text: dc.creator Sumpf, B. en_US dc.creator Meusel, I. en_US dc.creator Kronfeldt, H.- D. en_US dc.date.accessioned 2007-11-20T17:11:20Z dc.date.available 2007-11-20T17:11:20Z dc.date.issued 1995 en_US dc.identifier 1995-RL-07 en_US dc.identifier.uri http://hdl.handle.net/1811/29720 dc.description B. S. gratefully acknowledges the support of the ""Deutsche Forschungsgemeinschaft''. en_US dc.description Author Institution: Universität Berlin, Sekr. PN 0-1 Hardenbergstraße 36, 10623 Berlin, Germany en_US dc.description.abstract We present measurements of the broadening coefficient of absorption lines from the $\nu_{1}$ and $\nu_{3}$ bands of $H_{2}S$ in the wavenumber region between $2690 cm^{-1}$ and $2765 cm^{-1}$ measured with a diode laser spectrometer. These bands are of great interest because of the strong Coriolis interaction between the $\nu_{1}$ and $\nu_{3}$ bands as well as between the $2\nu_{2}$ and $\nu_{3}$ bands and additionally the Fermi interaction between the $2\nu_{2}$ and $\nu_{1}$ bands. Due to the weakness of these bands we had to apply a Herriott multipass cell with a path length of 4.7 m. The study includes 24 lines of the $\nu_{1}$ band with $3 \leq J^{\prime\prime} \leq 17, 0 \leq K_{a}^{\prime\prime} \leq 7$ and 6 lines of the $\nu_{3}$ band with $3 \leq J^{\prime\prime}\leq 7, 1 \leq K_{a}^{\prime \prime} \leq 7$. As perturbers we used $H_{2}S, N_{2}$, air, He, Ne, Ar, Kr, and Xe. We will discuss the quantum number dependence of the broadening coefficients and compare the results with those in the case of $SO_{2}$ where only weak interactions occur. en_US dc.format.extent 48651 bytes dc.format.mimetype image/jpeg dc.language.iso English en_US dc.publisher Ohio State University en_US dc.title PRESSURE BROADENING IN THE $\nu_{1}$ AND $\nu_{3}$ BANDS OF $H_{2}S$ en_US dc.type article en_US


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Solution for Show that the Relative Error in Computing the Volume of a Sphere, Due to an Error in Measuring the Radius, is Approximately Equal to Three Times the Relative Error in the Radius ? - CBSE (Commerce) Class 12 - Mathematics

Question

Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius ?

Solution

Let x be the radius of the sphere and y be its volume.

$\text { Let } ∆ x \text { be the error in the radius and ∆ V be the approximate error in the volume } .$

$y = \frac{4}{3}\pi x^3$

$\Rightarrow \frac{dy}{dx} = 4\pi x^2$

$\Rightarrow ∆ y = dy = \frac{dy}{dx}dx = 4\pi x^2 \times ∆ x$

$\Rightarrow ∆ y = 3 \times \frac{4}{3}\pi x^3 \times \frac{∆ x}{x}$

$\Rightarrow ∆ y = 3 \times y \times \frac{∆ x}{x}$

$\Rightarrow \frac{∆ y}{y} = 3\frac{∆ x}{x}$

Hence proved.

Is there an error in this question or solution?

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Solution Show that the Relative Error in Computing the Volume of a Sphere, Due to an Error in Measuring the Radius, is Approximately Equal to Three Times the Relative Error in the Radius ? Concept: Approximations.
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# American Institute of Mathematical Sciences

January & February  2004, 10(1&2): 459-472. doi: 10.3934/dcds.2004.10.459

## Boundary layer separation and structural bifurcation for 2-D incompressible fluid flows

 1 Department of Mathematics, Sichuan University, Chengdu 2 Department of Mathematics, Indiana University, Bloomington, IN 47405

Received  March 2003 Revised  August 2003 Published  October 2003

The main objective of this article and the previous articles [2, 3, 7] is to provide a rigorous characterization of the boundary layer separation of 2-D incompressible viscous fluids. First we establish a simple equation linking the separation location and time with the Reynolds number, the external forcing the boundary curvature, and the initial velocity field. Second, we show that external forcing with reverse orientation to the initial velocity field leads to structural bifurcation at a degenerate singular point with integer index of the velocity field at the critical bifurcation time. Necessary and sufficient kinematic conditions are given to identify the case for boundary layer separation.
Citation: Tian Ma, Shouhong Wang. Boundary layer separation and structural bifurcation for 2-D incompressible fluid flows. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 459-472. doi: 10.3934/dcds.2004.10.459
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2019 Impact Factor: 1.338


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Reading through IBM's intro to quantum computing and gates and I'm confused about the Hadamard gate. When you use an H gate it appears to rotate the qubit along the X axis pi/4 putting it in a superposition.

If my base state was |0> and I pass it through an H gate it will be put into |>. Another H gate will put it back into |0>.

If my base state was |1> then the same happens, where two H gates will return to |1>.

I'd expect two H gates would be the same as a NOT gate and flip |0> to |1>.

I see what is happening but I don't know why. Why doesn't two H gates turn |0> to |1> ?

• What do you mean by "|>"? – Nathaniel Oct 7 '17 at 6:04
• If by rotations, you refer to the Bloch sphere representation, the Hadamard gate is a rotation of $\pi$ about the vector $\hat{x}+\hat{z}$, not $\pi/4$ about the vector $\hat{x}$ as you stated. – user154997 Oct 7 '17 at 6:39

The most clear mathematical representation is to look at the Hadamard gate as a 2x2 matrix 1/$\sqrt{2}$ [[1,1],[1,-1]]. Square it and you get unity. It might also help to look into the Bloch sphere: Understanding the Hadamard gate on the Bloch sphere


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# How do you graph the inequality x<–2?

You first draw the line $x = - 2$. Then everything left of that line is part of the solution space.
Because of the $<$ this means that the line itself is not included.
The line $x = 2$ is a vertical line through $\left(- 2 , 0\right)$ and holds all the points $\left(- 2 , y\right)$, where $y$ may have any value.


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Question

# The unit vector in the direction of $\widehat i + \widehat j + \widehat k$ is be?a)$\dfrac{1}{{\sqrt 3 }}(\widehat i + \widehat j + \widehat {k)}$b)$\sqrt 3 (\widehat i + \widehat j + \widehat {k)}$c)$\dfrac{1}{{\sqrt 2 }}(\widehat i + \widehat j + \widehat {k)}$d)$\sqrt 2 (\widehat i + \widehat j + \widehat {k)}$

Hint: Here, we will use the formulae of unit vector in the direction of unit vector to solve.

Given,
Vector is$\widehat i + \widehat j + \widehat k$. Now, we need to find the unit vector in the direction of $\widehat i + \widehat j + \widehat k$. As, we know that a unit vector is given by dividing the vector by its magnitude, so the resulting vector has magnitude 1and is in same direction as the original vector.
Let$\widehat a = \widehat i + \widehat j + \widehat k$, Now magnitude of $\widehat a$is
$\begin{gathered} \Rightarrow \left| {\widehat a} \right| = \sqrt {{1^2} + {1^2} + {1^2}} \\ \Rightarrow \left| {\widehat a} \right| = \sqrt 3 \\ \end{gathered}$
As, we know the unit vector in the direction of $\widehat a$ is $\dfrac{{\widehat a}}{{\left| {\widehat a} \right|}}$.Now, the unit vector in the direction of $\widehat i + \widehat j + \widehat k$ will be
$\Rightarrow \dfrac{{\widehat i + \widehat j + \widehat k}}{{\sqrt 3 }}$
Therefore, the unit vector in the direction of $\widehat i + \widehat j + \widehat k$ is $\dfrac{{\widehat i + \widehat j + \widehat k}}{{\sqrt 3 }}$.
Hence, the required option for the given question is ‘A’.

Note: Here, we have been asked to find the unit vector in the direction of the vector, hence the sign of the unit vector is positive elsewhere. If we need to find the unit vector in the opposite direction of the given vector then the sign of the unit vector will be negative.


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# I'm a layman, but I'd like to know to to use GAMESS for some specific tasks

I have Avogadro and GAMESS. I modeled the sulfuric acid molecule using Avogadro, then I asked it to generate an input for GAMMES to calculate the transitional state (I'm hoping this will get me somehow closer to my computational modeling of real chemistry). But GAMESS says the job finished with an error, and I don't know why.

