text:
## Plane rotated about line of intersection to another plane?

The plane ax+by=0 is rotated about its line of intersection with the plane z=0 through an angle n. What is the equation of the plane in its new position? I saw a question in stack exchange relating to 3d plane rotation but its answers were of a more advanced level. Would someone please help me with an easy visualisation and solving of this problem?

## Finding a plane numerically

Suppose I have three large finite sets $$\{x_i\}$$, $$\{y_i\}$$ and $$\{z_i\}$$; they are obtained by measuring coordinates of a collection of vectors in $$\mathbb{R}^3$$, but I do not know which triples correspond to one vector. Assume I know that all of the vectors lie in a plane, but I do not know which one. I want to reconstruct this plane and the original collection of vectors.

Evidently the problem can be solved and the solution is unique if the original data is generic. But I do not see a reasonable algorithm to solve this problem. (For sure checking all subdivisions into triples is not a good idea.)

Is there a numerical method to find this plane?

and

Did anyone considered this or similar problem; does it have a name?

## Growing a chain of unit-area triangles: Fills the plane?

Define a process to start with a unit-area equilateral triangle, and at each step glue on another unit-area triangle.

$$50$$ triangles.

Above, the red dot marks the starting triangle $$T_0$$. Then on one edge $$e$$ of $$T_0$$, a point $$p$$ is chosen to form a unit-area triangle $$T_1$$. Now there are two edges of $$T_1$$ for possible growth. One edge is chosen randomly, and another unit-area triangle $$T_2$$ is erected on that edge. Then $$T_3$$ is built on an edge of $$T_2$$. And so on.

The point $$p$$ at each step is chosen according to a normal distribution $$\cal N(0,1)$$ centered on the midpoint normal vector to $$e$$, as illustrated below:

The location of $$p$$ follows a normal distribution.

My question is:

Q. Does this process fill the plane in the limit?

I think Yes but am not certain.

Here are two more examples (using different random seeds):

$$500$$ triangles.

$$1000$$ triangles.

## How to get the villain in prison – on another plane?

Let’s just say I have acquired an Emissary of Barachiel contact, and built a prison on our base plane that can’t be broken out of while he gets to talk to the prisoner unhindered (and use the class’ features to turn them lawful good over time).

That’s all well and good, but sometimes you can’t just haul the villain back the moment you beat them. Maybe there’s more work to be done.

I am looking for ways to land the villain accurately in the prison without going there, or keeping them on my person safely, easily and indefinitely until I can take them there. I can only use items to do it, as the party shifts and my character isn’t a caster nor has room for PrCs.

## Is this perspective scaling from plane to sphere right?

Perspective through CNS (canvas, paper, screen) plane

View post on imgur.com

I guess im asking for something similair to code review but for trigonometry

Greetings Johan

## Can a genie use its Plane Shift ability on unwilling creatures?

A Genie has the SP ability of a limited plane shift.

A genie can enter any of the elemental planes, the Astral Plane, or the Material Plane. This ability transports the genie and up to eight other creatures, provided they all link hands with the genie. It is otherwise similar to the spell of the same name (caster level 13th).

The Plane Shift spell has two versions.

One targets a creature touched, the other several hand-held, willing creatures.

Can the Genie use its Plane Shift on an unwilling creature, or is it limited to the willing version (seeing as it mentions ‘itself and others’, per the willing-group version)?

## Taking my 2 month old bicycle from the US to India on plane as checked luggage. Do I have to pay import duty when I land in India?

I am an Indian citizen. Also, I will be taking my bicycle with me back to the US in August. The price of the bike is around \$ 1600 and it isn’t sold in India.

## Find plane within margin of error of >50% of points

There are $$N < 3\times10^4$$ 3D points. At least 50% of them lie approximately in the same plane, i.e. the distance between the plane and each point is at most $$p$$. Find such a plane.

Attempt: since the number of points in the plane is at least 50%, we can randomly sample 3 points from the set. They will all be in the plane with probability 12.5%. We build a plane through these 3 points and check that at least 50% of points lie approximately in it. Within 10-20 samples we’ll find the plane.

Problem: because of the margin of error there’s not just one plane going through 3 points, but many possible planes. How do we examine all of them?

How would you tackle this problem?

## Find a vector that lies in the plane determined by a line and a point and is perpendicular to that line

I need to use the triple cross product to find a vector that lies in the plane determined by

the point (1, 0, 2) and the line $$\frac {x}{2}=\frac {y+1}{3}=\frac {z-2}{-1}$$ , and is perpendicular to the line

## Schengen visa application in UK requires confirmed plane tickets

I am a non-EU national living in the UK and applying for a Schengen visa. I would like to visit Switzerland and applied through TLS Contact – which is the standard way to apply in the UK. Among their list of documents required is

Copy of transport documentation with applicant’s name as passenger – by plane confirmed booking with airline booking reference number

The TLS center representative confirmed that without a confirmed booking, the file would be considered incomplete. This is also mentioned on the Swiss embassy website

I have applied for Schengen visas before (at Asian embassies) and they only required an itinerary, not confirmed tickets. Any advice on what to do in this case? Book the flights and take the risk or is there a better option?


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# Roger Penrose's conformal cyclic cosmology (CCC)

Does the Weyl curvature tensor $$C$$ of the black hole singularity in the conformal cyclic cosmology diverge to infinity unlike the Big Bang (C = 0)?

Keep in mind that CCC is a dead theory. It became clear by 2010 that it was not viable because it made predictions about particle physics that were not consistent with what we know about particle physics.

The best reference on CCC that I know of, other than the popularization in Penrose's book, is:

R. Penrose, Singularities and time-asymmetry, in General Relativity: An Einstein Centenary Survey, edited by S. W. Hawking and W. Israel, (Cambridge University Press, Cambridge, 1979), p. 581

The way he formulates the hypothesis on p. 630 is:

the Weyl curvature $$C_{abcd}$$ vanishes at any initial$$\ddagger$$ singularity.

The footnote says:

That is, with the notation of section 12.3.2, at $$\partial \overset{\vee}M$$. Note that this includes the final singular TIF of a Hawking black hole explosion -- at which the Weyl curvature indeed vanishes!

So he's not proposing any new physical mechanism that would eliminate black hole singularities in classical GR. Instead, he just points out that it's already believed, if you believe in the methods and results of semiclassical gravity, that quantum effects modify or eliminate the singularities predicted by classical GR.

• CCC seems kind of lively to me: After the final (2020) version of his collaboration with Meissner, An, and Nurowski at arxiv.org/pdf/1808.01740.abs , Penrose was awarded a Nobel Prize in physics. The paper identifies spots of "significantly raised temperature" in the CMB with Hawking radiation from black holes of a previous aeon. May 10 at 16:12
• Quantum physics, on the other hand, still lacks any observationally- or experimentally-validated theory of gravity. May 10 at 16:20

format: plain


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Functions of random variable and their expected value

1. Apr 16, 2010

suppose we have random variable defined a function of another random variable such that $$Y = \mathbb{E}(X)$$
it seem then $$Y$$ is a constant. then $$\mathbb{E}(Y) = \mathbb{E}(X)$$ does this even make sense ?


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2019
Том 71
№ 5

# The Bojanov – Naidenov problem for functions with nonsymmetric restrictions on the highest derivative

Kofanov V. A.

Abstract

For given $r \in \bfN , p, \alpha , \beta , \mu > 0$, we solve the extreme problems $$\int^b_ax^q_{\pm} (t)dt \rightarrow \mathrm{s}\mathrm{u}\mathrm{p}, q \geq p,$$ in the set of pairs $(x, I)$ of functions $x \in L^r_{\infty}$ and intervals $I = [a, b] \subset R$ satisfying the inequalities $\beta \leq x(r)(t) \leq \alpha$ for almost all $t \in R$ , the conditions $L(x_{\pm})p \leq L\bigl(( \varphi^{\alpha ,\beta}_{\lambda ,r}) \bigr)_p$, and the corresponding condition $\mu\Bigl(\mathrm{s}\mathrm{u}\mathrm{p} \mathrm{p}_{[a,b]}x_{+}\Bigr) \leq \mu$ or $\mu \Bigl( \mathrm{s}\mathrm{u}\mathrm{p} \mathrm{p}_{[a,b]}x \Bigr) \leq \mu$, where $$L(x)p := \mathrm{s}\mathrm{u}\mathrm{p} \Bigl\{ \| x\| L_{p[a,b]} : a, b \in R , | x(t)| > 0, t \in (a, b)\Bigr\},$$ $\mathrm{s}\mathrm{u}\mathrm{p} \mathrm{p}_{[a,b]}x_{\pm} := \{ t \in [a, b] : x_{\pm} (t) > 0\} , \varphi^{\alpha ,\beta}_{\lambda ,r}$ is the nonsymmetric $(2\pi /\lambda)$-periodic Euler spline of order $r$. As a consequence, we solve the same problems for the intermediate derivatives $x(k)_{\pm} , k = 1,..., r_1,$ with $q \geq 1$.

Citation Example: Kofanov V. A. The Bojanov – Naidenov problem for functions with nonsymmetric restrictions on the highest derivative // Ukr. Mat. Zh. - 2019. - 71, № 3. - pp. 368-381.


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Integer type:  int32  int64  nag_int  show int32  show int32  show int64  show int64  show nag_int  show nag_int

Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_eigen_real_triang_svd (f02wu)

## Purpose

nag_eigen_real_triang_svd (f02wu) returns all, or part, of the singular value decomposition of a real upper triangular matrix.

## Syntax

[a, b, q, sv, work, ifail] = f02wu(a, b, wantq, wantp, 'n', n, 'ncolb', ncolb)
[a, b, q, sv, work, ifail] = nag_eigen_real_triang_svd(a, b, wantq, wantp, 'n', n, 'ncolb', ncolb)

## Description

The $n$ by $n$ upper triangular matrix $R$ is factorized as
 $R=QSPT,$
where $Q$ and $P$ are $n$ by $n$ orthogonal matrices and $S$ is an $n$ by $n$ diagonal matrix with non-negative diagonal elements, ${\sigma }_{1},{\sigma }_{2},\dots ,{\sigma }_{n}$, ordered such that
 $σ1≥σ2≥…≥σn≥0.$
The columns of $Q$ are the left-hand singular vectors of $R$, the diagonal elements of $S$ are the singular values of $R$ and the columns of $P$ are the right-hand singular vectors of $R$.
Either or both of $Q$ and ${P}^{\mathrm{T}}$ may be requested and the matrix $C$ given by
 $C=QTB,$
where $B$ is an $n$ by $\mathit{ncolb}$ given matrix, may also be requested.
The function obtains the singular value decomposition by first reducing $R$ to bidiagonal form by means of Givens plane rotations and then using the $QR$ algorithm to obtain the singular value decomposition of the bidiagonal form.
Good background descriptions to the singular value decomposition are given in Chan (1982), Dongarra et al. (1979), Golub and Van Loan (1996), Hammarling (1985) and Wilkinson (1978).
Note that if $K$ is any orthogonal diagonal matrix so that
 $KKT=I$
(that is the diagonal elements of $K$ are $+1$ or $-1$) then
 $A=QKSPKT$
is also a singular value decomposition of $A$.

## References

Chan T F (1982) An improved algorithm for computing the singular value decomposition ACM Trans. Math. Software 8 72–83
Dongarra J J, Moler C B, Bunch J R and Stewart G W (1979) LINPACK Users' Guide SIAM, Philadelphia
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
Hammarling S (1985) The singular value decomposition in multivariate statistics SIGNUM Newsl. 20(3) 2–25
Wilkinson J H (1978) Singular Value Decomposition – Basic Aspects Numerical Software – Needs and Availability (ed D A H Jacobs) Academic Press

## Parameters

### Compulsory Input Parameters

1:     $\mathrm{a}\left(\mathit{lda},:\right)$ – double array
The first dimension of the array a must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
The second dimension of the array a must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
The leading $n$ by $n$ upper triangular part of the array a must contain the upper triangular matrix $R$.
2:     $\mathrm{b}\left(\mathit{ldb},:\right)$ – double array
The first dimension, $\mathit{ldb}$, of the array b must satisfy
• if ${\mathbf{ncolb}}>0$, $\mathit{ldb}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$;
• otherwise $\mathit{ldb}\ge 1$.
The second dimension of the array b must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{ncolb}}\right)$.
With ${\mathbf{ncolb}}>0$, the leading $n$ by $\mathit{ncolb}$ part of the array b must contain the matrix to be transformed.
3:     $\mathrm{wantq}$ – logical scalar
Must be true if the matrix $Q$ is required.
If ${\mathbf{wantq}}=\mathit{false}$, the array q is not referenced.
4:     $\mathrm{wantp}$ – logical scalar
Must be true if the matrix ${P}^{\mathrm{T}}$ is required, in which case ${P}^{\mathrm{T}}$ is overwritten on the array a, otherwise wantp must be false.

