I own an ecommerce website built with Magento that has many images in the homepage for promotional banners. What is the best way to improve load speed? Reducing the file size sacrifice quality, so is there any other way?  Here are some information:
I have a WordPress site which is 90% based on images.  I've installed Wp-Super-Cache, now it seems to load a little bit faster.   I've made a speed test on Pingdom Tools:   Page size 4.7MB Load time 5.09s Requests 153 Perf. grade 74/100   And also the Time Spent per Content Type:   Image    88.23%     So the problem is obviously the images.   My plan is to try as much as I can to optimize the images in terms of size, and then to add CDN support.  Is this enough in terms of improving the loading of images?
How do you prove the  from statistical mechanics? To prove entropy will only increase with time? How to prove? Please guide. A normal divided by the $\sqrt{\chi^2(s)/s}$ gives you a t-distribution -- proof let $Z \sim N(0,1)$ and $W \sim \chi^2(s)$.  If $Z$ and $W$ are independently distributed then the variable $Y = \frac{Z}{\sqrt{W/s}}$ follows a $t$ distribution with degrees of freedom $s$.  I am looking for a proof of this fact, a reference is good enough if you do not want to write down the complete argument. sql server 2008 management studio not checking the syntax of my query When the automorphism group is trivial...... If $G$ is a trivial group , obviously $Aut(G)$  is  trivial . Does the converse  hold $?$ .  When  we  are  given  that a  group $G$  has  trivial  automorphism  group , can we  conclude  that the group  will  be  trivial $?$ .  I  guess  not . For  one  thing , we know  that  $$G/Z(G)\cong Inn(G)$$. So , $Aut(G)$ being  trivial  would  imply  that $$G\cong Z(G)$$  i.e.  $G$  is  commutative . But I  see  nothing about $G'$s being trivial .   The problem  is  that  while I cannot  prove  it , I  could  not  find  a  counter example  either , from  among  the  groups  I  am  familiar  with .   What  is  the non-trivial  commutative  group  that  has  trivial  automorphism  group  $?$ Edelstein Theorem Let $(M,d)$ be a compact metric space and $d(f(x),f(y)) &lt; d(x,y) $ for all $ x\neq y$ Prove that if $f$ is a continuous fuction then there is a unique $x_0 \in M $ such that $f(x_0)=x_0$ I know that since $g(x) = d((f(x),f(y))$ is continuous then a continuous function in a compact space reaches its maximum and minimum. Then by proving that the minimum of $g(x)$ = 0 can I conclude that $x_0$ is a fixed point? How to describe arbitrary accelerations in special relativity Can't see a glass object through another glass object in Eevee I was just testing Eevee and found that you cannot view a glass object through another glass. Is there any workaround? It works fine only If I rotate the glass window or put my camera to the back side of the scene iPhone Storage Space Inaccuracy (No Storage Space) When I want to edit a tag of a question I get following message:     Your edit will be placed in a queue until it is peer reviewed.      We welcome all constructive edits, but please make them substantial. Avoid trivial, tiny one-letter edits unless absolutely necessary.   Now the question is: are tag edits (adding a needed tag to an under-untagged, replacing a mis-used tag) substantial enough?  For example the proc-tag-wiki is just about a Ruby feature called proc - but currenlty some questions about Oracle Pro*C (a embedded SQL preprocessor) or the Linux /proc filesystem are also tagged with proc. Btw, what tag should be used for /proc?  Say I come across a Pro*C Question which is tagged with proc - is a change to proc-sql considered substantial or not? Is there a typo in the name of the "Joga Bounito" hat? We have currently a hat called "Joga Bounito":    Bounito? Which language is that?  It is clearly a latin-derived language, so not English, German, Arabic, Chinese...   In Portuguese it should be "Joga Bonito" (which means "Plays beautifully"). I'm not sure about Spanish, but I guess that it should be then "Juega Bonito". I'm not sure about Italian either, but I guess that it should be "Gioca Bel". In French (not sure) it should be "Joue Beau". In Romen (really unsure) it should be "Joacă Frumos".   So, the best guess is that it is in Portuguese. Further this hat is basically a soccer ball, and in this year we had the FIFA World Cup in Portuguese-speaking Brazil, which is known for being a country where soccer is the main sport. So "Joga Bounito" would really be Portuguese.  But there is a small problem. It has a typo: It should not be "Bounito", it should be "Bonito". How does accepting an answer work? What does it mean to accept an answer? How do I accept an answer, and what are the rules? Can I accept my own self-answer? What are the reputation benefits? Which answer should I accept? Should I upvote the accepted answer? What should I do if none of the answers are suitable?      For more information, see "" in the . What happens when a field turns on or off? Short Setup  I am curious about the the mechanics of fields, whether , , etc.  So as a specific example in order to simplify (hopefully) how to ask this question, consider  or , specifically interactions between .  My specific curiosity is in how we handle the "sudden" creation or loss of a source and how the source then creates its associated field.  My naive guess is that the loss of a source (e.g., annihilation) might be easier to handle, but let's focus on creation of a source for now.  Questions  The specific example of pair production interested me because I was wondering:   How does the field arise from the sources?   Meaning, is it delayed until after the source  fully "condenses" from the , for instance? Or does the field slowly "turn on" as the source "condenses"?   