It's worth noticing Avogadro seems to spell one of the commands wrong, and I have to manually correct it. Avogadro issues the command \$STATTP but GAMESS does not recognize this command, so I change it to \$STSTEP, and it ends with an error, and I try the other keyword possible \$STPT and I also get an error. Here's my 2 inputs and outputs: http://pastebin.com/TabWC9wr This is what happens when I do what you told me, @Mitradip Das: ## INPUT ! File created by the GAMESS Input Deck Generator Plugin for Avogadro$BASIS GBASIS=STO NGAUSS=3 $END$CONTRL SCFTYP=RHF RUNTYP=SADPOINT $END$STATPT OPTTOL=0,0001 NSTEP=20 $END$DATA
Title
C1
S    16.0    -3.61564     3.32108     0.04978
O     8.0    -4.51377     4.03518    -0.82228
O     8.0    -2.75016     3.96121     1.00661
O     8.0    -2.67033     2.39549    -0.85711
O     8.0    -4.49699     2.21900     0.81326
H     1.0    -5.20320     1.93219     0.19859
H     1.0    -1.81232     2.32072    -0.38885
$END  ## OUTPUT (showing only the error part, full output can be viewed here (http://pastebin.com/HRh1fS4d)  CONSTANT LIST TOO LONG **** ERROR READING INPUT GROUP$STATPT   *****
THE PROBLEM IS WITH THIS INPUT LINE, NEAR THE X MARKER
$STATPT OPTTOL=0,0001 NSTEP=20$END
X
THE ONLY KEYWORDS ACCEPTED IN THIS GROUP ARE:
METHOD    UPHESS    NSTEP     NNEG      IFOLOW    DXMAX
RMIN      RMAX      RLIM      RESTAR    HESS      OPTTOL
IHREP     HSSEND    IFREEZ    NPRT      NPUN      PURIFY
ITBMAT    MOVIE     TRUPD     TRMAX     TRMIN     STPT
STSTEP    PROJCT    IFCART    NPRTHS    KDIAGH    IACTAT
IHMCON    FHMCON    SHMCON
TROUBLE INTERPRETING $STATPT OBTAINING INITIAL HESSIAN, HESS=READ ***** ERROR, YOU DID NOT SUPPLY A$HESS GROUP.
EXECUTION OF GAMESS TERMINATED -ABNORMALLY- AT Wed Jul 27 12:23:49 2016
580000  WORDS OF DYNAMIC MEMORY USED
STEP CPU TIME =     0.00 TOTAL CPU TIME =        0.0 (    0.0 MIN)
TOTAL WALL CLOCK TIME=        0.0 SECONDS, CPU UTILIZATION IS 100.01%

job aborted:

• In general, this is not the right place to ask these questions since they are entirely about the software you use. You should also try to work through at least the first few examples in the manual. Starting to learn a program with a saddle point optimisation is a very bad choice, since they really need some understanding of the program first. The error you get is problematic because it points you to the wrong position. Try opttol=0.001. You might also need to tell the program how to obtain the hessian. Jul 27 '16 at 15:45
• If the input geometry is not close to a transition state (which one? what do you want to find?), you might not get any conversion. Try running a single point calculation first. Don't rely on the avogadro input generator, it makes mistakes. Understand the keywords you are using and structure your input file accordingly. Leave comments in your input explaining what you are actually trying to achieve. Gamess is difficult to learn and even if your calculation runs without error, you might not get any meaningful results. Jul 27 '16 at 15:50
• I see. It is not a very intuitive program to use. even the command line to invoke it is verbose. Jul 27 '16 at 16:19
• You're asking it to do a transition state calculation (RUNTYP=SADPOINT ) which doesn't make sense. A transition state occurs between two different structures, such as between reactants and product or when ammonia goes through its umbrella. Try an equilibrium run with RUNTYP=OPTIMIZE instead. This should get you going. If you are having difficulty I will generate an input file for you. It is well worth persevering. Oct 31 '17 at 12:05

For GAMESS, the command is not $\$STATTP$, but it is$\$STATPT$. Also, please change the commas to dot, otherwise it considers it to be a part of the number.


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# AucTeX (in Emacs) doesn't seem to find certain packages

I am using AucTeX in emacs v23 in PFD-mode. When invoking the pdflatex compiler through C-c C-c LaTeX I get a [...] file <some_package>.sty not found error for some particular packages. For example, consider the following foo.tex file:

\documentclass{article}

\usepackage{algorithm}
\usepackage{algpseudocode}

\begin{document}

\begin{algorithm}
\begin{algorithmic}
\Function{Increment}{$x$}
\State \Call{Return}{$x+1$}
\EndFunction
\end{algorithmic}
\end{algorithm}

\end{document}

Compiling the file using AucTeX (C-c C-c LaTeX) yields:

ERROR: LaTeX Error: File algpseudocode.sty' not found.

However, if I invoke pdflatex foo.tex via the terminal, everything works alright.

The only packages I have so far experienced this behavior with are algpseudocode and fmtcount, included in the Linux packages texlive-science and texlive-latex-extra, respectively. The packages are, apparently, there; for example, I get the following in the terminal:

$locate -b fmtcount.sty /usr/share/texmf-texlive/tex/latex/fmtcount/fmtcount.sty$ dpkg -l | grep texlive-latex-extra
ii  texlive-latex-extra      2009-10ubuntu1           TeX Live: LaTeX  supplementary packages
ii  texlive-latex-extra-doc  2009-10ubuntu1           TeX Live: Documentation files for texlive-latex-extra

What I find particularly confusing is that I get no such error for package footmisc, which is also part of texlive-latex-extra.

(Please bear in mind that I do not have root access in the machine I'm experiencing this problem at. If it is needed, I can ask the administrators to do the fix - once I know what that might be - but I doubt they'd be willing to start attempting various approaches to it.)

Update

$kpsewhich algpseudocode.sty /auto/pkg/texlive-2009/texmf-dist/tex/latex/algorithmicx/algpseudocode.sty  It appears that the problem is caused by the pdflatex program invoked by AucTeX. As I mentioned above, if I run pdflatex foo.tex manually through the terminal, it works, and the first line of foo.log is: This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009) (format=pdflatex 2010.6.1) 15 FEB 2012 17:15  If, on the other hand, I invoke the compiler through C-c C-c LaTeX in AucTex, the foo.log file is as follows (notice the difference between the TeX distributions seen in the first line): This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=pdflatex 2011.4.5) 15 FEB 2012 13:24 entering extended mode **\input foo.tex (./foo.tex (/auto/pkg/tetex-3.0/share/texmf-dist/tex/latex/base/article.cls Document Class: article 2004/02/16 v1.4f Standard LaTeX document class (/auto/pkg/tetex-3.0/share/texmf-dist/tex/latex/base/size10.clo File: size10.clo 2004/02/16 v1.4f Standard LaTeX file (size option) ) \c@part=\count79 \c@section=\count80 \c@subsection=\count81 \c@subsubsection=\count82 \c@paragraph=\count83 \c@subparagraph=\count84 \c@figure=\count85 \c@table=\count86 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 \bibindent=\dimen102 ) (/auto/pkg/tetex-3.0/share/texmf-dist/tex/latex/algorithms/algorithm.sty Package: algorithm Document Style algorithm' - floating environment (/auto/pkg/tetex-3.0/share/texmf-dist/tex/latex/float/float.sty Package: float 2001/11/08 v1.3d Float enhancements (AL) \c@float@type=\count87 \float@exts=\toks14 \float@box=\box26 \@float@everytoks=\toks15 \@floatcapt=\box27 ) (/auto/pkg/tetex-3.0/share/texmf-dist/tex/latex/base/ifthen.sty Package: ifthen 2001/05/26 v1.1c Standard LaTeX ifthen package (DPC) ) \@float@every@algorithm=\toks16 \c@algorithm=\count88 ) ! LaTeX Error: File algpseudocode.sty' not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: sty) Enter file name: ! Emergency stop. <read *> l.5 ^^M *** (cannot \read from terminal in nonstop modes) Here is how much of TeX's memory you used: 346 strings out of 94499 4143 string characters out of 1173445 49441 words of memory out of 1000000 3593 multiletter control sequences out of 10000+50000 3640 words of font info for 14 fonts, out of 500000 for 2000 580 hyphenation exceptions out of 1000 23i,0n,17p,157b,36s stack positions out of 1500i,500n,5000p,200000b,5000s PDF statistics: 0 PDF objects out of 300000 0 named destinations out of 131072 1 words of extra memory for PDF output out of 65536 No pages of output.  I'm afraid I can't figure out how to point AucTeX to the correct pdflatex installation, though. In case it's useful, I have the following AucTeX-related lines in my .emacs file: (setq TeX-auto-save t) (setq TeX-parse-self t) (setq-default TeX-master nil) (add-hook 'LaTeX-mode-hook (lambda () (TeX-fold-mode 1))) (add-hook 'LaTeX-mode-hook 'visual-line-mode) (add-hook 'LaTeX-mode-hook 'flyspell-mode) (add-hook 'LaTeX-mode-hook 'LaTeX-math-mode) (add-hook 'LaTeX-mode-hook 'TeX-PDF-mode) (add-hook 'LaTeX-mode-hook 'turn-on-reftex) (setq reftex-plug-into-AUCTeX t)  - Could it be that Emacs is picking up a different latex installation? Auctex just calls pdflatex or whatever and so missing package messages are likely to be from pdflatex, not auctex. – PLK Feb 15 '12 at 19:27 We could do to see the .log file you get. Also, what does kpsewhich algpseudocode.sty give? – Joseph Wright Feb 15 '12 at 19:37 We'd like to keep answers separate from questions, so you should write a separate answer instead of editing your answer into the question. Self-answers are perfectly admissible, and a well-written answer may earn you additional reputation. – lockstep Feb 21 '12 at 22:55 @Sweeters: It shouldn’t be necessary to edit /etc/environment. Adjust the PATH in ~/.profile and restart the X server. ~/.profile is sourced during text as well as graphical login. Note that, in general, it is not a good idea to set environment variables such as PATH in ~/.bashrc. Use ~/.profile for this purpose. – mhp Feb 22 '12 at 8:32 @Sweeters: Check the system PATH exported in /etc/profile or /etc/environment, prepend the directories you additionally need to the system PATH in ~/.profile, ensure that neither ~/.bash_profile nor ~/.bash_login exist, ensure that the PATH is not modified either in /etc/bash.bashrc or ~/.bashrc, and, finally restart the display manager. Then the resulting PATH should be independent of the login mode. – mhp Feb 22 '12 at 20:07 ## 1 Answer The problem was being caused by invoking Emacs through the Gnome panel, which results in Emacs being oblivious of the PATH as it is set through .bashrc. A way to fix this is to have Emacs set its PATH to be the one seen by bash, by putting the following in the .emacs file (credit to Shane in here): (setenv “PATH” (shell-command-to-string “bash -i -c ‘echo -n$PATH’”))

-
Undoubtedly, this is a working fix. But the actual problem is that the PATH is set in ~/.bashrc (the initialization script for non-login interactive Bash), which means that applications such as Emacs might see a different environment, depending on whether they are invoked from a text or graphical terminal. –  mhp Feb 23 '12 at 8:25
Indeed you are right, mhp; and I would generally prefer the solution you posted above. The problem I have with avoiding setting the PATH through .bashrc is that there is a "central" .bashrc` file that's being sourced for all workstations in the network and I can only add my own customizations on top of that. Of course, I could ask that I self-administer my workstation, and then make sure that such customizations are set in the proper, so to speak, places, but then that might create a series of other complications I'd rather not deal with at the time. –  Sweeters Feb 24 '12 at 16:48


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# Definite integrals

Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof)

If f(x) is a function defined for a ≤ x ≤ b, we divide the interval [a,b] into n subintervals of equal

width Δx = (b-a)/n. We assume x0 =a, x1, x2,…, xn (=b) which denote the endpoints of these subintervals and we let x1 *, x2 *,…, xnbe any sample points in these subintervals. Then, the definite integral of f from a to b is written in calculus as:

provided this limit exists and it should provide the same value for all possible choices of sample points. If the limit exists, we say f is integrable on [a,b]. In this case, a is the lower limit of integration, and the number bis the upper limit of integration.

The precise meaning of the limit that defines the integral can be explained as follows:

For every number ε> 0 N is an integer which follows and for every integer n>N and for every choice of xi* in [xi-1, xi] as shown below

If f is continuous and nonnegative on the closed interval [a, b], then the area of the region bounded by the graph of f, the x-axis, and the vertical lines x = a and x = b can be interpreted as:

If the graph is nonpositive from a to b then

Areas of common geometric figures:

If f is continuous on [a, b], or if f has only a finite number of jump discontinuities, then
f is integrable on [a, b].That is, the definite integral $\int_{a}^{b}{f(x)dx}$ exists.

Let f be a continuous function defined on the closed interval [a, b] and F bean antiderivative of f. Then,

$\int_{a}^{b}{f(x)dx}=[F(x)]_{a}^{b}=F(b)-F(a)$

Definition of Two Special Definite Integrals:

1. If f is defined at a fixed point x = a, then
2. If f is integrable on [a, b], then

Example:

For calculating $\int_{a}^{b}{f(x)dx}$, use the following steps:

Find the indefinite integral∫ f x dx ( ) . Let this be F(x). There is no need to keep integration constant C because if we consider F(x) + C instead of F(x), we get $\int_{a}^{b}{f(x)dx}=[F(x)]_{a}^{b}=F(b)-F(a)$

Thus, the arbitrary constant disappears in evaluating the value of the definite integral and then we can evaluate the value of integral by plugging in b and a.

Example: Evaluate $\int_{0}^{1}{\frac{\tan ^{-1}x}{1+x^{2}}}$

Use substitution method, let t = $\tan ^{-1}x$ then dt = $dt= \frac{1}{1+x^{2}}dx$. In this case, the new limits for t are $x=0\to t=0;x=1\to t=\frac{\pi }{4}$

$\int_{0}^{1}{\frac{\tan ^{-1}x}{1+x^{2}}}=\int_{0}^{\frac{\pi }{4}}{t dt[\frac{t^{2}}{2}]_{0}^{\frac{\pi }{4}}}$

$\frac{1}{2}\lbrack \frac{\pi ^{2}}{16}-0\rbrack =\frac{\pi ^{2}}{32}$


text:
1. ## Linear operator

Please can you help me to track the question below.
Q. Let T:X-->Y be a linear operator and dim X= dim Y = n <\infty . show that range R(T)=Y if and only if T^-1 exist.

2. Originally Posted by kinkong
Please can you help me to track the question below.
Q. Let T:X-->Y be a linear operator and dim X= dim Y = n <\infty . show that range R(T)=Y if and only if T^-1 exist.

Hint

$\textrm{r}(T)=Y\Leftrightarrow \dim\textrm{r}(T)=n\Leftrightarrow \dim\ker(T)=0$

3. gee, does everything in linear algebra reduce to the rank-nullity theorem?

4. Originally Posted by Deveno
gee, does everything in linear algebra reduce to the rank-nullity theorem?

Everything related with that theorem.

5. your hint was useful but i couldnt figure where to go from there. please can you help me out...thanks

6. Originally Posted by kinkong
your hint was useful but i couldnt figure where to go from there. please can you help me out...thanks

$T$ is injective iff $\ker T=\{0\}$ and $T$ is surjective iff $r(T)=Y$ . Besides, there exists $T^{-1}$ iff $T$ is bijective.


text: IEVref: 171-07-31 ID: Language: en Status: Standard Term: average transinformation rate Synonym1: Synonym2: Synonym3: Symbol: T* Definition: quotient of the character mean transinformation content T′ by the mean duration of a pair of input and output characters T* = T′/t(X,Y) where X = {x1, …, xn} is the set of input characters xi (i = 1, …, n), Y = {y1, …, ym} is the set of output characters yj (j = 1, …, m) and $t\left(X,Y\right)=\sum _{i=1}^{n}\sum _{j=1}^{m}p\left({x}_{i},{y}_{j}\right)\cdot t\left({x}_{i},{y}_{j}\right)$ is the mean value of the duration t(xi,yj) of the pair of characters (xi,yj) which occurs with joint probability p(xi,yj).Note 1 to entry: The average transinformation rate can be expressed in a unit such as the shannon per character and second. Publication date: 2019-03-29 Source: IEC 80000-13:2008, 13-40, modified – Addition of information useful for the context of the IEV, and adaptation to the IEV rules Replaces: Internal notes: CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5:


text:
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Brain Connectivity Toolbox for Python

## Project description

# Brain Connectivity Toolbox for Python version 0.6.0

Author: Roan LaPlante <rlaplant@nmr.mgh.harvard.edu>

Tested against python 2.7 and 3.9.

## Copyright information

This program strictly observes the tenets of fundamentalist Theravada Mahasi style Buddhism. Any use of this program in violation of these aforementioned tenets or in violation of the principles described in the Visuddhimagga Sutta is strictly prohibited and punishable by extensive Mahayana style practice. By being or not being mindful of the immediate present moment sensations involved in the use of this program, you confer your acceptance of these terms and conditions.

Note that the observation of the tenets of fundamentalist Theravada Mahasi style Buddhism and the Visuddhimagga Sutta is optional as long as the terms and conditions of the GNU GPLv3+ are upheld.

## Packages used

BCTPY is written in pure python and requires only scipy and numpy. scipy is required for a couple of functions for its statistical and linear algebra packages which have some features not available in numpy alone. If you don’t have scipy, most functions that do not need scipy functionality will still work.

Note that graphs must be passed in as numpy.array rather than numpy.matrix. Other constraints/edge cases of the adjacency matrices (e.g. self-loops, negative weights) behave similarly to the matlab functions.

A small number of functions also depend on networkx. This notably includes Network-Based Statistic, a nonparametric test for differences in undirected weighted graphs from different populations. Ideally this dependency should be removed in the future.

Nosetests is used for the test suite. The test suite is not complete.

## About bctpy and other authors

BCT is a matlab toolbox with many graph theoretical measures off of which bctpy is based. I did not write BCT (apart from small bugfixes I have submitted) and a quality of life improvements that I have taken liberties to add. With few exceptions, bctpy is a direct translation of matlab code to python.

bctpy should be considered beta software, with BCT being the gold standard by comparison. I did my best to test all functionality in bctpy, but much of it is arcane math that flies over the head of this humble programmer. There are bugs lurking in bctpy, the question is not whether but how many. If you locate bugs, please consider submitting pull requests.

Many thanks to Stefan Fuertinger for his assistance tracking down a number of bugs. Stefan Fuertinger has a similar software package dealing with brain network functionality at http://research.mssm.edu/simonyanlab/analytical-tools/

Many thanks to Chris Barnes for his assistance in documenting a number of issues and facilitating a number of test cases.

Credit for writing BCT (the matlab version) goes to the following list of authors, especially Olaf Sporns and Mika Rubinov.

• Olaf Sporns

• Mikail Rubinov

• Yusuke Adachi

• Andrea Avena

• Danielle Bassett

• Richard Betzel

• Joaquin Goni

• Alexandros Goulas

• Patric Hagmann

• Christopher Honey

• Martijn van den Heuvel

• Rolf Kotter

• Jonathan Power

• Murray Shanahan

• Andrew Zalesky

In order to be a bit more compact I have removed the accreditations from the docstrings each functions. This does not in any way mean that I wish to take credit from the individual contributions. I have moved these accreditations to the credits file.

## Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

### Source Distribution

bctpy-0.6.0.tar.gz (95.7 kB view hashes)

Uploaded source

### Built Distribution

bctpy-0.6.0-py3.9.egg (198.7 kB view hashes)

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• Yesterday, 11:34
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• Yesterday, 11:28
There's no need to link to the commercial site you used. Thanks! :D
3 replies | 87 view(s)
• Yesterday, 00:26
Let's find the $p$th term. I think what I would do is set: \frac{n(n+1)}{2}=p Now solve for $n$... n(n+1)=2p
1 replies | 43 view(s)
• February 23rd, 2017, 22:15
Perhaps you meant how can we derive this formula. Let's begin with the definition of average acceleration: \overline{a}=\frac{\Delta v}{\Delta...
4 replies | 51 view(s)
• February 23rd, 2017, 20:43
I made a mistake in my above post...the IVP should be: \displaystyle \d{F}{t}=2-\frac{5F}{4(50-t)} where $F(0)=0$. So, this leads to: ...
7 replies | 104 view(s)
• February 23rd, 2017, 16:33
I would let $F(t)$ be the amount of fertilizer in the tank at time $t$. From the problem statement, we get the following IVP: ...
7 replies | 104 view(s)
• February 23rd, 2017, 14:31
I don't follow...it's already in the form we want to give us the acceleration. :D
4 replies | 51 view(s)
• February 23rd, 2017, 14:28
The kinematic formula you want is: \overline{a}=\frac{v_f^2-v_i^2}{2\Delta x}
4 replies | 51 view(s)
• February 23rd, 2017, 02:40
Our goal is to make MHB stand out as much as we can from our competitors by offering features you just don't see anywhere else. If we were to package...
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• February 23rd, 2017, 02:35
MarkFL replied to a thread Tapatalk... in Chat Room
Personally, I don't think Tapatalk is ready for vBulletin, much less sites using $\LaTeX$. From what I've gathered, many vBulletin admins refuse to...
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• February 23rd, 2017, 01:29
MarkFL replied to a thread Tapatalk... in Chat Room
I'd be happy if Tapatalk didn't lazily bypass most vBulletin PHP plugin hooks. (Giggle)
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• February 22nd, 2017, 04:08
Your solution to the given IVP isn't correct...we are given: \d{y}{x}=9x^8e^{-x^9} where y(0)=8 \int_{y(0)}^{y(x)}\,du=\int_0^x...
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• February 21st, 2017, 23:42
Hello, MHB Community! (Wave) We are pleased to announce a new method for embedding Desmos calculators in your posts, which we hope you will find...
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• February 21st, 2017, 12:24
MarkFL replied to a thread [SOLVED] 9.1.14 Use Euler's method to calculate in Calculus
Given: \d{y}{x}=f(x,y) Euler's method is the recursion: y_{n+1}\approx y_{n}+\Delta x\cdot f\left(x_n,y_n\right) Now, in the given...
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• February 19th, 2017, 11:04
MarkFL replied to a thread Hi everyone! in Introductions
Hello and welcome to MHB, Raisa! (Wave)
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• February 18th, 2017, 02:29
MarkFL replied to a thread 231.14.88 3d surface in Calculus
Multiplying through by $9+6x-8y$ and distributing the $26$, we obtain -x^2-y^2+z^2=156x-208y+234 -x^2-156x-y^2+208y+z^2=234 ...
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• February 15th, 2017, 20:29
You have two points on the graph, so you can compute the slope as follows: m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} Then, you can...
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# Is CFL an inductive load?

As far as I know, Compact Fluorescent Lamp (CFL) is an inductive load.
I understand that inductive load doesn't allow an immediate change in current. When the circuit was initially open (through open switch) then became close, the inductive load was energized. So opening again the circuit after a long period of time makes the inductive load to have enough energy to maintain its magnetic field, so voltage as well (I know it was called back emf).
I am afraid that our CFL at our bathroom will eventually find its time to break ( or unfortunately to blast and cause fire). Since it's a bathroom,the CFL is being switch on and off frequently. How do I manage to create a switch or circuit to avoid that back emf (or even reduce) which causes the low lifespan of our CFL thus preventing cause of fire (As my conclusion). I have seen in the internet about putting a flyback diode helps to prevent back emf but it is new to me so I need guidance.

So my query here is: I really don't know how to make a circuit for better switching of our CFL to prevent or reduce back emf , improve even a little bit the life span of the CFL and to avoid danger and fire. Please kindly help me. you can propose a circuit or help me to make one.

This is our CFL having 18 W, 220 VAC, 60 Hz:

Kindly help me to solve this problem to prevent any danger in our house.
By the way this can't be replace because it was preferred by our family members (yeah all of them).

dlgoff
Gold Member
I don't think there's enough induction to worry about as it uses a "switching power supply" (ballast) that's in the CFLs base.

Electronic ballasts contain a small circuit board with rectifiers, a filter capacitor and usually two switching transistors. The incoming AC current is first rectified to DC, then converted to high frequency AC by the transistors, connected as a resonant series DC to AC inverter. The resulting high frequency is applied to the lamp tube.

http://en.wikipedia.org/wiki/Compact_fluorescent_lamp

Doug Huffman
Doug Huffman
Gold Member
Your short CFL service life may be due to their need of an elevated operating temperature for efficiency (read low current).

Like my 12 y.o. 50 mpg diesel VW, I will not change while I can afford to buy replacement car parts or incandescent lamps. Incandescent lamp heat is not an inefficiency in an electrically heated home at N45° and 0°F ambient.

dlgoff and jim hardy
Averagesupernova
Gold Member
Your short CFL service life may be due to their need of an elevated operating temperature for efficiency (read low current).

Like my 12 y.o. 50 mpg diesel VW, I will not change while I can afford to buy replacement car parts or incandescent lamps. Incandescent lamp heat is not an inefficiency in an electrically heated home at N45° and 0°F ambient.
OMG finally someone who actually 'gets it'. I pointed this out to someone at a home show from an electrical cooperative who was demonstrating the efficiency of CFLs. They did not like to hear what I had to say.

davenn and Doug Huffman
Doug Huffman
Gold Member
LOL My standby lamp is a diesel powered Welsbach mantle lamp by Aladdin. It is specified at 60 We equivalent light that is white, odorless and with abundant heat. I've never had to run it long enough to estimate fuel consumption for actual heat output.

ETA More: House heat is primarily to keep pipes from freezing and plastics from cracking. We practice micro-heating with electric lap robes, mattress pad, shoulder wrap. My downstairs easy chair snuggles up to the main (read, only interior wall) electric baseboard.

When my house was built, we, my Island, produced all our electric power with big DE generators. To ensure sufficient load at night, electric heating was encouraged with subsidized heating power. I have two electric power meters, one for heat and one for utility power - lights and such.

Last edited:
jim hardy
Gold Member
Dearly Missed
Where i live CFL's are a capacitive load not an inductive one. Switching one on draws a big gulp of current.
In one room of my house it causes the touch-dimmer equipped incandescent lamps to turn off. So does switching on the computer. I think the neutral for that room's outlets is routed improperly creating a loop antenna.

If you are experiencing short life on your CFLs,
the main culprit is heat. Are they in a fixture that points down, trapping heat around the base ? Use a fixture that points up, or is ventilated.

Dont even think about using a dimmer on ordinary CFL's. It'll overheat the inrush limiter , there are reports of pyrotechnic results.

I'm with Doug - i bought a lifetime supply of 100 watt incandescents and touch dimmer modules.

NascentOxygen
Staff Emeritus
The best way to extend the life of a CFL is to replace it with a LED globe. :)

LEDs can cope with many on/off cycles. LED globes seem to have a poor power factor, but it's a low reactive power. Often a manufacturer offers the globe in two versions: dimmable and non-dimmable. The latter show slightly more lumens for a given power.

davenn
meBigGuy
Gold Member
This is off-topic, but I wonder if there are places in the US where electricity is cheaper than gas (near hydro projects, for example) to heat your house, so CFL actually causes the heating bill to go up?

As far as I know, Compact Fluorescent Lamp (CFL) is an inductive load.
I understand that inductive load doesn't allow an immediate change in current. When the circuit was initially open (through open switch) then became close, the inductive load was energized. So opening again the circuit after a long period of time makes the inductive load to have enough energy to maintain its magnetic field, so voltage as well (I know it was called back emf).
I am afraid that our CFL at our bathroom will eventually find its time to break ( or unfortunately to blast and cause fire). Since it's a bathroom,the CFL is being switch on and off frequently. How do I manage to create a switch or circuit to avoid that back emf (or even reduce) which causes the low lifespan of our CFL thus preventing cause of fire (As my conclusion). I have seen in the internet about putting a flyback diode helps to prevent back emf but it is new to me so I need guidance.

So my query here is: I really don't know how to make a circuit for better switching of our CFL to prevent or reduce back emf , improve even a little bit the life span of the CFL and to avoid danger and fire. Please kindly help me. you can propose a circuit or help me to make one.

This is our CFL having 18 W, 220 VAC, 60 Hz:View attachment 77502

Kindly help me to solve this problem to prevent any danger in our house.
By the way this can't be replace because it was preferred by our family members (yeah all of them).
Modern CFLs are electronically ballasted. Current they draw is typically heavily distorted. Displacement power factor is leading which means they present more capacitive than inductive load to the feeding network. Knowing their harmonics contaminate the network, that they are not as "green" as advertised, and die on average in service earlier than claimed by manufacturers, I don't like them at all. I don't have a single CFL bulb installed in my house.

jim hardy
Gold Member
Dearly Missed
Knowing their harmonics contaminate the network, that they are not as "green" as advertised, and die on average in service earlier than claimed by manufacturers, I don't like them at all. I don't have a single CFL bulb installed in my house.

from that Wikipedia link by Doug,

Voltage and current for a 120 V 60 Hz 30-watt compact fluorescent lamp.

I have a few of them.
One in kitchen fixture that stays on constantly. First one lasted seven years, second one a few months, third one four years and we're two years into third er, make that fourth one.
A couple others in fixtures that are hard to reach.
All my table lamps are incandescent with dimmers.

They are nice for in-the-ceiling fixtures that aren't well ventilated, because they make so much less heat therefore aren't so hard on the PVC insulation on house wiring.

I dislike their unnecessary expensive complexity, and the mercury in landfills.

Last edited:
davenn
russ_watters
Mentor
This is off-topic, but I wonder if there are places in the US where electricity is cheaper than gas (near hydro projects, for example) to heat your house, so CFL actually causes the heating bill to go up?
Probably not: with an interconnected grid, consumers don't buy power from one power plant, they buy it regionally, at retail prices.

Now, when the alternative is propane, it can start to get close.

