Showing a construction verifies the $\Omega$-axiom for monoid action
Character of the subobject classifier in the topos of $\mathbf{M}$-sets.
Determining a patients biological age? I am looking for an algorithm that shows the exact coefficients some variables that have on a hospital patient's chronological age versus their biological age.   I understand a lot of the variables that go into determining ones biological age (i.e. Blood pressure, diet, family history of disease, obesity etc.) but not the amount of impact that it has on the actual scoring of their age.  I have found many sites that will calculate it, however I need the actual variable coefficients and influence in order to produce a proper score for thousands of patient records.   Thanks in advance for your input! I need to run a program as a different user + make it run with admin privileges (Run as administrator).  I use the '' for running the program as a different user  How can I run the program as admin with that command? (or a different one so will give me my requirements)  EDIT :  I need 2 things   Run as a different user Run as admin - not just as the admin user but also with full permissions   As this image Installing gcc-7 (and newer packages) in Ubuntu 16.04 tasks package: items are in two line with 4 columns and 4 items I write some choice questions into beamer frame, after some research, here is my code:  \documentclass[aspectratio=169]{beamer} \usetheme{Berkeley} \usepackage{tasks,CJK} \begin{document} \begin{CJK*}{utf8}{bsmi} \begin{frame} \transwipe 1.Which one you want to choose? \begin{tasks}[counter-format=tsk[A].,debug=true](4) \task A \task B \task C \task D \end{tasks} \end{frame} \end{CJK*} \end{document}   output with pdflatex:  But I don't want the D choice goto the second line, I want them stay in one line, what should I do? Why can't I seem to grasp interfaces? Could someone please demystify interfaces for me or point me to some good examples? I keep seeing interfaces popup here and there, but I haven't ever really been exposed to good explanations of interfaces or when to use them.  I am talking about interfaces in a context of interfaces vs. abstract classes. How do I perform a biographical interview? I have a couple of elderly relatives who have not kept a journal and refuse to write down their "life story." I really would like to know their stories and who they were and who they are. They have their favorite stories that they rehash every time I see them, but I'd like to get more. I have no experience with "interviewing" and am looking for information on how to get their stories. Any websites, books, and or tips\techniques would be greatly appreciated. Cannot empty trash I am trying to empty my trash, and it keeps giving me an error message that says,      .Trash can't be opened right now because it's being used by another task...     I have tried restarting my computer, running Finder > Secure Empty Trash everything yields the same result and error message from above. Call marker color in Geojson to apply to leaflet.js in php Visas to travel the world I understand that you have to have visas to enter some countries, but I was wondering whether you have to pay for each visa separately or you can get a visa to go everywhere. You see videos and lists on what you should pack to travel the world, but no lists on the documentation needed. I'm teaching my self topology with the aid of a book. I'm trying to prove the following is a topology:     Let X be an infinite set. Show that $\mathscr{T}_2=\{U \subseteq X : U = \emptyset $ or $ X\setminus U $ is countable$ \} $ is a topology.   My book calls this set the ""  Please let me know if my proof is valid.     corollary [A]: The union of countable sets are countable.    proof: I'm going to take as a given that that the union of finite set are finite, and just prove the case of . A set is countable infinite if there is a bijection between the set and the natural numbers. Let $A$ and $B$ be a countable infinite sets. Now let $f$ be the bijection between $A$ and $\mathbb{N}$ and $g$ be $B$'s bijection.  $f:\mathbb{N}  \rightarrow  A$  $g:  \mathbb{N}  \rightarrow B$  There can always exist a bijection $h$ that maps $A \cup B $ to $\mathbb{N}$. To account for non disjoint sets, let $B' = B \setminus A$; (note: $A \cup B = A \cup B'$)  $h:  \mathbb{N}   \rightarrow  A \cup B'$  $ h(x) = \left\{         \begin{array}{ll}             f(\frac{1}{2}x); &amp; \quad x \in 2\mathbb{N} \\             g(\frac{x+1}{2}); &amp; \quad x \in 2\mathbb{N}+1         \end{array}     \right. $   $h^{-1}(x)$ would map $A$ to the even numbers, and $B'$ to the odd numbers.  Therefore, The union of countable sets are countable. (QED)  Now to verify the definition.     (i) X and Ø are elements of $\mathscr{T}$.   Ø is given in the definition of $\mathscr{T}_2$. Also, the empty set is considered finite, with cardinality zero. Thus $X$ is in $\mathscr{T}_1$ because its complement is finite, and finite numbers are countable.      (ii) $\mathscr{T}$ is closed under finite intersections.   Let:$V_k \subseteq X$ be any countable set. (ie: $V_1, V_2...$ are all countable sets)  So Then, $U_k = X \setminus V_k$, would be the subsets of $\mathscr{T}_2$.  $U_k \cap U_j = X \setminus (V_k \cup V_j) $, due to De Morgan's law.   Thus, $U_k \cap U_j \in  \mathscr{T}_2$, since the Union of two countable sets is also countable[A]. And This reasoning can be extended to any finite amount of intersections.       (iii) $\mathscr{T}$ is closed under arbitrary unions.   Let $A=\bigcup_{i \in I} U_i$ be an arbitrary union of sets whose complements are are countable.Then by De Morgan's law, $A=X \setminus (\bigcap_{i \in I}V_i)$, for some countable sets $V_i$. By the definition of intersection, $\bigcap_{i \in I}V_i \subseteq V_i$ for all $i \in I$. Since $V_i$ is countable so is any of its subsets.  Hence the complement of $A$ is countable. Prove that the difference between two rational numbers is rational This is a terribly simple question I'm sure, but I can't find a work-around in my proof. I must prove that the difference between two rational numbers is thus rational. Here is my attempt:     Let $a$ and $b$ be rational numbers. Therefore, \begin{align}  a=\frac{\lambda}{\beta},\:b=\frac{\xi}{\zeta},\:\ni\:\lambda,\beta,\xi,\zeta\in\mathbb{Z},\tag{1} \end{align} which gives us \begin{align}  a-b=\frac{\lambda}{\beta}-\frac{\xi}{\zeta}=\frac{\lambda\zeta-\xi\beta}{\beta\xi}.\tag{2} \end{align}   So I have shown that $a$ and $b$ are rational numbers which, by definition, can be represented by the quotient of two integers. But now how do I tackle the problem of the difference? By definition the difference between two integers is an integer. Does that require that this difference is thus rational?  Thank you for your time, I need to print an image at a certain size. What dimensions and resolution should I use? How do we know the brain flips images projected on the retina back around? Why do we turn images upside down again rather than dealing with them directly, still vertically rotated after passing through our lens?   I don't see how that would cause any problems, and how we'd ever be able to figure out if we are presented with flipped images after getting used to interacting based on visual input, whether flipped or not.   What am I missing? You can see the output from lscpu command -  jack@042:~$ lscpu Architecture:          x86_64 CPU op-mode(s):        32-bit, 64-bit Byte Order:            Little Endian CPU(s):                56 On-line CPU(s) list:   0-55 Thread(s) per core:    2 Core(s) per socket:    14 Socket(s):             2 NUMA node(s):          2 Vendor ID:             GenuineIntel CPU family:            6 Model:                 79 Model name:            Intel(R) Xeon(R) CPU E5-2690 v4 @ 2.60GHz Stepping:              1 CPU MHz:               2600.000 CPU max MHz:           2600.0000 CPU min MHz:           1200.0000 BogoMIPS:              5201.37 Virtualization:        VT-x Hypervisor vendor:     vertical Virtualization type:   full L1d cache:             32K L1i cache:             32K L2 cache:              256K L3 cache:              35840K NUMA node0 CPU(s):     0-13,28-41 NUMA node1 CPU(s):     14-27,42-55   I can see that there are 2 sockets (which is like a processor ??) and inside each of the socket we have 14 cores. So, in total 2x14=28 physical cores. Normally, a CPU can contain multiple cores, so number of CPUs can never be smaller than number of Cores. But, as shown in the output CPUs(s): 56 and this is what is confusing me.  