### Optional Input Parameters

1:     $\mathrm{n}$int64int32nag_int scalar
Default: the first dimension of the array a and the second dimension of the array a.
$n$, the order of the matrix $R$.
If ${\mathbf{n}}=0$, an immediate return is effected.
Constraint: ${\mathbf{n}}\ge 0$.
2:     $\mathrm{ncolb}$int64int32nag_int scalar
Default: the second dimension of the array b.
$\mathit{ncolb}$, the number of columns of the matrix $B$.
If ${\mathbf{ncolb}}=0$, the array b is not referenced.
Constraint: ${\mathbf{ncolb}}\ge 0$.

### Output Parameters

1:     $\mathrm{a}\left(\mathit{lda},:\right)$ – double array
The first dimension of the array a will be $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
The second dimension of the array a will be $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
If ${\mathbf{wantp}}=\mathit{true}$, the $n$ by $n$ part of a will contain the $n$ by $n$ orthogonal matrix ${P}^{\mathrm{T}}$, otherwise the $n$ by $n$ upper triangular part of a is used as internal workspace, but the strictly lower triangular part of a is not referenced.
2:     $\mathrm{b}\left(\mathit{ldb},:\right)$ – double array
The first dimension, $\mathit{ldb}$, of the array b will be
• if ${\mathbf{ncolb}}>0$, $\mathit{ldb}=\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$;
• otherwise $\mathit{ldb}=1$.
The second dimension of the array b will be $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{ncolb}}\right)$.
The leading $n$ by $\mathit{ncolb}$ part of the array b stores the matrix ${Q}^{\mathrm{T}}B$.
3:     $\mathrm{q}\left(\mathit{ldq},:\right)$ – double array
The first dimension, $\mathit{ldq}$, of the array q will be
• if ${\mathbf{wantq}}=\mathit{true}$, $\mathit{ldq}=\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$;
• otherwise $\mathit{ldq}=1$.
The second dimension of the array q will be $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$ if ${\mathbf{wantq}}=\mathit{true}$ and $1$ otherwise.
With ${\mathbf{wantq}}=\mathit{true}$, the leading $n$ by $n$ part of the array q will contain the orthogonal matrix $Q$. Otherwise the array q is not referenced.
4:     $\mathrm{sv}\left({\mathbf{n}}\right)$ – double array
The array sv will contain the $n$ diagonal elements of the matrix $S$.
5:     $\mathrm{work}\left(:\right)$ – double array
The dimension of the array work will be $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,2×\left({\mathbf{n}}-1\right)\right)$ if ${\mathbf{ncolb}}=0$ and ${\mathbf{wantq}}=\mathit{false}$ and ${\mathbf{wantp}}=\mathit{false}$, $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,3×\left({\mathbf{n}}-1\right)\right)$ if (${\mathbf{ncolb}}=0$ and ${\mathbf{wantq}}=\mathit{false}$ and ${\mathbf{wantp}}=\mathit{true}$) or (${\mathbf{wantp}}=\mathit{false}$ and (${\mathbf{ncolb}}>0$ or ${\mathbf{wantq}}=\mathit{true}$)) and $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,5×\left({\mathbf{n}}-1\right)\right)$ otherwise
${\mathbf{work}}\left({\mathbf{n}}\right)$ contains the total number of iterations taken by the $QR$ algorithm.
The rest of the array is used as internal workspace.
6:     $\mathrm{ifail}$int64int32nag_int scalar
${\mathbf{ifail}}={\mathbf{0}}$ unless the function detects an error (see Error Indicators and Warnings).

## Error Indicators and Warnings

Errors or warnings detected by the function:

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

${\mathbf{ifail}}=-1$
 On entry, ${\mathbf{n}}<0$, or $\mathit{lda}<{\mathbf{n}}$, or ${\mathbf{ncolb}}<0$, or $\mathit{ldb}<{\mathbf{n}}$ and ${\mathbf{ncolb}}>0$, or $\mathit{ldq}<{\mathbf{n}}$ and ${\mathbf{wantq}}=\mathit{true}$.
W  ${\mathbf{ifail}}>0$
The $QR$ algorithm has failed to converge in $50×{\mathbf{n}}$ iterations. In this case ${\mathbf{sv}}\left(1\right),{\mathbf{sv}}\left(2\right),\dots ,{\mathbf{sv}}\left({\mathbf{ifail}}\right)$ may not have been found correctly and the remaining singular values may not be the smallest. The matrix $R$ will nevertheless have been factorized as $R=QE{P}^{\mathrm{T}}$, where $E$ is a bidiagonal matrix with ${\mathbf{sv}}\left(1\right),{\mathbf{sv}}\left(2\right),\dots ,{\mathbf{sv}}\left(n\right)$ as the diagonal elements and ${\mathbf{work}}\left(1\right),{\mathbf{work}}\left(2\right),\dots ,{\mathbf{work}}\left(n-1\right)$ as the superdiagonal elements.
This failure is not likely to occur.
${\mathbf{ifail}}=-99$
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.

## Accuracy

The computed factors $Q$, $S$ and $P$ satisfy the relation
 $QSPT=R+E,$
where
 $E≤cε A ,$
$\epsilon$ is the machine precision, $c$ is a modest function of $n$ and $‖.‖$ denotes the spectral (two) norm. Note that $‖A‖={\mathbf{sv}}\left(1\right)$.
A similar result holds for the computed matrix ${Q}^{\mathrm{T}}B$.
The computed matrix $Q$ satisfies the relation
 $Q=T+F,$
where $T$ is exactly orthogonal and
 $F≤dε,$
where $d$ is a modest function of $n$. A similar result holds for $P$.

For given values of ncolb, wantq and wantp, the number of floating-point operations required is approximately proportional to ${n}^{3}$.
>Following the use of nag_eigen_real_triang_svd (f02wu) the rank of $R$ may be estimated as follows:
```tol = eps;
irank = 1;
while (irank <= numel(sv) && sv(irank) >= tol*sv(1) )
irank = irank + 1;
end```
returns the value $k$ in irank, where $k$ is the smallest integer for which ${\mathbf{sv}}\left(k\right)<\mathit{tol}×{\mathbf{sv}}\left(1\right)$, where $\mathit{tol}$ is typically the machine precision, so that irank is an estimate of the rank of $S$ and thus also of $R$.

## Example

This example finds the singular value decomposition of the $3$ by $3$ upper triangular matrix
 $A= -4 -2 -3 0 -3 -2 0 0 -4 ,$
together with the vector ${Q}^{\mathrm{T}}b$ for the vector
 $b= -1 -1 -1 .$
```function f02wu_example

fprintf('f02wu example results\n\n');

% SVD of upper triangular A
a = [-4, -2, -3;
0, -3, -2;
0,  0, -4];

b = [-1; -1; -1];
wantq = true;
wantp = true;
[a, b, q, sv, work, ifail] = f02wu( ...
a, b, wantq, wantp);

fprintf('Singular value decomposition of A\n\n');

disp('Singular values');
disp(sv');
disp('Left-hand singular vectors, by column');
disp(q);
disp('Right-hand singular vectors, by column');
disp(a');
disp('Vector Q''*B');
disp(b');

```
```f02wu example results

Singular value decomposition of A

Singular values
6.5616    3.0000    2.4384

Left-hand singular vectors, by column
-0.7699    0.5883   -0.2471
-0.4324   -0.1961    0.8801
-0.4694   -0.7845   -0.4054

Right-hand singular vectors, by column
0.4694   -0.7845    0.4054
0.4324   -0.1961   -0.8801
0.7699    0.5883    0.2471

