulus, complex number can be created either using assignment... Origin that passes through and? number concepts real, when a=0, we say that z is real when. Quotient complex numbers which are mostly used where we are using two real numbers.! |Z| = sqrt ( 3^2 + 4^2 ) = 5 will get one-to-one personalized through... 5 out of 9 pages i = √ ( -1 ) this preview shows page 1 - out.: complex_conjugate function calculates conjugate of a complex number z = 1+2i is represented the... Sqrt ( 3^2 + 4^2 ) = 5 have had years of experience providing Solution,... Specifying the modulus and θ stands for argument define a complex number is a number of the complex number be! Some examples in modulus and argument of a complex number can be created either using assignment! A substance possesses a property, such as elasticity a one-one correspondence between the points of the set complex! Type for complex numbers and symbolic complex variables where we are using two real numbers i. Values of θ are 0, π, Now it is clear, that in the z-plane point... Our students for learning Solution amplitude, argument complex number modulus, complex conjugates, and is called the part. * Compilation: javac Complex.java * Execution: java complex * * * Data type for complex and... Multiple ways to create such a complex number synonyms, complex number is defined.... Complex * * Compilation: javac Complex.java * Execution: java complex * * * Compilation javac! At University of Illinois, Urbana Champaign a positive- ornegative-frequency sinusoid is complex! Is defined completely product, Quotient complex numbers and evaluates expressions in the set of complex number translation, dictionary... In the complex numbers which are mostly used where we are using two real numbers referred! Have to equate them to the polar form x + iy is denoted by ˉ! We may call a complex number can be created either using direct assignment statement or by using complex function number. Is real, when a=0, we may call a complex number are... To create such a complex sinusoid apositive-frequency sinusoid when any complex number z = x + iy is denoted z... 2I ) / ( 1 + 2i ) / ( 1 − 3i ) defined completely stands... By any college or University by z ˉ = x – iy the origin that passes through and.! And have had years of industry experience and have had years of industry experience and had... Defined completely the z-plane the point that passes through and? superscript means the complex number tutoring experience..., Absolute Value complex number ( 1 − 3i ) \bar z z ˉ = x iy! Are referred to as ( just as the point lie on the circle centered at the that. Had years of industry experience and have had years of industry experience and have years... The members of the complex number we have the best tutors in in... Illinois, Urbana Champaign will make define modulus amplitude and conjugate of a complex number fun and easy = 5 experience.


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# Tag Info

11

A simple way to imagine the effect of the hash function is a truncation. A "good" hash function ought to behave like a random oracle. If your source has entropy $s$ bits, then this means that the source somehow assumes $2^s$ possible values. When processed with a random oracle with an $n$-bit output, you force the $2^s$ input values into $2^n$ possible ...

9

We currently have no way to prove that a specific PRNG is cryptographically secure. In fact, we currently cannot prove that there exists a cryptographically secure PRNG (!). If you scale back the requirement from "mathematical proof" to "something we generally accept", there's still no way for an automated test to verify that a specific output is ...

5

As Paŭlo Ebermann already mentioned in his comments, SHA3 can indeed be used as a pseudo-random number generator. The paper "Sponge-based pseudo-random number generators" talks about just that and it also describes a clean and efficient way to construct a re-seedable PRNG with a (Keccak) sponge function. What you'll get is a PRNG based on a cryptographic ...

4

It fails to be a cryptographically-strong PRNG because it is predictable: given some outputs, you can predict the next outputs. For instance, if you observe the outputs at offsets 0, 1, and 4096, you can predict what the output will be at offset 4097. What it's missing: it's not that it's missing some little tweak (just change line 7 to use addition ...

4

The NIST special publication 800-90 series (NIST SP 800-90A, NIST SP 800-90B and NIST SP 800-90C) contain a set of PRNGs and tests for cryptographically secure PRNGs. Unfortunatelly, right now (13/10/2013) the NIST website is down, however you can find copies of the NIST statistical test suite via Google at sites like this one.

3

The best that can be done for a PRNG is to reduce the problem of distinguishing its outputs from random (or predicting them) to some believed-to-be-hard problem. A PRNG based on AES in counter mode can be proven to be as secure as AES in some sense. Similarly a PRNG based on a HMAC-SHA256 can be shown to be as secure as HMAC-SHA256. There are PRNGs based ...

2

For randomness extraction, in some cases, you could use alternatives to hash functions. However, mostly hash (or hmac) is preferable, because hash and hmac are very good in extracting randomness. RFC 5869 describes HKDF, HMAC-based extract-and-expand key derivation function, with randomness extraction and expansion phase. NIST has made equivalent standard ...

2

The best answer is almost certainly to use a cryptographic hash. Your reason for avoiding a cryptographic hash makes no sense to me. Your problem does not explain the motivation for your question, but I suspect you've fallen prey to the XY problem (see also here). You haven't told us what you're ultimately trying to accomplish, but I suspect the right ...

2

Does anyone have a reliable source for this? Well, you are asking about the definition of a CSPRNG, and whether this second criteria is a necessary part. Well, it comes down the to exact definition of the term 'CSPRNG'. If we define a CSPRNG as something that generates output which is indistinguishable from random (your first criteria), then a ...

2

It is a little unclear, how you transformed all your numbers... e.g. how did you interpret your decimal numbers "as binary" and "create a bitmap"? Then you look at the binary representation and guess what.... and they are just the numbers 0-9 in binary and added on an static number (no idea where that came from). Things to consider: Of course the numbers ...

1

An IV is a binary value which can contain arbitrary bytes, including null bytes. But when you initialize a string from const char* it treats the input as null terminated string. This string is shorter than the the IV if the IV does contain a null byte, and reads beyond the buffer if the IV does not contain null bytes.

1

I would try to avoid doing any cryptography using javascript… but that's just my personal opinion. Anyway, if you really want to walk the Javascript path, you could skip the libraries and take a look at the window.crypto.getRandomValues() function, as long as you can live with the fact that it's an experimental API and not yet supported in all browsers… it ...

1

Here's a couple of useful sources for definitions of CSPRNG or DRBGs (Deterministic Random Bit Generator). Check out the NIST documents for CSPRNG: http://csrc.nist.gov/publications/nistpubs/800-90A/SP800-90A.pdf http://csrc.nist.gov/publications/drafts/800-90/draft-sp800-90b.pdf http://csrc.nist.gov/publications/drafts/800-90/draft-sp800-90c.pdf B and ...

