Gaokao Math-22, Jiangxi Province 2008:  Define a function $$f(x)=\frac{1}{\sqrt{1+x}}+\frac{1}{\sqrt{1+a}}+\sqrt{\frac{ax}{ax+8}}$$ Prove that, for all positive real number $a$, $1<f(x)<2$.  I tried differentiating but the derivatives got too messy. Tried applying AM GM inequality too but in vain. I believe there lies a more elegant solution to the problem. I' m out of ideas. Please also mention how you came up with the solution.

Let $a>0$, show that for $x>0$, $1<f(x)<2$, where $$f(x)=\frac{1}{\sqrt{1+x}}+\frac{1}{\sqrt{1+a}}+\sqrt{\frac{ax}{ax+8}}$$  I could take the derivative, find the maximum of the function and conclude. But that involves heady algebra and you have to solve a high degree polynomial. Is there an easier way simply using inequalities? Thanks, much appreciated


I have a few artistic fonts that I use in XeLaTeX with the fontspec package. However, they don't support smallcaps out of the box.  Is there a way to tell LaTeX to "fake" smallcaps by capitalizing everything and scaling the lowercase letters down a bit, similar to how Word or OpenOffice do it?   Minimal example, even though it's pretty obvious:  \documentclass{report}  \usepackage{fontspec}  % Really any font that doesn't include small caps definitions \newfontfamily\titlefont{Old London Alternate}  \begin{document} \titlefont \scshape Test Text \end{document}   The Test Text is not rendered in small caps, as it would be if the font supported small caps.  Thanks for pointing me to , which works fine in general, but has the drawback that it fails on UTF-8 encoded files with non-ASCII characters, which I need to use. If you have an idea how to modify that answer to also support non-ascii characters, please let me know.

Using XeTeX and fontspec, I use the Liberation font family in of my documents. Unfortunately those fonts (esp. Liberation Serif) do not natively support small caps.  Is there a way to enable fake small caps in fontspec?


I want to count the number of necklaces, with $n$ beads in total, where the alphabet of beads is $\{1,\ldots,k\}$, and where the number of beads with color $i$ is $n_i$. For example, if $n=4$, and $n_1 = n_2 = 2$, the following necklaces are the only possible $$1122$$ $$1212$$  I have been able to find formulas for different variations of the problem, but not this one. If there is no nice formula, a generating function is always a nice compromise.

Given n distinct objects, there are $n!$ permutations of the objects and $n!/n$ "circular permutations" of the objects (orientation of the circle matters, but there is no starting point, so $1234$ and $2341$ are the same, but $4321$ is different).  Given $n$ objects of $k$ types (where the objects within each type are indistinguishable), $r_i$ of the $i^{th}$ type, there are   \begin{equation*} \frac{n!}{r_1!r_2!\cdots r_k!} \end{equation*}  permutations.  How many circular permutations are there of such a set?


I was doing a little cleanup in a tag recently, and was wanting to find any questions with only that tag, since that often means they weren't tagged very well and are in need of a few more.  Unfortunately, there was no good way in the advanced search to do this. You can exclude a specific tag, but there doesn't appear to be a way to exclude all but one (or a subset). Also, tags can't be quantified with a range operator like, for example, answers can (i.e. answers:3 for all questions with 3 or more answers).  Is there a way to do this with the current search that I've overlooked? If not, could a tags:N search option be added to narrow down the search based on the number of tags a question has?

Is there any way to search for questions that have a specific tag and only that lonely tag?  In other words, I'd like to be able to do something like the following to find questions that have a single tag and no other:  [mytag] tagcount:1   This would be very useful for tag cleanup situations to be able to do house-cleaning before nuking a tag.


