Haro group 1 ci, CIKH5J7798
What is the purpose of a serial number?
Can I watch the progress of a `sync` operation? Density of finite rank operator in compact operators on Hilbert spaces How do I recover my password in Pokemon Go? Left/Right across multi-line equation I have a multi-line equation that I want to have matching sized parentheses. The advice I read online was to use \left( equation \right. \\ left. rest-of-equation \right) . However, this syntax leaves first half of the equation unaware of what is in the second half. For example, if you include a square root term after the break, the second parenthesis will be larger than the opening parenthesis. When you are using the aligned environment to split a long equation this can look somewhat offputting.    Compare the top equation to the bottom one. The parentheses match in size for the bottom equation, but the left hand parentheses for the top one is  noticeably smaller.  Top Code:   \begin{aligned}[t]   \gamma_{\text{u}} + \frac{1}{108}   \left(57\gamma_{\text{er}} \right. &amp;+  38\gamma_{\text{se}}\\ &amp; {}\pm  \left.\sqrt{2601 \gamma_{\text{er}}^2 + 3648  \gamma_{\text{er}}\gamma_{\text{se}} + 1444 \gamma_{\text{se}}^2}  \right)   \end{aligned}   Bottom Code:  \begin{aligned}[t] \gamma_{\text{u}} + \frac{1}{16} \left(9\gamma_{\text{er}}  +  6\gamma_{\text{se}} \pm  \sqrt{49 \gamma_{\text{er}}^2 + 76 \gamma_{\text{er}}\gamma_{\text{se}} + 36 \gamma_{\text{se}}^2} \right) \end{aligned} The Safari Back Button Problem I do some minor programming and web work for a local community college. Work that includes maintaining a very large and soul destroying website that consists of a hodge podge of VBScript, javascript, Dreamweaver generated cruft and a collection of add-ons that various conmen have convinced them to buy over the years.   A few days ago I got a call "The website is locking up for people using Safari!" Okay, step one download Safari(v3.1.2), step two surf to the site. Everything appears to work fine.  Long story short I finally isolated the problem and it relates to Safari's back button. The website uses a fancy-pants javascript menu that works in every browser I've tried including Safari, the first time around. But in Safari if you follow a link off the page and then hit the back button the menu no longer works.  I made a pared down webpage to illustrate the principle.  &lt;!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"&gt; &lt;html&gt; &lt;head&gt;&lt;title&gt;Safari Back Button Test&lt;/title&gt; &lt;meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"&gt; &lt;/head&gt; &lt;body onload="alert('Hello');"&gt; &lt;a href="http://www.codinghorror.com"&gt;Coding Horror&lt;/a&gt; &lt;/body&gt; &lt;/html&gt;   Load the page and you see the alert box. Then follow the link off the page and hit the back button. In IE and Firefox you see the alert box again, in Safari you do not.  After a vigorous googling I've discovered others with similar problems but no really satisfactory answers. So my question is how can I make my pages work the same way in Safari after the user hits the back button as they do in other browsers?  If this is a stupid question please be gentle, javascript is somewhat new to me. Pick random row from a file Side-by-side markdown title not so side-by-side In edit revisions where a long enough title has been edited, the side-by-side  markdown view shows a large overlap when the title wraps:    This is a repeat of  specific to the new Meta design. Looks like a line spacing adjustment is needed.  See this . Variation on Vandermonde's identity How can you show that $$ \binom{2n}{n}^2 = \sum_{m=0}^{n} \binom{2n}{2m} \binom{2m}m \binom{2n-2m}{n-m} $$?  I was fooling around with random walks, and apparently both expressions are supposed to be the number of unweighted random walks on a 2D square lattice of $2n$ steps that ends at the origin.  Whole thing reminds me of Vandermonde's identity but I can't it. Any hints? Is $\sqrt{x^2}=|x|$ or $=x$? Isn't $(x^2)^\frac12=x?$ $|x|=\sqrt{x^2}$ as  shows. But, as $(x^2)^\frac12=x$, I can't understand where am I wrong interpreting Square-root. I just upgraded to Ubuntu 18.04 but the UI did not change at all. For example I don't have the full screen app launcher; it's the same as it was back in 16 and 17. No notification center etc.   Do I need to somehow opt in? How does one show that $$\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$$ for each nonnegative integer $n$?  I tried using the  but I guess I am applying it incorrectly. With the snake oil technique we have $$F(x)= \sum_{n=0}^{\infty}\left\{\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}\right\}x^{n}.$$ I think I have to interchage the summation and do something. But I am not quite comfortable in interchanging the summation. Like after interchaging the summation will $$F(x)=\sum_{k=0}^{n}\sum_{n=0}^{\infty}\binom{n+k}{k}\frac{1}{2^k}x^{n}?