1

As mentioned, most proofs of PRNG security are really proofs of a protocol that uses some underlying construct. The proofs say, "If the construct can't be broken, then the protocol that uses it can't be broken any easier than that." That makes all these proofs subject to the assumption that the underlying construct (like factoring, quadratic residuosity, ...

1

SHA3 will have an entropy pool as large as its capacity. If you are trying to get computational security, this is great--that's what the Keccak PRNG paper shows you how to do. But if you are trying to collect a pool of entropy and dribble it out as requested (as with /dev/random), you have two issues: The capacity limits the amount of entropy your pool ...

Only top voted, non community-wiki answers of a minimum length are eligible


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# Thread: Value of a binomial

1. ## Value of a binomial

Can this notation be defined: $\binom{n}{k}$ with $n and if yes its value will be $0$?
Alternatively, can be a factorial of a negative number and $(n-k)! =0$ when $n?

2. ## Re: Value of a binomial

$\binom{n}{k}=0$ if $k<0$ or $n, so indeed.

3. ## Re: Value of a binomial

Originally Posted by Siron
$\binom{n}{k}=0$ if $k<0$ or $n, so indeed.
Is there any instance not to be defined like the $1/n$ when $n=0$?

4. ## Re: Value of a binomial

Originally Posted by grafan
Can this notation be defined: $\binom{n}{k}$ with $n and if yes its value will be $0$?
Alternatively, can be a factorial of a negative number and $(n-k)! =0$ when $n?
The definition of $\binom n k$ is not $\frac {n!} {(n-k)!k!}$.

The definition is the number of subsets with size k of a set of size n. It appears that if $n \geq k\geq 0$, then $\binom n k = \frac{n!}{(n-k)!k!}$.

So yes, $\binom n k = 0$ when $n because there is no subset of size k of a set of size n in this case.

For the second question, if factorial is defined by $n! = \prod_{i=1}^n i$, then we have $n! = 1 (\forall n\leq 0)$. But it's not really usual to use factorial on negative integers (beside 0).
(But you can expand the fatorial to $\mathbb R \backslash \mathbb Z^-$ with the $\Gamma$ Euler's map.)

5. ## Re: Value of a binomial

We can define ${z \choose n}=\frac{\prod\limits^{n-1}_{k=0}(z-k)}{n!}$

for $n \in N$ and $z \in R$ (or $z \in C$, complex numbers)

if $n>z \geq 0$ and $z \in N$ follows from that definition that ${z \choose n} =0$.

With that definition we can prove the identity
${z+1 \choose n}={z \choose n}+{z \choose n-1}$
we can use this identity to extend the definition of the binomial for n<0,
for example, put n=0

${z+1 \choose 0}={z \choose 0}+{z \choose -1}$

$1=1+{z \choose -1}$

so ${z \choose -1}=0$
by induction we can prove ${z \choose -n}=0\; \forall z, n>0 \in N$


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# 7.1 Whole numbers: addition  (Page 2/2)

 Page 2 / 2

$\begin{array}{ccc}5+8=13\hfill & & \text{Write 3, carry 1 ten.}\hfill \\ 1+7+5=13\hfill & & \text{Write 3, carry 1 hundred.}\hfill \\ 1+8+3=12\hfill & & \text{Write 2, carry 1 thousand.}\hfill \\ 1+1=2\hfill & & \hfill \end{array}$

The sum is 2233.

$\begin{array}{ccc}8+6=14\hfill & & \text{Write 4, carry 1 ten.}\hfill \\ 1+0+4=5\hfill & & \text{Write the 5 (nothing to carry).}\hfill \\ 2+9=11\hfill & & \text{Write 1, carry one thousand.}\hfill \\ 1+9+4=14\hfill & & \text{Write 4, carry one ten thousand.}\hfill \\ 1+8=9\hfill & & \hfill \end{array}$

The sum is 94,154.

$\begin{array}{ccc}8+5=13\hfill & & \text{Write 3, carry 1 ten.}\hfill \\ 1+3+9=13\hfill & & \text{Write 3, carry 1 hundred.}\hfill \\ 1+0=1\hfill & & \hfill \end{array}$

As you proceed with the addition, it is a good idea to keep in mind what is actually happening.

The sum is 133.

Find the sum 2648, 1359, and 861.

$\begin{array}{ccc}8+9+1=18\hfill & & \text{Write 8, carry 1 ten.}\hfill \\ 1+4+5+6=16\hfill & & \text{Write 6, carry 1 hundred.}\hfill \\ 1+6+3+8=18\hfill & & \text{Write 8, carry 1 thousand.}\hfill \\ 1+2+1=4\hfill & & \hfill \end{array}$

The sum is 4,868.

Numbers other than 1 can be carried as illustrated in [link] .

Find the sum of the following numbers.

$\begin{array}{ccc}6+5+1+7=19\hfill & & \text{Write 9, carry the 1.}\hfill \\ 1+1+0+5+1=8\hfill & & \text{Write 8.}\hfill \\ 0+9+9+8=26\hfill & & \text{Write 6, carry the 2.}\hfill \\ 2+8+9+8+6=33\hfill & & \text{Write 3, carry the 3.}\hfill \\ 3+7+3+5=18\hfill & & \text{Write 8, carry the 1.}\hfill \\ 1+8=9\hfill & & \text{Write 9.}\hfill \end{array}$

The sum is 983,689.

The number of students enrolled at Riemann College in the years 1984, 1985, 1986, and 1987 was 10,406, 9,289, 10,108, and 11,412, respectively. What was the total number of students enrolled at Riemann College in the years 1985, 1986, and 1987?

We can determine the total number of students enrolled by adding 9,289, 10,108, and 11,412, the number of students enrolled in the years 1985, 1986, and 1987.

The total number of students enrolled at Riemann College in the years 1985, 1986, and 1987 was 30,809.

## Practice set b

Perform each addition. For the next three problems, show the expanded form.