From what I understand, a global symmetry is a symmetry that holds at every point in space-time. On the other hand, a gauge symmetry is a redundancy in the description of a physical state.  Now, when localizing a global symmetry, we usually impose $\partial_\mu \rightarrow D_\mu = \partial_\mu + A_\mu$. For example, for scalar field theory we might have  $$\mathcal{L} = |\partial_\mu \phi|^2 \rightarrow |D_\mu \phi|^2$$  Now, this Lagrangian still enjoys the global symmetry $\phi \rightarrow e^{i\theta}\phi$ for constant $\theta$ after localizing the global symmetry as the global symmetry is a subset of the local symmetry. However, in performing this localization my understanding is that you end up gauging the symmetry.   How can I see that the global symmetry was originally not a gauge symmetry, but after localization is a gauge symmetry? Naively I expected $\phi \rightarrow e^{i\theta} \phi$ to correspond to physically equivalent states similar to how quantum states are only defined up to an overall phase factor. Are there general principles in which one can easily see that some symmetry is in fact a gauge symmetry?

Could somebody point me in the direction of a mathematically rigorous definition  and  for a given (classical) field theory?  Heuristically I know that global symmetries "act the same at every point in spacetime", whereas local symmetries "depend on the point in spacetime at which they act".  But this seems somehow unsatisfying. After all, Lorentz symmetry for a scalar field $\psi(x)\rightarrow \psi(\Lambda^{-1}x)$ is conventionally called a global symmetry, but also clearly $\Lambda^{-1}x$ depends on $x$. So naively applying the above aphorisms doesn't work!  I've pieced together the following definition from various sources, including . I think it's wrong though, and I'm confusing different principles that aren't yet clear in my head. Do people agree?  A global symmetry is a symmetry arising from the action of a finite dimensional Lie group (e.g. Lorentz group, $U(1)$)  A local symmetry is a symmetry arising from the action of an infinite dimensional Lie group.  If that's right, how do you view the local symmetry of electromagnetism $A^{\mu}\rightarrow A^{\mu}+\partial^{\mu}\lambda$ as the action of a Lie group?


I was going through his  Quote from that link  Use of the Network or Services to violate the security of any computer network, crack passwords or security encryption codes, transfer or store illegal material including that are deemed threatening or obscene, or engage in any kind of illegal activity is expressly prohibited.  Then I see this question  Is this not a violation of the Terms and Conditions? Or am I interpreting it in a different way? Also I am not sure what to tag it under so if you feel the tags have to be edited, please feel free to do so. EDIT MOVED FROM COMMENT The reason why I raised this question is because of this . Where it was suggested that the password be cracked and I wanted to be sure that it was against the TOS before I flag it.

I recently saw a question on Stack Overflow relating to the . The guy wasn't asking for code at all, meerly asking what the process involved.  It was immediately slapped with a comment directing him to the  (which after reading I still couldn't see why the asker was being directed there), and closed shortly thereafter as "Not a real question".  Since I asked this question, it has been suggested that the question was closed because the asker was asing whether he could ask a question, or because he may have been asking how to unlock his iPhone, where I assumed he was asking for the technical specifics of what happened. Both fair points, it may have been my mistake  As Brad has stated the question  received a very positive response. Another relevant question suggested by Brad, but received a negative response:   Now I know some people out there want to be the Stack Overflow Police, and some people are scared of questions that slightly hint at subversive or underhand methods, or that the asker is trying to do something illegal (either for the sake of the site, or for maintaining their own halos).  However in my opinion it is perfectly acceptable to ask about processes and methods, even in the areas of reverse engineering and programming practicies that are invariably used to exploit other software. Questions like "How do I crack software X?" are obviously unacceptable.  I'd like to know what the community thinks about this; what is your opinion?  Is it ok to ask about shady practices, for educational purposes, as long as they are non-specific (in terms of cacking a certain piece of software, or asking for code to unlock iPhones, etc.)


I'm Not able to install Android Studio through Terminal, Please Suggest me right way to install Android Studio in Ubuntu 15.04 .

Please tell me the full process of installing Android Studio and its necessary dependencies.


I have an old Compaq NC6000 computer, and the newest kernels don't work.  I need to use an older version of Lubuntu.  Where can I download the older versions lf Lubuntu?