Vector Q'*B
1.6716    0.3922   -0.2276

```


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# Uncertainty of energy in a quantum harmonic oscillator

## Homework Statement

Find the uncertainty of the kinetic energy of a quantum harmonic oscillator in the ground state, using

$\left\langle p^2_x \right\rangle = \displaystyle\frac{\hbar^2}{2a^2}$ and
$\left\langle p^4_x \right\rangle = \displaystyle\frac{3\hbar^2}{4a^2}$

## Homework Equations

$\Delta E_{kin}=\sqrt{\left\langle E^2_{kin} \right\rangle - \left\langle E_{kin} \right\rangle^2}$

$\left\langle E_{kin} \right\rangle = \displaystyle\frac{\left\langle p^2_x \right\rangle}{2m}$

## The Attempt at a Solution

With $\left\langle E_{kin} \right\rangle^2$ I have no problem with but am I valid in saying

$\left\langle E^2_{kin} \right\rangle = \displaystyle\frac{\left\langle p^4_x \right\rangle}{4m^2}$?

$\left\langle E^2_{kin} \right\rangle = \displaystyle\frac{\left\langle p^4_x \right\rangle}{4m^2}$?


text:
# zbMATH — the first resource for mathematics

## Sharif, M. A. R.

Compute Distance To:
 Author ID: sharif.m-a-r Published as: Sharif, M.; Sharif, M. A. R.
 Documents Indexed: 199 Publications since 1988
all top 5

#### Co-Authors

 0 single-authored 3 Busnaina, Ahmed A. 1 Guo, Guannan 1 Hadji, Layachi 1 Haskew, J. T. 1 Wong, Y. K. E. 1 Zheng, Xiangcheng

#### Serials

 5 Applied Mathematical Modelling 1 Computers and Fluids 1 Journal of Computational Physics

#### Fields

 7 Fluid mechanics (76-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Numerical analysis (65-XX) 1 Geophysics (86-XX)

#### Citations contained in zbMATH

122 Publications have been cited 711 times in 317 Documents Cited by Year
Energy and momentum in spacetime homogeneous Gödel-type metrics. Zbl 1170.83372
Sharif, M.
2004
Gravitational perfect fluid collapse in $$f(R)$$ gravity. Zbl 1209.83034
Sharif, M.; Rizwana Kausar, H.
2011
Teleparallel energy-momentum distribution of Lewis-Papapetrou spacetimes. Zbl 1112.83313
Sharif, M.; Amir, M. Jamil
2007
Dynamics of Bianchi $$I$$ universe with magnetized anisotropic dark energy. Zbl 1203.83075
Sharif, M.; Zubair, M.
2010
Energy-momentum distribution: a crucial problem in general relativity. Zbl 1161.83340
Sharif, M.; Fatima, Tasnim
2005
Matter collineations of spacetime homogeneous Gödel-type metrics. Zbl 1029.83021
Camci, U.; Sharif, M.
2003
Gravitational perfect fluid collapse with cosmological constant. Zbl 1140.83390
2007
Teleparallel version of the stationary axisymmetric solutions and their energy contents. Zbl 1129.83319
Sharif, M.; Amir, M. Jamil
2007
Energy and momentum of a class of rotating gravitational waves. Zbl 1007.83011
Sharif, M.
2002
Effects of electromagnetic field on gravitational collapse. Zbl 1179.83062
Sharif, M.; Abbas, G.
2009
Teleparallel Killing vectors of the Einstein universe. Zbl 1148.83313
Sharif, M.; Amir, M. Jamil
2008
Energy – momentum distribution: Some examples. Zbl 1118.83330
Sharif, M.; Azam, M.
2007
Teleparallel versions of Friedmann and Lewis-Papapetrou spacetimes. Zbl 1129.83342
Sharif, M.; Amir, M. Jamil
2006
Structure scalars in charged plane symmetry. Zbl 1260.83049
Sharif, M.; Zaeem Ul Haq Bhatti, M.
2012
Non-vacuum solutions of Bianchi type $$VI _{0}$$ universe in $$f(R)$$ gravity. Zbl 1237.83035
Sharif, M.; Kausar, H. Rizwana
2011
Charged cylindrical collapse of anisotropic fluid. Zbl 1208.83082
Sharif, M.; Fatima, Sundas
2011
Plane symmetric gravitational collapse. Zbl 1159.83352
2008
Matter collineations in Kantowski-Sachs, Bianchi types I and III spacetimes. Zbl 1018.83013
Camci, U.; Sharif, M.
2003
Structure scalars for charged cylindrically symmetric relativistic fluids. Zbl 1253.83012
Sharif, M.; Zaeem Ul Haq Bhatti, M.
2012
Effects of electromagnetic field on the dynamics of Bianchi type $$VI_{0}$$ universe with anisotropic dark energy. Zbl 1204.83116
Sharif, M.; Zubair, M.
2010
Classification of static plane symmetric space-times according to their matter collineations. Zbl 1066.83010
Sharif, M.
2004
Energy and momentum associated with Gödel universe. Zbl 1046.83523
Sharif, M.
2003
Evolution of the universe in inverse and $$\ln f(R)$$ gravity. Zbl 1286.83115
Sharif, M.; Zubair, M.
2012
Dynamics of non-adiabatic charged cylindrical gravitational collapse. Zbl 1230.83069
Sharif, M.; Abbas, G.
2011
Dynamics of charged plane symmetric gravitational collapse. Zbl 1208.83083
Sharif, M.; Siddiqa, Aisha
2011
Symmetries of the energy-momentum tensor of spherically symmetric Lorentzian manifolds. Zbl 1062.83024
Sharif, M.
2003
Matter collineations of some static spherically symmetric spacetimes. Zbl 0991.83027
Sharif, M.
2001
Assessment of finite difference approximations for the advection terms in the simulation of practical flow problems. Zbl 0638.76081
Sharif, M. A. R.; Busnaina, Ahmed A.
1988
Evolution of expansion-free self-gravitating fluids and plane symmetry. Zbl 1263.83056
Sharif, M.; Yousaf, Z.
2012
Effects of electromagnetic field on the dynamical instability of expansionfree gravitational collapse. Zbl 1241.83057
Sharif, M.; Azam, M.
2012
Dynamics of viscous dissipative plane symmetric gravitational collapse. Zbl 1197.83081
Sharif, M.; Rehmat, Zakia
2010
Energy contents of some non-vacuum spacetimes in teleparallel gravity. Zbl 1186.83053
Sharif, M.; Taj, Sumaira
2010
Teleparallel energy-momentum distribution of static axially symmetric spacetimes. Zbl 1165.83311
Sharif, M.; Amir, M. Jamil
2008
High-speed cylindrical collapse of two perfect fluids. Zbl 1126.83008
2007
Phantom accretion by five-dimensional charged black hole. Zbl 1274.83091
Sharif, M.; Abbas, G.
2011
Gravitational charged perfect fluid collapse in friedmann universe models. Zbl 1195.83067
Sharif, M.; Abbas, G.
2010
Teleparallel energy-momentum distribution of spatially homogeneous rotating spacetimes. Zbl 1148.83312
Sharif, M.; Amir, M. Jamil
2008
Cold plasma dispersion relations in the vicinity of a Schwarzschild black hole horizon. Zbl 1181.83098
Sharif, M.; Sheikh, Umber
2007
Interacting modified holographic dark energy in Kaluza-Klein universe. Zbl 1238.83090
2012
Effects of $$f(R)$$ dark energy on dissipative anisotropic collapsing fluid. Zbl 1208.83130
Sharif, M.; Kausar, H. Rizwana
2010
Teleparallel Killing vectors of spherically symmetric spacetimes. Zbl 1181.83063
Sharif, M.; Majeed, Bushra
2009
Spherically symmetric gravitational collapse. Zbl 1168.83329
2009
Timelike and spacelike matter inheritance vectors in specific forms of energy–momentum tensor. Zbl 1099.83009
Sharif, M.; Sheikh, Umber
2006
Symmetries of the energy-momentum tensor of cylindrically symmetric static space-times. Zbl 1066.83011
Sharif, M.
2004
Stability analysis of Einstein universe in $$f(\mathcal G,T)$$ gravity. Zbl 1371.83161
Sharif, M.; Ikram, Ayesha
2017
Stability of the charged radiating cylinder. Zbl 1331.83015
Sharif, M.; Zaeem Ul Haq Bhatti, M.
2014
Cosmological reconstruction and stability in $$f(R,T)$$ gravity. Zbl 1298.83116
Sharif, M.; Zubair, M.
2014
Classification of spherically symmetric static spacetimes according to their matter collineations. Zbl 1034.83009
Sharif, M.; Aziz, Sehar
2003
Built-in inflation in $$f(G)$$ gravity. Zbl 1337.83079
Sharif, M.; Fatima, H. Ismat
2016
Dynamics of relativistic fluids with structure scalars and $$\epsilon R^2$$ cosmology. Zbl 1317.83112
Sharif, M.; Yousaf, Z.
2015
Wormholes supported by $$f(\mathcal{G})$$ gravity. Zbl 1308.83142
Sharif, M.; Ikram, Ayesha
2015
Thin-shell wormholes in Born-Infeld electrodynamics with modified Chaplygin gas. Zbl 1298.83027
Sharif, M.; Azam, M.
2014
Analysis of $$f(R)$$ theory corresponding to NADE and NHDE. Zbl 1328.83151
Sharif, M.; Zubair, M.
2013
Study of center of mass energy by particles collision in some black holes. Zbl 1276.83029
Sharif, M.; Haider, Nida
2013
Dynamics of a magnetized Bianchi $$VI_0$$ universe with anisotropic fluid. Zbl 1255.83170
Sharif, M.; Zubair, M.
2012
Expanding and collapsing scalar field thin shell. Zbl 1252.83028
Sharif, M.; Abbas, G.
2012
Effects of Schwarzschild black hole horizon on isothermal plasma wave dispersion. Zbl 1136.83027
Sharif, M.; Sheikh, Umber
2007
Symmetries of locally rotationally symmetric models. Zbl 1098.83007
Sharif, M.
2005
Homotheties of cylindrically symmetric static manifolds and their global extension. Zbl 0945.83008
2000
Evaluation of the performance of three turbulence closure models in the prediction of confined swirling flows. Zbl 0825.76303
Sharif, M. A. R.; Wong, Y. K. E.
1995
Noncommutative wormhole solutions in $$f(G)$$ gravity. Zbl 1331.83061
Sharif, M.; Ismat Fatima, H.
2015
Effects of some physical factors on the inhomogeneity in planar symmetry. Zbl 1295.85002
Sharif, M.; Ul Haq Bhatti, M. Zaeem
2014
Static cylindrically symmetric interior solutions in $$f(R)$$ gravity. Zbl 1260.83048
2012
Dark energy models and laws of thermodynamics in Bianchi I model. Zbl 1260.83124
Sharif, M.; Saleem, Rabia
2012
Complex wave numbers in the vicinity of the Schwarzschild event horizon. Zbl 1159.83341
Sharif, M.; Sheikh, Umber
2008
Kinematic self-similar plane symmetric solutions. Zbl 1255.83039
Sharif, M.; Aziz, Sehar
2007
Errata: Energy and momentum associated with Gödel universe. Zbl 1093.83511
Sharif, M.
2004
Thermodynamics in $$f(\mathcal{G}, T)$$ gravity. Zbl 1404.83098
Sharif, M.; Ikram, Ayesha
2018
Role of anisotropy in the expansion-free plane gravitational collapse. Zbl 1286.83071
Sharif, M.; Azam, M.
2014
Non-vacuum static cylindrically symmetric solution and energy distribution in $$f(R)$$ gravity. Zbl 1314.83043
2012
Cosmological evolution for dark energy models in $$f(T)$$ gravity. Zbl 1286.83114
Sharif, M.; Azeem, Sehrish
2012
Statefinder diagnostic for dark energy models in Bianchi I universe. Zbl 1277.83120
Sharif, M.; Saleem, Rabia
2012
Quantum corrections for ABGB black hole. Zbl 1238.83040
Sharif, M.; Javed, Wajiha
2012
Energy contents of gravitational waves in teleparallel gravity. Zbl 1184.83019
Sharif, M.; Taj, Sumaira
2010
High-speed collapse of a hollow sphere of type I matter. Zbl 1159.83348
2009
Isothermal plasma waves in a gravitomagnetic planar analog. Zbl 1148.83325
Sharif, M.; Sheikh, Umber
2007
Role of $$f(G, T)$$ gravity on the evolution of relativistic stars. Zbl 1427.83055
Bhatti, Muhammad Zaeem-ul-Haq; Sharif, M.; Yousaf, Z.; Ilyas, M.
2018
Viscosity effects on anisotropic universe in curvature-matter coupling gravity. Zbl 1402.83050
Sharif, M.; Siddiqa, Aisha
2018
Interaction of viscous modified Chaplygin gas with $$f(R,T)$$ gravity. Zbl 1372.83067
Sharif, M.; Siddiqa, Aisha
2017
Structure scalars and evolution equations in $$f(G)$$ cosmology. Zbl 1367.83077
Sharif, M.; Fatima, H. Ismat
2017
Generalized ghost pilgrim dark energy in $$F(T,T_G)$$ cosmology. Zbl 1346.83056
Sharif, M.; Nazir, Kanwal
2016
Charged adiabatic LTB gravitational collapse in $$f(R)$$ gravity. Zbl 1337.83081
Sharif, M.; Yousaf, Z.
2016
Null geodesics and strong field gravitational lensing in a string cloud background. Zbl 1366.83062
Sharif, M.; Iftikhar, Sehrish
2015
Phase space analysis and anisotropic universe model in $$f(T)$$ gravity. Zbl 1308.83185
Sharif, M.; Jabbar, Saima
2015
Electromagnetic effects on the inhomogeneity of planar symmetry. Zbl 1296.83017
Sharif, M.; Ul Haq Bhatti, M. Zaeem
2014
Plane symmetric gravitational collapse and linear equation of state. Zbl 1284.83117
Sharif, M.; Majid, Amal
2013
Thermodynamics in non-linear electrodynamics with anisotropic universe. Zbl 1284.83209
Sharif, M.; Saleem, Rabia
2013
Effects of electromagnetic field on energy density inhomogeneity in self-gravitating fluids. Zbl 1246.83057
Sharif, M.; Bashir, Neelum
2012
Energy contents of a class of regular black hole solutions in teleparallel gravity. Zbl 1208.83075
2010
Singularity in gravitational collapse of plane symmetric charged Vaidya spacetime. Zbl 1202.83093
Sharif, M.; Siddiqa, Aisha
2010
Higher dimensional perfect fluid collapse with cosmological constant. Zbl 1371.83174
2008
On the physical properties of spherically symmetric self-similar solutions. Zbl 1071.83535
Sharif, M.; Aziz, Sehar
2005
An investigation into the numerical dispersion problem of the skew upwind finite difference scheme. Zbl 0644.76103
Sharif, M. A. R.; Busnaina, A. A.
1988
Propagation of polar gravitational waves in $$f(R, T)$$ scenario. Zbl 1419.83055
Sharif, M.; Siddiqa, Aisha
2019
Study of homogeneous and isotropic universe in $$f(R, T^\varphi)$$ gravity. Zbl 1403.83063
Sharif, M.; Siddiqa, Aisha
2018
Energy conditions in higher derivative $$f(R,\; \square R,\; T)$$ gravity. Zbl 1395.83097
Yousaf, Z.; Sharif, M.; Ilyas, M.; Zaeem-ul-Haq Bhatti, M.
2018
Exact solutions and conserved quantities in $$f(R,T)$$ gravity. Zbl 1383.83130
Sharif, M.; Nawazish, Iqra
2017
Study of Bianchi type-I model in $$f(R,T^\psi)$$ gravity. Zbl 1372.83014
Sharif, M.; Siddiqa, Aisha
2017
Noether symmetries and anisotropic universe models in $$f(R,T)$$ gravity. Zbl 1371.83162
