Is there a theorem that tells us that $\widehat{f\circ g}=\hat f(\hat g)?$ Here, $\hat f$ denotes the Fourier transform of $f$.
Given two functions $f$ and $g$, is there a formula for the Fourier transform of $f \circ g$ in terms of the Fourier transforms of $f$ and $g$ individually?  I know you can do this for the sum, the product and the convolution of two functions. But I haven't seen a formula for the composition of two functions.
how to reduce DC voltage using resistors? How would one go about using a 12 V DC power source to power something which needs 4.5 V DC using resistors? Is there a way to determine how much adding a resistor would drop the voltage? If a microsite uses the same logo as the main site, which "home" should it link to? Which 'home' should the microsite's logo link to - the main site or the microsite?  Consider that...    The content and layout of the microsite is the only differentiator  Half the users reach the microsite from the main site.   The microsite doesn't have it's own URL (it's www.mainurl/microsite) The microsite has the same logo and header style (so you almost can't tell you've left the main site) If $A\subseteq\mathbb N$ and $\sum\limits_{a\in A}\frac1a$ converges then $A$ has natural density $0$ In this  to a question about a series, a theorem was stated:     If $A= \{a_i \}$ is a set such that $\sum_{i = 1}^{\infty} \frac{1}{a_i}$ converges, then $d(A) = 0$, where $d(A)$ is the  of the set.   My background in number theory is basically zero and all my attempts to prove this have been utterly unseccessful; would anyone please help me, or at least provide me with a hint to prove it? Direct product of Sylow subgroups Proposition II.7.5 of Hungerford's Algebra goes     Proposition 7.5. A finite group is nilpotent if and only if it is the direct product of its Sylow subgroups.   Let $G = (\mathbb{Z}_6, +)$. $G$ is abelian, so it is nilpotent and thus by the proposition is the direct product of its Sylow subgroups.  The Sylow subgroups of $G$ are $H = (\mathbb{Z}_3, +)$ and $K = (\mathbb{Z}_2, +)$, so the proposition says $G = H \times K$. In particular, $0 \in H$ and $0 \in K$, so $(0,0) \in H \times K = G$... but that's not true, since $G = \{0,1,2,3,4,5\}$.  Where is/are my misunderstanding(s)? Why does inertia happen? In  R P Feynman relates a story where his father told him that, even though we know the word "inertia" and what it means, nobody knows why inertia happens. Is that still true? Command to move a file to Trash via Terminal I would like to know if there is a command I can issue in a terminal so I do not classically remove (rm) the file, but instead move it to trash (i.e. Nautilus Move to Trash behavior).  In case there is such a command, I would also be interested in knowing what it is. "Please ask a new question" encourages question repetition for duplicates I just had a case of a user who re-posted his question because his first question was closed as a duplicate. And, logically, I closed his re-post as a duplicate of his original, asking him to edit his original and explain why it's not a duplicate, so we can reopen it.  This process has worked like that for years now, but suddenly I realized that with the new message, question repetition is even encouraged:     This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.   Clearly, a new user who finds their questions closed will now be happy to just post their question again and again, until it's not a duplicate anymore, instead of just fixing their original post.  We need to be more explicit about this, and show this message to the OP of the question:     If those answers do not fully address your question, please edit your question and explain why it is not a duplicate.   The original message should still be visible to other users and visitors, as they can't fix that question, of course. Restrictions on the variables for this identity are as follows: $a \geq m \geq 0$ and $n \geq b \geq 0$.  I have not gotten far with this, but these are my very rudimentary thoughts: We need to define a special element, somehow, and then carve up the $m + n$ remaining elements to be chosen out of the remaining pool of $a + b$ elements by writing $a + b = a - i + b + i$. From the $a - i$ pile, we choose $m$ things. From the $b + i$ pile, we choose $n$ things. My problem is, what is going on with this special element? How is it being defined so as to split things in this precise way?  A hint would be great for the moment. When will my device get the Android 5.1 update (Lollipop)? Android 5.1 (Lollipop) was officially announced on March 9th, 2015.  You can review the high-level changes at the announcement on the official .  Of course, not all devices will get this update right away and others won't get it at all. Each manufacturer and carrier often choose to add their custom modifications which tend to delay the official release.  When will each device get Android 5.1, either officially or unofficially, if ever?  See also: My webcam just came on "out of the blue" SINGLE_EMAIL_LIMIT_EXCEEDED. What does it mean? Can an Indian citizen holding a valid USA visa visit Colombia without a visa? I am planning to travel to Colombia for about a week to attend an academic conference. I am an Indian passport holder currently living in USA with a F-1 visa. Do I need to obtain a visa beforehand from the Colombian consulate?  I have found   that claim that Indian citizens holding a valid USA visa are not required to apply for Colombian visa.     However, I am not sure if these sources are "official" and trustworthy.Is there a more official source? Also, does this rule apply to "tourists" only? Does anyone have any personal experience with this rule? Windows 10 Search not loading, showing blank window Why can't I destroy or place blocks? I'm playing on a Survival world with cheats on, "easy" difficulty, and at night in-game. I didn't have a sword or anything to make a sword with, and I was starving, so I switched to Creative to give myself a stack of food and a bed to set my spawn point. When I switched back to Survival, I couldn't destroy or place blocks. I'm on single player, and my Internet is fine, and I can destroy blocks still if I switch to creative. I've tried resetting the button one, and reloading the map, and it still doesn't work. I've even tried deleting everything I gave myself in Creative. This happened before on a different world and I ended up deleting it.  This only happens on this world. How do I fix it?  If I know I'm in the correct game mode, what else can cause this?  Are there different causes in multiplayer? What's the purpose (if any) of "javascript:" in event handler tags? I've been making a concerted effort to improve my javascript skills lately by reading as much javascript code as I can. In doing this I've sometimes seen the javascript: prefix appended to the front of event handler attributes in HTML element tags. What's the purpose of this prefix? Basically, is there any appreciable difference between:  onchange="javascript: myFunction(this)"   and  onchange="myFunction(this)"   ? How did Sauron remain in control of the Nazgûl? How can I trigger a command when a player is hit by a Snowball? I am trying to make a snowball that triggers a command when it hits a player in 1.15, but I don't know how to do that. When I do execute at @e[type=snowball] run gamemode spectator @a[distance=..2] it only runs the command if it goes right next to them. By default after a new user signs up, a redirect to the home page happens.  But in such case I want to redirect such user to another page like node/35.  In this node/35 I then want to display some content. This is a  about Licensing.    Questions on licensing are off-topic on Server Fault.  If your question has been closed as a duplicate of this question, then this is because we want to help you understand why licence questions are off topic rather than just telling you "it just is". In all likelihood, this question will not address your question directly, it was not meant to.    I have a question regarding software licensing. Can the Server Fault community please help with the following:   How many licenses do I need? Is this licensing configuration valid? What CALs do I need to be properly licensed? Can I run this product in a virtual environment? Can I downgrade this product to an earlier version? Am I entitled to feature X with license Y? How to change background and maintain realistic effect? I have like 30 different photos to process like this, but I want to know key things to maintain realistic photo by changing it's background, or maybe just modify background so it would be more pleasing to eye.(If you know tutorial related to my problem, please do provide it to me)  Here is the photo:   Here is my step 2:   Here is background:   Here is the result:   As you can see, it isn't any close to realistic feel. I fooled around with levels, but all I got was this and still it doesn't feels right.  First try:   Second try:   Update  Different background: