Distribution Function of ln(x)
Distribution of $-\log X$ if $X$ is uniform.
How to substantiate the claim that something is not known? I am writing a master's thesis (in Number Theory) and there are multiple places where I need to claim that something is not yet known. Since I am not an expert (and even if I were) I would like to reference some more authoritative source than myself or, say, Wikipedia.  For example, consider the following statement:     In 1980 Schmidt proved that [some property holds]. No other necessary or sufficient conditions are currently known, though.   For the first sentence I can cite Schmidt's original paper, but how can I substantiate the second claim? Query to list number of records in each table in a database Can't format / delete locked partition from GParted? We have an Always On "cluster" that consists of 2 servers (there will be more), so one is PRIMARY and other(s) is(are) SECONDARY. The idea was to dedicate SECONDARY as a readonly replica, so it would be a somewhat search-server.  I do know how to set ConnectionString in the C# so it will use SECONDARY replica - just add ApplicationIntent=ReadOnly.  But I don't understand how to address the SECONDARY from stored procedure if I'm using distributed query. Is there a way to set some parameters to the query (like WITH statements or something), so query would use only replica and not the PRIMARY node?  The thing is, obviously from the start server1 is PRIMARY and server2 is SECONDARY, but when server1 fails then server2 is PRIMARY and server1 will be SECONDARY after it get fixed. So I cannot just use the static server2's name.  So far I've managed to get current replica's server name as a variable and use it in EXEC:  -- find first available replica DECLARE @replicaServer nvarchar(50)  SELECT TOP 1     @replicaServer = RCS.replica_server_name FROM     sys.availability_groups_cluster AS AGC     INNER JOIN sys.dm_hadr_availability_replica_cluster_states AS RCS           ON RCS.group_id = AGC.group_id     INNER JOIN sys.dm_hadr_availability_replica_states AS ARS           ON ARS.replica_id = RCS.replica_id     INNER JOIN sys.availability_group_listeners AS AGL           ON AGL.group_id = ARS.group_id WHERE ARS.role_desc = 'SECONDARY'       AND connected_state = 1  -- and query it DECLARE @cmd nvarchar(MAX) = 'SELECT * FROM [' + @replicaServer + '].[somebase].[someschema].[sometable]' EXEC (@cmd)   But that's a shame, I guess. Problem working fontspec, babel and datetime with cyrillic I have discovered that fontspec with russian babel settings doesn't work with datetime package. I tried to compile such code:  \documentclass[a4paper,11pt]{article} \usepackage[T2A]{fontenc} \usepackage[utf8]{inputenc} \usepackage[main=russian,english]{babel} \usepackage{datetime} \usepackage[cm-default]{fontspec}  \begin{document} \today \end{document}   with a xelatex and got an error: Command \cyri unavailable in encoding EU1.  Is there any way to handle it?  UPDATE: I really bungle with charset in XeLateX. Thanks to egreg. I have removed fontenc and inputenc and used some cyrillic font, so my MWE now looks this way:  \documentclass[a4paper,11pt]{article} \usepackage[main=russian,english]{babel} \usepackage{fontspec} \setromanfont{PT Sans} \usepackage{datetime}  \begin{document} \today \end{document}   and I've got another error, if I used russian as a main language in babel: Undefined control sequence. \\monthnamerussian ...cyrm \cyra \cyrya \or \cyri  \cyryu \cyrn \cyrya \or \c...  Is it still because of XeLaTeX? Bibtex style for "Statistics and Computing" I would like to create a bibtex style which answers the requirements of Statistics and Computing journal. How could I do that? Here is an example of how the bibliography should look like:  Journal article: Hamburger, C.: Quasimonotonicity, regularity and duality for nonlinear systems of partial differential equations. Ann. Mat. Pura Appl. 169, 321–354 (1995) Book: Geddes, K.O., Czapor, S.R., Labahn, G.: Algorithms for Computer Algebra. Kluwer, Boston (1992) Book chapter: Broy, M.: Software engineering — from auxiliary to key technologies. In: Broy, M., Denert, E. (eds.) Software Pioneers, pp. 10–13. Springer, Heidelberg (2002)  In the text, the references should be as follows:  Negotiation research spans many disciplines (Hamburger 1995).  Thank you for your help! VHDL Transition Function While browsing I have received notification on Google "Unusual traffic from your computer network"   We're sorry..."your computer or network may be sending automated queries. To protect our users, we can't process your request right now." See Google Help for more information.  Right now I am using the "Ubuntu 12.04" 32 bit version.  Any suggestion, why this is happens &amp; How it resolve?  Thank you for your worthy suggestion. We have to shift our web-site to a new domain due to some unavoidable circumstances. The portal has been up and running there since 2009.  