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How to remove the left part of a string? I have some simple python code that searches files for a string e.g. path=c:\path, where the c:\path part may vary. The current code is:  def find_path(i_file):     lines = open(i_file).readlines()     for line in lines:         if line.startswith("Path="):             return # what to do here in order to get line content after "Path=" ?   What is a simple way to get the text after Path=? So, my friend just implemented a bunch of new mods into his SMP server, which meant a host of new commands to play with.  I thought I'd give the /mobspawn command a few goes, and see what I could achieve.  So I headed off to the server's jail (I forget why this particular location compelled me), and gave it a few spins.    I seem to have made a bit of an error in judgement.     What can I do to get rid of this mess?  Is there a command or some other technique I can use to clear out any mobs in my immediate vicinity? Let $A, B \in \mathcal M_n(\mathbb C)$, we want to know if there's any relation between their spectral radius and the spectral radius of $A + B$.  The first part of this exercise is giving examples of the three posibilities: $\rho(A) + \rho(B) &lt; \rho(A+B)$ ; $\rho(A) + \rho(B) &gt; \rho(A+B)$ and $\rho(A)+ \rho(B) =\rho(A+B)$. This part was easy because there are no conditions about A or B.  The second part is proving that if A and B are normal matrixes, (i.e. $ AA^* =A^*A$, where $A^*$ is its conjugate transpose), then $ \rho(A+B) \le \rho(A) + \rho(B) $.   So my first attempt was using the Schur's decomposition, so $A=U^{-1}D_AU$ where $D_A$ is a diagonal matrix with the eigenvalues of $A$ in its diagonal and U is an unitary matrix. Similarly, B is similar to a diagonal matrix $D_B$ with the eigenvalues of B in its diagonal. That way I have $\rho(A) = \rho(D_A)$ and $\rho(B) = \rho(D_B)$ so now since $D_A + D_B$ is a diagonal matrix with $\lambda_i + \mu_i$ for $ 1\le i \le n $, where $\lambda_i$ and $\mu_i$ are the eigenvalues of $A$ and $B$ respectively. From here it's easy to see that $ \rho(D_A+D_B) \le \rho(D_A) + \rho(D_B) $, since $ |\lambda_i+\mu_i|\le|\lambda_i|+|\mu_i| \ \forall i$. But I don't see how to include $\rho(A+B)$ in this.  And the last part of the exercise is proving that if $ \{X_i\}$ is a basis of eigenvectors, which is common to A and B, then $ \rho(A+B) \le \rho(A) + \rho(B) $.  Here's my attempt, but I would like to know if it's correct:  Let $\lambda_i$ and $\mu_i$ be eigenvalues of A and B associated to the vector $X_i$, then $AX_i=\lambda_i X_i$ and $BX_i = \mu_iX_i$, and if we sum both equalities, we have $AX_i + BX_i = \lambda_iX_i + \mu_iXi$ so $(A+B)X_i=(\lambda_i+\mu_i)X_i$ so $(\lambda_i+\mu_i)$ is an eigenvalor of $(A+B)$ associated to the eigenvector $X_i$. Then is again clear that $|\lambda_i+\mu_i|\le|\lambda_i|+|\mu_i| \le \rho(A) + \rho(B)\ \forall i$, and particularly, for $\max_i |\lambda_i+\mu_i| = \rho(A+B)$ so $ \rho(A+B)\le \rho(A) + \rho(B)$  Any kind of help is appreciated and thank you very much in advance! Why am I getting "No such file or directory" when I try to execute a binary? If $\sum (a_n)^2$ converges and $\sum (b_n)^2$ converges, does $\sum (a_n)(b_n)$ converge? If $\sum (a_n)^2$ converges and $\sum (b_n)^2$ converges, does $\sum (a_n)(b_n)$ converge?  Could someone help me to solve this or at least give me a hint?, I have tried using Cauchy's criterion, the Dirichlet test for convergence, etc, but I can´t prove it.Honestly I don´t know where to start. Any help will be appreciated. What are recommended, general strategies to start block-cipher design and/or analysis? Every integer is congruent to the sum of its digits mod 9 This is a question from the free Harvard online abstract algebra .  I'm posting my solutions here to get some feedback on them.  For a fuller explanation, see  post.  This problem is from assignment 6.  The notes from this lecture can be found .     Prove that every integer $a$ is congruent to the sum of its decimal digits modulo 9.   Let $s$ be an $(n+1)$-digit integer given by $s=a_n\cdot10^n+\dots+a_2\cdot10^2+a_1\cdot10^1+a_0\cdot10^0$ with $a_i\in\mathbb{Z}$ such that $0\leq a_i\leq9$.  Then $ \begin{align} s\,\mathrm{mod}\,9&amp;=\bar{s}\\ &amp;=\overline{a_n\cdot10^n+\cdots+a_2\cdot10^2+a_1\cdot10^1+a_0\cdot10^0}\\ &amp;=\overline{a_n\cdot10^n}+\overline{\cdots}+\overline{a_2\cdot10^2}+\overline{a_1\cdot10^1}+\overline{a_0\cdot10^0}\\ &amp;=\overline{\overline{a_n}\cdot\overline{10^n}}+\overline{\cdots}+\overline{\overline{a_2}\cdot\overline{10^2}}+\overline{\overline{a_1}\cdot\overline{10^1}}+\overline{\overline{a_0}\cdot\overline{10^0}}\\ &amp;=\overline{\overline{a_n}\cdot1}+\overline{\cdots}+\overline{\overline{a_2}\cdot1}+\overline{\overline{a_1}\cdot1}+\overline{\overline{a_0}\cdot1}\\ &amp;=\overline{a_n}+\overline{\cdots}+\overline{a_2}+\overline{a_1}+\overline{a_0}\\ &amp;=a_n\,\mathrm{mod}\,9+\cdots+a_2\,\mathrm{mod}\,9+a_1\,\mathrm{mod}\,9+a_0\,\mathrm{mod}\,9 \end{align} $  Again, I welcome any critique of my reasoning and/or my style as well as alternative solutions to the problem.  