I have a website of one of my clients that allows the user to delete pages by themselves with a form. When a page is deleted the website generates a 404 Error.  The deleted pages total about 5000, and the URLs deleted are still in the Sitemap submitted in the Search Console.   Are these 5000 404 Errors a problem? Should I use a 301 redirect pointing to a page with the message, "This page has been deleted"? Do I have to delete these deleted URLs from the sitemap?
Do the search engines take the number of 404 errors returned by a site into account when calculating the site rank? For example I have 8,000 404 errors and I am thinking that that's affecting my SEO in a negative way.  However, I read  about 404 errors which suggests that they are not always a negative quality indicator.   So I am confused...are high numbers of 404 errors harmful to a site or not?
What could cause exposure problems after my camera got wet? I had an unfortunate accident where my DSLR camera (and me) briefly ended up in a river. The camera wasn't fully submerged but it did get very wet. It still works, sort of, although the electrics are doing some random things. I'm hoping that's just a bit of dampness doing that, that will fix itself when it dries out fully.  More concerning is that the documents exposure metering seems to be all wrong when using the viewfinder. Pictures are extremely overexposed and nearly white. But if I use live view, then they are fine.  Why could cause this? I assume the light is routed a different way when using the viewfinder and maybe it is going through something with water/condensation on it? How does the color of a car influence its inner temperature change over time when parked outside in windless, hot and sunny regions?  I know what's the common idea about that: black cars are supposed to build up high temperatures faster because black objects absorb radiations instead of reflecting them off. Is it true? And then, what happens during the steady state? Some claim the black car will stay hotter, some others claim it will be the same whatever the color. Do all cars have the same temperature inside in the long run, or are some of them hotter?  I've Googled it but the best I could find was . It claims to be based upon ~20 articles. But there's not even a mention of absorption or emission spectrums. A priori, a black car could absorb all visible radiations and emit it as infrared while reflecting all of the Sun's infrared. And it's still only qualitative. I've found nothing on Physics stackexchange, the closest being . Possessive of a word that is already possessive If the cricket ground Lord's is a possessive, what if you want to describe something belonging to Lord's? Would you say:     I was very impressed by Lord's's customer services.   It doesn't look right, so what is the correct way of writing it? Changing user preferences via console? The machine that I'm currently using is an extremely slow netbook. Whenever I go to change user preferences in Blender, it stalls out. What I need to do is activate the "emulate 3 button mouse" checkbox. Is there a way to do this via console/script? extract string between double quotes I have requirement that i need to extract string using quotes. My string as follows.  "abcd efgh" "ijkl mnop" "qrst uvwxyz"   can you help me to get the string between second double quotes(ijkl mnop) using sed or grep command.  In other words if I say give me the string in first quotes I want the  first string; if I say second string it should give me string between second double quotes and similarly third one also. DOS of Van Hove singularity in 2D square lattice tight binding model For the simplest example, 2D square lattice tight binding model gives the energy band as $$\varepsilon_k=-2t(\cos k_x+\cos k_y) \, .$$ We know that $\mathbf{k}=(0,\pi)$ and related momentum points are saddle points which give $|\nabla_k \varepsilon_k|=0$ and thus some kind of singularity in density of state (DOS) since $$\rho(\varepsilon)\propto \int_{\varepsilon=\text{const}} \frac{d S}{|\nabla_k \varepsilon_k|} \, .$$ How can I get the $\ln$ divergence for DOS near $\varepsilon=0$? Should I only care about those singularity points and omit the integral from normal parts and do Taylor expansion near those saddle points?   Moreover, why are points like $(\pi/2,-\pi/2)$ or $(2\pi/3,-\pi/3)$ not called Van Hove points when those points are also lie in the $\varepsilon=0$ line and give $|\nabla_k \varepsilon_k|=0$? How do I make windows save their position on screen after re-attaching a display? Let $R$ be a sub-ring of a ring $S$. Let $f,g$ be non-zero polynomials in $R[x]$ and assume that the leading coefficient of $f$ is a unit in $R$. If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$.   