Why trigger.old cannot be operated on DML statements?
DML Statement in ‘after trigger’ and not in ‘before trigger’?
If there was a black hole on earth, what would it look like? If an answer does exist, I'd love to hear it. I'm trying to incorporate a doomed earth story in something I'm writing, and the end of the world I'm going for is a black hole.  Let's say the black hole was created in the Philippines (I chose it because it's on the equator). Here's  for reference.  If I was standing 90 degrees of that, in Kenya, or if I was standing 180 degrees of that, in Mexico; what would I see in those two separate instances? What if I was standing in Japan above it, or in Australia below it?  Let's also say I was riding a boat towards the source of the black hole. Unlike most imagined scenarios where I am orbiting the black hole and slowly falling into it, this time I'm no longer orbiting it - I'm getting sucked into it instead. I'm imagining that the black hole will "half" be inside Earth and "half" will be in the atmosphere. But as it pulls me in, what will it look like to me (if I was massless, so no tidal forces)? It's probably not going to be a black hemisphere sticking out of the ground. Light will be lensed around it in some way so as to appear like a hole in the air.  Also, if the black hole was very small, it probably won't have a strong gravitational pull, and assuming it doesn't disappear, you'd be able to look at it (or at least, its effect on the light in its surroundings). Of course, as you approach it, it would still have an event horizon, so spacetime would still be warped if you're near enough and the surroundings will still experience tidal forces.  As the black hole gains mass, it will get larger, and so its event horizon will increase. If I was standing in Kenya and the event horizon "washes over me," (as in a water wave) what will I see?  I've so far imagined that, at least when seen from outer space, there will be a hole on the ground and light will be lensed around it. When you are on the ground, though, it becomes a bit harder to imagine.  I do hope someone can lend me a hand!  Edit: Someone had previously answered this question, but I'm not sure why it's been deleted. It was pointed out to me, though, that a black hole cannot stay in place. So an additional question for me is, does that mean it is impossible to be standing still, and the event horizon "washes over you"?  Edit2: Here's a guiding thought experiment that could answer the question. Imagine that you are in outer space directly above the black hole, looking at the black hole that is on the earth's surface. Can you imagine what it would look like? It would simply be a hole with the surrounding light gravitationally lensed around it (possibly lensing the entire earth if it's big enough - but let's say it's not).  Now imagine that you are on the direct opposite of where you were above - you're right behind the black hole this time, looking directly at the black hole but unable to see it because the earth is blocking your view.  Now try to imagine, from the second image, rotate the earth into the first image. I find it a bit hard to do. Just as the black hole is appearing as you rotate the earth, how would the light be lensed? Combinations of sets raised to the power of a prime modulus: $\binom{p^{\alpha}-1}k \equiv (-1)^k \pmod p$ I have a list of items   John ID Matt ID John ID Scott ID Matt ID John ID Lucas ID   I want to shove them back into a list like so which also means I want to sort by the highest number of duplicates.   John ID 3 Matt ID 2 Scott ID 1 Lucas ID 1   Let me know how I can do this with LINQ and C#.  Thanks All  EDIT 2 Showing Code:      List&lt;game&gt; inventory = new List&lt;game&gt;();     drinkingforDataContext db = new drinkingforDataContext();     foreach (string item in tbTitle.Text.Split(' '))     {          List&lt;game&gt; getItems = (from dfg in db.drinkingfor_Games                                where dfg.game_Name.Contains(tbTitle.Text)                                select new game                                {                                    gameName = dfg.game_Name,                                    gameID = Boomers.Utilities.Guids.Encoder.EncodeURLs(dfg.uid)                                }).ToList&lt;game&gt;();          for (int i = 0; i &lt; getItems.Count(); i++)         {             inventory.Add(getItems[i]);         }     }      var items = (from xx in inventory                  group xx by xx into g                  let count = g.Count()                  orderby count descending                  select new                     {                         Count = count,                         gameName = g.Key.gameName,                         gameID = g.Key.gameID                     });      lvRelatedGames.DataSource = items;     lvRelatedGames.DataBind();   This query displays these results:   1 hello world times 1 hello world times 1 Hello World. 