We came across the more general form of faradays law in my EM lecture:  $\oint E \cdot \,dl=-\frac{\partial}{\partial t}(\int B \cdot dA)$  Pretty sure this is me misunderstanding magnetic fields in circuit theory, but in the case of a DC circuit, B is constant and so the rhs of the equation is 0, which gives KVL, the sum of the potential differences in a closed loop = 0. If the currents are varying, so will the magnetic fields they generate. In which case I can't see why in AC circuits KVL holds as the RHS no longer = 0. Can someone explain where my  reasoning has gone wrong.  Edit:  I am more specifically asking where my reasoning has gone wrong. I am already aware that it is valid under ideal circuit theory as an approximation to what really happens.
I'm having some difficulty with understanding why KVL (Kirchhoff voltage law) is valid when considering an AC circuit. I mean, the system is by definition not in steady state, right? That in turn means that the change in current causes a change in the magnetic field, which is manifested within the electric potential. I realize the potential is still defined and thus a line integral over a crossed curve of ALL of it's component should be zero.   However, what I often see (for, say, RLC circuits with an AC emf) is total disregard to the time varying components of the electric potential. Only the emf of the different components are considered and their sum is said to be zero. How can that be? What about the "second" part of the potentials?
Detecting EOF in C++ from a file redirected to STDIN There's an election going on. What's happening and how does it work? Rigid body simulation not interacting with objects that have an array modifier I am trying to write a condition into a SQL WHERE clause that forces the column comparison to a variable to be compared in lowercase. However the addExpression function isn't accomplishing this (since that is putting the expression in the field selection, not the where clause.  Here is what I have tried:  $category = 'mobile wifi'; $query = db_select('taxonomy_term_data', 'ttd')     -&gt;fields('ttd', array('tid')); $query-&gt;innerJoin('taxonomy_vocabulary', 'tv', 'ttd.vid = tv.vid'); $query-&gt;addExpression("LOWER(ttd.name) = $category"); $result = $query-&gt;condition('machine_name', 'images_cat', '=')     -&gt;execute()     -&gt;fetchAssoc();   And this:  $category = 'mobile wifi'; $query = db_select('taxonomy_term_data', 'ttd')     -&gt;fields('ttd', array('tid')); $query-&gt;innerJoin('taxonomy_vocabulary', 'tv', 'ttd.vid = tv.vid'); $result = $query-&gt;condition('machine_name', 'images_cat', '=')     -&gt;condition('LOWER(ttd.name)', $category, '=')     -&gt;execute()     -&gt;fetchAssoc();   The second one becomes invalid and the first one causes the problem I mentioned above. Any thoughts or suggestions?  Thanks, Patrick What is $(65!)^2$ congruent to mod $131$? How to recover data from a USB-connected hard disk that shows no partition? How can we prove that every odd perfect square is congruent to $1$ modulo $8$? I have a tag in my html like this:  &lt;h1&gt;My Website Title Here&lt;/h1&gt;   Using css I want to replace the text with my actual logo. I've got the logo there no problem via resizing the tag and putting a background image in via css. However, I can't figure out how to get rid of the text. I've seen it done before basically by pushing the text off the screen. The problem is I can't remember where I saw it. Why should you not use Number as a constructor? How do I get the member to which my custom attribute was applied? In Section 9 of Chapter 6, Lang constructrs for the first time a non-abelian extension as a splitting field $K$ of $X^n - a$ when the ground field $k$ does not contain primitive $n$-th roots of unity $\zeta_n$. He constructs an injective homomorphism of the Galois group $G(K/k)$ into the matrices of type   $$ M=\begin{pmatrix} 1 &amp; 0 \\ b &amp; d \end{pmatrix} \quad \hbox{with}\ b\in \mathbb{Z}/n\mathbb{Z} \quad \hbox{and} \quad d\in (\mathbb{Z}/n\mathbb{Z})^*,$$  where $(\mathbb{Z}/n\mathbb{Z})^*$ the multiplicative group of integers modulo n.  Afterwards, he states in Theorem 9.4 that if $n$ is an odd positive integer prime to the characterstic and $[k(\zeta_n):k]=\varphi(n)$ (i.e, the primitive roots of unity are not in the ground field), then the above homomorphism is, in fact, an isomorphism. Besides, the commutator group is $G(K/k(\zeta_n))$, so $k(\zeta_n)$ is the maximal abelian subextension of $K$.  Lang proves the theorem inductively over the number of prime factors in the decomposition of $n$ (i.e. if $n=9= 3\cdot 3$, then the proof "would take two steps" to complete). The induction start with $n$ prime is written clearly and I agree with it.   