What features make a lens good for astrophotography/low light photography?
What lens characteristics are important in star photography?
Infix to postfix not working as expected Which one is correct to say: "It's me" or "It's I"? I was taught at school that the following expression is not grammatically correct:  Who is there? It's me.  The correct one is:  Who is there? It's I.  Can you let me know which one is accurate? $\lim_{n→∞} f(n+x)=0$ results in $ \lim_{x→∞} f(x)=0$ $f\colon [0,\infty) \to \mathbb{R}$ is uniformly continuous.  If $\lim_{n\to \infty}f(n+x)=0$ where $x\in [0,1]$, then $\lim_{x\to\infty} f(x)=0$.  every my trying to solve this is wrong :(  how can i prove this?  and if $f$ is just continuous, what happens to the results Short story about aliens who want to trade items for information, stories, jokes etc Cycles in SHA-256 Let's say I start with a particular 256 bit value. Call this $v$. I then hash that value, and get another 256 bit value. Call this $\text{SHA256}(v)$. I take this value and get another 256 bit value. Call this $\text{SHA256}^2(v)$. More generally, let's call the result of hashing $v$ repeatedly $n$ times $\text{SHA256}^n(v)$.  Now my question is, how big will $n$ be, such that $\text{SHA256}^n(v) = v$?  It would seem to me, that if it's a giant sort of permutation, $n$ would have to be $2^{256}$, is that correct? Is that provable, or is there any information on this? (Just curiosity, really.)  Another question I had was, do all 256 bit strings have unique SHA256 values, and is there a way to show that? (Or, stated differently, can it be shown that there are no SHA-256 collisions in the language of all "256 bit strings"?) I have the following page (deadlink: http://www.workingstorage.com/Sample.htm ) that has a footer which I can't make sit at the bottom of the page. I want the footer to  stick to the window bottom when the page is short and the screen is not filled, and stay at the document end and move down as normal when there is more than a screenful of content (instead of overlapping the content).  The CSS is inherited and befuddles me. I can't seem to change it properly to put a minimum height on the content or make the footer go to the bottom. Reflection of sound waves from the open end of an organ pipe & relationship b/w nodes & pressure We know that standing waves are created when any wave traveling along the medium will reflect back when they reach the end. But in an open organ pipe, there is nothing to oppose the wave and reflect it back. So then how are standing waves created in such a case? In standing waves where is the pressure greater, at nodes or anti-nodes? 1.13 Detect if no mobs with a specific tag exist and execute commands My 1.12 solution can be found . When trying to update command blocks to 1.13, I have the following:  scoreboard objectives add invert dummy   (run at start) then:  scoreboard players set FakePlayer invert 1   (impulse unconditional repeat) chained into:  execute at @e[tag=summoned] run scoreboard players reset FakePlayer invert   (chain unconditional repeat) chained into:  execute if score FakePlayer invert = 1 invert run say "All summoned animals are dead!"   This should reset FakePlayers score continuously until all entities with tag "summoned" are dead, then it should run the final condition. This does not happen, and I can't see why. If $R$ is an infinite ring, then $R$ has either infinitely many zero divisors, or no zero divisors Please help me to prove that if $R$ is an infinite ring, then $R$ has either an infinite number of zero divisors, or it has no zero divisors. What is the expression on RegularExpressionValidator to check if the Textbox text is 6 or more characters long? Is there evidence that adding salt to water prior to boiling can damage a stainless steel pan? Prove $f(S \cup T) = f(S) \cup f(T)$ $f(S \cup T) = f(S) \cup f(T)$  $f(S)$ encompasses all $x$ that is in $S$ $f(T)$ encompasses all $x$ that is in $T$  Thus the domain being the same, both the LHS and RHS map to the same $y$, since the function $f$ is the same for both.  