Thanks. How quickly is the desired state of curl of the Electric Field around a point achieved where a Magnetic Field Vector has just begun changing? My question and context with explanation are given below. Thank you in advance.   Faraday’s Law () states that a time-changing magnetic field vector induces a curl of the Electric field around that point. However it does not specify how quickly the necessary spatial gradient is developed in the Electric Field to satisfy that curl. Of course, the Electric Field vectors around that point cannot just jump to the required values instantaneously in accompaniment as soon as the magnetic field starts changing at a fixed rate, since it is required that the Electric Field has a sensible rate of change to in turn induce a curl of the magnetic Field and continue the propagation of the wave. It would seem the exact rates at which the Electric and Magnetic Fields are changing is critical in the mechanism of an EM wave’s propagation. How would I then calculate the rate of change of E somewhere along the wave given I know the rate of change of the B vector that began it, and given the wave is restricted to one dimension for simplicity? There should after all be some delay in how the EM wave moves from point to point in space, seeing as it moves at the finite speed of causality (3*10^8 m/s), as shown in the first image:    Some of my ideas so far have been that perhaps the rate of change of E is determined such that it exactly cancels the growth of the time-changing E vector that gave rise to a curl of B before, which developed at such a rate to induce a curl of E, which demands this rate of change of E which I am talking about now. In this way the wave might level out the growth of the fields in its wake and spread the change further outwards, in the same way smoothening out a crease spreads it elsewhere. However I am stuck on how to show this rigorously.  I am open to any difficulty of maths, so long as the answer provides the explanation. Below are some diagrams to help visualize what I am talking about:    Faraday's Law requires that a curl of E is developed, which under these restrictions requires a spatial gradient of E to appear across that point. Since the field across that point was previously in some other state, it is required that the Electric Field vectors that are infinitesimally close to that point undergo a rate of change through time to achieve the desired state of curl. The question is, how quickly is this desired state of curl achieved? Two column float with [t] using the cas-dc template I am using the cas-dc template for Elsevier. When trying to use \begin{figure*}[t], except I get the error 'The module 'cas/fig' does not have a key called 'cas/fig/t'. Other templates I use work fine. I have included \usepackage{stfloats}. I don't see anything mentioned that strictly forbids it, unless I missed this. Anyone know why? I know SO's policy is &quot;you don't have to register to ask questions,&quot; but there are so many new members and so many hit-and-runs... The majority of the questions I see now are coming from new users (i.e., it's their first question). Although unregistered users should still be able to ask questions, I think we should encourage users to create an account. Here is a couple of ways we could do that:  Explicitly encourage people to get an account: there's currently nothing telling people to do that. Maybe tell people something like &quot;Get an account, it's easy!&quot; and maybe show some of the perks of having an account (and having rep).  Maybe give a few bonus points for registering; and have that enable a basic privilege. It could be taken from one of the , for example.   Of course getting people to register is just half of the battle. I don't know what the stats are on this, but I think there's a number of users who create multiple accounts anyways. We could curb that by:  Having smart(er)? duplicate account detection systems, alerting someone who is about to create a new account and possibly has an account already. Give them a message like &quot;Hey, it looks like you already have  account, are you sure you want to create a new one?&quot;  Create a new privilege (10k? 20k?) that gives users tools to detect possible duplicate accounts, eg: &quot;List users with the same e-mail,&quot; &quot;List users with the same IP addresses,&quot;  etc. (without revealing said emails and IPs). Then the 10k/20k can look at other stuff (e.g.: posts) and refer the new user to a moderator for a possible merge. Using SUMPRODUCT with ARRAYFORMULA I have the following random data in sheet one  A  orange D  yellow C  yellow B  orange B  orange C  blue A  yellow D  blue C  orange C  blue   In sheet two I use the following query function:  A1=UNIQUE(QUERY(Sheet1!A1:B10,"select A, B order by A asc")) C1=sumproduct(Sheet1!A:A=A1,Sheet1!B:B=B1) C2=sumproduct(Sheet1!A:A=A2,Sheet1!B:B=B2) C3=sumproduct(Sheet1!A:A=A3,Sheet1!B:B=B3) . . .   