How do I find ' % ' with the LIKE operator in SQL Server?
How do I escape a percentage sign in T-SQL?
How to implement keyboard shortcuts on websites Finding the radius of convergence for $\sum_{n=0}^{\infty} \frac{(n!)^kx^n}{(kn)!}$ I'm reviewing some calculus concepts right now, and this series stumped me. I'm trying to figure out what its radius of convergence is, but it's not falling for any of my old tricks. Using the root-test, I want to compute: $$ L_1=\lim_{n\rightarrow\infty} \left|\sqrt[n]{\frac{(n!)^k}{(kn)!}}\right| $$  where $k$ is some positive integer. Passing the limit through the absolute-value bars and $n$th root symbol, I now want to compute the simpler (?) $$ L_2 = \lim_{n\rightarrow\infty} \sqrt[n]{\frac{(n!)^k}{(kn)!}}$$  Which I can't seem to pin down. Numerical tests indicate it goes to 0, and that jives with an intuitive notion I have that there are always $k$ terms on the numerator, but $kn$ terms in the denominator. But since all of these terms themselves depend on $n$, proving that $L_2 = 0$ escapes me. Once we get this result (if it's correct), then clearly $L_1$ is also 0, and the radius of convergence of the series is $\mathbb{R}$. Thanks for any ideas you may have. How to uninstall Intel Linux Graphics Installer and revert to default drivers Any way to embed Pygame in webpages? If I press the "include alpha-button" in the Mix-Color-Node, I get white borders. Otherwise i've got a perfect alpha but no blue background. I am using Windows 10. I am trying to install 1 open source software.  In the readme.txt of that software, it says it requires Visual C++ 2008 Redistributable. I found that my Windows already has Visual Studio 2012 Redistributable installed.  After I install the open source software, it seems that it is working, even though I haven't installed Visual C++ 2008 Redistributable.  Do I need to install Visual C++ 2008 Redistributable if my Windows already has Visual Studio 2012 Redistributable? In the neural network literature, often we encounter the word "tensor".  Is it different from a vector? And from a matrix? Have you got any specific example that clarifies its definition?  I'm a bit confused about its definition. Wikipedia doesn't help and sometimes I have the impression that its definition depends on the specific machine learning environment used (TensorFlow, Caffee, Theano). Prove upper bound for recurrence I am working on  problem 3 from MIT's Fall 2010 OCW class 6.042J. This is covered in  which is about recurrences.  Here is the problem:  $$A_0 = 2$$ $$A_{n+1} = A_n/2 + 1/A_n, \forall n \ge 1$$  Prove   $$A_n \le \sqrt2 + 1/2^n,  \forall n \ge 0$$  I have graphed the recurrence and the upper bound and they seem to both converge on $\sqrt2$.    Also, if you ignore the boundary condition $A_0 = 2$ then you find that $\sqrt2$ is a solution to the main part of the recurrence. i.e. $\sqrt2 = \sqrt2/2 + 1/\sqrt2$.  The chapter and videos on recurrences have a lot to say about a kind of cookbook solution to divide and conquer recurrences which they call the Akra-Bazzi Theorem. But this recurrence does not seem to be in the right form for that theorem. If it were in the form $A_{n+1} = A_n/2 + g(n)$ then the theorem would give you an asymptotic bound. But $1/A_n$ is not a simple function of $n$ like a polynomial. Instead it is part of the recurrence.  Also, the chapter has a variety of things to say about how to guess the right solution and plug it into an inductive proof, but I haven't had much success. I have tried possible solutions of various forms like $a_n = \sqrt2+a/b^n$ and tried solving for the constants $a$ and $b$ but to no avail.  So, if someone can point me in the right direction that would be great. I always assume that the problem sets are based on something taught in the videos and in the text of the book but I am having trouble tracking this one down.  Bobby Are all multiplicative functions additive? Suppose $cf(x)=f(cx)$ and $f:\mathbb{R}\to\mathbb{R}$. I believe it follows that $f(x+y)=f(x)+f(y)$.   Proof: There is some $c$ such that $y=cx$. Then  $$f(x+y)=f\left((1+c)x\right)=(1+c)f(x)=f(x)+cf(x)=f(x)+f(cx)=f(x)+f(y)$$  QED.  I wonder if the same thing holds for when $f:\mathbb{R}^n\to\mathbb{R}^n$? I can't use the same trick, because all vectors are not scalar multiples.  I tried thinking of it in terms of basis units, but didn't get anywhere. Dirac Delta function inverse Fourier transform We know that the Fourier transform of the Dirac Delta function is defined as $$\int_{-\infty}^{\infty} \delta(t) e^{-i\omega t} dt = 1,$$  and if I were to reconstruct the function back in time domain, the inverse Fourier transform is defined as  $$\delta(t) = \frac{1}{2\pi}\int_{-\infty}^{\infty} e^{i\omega t} d\omega.