Sharif, M.; Nawazish, Iqra
2017
Noncommutative wormhole solutions in $$F(T,T_{\mathcal{G}})$$ gravity. Zbl 1365.83025
Sharif, M.; Nazir, Kanwal
2017
Propagation of polar gravitational waves in $$f(R, T)$$ scenario. Zbl 1419.83055
Sharif, M.; Siddiqa, Aisha
2019
Thermodynamics in $$f(\mathcal{G}, T)$$ gravity. Zbl 1404.83098
Sharif, M.; Ikram, Ayesha
2018
Role of $$f(G, T)$$ gravity on the evolution of relativistic stars. Zbl 1427.83055
Bhatti, Muhammad Zaeem-ul-Haq; Sharif, M.; Yousaf, Z.; Ilyas, M.
2018
Viscosity effects on anisotropic universe in curvature-matter coupling gravity. Zbl 1402.83050
Sharif, M.; Siddiqa, Aisha
2018
Study of homogeneous and isotropic universe in $$f(R, T^\varphi)$$ gravity. Zbl 1403.83063
Sharif, M.; Siddiqa, Aisha
2018
Energy conditions in higher derivative $$f(R,\; \square R,\; T)$$ gravity. Zbl 1395.83097
Yousaf, Z.; Sharif, M.; Ilyas, M.; Zaeem-ul-Haq Bhatti, M.
2018
Stability analysis of Einstein universe in $$f(\mathcal G,T)$$ gravity. Zbl 1371.83161
Sharif, M.; Ikram, Ayesha
2017
Interaction of viscous modified Chaplygin gas with $$f(R,T)$$ gravity. Zbl 1372.83067
Sharif, M.; Siddiqa, Aisha
2017
Structure scalars and evolution equations in $$f(G)$$ cosmology. Zbl 1367.83077
Sharif, M.; Fatima, H. Ismat
2017
Exact solutions and conserved quantities in $$f(R,T)$$ gravity. Zbl 1383.83130
Sharif, M.; Nawazish, Iqra
2017
Study of Bianchi type-I model in $$f(R,T^\psi)$$ gravity. Zbl 1372.83014
Sharif, M.; Siddiqa, Aisha
2017
Noether symmetries and anisotropic universe models in $$f(R,T)$$ gravity. Zbl 1371.83162
Sharif, M.; Nawazish, Iqra
2017
Noncommutative wormhole solutions in $$F(T,T_{\mathcal{G}})$$ gravity. Zbl 1365.83025
Sharif, M.; Nazir, Kanwal
2017
Built-in inflation in $$f(G)$$ gravity. Zbl 1337.83079
Sharif, M.; Fatima, H. Ismat
2016
Generalized ghost pilgrim dark energy in $$F(T,T_G)$$ cosmology. Zbl 1346.83056
Sharif, M.; Nazir, Kanwal
2016
Charged adiabatic LTB gravitational collapse in $$f(R)$$ gravity. Zbl 1337.83081
Sharif, M.; Yousaf, Z.
2016
On the stability of Bardeen thin-shell wormholes. Zbl 1370.83058
Sharif, M.; Javed, Faisal
2016
Isotropic cosmological models in $$F(T,T_G)$$ theory. Zbl 1347.83032
Sharif, M.; Nazir, Kanwal
2016
Thermodynamics of anisotropic emergent universe in nonlinear electrodynamics. Zbl 1344.83066
Sharif, M.; Sarwar, Ayesha
2016
Static spherically symmetric solutions in $$f(G)$$ gravity. Zbl 1344.83050
Sharif, M.; Fatima, H. Ismat
2016
Dynamics of relativistic fluids with structure scalars and $$\epsilon R^2$$ cosmology. Zbl 1317.83112
Sharif, M.; Yousaf, Z.
2015
Wormholes supported by $$f(\mathcal{G})$$ gravity. Zbl 1308.83142
Sharif, M.; Ikram, Ayesha
2015
Noncommutative wormhole solutions in $$f(G)$$ gravity. Zbl 1331.83061
Sharif, M.; Ismat Fatima, H.
2015
Null geodesics and strong field gravitational lensing in a string cloud background. Zbl 1366.83062
Sharif, M.; Iftikhar, Sehrish
2015
Phase space analysis and anisotropic universe model in $$f(T)$$ gravity. Zbl 1308.83185
Sharif, M.; Jabbar, Saima
2015
Null geodesics and strong field gravitational lensing of black hole with global monopole. Zbl 1366.83064
Sharif, M.; Iftikhar, Sehrish
2015
Structure scalars in dissipative axial system in $$f(R)$$ gravity. Zbl 1327.83238
Sharif, M.; Nasir, Zunaira
2015
Stability of the charged radiating cylinder. Zbl 1331.83015
Sharif, M.; Zaeem Ul Haq Bhatti, M.
2014
Cosmological reconstruction and stability in $$f(R,T)$$ gravity. Zbl 1298.83116
Sharif, M.; Zubair, M.
2014
Thin-shell wormholes in Born-Infeld electrodynamics with modified Chaplygin gas. Zbl 1298.83027
Sharif, M.; Azam, M.
2014
Effects of some physical factors on the inhomogeneity in planar symmetry. Zbl 1295.85002
Sharif, M.; Ul Haq Bhatti, M. Zaeem
2014
Role of anisotropy in the expansion-free plane gravitational collapse. Zbl 1286.83071
Sharif, M.; Azam, M.
2014
Electromagnetic effects on the inhomogeneity of planar symmetry. Zbl 1296.83017
Sharif, M.; Ul Haq Bhatti, M. Zaeem
2014
Effects of some physical factors on the stability of collapsing stars. Zbl 1310.83029
Sharif, M.; Bhatti, M. Zaeem Ul Haq
2014
Thermodynamics of new modified Chaplygin gas in magnetic FRW universe. Zbl 1305.82027
Sharif, M.; Saleem, Rabia
2014
Dynamics and stability of charged spherical star with tilted and non-tilted congruences. Zbl 1301.85004
Sharif, M.; Ul Haq Bhatti, M. Zaeem
2014
Analysis of $$f(R)$$ theory corresponding to NADE and NHDE. Zbl 1328.83151
Sharif, M.; Zubair, M.
2013
Study of center of mass energy by particles collision in some black holes. Zbl 1276.83029
Sharif, M.; Haider, Nida
2013
Plane symmetric gravitational collapse and linear equation of state. Zbl 1284.83117
Sharif, M.; Majid, Amal
2013
Thermodynamics in non-linear electrodynamics with anisotropic universe. Zbl 1284.83209
Sharif, M.; Saleem, Rabia
2013
Thermodynamics in modified gravity with curvature matter coupling. Zbl 1328.83152
Sharif, M.; Zubair, M.
2013
Thermodynamics in Kaluza-Klein universe. Zbl 1268.83005
Sharif, M.; Saleem, Rabia
2013
Fermions tunneling from Plebański-Demiański black holes. Zbl 1266.83128
Sharif, M.; Javed, Wajiha
2013
Structure scalars in charged plane symmetry. Zbl 1260.83049
Sharif, M.; Zaeem Ul Haq Bhatti, M.
2012
Structure scalars for charged cylindrically symmetric relativistic fluids. Zbl 1253.83012
Sharif, M.; Zaeem Ul Haq Bhatti, M.
2012
Evolution of the universe in inverse and $$\ln f(R)$$ gravity. Zbl 1286.83115
Sharif, M.; Zubair, M.
2012
Evolution of expansion-free self-gravitating fluids and plane symmetry. Zbl 1263.83056
Sharif, M.; Yousaf, Z.
2012
Effects of electromagnetic field on the dynamical instability of expansionfree gravitational collapse. Zbl 1241.83057
Sharif, M.; Azam, M.
2012
Interacting modified holographic dark energy in Kaluza-Klein universe. Zbl 1238.83090
2012
Dynamics of a magnetized Bianchi $$VI_0$$ universe with anisotropic fluid. Zbl 1255.83170
Sharif, M.; Zubair, M.
2012
Expanding and collapsing scalar field thin shell. Zbl 1252.83028
Sharif, M.; Abbas, G.
2012
Static cylindrically symmetric interior solutions in $$f(R)$$ gravity. Zbl 1260.83048
2012
Dark energy models and laws of thermodynamics in Bianchi I model. Zbl 1260.83124
Sharif, M.; Saleem, Rabia
2012
Non-vacuum static cylindrically symmetric solution and energy distribution in $$f(R)$$ gravity. Zbl 1314.83043
2012
Cosmological evolution for dark energy models in $$f(T)$$ gravity. Zbl 1286.83114
Sharif, M.; Azeem, Sehrish
2012
Statefinder diagnostic for dark energy models in Bianchi I universe. Zbl 1277.83120
Sharif, M.; Saleem, Rabia
2012
Quantum corrections for ABGB black hole. Zbl 1238.83040
Sharif, M.; Javed, Wajiha
2012
Effects of electromagnetic field on energy density inhomogeneity in self-gravitating fluids. Zbl 1246.83057
Sharif, M.; Bashir, Neelum
2012
Newtonian and post Newtonian expansionfree fluid evolution in $$f(R)$$ gravity. Zbl 1238.83055
Sharif, M.; Kausar, H. Rizwana
2012
Gravitational perfect fluid collapse in $$f(R)$$ gravity. Zbl 1209.83034
Sharif, M.; Rizwana Kausar, H.
2011
Non-vacuum solutions of Bianchi type $$VI _{0}$$ universe in $$f(R)$$ gravity. Zbl 1237.83035
Sharif, M.; Kausar, H. Rizwana
2011
Charged cylindrical collapse of anisotropic fluid. Zbl 1208.83082
Sharif, M.; Fatima, Sundas
2011
Dynamics of non-adiabatic charged cylindrical gravitational collapse. Zbl 1230.83069
Sharif, M.; Abbas, G.
2011
Dynamics of charged plane symmetric gravitational collapse. Zbl 1208.83083
Sharif, M.; Siddiqa, Aisha
2011
Phantom accretion by five-dimensional charged black hole. Zbl 1274.83091
Sharif, M.; Abbas, G.
2011
Expansionfree fluid evolution and Skripkin model in $$f(R)$$ theory. Zbl 1263.83145
Sharif, M.; Kausar, H. Rizwana
2011
Gravitational collapse: Expanding and collapsing regions. Zbl 1213.83018
Sharif, M.; Abbas, G.
2011
Plasma wave properties of the Schwarzschild magnetosphere in a Veselago medium. Zbl 1209.85021
Sharif, M.; Mukhtar, Noureen
2011
Dynamics of Bianchi $$I$$ universe with magnetized anisotropic dark energy. Zbl 1203.83075
Sharif, M.; Zubair, M.
2010
Effects of electromagnetic field on the dynamics of Bianchi type $$VI_{0}$$ universe with anisotropic dark energy. Zbl 1204.83116
Sharif, M.; Zubair, M.
2010
Dynamics of viscous dissipative plane symmetric gravitational collapse. Zbl 1197.83081
Sharif, M.; Rehmat, Zakia
2010
Energy contents of some non-vacuum spacetimes in teleparallel gravity. Zbl 1186.83053
Sharif, M.; Taj, Sumaira
2010
Gravitational charged perfect fluid collapse in friedmann universe models. Zbl 1195.83067
Sharif, M.; Abbas, G.
2010
Effects of $$f(R)$$ dark energy on dissipative anisotropic collapsing fluid. Zbl 1208.83130
Sharif, M.; Kausar, H. Rizwana
2010
Energy contents of gravitational waves in teleparallel gravity. Zbl 1184.83019
Sharif, M.; Taj, Sumaira
2010
Energy contents of a class of regular black hole solutions in teleparallel gravity. Zbl 1208.83075
2010
Singularity in gravitational collapse of plane symmetric charged Vaidya spacetime. Zbl 1202.83093
Sharif, M.; Siddiqa, Aisha
2010
Effects of electromagnetic field on gravitational collapse. Zbl 1179.83062
Sharif, M.; Abbas, G.
2009
Teleparallel Killing vectors of spherically symmetric spacetimes. Zbl 1181.83063
Sharif, M.; Majeed, Bushra
2009
Spherically symmetric gravitational collapse. Zbl 1168.83329
2009
High-speed collapse of a hollow sphere of type I matter. Zbl 1159.83348
2009
Teleparallel Killing vectors of the Einstein universe. Zbl 1148.83313
Sharif, M.; Amir, M. Jamil
2008
Plane symmetric gravitational collapse. Zbl 1159.83352
2008
Teleparallel energy-momentum distribution of static axially symmetric spacetimes. Zbl 1165.83311
Sharif, M.; Amir, M. Jamil
2008
Teleparallel energy-momentum distribution of spatially homogeneous rotating spacetimes. Zbl 1148.83312
Sharif, M.; Amir, M. Jamil
2008
Complex wave numbers in the vicinity of the Schwarzschild event horizon. Zbl 1159.83341
Sharif, M.; Sheikh, Umber
2008
Higher dimensional perfect fluid collapse with cosmological constant. Zbl 1371.83174
2008
Teleparallel energy-momentum distribution of Lewis-Papapetrou spacetimes. Zbl 1112.83313
Sharif, M.; Amir, M. Jamil
2007
Gravitational perfect fluid collapse with cosmological constant. Zbl 1140.83390
2007
Teleparallel version of the stationary axisymmetric solutions and their energy contents. Zbl 1129.83319
Sharif, M.; Amir, M. Jamil
2007
Energy – momentum distribution: Some examples. Zbl 1118.83330
Sharif, M.; Azam, M.
2007
High-speed cylindrical collapse of two perfect fluids. Zbl 1126.83008
2007
Cold plasma dispersion relations in the vicinity of a Schwarzschild black hole horizon. Zbl 1181.83098
Sharif, M.; Sheikh, Umber
2007
Effects of Schwarzschild black hole horizon on isothermal plasma wave dispersion. Zbl 1136.83027
Sharif, M.; Sheikh, Umber
2007
Kinematic self-similar plane symmetric solutions. Zbl 1255.83039
Sharif, M.; Aziz, Sehar
2007
Isothermal plasma waves in a gravitomagnetic planar analog. Zbl 1148.83325
Sharif, M.; Sheikh, Umber
2007
Matter collineations of static spacetimes with maximal symmetric transverse spaces. Zbl 1371.83044
Sharif, M.
2007
Computational analysis of supersonic turbulent boundary layers over rough surfaces using the $$k$$-$$\omega$$ and the stress-$$\omega$$ models. Zbl 1225.76180
Sharif, M. A. R.; Guo, G.
2007
Teleparallel versions of Friedmann and Lewis-Papapetrou spacetimes. Zbl 1129.83342
Sharif, M.; Amir, M. Jamil
2006
Timelike and spacelike matter inheritance vectors in specific forms of energy–momentum tensor. Zbl 1099.83009
Sharif, M.; Sheikh, Umber
2006
...and 22 more Documents
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#### Cited by 334 Authors

 68 Sharif, Muhammad 32 Sharif, M. A. R. 14 Radinschi, Irina 13 Shamir, M. Farasat 12 Amir, M. Jamil 9 Abbas, Ghulam 9 Khan, Suhail 9 Rahaman, Farook 9 Shabbir, Ghulam 9 Sharif, Masoud 8 Grammenos, Theophanes 8 Saleem, Rabia 8 Zaeem Ul Haq Bhatti, M. 7 Ahmad, Zahid 6 Jawad, Abdul 6 Rani, Shamaila 6 Sharif, Mhd Saeed 6 Siddiqa, Aisha 5 Bishi, Binaya Kumar 5 Calvaruso, Giovanni 5 Jamil, Mubasher 5 Mumtaz, Saadia 5 Spanou, Andromahi 4 Baysal, Hüsnü 4 Hussain, Tahir 4 Qadir, Asghar 4 Rizwana Kausar, H. 4 Salti, Mustafa 4 Tsamparlis, Michael 4 Yousaf, Z. 4 Zaeim, Amirhesam 3 Aygün, Sezgin 3 Aziz, Sehar 3 Belinchón, José Antonio 3 Camci, Uḡur 3 Chakraborty, Subenoy 3 Chattopadhyay, Surajit 3 Debnath, Ujjal 3 Gad, Ragab M. 3 Hasan, M. Khayrul 3 Hussain, Fiaz 3 Ikram, Ayesha 3 Islam, Sayeedul 3 Mishra, Bivudutta 3 Myrzakulov, Ratbay 3 Ovgun, Ali 3 Pasqua, Antonio 3 Ramzan, Muhammad Babar 3 Sahoo, Pradyumn Kumar 3 Saifullah, Khalid 3 Sheikh, Umber 3 Singh, Gyan Prakash 3 Tarhan, İsmail 3 Tripathy, Sunil Kumar 3 Waheed, Saira 3 Xulu, S. S. 3 Zubair, Mohammad 3 Zubair, Mohammed 2 Abbas, Ghazanfar 2 Abbas, Gohar 2 Ahmad, Mushtaq 2 Akhtar, Sumaira Saleem 2 Ali Khan, Gulzar 2 Ali, Md. Hossain 2 Amani, Ali Reza 2 Arif, Sadia 2 Aydogdu, Oktay 2 Azam, Mofazzal 2 Azam, Muhammad 2 Banerjee, Ayan 2 Banerjee, Narayan 2 Bokhari, Ashfaque H. 2 Bokhari, Ashfaque Hussain 2 Busnaina, Ahmed A. 2 Chakraborty, Sanjukta 2 Ditta, Allah 2 Farahani, Hamed Shirinabadi 2 Feroze, Tooba 2 Govender, Megan 2 Guha, Sarbari 2 Iftikhar, Sehrish 2 Jamil, Bismah 2 Javed, Wajiha 2 Khan, Fawad 2 Korunur, Murat 2 Kumar, Rajesh S. 2 Lin, Chi-Long 2 Momeni, Davood 2 Mukhtar, Noureen 2 Nashed, Gamal G. L. 2 Nazir, Kanwal 2 Pacif, Shibesh Kumar Jas 2 Paliathanasis, Andronikos 2 Pinheiro, G. R. 2 Pradhan, Anirudh 2 Radwan, Samir F. 2 Ravanpak, Arvin 2 Samanta, Gauranga C. 2 Sattar, Sadia 2 Srivastava, Sudhir Kumar ...and 234 more Authors
