How many physical CPU Cores does Windows (amd64, not arm) support? So with &quot;physical CPU Cores&quot; i mean that a CPU with 4 Cores and Hyperthreading counts as 4 and not 8 Cores. Also with &quot;Windows&quot; i mean the Versions (Workstations and Enterprise too) that target normal peoples consumer PCs, not Servers nor modified versions. (i dont want to know the maximal thread count a process can have) Question 1:I found a Table on Wikipedia which says the maximum would be 256 Cores and 4 CPU Sockets, but it is not noted that the maximum of 256 Cores is related to 1 CPU Socket or if its an overall limit? (so does it mean limit is 256 or 1024?) Question 2:Related to Hyperthreading, is Windows counting a CPU with 128 Cores and Hyperthreading as 256 Cores and with that reaches the limit? (so do i have to disable Hyperthreading if i install 4 CPUs with 64 Cores?) Link to Wikipedia:
I would like to build a new computer (it's been 7 years since the last one). Does Windows 10 support more than one ?
Google Search Console domain property not in the list of properties I can add to Google Analytics Let $(\mathcal{H}, (\cdot, \cdot))$ be a complex Hilbert space, and $A :  \mathcal{H} \to \mathcal{H}$ a positive, bounded operator ($A$ being positive means $(Ax,x) \ge 0$ for all $x \in \mathcal{H}$). Prove that $A$ is self-adjoint. That is, prove that $(Ax,y) = (x, Ay)$ for all $x,y \in \mathcal{H}$. Here's what I have so far. Because $A$ is positive we have $\mathbb{R} \ni (Ax,x) = \overline{(x,Ax)} = (x,Ax)$, all $x \in \mathcal{H}$. Next, I have seen some hints that tell me to apply the polarization identity: $$(x,y) = \frac{1}{4}((\lVert x+y \rVert^2 + \lVert x-y \rVert^2) - i(\lVert x + iy \rVert^2 - \lVert x - iy \rVert^2)),$$ where of course the norm is defined by $\lVert \cdot \rVert^2 = (\cdot, \cdot)$. So my guess is that I need to start with the expressions: $$(Ax,y) = \frac{1}{4}((\lVert Ax+y \rVert^2 + \lVert Ax-y \rVert^2) - i(\lVert Ax + iy \rVert^2 - \lVert Ax - iy \rVert^2)),$$ $$(x,Ay) = \frac{1}{4}((\lVert x+Ay \rVert^2 + \lVert x-Ay \rVert^2) - i(\lVert x + iAy \rVert^2 - \lVert x - iAy \rVert^2)),$$ and somehow show they are equal. But here is where I have gotten stuck. Hints or solutions are greatly appreciated. Which side of wave-particle duality to choose in a given situation This is a follow-up to an earlier question regarding .  Having achieved the left-alignment goal, I would now like the caption of the subfigure to be bottom-aligned, while having the subfigure itself be top-aligned. As an example, in the figure below, subfigures (a) and (b) would share an uppermost edge, and their captions would share a lowermost edge, and similarly for subfigures (c) and (d). This is most appropriate for the overall layout style of my document and also the content of the subfigures themselves.    \documentclass{article} \usepackage[font=footnotesize]{subcaption} \usepackage[draft]{graphicx}  \begin{document} \begin{figure}[!ht] \captionsetup[subfigure]{justification=justified,singlelinecheck=false} \centering \begin{subfigure}[b]{0.3\textwidth} \includegraphics[scale=0.8]{fig/workflow-S} \caption{workflow $S$} \end{subfigure} \begin{subfigure}[b]{0.5\textwidth} \includegraphics[scale=0.8]{fig/workflow-S-run} \caption{run of $S$} \end{subfigure} \vskip 8pt \begin{subfigure}[b]{0.3\textwidth} \includegraphics[scale=0.8]{fig/workflow-S'} \caption{workflow $S'$} \end{subfigure} \begin{subfigure}[b]{0.5\textwidth} \includegraphics[scale=0.8]{fig/workflow-S'-run} \caption{run of $S'$} \end{subfigure} \caption{Here's a figure} \end{figure} \end{document}   I've experimented with the minipage settings for subfigure, specifically using [t] instead of [b], but it seems to have no effect. I'm unsure as to whether a position of [t] would produce the right effect anyway, or whether it would shift the captions up as well.  Why is [t] not working here, and what's the right way to produce the layout I need?   The solution should generalise to an arbitrary number of subfigures per row, subfigures which are text or tables rather than images, and should not require any hard-coded sizes. Proof of $\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s)$ Word for a temporary project name In software development, and I imagine in many other fields, we often make up temporary nicknames for new projects or features. These are not meant to be the real names for the end product and are often funny, playful, or sarcastic in nature. These are also not intended to be "codenames" that hide the nature of the project or feature. Is there a word for such nicknames? I'm doing a masters course at a different university than I did my undergrad (both in maths). I did well in my undergrad but now I'm finding it very difficult. The shock of the change is hard to cope with.  I'm not just finding it very difficult, but I get zero feedback: we don't have any tests and I was not able to make friends so I don't know how others are finding it. I'm starting to think that I might be an idiot.   How can I build some confidence in my abilities at the same time as I rush and struggle to keep up with the massive rate of new material I need to learn? How might I get myself some reassurance that I can actually pass, or stop worrying about this so much? (I feel terribly guilty using so much money from my family to be here) It's possible that I don't really have a chance at all but knowing that would be fine. It is very easy to put a tilde over the symbol in math mode. Simply type $\tilde{a}$. But how to put a tilde under the symbol in math mode? CPT Template Not Showing - Getting 404 I'm developing a Custom Post Type plugin, which works fine in dev. Now that I've moved it to production, I'm getting a 404 when I try to display the template for the CPT.   So, two questions:  1- Is there some mechanism to determine the path WP took to get through the hierarchy?  2- Why wouldn't it just give me the single or index page?  I've dumped $wp_query and a stacktrace at the end of the 404. Here's part of what I found:  [query] =&gt; Array     (         [page] =&gt;          [pagename] =&gt; refletters/proximity     )  [request] =&gt; SELECT   wp_posts.* FROM wp_posts  WHERE 1=1  AND (wp_posts.ID = '0') AND wp_posts.post_type = 'page'  ORDER BY wp_posts.post_date DESC  [posts] =&gt; Array     (     )  [queried_object] =&gt;  [queried_object_id] =&gt; 0   And the stack trace:  2013-04-27 22:16:41 - 24.52.197.40 - TRACE - index.php - 404.php[39] -      wordpress/wp-content/themes/notoriousconsultant/404.php[39] - aaLog-&gt;logtrace     wordpress/wp-includes/template-loader.php[50] - include     wordpress/wp-blog-header.php[16] - require_once     wordpress/index.php[17] - require   Thanks for your help. WinterBash site exhibits some strange 404 behavior I was poking around winterba.sh for secret hats and I figured there may be a secret hat linked to a URL so I decided to look at some different URLs and got plenty of 404s but, some pages throw different 404s than others. Why?  Example:  throws the classic "Page Not Found" winterbash style... but  just has the text "404"  ( used to throw just the text "404" but since that has changed)  Still happening at 2016 with . $$\int^2_{-2}\frac{x^2}{1+5^x}$$  How do I start to integrate this?  I know the basics and tried substituting $5^x$ by $u$ where by changing the base of logarithm I get $\frac{\ln(u)}{\ln 5}=x$, but I got stuck.  Any hints would suffice preferably in the original question and not after my substitution.  (And also using the basic definite integrals property.)  Now I know only basic integration, that is restricted to high school, so would prefer answer in terms of that level. How can I solve this integral using the Residue theorem? $$ \int_{-\infty}^\infty \frac{\sin(x)}{x^2 + 4x + 5}dx$$  What I now is you can use residue theorem, and evaluate this integral  $$ \oint \frac{e^{iz}}{z^2 + 4z + 5}dz$$ and through calculating the residues and using the residue theorem I get that the answer for the above integral is $$\pi e^{-1-2i}$$  However after this I am completely lost.  Any guidance will be much appreciated. I would like to know why I can evaluate the integral as an exponential integral as well. Close vote review audit flawed - fails without casting vote Having just  from any of the queues, it was reviewing close votes; however, this audit was flawed in that I didn't even cast a close vote.  Often I press the Close button to preview greater detail and sentiment of the closure, spawning the Why should this question be closed dialog box:    Especially for duplicates, where functionality is solely dependent on spawning this dialog.  From Closing > Duplicate, I can search or view selected duplicates:    Although, I realize general closure reasons are summarized on the page:    This question had 6-upvotes, but seemed very localized referencing subjective query is "taking too long" and even had a sqlfiddle link.  Maybe overly broad regarding performance tuning, the OP was posting like a forum with two answer posts to his own question  and  with one of those answers asking follow-up questions.    Wanting to gauge community response, current closure totals struck my curiosity.  So, I pressed the Close button and boom - oh, the humanity!  I failed, and didn't even cast a close vote.    