I want to know where I can find updated information about all the stable and in-development versions of Ubuntu, where I can find this information?     This question is meant to be a canonical question. It expects to answer the following questions:         Is X version stable yet?   Is X version in beta?   Is X version still supported?   What versions are still supported?   What are the versions in Beta/Alpha?   Until where X version will be supported?   Have X version ceased support?   When will be X version released?   Where I can download any release?   When will the next LTS version of Ubuntu be released?         The list is not exhaustive.


I used to install packages with dpkg -i *.deb command for off-line installation. Because all deb files are in one folder.  I want to avoid dependency error and stop installing packages as broken.      Ultimately my aim is to check dependencies and generate download script (if all dependencies are not satisfied) for only those package   which is missing in mentioned folder. so-that I can first download missing packages and Then confidently    install package by dpkg -i *.deb   apt-cache showpkg $(find -iname '*.deb' -exec dpkg --info '{}' \; | awk '/Package:/ {print $2}') shows dependencies but long list and not helpful to check whethter it is satisfied (exist) in mentioned folder or not. Also dpkg -I *.deb errors following:      dpkg-deb: 'cabextract_1.4-4_i386.deb' contains no control component 'chromium-codecs-ffmpeg-extra_34.0.1847.116-0ubuntu2_i386.deb'    dpkg-deb: 'cabextract_1.4-4_i386.deb' contains no control component 'flashplugin-installer_11.2.202.350ubuntu1_i386.deb' .. .. so on for each deb   Hence, That commands are not useful for me.  Further Clarification:   First check all deb dependencies in my folder. according to package already installed, check this deb's are able to installed without dependency error or not. if yes then execute dpkg -i *.deb else list missing package which not fond installed or in mentioned folder   Thanks.

How can I check dependency list for a deb package. I am running Ubuntu 11.10 and I have backed up all deb packages from var/cache/apt/archives. I want to format my pc and re-install selected applications only. Also how can I get the list of installed packages and dependencies.


This is a schematic of a ATmega328P used circuit. It has paralleled two 100nF capacitors between Vcc and GND. (C8 and C9) What is the function of this two capacitors and why they are paralleled?

What is a decoupling capacitor (or smoothing capacitor as referred to in the link below)?  How do I know if I need one and if so, what size and where it needs to go?    mentions many chips needing one between VCC and GND; how do I know if a specific chip is one?   Would an  4-bit parallel access shift register used with an Arduino need one? (To use my current project as an example) Why or why not?  I feel like I'm starting to understand the basics of resistors and some places they're used, what values should be used in said places, etc, and I'd like to understand capacitors at the basic level as well.


Which season do you like (better / best), spring or winter?   I was told the answer is better, but why is that so?  Both better and best would make sense, I think.

When speaking with my mother a couple of days ago, I read to her a message I was sending to my cousin on her behalf ending with: "... the birthday of your youngest." [implying her child]  She immediately leapt on this and said that as my cousin only had two children, the use of the superlative was not permitted and the comparative must be used instead: "... the birthday of your younger child."  She was adamant that this was a solid grammatical rule that she was taught throughout her education.  As a younger Briton, I have relatively little formal grammatical education to older people who were better taught in this regard, so I usually defer to her on grammatical rule knowledge.  Is she right?  Are superlatives not permitted when the domain of the object is only two?  To me it seems bizarre.  The minimum or maximum of any set does not only exist when there are different minima and maxima, or indeed something which is neither.


When no one is looking it starts to assemble either itself or other robot creatures from objects found around the room.  This is NOT one of the recent Transformer movies, it probably dates back to the 80's as I rented it on VHS.

I saw this on TV in mid 90s I think. One or more people travel to another celestial body (might or might not be the/a moon or mars), they find an American football. The football transforms into a robot that is hostile. They later find LOTS of these footballs/disguised robots.  Since there are lots of robotic projects with "football robots" or " robots", it is very hard to filter search results using Google etc.


I want to use an animated object to determine where liquid pours out from, but I cannot for the life of me find the option that dictates this... Previously this option was in Blender 2.79 So far, after several days of looking, my search efforts have gone in vain. Hopefully this question isn't too redundant!