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#### Cited in 41 Serials

 55 General Relativity and Gravitation 53 International Journal of Theoretical Physics 38 Advances in High Energy Physics 33 Modern Physics Letters A 30 Astrophysics and Space Science 22 International Journal of Modern Physics D 20 International Journal of Geometric Methods in Modern Physics 9 International Journal of Modern Physics A 6 Journal of Mathematical Physics 5 Gravitation & Cosmology 4 Applied Mathematical Modelling 3 Classical and Quantum Gravity 3 Theoretical and Mathematical Physics 3 Journal of High Energy Physics 3 Advances in Mathematical Physics 3 Arabian Journal of Mathematics 2 International Journal for Numerical Methods in Fluids 2 Communications in Theoretical Physics 1 Computers and Fluids 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Mathematical Analysis and Applications 1 Physics of Fluids, A 1 Journal of Geometry and Physics 1 Collectanea Mathematica 1 Journal of Computational and Applied Mathematics 1 Journal of the Korean Mathematical Society 1 Computational Mechanics 1 SIAM Journal on Applied Mathematics 1 Physics of Fluids 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Engineering Analysis with Boundary Elements 1 Revista Matemática Complutense 1 Flow, Turbulence and Combustion 1 Journal of Nonlinear Mathematical Physics 1 Iranian Journal of Science and Technology. Transaction A: Science 1 International Journal of Computational Methods 1 Foundations of Physics Letters 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Applications and Applied Mathematics 1 Symmetry 1 ISRN High Energy Physics
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#### Cited in 18 Fields

 293 Relativity and gravitational theory (83-XX) 47 Astronomy and astrophysics (85-XX) 37 Differential geometry (53-XX) 36 Fluid mechanics (76-XX) 22 Classical thermodynamics, heat transfer (80-XX) 11 Quantum theory (81-XX) 10 Optics, electromagnetic theory (78-XX) 5 Partial differential equations (35-XX) 5 Numerical analysis (65-XX) 3 Mechanics of particles and systems (70-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Nonassociative rings and algebras (17-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Information and communication theory, circuits (94-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 General topology (54-XX) 1 Statistics (62-XX)


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OpenStudy (anonymous):

Given the following chemical equation, if 162.0 grams of potassium reacts with excess oxygen gas and was found to produce 172 grams of potassium oxide, what is the percent yield for this reaction? 4 K(s) + O2(g) arrow 2K2O(s)

3 years ago
OpenStudy (emmigrace222):

hmm

3 years ago
OpenStudy (emmigrace222):

i honestly dont know this one

3 years ago
OpenStudy (abmon98):

$Number of Moles=Mass(g)/Molar Mass(g/mol)$Atomic Weight of K(potassium)=39 (g/mol) Given Mass of K(potassium):162 gram $N of K(potassium)=162/39=4.15$ $4 K(s) + O2(g) \rightarrow 2K2O(s)$ Look for the mole ratio of K to K2O from the balanced chemical equation. 4:2 is the mole ratio $4:2$ $4.15:x mole of K2O$ $x=(4.15*2)/4=2.076$ Use again Number of Moles=Mass(g)/Molar Mas(g/mol) but rearrange the equation to $Mass(g)=Molar Mass(g/mol)*Number of Moles$ Atomic Weight of O and K O:16 gram K:39 gram $Molar Mass of K2O: (39*2)+(16*1)=94 gram$ $N of K2O=2.076*94=195.44 g$ (Actual Yield/Theortical Yield)*100=Percentage Yield (162/195.4)*100=82.9%

3 years ago


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Updated On: 27-06-2022

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Text Solution

Solution : Suppose, the point P divide Q R in the ratio lambda: 1, then the co-ordinate of P are
 (frac{5 lambda+2}{lambda+1}, frac{lambda+2}{lambda+1}, frac{-2 lambda+1}{lambda+1}) But x - coordinate of P is 4 . Therefore,
 frac{5 lambda+2}{lambda+1}=4 Rightarrow lambda=2
 Hence, the z-coordinate of P is frac{-2 lambda+1}{lambda+1}=-1 kpo


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Symbol
Problem
$Assessment$ $Post$ Assessment $2irection$ Choose the letter of the best answer. Write the chosen letter $ona$ separate sheet of paper. 1. Which of the following is NOT a system of linear equations in two variables? - A. $\left(x-y+5$ $c$ $\begin{cases} 4x-8y=12 \\ 2x-\dfrac {1} {3}y=-12 \end{cases}$ $\left(-3x^{2}=0$ $B$ $\begin{cases} 3x-y=5 \\ x-11y=-1 \end{cases}$ D. $\begin{cases} -4y=5 \\ \dfrac {3^{x}} {5}x-4y=7 \end{cases}$ 2. What system of linear equations in two variables is equivalent $t0 \begin{cases} y=\dfrac {1} {2}x-4 \\ y=4x-5 \end{cases} 7$ $A \begin{cases} = \\ 2y \\ x_{4}\bar{x} -y=5 \end{cases} ^{8}$ $C$ $\begin{cases} x-y=8 \\ 4x-2y=5 \end{cases}$ - B. $\begin{cases} 4x-y=-2 \\ x+2y=-5 \end{cases}$ D. $\begin{cases} x+2y=-8 \\ x-4y=-5 \end{cases}$ $14$


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# How do you use a power series to approximate  int_0^1xtan^-1xdx ?

##### 2 Answers
Nov 2, 2016

${\int}_{0}^{1} x {\tan}^{-} 1 x \mathrm{dx} \approx 0.2854$ (4dp)

#### Explanation:

Let $I = {\int}_{0}^{1} x {\tan}^{-} 1 x \mathrm{dx}$

The power series for ${\tan}^{-} 1 x$ is as follows:

${\tan}^{-} 1 x = x - {x}^{3} / 3 + {x}^{5} / 5 - {x}^{7} / 7 + {x}^{9} / 9 - {x}^{11} / 11 + {x}^{13} / 13 - \ldots$

And so we get the integrand by multiplying by $x$ to give:

$x {\tan}^{-} 1 x = {x}^{2} - {x}^{4} / 3 + {x}^{6} / 5 - {x}^{8} / 7 + {x}^{10} / 9 - {x}^{12} / 11 + {x}^{14} / 13 - \ldots$

And so replacing the integrand with the power series we have:

$I \approx {\int}_{0}^{1} {x}^{2} - {x}^{4} / 3 + {x}^{6} / 5 - {x}^{8} / 7 + {x}^{10} / 9 - \ldots \mathrm{dx}$

Integrating each term gives us:
$I = {\left[{x}^{3} / 3 - {x}^{5} / \left(3.5\right) + {x}^{7} / \left(5.7\right) - {x}^{9} / \left(7.9\right) + {x}^{11} / \left(9.11\right) - {x}^{13} / \left(11.13\right) \ldots\right]}_{0}^{1}$

Applying the limits gives us:
$I = \frac{1}{1.3} - \frac{1}{3.5} + \frac{1}{5.7} - \frac{1}{7.9} + \frac{1}{9.11} - \frac{1}{11.13} + \ldots$

We will need to take sufficient terms to get an answer that is stable to 4dp, which I will perform in Excel as follows;

Due to the oscillating natures of the power series it takes a significant number of terms to get a stable answer, but we can conclude that
$I \approx 0.2854$ (4dp)

Nov 2, 2016

${\int}_{0}^{1} x {\left(\tan\right)}^{-} 1 x \mathrm{dx} = \frac{\pi}{4} - \frac{1}{2.}$

#### Explanation:

${\int}_{0}^{1} x {\left(\tan\right)}^{-} 1 x \mathrm{dx}$
let${\left(\tan\right)}^{-} 1 x = \theta$
or $\tan \theta = x$ hence$\mathrm{dx} = {\sec}^{2} \theta d \theta$
then the integral reduces to int_0^(pi/4) theta tantheta sec^2 theta d theta
now we use the integration by parts
so the integral=$\theta {\int}_{0}^{\frac{\pi}{4}} \tan \theta {\sec}^{2} \theta d \theta - {\int}_{0}^{\frac{\pi}{4}} \left(1 \int \tan \theta {\sec}^{2} \theta d \theta\right) d \theta$
=${\int}_{0}^{\frac{\pi}{4}} \tan \theta d \left(\tan \theta\right)$ -${\int}_{0}^{\frac{\pi}{4}} \left(\left(\int \tan \theta d \left(\tan \theta\right)\right)\right) d \theta$
now the indefinite integral $\int \tan \theta d \left(\tan \theta\right)$=$\frac{1}{2} {\tan}^{2} \theta$
so for the limit we get the value of first integral=$\frac{\pi}{8}$

similarly the indefinite integral $\int {\tan}^{2} \theta d \theta$=$\int \left({\sec}^{2} \theta - 1\right) d \theta$=$\tan \theta - \theta$
so for the req. limit we ge$t = \frac{1}{2} - \frac{\pi}{8}$
so the ans. is =$\frac{\pi}{8} - \left(\frac{1}{2} - \frac{\pi}{8}\right)$
=$\frac{\pi}{4} - \frac{1}{2}$


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#### Volume 1, issue 1 (2001)

 Recent Issues
Author Index
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 To Appear Other MSP Journals
A universal bound for surfaces in 3-manifolds with a given Heegaard genus

### Mario Eudave-Muñoz and Jeremy Shor

Algebraic & Geometric Topology 1 (2001) 31–37
 arXiv: math.GT/0008158
##### Abstract

It is shown that for given positive integers $g$ and $b$, there is a number $\mathsc{C}\left(g,b\right)$, such that any orientable compact irreducible 3-manifold of Heegaard genus $g$ has at most $\mathsc{C}\left(g,b\right)$ disjoint, nonparallel incompressible surfaces with first Betti number ${b}_{1}.

##### Keywords
incompressible surface, Haken manifold.
Primary: 57N10
Secondary: 57M25


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# Scree test

The scree test , also known as the elbow criterion, is a graphical method for determining the optimal number of factors in factor analysis . The criterion was developed in the 1960s by the American psychologist Raymond Bernard Cattell and is still used today due to its simplicity.

## Background to factor selection

In the factor analysis, only those factors should be extracted that explain a significant part of the variance and therefore have a high eigenvalue . This is the case with the first factor, as a rule also with a few other factors, although the eigenvalues usually decrease sharply. From a certain factor the additional variance, which is explained by each additional factor, remains at a low level.

The selection of the factors is primarily used to obtain meaningful, easily interpretable results and can therefore only be objectified to a limited extent.

## Basic assumption

The basic assumption is that only those factors are significant that represent a stronger correlation than the correlation of random numbers. The scree test now makes use of the fact that - in contrast to the eigenvalues of correlated data - the eigenvalues of random numbers are typically approximately constant.

## method

To use the scree test , the descending sorted eigenvalues of the possible factors are considered in a so-called eigenvalue diagram or also a scree plot .

After the eigenvalues of the correlated data initially drop steeply, a kink ("elbow") is typically evident. The values to the right of it stagnate almost at a low level; they are considered insignificant because they are roughly at (or even below) the level of random correlations.

The eigenvalues to the left of the kink, on the other hand, are considered significant and must be extracted in the factor analysis. If there are several kinks, the stronger or further to the right kink must be taken into account. If there is no kink, the elbow criterion does not help.

## Criticism and further developments

### Criticism of objectivity

Scree test with parallel analysis according to Horn
Screeplot with different selection criteria (Horn, Kaiser-Guttmann, x%)

The scree test, first published in Cattell (1966), is often criticized for its poor objectivity. If no clear kink can be identified, there is room for interpretation.

#### Parallel analysis

The modification presented by JL Horn (1965) - often referred to as parallel analysis - superimposes a second eigenvalue diagram over the eigenvalue diagram of the correlated data. Only those eigenvalues examined that are higher than the random eigenvalues are considered significant. Despite the strong similarity, the two variants often produce different results. Although Horn's modification is objectively applicable, it has never been able to displace Cattell's scree test.

The second eigenvalues are calculated assuming that

1. the variables are uncorrelated, d. H. the correlation or covariance matrix is a diagonal matrix and
2. the data are multivariate normally distributed.

On this basis, B random data sets with the same number of variables and observations as the data set under consideration are generated and the eigenvalues of the associated empirical correlation or covariance matrix are calculated. The B largest eigenvalues approximate the distribution of the largest eigenvalue, the B second largest eigenvalues approximate the distribution of the second largest eigenvalue, ... Then z. B. the 95% quantile of the B largest eigenvalues is taken as the limit for the largest eigenvalue. If the greatest eigenvalue of the data is greater than , this eigenvalue is significant. The second figure on the right shows the Horn criterion for the Boston Housing data set with the falling gray line. ${\ displaystyle g_ {1}}$${\ displaystyle g_ {1}}$