Now come the questions:   I do not understand Lang's argument to prove that the commutator subgroup is the subgroup $\begin{pmatrix}1 &amp; 0 \\ b &amp; 1\end{pmatrix}$, $b\in \mathbb{Z}/n\mathbb{Z}$. What is this projection on the diagonal and how does one see that the factor group of the commutator group is isomorphic to $(\mathbb{Z}/n\mathbb{Z})^*$?   By the way, direct computation of $x\, y\, x^{-1}\, y^{-1}$ for two arbitrary matrices $x=\begin{pmatrix} 1 &amp; 0 \\ b &amp; d \end{pmatrix}$, $y=\begin{pmatrix} 1 &amp; 0 \\ c &amp; e \end{pmatrix}$ yields a matrix $\begin{pmatrix} 1 &amp; 0 \\ b(1-e)+c(d-1) &amp; 1 \end{pmatrix}$. As $n$ is odd, $2 \in (\mathbb{Z}/n\mathbb{Z})^*$, so taking $e=1$ and $d=2$, we indeed reconstruct the above-mentioned group.   The second (inductive) part of the proof is a complete mystery to me with virtually every sentence being a Theorem which needs an extra proof. Can someone give me some hints?   2.a. Lang writes $n=p\,m$ and takes $\alpha$ to be the root of $X^n-a$. It is clear that $\beta=\alpha^p$ is a root of $X^m -a$. Now comes the argument "By induction we can apply the theorem to $X^m-a$". I agree that we can apply it here but the result is that $K=k(\beta,\zeta_m)$ is the splitting field of $X^m-a$. In the diagram below, there appears $k(\beta,\zeta_n)$ out of nowhere.   2.b. Now Lang proceeds to apply the theorem on $X^p-\beta$ over $k(\beta)$. Bergman's "Companion" reminds to check that $[k(\beta,\zeta_p):k(\beta)]=\varphi(p)$ before applying the theorem and gives a hint "$[k(\zeta_p):k]$ and $[k(\beta):k]$ are relatively prime". I disagree with this hint. Take $n=21= m p$ where $m=3$ and $p=7$. Then $[k(\zeta_p):k]=\varphi(p)=p-1=6$ but $[k(\beta):k]=m=3$ and both are not co-prime. Can we apply the theorem here at all? Or if so what is the argument? If Bergman's argument is valid, where is the fault in my logic?  2.c. Even assuming that we can apply the theorem in 2.b., then we can say something about $k(\alpha, \zeta_p)$ and not $k(\alpha,\zeta_n)$. How do we proceed to checking everything Lang states in the last section of the proof (basically, everything after the diagram)?  EDIT: I have found the essentially same question Vertex groups can not be named in blender 2.70 For some reason the name text field doesn't appear for vertex groups in blender 2.70. I tried in 2.69 and it's there and works fine. Was this feature removed in 2.70 or am I missing something? Make specific color in a texture transparent I am working with very old model files that have BMP textures. The designers did not use a transparency in the textures or a separate alpha b/w texture. They used a specific color value that was then removed by the engine to create a transparency, similar to a chroma key. In this case, all textures used a bright purple/pink color.   I cannot modifying the original texture images by converting them to PNG and add an alpha. I would like to figure out how to do it all in nodes.  The goal is to have this value keyed out and transparent. I have been messing around in the shader editor and cannot figure this out.  I've also been looking around online and in this forum, but the only search terms I can think of are chroma-keying which only results in Compositing results, which I don't believe is what I'm looking for.  Here is an example of the texture (its very small) and it's context:      Any help or direction would be much appreciated! Two identical files; Apache says one is forbidden I've got this one file, favicon.ico. It's actually a large group of nested files, but purely for example, just this one.  If I do cp favicon.ico favicon2.ico, Apache can read the second one just fine.  If I do mv favicon.ico favicon3.ico, Apache throws a 403 on favicon3.ico.  If I su apache, I can read the file as apache.  stat says both files are identical, except for the inode number.  Is there some hidden flag somewhere or something that I'm missing? I've never seen anything like this.  error_log says (13)Permission denied: access to /favicon3.ico denied How to import Illustrator swatch libraries into InDesign - Adobe Indesign Mac? I have a very reach swatch library in adobe-illustrator like food colors and.... But in adobe-indesign I don't have many colors. Why? Can I import them to indesign? Are there difference between those sentences?        Alex is getting married next month.     Alex will get married next month.      Seems that the first one is expressed in present continues, and the second on in future tense. Am I correct? Plagiarism of Lecture Slides Original Post:  I recently attended a lecture with highly technical content.  