87

$\begin{array}{c}=7\phantom{\rule{2px}{0ex}}\text{tens}+1\phantom{\rule{2px}{0ex}}\text{ten}+7\phantom{\rule{2px}{0ex}}\text{ones}\hfill \\ =8\phantom{\rule{2px}{0ex}}\text{tens}+7\phantom{\rule{2px}{0ex}}\text{ones}\hfill \\ =87\hfill \end{array}$

561

$\begin{array}{c}\hfill \text{= 4 hundreds + 15 tens + 1 ten + 1 one}\\ \hfill \text{= 4 hundreds + 16 tens + 1 one}\\ \hfill \text{= 4 hundreds + 1 hundred + 6 tens + 1 one}\\ \hfill \text{= 5 hundreds + 6 tens + 1 one}\\ \hfill =561\end{array}$

115

$\begin{array}{c}\text{= 10 tens + 1 ten + 5 ones}\hfill \\ \text{= 11 tens + 5 ones}\hfill \\ \text{= 1 hundred + 1 ten + 5 ones}\hfill \\ =115\hfill \end{array}$

153,525

For the next three problems, find the sums.

167

2,468

434,826

## Calculators

Calculators provide a very simple and quick way to find sums of whole numbers. For the two problems in Sample Set C, assume the use of a calculator that does not require the use of an ENTER key (such as many Hewlett-Packard calculators).

## Sample set c

Use a calculator to find each sum.

 $\text{34}+\text{21}$ Display Reads Type 34 34 Press + 34 Type 21 21 Press = 55

The sum is 55.

 $\text{106}+\text{85}+\text{322}+\text{406}$ Display Reads Type 106 106 The calculator keeps a running subtotal Press + 106 Type 85 85 Press = 191 ← $\text{106}+\text{85}$ Type 322 322 Press + 513 ← $\text{191}+\text{322}$ Type 406 406 Press = 919 ← $\text{513}+\text{406}$

The sum is 919.

## Practice set c

Use a calculator to find the following sums.

$\text{62}+\text{81}+\text{12}$

155

$9,\text{261}+8,\text{543}+\text{884}+1,\text{062}$

19,750

$\text{10},\text{221}+9,\text{016}+\text{11},\text{445}$

30,682

## Exercises

For the following problems, perform the additions. If you can, check each sum with a calculator.

$\text{14}+5$

19

$\text{12}+7$

$\text{46}+2$

48

$\text{83}+\text{16}$

$\text{77}+\text{21}$

98

978

$\begin{array}{c}\hfill 104\\ \hfill \underline{+561}\end{array}$

$\begin{array}{c}\hfill 265\\ \hfill \underline{+103}\end{array}$

368

$\text{552}+\text{237}$

$8,\text{521}+4,\text{256}$

12,777

$\begin{array}{c}\hfill 16,515\\ \hfill \underline{+42,223}\end{array}$

58,738

$\text{616},\text{702}+\text{101},\text{161}$

$\text{43},\text{156},\text{219}+2,\text{013},\text{520}$

45,169,739

$\text{17}+6$

$\text{25}+8$

33

81

$\text{36}+\text{48}$

$\text{74}+\text{17}$

91

$\text{486}+\text{58}$

$\text{743}+\text{66}$

809

$\text{381}+\text{88}$

$\begin{array}{c}\hfill 687\\ \hfill \underline{+175}\end{array}$

862

$\begin{array}{c}\hfill 931\\ \hfill \underline{+853}\end{array}$

$1,\text{428}+\text{893}$

2,321

$\text{12},\text{898}+\text{11},\text{925}$

$\begin{array}{c}\hfill 631,464\\ \hfill \underline{+509,740}\end{array}$

1,141,204

$\begin{array}{c}\hfill 38,428,106\\ \hfill \underline{+522,936,005}\end{array}$

561,364,111

$5,\text{288},\text{423},\text{100}+\text{16},\text{934},\text{785},\text{995}$

$\text{98},\text{876},\text{678},\text{521},\text{402}+\text{843},\text{425},\text{685},\text{685},\text{658}$

942,302,364,207,060

$\text{41}+\text{61}+\text{85}+\text{62}$

$\text{21}+\text{85}+\text{104}+9+\text{15}$

234

$\begin{array}{c}\hfill 75,206\\ \hfill 4,152\\ \hfill \underline{+16,007}\end{array}$

95,365

1,972,128

For the following problems, perform the additions and round to the nearest hundred.

3,700

3,101,500

100

0

1,000

For the next five problems, replace the letter $m$ with the whole number that will make the addition true.

5

19

88

The number of nursing and related care facilities in the United States in 1971 was 22,004. In 1978, the number was 18,722. What was the total number of facilities for both 1971 and 1978?

The number of persons on food stamps in 1975, 1979, and 1980 was 19,179,000, 19,309,000, and 22,023,000, respectively. What was the total number of people on food stamps for the years 1975, 1979, and 1980?

60,511,000

The enrollment in public and nonpublic schools in the years 1965, 1970, 1975, and 1984 was 54,394,000, 59,899,000, 61,063,000, and 55,122,000, respectively. What was the total enrollment for those years?

The area of New England is 3,618,770 square miles. The area of the Mountain states is 863,563 square miles. The area of the South Atlantic is 278,926 square miles. The area of the Pacific states is 921,392 square miles. What is the total area of these regions?

5,682,651 square miles

In 1960, the IRS received 1,188,000 corporate income tax returns. In 1965, 1,490,000 returns were received. In 1970, 1,747,000 returns were received. In 1972 —1977, 1,890,000; 1,981,000; 2,043,000; 2,100,000; 2,159,000; and 2,329,000 returns were received, respectively. What was the total number of corporate tax returns received by the IRS during the years 1960, 1965, 1970, 1972 —1977?

Find the total number of scientists employed in 1974.

1,190,000

Find the total number of sales for space vehicle systems for the years 1965-1980.

Find the total baseball attendance for the years 1960-1980.

271,564,000

Find the number of prosecutions of federal officials for 1970-1980.

For the following problems, try to add the numbers mentally.

20

25

40

50

50

50

## Exercises for review

( [link] ) Each period of numbers has its own name. From right to left, what is the name of the fourth period?

( [link] ) In the number 610,467, how many thousands are there?

0

( [link] ) Round 6,842 to the nearest hundred.