I'm trying to make a liquid simulation with Mantaflow where the flow of the liquid respects the flow object's local rotation, so it looks like water spraying in different directions. It looks like the options on the flow object only work for 'world' coordinates and doesn't take into account the coordinates of the object. How do I make the water 'fire' (like a hose) into a specific direction that uses local coordinates instead of world ones?


Let's consider this example: A lvl 12 Druid has a +4 proficiency bonus. They proceed to wild shape into an ape, whose attacks have a +5 bonus to attack rolls, easily calculated to be +3 from its Strength and a +2 proficiency modifier. Does the wildshaped druid attack at +5, or at +7? I've seen the first interpretation to be more common but I'd like to know the reasoning for such.

I understand that the druid uses his or the beast's proficiency when wild shaping and using skills or saving throws because it is specified in the book. But how about the creature's attacks? For example the polar bear has an attack bonus with his claws of +7, which is strength +5, plus its proficiency bonus +2. But a 5th level characters proficiency bonus is +3, so if he/she used their proficiency bonus it would be strength +5, plus proficiency +3 making the attack bonus +8. Is this right?


I'm installing 200 amp service in a shop, and I am going to feed my house with a 100 amp sub panel. I want to use aluminum wire for this run. What gauge of wire I should use?

I am adding an attached garage to my house.  I'm going to be putting in a 100 Amp subpanel which is about 60 feet away and run through the basement joists.    What gauge wire do you recommend for either aluminum and copper?  Also, do you recommend one or the other?


When I try to get on my servers it says "Outdated Server". I know it's because of the update but what do i need to do to fix it? Do I need to wait for the servers to update or what?

Similar to  on the bugs in Minecraft, I would like a complete list of what error codes exist in Minecraft and how they occur, as well as how they can be resolved.


So candies read as a total amount no matter what Pokemon you look at of the same type or evolution, for example you'll have 5 Rattatas and 5 Raticates and 30 candies in total that you see when you look at any Pokemon.   But to my knowledge there isn't really a bag for the candies themselves.   If you got rid of all but one Rattata, you would see that you would have 39 candies, but what happens to the candies if you get rid of that last Pokemon?  Do the candies disappear with it or will they return when you catch another same-type Pokemon?

If I get rid of the last Pokemon I have from a family do I still keep the candies from that family when I catch another one of the same family?


I'm trying to run my first script, just a simple cd reroute. Unfortunately, I can't seem to get it to work. the script is basically #!bin/bash echo "moving you to Desktop" cd /mnt/c/Users/duanj/Desktop echo "finished moving"  and both the echo statements end up printing. But no redirect. Also, when I type the cd command in verbatim into my terminal it works.

I'm trying to write a small script to change the current directory to my project directory:  #!/bin/bash cd /home/tree/projects/java   I saved this file as proj, added execute permission with chmod, and copied it to /usr/bin. When I call it by: proj, it does nothing. What am I doing wrong?


When I insert the double money sign $$ we have the equation stressed centered. I would like to know if it's possible to have a substitute for the double money sign $$. I'm looking for a symbol to get the equation stressed and written from the left side to the right side of the page instead to have the equation centered.  Thanks

I'm using scrreprt class and I'm having troubles with different behavior of $$ and \[ \]-written equations and equation environment. The problem is that alignment is not the same: $$ equations are centered while equations in equation environment are left aligned.  For example, the following code  Equations: \begin{equation}\label{nelineq} f(x)=0 \end{equation} \begin{equation*}\label{nelineq} f(x)=0 \end{equation*} $$ f(x)=0 $$ \[ f(x)=0 \]   produces   I would like to make all three usages consistent (not yet sure if centered or left aligned).  The question is, how to permanently change default alignments for all three cases? But without use of align or similar environments (dont want to edit all existing equations).  I know that $$ is deprecated, but what about other two methods?


I tried mentioning 2 users in a comment on my question, but I got the message:     Only one additional @user can be notified; the post owner will always be notified   I am the owner, and I was only trying to ping one additional @user. This message is misleading as we can only notify one @user (with a default owner notification).  Shouldn't the text be:     Only one @user can be notified per comment. The post owner will always be notified.   when I'm pinging two people in the thread who are not the owners?

