Is a function that maps every connected set to a connected set continuous?
Continuity of function mapping connected set to connected set
Often called "He-Who-Must-Not-Be-Named" and "You know who", was it common knowledge at the Ministry of Magic that Voldemort was the same person as Tom Riddle? How can i limit the character length in excerpt? Possible Duplicate:          I have a question after reading this post (). I like this function(Search Term Without Plugin) very much but the character length is too long. What php code should i add to make the excerpt shorter? Would appreciate if someone can suggest it. Thank you! Creating if-else condition with ArcGIS API for JavaScript combo boxes? Where to place 'only' Why do statisticians like "$n-1$" instead of "$n$"? Is 'acronymise/ze' a word? Is it used only colloquially, if at all? I just sent a text to a friend, who didn't understand an acronym I used for a game:      "Ah, I said it in a previous text so thought it was ok to abbreviate   it."   Though, since it was an acronym I had created, could I have used the word 'acronymise/ze' to be more specific?   I'm pretty sure it isn't a (formally used) word, but I wondered, as you often refer to acronyms specifically as acronyms, rather than abbreviations. Can you be more specific with a verb, too?  It sounds too odd to me, so I'm guessing generally no. But I wondered—so perhaps I'm wrong. Or half wrong. Empty vector menu in QGIS on PC with French as default language CPU governor changes automatically to "performance" under load I have a Lenovo T570 with Xubuntu 18.04 LTS. My current issue is that my cpu speed stepping is kind of going nuts and does what ever it thinks its best.  Sample: when I run my IDE and cpu load increases during build time, the governor changes automatically. I caught the moment during compiling my project with the following call:  martin@martin-ThinkPad-T570:~$ while cat /sys/devices/system/cpu/cpu0/cpufreq/scaling_governor; do sleep 1; done powersave powersave performance performance   cpufreq-info tells me this:  martin@martin-ThinkPad-T570:~$ cpufreq-info  cpufrequtils 008: cpufreq-info (C) Dominik Brodowski 2004-2009 Report errors and bugs to cpufreq@vger.kernel.org, please. analyzing CPU 0:   driver: intel_pstate   CPUs which run at the same hardware frequency: 0   CPUs which need to have their frequency coordinated by software: 0   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.25 GHz. analyzing CPU 1:   driver: intel_pstate   CPUs which run at the same hardware frequency: 1   CPUs which need to have their frequency coordinated by software: 1   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.36 GHz. analyzing CPU 2:   driver: intel_pstate   CPUs which run at the same hardware frequency: 2   CPUs which need to have their frequency coordinated by software: 2   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.26 GHz. analyzing CPU 3:   driver: intel_pstate   CPUs which run at the same hardware frequency: 3   CPUs which need to have their frequency coordinated by software: 3   maximum transition latency: 4294.55 ms.   hardware limits: 400 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 3.50 GHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 3.36 GHz.   Please take a look at     current policy: frequency should be within 3.50 GHz and 3.50 GHz.       The governor "performance" may decide which speed to use   Afterwards to go back to powersave I use my little script:  martin@martin-ThinkPad-T570:~$ cat cpu_freq_save.sh  #!/bin/bash sudo cpufreq-set -g powersave -c 0 --min 400MHz sudo cpufreq-set -g powersave -c 1 --min 400MHz sudo cpufreq-set -g powersave -c 2 --min 400MHz sudo cpufreq-set -g powersave -c 3 --min 400MHz   Which resets the min frequency and the governor but as soon as I compile again with my IDE every time the governor and the min frequency changes again.  Any idea how I can disable that automatic change?  PS: If you need more details, just tell me where to find them and I will provide them Can someone identify the fonts used in the words "nature methods" in the following image?    I think that the word "nature" is in Times or Times New Roman (?) but can't figure out what font the word "methods" is in.  Any ideas? Which offences result in indirect free kicks? If a player commits a direct free kick offence in their own penalty area, this results in a penalty kick instead of a direct free kick. However, if the offence is an indirect free kick offence, it remains as an indirect free kick .  What offences result in an indirect free kick? Every separable Banach space is isomorphic to $\ell_1/A$ for some closed $A\subset \ell_1$ How to prove the following mind-blowing fact?     Let $X$ be a separable Banach space and let $\ell_1$ be the space of all absolutely summable scalar sequences. Then there exists such closed subspace $A\subset \ell_1$ that factor space $\ell_1/A$ and $X$ are isomorphic as normed spaces.   