Doug Huffman
Gold Member
I dislike their unnecessary expensive complexity, and the mercury in landfills.
Last I saw, and it has been a while, the regulatory requirements for cleaning an Hg spill as from a broken florescent bulb/tube are not trivial.

Propane is my alternate heat source and primary cooking heat source, a 500 USgal tank that I have never significantly depleted. I order it topped off when I can guess the cost the lowest, this past refill at <US$2.60/USgal. During the crunch last winter, my provider did not exceed US$5.00.USgal propane and freely extended credit to those caught short.

1000KWH heat costs US$110 by the rate sheet that I just looked at, the meter-base charge is$7.00. My winter electric bill runs about $500/mo roughly evenly divided between heat and utility. The linked wiki article is quite misleading/wrong about some aspects of use of CFLs. For instance: The use of CFLs in homes has no appreciable effect on power quality, but significant quantities of them in a large facility can have an impact. The power factor of CFLs does not significantly affect their energy-saving benefits for individual consumers, but their use in large numbers—such as in commercial applications or across millions of homes in a distribution system—could require infrastructure upgrades. In such cases, CFLs with low (below 30 percent) total harmonic distortion (THD) and power factors greater than 0.9 should be selected. This claim doesn't hold for LV and distribution parts of the network. Massive use of CFLs in domestic installations has noticable effect on power quality there. This is more expressed in LV network parts located far from HV grid and at peripheries of EES. Average Joe doesn't care about harmonics junk his electronic devices and CFLs put back in the network, won't buy more expensive CFLs with low THD. He doesn't care about possibility of installation of electrical filter(s) too. Averagesupernova Science Advisor Gold Member This is off-topic, but I wonder if there are places in the US where electricity is cheaper than gas (near hydro projects, for example) to heat your house, so CFL actually causes the heating bill to go up? http://www.efficiencymaine.com/at-home/home-energy-savings-program/heating-cost-comparison/ The above link can tell you a little bit. In my location electricity for electric heat has a sub-meter and it is$.0586/kwh. It is the cheapest heat there is right now.

mheslep
So are you all telling me that I should not mind the effect of switching (frequently) of CFL on our comfort room because switching frequently has no significant effect to CFL (which is an inductive load)? Is that what you want to tell me?

jim hardy
Gold Member
Dearly Missed
So are you all telling me that I should not mind the effect of switching (frequently) of CFL on our comfort room because switching frequently has no significant effect to CFL (which is an inductive load)? Is that what you want to tell me?

well, it's a capacitive not an inductive load.
In practice, switching it ON does apply a harsh transient called "inrush" to the electronic components.
If it's well designed and built it should withstand that transient repeatedly with no significant effect. That's a function of who built it. You get what you pay for.
Switching it OFF is by contrast a gentle transition.

anorlunda
Staff Emeritus
This is off-topic, but I wonder if there are places in the US where electricity is cheaper than gas (near hydro projects, for example) to heat your house, so CFL actually causes the heating bill to go up?

22 municipalities in New York State were grandfathered by law to buy Niagara Falls power at 2 cents/kwH, while others in the same state paid as much as 29 cents/kwH. Politics need not be rational, nor fair.

My info is 10 years old. I don't know if things have changed since then.

jim hardy
Gold Member
Dearly Missed
Niagara Falls is an interesting area.
Here's a history of the power project.
http://www.niagarafrontier.com/power.html#Nfpower

As recently as 1970's industries around the Falls could buy power for 0.2 cent per kwh.
There were no transmission costs to be covered so everybody thought it fair enough.
When other parts of the state cried "foul" NYPA took over and levelled rates.
That made much of the local industry no longer economically viable.
Carborundum for example moved its factory from Niagara Falls to Brazil.

So, what's "fair" ?

Last edited:
mheslep
Gold Member
This is off-topic, but I wonder if there are places in the US where electricity is cheaper than gas (near hydro projects, for example) to heat your house, so CFL actually causes the heating bill to go up?

Probably not: with an interconnected grid, consumers don't buy power from one power plant, they buy it regionally, at retail prices.

Now, when the alternative is propane, it can start to get close.

Russ - are you comparing gas heat to electric IR heating, or to electric heat pumps?

Edit: I see AverageSupernova answered earlier with:
http://www.efficiencymaine.com/at-home/home-energy-savings-program/heating-cost-comparison/

Last edited:
Averagesupernova
Gold Member
I plugged in $.0586 per KWH into the link I provided for the baseboard electric heat. This is the sub-metered rate for electricity on heating and cooling systems in my area. I then dialed the other numbers around and came up with the following: Propane energy star furnace needs to have propane drop to$1.04 a gallon to compete with electricity.
Natural gas energy star furnace needs to have natural gas drop to $1.16 to compete with electricity. Oil fired energy star furnace needs to have fuel oil drop to$1.41 to compete with electricity.
-
This is figuring resistance heat. Using geothermal and air to air heat pumps I came up with the following:
To compete with fossil fuels at the above prices (which are severely cheaper than what people are paying now) a geothermal heat pump could have electricity go up to around $.19 and still compete. The air to air heat pump could have electricity go to about$.17 and still compete.
-
My parents house is heated with fuel oil. They paid $2.25 per gallon on their last fill. Going by the chart electricity can go to$.093 with resistance heating, which is what incandescents are, and be competitive with oil at $2.25 a gallon. So if your main electric rate is less than 9 cents compact florescent and LED bulbs are losing you money in the winter at fossil fuel prices that fall in line with$2.25 a gallon oil.
-
Edit: Actually the parents have a dual fuel setup. They have an air to air heat pump with backup being fuel oil. And their electric rate is \$.0586 per kwh on heating and cooling.

Last edited:
jim hardy
Here's an article written by somebody who dislikes CFL lamps as much as i do.
http://www.rense.com/general96/214law.html
I had joined "dislikers club" even before production of incadescent bulbs was banned. To certain extent I tolerate FL with HPF designed magnetic ballasts, but I never liked CFLs.
Niagara Falls is an interesting area.
Here's a history of the power project.
http://www.niagarafrontier.com/power.html#Nfpower
First Niagara Falls generators were 2 phase, 25 Hz machines. And such was power transmission too. It was much later when 3 phase generation/transmission of electrical power was adopted. Interestingly enough, frequencies like 25 Hz or 16.67 Hz can be found even today in some countries (used mostly to power railways)

dlgoff


text:
# Activity

Study Groups

Autumn 2015 – Ringel-Hall algebras
Autumn 2015 – Auslander-Reiten Theory
Spring 2015 – Cellular algebras
Autumn 2014 – Quasi-hereditary algebras and their generalizations
Autumn 2014 – Algebraic groups (Springer)
Autumn 2013 – Representation Theory and Complex Geometry (Chriss & Ginzburg)
Autumn 2013 /Spring 2014 – Homological Algebra (Wiebel)
Autumn 2013 – Noncommutative algebra (Lam)

Talks

March 2016 – BLOC at BMC Bristol – Properly stratified quotients of quiver Hecke algebras
March 2016 – Leeds algebra seminar – Properly stratified quotients of quiver Hecke algebras
February 2016 – Cambridge junior algebra seminar – Properly stratified quotients of quiver Hecke algebras
November 2014 – Queen Mary algebra seminar – Properly stratified quotients of Khovanov-Lauda-Rouquier algebras
November 2014 – UEA pure maths research seminar – Properly stratified quotients of Khovanov-Lauda-Rouquier algebras

PGR Seminars

October 2015 – Voting, elections and representation theory of the symmetric group

Conferences

April 2015 – Joint BMC & BAMC – University of Cambridge, UK
July 2014 – Representations of symmetric groups, Hecke algebras and KLR algebras – University of Birmingham, UK
October 2013 – Special 63rd BLOC meeting – University of Oxford, UK
August 2013 – Kent Algebra Days – University of Kent, UK

Since 2012 I have regularly attended BLOC conferences. You can find details on past and upcoming BLOC events here.

“Summer” schools

June 2015 – Representation Theory – Universidade de Coimbra, Portugal
August 2014 – Algebraic Lie Theory and Representation Theory – University of Glasgow, UK
July 2014 – Kent Algebra Days Young Researchers – University of Kent, Canterbury, UK
June 2014 – Quiver Hecke Algebras – d’Etudes Scientifiques de Cargese, Corsica, France
-I will give the fifth lecture titled Quiver Hecke Algebras.
August 2013 – Category $\mathcal{O}$ – University of Frieburg, Germany
March 2013 – Soergel bimodules and Kazhdan-Lusztig conjectures – Centre for Quantum Geometry and Moduli Spaces, Aarhus University, Denmark

Teaching

This semester (Spring 2016) I am marking for Cryptography.

In the past I have marked and taken seminars for Calculus and Probability, Linear Algebra, Algebra, Combinatorics, Point Set Topology, Analysis, Fermat’s Last Theorem, Theory of Finite Groups and Representation Theory. I have also given revision lectures for Linear Algebra and Representation Theory. I have been involved in the pure maths drop-in sessions since their inception, and have jointly given lectures on how to give a mathematical presentation.

I initiated the inclusion of external speakers are the PGR seminar series and organised that seroed at UEA in the Autumn term of 2014. Details of the talks can be found here.
I was a member of the Equality and Diversity committee, and am pleased to announce that the department was recently granted an Athena Swan bronze award.
I was a member of the Green Impact steering committee.