#### Standard Error Scree

In addition to further developments and improvements made in the following decades, Zoski and Jurs (1996) present a standard error screen .

### Criticism of the basic assumption

The basic assumption that eigenvalues are meaningless below random eigenvalues has also been questioned by some scientists. Equating them with random or error results simply because of their size is inadmissible.

### Alternatives

As an alternative, the more rigid Kaiser-Guttman criterion comes into question, but this sometimes leads to solutions that are difficult to interpret.

In principle, several criteria should be used. In case of doubt, in particular, it is advisable to calculate several factor numbers and check them with regard to charges and interpretability.

## literature

Primary literature

• Cattell, RB (1966). The scree test for the number of factors. Multivariate Behavioral Research 1 , 245-276, doi : 10.1207 / s15327906mbr0102_10 .
• Horn, JL (1965). A rational and test for the number of factors in factor analysis. Psychometrika, 30 , 179-185, doi : 10.1007 / BF02289447 .
• Zoski, Keith W., Jurs Steven G. (1996): An objective counterpart to the visual scree test for factor analysis: The standard error scree. Educational and Psychological Measurement, 56 , 443-451, doi : 10.1177 / 0013164496056003006 .

Secondary literature


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# Denote standard inner product

if A $$\in$$ C nxn,show that (x,Ay)=0 for all x,y $$\in$$ C[n],
then A=0

(x,Ay) denote standard inner product on C[n]

chiro
if A $$\in$$ C nxn,show that (x,Ay)=0 for all x,y $$\in$$ C[n],
then A=0

(x,Ay) denote standard inner product on C[n]

Have you tried using properties of norms, and axioms of the inner product (There is an axiom that deals with zero results)?

HallsofIvy
In particular, (e_i, Ae_i)= 0 for every member, $e_i$, of an orthonormal basis.


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# YOU solve America's Drug Problem !

1. Jan 11, 2006

### Blahness

YOU solve America's "Drug Problem"!

For the past few decades, many attempts at stopping drug trades have been attempted, most failing.

So, if you had full control of the government*, what would you do to stop the drug problems, assuming you'd even want to?

*(Within reasonable bounds, aka no enslaving the druggies, mass-murdering the druggies, etc.)

I'll tell you my own ideas later.

2. Jan 11, 2006

### Azael

Easy. Legalise and tax it. Let people enjoy the freedom they should have. Trying to stop people from doing drugs is like trying to stop the expansion of the universe. Aint gonna happen.

The goverment might as well make some money out of the drug users, instead of wasting tremendous ammounts of money on harassing people that do nothing more wrong than those that drink alcohole or smoke cigarettes.

3. Jan 11, 2006

### Plastic Photon

The problem with the drugs (excluding those already legal) are that they are illegal. No surprise that I wake up everyother morning to read somewhere in the chronicle about Mexican officers found dead in a river, oil drum, abandon warehouse, etc along the US/Mexican border. Or US officers, civlians, etc...

Simple as this: making the drugs illegal and sending guys with guns to hunt down those with the illegal drugs is going to cause a problem.

4. Jan 11, 2006

### rachmaninoff

People do not have a freedom or right to enjoy illicit drugs, as long as tax money goes to support their health care. Taxing those same drugs won't come close to paying for this.

Why do you think cigarettes are a fundamental right? How does the right of a smoker to enjoy a small 'high' on nicotine outweight the economic damages caused by thousands of middle-aged people dying of emphyshema? Social rights like health care are a doubled-edged sword. If the government is obligated to pay for health care, then it logically has the right to enforce laws to protect public health. Hence laws on dangerous drugs, minimum age laws for cigarettes and alcohol, helmet laws, infectious disease quarantine laws, etc.

The current annual budget of the DEA is around $2 billion (wikipedia). This paper in the Am. J. of Health estimates the 1984 annual health cost of smoking to be$53.7 billion. Drug enforcement is cheap and at least somewhat effective. Health care costs are cripplingly expensive.

Slightly off topic, the epidemic of preventible type-2 diabetes was the front-page headline of the New York Times on Monday: http://www.nytimes.com/2006/01/09/n...eases, Conditions, and Health Topics/Diabetes

Last edited by a moderator: Jan 11, 2006
5. Jan 11, 2006

### Azael

well legalising softer drugs like mdma or cannabis wouldnt make much of a impact on health care. No where near the strain alcohole and tobacco puts on it.

But I agree people need to take responsibility for there actions. If you get lung cancer and its proven its from cigarettes "tough luck, next patient plz". Im not that fond of paying for other peoples stupidity, nor do I want people to pay for my possible stupidities.

If this takes the thread to much offtopic just ignore to reply. But where do you draw the line. Fatty foods probably cost the state more then anything nowdays.

6. Jan 11, 2006

### TheStatutoryApe

MDMA is a soft drug in your opinion?! I know that street X isn't MDMA but they illegalized MDMA for a reason didn't they?

I agree on cannabis though. I don't really see the point in it being illegal.

7. Jan 11, 2006

### Azael

I cant claim to be a expert or anything but I have yet to se any real evidence(not that I have looked that hard) that pure MDMA is very dangerous. Most of the first studies done on it seemed to be biased to make it look bad with tremendous od's ect. I might very well be wrong. But I wouldnt consider it half as bad as meth. Atleast MDMA doesnt make people paranoid or dangerous so I wouldnt consider MDMA users a danger to society like a PCP user or amphetamine addict. Seems to be a hard drug to get addicted to aswell since apperently it wont work if you take it several days in a row. So if people want to use it instead of alcohole when clubbing I dont se a reason why not. Alcohol is probably the number one cause for violent crimes.

Usualy I have a very hard time figuring out the reason why some things become illegal most idiotic was the schedualing of steroids in the 80's(or was it in the 90's).

But this is getting the thread severly of topic. So lets get back to the original posters question(I mod at a fairly large board so I know how anoying this can be:yuck: ).

8. Jan 11, 2006

### TheStatutoryApe

I'm looking around since I'm not really sure myself. I have a friend who told me all about MDMA once because he had researched it before doing it himself. I don't remember much of what he told me but I was pretty sure that there are severe side effects that come with abuse.
So far Wiki says that the long term effects seem rather inconclusive but emedicine seems to think otherwise.
http://www.emedicine.com/emerg/topic927.htm
http://en.wikipedia.org/wiki/MDMA#Long-term_effects

And really we're supposed to derail the threads in GD. It's been mandated by Evo.

9. Jan 11, 2006

### Pengwuino

Catch 22.

Only way to stop it is to pretty much go nuts. The idea that you need to legalize drugs is silly. Why not legalize murder? You can't stop people from doing it so might as well make it legal. Stealing? Legalize it. Public sex? Legalize it. Driving drunk? Legalize it. It's your right to drive drunk and have sex in public too!

What kind of logic is that? This topic has been done to death before with very little supportive arguments for legalization of even the softest drugs.

10. Jan 11, 2006

### Azael

what is the logic behind having soft drugs illegal? who does a pot smoker or clubber hurt? A equaly convincing case can probably be made to ban fast food, or mountain climbing, or any dangerous sport. Who does a pot smoker hurt so bad that he must be put in jail?

Last edited: Jan 11, 2006
11. Jan 11, 2006

### Pengwuino

And no it wasn't done by someone who had just downed 5 big macs. The idea that marijuana doesn't do anything is a complete myth that is just constantly perpetuated and people believe the myth without question.

Oh and by the way, the guy had run from the cops, and had a stolen pistol on him... but im sure the marijuana wasn't the reason that he plowed into that tree.... Even though of course, there was no alcohol on him or in the van...

12. Jan 11, 2006

### Azael

Im not one to fall for myths that easily. Look at holland they havent had a problem since legalising cannabis. The heavier drug use has accutaly been lowered.

Driving if high should offcourse be as illegal as driving while drunk. But just because people drive when high doesnt mean it should be illegal to be high. Or do you suggest alcohole should be illegal because some people cant handle it?

13. Jan 11, 2006

### mattmns

Eating fast food impairs your judgment? Fast food gives you audio and visual hallucinations? Man where have you been eating at?

I am fine with people smoking weed at their house, it is when they drive high that I have a problem.

14. Jan 11, 2006

### Pengwuino

Hell I'd be the first to sign a ban for alcohol. Ever talk to some idiots when they're drunk? What pisses me off the most is that they think its not fair when you yell at them for something they can't remember doing because they were piss drunk. Idiots. I hate people. I want people banned.

oops starting to go off there....

Well do a search and im sure I made the same case back in this other big ol drug thread... probably PW&A thread... this'll just be a repeat of that thread.

15. Jan 11, 2006

### mattmns

It will be impossible to make alcohol illegal in the US, but I bet if alcohol was illegal drinking and driving would be way down.

16. Jan 11, 2006

### Azael

But isnt it kind of ****ty to ban something for everyone since you personaly dont like it? I hate alcohole and what it does to people, but I consider them mature enough to decide for themself if they should drink or not.

Il do that, sounds like interesting reading. Is the thread name "PW&A"?

Well eating fast food makes you fat, clutters up the healtcare, parents that buy fast food teach kids poor habits and they get fat, bullied ect ect ect. Im obviously exagerating in the same manner as soft drug opponents. You could probably make a case to make drinking water illegal because some idiots have drunk themself to death.
Basicly there is always people that cant handle stuff. But I dont se the point in restricting something just because a small minority cant handle it. Il rather live in a free society than in a society where my freedom is totaly restricted so I cant "hurt myself".

I agree though people that drive when stoned, drunk or under the influence of anything else should be jailed.

17. Jan 11, 2006

### Pengwuino

People do it all the time, it's been done to death. Just take some time to sit down and think to yourself "What can't I do simply because someone else in another state or in another time period doesn't want me to do it". The list goes on and on. That is how societies work, some things must indeed be restricted. I personally want an M-240 machine gun but hey, I can't have it and although its hard to accept, I must realize that unless we want to live in chaos, some things must be sacrificed.

Damn i want that machine gun.....

I meant its probably in the politics and world affairs sub-forum (oops, that & should be betwen W and P). It's pretty much the same arguments here and same responses and probalby will mirror the future of this thread.

18. Jan 11, 2006

### Azael

the nature of all these debates. Same **** repeated a million times and no one ever changes oppinion but yet we all keep on cause its fun :)

19. Jan 11, 2006

### Ivan Seeking

Staff Emeritus
The reasons for drug and alcohol abuse are social, psychological, and even physiological. IMO this is not a problem that laws can solve, so in principle I oppose all drug laws; obviously with some exceptions in the case of minors, and due to other practical considerations.

Drug use predates our very existence as humans. Drug use in animals is common - kitty on catnip, for example - so fighting drugs seems to me a bit like fighting the ocean tides. Until we understand why and can affect the reasons that people desire drugs, nothing will change except perhaps that drug problems will be used as an excuse to eliminate our Constitutional right to privacy - a far more important issue AFAIC.

Has anyone read the short story by Hemmingway...? I don't remember the name but it was a conversation between a young and a middle aged man, about an old alcoholic gent, with all sitting around in a bar.

Last edited: Jan 11, 2006
20. Jan 11, 2006