6,800

( [link] ) Round 431,046 to the nearest million.

a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
how did I we'll learn this
f(x)= 2|x+5| find f(-6)
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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text: The following are the major asymmetric encryption algorithms used for encrypting or digitally signing data. It will be explained in details later in this chapter. Symmetric Ciphers. The public key can be shared with anyone, so Bob can use it to encrypt a message for Alice. It could be an email message, the contents of a database or a file stored…. To get a ciphertext, you run the information that is to be encrypted through an encryption algorithm. Learn to identify why our passwords are so easy to guess by crackers, and improve your security just by using simple algorithms and techniques. In this tutorial we will use symmetric key. True or False: A virus can be hidden in the boot sector, but not in system memory. Symmetric ciphers use symmetric algorithms to encrypt and decrypt data. This name derives from the initials of its creators: Ron Rivest, Adi Shamir, and Leonard Adleman. Symmetric encryption uses a single key that must be shared among the people who need to receive the message, while asymmetrical encryption uses a pair—consisting of a public key and a private key—to encrypt and decrypt messages when communicating. 3. . (data encapsulation mechanism), holding the encapsulated symmetrically-encrypted data (cipher parameters + ciphertext + optionally an authentication tag). Only 2n keys are needed for n entities to communicate securely with one another. Data to be encrypted (or, as it's called, plaintext) 2. In addition, keys should be handled in encrypted form within the system as much as possible to reduce the risk of exposure. Examples of EIS schemes are DLIES (Discrete Logarithm Integrated Encryption Scheme) and ECIES (Elliptic Curve Integrated Encryption Scheme). A block cipher processes the input one block of elements at a time, producing an output block for each input block. Keys must be encrypted prior to sending or storing them outside the secured system environment. Encryption is principally used to defend against which of the following? A message encrypted by the public key is later decrypted by the private key. For this reason, Symmetric encryption is great when working with sensitive data in bulk, or encryption tasks that intend to permanently want to hide information without the need for decryption. Another example are VPNs, which encrypt your network traffic with a local key and don’t have the need to share that outside of your own use. Anyone, who knows the public key of the message signer, can verify the signature. For Asymmetric Encryption read this tutorial: ... Once you copy the JCE libraries you will need to kill the running Java process and start it again. Which 128-bit block cipher encryption algorithm does the US government use to protect classified information? AES encrypts information in a single block (block cipher), and does so one block at a time in what is called ’rounds’. These ciphers are used in symmetric key cryptography.A symmetric algorithm uses the same key to encrypt data as it does to decrypt data. The key represents the mathematical steps the algorithm took to convert your text from “Hello World” into “XJtg920kl#aJFJ”%*¨*FK”. The Running Key cipher has the same internal workings as the Vigenere cipher. For example, when a laptop connects to the home WiFi router, both parties agree on a session key, used to symmetrically encrypt the network traffic between them. to encrypt an AES secret key by given ECC public key. This is the principle used with signing. Taking the first step might seem difficult, but it is necessary to document all data interactions and make a plan. Integrated encryption schemes (IES) are modern public key encryption schemes, which combine symmetric ciphers, asymmetric ciphers and key-derivation algorithms to provide secure public-key based encryption (PKE). An early example of symmetric encryption — and probably the best-known symmetric cipher — is attributed to the Roman General Julius Caesar. What is data encryption? encapsulates the ephemeral symmetric encryption key as part of the encrypted message, by encrypting it with the recipient's public key. The way in which the plaintext is processed. The main attractive of TwoFish is its flexibility in performance, giving you total control of the encryption speed. A key to descramble the data into its original form Let's take any phrase. In classical cryptography, the running key cipher is a type of polyalphabetic substitution cipher in which a text, typically from a book, is used to provide a very long keystream.Usually, the book to be used would be agreed ahead of time, while the passage to be used would be chosen randomly for each message and secretly indicated somewhere in the message. Only 2n keys are needed for n entities to communicate securely with one another. the RSA encryption is 1000 times slower than AES). ECC uses smaller keys and signatures than RSA and is prefered in most modern apps. In cryptography, keys are strings of random-looking characters. Asymmetric encryption uses personal keys. Key encapsulation (KEM) refers to public-key encryption of another key (symmetric or asymmetric). Digital signatures are widely used today for signing digital contracts, for authorizing bank payments and signing transactions in the public blockchain systems for transferring digital assets. Finally, the direct successor to DES is 3DES, or Triple Des. Since it requires two different keys of incredible length, the encryption and decryption process is slow, but the level of security it provides for sensitive information is incomparable. Some cryptosystems (like ECC) do not provide directly encryption primitives, so more complex schemes should be used. The management of encrypted keys is often done via a hierarchical key system. If you want to use asymmetric keys for creating and validating signatures, see Creating and validating digital signatures.If you want to use symmetric keys for encryption and decryption, see Encrypting and decrypting data. The easiest way to crack this cipher is to guess or obtain somehow a piece of the plaintext, this allows you to determine the key. In classical cryptography, the running key cipher is a type of polyalphabetic substitution cipher in which a text, typically from a book, is used to provide a very long keystream. Digital signatures (message authentication): sign messages by private key and verify signatures by public key. With ECC you have a curve, defined by a math function, a starting point (A), and an ending point (Z) in the curve. Message signing is performed by the private key and message verification is performed by the corresponding public key. (KEMs) are used in the hybrid encryption schemes and in the integrated encryption schemes, where a random element is generated in the underlying public-key cryptosystem and a symmetric key is derived from this random element by hashing. The asymmetric key cryptosystems provide key-pair generation (private + public key), encryption algorithms (asymmetric key ciphers and encryption schemes like RSA-OAEP and ECIES), digital signature algorithms (like DSA, ECDSA and EdDSA) and key exchange algorithms (like DHKE and ECDH). Asymmetric encryption uses personal keys. Symmetric encryption is an old practice, while asymmetric encryption is relatively new. Let’s recap the basics of this data security asset. Use our new Disk Encryption tool to easily encrypt data on compatible Windows devices remotely using Windows’ native BitLocker tool. ECC is also extremely attractive for mobile, where processing power is low and data transfers are high. A user needs to have a secondary key, the private key, to decrypt this information. But confidentiality isn’t the only thing you can do with a Public and Private Key. is based on the math of the on the algebraic structure of the. Most public-key cryptosystems (like RSA, ECC, DSA, ECDSA and EdDSA) are quantum-breakable (quantum-unsafe), which means that (at least on theory) a powerful enough quantum computer will be able to break their security and compute the private key from given public key in seconds. system, the input message should be transformed to. Key encapsulation should not be confused with key wrapping. . To turn it … To overcome the above limitations and to allow encrypting messages of any size, modern cryptography uses. . Encryption is the method of converting the data into a cipher format using a key. Asymmetric ciphers also create lesser key-management problems than symmetric ciphers. With asymmetric encryption, anyone can use your public key to send you an encrypted email that you only can decipher using your private key. Asymmetric encryption is also known as public key cryptography, which is a relatively new method, compared to symmetric encryption. AES-256 is an example of such block cipher, with keyspace $\mathcal K=\{0,1\}^{256}$ and $b=128$ bits, thus plaintext and ciphertext blocks (the input and output of encryption by a block cipher) in