I have read many posts on the pros and cons of the down-vote system. Reputation points have no real value, yet I feel insulted when a question I asked is down-voted. From a personal point of view, I feel as though my input is being rejected by an entire community.   It is hard to describe how it makes me feel when I pose a question that I would want to know the answer to, only to be subjected to hostility. This may not be the intent but it's most definitely the message I receive.    Should I take down-votes personally?
I've posted a question or an answer, and I have received one or more downvotes. I am not really sure why I was down voted, or I think I know why, but I disagree.  Why did this happen, and what should I do about it?
If you hash a string using SHA-256 on your computer, and I hash the same string using SHA-256 on my computer, will we generate the same value? Does the algorithm depend on a seed (so we'd both need the same seed) or some other such parameter?  edit:  To clarify, by 'string' I meant 'the same byte input', which as the comments and @ispiro's answer point out, may be different for the same character string depending on the encoding. Show $R \setminus S$ is a union of prime ideals I'm stuck on the following question:     Let $R$ be a commutative ring with $1$, and $S \subseteq R$ a saturated multiplicative set (that is, $1 \in S$ and $x, y \in S$ if and only if $xy \in S$).  Show that $R \setminus S$ is a union of prime ideals.     Here's my attempt so far.  If $a \in R \setminus S$, then the ideal $Ra$ does not intersect $S$, because if $ra$ were in $S$ for some $r \in R$, then $a$ would have to be in $S$.  Thus, it follows by Zorn's lemma that there exist ideals $I$ of $R$ which are maximal with respect to the property that $I \cap S = \emptyset$.  Let $I$ be any such ideal.  If I can show that $I$ is prime, the conclusion will follow.  Let $xy \in I$.  I want to show that $x$ or $y$ is in $I$.  Suppose $x \not\in I$.  Then $I + Rx$ intersects $S$, so there exists $s \in S, a \in I, r \in R$ such that $s = a + rx$.  Then $sy = ay + rxy \in I$, so $sy$, and hence $y$, cannot be in $S$.  Similarly if $y$ is not in $I$, then $x \not\in S$.  So we are reduced to proving the following is impossible: $xy \in I$, $x$ and $y$ are not in $S$, but they aren't in $I$ either. Using a new document class/template with LyX? I tried googling this elsewhere but I'm new to LaTeX and extremely confused about certain things. Basically I downloaded MikteX and I'm using the latest version of Lyx with it. Now all I basically know how to do is make pretty looking mathematics and add contents pages/titles/references/etc.  I'm looking to make a dissertation and my unviersity provides a template,  (available for download at that link).  So, what exactly do I need to do (and please be super specific as I am totally clueless to all the jargon I read).   Basically, I need to download ociamthesis.cls in the first line of that webpage. Does it matter where I save it? What exactly do I do next? How is it possible that Dumbledore worked on the Philosopher's stone with Flamel? I apologize in advance if this is a common question, I searched for "flamel" here first and couldn't find the answer.  If Nicolas Flamel is several hundreds of years old, how did Dumbledore work on the Philosopher's Stone with him? Did he use it a bit himself?  To clarify, Flamel would've died without the PS, at a reasonable age -- so it can be assumed he made it about ~500 years ago. But I seem to recall the book saying that Dumbledore helped him make it. So either Dumbledore used the stone as well (unlikely it seems) or Flamel had already artificially extended his life, or Dumbledore is somehow hundreds of years old.  Am I remembering this incorrectly?  Thank you! Vectorization operator Violation of linearity assumption in Logistic Regression I built a logistic model with 7 continuous independent variable and 8 categorical (dummy) variables in R. I tested for the linearity assumption using the Box Tidwell test and all my variables show high significance.  I am wondering now, if the assumption is violated what it would mean for the coefficient estimates and if I still can run the model with caution.   I read about the approach of using regression splines but I am confused how I would determine those and interpret the model then. Force.com IDE 35.0.0.201510211056 in Eclipse missing run test class option Force.com IDE 35.0.0.201510211056 and Force.com IDE Debugger 35.0.0.201510211056 in eclipse but it doesn't show this option to run test class, is their any way i can see it because it show the Apex_Test_Result panel but running a test class option is missing. plz help This might be subjective, I don't know. However, it's a serious problem for me. My electrical bill is outrageous. It's three times as large as my next-door neighbor, and four or five times the size of my neighbor's across the street. It's worse in the summer (I live in central TX), but I've had the air conditioner inspected, and while the house is right at the maximum capacity for our unit, the unit should still be able to take care of the load. That also doesn't explain why our winter bills are larger than the comparables.  What I would like to do is check the amount of current drawn by each running appliance and calculate where all my money is going. I just don't know how to go about doing this. Prove that : $$\sum_{k=0}^{\infty} \frac{(-1)^{k}}{(2k+1)^3}=\frac{\pi^3}{32}.$$    I think this is known (see ), I appreciate any hint or link for the solution (or the full solution). How do you left pad an int with zeros when converting to a String in java?  