How do the comment replies (aka "pinging users") work?  Who can I send an @reply to? How do I respond to a specific user when entering my comment? Will they be notified? What do people mean when they talk about "pinging" another user?  Related:


Is there a way to  specify using regex to show results not containing specific text.Something similar to      Select * from table where id not in {3,4,6};

I know it's possible to match a word and then reverse the matches using other tools (e.g. grep -v). However, is it possible to match lines that do not contain a specific word, e.g. hede, using a regular expression?   Input:  hoho hihi haha hede   Code:  grep "<Regex for 'doesn't contain hede'>" input   Desired output:  hoho hihi haha


This limit was a trivia question.  The trivia league is set up so you have all day to mull over questions and submit your answer, but it's not "trivia for mathematicians."  The questions tend to be tough, but I wouldn't expect them to ask a really really hard Calculus problem...     $$\lim_{n\to\infty}\frac{(n+1)^{n+1}}{n^n}-\frac{n^n}{(n-1)^{n-1}}$$   I can provide the correct answer but it's easy to guess by plugging in a large number for $n$.  No calculators allowed!

My friend's trivia league had this math question:  $$\lim_{n \to \infty} \left[\frac{(n+1)^{n + 1}}{n^n} - \frac{n^{n}}{(n-1)^{n-1}} \right]$$  After computing a few values, one could guess the answer is $e$ = 2.718...But how can we prove that is the limit?  Someone offered up a hand-wavy proof like this:  \begin{align} \lim_{n \to \infty} \left[\frac{(n+1)^{n + 1}}{n^n} - \frac{n^{n}}{(n-1)^{n-1}} \right] & = \lim_{n \to \infty} \left[\frac{(n+1)(n+1)^{n}}{n^n} - \frac{n \cdot n^{n-1}}{(n-1)^{n-1}} \right] \\ &= \lim_{n \to \infty} \left[(n+1)\frac{(n+1)^{n}}{n^n} - n\frac{n^{n-1}}{(n-1)^{n-1}} \right] \\ &= \lim_{n \to \infty} \left[(n+1)\left(1 + \frac{1}{n} \right)^n - n\left(\frac{n - 1 + 1}{n-1} \right)^{{n-1}} \right] \\ &= \lim_{n \to \infty} \left[(n+1)\left(1 + \frac{1}{n} \right)^n - n\left(1 + \frac{1}{n-1} \right)^{n-1} \right] \\ &= \lim_{n \to \infty} \left[(n+1)e - n \cdot e \right] \\ &= \lim_{n \to \infty} e \\ &= e \end{align}  The part about substituting $e$ is hand-wavy since technically this is an indeterminate form of $\infty - \infty$. And using $e$ as as upper bound did not lead me to an easy proof either.  Is there a way to rigorously prove the limit? I tried a few approaches: (a) sandwiching the limit--I could prove $e$ was a lower bound, but I could not find a suitable upper bound converging to $e$, (b) using L'Hopital's rule with no luck, (c) using the mean value theorem--but that also got complicated.  So this is a pretty tough problem to ask at trivia! Is there a way to prove this limit formally?  Sources  Trivia question:   Thread on trivia:   Hand-wavy proof:   Idea for mean value theorem:


I've hp 15 au004tx laptop. Intel i7 6500u Nvidia 940MX 4GB 8 GB DDR4 RAM 1TB 5400rpm hard drive.    I want to upgrade my laptop with an SSD. I want to use SSD for OS installation and HDD for data storage. On which port should I connect the SSD, on default sata port(where HDD is connected) or on CD drive port?

My laptop has a built-in hard disk (HGST 500GB). I want to use SSD as boot/C: drive. I mainly use windows 8.1 (I may need to install ubuntu alongside it). My laptop model is HP Pavillion n004tx.   Is it possible to install SSD on caddy(CD drive replacement) and use it as C drive? Which would be more efficient SSD in place of my existing Hard Drive or SSD in the caddy(CD drive replacement)?


I have a dataset of 150 observations and I want to make a linear model to try to explain relations. I use backwards regression. When I keep all variables (10), I have an adjusted R² value of 0.8076. When I remove the variables with p-values higher than 5% in order from highest to lowest, the adjusted R² value goes up to 0.8189. This leaves me with 6 variables, which is still quite a lot. Adding the $log_{10}$ of one of the variables also improves the R² variable ever so slightly to 0.8259, doing this let's me remove a different variable since its p-value has rised to 16%. Removing more variables drops the adjusted R² value to $\approx$ 0.79xx depending on which variable I remove. My question is, when should I stop removing variables? As soon as I see the adjusted R²-value drop or should I wait until my adjusted R² value drops below a certain value? Or should I look at something else? Thanks in advance!

I have run a multiple linear regression using stepwise regression to select the best model, however the best model returned has a non-significant variable. When I remove this the AIC value goes up indicating the model without the significant variable is a worse fit. Should I remove the non-significant predictor or should I leave it in as it is a better model?


I'm working on the following qual problem and I'm not sure how to do parts b and c.    a) This uses a nifty argument with considering the map $N_G(S) \to \operatorname{Aut}(S)$ via conjugation. And using the fact that $|N_G(S)/C_G(S)|$ is odd, and divides the order of $\operatorname{Aut}(S)$ so it must be 1.  b) Not sure how to proceed after the hint.  I think we're supposed to use strong Cayley's theorem here by saying that the kernel of this homomorphism is the largest normal subgroup of $G$ contained in $S$.  c) No idea how to do this one, but I was thinking if we can show the subgroup has order n(from part b) then we note that $|N||S| = |G|$ and so $NS = G$.

I want to prove the following:          Let $G$ be a group of order $2^nm$, where $m$ is odd, having a cyclic Sylow $2$-subgroup.     Then $G$ has a normal subgroup of order $m$.      ATTEMPT:  We will show that $G$ has a subgroup of order $m$. Let $\theta:G\to \text{Sym}(G)$ be the homomorphism which is defined as $$  \theta(g)=t_g,  \quad  \forall g\in G $$ where $t_g:G\to G$ is defined as: $$  t_g(x)=gx,  \quad  \forall x\in G. $$ Let $g$ be an element of order $2^n$ in $G$. (There exists such an element since $G$ has a cyclic Sylow $2$-subgroup.)  The cyclce representation of $t_g$ is a product of $m$ disjoint cycles each of length $2^n$. Therefore $t_g$ is an odd permutation.  Thus the homomorphism $\epsilon\circ \theta:G\to\{\pm 1\}$, where $\epsilon:\text{Sym}\to\{\pm 1\}$ is the sign homomorphism, is a surjection.  By the First Isomprphism Theorem, we conclude that the kernel $K$ of $\epsilon\circ \theta$ is of order $2^{n-1}m$.  If $n$ were equal to $1$ then we are done.  If $n>1$ then note that any Sylow $2$-subgroup of $K$ is also cyclic. This is because each Sylow $2$-subgroup of $K$ is contained in a Sylow $2$-subgroup of $G$, where the latter is cyclic.  Now we can inductively show that $K$ has a subgroup of order $m$.    What I am struggling with is showing the normality.  Can anybody please help me with this.  Thanks.


I am getting the below error when trying to create an "Account" object in salesforce org by SOAP request. Request: <soapenv:Envelope xmlns:soapenv="http://schemas.xmlsoap.org/soap/envelope/" xmlns:urn="urn:enterprise.soap.sforce.com" xmlns:urn1="urn:sobject.enterprise.soap.sforce.com">    <soapenv:Header>       <urn:SessionHeader>          <urn:sessionId> *Session ID given*</urn:sessionId>       </urn:SessionHeader>    </soapenv:Header>    <soapenv:Body>       <urn:create>           <urn:sObjects>             <urn:sObjects xsi:type="urn1:Account" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">             <Name>Bluebeards Grog House</Name>             <Description>It is better than Blackbeards.</Description>          </urn:sObjects>       </urn:create>    </soapenv:Body> </soapenv:Envelope>   Response: <soapenv:Envelope xmlns:soapenv="http://schemas.xmlsoap.org/soap/envelope/" xmlns:sf="urn:fault.enterprise.soap.sforce.com" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">    <soapenv:Body>       <soapenv:Fault>          <faultcode>sf:INVALID_TYPE</faultcode>          <faultstring>INVALID_TYPE: Must send a concrete entity type.</faultstring>          <detail>             <sf:InvalidSObjectFault xsi:type="sf:InvalidSObjectFault">                <sf:exceptionCode>INVALID_TYPE</sf:exceptionCode>                <sf:exceptionMessage>Must send a concrete entity type.</sf:exceptionMessage>                <sf:row>-1</sf:row>                <sf:column>-1</sf:column>             </sf:InvalidSObjectFault>          </detail>       </soapenv:Fault>    </soapenv:Body> </soapenv:Envelope>