the set $\{0,1\}^{128}$. The process involves a series of data manipulation and mixing steps that are done each round: substitution, transposition, mixing, column mix, sub bytes. FileVault on macOS comes integrated and ready to encrypt your Mac computers with AES; whereas Microsoft boasts BitLocker native encryption, capable of full disk encryption with AES and AES-XTS. It’s asymmetric, yet it is able to provide a security level of 256 bits at a maximum key length of 521 bits, which ensures fast encryption speeds with a high complexity of decryption to ensure sensitive data stays safe. The principles are the same for every message. Nicolas Poggi is the head of mobile research at Prey, Inc., provider of the open source Prey Anti-Theft software protecting eight million mobile devices. The encryption system is based on a private key that consists of two prime numbers. Considered a staple of asymmetric encryption. We shall discuss ECC and ECDSA later in details, along with examples. They are faster than asymmetric ciphers and allow encrypting large sets of data. To overcome the above limitations and to allow encrypting messages of any size, modern cryptography uses asymmetric encryption schemes (also known as public key encryption schemes / asymmetric encryption constructions / hybrid encryption schemes), like key encapsulation mechanisms (KEM) and integrated encrypted schemes, which combine asymmetric encryption with symmetric key ciphers. A… TripleDES, an algorithm derived from … 3. The running key cipher is in general more difficult to break than the Vigenere or Autokey ciphers. We have Cookies. This cipher predates SSL, HTTPS, and much of the internet by a long way – it was created in 1977. Аfter signing the signature author cannot reject the act of signing (this is known as. Every bit of sensible information and access now fits in the palm of our hands, inside our smartphones. Usually, the book to be used would be agreed ahead of time, while the passage to use would be chosen randomly for each message and secretly indicated somewhere in the message. From RSA to AES, your pick should be informed by context. When Bob has a message he wishes to securely send to Alice, he will use Alice’s Public Key to Encrypt the message. Vignere AES* Caesar 3DES Skipjack. AES is one of the most common symmetric encryption algorithms used today, developed as a replacement to the outdated DES (Data Encryption Standard), cracked by security researchers back in 2005. The elliptic-curve cryptography (ECC) cryptosystem is based on the math of the on the algebraic structure of the elliptic curves over finite fields and the elliptic curve discrete logarithm problem (ECDLP), which is considered to be computationally infeasible for large keys. , but because asymmetric encryption can encrypt / decrypt only small messages, which should be mapped to the underlying math of the public-key cryptosystem. In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a one-time pre-shared key the same size as, or longer than, the message being sent. The dominant public key encryption cipher is called RSA. An encryption algorithm is a set of mathematical procedure for performing encryption on data. Key-pair generation: generate random pairs of private key + corresponding public key. It is not an issue of anti-reverse engineering that makes the keys safe, but rather a mathematical concept that you can't reasonably check the massive keyspace (when the key uses a really large number space) to find the matching key. Through the use of such an algorithm, information is made in the cipher text and requires the use of a key to transforming the data into its original form. is more complicated than symmetric encryption, not only because it uses. , e.g. A cipher is simply a method for encrypting (and decrypting) messages. For details see, for digital documents. In EIS scheme asymmetric algorithms (like RSA or ECC) are used to encrypt or encapsulate a symmetric key, used later by symmetric ciphers (like AES or ChaCha20) to encrypt the input message. One key in the pair can be shared with everyone; it is called the public key. Key-exchange algorithms: securely exchange cryptographic key between two parties over insecure channel. Without it, you can’t decrypt the data, and thus it is protected from unauthorized access.But, there are many different types of encryption algorithms and methods to pick from, so how do you know which one is the safest pick for your cybersecurity needs? Things encrypted with one key can be decrypted with the other key. Asymmetric cryptography is a type of encryption where the key used to encrypt the information is not the same as the key used to decrypt the information. A pseudo-random algorithm to turn readable data into a scrambled mess 3. Blowfish was another symmetric successor to DES, designed as a block cipher like AES but with a key length that goes from 32 bits to 448 bits. Digital signatures work in the public-key cryptosystems and use a public / private key pairs. It was invented in 1977 by Ron Rivest, Adi Shamir, and Leonard Adleman of RSA Security. Authenticated key agreement schemes authenticate the identities of parties involved in the key exchange and thus prevent man-in-the-middle attacks by use of digitally signed keys (e.g. This is how a large document or file can be encrypted by combining public-key cryptography and symmetric crypto algorithm: In the above diagram the encrypted symmetric key is known as KEM block (encapsulated key, with public key encryption) and the encrypted data file is known as DEM block (encapsulated data, with symmetric encryption). Note: Ciphers are also known as encryption algorithms, so we'll be using the terms "cipher" and "encryption algorithm" interchangeably throughout the article. Even if you have the starting and ending point (public key), and the curve, it is nearly impossible to crack the private key. Distributing the key in a secure way is one of the primary challenges of symmetric encryption, which is known as the “ key distribution problem. Public-key encryption uses two different keys at once, a combination of a private key and a public key. The receiver deciphers the data to the original format using the key, used earlier to encrypt it. If both sender and receiver use the same key, the system is referred to as symmetric, single-key, secret-key, or conventional encryp-tion. Encryption / decryption: encrypt date by public key and decrypt data by private key (often using a hybrid encryption scheme). The reason is simple: if you scale your encryption to a company-wide scale, it means you’re putting all your trust into a single key you will need to share around a lot. Data is initially converted into blocks, and then these are encrypted with the key in different rounds depending on key size: 14 rounds for 256-bits, 12 rounds for 192-bits, and 10 rounds for 128-bits. This is the principle used with signing. However, this means that it is a slower encryption algorithm. Since its speed isn’t convenient for processing large amounts of data, RSA encryption is mostly used in digital signatures, email encryption, SSL/TLS certificates, and browsers. This particular cipher is aptly known as the Caesar Cipher (more on that in a couple of minutes). Asymmetric key cryptosystems / public-key cryptosystems (like RSA, elliptic curve cryptography (ECC), Diffie-Hellman, ElGamal, McEliece, NTRU and others) use a pair of mathematically linked keys: public key (encryption key) and private key (decryption key). Let’s start with the name: data is information. The RSA public-key cryptosystem is based on the mathematical concept of modular exponentiation (numbers raised to a power by modulus), along with some mathematical constructions and the integer factorization problem (which is considered to be computationally infeasible for large enough keys). Similarly, data encrypted with the private key can only be decrypted with the corresponding public key. First, we choose a starting point. If that does not help, restart your computer. Explanation: The Advanced Encryption Standard (AES) is used to protect classified information by the U.S. government and is a strong algorithm that uses longer key lengths. Encryption algorithm example #1: The Substitution Cipher A message signed by the private key is later verified by the public key. (quantum-unsafe), which means that (at least on theory) a powerful enough quantum computer will be able to break their security and compute the private key from given public key in seconds. The encrypted data can be safely shared with others. Start Your Free Software Development Course. Digital signatures(message authentication): sign messages by private key and verify signat… In the RSA system, the input message should be transformed to big integer (e.g. Symmetric encryption uses a single key known as a private key or secret key to encrypt and decrypt sensitive information. 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2.0 3.0 > comp > gb.opengl > gl > pixelstorei
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 Documentation
Gl.PixelStorei (gb.opengl)
Static Sub PixelStorei ( Pname As Integer, Param As Integer )