I'm basically looking to pad out integers up to 9999 with leading zeros (e.g. 1 = 0001). Which graphics cards are supported by the new AMDGPU driver in Ubuntu 16.04? The new open source AMDGPU driver pre-installed in Ubuntu 16.04 should support all the "Volcanic Islands" cards out-of-the-box. This means that AMD Radeon R9 285, R9 380/380X and R9 Fury/FuryX graphics cards will be supported out-of-the-box if Ubuntu 16.04 LTS is installed.  However I read that the open source AMDGPU driver has an experimental support for the "Sea Islands" graphics cards (HD7790, R7 260, R9 290, R7 360, R9 390). Is this support enabled by default on Ubuntu 16.04, or will these graphics cards use the Radeon driver?  Thanks Intuitive Bernoulli numbers Conditional typesetting / build Let's say I have .tex file which is a set of problems and solutions, of which I want to make two pdf files, one which includes the solutions and one which doesn't. so I need to build the .tex file under two different modes, and specify that parts of the document be ignored under one of the modes.  This is something common in programming context. e.g. in C++ i can code  #ifdef DEBUG   // do this additional stuff ... #endif   How can I do something equivalent in latex? Is this study stating red algae reduces cold virus by 92% believable? I was using this spray meant to hasten recovery from the common cold. , sponsored by the pharmaceutical company that produces the spray, stated it reduced virus by 92%, and so shortens the duration of the common cold.  Meanwhile a doctor told me that these kinds of things don't work.  Does someone have some perspective on this? Is this a believable study? Was it well designed, and has it been duplicated?   If so, why wouldn't the pharmaceutical produced a certified and expensive drug instead of a no-prescription drug? What is the difference between can and could in 'Can/could you please explain this to me?' Relevance of cycle detection in Pollard's rho integer factorization algorithm I've recently learned about Pollard's rho factorization algorithm, and the way I understand it, it works by using a pseudorandom sequence of integers $x_{k}$ ranging from $0$ to $n-1$, where $n$ is the number to be factored, to find repetitions in an unknown sequence $y_{k} = x_{k} \bmod p$, where $p$ is an unknown, non-trivial factor of $n$. Such a repetition $y_{i}=y_{j}$ occurs when $x_{i}\equiv x_{j} \bmod p$, which can be detected by checking whether $\gcd(x_{i}-x_{j}, n)\gt 1$.  From what I could find on the Internet, Floyd's cycle detection algorithm or a variant thereof is used to find such repetitions. And the reason for this is what I don't understand.   First, Floyd's algorithm requires that each element in the sequence depends solely on the element before it, which, even if it is the case for $x_{k}$, is not necessarily the case for $y_{k}=x_{k}\bmod p$. For example, assuming we want to factorize $6$, let's take the sequence $5, 3, 2, 4, 1, 0, 5, 3, 2, 4, 1, 0,\ldots$. The cycle period is $5, 3, 2, 4, 1, 0$, where every element is contained only once. However, if we take this sequence $\bmod 2$, we get $1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0,\ldots$. Floyd's algorithm cannot be applied here to find the cycle period $1, 1, 0, 0, 1, 0$. Besides, we are not even interested in a cycle, only in repetitions. Whether we find the congruence $\bmod 2$ between $5$ and $3$, $5$ and $1$, or $4$ and $2$ in the first sequence is irrelevant.   Please correct me if my understanding of Pollard's rho algorithm as described above is wrong. But if it is not, it seems to me that one could just as well try out some random numbers between $2$ and $n-1$ and see if they share a divisor with $n$ other than $1$. So what is the benefit of using a cycle detection method like Floyd's algorithm?  I also found , but it is not answered, and the comment on the question does not really answer the question either. Solve $x\equiv 1\pmod2$, $x\equiv 2\pmod3$, $x\equiv 3\pmod4$, $x\equiv 4\pmod5$, $x\equiv 5\pmod6$ and $x\equiv 0\pmod7$ $$\begin{align*} x&amp;\equiv 1\pmod2\\ x&amp;\equiv 2\pmod3\\ x&amp;\equiv 3\pmod4\\ x&amp; \equiv 4\pmod5\\ x&amp;\equiv 5\pmod6\\ x&amp;\equiv 0\pmod7\\ \end{align*}$$  So the solution says we can eliminate $x\equiv 5(\bmod6)$ because the first two cases cover it, but I don't really know how it does. How do we solve it in cases like this where the moduli are not mutually relatively prime. Arrows linking table cells I'm currently trying to add arrows in my synthetic division example to show people clearly how synthetic division works. I'm working on Overleaf.   The code for my synthetic division right now is:  \begin{tabular}{c |r r r r r}     &amp;1&amp; 4 &amp; -1&amp;16&amp;-20\\   1&amp;&amp; 1 &amp; 5 &amp; 4&amp;20\\   \hline    &amp;1 &amp;5 &amp; 4 &amp; 20 &amp;\rule{3pt}{16pt}\;0\\   \end{tabular}   How would I add arrows to this? For instance, a down arrow going from the first 1 to 1, then an upwards arrow pointing right from 1 to 1, then an arrow pointing down from 1 to 5, etc. Basically I would like to add arrows that look like this: I am looking for a injective cochain map $\psi: C^*\rightarrow D^*$ such that the map $\Psi^i$ from $C^i$ to $D^i$ is injective, but the map $\psi^*$ from  $H^i(C^*)$ to $H^i(D^*)$ is not injective for any $i\geq0$. I am using QGIS and I created a vector grid on a crop field in order to cut it into plots. I want to save each grid cell into individual polygon shapefiles automatically.  Here is an example of a vector grid I would like to split into 117 shapefiles:    Eventually, I did it manually with the selection tool and "Save as" but it is really time-consuming when there are more than 100 plots to save.    Is there any way to do it faster and more automatically?  Each plot as an attribute named "Plot" that can discriminate against them (basically being id + 1). It's the attribute used here to label them.