Edit: So what, this is like a classification up to isomorphism of all separable Banach spaces? Each separable Banach space corresponds to some closed subspace of $\ell_1$? Prove that every isometry on $\mathbb{R}^2$ is bijective SQL Server Max Memory not limiting use of RAM I would like your input on this. I have a sql server 2008r2 Ent. Ed. 64bit with 16 cores and 64GB RAM. There is one instance of SQL server patched fully as of 20111014.  The max ram is set to 60000MB. Amount of free ram is 0 according to task manager after a few days online.  If I change the max ram to below 53GB it will after a few days to stabilize and have some free ram.   It is the sql process that does allocate the ram according to task manager. How do i come to terms with what the problem really is? It goes without saying that i did alot of testing already but havn't solved this to my liking yet. and ohh we do not get the typical memory starvation lagging when the available ram is down to 0 free.  Update 1:  Inspired by another Q/A related to RAM on this page  . I used these two to see what the RAM is being used for.  SELECT TOP ( 10 )         [type] AS [Memory Clerk Type] ,         SUM(single_pages_kb) AS [SPA Mem, Kb] FROM    sys.dm_os_memory_clerks GROUP BY [type] ORDER BY SUM(single_pages_kb) DESC OPTION  ( RECOMPILE ) ;  SELECT  DB_NAME(database_id) AS [Database Name] ,         COUNT(*) * 8 / 1024.0 AS [Cached Size (MB)] FROM    sys.dm_os_buffer_descriptors --WHERE   database_id &gt; 4 -- system databases --        AND database_id &lt;&gt; 32767 -- ResourceDB GROUP BY DB_NAME(database_id) ORDER BY [Cached Size (MB)] DESC OPTION  ( RECOMPILE ) ;   The amount used shown by these are  first select 7948432    Kb second one 44030,57812  MB that is a total of about 52GB used by sql server... so where did the rest of my RAM go? :-) Task manager show right now cached 363, available 401, free 40 and sqlservr.exe has Memory private set 64 459 656. Max Ram set to 60000MB as before. That's basically the question, is there a "right" way to implement operator&lt;&lt; ? Reading  I can see that something like:  friend bool operator&lt;&lt;(obj const&amp; lhs, obj const&amp; rhs);   is preferred to something like   ostream&amp; operator&lt;&lt;(obj const&amp; rhs);   But I can't quite see why should I use one or the other.  My personal case is:  friend ostream &amp; operator&lt;&lt;(ostream &amp;os, const Paragraph&amp; p) {     return os &lt;&lt; p.to_str(); }   But I could probably do:  ostream &amp; operator&lt;&lt;(ostream &amp;os) {     return os &lt;&lt; paragraph; }   What rationale should I base this decision on?  Note:   Paragraph::to_str = (return paragraph)    where paragraph's a string. I know that the harmonic series $$\sum_{k=1}^{\infty}\frac{1}{k}  = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \cdots + \frac{1}{n} + \cdots \tag{I}$$ diverges, but what about the alternating harmonic series   $$\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k}  = \frac{1}{1} - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{6} + \cdots + \frac{(-1)^{n+1}}{n} + \cdots \text{?} \tag{II}$$  Does it converge?   If so, what is its sum? What’s the correct URL for placing a call on an iPhone? Discord suddenly very slow How does transvoxel algorithm work and how can I implement It? Frequentism and priors Robby McKilliam says in a comment to  post:     It should be pointed out that, from the frequentists point of view, there is no reason that you can't incorporate the prior knowledge into the model. In this sense, the frequentist view is simpler, you only have a model and some data. There is no need to separate the prior information from the model   Also, , @jbowman says that frequentists use regularization by a cost/penalty function, while bayesians can make this a prior:     Frequentists realized that regularization was good, and use it quite commonly these days - and Bayesian priors can be easily interpreted as regularization.   So, my question is, can frequentists in general incorporate into their models what Bayesians specify as priors? Taking the regularization as an example, is the cost/penalty function really integrated into the model, or is this a purely artificial means of adjusting the solution (as well as making it unique)? Kernels and reduced row echelon form - explanation The following text is written in my textbook and I don't really understand it:     If $A = (a_{ij}) \in$ Mat$(m x N, F)$ is a matrix in reduced row echelon form with $r$ nonzero rows and pivots in the columns numbered $j_1 &lt; ... &lt; j_r$, then the kernel ker$(A)$ is generated by the $n-r$ elements $ w_k = e_k - \sum\limits_{1 \le i \le r, j_i \le k} a_{ik}e_{j_i}$ for $k \in {1, \cdots , n} \ {j_1, \cdots, j_r}$, where $e_1, \cdots, e_n$ are the standard generators of $F^n$.    There are no computational examples and the notation is a bit overwhelming so I don't know how I can use it. Can somebody give an example of this in practice?