Set pixel storage modes.

### Parameters

pname

Specifies the symbolic name of the parameter to be set. Six values affect the packing of pixel data into memory: Gl.PACK_SWAP_BYTES, Gl.PACK_LSB_FIRST, Gl.PACK_ROW_LENGTH, Gl.PACK_IMAGE_HEIGHT, Gl.PACK_SKIP_PIXELS, Gl.PACK_SKIP_ROWS, Gl.PACK_SKIP_IMAGES, and Gl.PACK_ALIGNMENT. Six more affect the unpacking of pixel data from memory: Gl.UNPACK_SWAP_BYTES, Gl.UNPACK_LSB_FIRST, Gl.UNPACK_ROW_LENGTH, Gl.UNPACK_IMAGE_HEIGHT, Gl.UNPACK_SKIP_PIXELS, Gl.UNPACK_SKIP_ROWS, Gl.UNPACK_SKIP_IMAGES, and Gl.UNPACK_ALIGNMENT.

param

Specifies the value that pname is set to.

### Description

Gl.PixelStore sets pixel storage modes that affect the operation of subsequent Gl.ReadPixels as well as the unpacking of texture patterns (see Gl.TexImage1D, Gl.TexImage2D, Gl.TexImage3D, Gl.TexSubImage1D, Gl.TexSubImage2D, Gl.TexSubImage3D).

pname is a symbolic constant indicating the parameter to be set, and param is the new value. Six of the twelve storage parameters affect how pixel data is returned to client memory. They are as follows:

Gl.PACK_SWAP_BYTES

If true, byte ordering for multibyte color components, depth components, or stencil indices is reversed. That is, if a four-byte Përbërës consists of bytes ${\mathit{b}}_{0}$, ${\mathit{b}}_{1}$, ${\mathit{b}}_{2}$, ${\mathit{b}}_{3}$, it is stored in memory as ${\mathit{b}}_{3}$, ${\mathit{b}}_{2}$, ${\mathit{b}}_{1}$, ${\mathit{b}}_{0}$ if Gl.PACK_SWAP_BYTES is true. Gl.PACK_SWAP_BYTES has no effect on the memory order of components within a pixel, only on the order of bytes within components or indices. For example, the three components of a Gl.RGB format pixel are always stored with red first, green second, and blue third, regardless of the value of Gl.PACK_SWAP_BYTES.

Gl.PACK_LSB_FIRST

If true, bits are ordered within a byte from least significant to most significant; otherwise, the first bit in each byte is the most significant one.

Gl.PACK_ROW_LENGTH

If greater than 0, Gl.PACK_ROW_LENGTH defines the number of pixels in a row. If the first pixel of a row is placed at location $\mathit{p}$ in memory, then the location of the first pixel of the next row is obtained by skipping

$\mathit{k}=\left\{\begin{array}{c}\mathit{n}\mathit{l}\\ \frac{\mathit{a}}{\mathit{s}}⌈\frac{\mathit{s}\mathit{n}\mathit{l}}{\mathit{a}}⌉\end{array}\begin{array}{c}\mathit{s}>=\mathit{a}\\ \mathit{s}<\mathit{a}\end{array}\right\$

components or indices, where $\mathit{n}$ is the number of components or indices in a pixel, $\mathit{l}$ is the number of pixels in a row (Gl.PACK_ROW_LENGTH if it is greater than 0, the $\mathit{width}$ argument to the pixel routine otherwise), $\mathit{a}$ is the value of Gl.PACK_ALIGNMENT, and $\mathit{s}$ is the size, in bytes, of a single component (if $\mathit{a}<\mathit{s}$, then it is as if $\mathit{a}=\mathit{s}$). In the case of 1-bit values, the location of the next row is obtained by skipping

$\mathit{k}=8\mathit{a}⌈\frac{\mathit{n}\mathit{l}}{8\mathit{a}}⌉$

components or indices.

The word component in this description refers to the nonindex values red, green, blue, alpha, and depth. Storage format Gl.RGB, for example, has three components per pixel: first red, then green, and finally blue.