It has good index in various search engines and we are getting a good number of page hits on daily basis.  Losing the search hits and index are our big concern. We are not sure how best we can handle this.  What all can be done to preserve as much as possible while shifting to new domain name. Determining the dimension of span$\{AB-BA : A,B \in M_{n \times n}(\mathbb R) \}$ Let $S$ be the subspace , of  $M_{n \times n}(\mathbb R)$ (the vector space of all $n \times n$ real matrices ) , generated by matrices of the form $AB-BA$ , where $A,B \in M_{n \times n}(\mathbb R)$ , then how do we prove that $\dim S=n^2-1$ ? The only thing that I can determine is that the trace of all matrices of $S$ is $0$ . Please help Show all comments if there is just "1" extra comment to show When looking at a question or answer with comments, I think it would be better to just show that one extra comment if the threshold is "Show 1 more comment".  In other words, if there are 6 comments, show all 6 comments.  If there are 7 comments, then show 5 comments and the link "Show 2 more comments".  Etc for more comments. How can I rotate about an arbitrary point in 3D (instead of the origin)? I have some models that I want to rotate using quaternions in the normal manner, except instead of rotation about the origin, I want it to be offset slightly. I know that you don't say, in 3d space, that you rotate about a point; you say you rotate about an axis. So I'm visualizing it as rotating about a vector whose tail is positioned not at the local origin.  All affine transformations in my rendering / physics engine are stored using SQT (scale, quaternion, translation; an idea borrowed from the book Game Engine Architecture.) So I build a matrix each frame from these components and pass it to the vertex shader. In this system, translation is applied, then scale, then rotation.  In one specific case, I need to translate an object in world space, scale it, and rotate it about a vertex not centered at the object's local origin.  Question: Given the constraints of my current system described above, how can I achieve a local rotation centered about a point other than the origin? Automatic upvote to anyone who can describe how to do this using only matrices as well :) Novel(s) based on humanity fleeing from Earth and regressing to a pre-industrial state on a Colony so as to escape detection Shortly before his death, my father spoke to me about a series of novels that he had just finished reading which had a fascinating concept.  However I soon forgot the title(s) and author and I've been absolutely desperate to find out what they were.  The premise (as I understood) was that humanity had expanded out from the solar system into the local star systems before coming into contact with an incredibly aggressive species which was focused on wiping out the entire species.  Earth and her colonies were lost as remnants of the species fled.  Eventually it was decided by the military leadership to set up a colony in order to rebuild the human race.  However, in order for this colony to escape detection and to keep humanity from going back out into space and thus potentially running into this hostile alien race again, a series of satellites were set up around the planet chosen that would lock onto and destroy any form of technology (and usually the surrounding city) that went beyond pre-industrial standards.    One of the series protagonist is a long living android who possesses the consciousness of a human who was present at the original founding of the colony (and who seems shielded from detection) which observes as civilization is repeatedly regrown and torn down again and who attempts to try and reverse humanities self imposed lot in life.      From what I understood this was a series of novels, but I could be wrong. I've been trying to find this for years on my own with only a rough plot line as a guide and it's gotten me nowhere. I currently have a Yongnuo YN560-TX trigger and a Yongnuo YN-560 Mark III. I would like to get a iTTL flash that also works with remote triggering.  How compatible are are different flash brands (Neewer, Yongnuo, etc.) when it comes to things like setting zoom, etc. ? How to pipe the result of 'date' command to 'mv' command I want to rename my file to the current timestamp.I know how to get the current timestamp("date +%s") but how can I pipe it to 'mv' command? Why should the substitution be injective when integrating by substitution? I made a silly mistake in evaluating some integral by using a non-injective $u$-substitution.  But why should $u$-substitutions be injective in the first place?  I reasoned in the following way: the formula $$ \int_{\phi(a)}^{\phi(b)}g(x)\ dx = \int_a^b g(\phi(t))\phi^\prime(t)\ dt $$ holds for a general $C^1$ function $\phi$, even if it is not injective.  