One of the middle slides in the deck had a particular phrase that reminded me of something that I had read several years before.  It took me a few minutes, but I found the original source (another slide deck) and am shocked to find that the professor lifted 35 slides verbatim from the original source.  The University holds students accountable for plagiarism and strictly defines plagiarism such that this clearly fits.  The slides were used verbatim and no credit or reference was provided.  Further, logos were added and color schemes were changed to make make them look slightly more like original content.  What should I do?  This professor has a professional full time job and I can imagine this getting swept under the rug, but this is clearly plagiarism and is spelled out very clearly in the student conduct code.  Is this an overreaction or should I pursue this?  This is confounded by the fact that I am very disappointed by the rigor of the course and feel like the professor lacks adequate technical background to teach the course (I guess my suspicions came true).  I'm really busy at work so don't want to deal with a big todo, but believe this really discredits the academic integrity of the course.  Additional content in response to comments:  The University defines plagiarism as "Using another writer's words without proper citation."  There is no proper citation given here, and these are not educational materials.  This is 35 slides from someone else's tutorial presentation.  I do not believe that the professor and the author of the original content have a relationship.  I have emailed the author to enquire about any permissions or relationship.  Still, even with permission, this is still plagiarism as defined be most people and as defined by the University.  All original works in the US are implicitly copyright protected, so there is also a copyright issue, but this is not currently my concern, though it could be of interest to the original author.  I have emailed him, so this is up to him.  This is a US institution and is a top tier highly respected school.  I am also not a lay student, but a Ph.D. with a degree from a top tier university who has served as a faculty member at two top tier universities (including this one).  I have also taught undergraduate courses in the past.  I have never engaged in this type of plagiarism, have never known colleagues to do so, and am shocked that so many people suggest this is par for the course in teaching.  My doctorate is from a school that prides itself on its honor code and takes honor code violations very seriously and I have served on the honor council and deliberated on a case of plagiarism in the past.  I really am shocked by this incident.  Response from Original Author of the Slides:  I have received a response from the author of the slides and he states that the work is his original work, that there are no additional authors of the work, that no one has been given permission to present the work, and that he believes his copyright on the work has been infringed upon.  He has requested additional information to assert his claim on the copyright. The Wikipedia page () proves that $$f(x) = \begin{cases}  \exp(-1/x),  &amp; \mbox{if }x&gt;0 \\ 0, &amp; \mbox{if }x\le0 \end{cases}$$ is a non-analytic smooth function. But I don't understand why the fact that "the Taylor series of $f$ at the origin converges everywhere [where does "everywhere" mean here?] to $0$" implies the Taylor series converges to $0$ when $x&gt;0$? Can someone explain this in greater detail? I guess there should be a gap in my understanding of power series. Comma — a punctuation error? Consider:     This book provides a solid psychological understanding of these experiments, and adds a few expansions and conclusions of its own. It also provides …   My question regards the comma. I have been told that having the comma there is an error.  According to  this seems to be the case according to “some style guides”. The reason is that the stuff after the comma is not independent; it’s dependent on what comes before.  What do you think? It would seem to me the comma helps a lot, because those two “and”s without any comma make the sentence rather cluttered. That’s why I put the comma there. So I’m not sure. I am wondering why matrix factorization techniques in the machine learning domain almost always expect the provided matrix to be non-negative. What is the advantage of this constraint?  Background: I want to use matrix factorization algorithms for a sparse user-item matrix containing positive and negative implicit feedback. Is there any another possibility to set interactions with negative indications apart from fields that denote that no interaction happened between the user and the item?