I am getting errors when attempting to 'Create' a custom "O2C_Alert__c" object with a SOAP request.  My request is:  <soapenv:Envelope xmlns:soapenv="http://schemas.xmlsoap.org/soap/envelope/" xmlns:urn="urn:enterprise.soap.sforce.com" xmlns:urn1="urn:sobject.enterprise.soap.sforce.com">    <soapenv:Header>       <urn:SessionHeader xmlns:urn="urn:enterprise.soap.sforce.com">          <urn:sessionId>SESSION_ID</urn:sessionId>       </urn:SessionHeader>    </soapenv:Header>    <soapenv:Body>       <urn:create>          <!--Zero or more repetitions:-->          <urn1:sObjects>             <!--Zero or more repetitions:-->             <urn1:type>O2C_Alert__c</urn1:type>                 <urn1:CreatedDate>20151231</urn1:CreatedDate>                 <urn1:Alert_Code__c>STD</urn1:Alert_Code__c>                 <urn1:Status__c>New</urn1:Status__c>                 <urn1:Customer_Id__C>0123456789</urn1:Customer_Id__C>                 <urn1:Name>Kroger</urn1:Name>                 <urn1:Order_Id__c>0123456789</urn1:Order_Id__c>          </urn1:sObjects>       </urn:create>    </soapenv:Body> </soapenv:Envelope>   The response I am getting back is:  <soapenv:Envelope xmlns:soapenv="http://schemas.xmlsoap.org/soap/envelope/" xmlns:sf="urn:fault.enterprise.soap.sforce.com" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">    <soapenv:Body>       <soapenv:Fault>          <faultcode>sf:INVALID_TYPE</faultcode>          <faultstring>INVALID_TYPE: Must send a concrete entity type.</faultstring>          <detail>             <sf:InvalidSObjectFault xsi:type="sf:InvalidSObjectFault">                <sf:exceptionCode>INVALID_TYPE</sf:exceptionCode>                <sf:exceptionMessage>Must send a concrete entity type.</sf:exceptionMessage>                <sf:row>-1</sf:row>                <sf:column>-1</sf:column>             </sf:InvalidSObjectFault>          </detail>       </soapenv:Fault>    </soapenv:Body> </soapenv:Envelope>   Thanks for any and all help.


How to check in javascript how many direct properties object has? I want to know amount of direct properties in one object, not in prototypes chain. Is there any method to do so?

What's the fastest way to count the number of keys/properties of an object?  It it possible to do this without iterating over the object?  i.e. without doing  var count = 0; for (k in myobj) if (myobj.hasOwnProperty(k)) count++;   (Firefox did provide a magic __count__ property, but this was removed somewhere around version 4.)


I do not understand whether the first or the second sentence is correct, or perhaps both?    No other metal is so useful as iron. No other metal is as useful as iron.    Although the latter feels correct to me. Any light shed on the above would be much appreciated!

I just googled the difference between as long as and so long as. The difference has alredy been discussed . There are, it seems, two contexts for these expressions:    lengths and physical comparisons (time, distance, etc.) “This bridge is as long as that bridge.” some logical implication or synonym for provided that or something like this.  “You can do that so long as you keep in mind that. . . .”   Somewhere else I found that you can use both expressions for context #2, but should avoid so long as in cases of context #1.  Now,  that so long as might be colloquial — or as he put it, “casual”. It seems that it’s possible to never use so long as, since according to what I have been told, you can use either expression in cases of context #1. Given that I am writing academic papers, my questions are:    Is so long as truly non-academic or non–high-style? Should so long as therefore be avoided altogether?