I can see that Thread(s) per core:    2, so these 28 cores can behave like 2x28=56 logical cores.  Question 1: What does this CPUs(s): 56 denote? Does CPU(s) denote number of Virtual/Logical core, as it cannot be a Physical core core atleast?  Question 2: What does this NUMA node mean? Does it represent the socket? Because of a former error in our ASP.Net application, created by my predecessor and undiscovered for a long time, thousands of wrong URLs where created dynamically. The normal user did not notice it, but Google followed these links and crawled itself through these incorrect URLs, creating more and more wrong links.  To make it clearer, consider the url     example.com/folder   should create the link     example.com/folder/subfolder   but was creating     example.com/subfolder   instead. Because of bad url rewriting, this was accepted and by default showed the index page for any unknown url, creating more and more links like this.     example.com/subfolder/subfolder/....   The problem is resolved by now, but now I have thousands of 404 errors listed in the Google Webmaster Tools, which got discovered 1 or 2 years ago, and more keep coming up.  Unfortunately the links do not follow a common pattern that I could deny for crawling in the robots.txt.  Is there anything I can do to stop google from trying out those very old links and remove the already listed 404s from Webmaster Tools? If you give a user sudo privileges how can I remove the sudo privileges and make the user become just a regular user?  I used:  sudo adduser username sudo   Now I've changed my mind. I want to get that fancy LaTeX symbol to put in one of my documents but I cannot find it anywhere.  All searching for things like latex symbol have not resulted in the symbol but other symbols. I have a table with a column for ID, Date and Frequency of occurrence for that particular date and ID.  ID    date          Frequency 1     2014-05-18      5 1     2014-05-19      4 1     2014-05-20      25 2     2014-05-20      7 3     2014-05-18      4 3     2014-05-20      1 4     2014-05-18      6   I'm looking to insert the dates for each ID that aren't currently there (assuming that the date ranges from 2014-05-18 to 2014-05-20) and add a value of 0 in Frequency for those.  For example, you can see that  ID 1 has an observation for all three dates;  ID 2 is missing 2014-05-18 and 2014-05-19;   ID 3 is missing 2014-05-19;   ID 4 is missing 2014-05-19 and 2014-05-20.  Therefore, the output should look like this  ID    date          Frequency 1     2014-05-18      5 1     2014-05-19      4 1     2014-05-20      25 2     2014-05-18      0 2     2014-05-19      0 2     2014-05-20      7 3     2014-05-18      4 3     2014-05-19      0 3     2014-05-20      1 4     2014-05-18      6 4     2014-05-19      0 4     2014-05-20      0   I've attempted the following from . However, that will only add dates with 0 Frequency that aren't present throughout the entire table instead of on an ID level.   DECLARE @s DATE = '20140518', @e DATE = '20140520';  SELECT c.date, Frequency = COALESCE(a.Frequency,0) FROM dbo.Calendar AS c LEFT OUTER JOIN dbo.table AS a ON c.date = s.[date] WHERE c.d &gt;= @s AND c.d &lt; DATEADD(DAY, 1, @e); 'find' utility does not output all files when using wildcards Running:  $find . -name *.exe   gives:  ./MakeItSo_1.2.2/MakeItSo_1.2.2/MakeItSo.exe ./MakeItSo.exe   but those are not the only exe files in the directory. For example, running  $find . -name ATLTester.exe   gives:  ./Debug/ATLDmoVexaTester.exe What is the closest general-relativistic equivalent of a "time slice"? In a newtonian universe, one can talk of a "time slice", that is, the state of the universe at a given point in (global) time. In a "typical" classical universe, a time slice would contain enough information to fully compute the state of the universe at any other point in time, backwards or forwards.  So, disregarding what we know of quantum effects and talking purely of a general-relativistic universe, which concept is closest to a time slice?