Projection of a space curve
A key doubt about the resultant of two polynomials and their common zero locus
Does wind raise air temperature? In my undergrad physics classes, temperature was described as "the average kinetic energy of molecules".  By simple, and probably naive, logic, one could then conclude that wind, which is basically just moving air, would raise the temperature of the air.  However, this seems too simple to be true.  Does wind actually slightly raise air temperature?  I can see a couple potential arguments against this idea:   It could be the case that the macroscopic wind and the microscopic kinetic energy of the air molecules don't really "interact", for lack of a better word. It could be the case that the macroscopic and the microscopic motions do "interact", but since the macroscopic wind is on such a large scale compared to the average kinetic energy of individual molecules, any system in which we use the average kinetic energy of the molecules is so small that the wind is effectively constant, and so it could be ignored. Regardless, I'm guessing that the temperature only depends on the relative motion of the air molecules, so the wind just isn't even relevant   Can anybody provide some more educated input? mknod /tmp/oracle.pipe p  sqlplus / as sysdba &lt;&lt; _EOF set escape on  host nohup gzip -c &lt; /tmp/oracle.pipe &gt; /tmp/out1.gz \&amp; spool /tmp/oracle.pipe select * from employee; spool off  _EOF  rm /tmp/oracle.pip   I need to insert a trailer at the end of the zipped file out1.gz , I can count the lines using  count=zcat out1.gz |wc -l   How do i insert the trailer  T5 (assuming count=5)   At the end of out1.gz without unzipping it. The repository 'http://ppa.launchpad.net/mdeguzis/libregeek/ubuntu focal Release' does not have a Release file I'm searching how to remove the chapter+section number on the theorem numbering with a section counter.  With no section counter it's like:  \newtheorem{thm}{Title} Chapter1 ----Section 1 --------thm 1 --------thm 2 ----Section 2 --------thm 3 --------thm 4 Chapter2 ----Section 1 --------thm 5 --------thm 6 ----Section 2 --------thm 7 --------thm 8   And with the section counter:  \newtheorem{thm}{Title}[section] Chapter 1 ----Section 1 --------thm 1.1.1 --------thm 1.1.2 ----Section 2 --------thm 1.2.1 --------thm 1.2.2 Chapter 2 ----Section 1 --------thm 2.1.1 --------thm 2.1.2 ----Section 2 --------thm 2.2.1 --------thm 2.2.2   And I want numbering my theorems like this:  \newtheorem???????? Chapter 1 ----Section 1 --------thm 1 --------thm 2 ----Section 2 --------thm 1 --------thm 2 Chapter 2 ----Section 1 --------thm 1 --------thm 2 ----Section 2 --------thm 1 --------thm 2   I know it's always a pain to remove such things, thanks for whoever will help me ^^ I asked a question on Stack Overflow: . I want to award my bounty to  by user  However, my Stack Overflow account is suspended recently for 7 days, and the suspension still has 5 more days to end.And I know I can't vote, ask, answer or comment as pointed on  by  with the sentence below.  You will be unable to vote, ask, answer, or comment.  I couldn't find anything about not being able to accept an answer or award bounty so I tried to accept the mentioned answer above and award my bounty to it and I got a  Suspended users cannot vote  rejection which can be seen below with a screenshot.  I know this  If you do not award your bounty within 7 days, the highest voted answer created after the bounty started with at least 2 upvotes will be awarded half the bounty amount.  from . None of the answer given to my question is upvoted and the answer I mentioned is not the oldest one after the bounty started so it won't be awarded by community. What can I do? (except being a good guy and not get suspended :)) I did setup an easy scene with an area light behind a window. In the glass (simple plane) which is in front the area light is visible - how can I turn this off so that the background is shining throgh? Compute $\sum_{n=1}^\infty \frac{1}{(n+1)\sqrt[]{n}+n\sqrt[]{n+1}}$ Compute   $\sum_{n=1}^\infty \frac{1}{(n+1)\sqrt[]{n}+n\sqrt[]{n+1}}$ Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic I'm a fourth year undergraduate student in a university in the U.S., and this is my last semester. I have already applied to graduate schools, and I'm currently awaiting responses. Since I have already finished all my requirements and am ready to graduate, I wanted to go part time this semester. I am aware of how it affects my financial aid; however, I do not know if it has an effect on my admittance to graduate school. I do not mean whether or not I get accepted (the decisions will happen without knowledge of my current semester), but whether I am eligible to attend graduate school if I have been part time for a semester. That is, will there be any potential issues when the schools that have accepted me see my final transcript and see I was part time? Is there a universal answer to this? Or should I contact each school individually and ask about their policy?   Also, are there any other potential issues with going part time that I haven't mentioned? Anything noteworthy I might have missed? Suppose we rotate the graph of $y = f(x)$ about the $x$-axis from $a$ to $b$.  Then (using the disk method) the volume is $$\int_a^b \pi f(x)^2 dx$$ since we approximate a little piece as a cylinder.  