Bold names of some authors with prefixes
Bold name in bib when having a prefix in last name
Is $R^2$ useful or dangerous? How do I get rid of this unwanted bar from Eclipse? How to obtain Hamiltonian formalism and phase space for Lagrangian with second-derivatives? AES Mix Column Transformation Section 3.4.3 "The MixColumns Step"(page 39) of , it states     The columns of the state are considered as polynomials over   $\operatorname{GF}(2^8)$ and multiplied modulo $x^4 + 1$ with a fixed polynomial $c(x)$.      The polynomial $c(x)$ is given by   $c(x) = \mathtt{03} \cdot x^3 + \mathtt{01} \cdot x^2 + \mathtt{01} \cdot x + \mathtt{02}$      Let $b(x) \equiv c(x) \cdot a(x) \pmod{x^4 + 1}$. Then         How this polynomial multiplication modulo $x^4+1$ is converted to Matrix Multiplication? Continuous extension of a real function Related;    This is the theorem i need to prove;  "Let $E(\subset \mathbb{R})$ be closed subset and $f:E\rightarrow \mathbb{R}$ be a contiuous function. Then there exists a continuous function $g:\mathbb{R} \rightarrow \mathbb{R}$ such that $g(x)=f(x), \forall x\in E$."  I have tried hours to prove this, but couldn't. I found some solutions, but ridiculously all are wrong. Every solution states that "If $x\in E$ and $x$ is not an interior point of $E$, then $x$ is an endpoint of a segment of at most countable collection of disjoint segments.". However, this is indeed false! (Check Arthur's argument in the link above)  Wrong solution Q4.5;    Just like the argument in this solution, i can see that $g$ is continuous on $E^c$ and $Int(E)$. But how do i show that $g$ is continuous on $E$? Does a monk's Unarmored Movement speed increase apply to the fly speed gained from a Fly spell? I want to remotely control my Android device from my PC without rooting it. Is this possible? I am trying to find a story where a children's nursery turns into a jungle I read this short story(I believe it was under novella length, but I could be mistaken) a while back, and I am trying to identify the title for a friend.   Plot:      Parents(male and female) get a computer aided/holographic nursery for their children. The mother becomes increasingly agitated as the children withdraw more. The children are barely even featured in the story, and the ending concludes with lions possibly eating the parents.   Publishing date: Years ago.   Tech level: Seemingly functional AI, not much more. Exclusive lighting Is (or will be) there any sort of light linking in Cycles, or a method to get a light to affect only certain objects that doesn't involve compositing two or more different render layers? Sort of what 3Dstudio does with the Include/Exclude methods. Rich Wizards, Poor Muggles My question comes from what I learned in the movies, considering I have not yet been able to read the books. I would just like to know why Severus Snape called himself the Half-Blood Prince? Did many people call him that or did he just think that it was a cool nickname? This question might be answered in the books so feel free to quote from it. How can I find the number of partitions of $n$ into exactly $k$ distinct parts, where each part is at most $M$?  The number of partitions $p_k(\leq M,n)$ of $n$ into at most $k$ parts, each of size at most $M$, is given by the generating function: $$  \binom{M+k}{k}_{x} = \prod_{j=1}^{k}\frac{1-x^{M+k-j+1}}{1-x^j}= \sum_{n=0}^{kM} p_{k}(\leq M,n) x^n $$  For the number of the partitions $p_k(\mathcal{D},n)$ of $n$ into at most $k$ parts there is the recurrence relationship: $$   p_{k}(\mathcal{D},n) = p_{k}(\mathcal{D},n-k) + p_{k-1}(\mathcal{D},n) $$  But what, if I want to count only the partitions with distinct parts and restricted number of parts and restricted part size?  