$$  How do I compute this integral analytically? Determining members of local groups via C# I wondered whether anybody knows how to obtain membership of local groups on a remote server programmatically via C#. Would this require administrator permissions? And if so is there any way to confirm the currently logged in user's membership (or not) of these groups? In RSA, why is it important to choose e so that it is coprime to φ(n)? When choosing the public exponent e, it is stressed that $e$ must be coprime to $\phi(n)$, i.e. $\gcd(\phi(n), e) = 1$.   I know that a common choice is to have $e = 3$ (which requires a good padding scheme) or $e=65537$, which is slower but safer.  I also know that for two primes $p,q$, we have $\phi(pq) = (p - 1) (q - 1)$  Now, let me give a (simple) example:  Say I choose $e = 3$, and two random primes $p = 5$ and $q = 13$.  I can now compute $\gcd(3, \phi(5 \cdot 13)) = 3$.  This reveals that $3$ and $\phi(n)$ are not coprime. I assume this could also happen for large values of $p$ and $q$, and likewise for another $e$. I therefore assume that the RSA algorithm must check that $\gcd(e, \phi(pq)) = 1$. But let's assume it doesn't.  How does RSA become vulnerable if $\gcd(e, \phi(pq)) \neq 1$? How to restore cloth presets? Is there anyway to restore the Blender default Cloth settings? Or is there anyway to find what the default settings are?  I didn't realize at the time that by changing the values I was overriding the default values.  Using Blender v2.76. In JavaScript:  encodeURIComponent("©√") == "%C2%A9%E2%88%9A"   Is there an equivalent for C# applications? For escaping HTML characters I used:  txtOut.Text = Regex.Replace(txtIn.Text, @"[\u0080-\uFFFF]",     m =&gt; @"&amp;#" + ((int)m.Value[0]).ToString() + ";");   But I'm not sure how to convert the match to the correct hexadecimal format that JS uses. For example this code:  txtOut.Text = Regex.Replace(txtIn.Text, @"[\u0080-\uFFFF]",     m =&gt; @"%" + String.Format("{0:x}", ((int)m.Value[0])));   Returns "%a9%221a" for "©√" instead of "%C2%A9%E2%88%9A". It looks like I need to split the string up into bytes or something.  Edit: This is for a windows app, the only items available in System.Web are: AspNetHostingPermission, AspNetHostingPermissionAttribute, and AspNetHostingPermissionLevel. Is there a website or some other way to find out if I need a transit visa for a short stop in the UK on my way somewhere else? Ideally this should give me the answer for all nationalities, and take into account any other visas I may have. Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$ Well, the problem I'm trying to solve is this:      Let $A$ be the ring of all continuous functions from $\mathbb{R} \to \mathbb{R}$. Show that $M = \{f \in A: f(0)=0\}$ is a maximal ideal of $A$.   I tried to show that if $J$ is an ideal of A that properly contains M, so $J = A$: we know that there is a function $g \in J$ with $g(0) \neq 0$. So, we have that $$J \supseteq \langle g, M\rangle=\{ag+f;a \in A, f\in M\}$$   I tried to show that 1 $\in$ $\langle g,M\rangle$. However I'd have to find some function $h(x)\in A$ such that $h(x)(ag+f) = 1$, but this function $h$ has to be different from 0 for all x $\in \mathbb{R}$, so I don't know how to find this function.  My second idea to solve this problem was prove that the quocient $A/M$ is a field. We have that $$A/M = \{h(x) + M; h(x) \in A\},$$ but again I have the problem to show that all elements of $A/M$ are units.  If someone could help, I would be really grateful (: I have a question, I think it concerns with field theory.     Why the polynomial $$x^{p^n}-x+1$$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$?   Thanks in advance. It bothers me for several days. What's the difference between "these" and "those"? First of all, I'm not a native English speaker, but in school I learned that these is used if referring to something near, and those is used when referring to something far away (temporally or locally). But now I'm sometimes watching English movies and notice sentences like "Have you seen those boots?" while the boots were only centimeters away. Is this just not correct, or have I learned the wrong rules?  Another question is, what if I'm referring to something abstract such as ideas or thoughts so that I can't say if they are far away or not. Should I use those or these?  Edit  So it can't be really wrong in any case if I use these respectively those? How can I profile a multithread program in Python? I'm developing an inherently multithreaded module in Python, and I'd like to find out where it's spending its time. cProfile only seems to profile the main thread. Is there any way of profiling all threads involved in the calculation? Check if wp-login is current page How can I check if the current page is wp-login.php or wp-signup.php ?  Are there more elegant solutions than using $_SERVER['REQUEST_URI'] ?