When you calculate an integral of the form $\int_a^b f(\phi(t))\ dt$, to use the formula above from right to left, you should find a function $f$ such that $$ f(\phi(t)) = g(\phi(t))\phi^\prime(t), $$ which do not exist if $\phi$ is not injective, i.e., $\phi(t) = 0$ for some $t$. This is why substitutions should be injective.  Is my reasoning correct?  If so, I believe that if $\phi^\prime(t) = 0 \Rightarrow f(\phi(t)) = 0$, a function $g$ that satisfies the formula above may exist and $\phi$ should not necessarily be injective.  Is this right?  I am often confused about the fact $\phi$ should be injective.  Is there an intuitive way to interpret this fact, so that I always remember to take a $\phi$ that is injective?  I would be grateful if you could help me understand this matter. More than one optional argument for newcommand The \newcommand macro allows to use an optional argument for the first parameter #1 with:  \newcommand{\mycommand}[3][defaultfor1]{blah blah blah}   Is it possible to have more than one option with \newcommand? How did Google find my unlinked newly created pages? I am building a new site, but creating the content using a subdirectory on an existing site. I have never posted a link to this subdirectory anywhere, yet searching Google reveals that Google has found these pages on my site and indexed them.  Further, I updated the site with a robots.txt file that WMT reports as being read, and testing the blocked pages using the WMT test tool indicates that the pages will not be indexed. Apparently this does not remove the pages from existing results, though I submitted a request to do so.  How did Google find these pages to begin with? Is it because I used a common subdirectory name and Google guesses at common subdirectories? I recently upgraded to Ubuntu 20.04 lts from 18.04 lts. After reboot audio is not working. I tried to reinstall pulseaudio and alsa but still not working. sudo apt-get install --reinstall alsa-base pulseaudio sudo alsa force-reload still not working. output  └─▶ inxi -SMA System:    Host: Wizard Kernel: 5.4.0-26-generic x86_64 bits: 64 Desktop: Gnome 3.36.1 Distro: Ubuntu 20.04 LTS (Focal Fossa)  Machine:   Type: Portable System: Dell product: Vostro 2520 v: N/A serial: &lt;superuser/root required&gt;             Mobo: Dell model: 0V1NDP v: A11 serial: &lt;superuser/root required&gt; BIOS: Dell v: A11 date: 02/24/2014  Audio:     Device-1: Intel 7 Series/C216 Family High Definition Audio driver: snd_hda_intel             Sound Server: ALSA v: k5.4.0-26-generic     output └─▶ lspci  00:00.0 Host bridge: Intel Corporation 3rd Gen Core processor DRAM Controller (rev 09) 00:02.0 VGA compatible controller: Intel Corporation 3rd Gen Core processor Graphics Controller (rev 09) 00:16.0 Communication controller: Intel Corporation 7 Series/C216 Chipset Family MEI Controller #1 (rev 04) 00:1a.0 USB controller: Intel Corporation 7 Series/C216 Chipset Family USB Enhanced Host Controller #2 (rev 04) 00:1b.0 Audio device: Intel Corporation 7 Series/C216 Chipset Family High Definition Audio Controller (rev 04) 00:1c.0 PCI bridge: Intel Corporation 7 Series/C216 Chipset Family PCI Express Root Port 1 (rev c4) 00:1c.3 PCI bridge: Intel Corporation 7 Series/C216 Chipset Family PCI Express Root Port 4 (rev c4) 00:1c.5 PCI bridge: Intel Corporation 7 Series/C210 Series Chipset Family PCI Express Root Port 6 (rev c4) 00:1d.0 USB controller: Intel Corporation 7 Series/C216 Chipset Family USB Enhanced Host Controller #1 (rev 04) 00:1f.0 ISA bridge: Intel Corporation HM75 Express Chipset LPC Controller (rev 04) 00:1f.2 SATA controller: Intel Corporation 7 Series Chipset Family 6-port SATA Controller [AHCI mode] (rev 04) 00:1f.3 SMBus: Intel Corporation 7 Series/C216 Chipset Family SMBus Controller (rev 04) 07:00.0 Network controller: Broadcom Inc. and subsidiaries BCM43142 802.11b/g/n (rev 01) 09:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 07) Finding a basis for a certain vector space of periodic polynomials I am having a little bit of trouble solving an homework question.  I found that $S={ p(x) \in R_4[x]} \big| p(x)=p(x-1) $ is a vector space.  Now I need to find some set, K that holds ${span(k)=S}$  My idea was to substitute: $ a+bx+cx^{2}+dx^{3}+ex^{4}=a+b(x-1)+c(x-1)^{2}+d(x-1)^{3}+e(x-1)^{4}$  But here I get something that seems a little bit weird, I'd like to look if I have any mistakes that I did not notice. and if I had mistakes, how to make my answer right. I calculated the right side of the equation and I got to  :  $a+b(x-1)+c(x-1)^{2}+d(x-1)^{3}+e(x-1)^{4}=a+bx-b+cx^{2}-2cx+c+dx^{3}-3dx^{2}+3dx-d+ex^{4}-4ex^{3}+6ex^{2}-4ex+e= (a-b+c-d+e)+(b-2c+3d-4e)x+(c-3d+6e)x^{2}+(d-4e)x^{3}+ex^{4}  $  From here, $ (a-b+c-d+e)+(b-2c+3d-4e)x+(c-3d+6e)x^{2}+(d-4e)x^{3}+ex^{4}=a+b(x-1)+c(x-1)^{2}+d(x-1)^{3}+e(x-1)^{4}\Rightarrow $  $(-b+c-d+e)+(-2c+3d-4e)x+(-3d+6e)x^{2}+(d-4e)x^{3}=0+0x+0x^{2}+0x^{3}+0x^{4}$  And the solution to this equation is only whan $a=b=c=d=e=0$.  I think that I am maybe not in the right direction. Do you have any Idea how to find a set $K\Rightarrow span(K)=S$ ?  Thanks in advance.