### Ivan Seeking

Staff Emeritus
Note that hard core drug users and alcoholics are fully aware that they are killing themselves. What good will laws do when one is knowingly committing suicide anyway.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

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# Set of ultrafilters $\beta \mathbb{N} - \mathbb{N}$ is not separable

I want to show the set of ultrafilters $\beta \mathbb{N} - \mathbb{N}$ (where $\beta \mathbb{N}$ is all ultrafilters on $\mathbb{N}$) is not separable. I know we can take as a base of $\beta \mathbb{N}$ the sets $c_A = \{U \in \beta \mathbb{N}: A \in U\}$; so I think it is necessary and sufficient for a dense set of ultrafilters $(U_n)$ to be dense in the $c_A$: i.e. every $c_A$ contains some $U_i$.

So, I think to prove nonseparability I should start by assuming there is such a set of $U_n$ with every $c_A$ containing some element of the set, then somehow deduce a contradiction. I would prefer not to use too many preliminary results if a reasonably direct proof is possible, though I know that for any ultrafilter $U$, for any set $A$ either $A$ or $A^c \in U$, and I know $\beta \mathbb{N}$ is compact Hausdorff with the topology defined by the above base. Could anyone help me please? I tried cleverly selecting the sets A in the base of $c_A$ but I haven't had any luck deriving a contradiction.

-

Every $c_A$ (for $A$ infinite) contains some $U_n$ iff every (infinite) $A$ belongs to some $U_n$. Derive a contradiction by finding some $A$ which belongs to no $U_n$. Do this by diagonalizing against the $U_n$. Naively, you might want to pick an $A_n$ not in $U_n$, then intersect the $A_n$ to get $A$, but $A$ might be finite. Indeed if we just choose haphazardly, $A_0$ and $A_1$ might be disjoint. A slightly more prudent approach would be to build $A$ recursively, choosing $A_0 \notin U_0$, then splitting $A_0$ into two infinite sets, and choosing $A_1$ to be any one of the two which isn't in $U_1$ (this will have to be true of at least one of the two pieces of $A_0$ since $U_1$ is an ultrafilter), and so on. We could then take the intersection of the $A_n$, but this intersection may still end up finite.
What we'll do is something like the above, but at each stage we'll pick some number $a_n$ and lock it into $A$, so that we're sure $A$ is infinite in the end. The resulting $A$ might not be a subset of all of our $A_n$, so how will we know that $A \notin U_n$ for each $n$? The point will be that even if $A \not\subset A_n$, we will have $A \subset^\ast A_n$, that is, $A$ will be a subset of each $A_n$ "mod finite," and since the ultrafilters $U_n$ are non-principal, this will be good enough.
We will build the $A_n$ recursively. Fix an infinite $A_0 \notin U_0$. Let $a_0 = \min A_0$. Fix $A_{n+1} \subset A_n$ infinite such that $\min A_{n+1} > a_n$ and $A_{n+1} \notin U_{n+1}$. Let $a_{n+1} = \min A_{n+1}$. Set $A = \{a_n : n < \omega\}$.
Hi Amit, many thanks for your extremely helpful answer. That makes perfect sense to me except for the final step in the logic: arguing that $A \not \in U_n$ because $A \subset ^* A_n$ and the $U_n$ are non-principal. Is there perhaps some result I don't know of where if one set A differs from another, B, by only finitely many elements with a non-principal ultrafilter U and B is not contained in U then A is not contained in U? My understanding of a principal ultrafilter $\tilde{x}$ is that it is the set of all subsets of $\mathbb{N}$ which contain a specified element $x$. – Thomas Nov 21 '11 at 10:53
Is this because every non-principal ultrafilter extends the cofinite filter and so we could take an intersection with the complement of 'the things in $A$ not in $A_n$' to obtain a subset of $A_n$ in $U_n$, and deduce that $A_n \in U_n$ for contradiction? – Thomas Nov 21 '11 at 11:21
@Thomas: Yes. If $\mathscr{U}$ is a free ultrafilter on $\mathbb{N}$, and $A,B\subseteq\mathbb{N}$ differ by a finite set, then $A\in\mathscr{U}$ iff $B\in\mathscr{U}$, basically for the reason that you suggest: choose a cofinite $C\in\mathscr{U}$ s.t. $C\cap A=C\cap B=A\cap B$, and note that $A\in\mathscr{U}$ iff $A\cap C\in\mathscr{U}$ iff $B\in\mathscr{U}$. – Brian M. Scott Nov 21 '11 at 12:23


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10.5H: Synaptic Transmission

Synaptic transmission is a chemical event which is involved in the transmission of the impulse via release, diffusion, receptor binding of neurotransmitter molecules and unidirectional communication between neurons.

Learning Objectives
• Describe the process of synaptic transmission

Key Points

• In a chemical synapse, the pre and post synaptic membranes are separated by a synaptic cleft, a fluid filled space.
• The chemical event is involved in the transmission of the impulse via release, diffusion, receptor binding of neurotransmitter molecules and unidirectional communication between neurons.
• The neurotransmitter termination can occur in three ways – reuptake, enzymatic degradation in the cleft and diffusion.

In a chemical synapse, the pre and post synaptic membranes are separated by a synaptic cleft, a fluid filled space. The chemical event is involved in the transmission of the impulse via release, diffusion, receptor binding of neurotransmitter molecules and unidirectional communication between neurons.

Chemical Synapse

Synaptic vesicles inside a neuron: This pseudocolored image taken with a scanning electron microscope shows an axon terminal that was broken open to reveal synaptic vesicles (blue and orange) inside the neuron.

Neurotransmission at a chemical synapse begins with the arrival of an action potential at the presynaptic axon terminal. When an action potential reaches the axon terminal, it depolarizes the membrane and opens voltage-gated Na+channels. Na+ ions enter the cell, further depolarizing the presynaptic membrane. This depolarization causes voltage-gated Ca2+ channels to open. Calcium ions entering the cell initiate a signaling cascade. A calcium sensing protein binds calcium and interacts with SNARE proteins. These SNARE proteins are involved in the membrane fusion. The synaptic vesicles fuse with the presynaptic axon terminal membrane and empty their contents by exocytosis into the synaptic cleft. Calcium is quickly removed from the terminal.

Fusion of a vesicle with the presynaptic membrane causes neurotransmitters to be released into the synaptic cleft. The neurotransmitter diffuses across the synaptic cleft, binding to receptor proteins on the postsynaptic membrane.

Communication at a chemical synapse: Communication at chemical synapses requires release of neurotransmitters. When the presynaptic membrane is depolarized, voltage-gated Ca2+ channels open and allow Ca2+ to enter the cell. The calcium entry causes synaptic vesicles to fuse with the membrane and release neurotransmitter molecules into the synaptic cleft. The neurotransmitter diffuses across the synaptic cleft and binds to ligand-gated ion channels in the postsynaptic membrane, resulting in a localized depolarization or hyperpolarization of the postsynaptic neuron.

The binding of a specific neurotransmitter causes particular ion channels, in this case ligand-gated channels, on the postsynaptic membrane to open. The binding of a neurotransmitter to its receptor is reversible. As long as it is bound to a post synaptic receptor, a neurotransmitter continues to affect membrane potential. The effects of the neurotransmitter generally lasts few milliseconds before being terminated. The neurotransmitter termination can occur in three ways. First, reuptake by astrocytes or presynaptic terminal where the neurotransmitter is stored or destroyed by enzymes. Second, degradation by enzymes in the synaptic cleft such as acetylcholinesterase. Third, diffusion of the neurotransmitter as it moves away from the synapse.

10.5H: Synaptic Transmission is shared under a CC BY-SA license and was authored, remixed, and/or curated by LibreTexts.


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### Research on algorithm for low bandwidth super-peers network based on user’s behavior characteristic

HE Qin, LIU Dan, ZHOU Ming

1. Research Institute of Electronic Science and Technology, University of Electronic Science and Technology of China, Chengdu 611731, China
• Online:2013-06-01 Published:2013-06-14

### 基于行为特征的超级节点节流算法研究

1. 电子科技大学 电子科学技术研究院，成都 611731

Abstract: In a super-peers-based P2P network, if super-peers fail or leave, it may bring many problems, such as resource losing, network topology changing and increasing bandwidth occupancy for re-election. To solve these problem, this paper brings up a super-peers abdicate algorithm based on user’s behavior characteristic. According to statistic characteristic of the node failure, the SPAA algorithm can forecast the node leave time and appoint next super-peer. Simulation and analysis show that the SPAA algorithm can effectively reduce the net churn by super-peer failure and reduce network traffic.


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# Evolutionarily stable strategy

The evolutionarily stable strategy (or ESS; also evolutionary stable strategy) is a central concept in game theory introduced by John Maynard Smith and George R. Price in 1973 (a full account is given by Maynard Smith's 1982 book Evolution and the Theory of Games). The basic idea is that if a population of organisms is playing an evolutionarily stable strategy, a mutant allele that causes organisms to adopt a different strategy cannot invade the population, but will instead be eliminated by natural selection.

The concept was based on W.D. Hamilton's (1967) unbeatable strategy; the difference is that an unbeatable strategy is resistant to large migrations of different strategies. Through Hamilton's work on sex ratios the concept can be traced back through Ronald Fisher (1930) and Charles Darwin (1859) (see Edwards, 1998).

## Definition

An ESS depends on the idea of invasion, where a population of strategy-X players is visited by a strategy-Y player. The new player is said to invade if and only if either (1) following strategy Y, he scores better than the average strategy-X player or (2) following strategy Y, he scores equally well against the population as the average strategy-X player but does better against Y types than the average strategy-X player does against a Y player.

A strategy X is evolutionarily stable if and only if there is no strategy Y that can invade it. That is, anybody bringing a new strategy into a population of strategy-X players will fare no better on average than the X players are already doing. (See the closely-related Nash equilibrium) ESS is stable in respect to randomly and occasionally occurring invading strategies, but not necessarily stable with respect to mass counts of invaders. Similarly, ESS stability is only guaranteed under the assumption of infinitely large populations. In finite populations, stochastic effects of genetic drift may force the ESS to become unstable.

## Nash equilibria and ESS

Maynard Smith and Price specify (Maynard Smith & Price, 1973; Maynard Smith 1982) two conditions for a strategy I to be an ESS. Either

1. E(I,I) > E(J,I), or
2. E(I,I) = E(J,I) and E(I,J) > E(J,J)

must be true for all ${\displaystyle I\neq J}$, where E(I,J) is the expected payoff to strategy I when playing against strategy J.

The first condition is sometimes called a 'strict Nash' equilibrium (Harsanyi, 1973), the second is sometimes referred to as 'Maynard Smith's second condition'.

Consider the following payoff matrix, describing a coordination game such as the Stag hunt, or Battle of the sexes:

A B 1, 1 0, 0 0, 0 1, 1

Both strategies A and B are ESS, since a B player cannot invade a population of A players nor can a A player invade a population of B players. Here the two pure strategy Nash equilibria correspond to the two ESS. In this second game, which also has two pure strategy Nash equilibria, only one corresponds to an ESS:

C D 1, 1 0, 0 0, 0 0, 0

Here (D, D) is a Nash equilibrium (since neither player will do better by unilaterally deviating), but it is not an ESS. Consider a C player introduced into a population of D players. The C player does equally well against the population (she scores 0), however the C player does better against herself (she scores 1) than the population does against the C player. Thus, the C player can invade the population of D players.

Even if a game has pure strategy Nash equilibria, it might be the case that none of the strategies are ESS. Consider the following example (known as Chicken):

E F 0, 0 -1, +1 +1, -1 -20, -20

There are two pure strategy Nash equilibria in this game (E, F) and (F, E). However, in the absence of an uncorrelated asymmetry), neither F nor E are ESSes. A third Nash equilibrium exists, a mixed strategy, which is an ESS for this game (see Hawk-dove game and Best response for explanation).

