I am in the situation where I want delimiters that are bigger that \big, but smaller than \Big (see example).  \documentclass{article}  \usepackage{mathtools} \usepackage[libertine]{newtxmath} \begin{document} \[\Bigl(\bigl(\text{some formula}\bigr)\Bigr)\] \end{document}   With newtxmath, the outside delimiters are a lot bigger than the  \bigdelimters inside, but I want them only slightly bigger. scalebox from the graphicxpackage doesn't seem to be satisfactory.
This question has bugged me for a while. I want to write a nested function, f(g(x)). If I naively enter it:  \begin{align}     f(g(x))=y \end{align}     The problem is that each and every parenthesis is the same size as all of the others. Shouldn't the outer parentheses be larger? But if I do this:  \begin{align}     f\left(g(x)\right)=y \end{align}     Now it looks even less like the functions are nested. What's the proper way to do this?
Where can I post my photos and get reviews, comments, and critiques from the community, in order to learn to become a better photographer?  Here is a list of places to get feedback.  Please use answer wikis to comment and rate each one.    As you get more advanced you might also want to try out photo contests, both online and local. Create an instance of a class from a string Sorry for the vague title--I don't want the title to be a spoiler.  I've seen the movie three times, and the last two times I looked specifically for clues to this question, but found none.  The final scene in  shows       Cobb's top spinning, as he goes off to be reunited with his children.  The top continues to spin, then the movie ends, without telling us if the top topples--and therefore revealing whether he's in the "real world" or still in a dream. Do we know if he was in a dream at the end of the movie?   I'm assuming the answer is that we simply cannot know.  But did I miss anything?  Were there clues that I missed? What are the best JVM settings you have found for running Eclipse? Difference between spin and polarization of a photon I understand how one associates the spin of a quantum particle, e.g. of a photon, with intrinsic angular momentum. And in electromagnetism I have always understood the polarization of an EM wave as the oscillations of the E and M field, not necessarily being  aligned with the direction of propagation of the wave.     Questions:   But when one talks about the polarization of a photon in Quantum Mechanics, how does it really differ from its spin?  Are they somehow related and what's the physical idea behind photon polarization in contrast to photon-spin? Feel free to use mathematical reasonings as well if you see it fit! Understanding hard drive space How to find the sum $$\sum^n_{k=1} (k^2+k+1)k!$$  What I tried as follows :   $$\sum^n_{k=1} (k^2+k+1)k!$$  =$$\sum^n_{k=1} (k^2)k!+ \sum^n_{k=1} (k)k! + \sum^n_{k=1} (1)k!$$  Now we can write $\sum^n_{k=1} (k^2) $ as $$\frac{n(n+1)(2n+1)}{6}$$ but what to do with $k!$ please guide thanks....... I bought an audio book from audible and want to convert it to mp3 from aa because my phone doesn't support the format. Is there any way to do that? Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$ I'd like to show that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$ for all $x,y \ge 0$ and $p \in [0,1]$. I started out by defining a function $f(x,y)=(1+x)^p(1+y)^{1-p}$ and checking for critical points, but there are none in the domain I'm interested in. I think I'm probably missing a slick application of Jensen's or Holder's inequalities, but so far a proof eludes me. Any suggestions would be appreciated. Prove that the natural map $\alpha : \text{Hom}(X,\text{Spec} A) \rightarrow \text{Hom}(A,\Gamma(X,\mathcal{O}_X))$ is an isomorphism This is question 2.4 in Hartshorne. Let $A$ be a ring and $(X,\mathcal{O}_X)$ a scheme. We have the associated map of sheaves $f^\#: \mathcal{O}_{\text{Spec } A} \rightarrow f_* \mathcal{O}_X$. Taking global sections  we obtain a homomorphism $A \rightarrow \Gamma(X,\mathcal{O}_X)$. Thus there is a natural map $\alpha : \text{Hom}(X,\text{Spec} A) \rightarrow \text{Hom}(A,\Gamma(X,\mathcal{O}_X))$. Show $\alpha$ is bijective.  