Outreach

February 2016
– The mathematics of a zombie apocalypse (Yr 9) – Highgate School (North London)

October 2015
– Hunting for Platonic solids (Yr 9) – UEA

September 2015
– Modelling a zombie apocalypse (Yr 7) – UEA

April 2015
– Fun with shapes – Highgate School (North London)

March 2015
– Explore Maths (Yr10): Hunting for Platonic solids – UEA

Aug 2014
– Summer School (Yr10): Hunting for Platonic solids – UEA

July 2014
Nrich Day (Yr12): Hunting for Platonic solids – UEA
Summer School (Yr9): Zombie apocalypse: modelling diseases – UEA

May 2014
– The mathematics of a zombie apocalypse– Highgate School (North London)

April 2014
Explore Maths (Yr10): Hunting for Platonic solids – UEA
Explore Maths (Yr10): Infectious mathematics – UEA

Abstract for outreach titles:
Hunting for Platonic solids Platonic solids are shapes whose beauty has provided inspiration to mathematicians for millennia. Pythagoras discovered them, Plato based his philosophy on them and Keplar even thought they could model the solar system, but what are they and how many are there? Discover the answer to these questions (and more) by building shapes from polydrons.
Infectious mathematics Contagious diseases survive and spread by infecting new hosts. In many situations it is beneficial to understand how a disease spreads through a population, and therefore answer questions about how quickly it spreads, and whether it will spread to the whole population. Using a series of interactive games we will create and improving a model for the spread of a disease.

Fun facts

Mathematics has caused me to travel approximately 7572 Miles. (Car: 647M, Bus 344M, Train 3125M, Plane 3456M)

A useful website for calculating the distance of a flight: www.webflyer.com/travel/mileage_calculator/


text:
Home » Uncategorized » On a limit with summation

# On a limit with summation

Let . Prove that

Solution

Let us begin with the simple observation that

Now, here comes a handy lemma.

Lemma: Let be a differentiable function with continuous derivative. It holds that

Proof: The derivation of the theorem follows from application of MVT in the interval .

Hence the limit follows to be .

Note: Applying Euler  – MacLaurin we have


text:
Use Laplace Approximations to improve linear approximations to the posterior

Description

The approximation provided by linear.bayes can be improved by performing Laplace approximations. This function is a development version of a wrapper to do that for all of the returned by linear.bayes.

Usage

adjust.linear.bayes(lbo, ana.obj=lbo$call$ana.obj, ...)

Arguments

 lbo The object returned by linear.bayes ana.obj The analysis.object used to create lbo. This need not be given explicitly, iff the original version is in the search path. ... currently unused

Value

A list of class "adjust.linear.bayes" containing:

 odds A vector, typically of length k giving the odds for models of size 1, 2, ..., k under a uniform posterior relative to a model with no genes. loc.posterior The marginal posterior probabilities by locus coefficients The marginal posterior means of the coefficients one.gene.adj Results of fits for one gene models n.gene.adj Results of fits for modles with more than one gene call the call to adjust.linear.bayes

Note

For large linear.bayes objects invloving many gene models, this can require a very long time to run.

Author(s)

Charles C. Berry cberry@ucsd.edu

linear.bayes


text:
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# A number of scientists’ salaries were reported; physicists’

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A number of scientists’ salaries were reported; physicists’ [#permalink]  30 Jul 2018, 09:09
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A number of scientists’ salaries were reported; physicists’ salaries clustered around a mean of $100,000 and biologists’ clustered around a mean of$70,000. Which of the following statements could be true, according to the graph above?

Indicate all such statements.

A. Some biologists earn more than some physicists.
B. Both biologists’ and physicists’ salaries are normally distributed.
C. The range of salaries is greater than $150,000. [Reveal] Spoiler: OA _________________ Sandy If you found this post useful, please let me know by pressing the Kudos Button Try our free Online GRE Test Intern Joined: 21 Jun 2018 Posts: 35 Followers: 0 Kudos [?]: 5 [0], given: 11 Re: A number of scientists’ salaries were reported; physicists’ [#permalink] 05 Aug 2018, 03:51 sandy wrote: Attachment: Capture.PNG A number of scientists’ salaries were reported; physicists’ salaries clustered around a mean of$100,000 and biologists’ clustered around a mean of $70,000. Which of the following statements could be true, according to the graph above? Indicate all such statements. A. Some biologists earn more than some physicists. B. Both biologists’ and physicists’ salaries are normally distributed. C. The range of salaries is greater than$150,000.

Can you please explain why C is correct?
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Re: A number of scientists’ salaries were reported; physicists’ [#permalink]  10 Aug 2018, 07:16
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Because it could be correct. The answer is not asking for must be correct . Its asking for could be
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Re: A number of scientists’ salaries were reported; physicists’ [#permalink]  12 Aug 2018, 09:49
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A number of scientists’ salaries were reported; physicists’ salaries clustered around a mean of $100,000 and biologists’ clustered around a mean of$70,000. Which of the following statements could be true, according to the graph above?

Indicate all such statements.

A. Some biologists earn more than some physicists.
B. Both biologists’ and physicists’ salaries are normally distributed.
C. The range of salaries is greater than \$150,000.

Could you please explain how (A) is correct? Since the curve of biologists' salary begin only at the end of physicists' salary, wouldn't the physicists as a collective have higher salaries than all biologists under study?
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Re: A number of scientists’ salaries were reported; physicists’ [#permalink]  12 Aug 2018, 20:51
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Nowhere in the question it is mentioned that physicists' curve begin where the biologists' curve ends. The two curve collides at the right bottom of biologists' curve, so it's possible that some biologists at the bottom may have higher salary then physicists at the bottom of the curve.The questions ask for the possible conditions which might be true and not for ones which must be.
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Re: A number of scientists’ salaries were reported; physicists’ [#permalink]  13 Aug 2018, 03:11
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khrystal wrote:
Nowhere in the question it is mentioned that physicists' curve begin where the biologists' curve ends. The two curve collides at the right bottom of biologists' curve, so it's possible that some biologists at the bottom may have higher salary then physicists at the bottom of the curve.The questions ask for the possible conditions which might be true and not for ones which must be.

Yeah all scientists are in the two peak distribution as shown above. Some biologists would have higher salaries than physicists.
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Re: A number of scientists’ salaries were reported; physicists’   [#permalink] 13 Aug 2018, 03:11
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# Direction cosines and direction ratios of a line joining two points

Let a line AB in 3D space make angles α, β, γ respectively with the +ve direction of coordinate axes X, Y, Z. Therefore, we express cosα, cosβ, cosγ as direction cosines of the line AB in the 3D space. Clearly; direction cosines fix the direction cosines of a line in space. Also, parallel lines have the same direction cosines. Direction cosines are denoted by l, m, n respectively. i.e. l = cosα, m = cosβ and n = cosγ. The direction of a line cannot be fixed in space by knowing anyone or any two angles.

If a line in space makes angles α, β, γ respectively with the +ve direction of X, Y, Z axes then we can assume that the line will make angles π – α, π – β, π – γ with the -ve direction of axes. Therefore, the direction cosines can also be written as cos π -α, cos π -β, cos π –γ. Thus, direction cosines of the same line may also be taken as – cosα, –cosβ, –cosγ.

Three numbers a, b, c proportional to direction cosine l, m, n of a line in space. These numbers are called direction ratios OR direction numbers of the line. Therefore, the direction cosines of a line will be fixed but not the direction ratios:

$\frac{a}{l}=\frac{b}{m}=\frac{c}{n}$

Let direction cosine of any line in space be l, m, n and d.r.’s are a:b:c.Let P(x,y,z) be any point on the line and PM is perpendicular from P on X-axis. Then, in right triangle PMO,

We can see that $\cos \alpha =\frac{OM}{OP}=\frac{x}{r}$ . In this case x = OM and r = OP or $l=\frac{x}{r}$

Similarly, we take the perpendicular point P on y and axis to obtain: $m=\frac{y}{r}; n=\frac{z}{r}$

Hence, we conclude that

$l^{2}+m^{2}+n^{2}=(\frac{x}{r})^{2}+(\frac{y}{r})^{2}+(\frac{z}{r})^{2}$

$=\frac{x^{2}+y^{2}+z^{2}}{r^{2}}=(\frac{r}{r})^{2}=1$

$l^{2}+m^{2}+n^{2}=1$

Recall that $\frac{a}{l}=\frac{b}{m}=\frac{c}{n}$

Then we can elaborate by the properties of ratio and proportion that:

$\frac{a}{l}=\frac{b}{m}=\frac{c}{n}=\frac{\sqrt{a^{2}+b^{2}+c^{2}}}{\sqrt{l^{2}+m^{2}+n^{2}}}=\frac{\sqrt{a^{2}+b^{2}+c^{2}}}{1}$

Hence we can conclude that:

$l=\frac{a}{\sqrt{a^{2}+b^{2}+c^{2}}}$

$m=\frac{b}{\sqrt{a^{2}+b^{2}+c^{2}}}$

$n=\frac{c}{\sqrt{a^{2}+b^{2}+c^{2}}}$

To find direction ratio of a line if its two points are known:

Let AB be a line that is inclined at angles α, β, γ with positive x, y, z-axis at points A (x1, y1, z1) and B at (x2, y2, z2) to form direction ratios. Line AB makes angle γ with the z-axis which is a part of a right angle triangle ∆ARB where,

$n=\cos \gamma =\frac{BR}{AB}=\frac{z_{2}-z_{1}}{AB}$

Also,

$l=\cos \alpha =\frac{x_{2}-x_{1}}{AB}$

$m=\cos \beta =\frac{y_{2}-y_{1}}{AB}$

Therefore, l:m:n = $\frac{x_{2}-x_{1}}{AB}, \frac{y_{2}-y_{1}}{AB},\frac{z_{2}-z_{1}}{AB}$= $(x_{2}-x_{1}), (y_{2}-y_{1}), (z_{2}-z_{1})$


text:
Pages

A quadratic expression can be written in three different ways:

General Form

ax^2 + bx + c

Intercept Form

a(x - p)(x - q)

Vertex Form

a(x - h)^2 + k
Each of the above forms has its own significance, which is discussed in each form's separate post.


text:
# How/Why does voltage reflect?