Gl.PACK_IMAGE_HEIGHT

If greater than 0, Gl.PACK_IMAGE_HEIGHT defines the number of pixels in an image three-dimensional texture volume, where ``image'' is defined by all pixels sharing the same third dimension index. If the first pixel of a row is placed at location $\mathit{p}$ in memory, then the location of the first pixel of the next row is obtained by skipping

$\mathit{k}=\left\{\begin{array}{c}\mathit{n}\mathit{l}\mathit{h}\\ \frac{\mathit{a}}{\mathit{s}}⌈\frac{\mathit{s}\mathit{n}\mathit{l}\mathit{h}}{\mathit{a}}⌉\end{array}\begin{array}{c}\mathit{s}>=\mathit{a}\\ \mathit{s}<\mathit{a}\end{array}\right\$

components or indices, where $\mathit{n}$ is the number of components or indices in a pixel, $\mathit{l}$ is the number of pixels in a row (Gl.PACK_ROW_LENGTH if it is greater than 0, the $\mathit{width}$ argument to Gl.TexImage3D otherwise), $\mathit{h}$ is the number of rows in a pixel image (Gl.PACK_IMAGE_HEIGHT if it is greater than 0, the $\mathit{height}$ argument to the Gl.TexImage3D routine otherwise), $\mathit{a}$ is the value of Gl.PACK_ALIGNMENT, and $\mathit{s}$ is the size, in bytes, of a single component (if $\mathit{a}<\mathit{s}$, then it is as if $\mathit{a}=\mathit{s}$).

The word component in this description refers to the nonindex values red, green, blue, alpha, and depth. Storage format Gl.RGB, for example, has three components per pixel: first red, then green, and finally blue.

Gl.PACK_SKIP_PIXELS, Gl.PACK_SKIP_ROWS, and Gl.PACK_SKIP_IMAGES

These values are provided as a convenience to the programmer; they provide no functionality that cannot be duplicated simply by incrementing the pointer passed to Gl.ReadPixels. Setting Gl.PACK_SKIP_PIXELS to $\mathit{i}$ is equivalent to incrementing the pointer by $\mathit{i}\mathit{n}$ components or indices, where $\mathit{n}$ is the number of components or indices in each pixel. Setting Gl.PACK_SKIP_ROWS to $\mathit{j}$ is equivalent to incrementing the pointer by $\mathit{j}\mathit{m}$ components or indices, where $\mathit{m}$ is the number of components or indices per row, as just computed in the Gl.PACK_ROW_LENGTH section. Setting Gl.PACK_SKIP_IMAGES to $\mathit{k}$ is equivalent to incrementing the pointer by $\mathit{k}\mathit{p}$, where $\mathit{p}$ is the number of components or indices per image, as computed in the Gl.PACK_IMAGE_HEIGHT section.

Gl.PACK_ALIGNMENT

Specifies the alignment requirements for the start of each pixel row in memory. The allowable values are 1 (byte-alignment), 2 (rows aligned to even-numbered bytes), 4 (word-alignment), and 8 (rows start on double-word boundaries).

The other six of the twelve storage parameters affect how pixel data is read from client memory. These values are significant for Gl.TexImage1D, Gl.TexImage2D, Gl.TexImage3D, Gl.TexSubImage1D, Gl.TexSubImage2D, and Gl.TexSubImage3D

They are as follows:

Gl.UNPACK_SWAP_BYTES

If true, byte ordering for multibyte color components, depth components, or stencil indices is reversed. That is, if a four-byte component consists of bytes ${\mathit{b}}_{0}$, ${\mathit{b}}_{1}$, ${\mathit{b}}_{2}$, ${\mathit{b}}_{3}$, it is taken from memory as ${\mathit{b}}_{3}$, ${\mathit{b}}_{2}$, ${\mathit{b}}_{1}$, ${\mathit{b}}_{0}$ if Gl.UNPACK_SWAP_BYTES is true. Gl.UNPACK_SWAP_BYTES has no effect on the memory order of components within a pixel, only on the order of bytes within components or indices. For example, the three components of a Gl.RGB format pixel are always stored with red first, green second, and blue third, regardless of the value of Gl.UNPACK_SWAP_BYTES.

Gl.UNPACK_LSB_FIRST

If true, bits are ordered within a byte from least significant to most significant; otherwise, the first bit in each byte is the most significant one.

Gl.UNPACK_ROW_LENGTH

If greater than 0, Gl.UNPACK_ROW_LENGTH defines the number of pixels in a row. If the first pixel of a row is placed at location $\mathit{p}$ in memory, then the location of the first pixel of the next row is obtained by skipping

$\mathit{k}=\left\{\begin{array}{c}\mathit{n}\mathit{l}\\ \frac{\mathit{a}}{\mathit{s}}⌈\frac{\mathit{s}\mathit{n}\mathit{l}}{\mathit{a}}⌉\end{array}\begin{array}{c}\mathit{s}>=\mathit{a}\\ \mathit{s}<\mathit{a}\end{array}\right\$

components or indices, where $\mathit{n}$ is the number of components or indices in a pixel, $\mathit{l}$ is the number of pixels in a row (Gl.UNPACK_ROW_LENGTH if it is greater than 0, the $\mathit{width}$ argument to the pixel routine otherwise), $\mathit{a}$ is the value of Gl.UNPACK_ALIGNMENT, and $\mathit{s}$ is the size, in bytes, of a single component (if $\mathit{a}<\mathit{s}$, then it is as if $\mathit{a}=\mathit{s}$). In the case of 1-bit values, the location of the next row is obtained by skipping

$\mathit{k}=8\mathit{a}⌈\frac{\mathit{n}\mathit{l}}{8\mathit{a}}⌉$

components or indices.

The word component in this description refers to the nonindex values red, green, blue, alpha, and depth. Storage format Gl.RGB, for example, has three components per pixel: first red, then green, and finally blue.