Which returns the following:  A   orange 1 A   yellow 1 B   orange 2 C   yellow 1 C   blue   2 C   orange 1 D   yellow 1 D   blue   1   Instead of using sum product in each row, I want arrayformula to expand automatically.  When I use E1=ArrayFormula(sumproduct(A1:A10=C1:C,B1:B10=D1:D)) I get     Error: Array arguments to EQ are of different size.   Please help me out. Two days had passed since she had last eaten or slept.   Or should it be:     Two days have passed since she last ate or slept.   Or something else? And why? The combinatorial explosion of past simple, past perfect and present perfect is killing me. Meaning of "kernel" In analysis, there are at least three kinds of "" concepts:   In probability theory, there is a concept called , also called probability kernel, from one measure space $X$ to another $Y$. It is actually a family of measures on $Y$, indexed by members of $X$. It can transform a measure on $X$ to a measure on $Y$, in terms of integration.  A special case is  of probability density function in statistics, where the  is actually a probability kernel. In real/complex analysis, there is a concept called  from a product space $X \times Y$ to $\mathbb{R}$ or $\mathbb{C}$. It can transform some special function: $X \to \mathbb{R}$ or $\mathbb{C}$ to another one:$Y \to \mathbb{R}$ or $\mathbb{C}$. This is used for defining integral transformation In Hilbert space theory, there is concept called , which is a family of bounded mappings for a family of Hilbert spaces. For every two Hilbert spaces $X$ and $Y$ in the family, there are exactly two members of the kernel, one mapping from $X$ to $Y$ and the other from $Y$ to $X$.   I wonder    Are they related concepts, since they seem to share some indescribable similarity? Can they be unified?   In particular, the first two are similar to each other as the kernels induce transformations on measures and on functions in terms of integrals.  It is however not obvious to me how the third one, i.e. the Hilbert space one, is related to the second one. Are they related to the  concepts? Or even to the  concept?   I feel like some insights and references for catching the general ideas shared across as many kinds of "kernels" as possible.  Thanks and regards! Which is easier, pushing or pulling? It is generally assumed, from a person's perspective, that pushing a cart is more easier than pulling one. But why? Is there any difference in terms of force required to achieve the same amount of displacement?  Or is it merely human perception?  Why is it that almost all automobiles transfer torque to the back axle. But then, why do trains have engines in the front? Make font size bigger than max limit of 1296 pt in Adobe Illustrator (2015)? For some reason and for many years there's a limit for font size in Illustrator. It is 1296 points max, so you can't go bigger without converting type to outlines first. Converting to outlines means you will not be able to edit type parameters and text it-self. Don't know how about you, but this makes me sad in non-destructive editing era.  What's your workaround? How do the PHP equality (== double equals) and identity (=== triple equals) comparison operators differ? What is the difference between == and ===?  How exactly does the loosely == comparison work? How exactly does the strict === comparison work?  What would be some useful examples? Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ . I'm looking for a simple proof that up to isomorphism every group of order 2p (p prime) is either $\mathbb{Z}_{2p}$ or $D_{p}$ (The Dihedral group of order 2p).  I should note that by simple I mean short and elegant and not necessarily elementary. So feel free to use tools like Sylow Theorems, Cauchy Theorem and similar stuff.  Thanks a lot! How to make tr aware of non-ascii(unicode) characters? Firstly, how do you gain the score exactly? I know it shows in the bar on the side of the map, but I remember a match where I was lone-wolfing and still got a pretty high score in that bar. I suppose my other squad members were together, but do I also gain for their work?  Also, does the score reset when I start a new game? I mean, I play support with the Offensive perk and it took me a long game of conquest to just unlock lvl-3 extra grenade. In the next match, that 'nade is gone. Don't I keep it forever? Probability that an integer number having Poisson distribution is even The probability $P(X=n)$ that an event X takes place $n$ times in a fixed period of time follows the Poisson distribution with parameter $\lambda$ i.e.  $$ P(X = n) = e^{-\lambda} \frac{\lambda ^ n}{n!}$$  I have to evaluate the probability that the event $X$ takes place an even number of times. I know that:   $$ P(X \text{ is even} ) = e^{-\lambda} \cdot \sum_{k=0}^{+\infty} \frac{\lambda^{2k}}{(2k)!}$$  but I can't solve the series.  I guess that I have to use the fact that $e^\lambda = \sum_{n = 0}^{+\infty} \lambda^n/n!$, but I got stuck.  How can I evaluate $P(X \text{ is even})$ (alternative solutions appreciated).