I'm trying to understand antenna theory again, and I'm again stumped by the concept of VSW (voltage standing waves). I understand standing waves, I remember these from a physics clases, however I do not really understand how voltage can be a wave, and how it reflects.

From my understanding of voltage it is really hard to understand how it can reflect.

A voltage is the difference in electrical potential energy (per unit charge) between two places. This electrical potential energy (per unit charge) difference describes the force on that unit charge (due to the electric fields), and the distance this charge will travel.

For example, with an electrical potential energy (per unit charge) difference of $10\, \mathrm{V}$ or $10\, \mathrm{J}/\mathrm{Q}$, an electron at the higher potential will travel to the lower potential. If the distance between these two potentials is $2\, \mathrm{m}$, the force on the electron will be $5\, \mathrm{N}$, as it travels from one potential to the other. (Only if the electric field is constant between the two potentials. If it is not, the integral of the force across the $2\, \mathrm{m}$ will still equal $10$, however the force will vary at different distances)

Voltage is just a made up concept to help explain the forces that charged particles experience. It isn't a real thing that can be reflected. So what is being reflected? I'm guessing it is the electric field, as this has an actual propagation speed, and even though the electric field is also a made up concept to describe the force a charged particle will experience at that point in the field, it is easier to imagine this being reflected.

So can someone please explain to me how this all ties together? How does an electric field propagate through a conductor? Do the vectors in this vector field change direction when there is a bend in the wire, and why do they do this? Why wouldn't the electric field escape outside of the conductor? And how does an electric field (or voltage) reflect at a short?

• It is electromagnetic waves that propagate along a transmission line and reflect (at discontinuities). When there is both a forward and reflected wave propagating along the line, the result is a standing wave. – Alfred Centauri Nov 20 '13 at 3:21
• Perhaps this is best asked as a question but isn't a voltage induced by a signal a "pressure wave" of electrons much the same way sound is a pressure wave of air molecules? Bunch up the electrons on one end of a conductor and the higher voltage will push electrons nearby and cause a traveling pressure wave in the electric field as electrons being bunched up together. – Brandon Enright Nov 20 '13 at 5:07
• I wrote an answer on EE.SE that might partially answer your question. Especially read the last paragraph. electronics.stackexchange.com/questions/93232/… – The Photon Dec 20 '13 at 19:29
• @BrandonEnright, that's not a good description. An EM wave propagates with or without electrons present. For example radio waves or light from the sun can travel through vacuum, where no electrons are present to form a "pressure wave". – The Photon Dec 20 '13 at 19:32
• @ThePhoton my comment was obviously imprecise and limited to an electric potential propagating in a conductor only. – Brandon Enright Dec 20 '13 at 20:29

Your query is valid: How is voltage a 'wave' that reflects and creates standing waves? Well, the answer is quite simple when you stop and think about it. All signals travelling across transmission lines are merely electromagnetic waves. Now these lines are commonly driven by voltage sources, hence they are 'voltage waves'. This makes perfect sense: If a simple circuit is driven by a sinusoidal voltage source, you expect that the resultant voltage(amplitude) will vary like the sine wave.

If you extend your thinking a bit, you will see that the same question can apply to any circuit with a sinusoidal voltage source. We don't usually apply the concept of 'waves' to a simple circuit (the concept is only useful for the analysis of TLs since reflections can be a bit of nuisance and at radio frequencies are important), but its present. Ever heard of LC circuits? These circuits are basically resonators where the energy from the source (a voltage source) keeps on changing forms. But how can that happen, if the source is a 'voltage'? This analogy would help you understand that all signals are just electromagnetic waves. The reason we call them 'voltage waves' in RF engineering is simply because at those frequencies the wavelike behavior of the source helps us in the analysis/design of the circuit (through the use of matching circuits, tuning circuits etc). Hope this answers your query. Feel free to inquire more.

OK it seems you have a few more queries. Let's get to them.

1) Yes, an EM wave doesn't require any medium to travel (that's how antennas in space work). However, 'containing' an EM wave inside a conductor isn't a big deal. Its a simple matter of creating a potential difference and letting it do all the work. You could, ofcourse, ask the same question when you connect a simple wire to a voltage source. The explanation remains the same.

2) Now why does the wave reflect at an open circuit? The answer to this question you will encounter in your course, but I will give a simple version of it here. At the open circuit point the current in the line is zero (by the definition of an open circuit). Since charge continues to arrive at the end of the line through the incident current, but no current is leaving the line, then conservation of electric charge requires that there must be an equal and opposite current into the end of the line. Essentially, this is Kirchhoff's current law in operation. This equal and opposite current is the reflected current and by Ohm's law, it creates a reflected voltage wave.

3) What Brandon Enright posted about is the tried and tested, age-old analogy between electricity/electronics and hydraulics, which every engineer has used at some point. It is perfectly correct. Please refer this link (http://en.wikipedia.org/wiki/Hydraulic_analogy) to further understand it and relate it to your query.

• Thank you sam29! That answer was very helpful and is much appreciated. I just have a few questions about your answer, if you don't mind answering: – Blue7 Nov 20 '13 at 12:15
• 1)You say "all signals traveling across transmission lines are merely electromagnetic waves". I thought that EM waves do not need a medium to travel through, so how are they contained inside the transmission line? – Blue7 Nov 20 '13 at 12:17
• 2)Say you have a source that produces an alternating potential, when it is at the higher potential, a positive electric field propagates down the transmission line, and when it is at the lower potential a negative electric field propagates down the transmission line. These fields propagate at the speed of light. the transmission line is an open circuit, so the electric field will reflect, and superimpose with the incident wave. But why does this wave reflect, and what happens when this reflected wave reaches the source? – Blue7 Nov 20 '13 at 12:18
• 3) And finally, is Brandon Enright definitely correct when he says the signal traveling down the wire is a "pressure wave" of electrons, much like sound is a "pressure wave" of air molecules? I've heard someone say this before but I can't find any sources on the internet to verify this. How true is this description? And can you please explain how these propagating electric fields and "pressure waves" of electrons are related to each other? Thanks! – Blue7 Nov 20 '13 at 12:23


text:
Volume 360 - ALPS 2019 An Alpine LHC Physics Summit (ALPS2019) - Flavour physics
B-physics anomalies, fluctuations and patterns: a status report
S. Descotes-genon
Full text: pdf
Published on: February 08, 2021
Abstract
I review the current status of the $B$ anomalies in $b\to c\ell\bar\nu_\ell$ and $b\to s\ell\ell$ transitions. After recalling the experimental situation in each case, I discuss the elements of the Standard Model (SM) predictions and the patterns of New Physics arising in model-independent analyses, before discussing some of the models beyond the SM proposed to explain these patterns.
DOI: https://doi.org/10.22323/1.360.0016
How to cite

Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.

Open Access


text:
New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education

Analytic Number Theory: A Tribute to Gauss and Dirichlet
Edited by: William Duke, University of California Los Angeles, CA, and Yuri Tschinkel, Courant Institute - New York University, NY
A co-publication of the AMS and Clay Mathematics Institute.
 SEARCH THIS BOOK:
Clay Mathematics Proceedings
2007; 256 pp; softcover
Volume: 7
ISBN-10: 0-8218-4307-9
ISBN-13: 978-0-8218-4307-9
List Price: US$50 Member Price: US$40
Order Code: CMIP/7

Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Göttingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet.

The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet. Among the topics are the distribution of primes (long arithmetic progressions of primes and small gaps between primes), class groups of binary quadratic forms, various aspects of the theory of $$L$$-functions, the theory of modular forms, and the study of rational and integral solutions to polynomial equations in several variables.

Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Graduate students and research mathematicians interested in number theory.

• J. Elstrodt -- The life and work of Gustav Lejeune Dirichlet (1805-1859)
• T. D. Browning -- An overview of Manin's conjecture for del Pezzo surfaces
• J. Brüdern and T. D. Wooley -- The density of integral solutions for pairs of diagonal cubic equations
• A. Diaconu and D. Goldfeld -- Second moments of $$GL_2$$ automorphic $$L$$-functions
• J. Funke -- CM points and weight 3/2 modular forms
• D. A. Goldston, J. Pintz, and C. Y. Yıldırım -- The path to recent progress on small gaps between primes
• A. Granville and K. Soundararajan -- Negative values of truncations to $$L(1,\chi)$$
• B. Green -- Long arithmetic progressions of primes
• P. Michel and A. Venkatesh -- Heegner points and non-vanishing of Rankin/Selberg $$L$$-functions
• K. Ono -- Singular moduli generating functions for modular curves and surfaces
• P. Salberger -- Rational points of bounded height on threefolds
• P. Sarnak -- Reciprocal geodesics
• K. Soundararajan -- The fourth moment of Dirichlet $$L$$-functions
• H. M. Stark -- The Gauss class-number problems


text:
# Message from NASA Astrophysics Division Director, July 2014

By Paul Hertz, Director, NASA Astrophysics Division

July 2014

As we reach the end of the fiscal year, it is time to reflect on our achievements and shortcomings, and plan for challenges ahead. We have been extremely fortunate that our space-based missions, both large and small, have continued to make headlines with spectacular scientific discoveries that capture the mind of the public. We have learned more about the way the universe works, birth of stars and galaxies, and have made great strides in discovering and understanding exoplanets.