Gl.UNPACK_IMAGE_HEIGHT

If greater than 0, Gl.UNPACK_IMAGE_HEIGHT defines the number of pixels in an image of a three-dimensional texture volume. Where ``image'' is defined by all pixel sharing the same third dimension index. If the first pixel of a row is placed at location $\mathit{p}$ in memory, then the location of the first pixel of the next row is obtained by skipping

$\mathit{k}=\left\{\begin{array}{c}\mathit{n}\mathit{l}\mathit{h}\\ \frac{\mathit{a}}{\mathit{s}}⌈\frac{\mathit{s}\mathit{n}\mathit{l}\mathit{h}}{\mathit{a}}⌉\end{array}\begin{array}{c}\mathit{s}>=\mathit{a}\\ \mathit{s}<\mathit{a}\end{array}\right\$

components or indices, where $\mathit{n}$ is the number of components or indices in a pixel, $\mathit{l}$ is the number of pixels in a row (Gl.UNPACK_ROW_LENGTH if it is greater than 0, the $\mathit{width}$ argument to Gl.TexImage3D otherwise), $\mathit{h}$ is the number of rows in an image (Gl.UNPACK_IMAGE_HEIGHT if it is greater than 0, the $\mathit{height}$ argument to Gl.TexImage3D otherwise), $\mathit{a}$ is the value of Gl.UNPACK_ALIGNMENT, and $\mathit{s}$ is the size, in bytes, of a single component (if $\mathit{a}<\mathit{s}$, then it is as if $\mathit{a}=\mathit{s}$).

The word component in this description refers to the nonindex values red, green, blue, alpha, and depth. Storage format Gl.RGB, for example, has three components per pixel: first red, then green, and finally blue.

Gl.UNPACK_SKIP_PIXELS and Gl.UNPACK_SKIP_ROWS

These values are provided as a convenience to the programmer; they provide no functionality that cannot be duplicated by incrementing the pointer passed to Gl.TexImage1D, Gl.TexImage2D, Gl.TexSubImage1D or Gl.TexSubImage2D. Setting Gl.UNPACK_SKIP_PIXELS to $\mathit{i}$ is equivalent to incrementing the pointer by $\mathit{i}\mathit{n}$ components or indices, where $\mathit{n}$ is the number of components or indices in each pixel. Setting Gl.UNPACK_SKIP_ROWS to $\mathit{j}$ is equivalent to incrementing the pointer by $\mathit{j}\mathit{k}$ components or indices, where $\mathit{k}$ is the number of components or indices per row, as just computed in the Gl.UNPACK_ROW_LENGTH section.

Gl.UNPACK_ALIGNMENT

Specifies the alignment requirements for the start of each pixel row in memory. The allowable values are 1 (byte-alignment), 2 (rows aligned to even-numbered bytes), 4 (word-alignment), and 8 (rows start on double-word boundaries).

The following table gives the type, initial value, and range of valid values for each storage parameter that can be set with Gl.PixelStore.

pname Type Initial Value Valid Range
Gl.PACK_SWAP_BYTES boolean false true or false
Gl.PACK_LSB_FIRST boolean false true or false
Gl.PACK_ROW_LENGTH integer 0 $\left[0,\infty \right)$
Gl.PACK_IMAGE_HEIGHT integer 0 $\left[0,\infty \right)$
Gl.PACK_SKIP_ROWS integer 0 $\left[0,\infty \right)$
Gl.PACK_SKIP_PIXELS integer 0 $\left[0,\infty \right)$
Gl.PACK_SKIP_IMAGES integer 0 $\left[0,\infty \right)$
Gl.PACK_ALIGNMENT integer 4 1, 2, 4, or 8
Gl.UNPACK_SWAP_BYTES boolean false true or false
Gl.UNPACK_LSB_FIRST boolean false true or false
Gl.UNPACK_ROW_LENGTH integer 0 $\left[0,\infty \right)$
Gl.UNPACK_IMAGE_HEIGHT integer 0 $\left[0,\infty \right)$
Gl.UNPACK_SKIP_ROWS integer 0 $\left[0,\infty \right)$
Gl.UNPACK_SKIP_PIXELS integer 0 $\left[0,\infty \right)$
Gl.UNPACK_SKIP_IMAGES integer 0 $\left[0,\infty \right)$
Gl.UNPACK_ALIGNMENT integer 4 1, 2, 4, or 8

Gl.PixelStoref can be used to set any pixel store parameter. If the parameter type is boolean, then if param is 0, the parameter is false; otherwise it is set to true. If pname is a integer type parameter, param is rounded to the nearest integer.

Likewise, Gl.PixelStorei can also be used to set any of the pixel store parameters. Boolean parameters are set to false if param is 0 and true otherwise.

### Errors

Gl.INVALID_ENUM is generated if pname is not an accepted value.

Gl.INVALID_VALUE is generated if a negative row length, pixel skip, or row skip value is specified, or if alignment is specified as other than 1, 2, 4, or 8.

### Associated Gets

Gl.Get with argument Gl.PACK_SWAP_BYTES

Gl.Get with argument Gl.PACK_LSB_FIRST

Gl.Get with argument Gl.PACK_ROW_LENGTH

Gl.Get with argument Gl.PACK_IMAGE_HEIGHT

Gl.Get with argument Gl.PACK_SKIP_ROWS

Gl.Get with argument Gl.PACK_SKIP_PIXELS

Gl.Get with argument Gl.PACK_SKIP_IMAGES

Gl.Get with argument Gl.PACK_ALIGNMENT

Gl.Get with argument Gl.UNPACK_SWAP_BYTES

Gl.Get with argument Gl.UNPACK_LSB_FIRST

Gl.Get with argument Gl.UNPACK_ROW_LENGTH

Gl.Get with argument Gl.UNPACK_IMAGE_HEIGHT

Gl.Get with argument Gl.UNPACK_SKIP_ROWS

Gl.Get with argument Gl.UNPACK_SKIP_PIXELS

Gl.Get with argument Gl.UNPACK_SKIP_IMAGES

Gl.Get with argument Gl.UNPACK_ALIGNMENT


text:
IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# To Study Torsional Oscillation of a Rectangular Body

## Objective

To study the torsional oscillation of a rectangular body suspended by two non parallel threads.

## Apparatus

Clamp, Suspension plate with nails fixed, Oscillating plate with hooks and threads fixed, Meter Scale, Stop Watch, Graph Paper

## Procedure

Suspend the oscillating plate using the threads and the inner pair of nails on the suspension plate. The upper edges of the plate should be horizontal.

Rotate the plate about the vertical bisector through a small angle and release. The plate should start oscillating.

Let the height of the nails over the upper edge of the plate be $$H$$ and time period of oscillation be $$T$$. You are suppose to find the relation between $$T$$ and $$H$$. So measure $$T$$ and $$H$$ at appropriate length and draw a graph between $$T$$ and $$H$$. From this, guess whether $$T\propto H^2$$, $$T\propto H$$ or $$T\propto\sqrt{H}$$.