Update: Now I know the generating function for the number of distinct restricted partitions $p_k(\leq M, \mathcal{D},n)$ of $n$ into exactly $k$ distinct parts, all at most $M$ is $$    \prod_{j=1}^{M} (1+xq^{j}) = \sum_{k,n=0}^{\infty}p_k(\leq M, \mathcal{D},n)x^{k}q^{n} $$ and there is also a recurrence relation $$    p_k(\leq M, \mathcal{D},n) =         p_{k-1}(\leq M-1, \mathcal{D},n-k) +         p_k(\leq M-1, \mathcal{D},n-k) $$ How can I prove this? Could you recommend a book, where I could read about this? Rough Smart objects problem in Photoshop I am using Adobe CC(2015) latest version and the behaviour of the smart objects isn't normal. When I paste a vector from Illustrator to Photoshop, the vector looks low quality or rough.   ORIGINAL  IN PHOTOSHOP   However, if I click over the smart object layer(in Photoshop)and this is opened in Illustrator, the vectors looks as the original one.   VECTOR OPENED IN ILLUSTRATOR FROM PHOTOSHOP SMART OBJECT   How can I solve this? I am on SharePoint 2013 and do not have access to Designer, as a preface.  I am trying to create a list view that filters items by whether or not they were added in the last hour.  I had done this earlier, only with items that were added in the current week, by creating two columns, 'Week Start' and 'Week End', and filtering by Created falling between those two.  Simple enough.  However, filtering list views does not allow for complex functions, nor does the [Today] function recognize time, causing an issue.  Is there any workaround for this?  Thanks. Inequality involving $\limsup$ and $\liminf$: $ \liminf(a_{n+1}/a_n) \le \liminf((a_n)^{(1/n)}) \le \limsup((a_n)^{(1/n)}) \le \limsup(a_{n+1}/a_n)$ Comma as decimal marker with siunitx (Spanish usage) I'm using siunitx to input some big numbers and units in my document.  Is there a way to make the output of \num{3.14} be "3,13" instead of "3.13"? In Spanish, we use the first one. What is the word that is used to describe the oversimplification or non-academic discussion of a complex issue?   Typically, I'm looking for a word like pedantic, or puerile, except that the word covers the fact that the discussion is particularly non-academic. I know that such a word exists since I have used it before, but it has skipped my mind. Why is $1^{\infty}$ considered to be an indeterminate form From : In calculus and other branches of mathematical analysis, an indeterminate form is an algebraic expression obtained in the context of limits. Limits involving algebraic operations are often performed by replacing subexpressions by their limits; if the expression obtained after this substitution does not give enough information to determine the original limit, it is known as an indeterminate form.    The indeterminate forms include $0^{0},\frac{0}{0},(\infty - \infty),1^{\infty}, \ \text{etc}\cdots$   My question is can anyone give me a nice explanation of why $1^{\infty}$ is considered to be an indeterminate form? Because, i don't see any justification of this fact. I am still perplexed. Find all polynomials $P:\mathbb{C}\rightarrow\mathbb{C}$ such that $$P(x^2)=P(x)^2 .$$   Here is what I tried:  First, it is easy to see the constant solutions, namely $P\equiv 0,P\equiv 1$.  Let $r$ be a root of $P$ (i.e. $P(r)=0$). It follows that all terms in the infinite sequence $r,r^2,r^4,\dots,r^{2n},\dots$ are roots of $P$. To avoid a polynomial with infinite roots, we have to have the sequence be periodic. So it turns out that either $r=0$, or the roots of $P$ are roots of unity of degree $2n$ for some $n\in\mathbb{N}$.  In the first case, we get $P(x)=xQ(x)$. Plugging in, we get $$x^2Q(x^2)=x^2Q(x)^2\implies Q(x^2)=Q(x)^2 ,$$ i.e. that $Q$ satisfies the same condition as $P$.  In the second case, we have $P(x)=(x^{2n}-1)Q(x)$. Plugging in, we get $(x^{2n}-1)Q(x^2)=(x^{2n}-2x^n+1)Q(x)^2$. I was not sure how to proceed from here. Can you re-equip equipment to the same creature?