As I described during the NASA Town Hall at the American Astronomical Society meeting in Boston on June 2, 2014, we have made progress toward addressing the priorities of the 2010 Decadal Survey for Astronomy and Astrophysics. The appropriation that NASA Astrophysics received for Fiscal Year (FY) 2014 and the Administration’s FY 2015 budget request both support our plans for continued progress. The progress we are making toward the major recommendations of the 2010 Decadal Survey includes:

• A goal of the Astrophysics Division is to be prepared to start a new strategic NASA Astrophysics mission to follow the James Web Space Telescope (JWST) as soon as funding becomes available. Preformulation and focused technology development for a 2.4-meter version of the Wide-Field Infrared Survey Telescope (WFIRST), a mission concept referred to as the Astrophysics Focused Telescope Assets (AFTA), are underway. NASA received $56 million in directed funding for in FY 2014 for WFIRST/AFTA to continue preformulation activities and technology development. A recent National Research Council (NRC) study on WFIRST/AFTA offers a positive view of WFIRST/AFTA in the context of the Decadal Survey with concerns about technology and cost risks. The Administration’s FY15 budget request supports an agency/administration decision for formulation of WFIRST/AFTA to begin no earlier than FY 2017, should funding be available. • A new Research Opportunities in Space and Earth Sciences (ROSES) element, WFIRST Preparatory Science, was announced on April 21, with a goal to bridge from basic theory to observational modeling for WFIRST/AFTA. Investigators selected will coordinate efforts with the WFIRST Study Office and the WFIRST/AFTA Science Definition Team. • The Administration’s FY 2015 budget request includes augmentation to the Explorer program to enable more frequent flight opportunities, including a planned Small Explorers Mission (SMEX) Announcement of Opportunity (AO) later this year (see the community announcement at http://explorers.larc.nasa.gov/APSMEX/) and a Medium Class Explorers Mission (MIDEX) around 2017. • Strategic technology investments are being made and partnerships are being discussed with the European Space Agency (ESA) in their gravitational wave and X-ray observatories. • A Dear Colleague Letter was issued on June 30, 2014, soliciting applications and nominations for individuals affiliated with U.S. institutions to participate in the ESA Science Study Team for the recently selected mission concept, "Advanced Telescope for High-ENergy Astrophysics" (ATHENA). • Strategic technology investments are being made to advance the medium scale programs including technology for exoplanet missions and technology for detection of polarization of the cosmic microwave background. • Modest augmentations have been made to small programs. The FY 2014 appropriation for NASA provides$658 million for JWST and $668 million for the rest of NASA astrophysics. The FY 2015 Administration’s budget request would provide$645 million for JWST and \$607 million for the rest of NASA astrophysics. Both budgets support the continued development of JWST on plan toward its launch in 2018, and both budgets include funding for continued preformulation of WFIRST as described above. Both budgets also include funding for several new missions including the Transiting Exoplanet Survey Satellite (TESS), the next Astrophysics Explorer mission, the Neutron Star Interior Explorer (NICER), the next Astrophysics Explorer Mission of Opportunity, and the NASA contribution to ESA's Euclid mission.

The Administration’s FY 2015 budget proposes to place SOFIA into storage by FY 2015 unless partners are able to support the U.S. portion of SOFIA costs. The NASA appropriation subcommittees in both houses of Congress, however, have proposed continued funding for SOFIA at a level sufficient to continue operations. NASA has continued to conduct the SOFIA program as planned during FY 2014.

Other program highlights since my last Newsletter include:

• SOFIA formally entered the Operations Phase in May. Second generation instruments, HAWC+ (U.S.; far-infrared camera), and upGREAT (German; heterodyne spectrometer) are under development.
• Astrophysics research funding remains flat, retaining the growth realized since the Decadal Survey, with the success rate of proposals hovering between 15-24 percent. This is caused by a sharp increase in the number of proposals received.
• A Senior Review of operating missions was conducted in April. Other than the Spitzer mission, all others were approved for continued operation. The reactivated Near-Earth Objects Wide-field Infrared Survey Explorer (NEOWISE-R) data analysis proposal, MaxWISE, was not approved for funding. A full report of the Senior Review may be found at http://science.nasa.gov/astrophysics/2014-senior-review-operating-missions/
• In July, the Science Mission Directorate made the decision to extend Spitzer operations for the next two years. The Spitzer observatory is an important resource for on-going infrared observations for research programs across the Science Mission Directorate, and, subject to the availability of Congressional appropriations in FY 2015, it will be continued.
• Astrophysics approved some funds for education activities in FY2014 and has continued a limited number of high impact activities.

Major activities planned for FY 2015 include confirmation of the Transiting Exoplanet Survey Satellite (TESS) Explorer mission, launch of the International Space Station- Cosmic Ray Energetics and Mass (ISS-CREAM) experiment to the Space Station, Step 1 selection of the next Small Astrophysics Explorer and Explorer Mission of Opportunity Phase A studies, launch of ESA’s Laser Interferometer Space Antenna (LISA) Pathfinder with NASA’s Space Technology 7 (ST-7) disturbance reduction system, completion of the WFIRST/AFTA science definition team report, conduct of the Astrophysics Archives Senior Review, start of the NRC Mid-Decade Review, and celebration of 25 years of operation of the Hubble Space Telescope. All Astrophysics programs flow from the recently completed NASA 2014 Science Plan, which is available at http://science.nasa.gov/about-us/science-strategy/.

My entire presentation to the American Astronomical Society meeting is available at http://science.nasa.gov/astrophysics/documents/.

Paul Hertz
Director, Astrophysics Division
NASA Science Mission Directorate


text:
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# Biology 2015

## Educators

JA
+ 4 more educators

### Problem 1

For questions 1–4, match each stage of the cell cycle to its correct description.
Key:
$\begin{array}{ll}{\text { a. } G_{1} \text { stage }} & {\text { b. S stage }} \\ {\text { c. } G_{2} \text { stage }} & {\text { d. } M(\text { mitotic }) \text { stage }}\end{array}$

At the end of this stage, each chromosome consists of two attached chromatids.

Eric T.

### Problem 2

For questions , match each stage of the cell cycle to its correct description.
Key:
$\begin{array}{ll}{\text { a. } G_{1} \text { stage }} & {\text { b. S stage }} \\ {\text { c. } G_{2} \text { stage }} & {\text { d. } M(\text { mitotic }) \text { stage }}\end{array}$

During this stage, daughter chromosomes are distributed to two daughter nuclei.

Nalvi D.

### Problem 3

For questions , match each stage of the cell cycle to its correct description.
Key:
$\begin{array}{ll}{\text { a. } G_{1} \text { stage }} & {\text { b. S stage }} \\ {\text { c. } G_{2} \text { stage }} & {\text { d. } M(\text { mitotic }) \text { stage }}\end{array}$

The cell doubles its organelles and accumulates the materials needed for DNA synthesis.

JA
Jamelia A.

### Problem 4

For questions , match each stage of the cell cycle to its correct description.
Key:
$\begin{array}{ll}{\text { a. } G_{1} \text { stage }} & {\text { b. S stage }} \\ {\text { c. } G_{2} \text { stage }} & {\text { d. } M(\text { mitotic }) \text { stage }}\end{array}$

The cell synthesizes the proteins needed for cell division.

Nalvi D.

### Problem 5

Which is not true of the cell cycle?

a. The cell cycle is controlled by internal/external signals.
b. Cyclin is a signaling molcule that increases and decreases as the cycle continues.
c. DNA damage can stop the cell cycle at the G1 checkpoint.
d. Apoptosis occurs frequently during the cell cycle.

Alexander C.

### Problem 6

The diploid number of chromosomes

a. is the 2n number.
b. is in a parent cell and therefore in the two daughter cells following mitosis.
c. varies according to the particular organism.
d. is present in most somatic cells.
e. All of these are correct.

Nalvi D.

### Problem 7

The form of DNA that contains genes that are actively being transcribed is called

a. histones.
b. telomeres.
c. heterochromatin.
d. euchromatin.

Alyssa M.

### Problem 8

Histones are involved in

a. regulating the checkpoints of the cell cycle.
b. lengthening the ends of the telomeres.
c. compacting the DNA molecule.
d. cytokinesis.

Nalvi D.

### Problem 9

At the metaphase plate during metaphase of mitosis, there are

a. single chromosomes.
b. duplicated chromosomes.
c. G1 stage chromosomes.
d. always 23 chromosomes

Bryan L.

### Problem 10

During which mitotic phases are duplicated chromosomes present?

a. all but telophase
b. prophase and anaphase
c. all but anaphase and telophase
d. only during metaphase at the metaphase plate
e. Both a and b are correct.

Nalvi D.

### Problem 11

Which of these is paired incorrectly?

a. prometaphase - the kinetochores become attached to spindle fibers
b. anaphase- daughter chromosomes migrate toward spindle poles
c. prophase - the nucleolus disappears and the nuclear envelope disintegrates
d. metaphase - the chromosomes are aligned in the metaphase plate
e. telophase - a resting phase between cell division cycles

KA
Kemi A.

### Problem 12

Which of the following is not characteristic of cancer cells?

a. Cancer cells often undergo angiogenesis.
b. Cancer cells tend to be nonspecialized.
c. Cancer cells undergo apoptosis.
d. Cancer cells often have abnormal nuclei.
e. Cancer cells can metastasize.

Nalvi D.

### Problem 13

Which of the following statements is true?

a. Proto-oncogenes cause a loss of control of the cell cycle.
b. The products of oncogenes may inhibit the cell cycle.
c. Tumor suppressor gene products inhibit the cell cycle.
d. A mutation in a tumor suppressor gene may inhibit the cell cycle.

Bryan L.

### Problem 14

In contrast to a eukaryotic chromosome, a prokaryotic chromosome

a. is shorter and fatter.
b. has a single loop of DNA.
c. never replicates.
d. contains many histones.
e. All of these are correct.

Nalvi D.