However, if we want to find the surface area, then we approximate it as part of a cone and the formula is $$\int_a^b 2\pi f(x)\sqrt{1+f'(x)^2} dx.$$  But if approximated it by a circle with thickness $dx$ we would get $$\int_a^b 2\pi f(x) dx.$$  So my question is how come for volume we can make the cruder approximation of a disk but for surface area we can't. Is there any example of a non-measurable set whose proof of existence doesn't appeal to the Axiom of choice? Is there any example of a non-measurable set whose proof of existence doesn't appeal to the Axiom of choice?  What would it imply if there was such an example?  EDIT: For instance, maybe this will help understand the kind of example I had in mind, it is known that an important feature to determine that the AC is needed in the Banach-Tarski case is the non-transitivity of rotations on Euclidean space, one might find an example of a transitive group for some given space keeping the rest equal and make the AC unnecessary?  I guess then it might be said that this transitivity will be in this particular case equivalent to the AC or some amount of it, but I guess that it would be important to show this if it hadn't been realized before. De Rham Cohomology of the tangent bundle of a manifold I would like to compute the de Rham cohomology of the tangent bundle $TM$ of a manifold $M$. It seems to me that we can just homotopy each fibre to a point, and that this would give a homotopy equivalence between $TM$ and $M$. Since de Rham cohomology is a homotopy invariant, this would imply that $H^*_{\text{dR}}(TM) \cong H^*_{\text{dR}}(M)$.     Is it always true that the tangent bundle of a manifold is homotopic to the manifold itself by the homotopy of each fibre with a point? What happens when a black hole dies? Does it just vanish into space leaving nothing behind or does it expel some material?    Also, talking more about black holes, as far as I understand the term "temperature", it is defined by the amount of kinetic energy of the particles of a body and from what I have read, there are no particles inside a black hole, I know that you can find the temperature of a black hole by analyzing its Hawking radiation but I cant really understand how the term "temperature" can be applied to a black hole. Does it mean that whatever is that it is inside a black hole has kinetic energy? Have physicist already experienced the death of any regular black hole (by regular I mean space-sized black holes not micro ones created in labs)? Also, where is the Hawking radiation form? Because if it is released by the black hole I bet it must have formed outside the event horizon, but how exactly? $f$ differentiable except in $1$ point Assume we have a function $f : \mathbb{R} \rightarrow \mathbb{R}$ such that  $f$ is differentiable for all non-zero $x$, $f$ is continuous at $0$ and  $$\lim_{x \uparrow 0} f'(x) = \lim_{x \downarrow 0} f'(x) &lt; \infty. $$  Is it then true that $f$ is also differentiable at $0$?  If we drop the hypothesis that $f$ is continuous, this is not true since the signums function is a simple counterexample. But what if $f$ is continuous? I don't think this is true but I can't find a counterexample... Embedding DLLs in a compiled executable Is it possible to embed a pre-existing DLL into a compiled C# executable (so that you only have one file to distribute)? If it is possible, how would one go about doing it?  Normally, I'm cool with just leaving the DLLs outside and having the setup program handle everything, but there have been a couple of people at work who have asked me this and I honestly don't know. Can someone give me a short description and comparison of the different road cycling pedal / shoe systems? I am looking at buying a pedal/shoe system as the clips and straps I am using are hurting my feet again.  It's been a long time since I have bought a road pedal / shoe system, and I have forgotten the differences between SPDs, Look pedals and all the others.    Can someone give a short comparison of each pedal system with pros and cons of each? My usage is/will be mainly city street cycling and then road cycling (recreation, not racing).  I'd prefer if people would give the pros and cons of each and not their opinion on the "pedal system war".  :) However, "I use them because I find XYZ and it helps in ABC ways" is very useful. Do you know any open source tool to automatically align images, similar to the auto align feature in Photoshop? Under what circumstances will a passive HDMI-to-VGA adapter work? I have bought a no-brand, passive HDMI Male to VGA Female adapter, to link up a PC with a more dated monitor. It did not work.  After doing some reading, I have learned that buying such an adapter is often discouraged because in many cases it will not convert the signal from Digital to Analog, or the Motherboard/CPU on a specific computer might not be compatible with that particular adapter.   So my question is: seeing how there are so many of these passive adapters on the market, are there circumstances under which they actually do suffice to connect an HDMI output to a VGA input? Or are they generally just a rip-off?  Example of the kind of adapter I bought: Do users get notifications when @ was edited in How does DES decryption work? Is it the same as encryption or the reverse? If DES decryption is the same as encryption done in reverse order, then how can the reversed S-Box convert 4 bits into 6 bits?