I found some sentences like "Most people work by day and sleep by night." Is it appropriate to use these sort of wordings like "sleep by night"?  If so, what's difference between "sleep by night" and "sleep at night"?
say by has the meaning of      6. indicating the period in which something happens: ‘this animal always hunts by night’   Then do we need to say, ‘Why does the sky glitter by night?’ And can’t we say, ‘Why does the sky glitter at night?’?   If we can use both, what’s the difference between the two?
How to prove Vandermonde's Identity: $\sum_{k=0}^{n}\binom{R}{k}\binom{M}{n-k}=\binom{R+M}{n}$? How can we prove that     $$\sum_{k=0}^{n}\binom{R}{k}\binom{M}{n-k}=\binom{R+M}{n}?$$   (Presumptive) Source: Theoretical Exercise 8, Ch 1, A First Course in Probability, 8th ed by Sheldon Ross. $f$ holomorphic on $D\setminus \{0\}$ and takes no values in $(-\infty,0],$ then $0$ removable If $f$ is holomorphic on $D\setminus \{0\}$ and takes no values in $(-\infty,0]$ then $0$ is a removable singularity.   I thought to prove this by elimination, but I can't really tell anything about the behavior of $f$ around $0$. How can one translate the information about the definition of $f$ in semi-open interval $(-\infty,0]$. How to automatically add &raquo; (») to  elements using CSS? Print file content without the first and last lines Suddenly mysql/mariadb won't start Let us assume a shared ownership house, where everything is 50/50 in terms of deposit, monthly payments, bills, and eventually estate agent costs, and lawyer costs when the house is sold.  If the mortgage is over 25 years and for the first 5 years both owners live in the house and split everything 50/50, how do the calculations and ownership percentages change if one of the owners decides to move on and rent elsewhere, leaving the other owner to pay 100% of the mortgage bills etc etc?  After the 25 years, do both owners still get 50/50 when the house is sold? Every time since a few days ago after I caught Mespirit, when I go to the portal in the Nameless Cavern and I press A to interact. All that happens is a short dialog sequence and nothing else. I know the requirements are along the lines of having 3 max happiness Pokemon with you in your party which I do. I have also downloaded the recent update/patch from the eShop if that helps at all. How can I make Uxie and Azelf appear in the cavern? Proof for triangle inequality for vectors Generally,the length of the sum of two vectors is not equal to the sum of their lengths. To see this consider the vectors $u$ and $v$ as shown below.  By considering $u$ and $v$ as two sides of a triangle, we can see that the lengths of the third side is $\| u + v \|$ and we have $\| u + v \| \leq \|u\| + \|v\|$.  Under what circumstance equality occurs and how can one prove that? I generated a key and copied it to my target:  ssh-keygen ssh-copy-id username@hostname   I left the the location of the key as default and did not set any passphrase.  For a small while after that, I was able to ssh username@hostname without being prompted for a password, and then it stopped working for some reason. My model has a clear plastic (or glass) dome with objects inside.  The objects appear dark.  I've tried the glass shader with color 100% RGB, with very small IOR, and using just a refraction shader.    I know Cycles has problems with caustics, but I just want broad illumination to fall clean through the glass.  The light-to-column path can ignore refraction, but is blocked or tremendously attenuated. The camera-column path needs refraction, and seems to work fine anyway.  This demo image offers all optical paths of interest:   light upon object, seen directly light upon object, seen through glass (looks okay) light through glass onto object, seen directly. This is the shadow on the lit side of the column just below the glass tubing.  I expect full illumination, but there is shadow.  There is some light, but it's diffuse light from the floor. light through glass onto object, seen through glass. This     I did at one point try non-progressive rendering, and find extremely coarse light where there shouldn't be shadow, but this is not a practical way to make nice images. I've even tried cranking up certain sampling settings to many thousands, but still get bad noise though less, at the cost of long render times. I  would like to finish my creations sometime before "Star Trek, the Generation After the Next" becomes real life, if you know what I mean.  The next image is an example. I think Transmission in Sampling was 5000, but not sure.    I'm using Cycles in Blender 2.67 on a quad core Linux machine, 16GB RAM. Machine limits have never been a problem for 3D rendering.  Possibly, I screwed up some setting when I made my startup file, and just need to fix it. OTOH maybe this is just a limitation of path tracing, or of the way Cycles does it. If that's the case, what to real-world Blender artists do when they need to produce images on a budget and schedule?  What is the practical real-world fix? Tag info not updated regularly on profile? From my , I learned that all tag related info on profile will be updated daily at UTC 03:00.  However, something is wrong here. It's now UTC 05:00+, but my tag number, say 93 (c++) is not updated against yesterday. I am pretty sure about this and I did earn some more points throughout the day. Sorry for not be able to capture the screenshot yesterday, but I did check this number 10 hours ago (which belongs to yesterday, also 93).  Is there a bug happening here? Or updating time different?    UPDATE: As of 24 Jan, the tags are still not updated with the proper values.  UPDATE2: Fixed around 25 Jan, UTC 03:00, at least for me. Is there any way to fix the wavy lines that appear when photographing a striped dress?   It's not just in viewing online: when it was printed at wallet size, the wavy lines showed up. Why marinade meat with acid or enzymes? Two different solutions to integral How do I brew an X potion? The problem from Burton: show that the equation $n^2 + (n+1)^2 = m^3$ has no solution in the positive integers.  So far, I can see that gcd($n$,$n+1$)$=1$ and $m \equiv_4 1$ and $m=a^2 + b^2$ for some integers a,b. I'm guessing I need to reach a contradiction.  At this point, I am stuck. Any hints? During the 'Hard Answers' Thieves Guild quest, Karliah asked me to meet her at the Ragged Flagon.  However, it seems that she doesn't show up at the rendezvous point.  Where do I find her? Hill cipher, unknown letter value I've been struggling on this problem for a while now : the Hill cipher is well-known to be vulnerable to known-plaintext attack due to its linearity. Given a key matrix $K$ of size $n\times n$, one can retrieve the key with as little as $n^2$ plaintext/cipher text couples.  All examples found on the Internet assume an alphabet where $A=0, B=1 \dots Z=25$, but how could we break the Hill cipher using a know-plaintext attack without any clue over the alphabet permutation nor the key matrix ?  I've tried several things such as  the whole set of equations together, however it requires several divisions in $\bf{Z}_{26}$ which aren't possible (i.e. division by even numbers or 13) On any SE post one can use the backtick symbol ("`") in order to mark some text as being a piece of code, or computer output. For example: void main().  Is there a way to make use of "`" the same way in a LaTeX document? SQL Coalesce in WHERE clause I'm trying to implement optional parameters in a stored procedure that I have but I am running into a problem. Here's a simplified query to illustrate the issue:  SET ANSI_NULLS OFF  DECLARE @MiddleName VARCHAR(20); SET @MiddleName = NULL;  SELECT * FROM [Customer] WHERE [LastName] = 'Torres' AND [MiddleName] = COALESCE(@MiddleName, [MiddleName])   When I run this query I need to get one row back because one Torres has NULL in the [MiddleName] column. But the query returns zero rows. Using IFNULL() produces the same result. From researching COALESCE, I was under the impression that NULL would be returned if all expressions are NULL. As I am not a SQL expert I assume that I am missing something, but what is it.....  Thanks in advance for any help.