Perhaps I should have asked whether it we know if it takes time for sources to form (I assume it does).  If so, can we describe this from first principles or is it empirically based?  Am I asking that in a very uncomfortable manner?  If so, I would appreciate any suggestions.  For instance, is there a better word than "condense"?  I was thinking about water condensation as a very loose analogy to the purpose of the Higgs field in the formation of massive objects.  Why can they be produced without immediately recombining?   That is, how "close" are the two sources spatially after formation and what energies are needed to overcome the associated potential?  Does the field emanate/propagate as if from a point source?   I ask because I am trying to determine whether this is a simple  issue (i.e., far away it's just like a point source) or if the field emanates only from the "surface" of the source (e.g., ). If it starts from "within" the source as the source forms, do we know how to handle this mathematically?   My concern arises from the "similar" problem of bubble formation, where the bubble starts with zero radius which would require an infinite energy.  Perhaps the analogy is not appropriate?     Purpose  I ask these questions because it struck me this morning, while driving to work, that I did not know how and when a field "turned on."  I started to think about pair production and then quickly became confused (not difficult to do) and thought many of the quantum whisperers on this site would be much better at explaining these nuances than any of my failed rummaging through Wikipedia or scholarly articles and old text books. I have a Windows 8 (64-bit, not Pro) machine, and I want to limit the Internet bandwidth available to Windows Update. I read about BITS and GPMC methods, but I don't know how to open the BITS window, and GPMC seems like a Windows Server feature.  How can I control how much bandwidth is available to Windows Update and BITS? Why does $A\sin{k(x+c)}=a\sin{kx}+b\cos{kx}$ imply that $A=\sqrt{a^2+b^2}$ and $\tan{c}=-b/a$? I don't understand this. These identities are given in the online notes for MIT's 18.01 calculus class. It's related to taking the sum of two trig functions and transforming them into a single trig function. I can use the formulas to do this, but I am having trouble finding anything on the internet to use a proof for my understanding.  Thanks for any responses!  EDITED (added after the first answer):  Sorry, the identity goes like this:  $A\sin{k(x-c)}=a\sin{kx}+b\cos{kx}$ ,  with the relationships  $a=A\cos{kc}$ , $b=-A\sin{kc}$ , $A=\sqrt{a^2+b^2}$ , and $\tan{kc}=-b/a$ Duplicate flag lists "you have already raised this flag" after flagging as "Unclear what you're asking" Is it acceptable to vote to close a question without leaving a comment? Although  is obviously an exceptionally poor question, it still amazes me that 5 people can vote to close and yet not one of them leave a comment to help explain how the poster can improve their question.  I see loads of similar examples where questions from new users are closed and heavily voted down without anyone taking any effort to explain why - not a pleasant experience for new users.  Is there anything that can be done to encourage users to leave comments when voting to close? Why does a bigger sensor lead to a shallower depth of field? It has been mentioned at    that a larger sensor results in images with a shallower depth of field. Example image:          I understand how sensor size would relate to, for example, field of view, but the relationship with depth of field does not seem straightforward.  It actually seems contradictory - I have more wells on my sensor, and I am able to focus on less number of points.  What is the reason for this effect? How did Harry, Ron and Hermione buy presents for each other? I have been re-reading the Harry Potter books again and I noticed that Harry, Ron and Hermione have been giving each other Christmas presents each year at Hogwarts. How have they been able to buy each other presents if they are not allowed to go out of Hogwarts?   From their third year on they could visit the village and buy presents there, but what about the first two years? Did they give their personal belongings? Or did they just happen to have boxes of chocolates or books to give each other? 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). Use of very as an adjective is (in my experience) most frequently attested in phrases like     ...the very person I was looking for.   To use adjective very with the indefinite article sounds quite bizarre in this case:     ?...a very person I was looking for.   But consider this sentence, where indefinite a is used:     Visualizing a very transformation of the master-slave relation, Thomas presses further: the slave is brother to the master, even doubly a brother.   OED treats the two uses as separate senses of the word, with the following definitions:           (first use):&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;With limitation (usually expressed by the or a possessive) to particular instances      (second use): Really or truly entitled to the name or designation   Here are two respective examples quoted in OED:     What would you say to me now, and I were your verie, verie Rosalind? (1616)   Thence we went into Queen Mary's room, and saw that beautiful portrait—that very queen and very woman. (1857)   Clearly, the difference in meaning between the two senses is quite light, and it seems to me like a kind of difference which is recurrent enough to have its own term. What is the proper term? Are there other English words having similarly related pairs of senses? And lastly, is OED jumping the gun in treating these as two senses? Could the difference in meaning instead be due to the choice of determiner?