Can you post the solution? I am trying to solve an exercise in Shankar's QM book (concretely 4.2.1), and I am asked the probability of each possible value for the operator $L_x$ when the particle is in a certain eigenstate of another operator $L_z$. I understand that I have to "expand" the state vector in the $L_z$ basis, which in this case is just the appropriate eigenvector, and then change the base to that of $L_x$, i.e to write the $L_z$ eigenstate in the $L_x$ base. The problem is that there is just no way of doing it, since the eigenvectors of $L_x$ don't span the whole Hilbert Space.   I thought all quantum operators had a set of eigenvectors that spanned the whole space, am I wrong on that or am I wrong on my algebra? Closed form for $ \int_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$ I've been looking at  $$\int\limits_0^\infty  {\frac{{{x^n}}}{{1 + {x^m}}}dx }$$  It seems that it always evaluates in terms of $\sin X$ and $\pi$, where $X$ is to be determined. For example:  $$\displaystyle \int\limits_0^\infty  {\frac{{{x^1}}}{{1 + {x^3}}}dx = } \frac{\pi }{3}\frac{1}{{\sin \frac{\pi }{3}}} = \frac{{2\pi }}{{3\sqrt 3 }}$$  $$\int\limits_0^\infty  {\frac{{{x^1}}}{{1 + {x^4}}}dx = } \frac{\pi }{4}$$  $$\int\limits_0^\infty  {\frac{{{x^2}}}{{1 + {x^5}}}dx = } \frac{\pi }{5}\frac{1}{{\sin \frac{{2\pi }}{5}}}$$  So I guess there must be a closed form - the use of $\Gamma(x)\Gamma(1-x)$ first comess to my mind because of the $\dfrac{{\pi x}}{{\sin \pi x}}$ appearing. Note that the arguments are always the ratio of the exponents, like $\dfrac{1}{4}$, $\dfrac{1}{3}$ and $\dfrac{2}{5}$. Is there any way of finding it? I'll work on it and update with any ideas.    UPDATE:  The integral reduces to finding   $$\int\limits_{ - \infty }^\infty  {\frac{{{e^{a t}}}}{{{e^t} + 1}}dt} $$  With $a =\dfrac{n+1}{m}$ which converges only if   $$0 &lt; a &lt; 1$$  Using series I find the solution is     $$\sum\limits_{k =  - \infty }^\infty  {\frac{{{{\left( { - 1} \right)}^k}}}{{a + k}}} $$ Since humans are not large in mass, do we exert enough gravitational force for a small object to orbit around us? (Assuming that the only gravitational force acting on the object is from the human). Using Newton's law of gravity and using myself as the human mass, I exert a 10^-8 force on a 1 kg object .5 meter away, but I am not sure if even this small of a force will be acceptable. What is the baseline "force" between two objects for 1 to orbit another?  Edit: I am not sure if this is a SpaceExchange question. In Postgres txid_current() should return biginteger but instead an integer is returned In Postgres 11, according to documentation, txid_current() should return biginteger but I'm getting small integer that doesn't look like is extended by epoch counter. My txid looks like this: 1123  "The internal transaction ID type (xid) is 32 bits wide and wraps around every 4 billion transactions. However, these functions  export a 64-bit format that is extended with an “epoch” counter so it will not wrap around during the life of an installation."     Am I interpreting documentation incorrectly? Are there any drawbacks to using a wish spell to increase ability scores? If not then what would stop players from just using wish repeatedly and raising their ability scores to 30?  I'm just getting back into RPGs with D&amp;D 5e after not playing for years, and I seem to remember this being covered in the editions we played back then. Uniformly convergence of $f_{n+1}(x)= \int^x_0 f_n(t)dt$ In my lecture, the lecturer said:      Let $K$ be the key generation algorithm. Given a security parameter represented in unary, $1^k$, $K(1^k)$ will output a keypair $(pk; sk)$, known as the public key and the private (or secret) key, respectively.    My question is: When I want to implement the cryptosystem, how should I represent this $1^k$?  When I implement the key generation procedure, do I literally require callers to pass me a string of $k$ one-bits that the procedure will never use?  And, if so, why is it there in the first place? I have Ubuntu 14.04 and two monitors. When I open applications I need some of them to be on the primary monitor and others On the secondary. At the moment, apps always open in the primary monitor.   I have dash icons only on one (left) display, so I can't launch apps using the cursor or active window setting from Compiz.