1 hello world times 1 hello world times 1 hello world times 1 Hello World. 1 hello world times   It gives me the count and name, but it doesn't give me the ID of the game....  It should display:   6 hello world times   234234 2 Hello World.  23432432 Desktop shows a white or black background instead of wallpapers Homotopy equivalence of universal cover As part of am exam question (Q21F ), I'm trying to prove that if $X$ and $Y$ are path-connected, locally path-connected spaces with universal covers $\widetilde{X}$ and $\widetilde{Y}$, respectively, then if $X \simeq Y$ then $\widetilde{X} \simeq \widetilde{Y}$.  My attempt might be correct, but it seems too complicated and amongst the jumble I may have made some incorrect assumptions. So what I'm looking for is (a) verification or correction; and (b) ideas as to how I could simplify my argument.    My argument:  Let $p:\widetilde{X} \to X$ and $q:\widetilde{Y} \to Y$ be the covering maps, and let $X \overset{f}{\underset{g}{\leftrightarrows}} Y$ be a homotopy equivalence.  Fix a point $\widetilde{x} \in \widetilde{X}$, let $x=p(x) \in X$ and $y=f(x) \in Y$, and fix $\widetilde{y} \in q^{-1}(\{y\}) \subseteq \widetilde{Y}$. Also let $x' = g(y) \in X$ and fix $\widetilde{x'} \in p^{-1}(\{x'\}) \subseteq \widetilde{X}$.  Define a map $\widetilde{f} : \widetilde{X} \to \widetilde{Y}$ as follows. For $\widetilde{z} \in \widetilde{X}$ let $\widetilde{u}:[0,1] \to \widetilde{X}$ be a path from $\widetilde{x}$ to $\widetilde{z}$. Let $z=p(z)$ so that $u=p\widetilde{u}$ is a path in $X$ from $x$ to $z$. Let $v=fu$, so that $v$ is a path in $Y$ from $y$ to $f(z)$. Lift $v$ to a path $\widetilde{v}$ in $\widetilde{Y}$ with $\widetilde{v}(0) = \widetilde{y}$. Define $\widetilde{f}(\widetilde{z}) = \widetilde{v}(1)$.  Notice that $q\widetilde{v}=v$ so that $q\widetilde{f} = fp$.  Define $\widetilde{g}:Y \to X$ analogously: For $\widetilde{z} \in \widetilde{Y}$ let $\widetilde{a}:[0,1] \to \widetilde{Y}$ be a path from $\widetilde{y}$ to $\widetilde{z}$. Let $z=q(z)$ so that $a=q\widetilde{a}$ is a path in $Y$ from $y$ to $z$. Let $b=fa$, so that $b$ is a path in $X$ from $x'$ to $g(z)$. Lift $b$ to a path $\widetilde{b}$ in $\widetilde{X}$ with $\widetilde{b}(0) = \widetilde{x'}$. Define $\widetilde{g}(\widetilde{z}) = \widetilde{b}(1)$.  Likewise, notice that $p\widetilde{g}=gq$.  Claim: $\widetilde{X} \overset{\widetilde{f}}{\underset{\widetilde{g}}{\leftrightarrows}} \widetilde{Y}$ is a homotopy equivalence.  We have $p\widetilde{g}\widetilde{f} = gq\widetilde{f}=gfp \simeq p$ and $q\widetilde{f}\widetilde{g} = fp\widetilde{g} = fgq \simeq q$.  This shows that $\widetilde{g}\widetilde{f}$ and $\widetilde{f}\widetilde{g}$ are covering translations (deck transformations) and are therefore homotopic to the respective identity maps. So we have a homotopy equivalence.    Any comments would be appreciated. Preventing brute force attacks against ssh? What tool or technique do you use to prevent brute force attacks against your ssh port. I noticed in my Security logs, that I have millions of attempts to login as various users through ssh.  This is on a FreeBSD box, but I imagine it would be applicable anywhere. Am I on the right track to proving this statement about composite function? Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$ Reference undefined I receive the a Reference "LastPage" undefined error when trying to compile a document with this syntax:  \fancyfoot[R]{\thepage/\pageref{LastPage}}   What is necesarry to prevent this error? I'm using TeXworks Version 0.4.3 (MiKTeX 2.9) and pdfLaTeX. I wonder a generalization of Jensen's inequality: let $\mathbf{X,Y}$ be two positive definite matrices, can we obtain the following Jensen like inequality $$(1-\lambda)\mathbf{X}^{-1}+\lambda\mathbf{Y}^{-1} \succeq((1-\lambda)\mathbf{X}+\lambda\mathbf{Y})^{-1}$$ for any $\lambda \in (0,1)$, where the notation $\mathbf{A}\succeq \mathbf{B}$ represents matrix $(\mathbf{A-B})$ positive semi-definite. How to load up CSS files using Javascript? Is it possible to import css stylesheets into a html page using Javascript? If so, how can it be done?  P.S the javascript will be hosted on my site, but I want users to be able to put in the &lt;head&gt; tag of their website, and it should be able to import a css file hosted on my server into the current web page. (both the css file and the javascript file will be hosted on my server). Exercise $7$, page 51 from Hungerford's book Algebra.     Show that $N=\{(1),(12)(34), (13)(24),(14)(23)\}$ is a normal subgroup   of $S_{4}$ contained in $A_{4}$ such that $S_{4}/N\cong S_{3}$ and   $A_{4}/N\cong \mathbb{Z}_{3}$.   I solved the question after many calculations. I would like to know if is possible to define an epimorphism $\varphi$ from $S_{4}$ to $S_{3}$ such that $N=\ker(\varphi)$.  Thanks for your kindly help. Is it now considered acceptable to follow a proper noun ... or any noun ... with a pronoun? E.g.      The President he issued a new executive order. "In the Internet" vs. "on the Internet" When should I use "in the Internet" and when "on the Internet"? How to visualize a value resulted from math node,or just to know it. I tried the way of scaling this value to the scene size and then pick the color and get the value but I want more effective way to do this. How to show that when the linear transformation $\Phi =\psi \circ \phi : E \rightarrow G$ is injective, then $\phi$ is also injective? How to show that when the linear transformation $\Phi =\psi \circ \phi : E \rightarrow G$  (where $\phi : E \rightarrow F$ and $\psi : F \rightarrow G$) is (1) injective, then $\phi$ is injective and when (2) $\Phi$ is surjective, then $\psi$ is also surjective ?  I've tried to prove it by the definition of injection and surjection, but I'm not convinced myself by it.  For example, in the first case :  If $\Phi$ is injective, $\forall g \in G$, we have $0$ or $1$ $e \in E$ such as $\Phi(e)=g$.  $\Rightarrow \Phi(e) = \psi(\phi(e)) = \psi(f) =g$.   So $\forall f \in F$, we also have $0$ or $1$ $e \in E$ such as $\phi(e)=f \in F$.   $\Rightarrow \phi$ is injective.  Is this right or did I prove nothing at all ? I think it is easier to convince myself/ to understand with surjectivity but still.. Using select by attributes then calculate field on selection in ArcPy? ArcGIS Pro 2.3  I want to create a standalone script which runs outside of ArcGIS Pro (for automation purposes), which selects features (with blank attributes) in a feature class and runs calculate field on those selections.  The code below doesn't work. It updates all fields, not the selected ones.  import arcpy arcpy.management.SelectLayerByAttribute(r"C:\Automation\Categories\Coal\Coal_automation.gdb\CLAIMS", "NEW_SELECTION", "Claim_Spend_in_£ = ''", None)  arcpy.management.CalculateField(r"C:\Automation\Categories\Coal\Coal_automation.gdb\CLAIMS", "Claim_Spend_in_£", '"Unrecorded"', "PYTHON3", None) print ("Done")   How can I write the code to run calculate field on a selection? Basic Electronics Book I need basic electronics books  (diodes,transistors,current.. etc) as I am just starting out with electronics and want to have something to read over the holiday.  Any suggestions of good beginners' books? Does measurement, quantum in particular, always increase the total entropy? Let $K$ be a field and $f \in K[x]$ a polynomial of degree $n&gt;0$. Assume that $E$ is an extension of $K$ such that $f$ can be expressed as a product of linear factors over $E$:  $$f(x)=\gamma (x-\alpha_1)(x-\alpha_2)\dots(x-\alpha_n).$$  I want to show that $\lvert K(\alpha_1,\dots,\alpha_2) : K \rvert$ is a divisor of $n!$. I also want to show that if $\lvert K(\alpha_1,\dots,\alpha_n): K \geq (n-1)!$ then $f$ is irreducible over $K$ or $f$ already has a root in $K$.  The problem has a hint. It says: "Use induction on $n=\deg f$. If $f=gh$ in $K[x]$ with $\deg g =r$ and $\deg h=n-r$, then $r!(n-r)!$ is a divisor of $n!$.  Any idea for solving this problem would be appreciated.