Unable to install "google-chrome-stable_current_amd64.deb" pakage? ~$ sudo dpkg -i google-chrome-stable_current_amd64.deb   dpkg: error processing archive google-chrome-stable_current_amd64.deb (--install): package architecture (amd64) does not match system (i386) Errors were encountered while processing:  google-chrome-stable_current_amd64.deb   Also did:  ~$ sudo dpkg --install google-chrome-stable_current_amd64.deb    dpkg: error processing archive google-chrome-stable_current_amd64.deb (--install):  package architecture (amd64) does not match system (i386) Errors were encountered while processing:  google-chrome-stable_current_amd64.deb   And Also did:  ~$ wget https://dl-ssl.google.com/linux/direct/google-chrome-stable_current_i386.deb --2016-05-27 11:37:16--  https://dl-ssl.google.com/linux/direct/google-chrome-stable_current_i386.deb Resolving dl-ssl.google.com (dl-ssl.google.com)... 74.125.68.93, 74.125.68.91, 74.125.68.136, ... Connecting to dl-ssl.google.com (dl-ssl.google.com)|74.125.68.93|:443... connected. HTTP request sent, awaiting response... 404 Not Found 2016-05-27 11:37:16 ERROR 404: Not Found.   What is the exact issue? is anyone there to help me out!!!  Note: i386 package is not available anymore,anyone there to help me out regarding this issue. Sometimes Ubuntu sounds frustrated, what to do with these kinds of issue.  Used few links to troubleshoot but not resolving with those:
No more updates for Google Chrome 32-bit I am using Google Chrome 48.0 32-bit. Today when I launched Google Chrome, I got this message:    This computer will soon stop receiving Google Chrome updates because this Linux system will no longer be supported   I thought Ubuntu 14.04 is supported for five years, what's exactly happening here?  And on 64-bit Ubuntu, I get an error from Update Manager and apt-get update:  Failed to fetch http://dl.google.com/linux/chrome/deb/dists/stable/Release  Unable to find expected entry 'main/binary-i386/Packages' in Release file (Wrong sources.list entry or malformed file)   Some index files failed to download.   They have been ignored, or old ones used instead.
Java generics super keyword Is there a dominant gene for right-handedness? Has there been any definitive research about handedness being genetic? Also, why is right-handedness clearly dominant in humans? I'm interested in evolutionary theories, as well as any molecular explanation (if known). This question arises when I try to describe my itinerary to ticket service in the UK. Take for example, I plan to buy a ticket from A to B. B is the terminal. How to say its counter part A? I cannot find a proper term. I have to say "I will depart from A" or "I plan to go to B from A". Or I even use "departure place" to refer to B. mkdir -p will create a directory; it will also make parent directories as needed.  Does a similar command exist for files, that will create a file and parent directories as needed? Can a massless rope accelerate? Quadratic models with R. The use of poly(..) and I(..) functions (R-language) What causes the different results below?    var1 = c(0.04875,0.13725,0.28350,0.50975,0.77425,0.94700,0.05325,0.14050,0.29725,0.51525,0.79000,0.95400,0.04625,0.15250,0.29000,0.53300,0.79825,0.95225,0.05025,0.14625,0.28800,0.52625,0.78200,0.95925,0.04700,0.14225,0.30325,0.53500,0.79325,0.95875,0.04775,0.13850,0.28675,0.54250,0.78300,0.95175,0.05150,0.12725,0.30175,0.54725,0.79475,0.96275,0.05375,0.14100,0.30050,0.53275,0.78100,0.96175,0.05450,0.15300,0.29650,0.52850,0.80100,0.95675,0.05425,0.13975,0.30875,0.56025,0.80575,0.96100,0.05100,0.15350,0.31175,0.53300,0.78900,0.96000,0.04650,0.13525,0.29600,0.53625,0.78475,0.96375,0.05375,0.13900,0.29600,0.53725,0.78700,0.95800,0.05075,0.14350,0.29225,0.54525,0.80275,0.95800,0.05050,0.13200,0.29850,0.52700,0.80525,0.96150,0.05150,0.14050,0.29450,0.54375,0.79450,0.96375,0.05375,0.13525,0.30475,0.55250,0.79425,0.96025,0.04950,0.14500,0.29425,0.52250,0.78475,0.95650,0.05225,0.14425,0.29225,0.53150,0.80425,0.95375)  var2 = c(1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6)  var3 = c(4,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8,8,10,10,10,10,10,10,12,12,12,12,12,12,14,14,14,14,14,14,16,16,16,16,16,16,18,18,18,18,18,18,20,20,20,20,20,20,22,22,22,22,22,22,24,24,24,24,24,24,26,26,26,26,26,26,28,28,28,28,28,28,30,30,30,30,30,30,32,32,32,32,32,32,34,34,34,34,34,34,36,36,36,36,36,36,38,38,38,38,38,38,40,40,40,40,40,40)   summary(aov(var1~as.factor(var2)*var3)) summary(aov(var1~as.factor(poly(var2,1))*poly(var3,1)))   I might not understand well how poly(..) and I(..) work. Could you give me some hints about these two functions?  (I aim to create models of different degree (quadratic, cubic, etc..) and compare their BIC (or AIC)). The square of an integer is congruent to 0 or 1 mod 4 How do I build a loop in JavaScript? How can I build a loop in JavaScript? Characterizing Dense Subgroups of the Reals How do the Chitauri "ships" propel themselves? In the 2012 The Avengers film, the Chitauri army arrives through the portal along with these big robot alien whale Chitauri dudes. Here's one chasing Iron Man:  These guys basically swim through the air like... giant robot alien whales. I don't see any means of propulsion. Other, more humanoid Chitauri soldiers fly around on things that seem to be mechanical &quot;speeders&quot; of sorts. What are these guys? Are they ships, creatures, or both? Is there an explanation anywhere in the Avengers universe for how they defy gravity and swim through the air? X Windows special programs: do some of these still exist? How to Redirect Pages with Query String? I want to Redirect as seen below:  https://example.com/p1/p2?sort=p.model&amp;order=ASC&amp;page=2   to  https://example.com/p3/p4?sort=p.model&amp;order=ASC&amp;page=2   Also, I have this code in my .htaccess file :  RedirectMatch 410 ^/p1/p2&amp;   I have used below code, but I just see 410 code for that URL :  RewriteRule ^/p1/p2?sort=p.model&amp;order=ASC&amp;page=2$ /p3/p4?sort=p.model&amp;order=ASC&amp;page=2 [QSD, R=301,L]   So, I have changed RedirectMatch 410 ^/p1/p2&amp; to Redirect 410 ^/p1/p2&amp; , but this time I have seen 404 Code for my Request URI. What should I do? Here $n$ belongs to natural numbers. Firstly, I proved the relation by putting $n = 1$ . Then, taking $$|\sin(mx)| \leq m|\sin x|$$ true, I had to prove $$|\sin(m + 1)x| \leq (m + 1)|\sin x|$$  Now, here I got stuck. How to prove it?? Please help. Proving AM-GM with induction I am trying to prove AM-GM with the following steps:    Prove that AM-GM holds for two variables Prove that if AM-GM holds for $k$ variables then it holds for $2k$ variables Prove that if AM-GM holds for $k$ variables then it holds for $k-1$ variables   If I prove all of these, I will have proved AM-GM. I have proved (1) and (2), but I am still struggling with (3).   Proof for (1)  By the Trivial Inequality, we know that the first statement is true. Therefore \begin{align} (a-b)^2 \ge 0 \implies\\ a^2-2ab+b^2 \ge 0 \implies \\ a^2+2ab+b^2 \ge 4ab  \implies\\ a+b \ge 2\sqrt{ab}  \implies\\ \frac{a+b}{2} \ge \sqrt{ab}\hspace{3mm}\blacksquare\\ \end{align}  Proof for (2)  Let our numbers be $a_1, a_2, a_3, \ldots, a_{2k}$. Denote $$x = \frac{\displaystyle\sum_{i=1}^{k}a_i}{k}, y = \frac{\displaystyle\sum_{i=k+1}^{2k}a_i}{k}$$  We know that by AM-GM for 2 variables, that $$\frac{x+y}{2}\ge \sqrt{xy}$$ By our definition of $x, y$ this means that $$\frac{x+y}{2} = \frac{\frac{\displaystyle\sum_{i=1}^{2k}a_i}{k}}{2}=\frac{a_1+a_2+a_3+\ldots+a_{2k}}{2k}$$ Again by definition, $$\sqrt{xy} = \sqrt{\left(\frac{x_1+x_2+\ldots+x_k}{k}\right)\left(\frac{x_{k+1}+x_{k+2}+\ldots+x_{2k}}{k}\right)}$$ By AM-GM for $k$ variables, $$\sqrt{\left(\frac{x_1+x_2+\ldots+x_k}{k}\right)\left(\frac{x_{k+1}+x_{k+2}+\ldots+x_{2k}}{k}\right)} \ge \sqrt{\sqrt[k]{x_1x_2\ldots x_k}\sqrt[k]{x_{k+1}x_{k+2}\ldots x_{2k}}}$$ This is simply equal to $$\sqrt[2k]{x_1x_2x_3\ldots x_{2k}}\hspace{3mm}\blacksquare$$  However, I have no idea how to proceed on (3). I tried using the definition of AM and GM but did not come up with anything useful. Feel free to point out any errors or flaws on my proofs for (1) and (2). Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$ It's not difficult to show that  $$(1-z^2)^{-1/2}=\sum_{n=0}^\infty \binom{2n}{n}2^{-2n}z^{2n}$$  On the other hand, we have $(1-z^2)^{-1}=\sum z^{2n}$.  Squaring the first power series and comparing terms gives us  $$\sum_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}2^{-2n}=1$$  that is,  $$\sum_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$$  My question: is there a more direct, combinatorial proof of this identity?  I've been racking my brains trying to come up with one but I'm not having much success. NULL values inside NOT IN clause This issue came up when I got different records counts for what I thought were identical queries one using a not in where constraint and the other a left join. The table in the not in constraint had one null value (bad data) which caused that query to return a count of 0 records. I sort of understand why but I could use some help fully grasping the concept.  To state it simply, why does query A return a result but B doesn't?  A: select 'true' where 3 in (1, 2, 3, null) B: select 'true' where 3 not in (1, 2, null)   This was on SQL Server 2005. I also found that calling set ansi_nulls off causes B to return a result. Where to start with Oracle? This question only needs one answer: a list of great resources for getting started with Oracle, including Database Administration, PL/SQL and SQL.   You may find your question has been closed as a duplicate of this one, if so, please don't be offended: we are trying to be as helpful as we can without . Closing a question as a duplicate of this one is us saying "What you really need is to spend some time reading some of the best resources available rather than have your specific question answered right now. If you do get through these resources, you'll soon be back with more ! Quantum mechanical books for mathematicians I'm a mathematician. I have good knowledge of superior analysis, distribution theory, Hilbert spaces, Sobolev spaces, and applications to PDE theory. I also have good knowledge of differential geometry. I would like to study the Semiclassic Analysis, but perhaps I must first study the foundations of quantum mechanics. So I would like to know what book you recommend me to begin studying quantum mechanics. I'm primarily interested in a mathematical point of view. I have seen some books of this type, but I would like to have some other opinion.  Thanks for every reply I've just seen that the reason of closing is missing in the reviewing page of closing votes.    Is it a temporary error or it's a bug?  EDIT: Seems that only when there are audits the reason is missing.  If I cannot upload image I will make an ASCII art:  Should this question be closed as: ? 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I decided to read the original RSA paper A Method for Obtaining Digital Signatures and Public-Key Cryptosystem because of a question I had about RSA (which is not the question I'm about to ask, but may be a question on here at some time) and came across something I had never seen before in any textbook description of RSA (Note: this comes from the beginning of ).  for any integer (message) $M$ which is relatively prime to $n$, $M^{\phi(n)} \equiv 1\pmod{n}$  The part I don't recall ever hearing in class, or coming across in a text book, or seeing in any description of RSA I've ever read is that $M$ and $n$ must be relatively prime. So, I decided to play around with a toy example of RSA to see what would happen. I use $p=13$, $q=31$, $e=7$ and $M=2p=26$ (for completeness: $d=103$, $\phi(n)=360$, $n=403$). I observed the following using my toy instance of RSA: $M^e\equiv M\pmod{n}$, $M^e\equiv 0\pmod{p}$ and $M^e\equiv M\pmod{q}$. Do these equivalences hold for all $M,p,q$ when $M$ and $n$ are not relatively prime? How would I prove this? What is the real-world effect of this?