I figure we need to start off with the fact that we can cover $X$ with affine open $U_i$, and that a homomorphism $A \rightarrow \Gamma(X,\mathcal{O}_X)$ induces a morphism of schemes from each $U_i$ to $\text{Spec} A$ and some how glue them together. But I have no idea how to show that the induced morphisms agree on intersections. How does this work? Sorting an array of an array of objects in PHP by key value Basically I have a setup like the following:  Array (  [0] =&gt; Array ( [0] =&gt; stdClass Object ( [nid] =&gt; 1 [title] =&gt; title1 [uid] =&gt; 1 [parent] =&gt; 0 [weight] =&gt; -15 [name] =&gt; name1 [value] =&gt; 0 )                [1] =&gt; stdClass Object ( [nid] =&gt; 2 [title] =&gt; title2 [uid] =&gt; 1 [parent] =&gt; 0 [weight] =&gt; -7 [name] =&gt; name2 [value] =&gt; 100 )                [2] =&gt; stdClass Object ( [nid] =&gt; 3 [title] =&gt; title3 [uid] =&gt; 2 [parent] =&gt; 0 [weight] =&gt; -1 [name] =&gt; name3 [value] =&gt; 0 )                [3] =&gt; stdClass Object ( [nid] =&gt; 4 [title] =&gt; title4 [uid] =&gt; 2 [parent] =&gt; 0 [weight] =&gt; 1 [name] =&gt; name4 [value] =&gt; 80 )               )   )   What I need is a way to sort all the arrays inside the parent array by the [value] key in the Object. I've been trying for about 2 days now with usort and different methods but I just can't seem to get my head around it. The [value] key will range anywhere from 0 to 100 and I need all of the arrays sorted in decreasing order (IE: 100 down to 0). Showing $\sup \{ \sin n \mid n\in \mathbb N \} =1$ Infinitely many primes for quadratic residues Congruent Modulo $n$: definition In an Introduction to Abstract Algebra by Thomas Whitelaw, he gives examples of the congruence mod operation, such as $13 \equiv5 \pmod4$,  and $9 \equiv -1 \pmod 5$. But when I first learned about the modulo operation my junior year, I would have told you that $13 \equiv 1 \pmod 4$, and that $9 \equiv 4 \pmod 5$.     Is this just a difference in the definition of modulo? Or is this pretty typical (to not take it to the largest factor, or one over)? What will Sony do if someone uses my account as primary on another ps4 without my knowledge? What will Sony do if someone uses my account as primary on another ps4 without my knowledge? Will the account be banned? Or will the other guy that has my account as primary be banned? After how long? I have no credit card on my account so I don't care too much but I want to know.   He uses my account on his ps4 as a primary account. I think to use my digital games as free (Sharing, but without my knowledge). E.g.: If your Gmail ID is abc.xyz@gmail.com, it considers this the same as abcxyz@gmail.com.  Why is this so? What is gravity and what causes objects to act against it? So I understand the concept of gravity, in that it's not actually a force, but more of a displacement in the spacetime grid. An object with a big enough mass will bend the spacetime, causing smaller objects to "attract" to it (not really, but good enough for what I am trying to figure out)   Ok so that makes sense, but what I am not understanding is, how come planets don't just get engulfed by the Sun? There must be something acting against the gravity for the planet to be a certain distance away from the sun. Am I not understanding this concept correctly? Your Mileage May Vary In the United States we have a saying, "your mileage may vary", which means "your experience may be different".  In English-speaking countries that don't use Imperial miles, is there an equivalent expression? How to make number input area initially empty instead of 0 or 0.00? I am currently in the process of trying to repair a power supply that has had one of its DC rails fail. A resistor in the PSU has exploded and I am trying to find what value it is.    Band 1: White Band 2: Brown Band 3: Silver (Possibly Grey?) Band 4: Gold Band 5: Green    The weird thing is that the middle band appears to be silver, which should be invalid as far as I can tell. If you assume the silver is grey (although this is unlikely, as there still needs to be a grey colour as well and the band is metallic), it produces a value of resistor which is incredibly uncommon to the point it does not exist (91.8 Ohms 0.5%).  Apologies for the noobie question, I'm just stumped after hours of trying to understand why this is and coming up short :).