Votes are not cast until a reason for closure is selected and Vote to Close is pressed.  Taking any review very seriously on this site, it only seems fair that my review quality is tested through actionable steps instead of clicking for more detailed information, leveraging the functional design of the close vote user interface.  Sure, it's complex to seed fake vote totals, and then there's controversy of mindless voting in the majority or people who simply cherry pick 4-vote questions.  Still though, it seems unfair I should hesitate to review further information of vote totals and duplicates before skipping due to the implementation of this audit. Graphing the amount of time a function takes This is almost surely an Arzela-Ascoli question, since it comes from an old exam of which such problems are quite common. Unfortunately, I can't seem to get it though.  $\{ f_n \}$ is a sequence of functions $[0,1] \to \mathbb{R}$ satisfying $|f_n'(x)| \leq \frac{1 + |\ln (x)|}{\sqrt{x}}$ and $-10 \leq \int_0^1 f_n(x) dx \leq 10$ for every $n$. The question is to show the existence of a uniformly convergent subsequence.  In these kinds of situations, the bounds given usually turn into something nice  to force uniform boundedness. Maybe I could hope to establish equicontinuity using the integral somehow, but I'm not told that the $f_n$ are always positive, so the absolute values would probably screw things up anyway.  Is it an easy problem I'm missing or is this totally the wrong track? If so, what's the right track? How to compute the determinant of a tridiagonal matrix with constant diagonals? How to show that the determinant of the following $(n\times n)$ matrix  $$\begin{pmatrix} 5 &amp; 2 &amp; 0 &amp; 0 &amp; 0 &amp; \cdots &amp; 0 \\ 2 &amp; 5 &amp; 2 &amp; 0 &amp; 0 &amp; \cdots &amp; 0 \\ 0 &amp; 2 &amp; 5 &amp; 2 &amp; 0 &amp; \cdots &amp; 0 \\ \vdots &amp; \vdots&amp; \vdots&amp; \vdots &amp; \vdots &amp; \vdots &amp; \vdots \\ 0 &amp; \cdots &amp; \cdots &amp; 0 &amp; 2 &amp; 5 &amp; 2 \\ 0 &amp; \cdots &amp; \cdots &amp; \cdots &amp; \cdots &amp; 2 &amp; 5 \end{pmatrix}$$  is equal to $\frac13(4^{n+1}-1)$?    More generally:     How does one compute the determinant of the following  (where the three diagonals are constant)?      $$M_n(a,b,c) = \begin{pmatrix} a &amp; b &amp; 0 &amp; 0 &amp; 0 &amp; \cdots &amp; 0 \\ c &amp; a &amp; b &amp; 0 &amp; 0 &amp; \cdots &amp; 0 \\ 0 &amp; c &amp; a &amp; b &amp; 0 &amp; \cdots &amp; 0 \\ \vdots &amp; \vdots&amp; \vdots&amp; \vdots &amp; \vdots&amp; \vdots &amp; \vdots \\ 0 &amp; \cdots &amp; \cdots &amp; 0 &amp; c &amp; a &amp; b \\ 0 &amp; \cdots &amp; \cdots &amp; \cdots &amp; \cdots &amp; c &amp; a \end{pmatrix}$$      Here $a,b,c$ can be taken to be real numbers, or complex numbers.   In other words, the matrix $M_n(a,b,c) = (m_{ij})_{1 \le i,j \le n}$ is such that $$m_{ij} = \begin{cases} a &amp; i = j, \\ b &amp; i = j - 1, \\ c &amp; i = j + 1, \\ 0 &amp; \text{otherwise.} \end{cases}$$  There does not seem to be an easy pattern to use induction: the matrix is not a diagonal  of the type $M = \bigl(\begin{smallmatrix} A &amp; C \\ 0 &amp; B \end{smallmatrix}\bigr)$ (where we could use $\det(M) = \det(A) \det(B)$ for the induction step), and there are no lines or columns with only one nonzero entry, so  gets complicated quickly.  Is there a general pattern that one could use? Or is the answer only known on a case-by-case basis? It's possible to compute the determinant by hand for small $n$:  $$\begin{align} \det(M_1(a,b,c)) &amp; = \begin{vmatrix} a \end{vmatrix} = a  \\ \det(M_2(a,b,c)) &amp; = \begin{vmatrix} a &amp; b \\ c &amp; a \end{vmatrix} = a^2 - bc \\ \det(M_3(a,b,c)) &amp; = \begin{vmatrix} a &amp; b &amp; 0 \\ c &amp; a &amp; b \\ 0 &amp; c &amp; a \end{vmatrix} = a^3 - 2abc \end{align}$$  But there is no readily apparent pattern and the computation becomes very difficult when $n$ gets large. Simulating the Windows key on an old keyboard A word that means stage-fright, but for a person? Suppose you met a famous person, and you were shy and anxious and almost overwhelmed by them.   Is there a word for describing that? Similar to getting stage fright, or "choking", except in this case for a person?     When he said hello to me, I couldn't respond. I (was) __________. Countable or uncountable; family of disjoint triangles? If we say that $\mathcal{S}$ is a family of disjoint triangles on a plane, is $\mathcal{S}$ a countable or an uncountable set?  I believe that it is an uncountable set since $\mathbb{R}$ is uncountable and our triangles' corner coordinates are $\in \mathbb{R}$, but I cannot prove this formally, any tip would help. How do I fix gaps around my lean-to greenhouse?