$$ Even if I continue with this I am unable to get the correct answer.  How does one prove this using the Snake oil technique?  A combinatorial proof is also welcome, as are other kinds of proofs. Improving upon ArcGIS Buffer/Dissolve performance? How do I completly remove XP from my pc. I currently have a dual boot with XP and Windows 7. Since installing Windows 7, I have never used XP. Can I remove it without causing problems with Windows 7? Prove  that the function $\displaystyle f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$. You should give a proof that is directly based on the  definition of continuity.   I saw many similar questions on this website, but none of them gave me a satisfactory answer. I more or less understand how epsilon-delta proofs work but my problem lies more in the algebraic manipulations probably. So here's my "attempt".  Definition of continuity; for $f:A \to \mathbb{R}$     $$\forall \varepsilon &gt;0 \ \exists\delta&gt;0\ \forall x \forall x_0 \in A:|x-x_0|&lt;\delta \Rightarrow |f(x)-f(x_0)|&lt;\varepsilon$$   So from what I understand, the procedure for epsilon-delta proofs are as follows: 1. Plug the point of interest $x_0$ into $|f(x)-f(x_0)|&lt;\varepsilon$ 2. Write $x$ in terms of $\varepsilon$ 3. Then plug $x$ into $|x-x_0|&lt;\delta$ 4. Find $\delta$ in terms of $\varepsilon$. Done    At step 1, we have $\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Step 2 is where I'm stuck because of the 2nd degree polynomial in the denominator. First, I did this: $\left|\dfrac{x}{x^2+1}\right|&lt;\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Then, I wasn't too sure about what to do, I thought about getting rid of the "$1$", but that would screw up my inequality. I thought about factoring $x^2+1$, but it doesn't have any real roots. I tried inverting the fraction, but that led me to nowhere. And I've already exhausted the tools I have. How do I proceed?  Apparently, epsilon-delta proofs are the most basic building blocks of analysis. And I'm already failing, this is both embarrassing and depressing... How to work with iAds using xcode 3.1.3 Copy material to another object? I saw a video where the person copied a material from one object to another (Cycles).  How can I accomplish this? Prove that $\int_0^1t^{p-1}(1-t)^{q-1}\,dt=\frac{\Gamma(p)\Gamma(q)}{\Gamma(p+q)}$ for positive $p$ and $q$ I'm trying to prove that for $p,q&gt;0$, we have $$\int_0^1t^{p-1}(1-t)^{q-1}\,dt=\frac{\Gamma(p)\Gamma(q)}{\Gamma(p+q)}.$$    The hint given suggests that we express $\Gamma(p)\Gamma(q)$ as a double integral, then do a change of variables, but I've been unable thus far to express it as a double integral.  Can anyone get me started or suggest an alternate approach?  Note: This wasn't actually given to me as the $\Gamma$ function, just as a function $f$ satisfying $$f(p)=\int_0^\infty e^{-t}t^{p-1}\,dt$$ for all $p&gt;0$, but I recognized that. This is in the context of an advanced calculus practice exam. I was just reviewing my "capitalization standards" for titles and such and was wondering if there's a macro to do the same thing I'm forced to do by hand nowadays. My personal rules (feel free to disagree/comment on them) are as follows:   the first letter (a number is a letter too for the sake of these rules) always gets capitalized, every word gets capitalized individually, the exception to the rule above (and just the rule above) are  such as prepositions and the like.   In other words: I'd like a capitalization command (like \MakeUppercase) that will capitalize every word not included in a list of words and that will always capitalize the first word of its argument.  Doable?  PS: one such "list" of closed class words (also known as "function words") can be found . Does somebody has an example where the left $R$-modules $R^m$ and $R^n$ are isomorphic for all positive integers $m$, and $n$? How many solutions are there to $x_1 + x_2 + ... + x_5 = 21$? How many solutions are there to the equation      $x_1 + x_2 + x_3 + x_4 + x_5 = 21$    where $x_1, i = 1,2,3,4,5$ is a nonnegative integer such that $0 ≤ x_1 ≤ 3, 1 ≤ x_2 &lt; 4$, and $x_3 ≥ 15$?  I have correctly completed the previous parts of the question but am having trouble with this particular restriction.  The total number of solutions to the equation is $C(25,21) = 12650$.  I have tried to do each restriction individually:  For $0 ≤ x_1 ≤ 3$, I solved this by subtracting the number of solutions when $x_1 ≥ 4$ from the total number of solutions. This is $C(25,21) - C(21,17) = 5985$.  For $1 ≤ x_2 &lt; 4$, I have $C(24,20) - C(21,17) = 5985$.  For $x_3 ≥ 15$, I have $C(10,6) = 210$.  However, the restriction is when these are all together. I am not sure how to proceed. The answer is $106$.