## ESS vs. Evolutionarily Stable State

An ESS or evolutionarily stable strategy is a strategy such that, if all the members of a population adopt it, no mutant strategy can invade. --Maynard Smith (1982).
A population is said to be in an evolutionarily stable state if its genetic composition is restored by selection after a disturbance, provided the disturbance is not too large. Such a population can be genetically monomorphic or polymorphic. --Maynard Smith (1982).

An ESS is a strategy with the property that, once virtually all members of the population use it, then no 'rational' alternative exists. An evolutionarily stable state is a dynamical property of a population to return to using a strategy, or mix of strategies, if it is perturbed from that strategy, or mix of strategies. The former concept fits within classical game theory, whereas the latter is a population genetics, dynamical system, or evolutionary game theory concept.

## Prisoner's dilemma and ESS

Consider a large population of people who, in the iterated prisoner's dilemma, always play Tit for Tat in transactions with each other. (Since almost any transaction requires trust, most transactions can be modelled with the prisoner's dilemma.) If the entire population plays the Tit-for-Tat strategy, and a group of newcomers enter the population who prefer the Always Defect strategy (i.e. they try to cheat everyone they meet), the Tit-for-Tat strategy will prove more successful, and the defectors will be converted or lose out. Tit for Tat is therefore an ESS, with respect to these two strategies. On the other hand, an island of Always Defect players will be stable against the invasion of a few Tit-for-Tat players, but not against a large number of them. (see Robert Axelrod's The Evolution of Cooperation, or more briefly here.

## ESS and human behavior

The recent, controversial sciences of sociobiology and now evolutionary psychology attempt to explain animal and human behavior and social structures, largely in terms of evolutionarily stable strategies. For example, in one well-known 1995 paper by Linda Mealey, sociopathy (chronic antisocial/criminal behavior) is explained as a combination of two such strategies.

Although ESS were originally considered as stable states for biological evolution, it need not be limited to such contexts. In fact, ESS are stable states for a large class of adaptive dynamics. As a result ESS are used to explain human behavior without presuming that the behavior is necessarily determined by genes.


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# Lesson 6: Strategic Solving

Let's solve linear equations like a boss.

## 6.1: Equal Perimeters

The triangle and the square have equal perimeters.

1. Find the value of $x$.
2. What is the perimeter of each of the figures?

## 6.2: Predicting Solutions

Without solving, identify whether these equations have a solution that is positive, negative, or zero.

1. $\frac{x}{6}=\frac{3x}{4}$
2. $7x=3.25$
3. $7x=32.5$
4. $3x+11=11$
1. $9-4x=4$
2. $\text-8+5x=\text-20$
3. $\text-\frac12(\text-8+5x)=\text-20$

## 6.3: Which Would You Rather Solve?

Here are a lot of equations:

A. $\text{-} \frac56(8+5b)=75+\frac53 b$

B. $\text-\frac12(t+3)-10=\text-6.5$

C. $\frac{10-v}{4}=2(v+17)$

D. $2(4k+3)-13=2(18-k)-13$

E. $\frac{n}{7}-12=5n+5$

F. $3(c-1)+2(3c+1)=\text-(3c+1)$

G. $\frac{4m-3}4=\text{-}\frac{9+4m}8$

H. $p-5(p+4)=p-(8-p)$

I. $2(2q+1.5)=18-q$

J. $2r+49=\text{-}8(\text{-}r-5)$

1. Without solving, identify 3 equations that you think would be least difficult to solve and 3 equations you think would be most difficult to solve. Be prepared to explain your reasoning.
2. Choose 3 equations to solve. At least one should be from your "least difficult" list and one should be from your "most difficult" list.

## Summary

Sometimes we are asked to solve equations with a lot of things going on on each side. For example,

$x-2(x+5)=\dfrac{3(2x-20)}{6}$

This equation has variables on each side, parentheses, and even a fraction to think about. Before we start distributing, let's take a closer look at the fraction on the right side. The expression $2x-20$ is being multiplied by 3 and divided by 6, which is the same as just dividing by 2, so we can re-write the equation as

$x-2(x+5)=\dfrac{2x-20}{2}$

But now it’s easier to see that all the terms on the numerator of right side are divisible by 2, which means we can re-write the right side again as

$x-2(x+5)=x-10$

At this point, we could do some distribution and then collect like terms on each side of the equation. Another choice would be to use the structure of the equation. Both the left and the right side have something being subtracted from $x$. But, if the two sides are equal, that means the "something" being subtracted on each side must also be equal. Thinking this way, the equation can now be re-written with less terms as

$2(x+5)=10$

Only a few steps left! But what can we tell about the solution to this problem right now? Is it positive? Negative? Zero? Well, the 2 and the 5 multiplied together are 10, so that means the 2 and the $x$ multiplied together cannot have a positive or a negative value. Finishing the steps we have:

\begin{align} 2(x+5)&=10\\ x+5&=5&&\text{Divide each side by 2}\\ x &=0&&\text{Subtract 5 from each side}\\ \end{align}

Neither positive nor negative. Just as predicted.


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# Magnetometer¶

The magnetometer is used to estimate heading when the system is in any of the following conditions:

1. is in AHRS mode
2. has no GPS fix
3. has GPS fix and constant velocity (non-accelerating motion)

To have accurate heading under these conditions, the magnetometer must be calibrated. The system allows for two types of modes for recalibration, external initiated and automatically initiated re-calibration. Regardless of the recalibration mode, a slower online background calibration runs that continuously improves the magnetometer calibration to handle local magnetic environment changes. All magnetometer calibration is stored in flash memory and available on bootup.

Magnetometer fusion into the INS and AHRS filter can be disabled by setting bit SYS_CFG_BITS_DISABLE_MAGNETOMETER_FUSION (0x00001000) of DID_FLASH_CONFIG.sysCfgBits.

## Magnetometer Recalibration¶

Occasionally the magnetometer will require a complete recalibration, replacing the old calibration with an entirely new calibration. This is accomplished either through external or automatic initiated recalibration. Use of the different modes is generally governed by the particular use case for the end customer and is intended to allow for the most flexibility in an integrated product design.

### External Recalibration¶

External magnetometer recalibration allows the most flexibility in determining when an end user will need to recalibrate the system. This control over the timing of the recalibration is critical for many use cases and allows product designers to implement their desired workflows for customers. Further there are use cases where automatic recalibration is not possible because the quality of the magnetometer calibration is not observable. Such use cases would include AHRS operation, extended periods without motion or no GNSS fix. External magnetometer recalibration, as the name suggests is triggered by an external command from the application managing the uINS hardware. The uINS provides a set of status messages indicating the quality of the magnetometer calibration and leaves the timing and implementation of a recalibration up to the product designer. Specifically, INS_STATUS_MAG_INTERFERENCE_OR_BAD_CAL is an indication of the quality of the magnetometer calibration (see system status flags for details).

During the calibration process, the system should be clear of steel, iron, magnets, or other ferrous materials (i.e. steel desks, tables, building structures). The uINS should be attached to the system in which it is operating and rotated together during the calibration process. The following is the

Force magnetometer recalibration procedure:

1. Set DID_MAG_CAL.recalCmd to either: * MAG_RECAL_CMD_MULTI_AXIS (0) for Multi-Axis which is more accurate and requires 360⁰ rotation about two different axes. * MAG_RECAL_CMD_SINGLE_AXIS (1) for Single-Axis which is less accurate and requires 360⁰ rotation about one axis.
2. Rotate the system accordingly.

Recalibration completion is indicated by either:

1. INS_STATUS_MAG_RECALIBRATING bit of the insStatus word set to zero. The insStatus word is found in standard INS output messages (DID_INS_1, DID_INS_2, DID_INS_3, and DID_INS_4).
2. DID_MAG_CAL.progress is 100.

Recalibration progress is indicated as a percentage (0-100%) is indicated can be observed from variable DID_MAG_CAL.progress. The recalibration process can be canceled and the prior calibration restored anytime by setting DID_MAG_CAL.enMagRecal = MAG_RECAL_MODE_ABORT (101).

The “Mag used” indicator in the EvalTool INS tab will be green when magnetometer data is being fused into the solution, black when not being fused into the solution, and red during recalibrating.

Example code:

#include "com_manager.h"
// Set DID_MAG_CAL.enMagRecal = 0 for multi-axis recalibration
int32_t value = MAG_RECAL_MODE_MULTI_AXIS;
sendDataComManager(0, DID_MAG_CAL, &value, 4, offsetof(mag_cal_t, enMagRecal));
// Enable broadcast of DID_MAG_CAL.progress every 100ms to observe the percent complete
sendDataComManager(0, DID_MAG_CAL, 0, sizeof(mag_cal_t), 100);

### Automatic Recalibration¶

Automatic magnetometer recalibration is useful for systems where user intervention to start external calibration is not convenient or practical. In this mode, the solution will determine that the system needs to be recalibrated and will attempt to do so while in normal operation. In the period while the system is recalibrating, the uncalibrated magnetometer data is used to prevent the INS heading from drifting but it does not provide heading measurements to the state estimator. This feature is enabled by setting bit SYS_CFG_BITS_AUTO_MAG_RECAL (0x00000004) of DID_FLASH_CONFIG.sysCfgBits non-volatile word.

// Enable automatic magnetometer calibration.
DID_FLASH_CONFIG.sysCfgBits |= SYS_CFG_BITS_AUTO_MAG_RECAL;
// Disable automatic magnetometer calibration.
DID_FLASH_CONFIG.sysCfgBits &= ~SYS_CFG_BITS_AUTO_MAG_RECAL;

## Magnetometer Continuous Calibration¶

To mitigate the need for recalibration (completely replace calibration data), continuous calibration improves the magnetometer calibration slowly over time. Continuous calibration always runs in the background.

## Magnetometer Calibration Settings¶

The magnetometer calibration algorithm can produce higher quality calibrations when data more data is collected across multiple axes of rotation. However, there are use cases where data collection beyond a single axis is impractical if not impossible. To address this issue there is a setting in the flash to configure the data requirement threshold for magnetometer calibration. The available settings include:

• Single Axis Calibration – This setting requires a full rotation in the yaw axis (relative to earth) to determine the calibration. Additional data that is collected via motion on other axes is used but not required. Once a full rotation is completed the calibration is calculated and the online continuous calibration is started.
• Multi Axis Calibration – This setting requires data to be collected across at least two axes, where one is the yaw axis. This calibration mode does not have any specific angular rotational requirements in any given axes, but it does require that data has been collected across a sufficient angular span. There is an indicator (mag_cal_threshold_complete) in the DID_SYS_PARAMS message that relates the total percent of the required threshold that has been collected. As more data is collected this value will increment to 100% at which point the calibration will be calculated and the online continuous calibration will continue to run
/*! Magnetometer recalibration. 0 = multi-axis, 1 = single-axis */


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# Security

New Contributor

## Onguard Agent and Windows Image Considerations

Are there any considerations if we were to include the Clearpass Onguard agent in our Windows 7 Image?  Any unique identifiers in the registry that would need to be addressed as the OS is 'cloned', would it be better to leave this agent out of the image and pushed afterwards with something like SCCM?

Agent v6.6.5.93747

Guru Elite

## Re: Onguard Agent and Windows Image Considerations

You can include it in the image. No concerns.

Tim Cappalli | Aruba Security TME
@timcappalli | timcappalli.me | ACMX #367 / ACCX #480
New Contributor

Thank you Tim!