Thoughts: If $f$ divides $g$ in $S[x]$, then  $g(x) = f(x)q(x)$ for some $q(x)$ in $S[x]$. From here I'm not sure what the question is asking. Do I have to show that $q(x)$ is an element of $R[x]$ ? Insights appreciated. How can we evaluate this series  $$\sum_{n=1}^\infty \frac{n^a}{b^n}?$$  Here $a$ and $b$ are positive integers. If $b=1$ then series will be diverging, in other cases, it will be converging, but how to find this sum?  Isn't there a simple solution which doesn't involve Stirling numbers? Can Cycles physically mix colours? $C \otimes A \cong C \otimes B$ does not imply $A \cong B$ Let $R$ be a commutative unital ring and let $M$ be an $R$-module and let $S$ be a multiplicative subset of $R$.  Today I proved both of the following: $$ S^{-1} R\otimes_R S^{-1}M \cong S^{-1} M$$ and $$ S^{-1} R \otimes M \cong S^{-1} M$$  Now I'm slightly confused.      Either my proofs are wrong or $C \otimes A \cong C \otimes B$ does not imply $A \cong B$. But I can't come up with an example. Can someone give me an example? (Or tell me that my proofs are wrong.) An example of a lattice that's not totally ordered How can I undo git reset --hard HEAD~1? when calling SCP in PuTTY on my Win7 box, it doesn't let me use C:/, but I also have no idea where on my local machine it will look for files by default. None of program directory or user directory worked. For example, I saved file.txt next to PuTTY.exe, and also in C:\Users\Me but calling SCP file.txt file.txt in PuTTY failed both times with      cp: cannot stat 'file.txt'   So, how do I transfer a file to my server using PuTTY?  EDIT: Also, calling SCP file.txt myserver:file.txt gives a similar error: file.txt: No such file or directory Let $A,B$ be two sets. The  states that if there is an injection $f\colon A\to B$ and an injection $g\colon B\to A$, then there exists a bijection $h\colon A\to B$.  I was wondering whether the following statements are true (maybe by using the AC if necessary):   Suppose $f \colon A\to B$ and $g\colon B\to A$ are both surjective, does this imply that there is a bijection between $A$ and $B$. Suppose either $f\colon A\to B$ or $g\colon  A\to B$ is surjective and the other one injective, does this imply that there is a bijection between $A$ and $B$. file /dev/* prints the description of a bunch of files as "block special (M/N)" and "character special (M/N)", where M and N are numbers. For example:  $ file /dev/null /dev/null: character special (1/3)   man file doesn't seem to document these, but refers vaguely to man stat, which seems to refer to these as major and minor device types. apropos 'device type' finds nothing. So what do these numbers mean? i would like to know how to prove that if $a^2+b^2=c^2$ then   a) $3|a$ or $3|b$  b) $5|a$ or $5|b$ or $5|c$  c) $4|a$ or $4|b$   Also that $a^2+b^2+c^2+1$ can't be divisible by 8  Thank you very much! What do I if I used "Reset All" or "Erase All Content and Settings" on a jailbroken iOS Device? I recently received an iOS device and it was jailbroken. When I wanted to unjailbreak it, I used "Erase All Content and Settings." The loading screen came on and it has not changed. After rebooting the device, it is now stuck at the Apple logo. What should I do? What is the explanation of the non-existence of magnetic monopoles? I came across this problem when I was at a book store inside of a book made to prepare Berkeley graduates to pass a mandatory exam. I wanted to buy the book, but, alas, I didn't have the money (forty bucks is a lot of money when you don't have a job). So I took my phone out and started taking as many pictures as I could. Unfortunately, I didn't take any pictures of the solutions!  Enough backstory. Time for math. The problem is as follows:  Prove that $\cos^p( \theta) \le \cos(p \theta)$ if $0\le\theta\le\frac\pi2$ and $0\le p\le 1$.  I tried using the series expansion for cosine, but that seemed to be a dead end. Then I tried using Euler's theorem, but I got stuck. Then I got distracted and started to think about other cosine identities. For example, $$\cos\left(\frac\theta2\right)=\pm\sqrt{\frac{1+\cos(\theta)}{2}}.$$ Then what is $\cos(\frac\theta3)$ equal to? I tried to figure it out then I realized that I needed to find the root of a cubic polynomial. Then I realized that I'm better at staying focused than finding the roots of cubic polynomials.  Anyways, a proof would be nice here. I really appreciate any hints or answers. I apologize for my digressions!