I'm preparing a small workbook. I'm using gray empty underlines as in  to make empty fields for handwritten text. I'm using \documentclass[a4paper,11pt]{book}.   \documentclass[a4paper,11pt]{book} \usepackage[francais]{babel} \usepackage{geometry} \usepackage{xcolor} \geometry{paperwidth=21cm,paperheight=29.7cm, body={18cm,25.7cm}, top=2.5cm, left=1.5cm}  \begin{document} {  \frontmatter \tableofcontents \cleardoublepage  \mainmatter   \chapter{Hi} Mathematics is the study of numbers, quantity, space, structure, and change. Mathematics \color{gray}\underline{\hspace{5cm}}\color{black} is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discove  \end{document}   I get the following output    As you can see, the underline gets out of the margins and the word "is" following it is not shown. How can I make latex treat these fields as ordinary text so for example, in \color{gray}\underline{\hspace{5cm}}\color{black} latex should treat it as \color{gray}\underline{\hspace{1.5cm}}\color{black} \\ \color{gray}\underline{\hspace{3.5cm}}\color{black} or something like that?

I'd like to create an "answer blank" in a document.  It should basically look like an underline with nothing above it.  I found a question about it (  ), but that doesn't deal with the main problem I'm having, which is that I want the blank to wrap normally to the text width.  The solutions using \hspace or \rule cause the line to extend into the margin.  I'm looking for something that wraps just like normal text and so won't extend into the margin.  It should be an underlined blank that has a specified length, but that length might be wrapped across multiple lines in the output document.


I have used find command in many directories but when running the following from /etc:  find /etc -name *.conf   it errors out and cannot figure it out. It is only happening with the /etc directory. I can run this exact command from any other directory and works fine. Call this an OCD thing, I just have to know why.

I am running the following command, but it is not performed recursively:  find . -name *.java   I know there are java files further down in the current directory but it is performing the find on the current directory only. I am using OS X, 10.9.


I have 40 mp4 files in a folder.  Every file starts with video_. Every file is of format video_*.mp4.  I need to rename all the files with video_ removed from the begining of every file. How can I do that from terminal?

One of the ways I quickly rename files in Windows is   F2 > Rename > Tab (to next file) > Rename ...   But in Ubuntu/Nautilus, I can't tab to next file. But being on Linux, I think there must be a command line alternative.  However, sometimes, I may want more control over how to rename specific files. In that case, perhaps its better to be able to tab to the next file


When talking about how muons reach earth even though their half-life is very short the explanation of time dilation is given. From earth's frame of reference, the Muon's clock is "slowed down" so is has longer to live and keep racing at it's speed, I think I understand this.   However, will the length between the Muon and the earth when seen from earth's reference also contract? If so, why is this never included in the calculation of amount of muons reaching the earth?  Also, from the muon's perspective the earth contracts which I understand but nobody talks about the time dilation for the earth. (Although this I understand better because it doesn't really matter how "fast" time flows for the earth relative to the muon, the earth will still take the same amount of time to reach the muon wether time dilation is included or not) Examples of places where they discuss these phenomena without including the length contraction (from earth's frame of reference):

I am a bit confused about the implications of length contractions;   For example, in the muon decay problem, we assume that the distance between the muon and the earth is contracted only in the frame of reference of the muon (I've heard justification saying this is because it is Earth's atmosphere) but suppose there were no atmosphere then in the reference frame of Earth shouldn't the length between them also be contracted?  What I don't get is if one object is moving at a speed relative to another object, shouldn't this movement affect the distance between them in the reference frames of both of them, since their movement is merely relative?


I am newbie in C# and recently I tried to make a MD5 hash calculator. But everytime  i check some file, the data remains in RAM until i close the program. In 50kb files or so it doesnt matter, but bigger files may not work. Any clues how can it be disposed or cleared after showing the result ? Thanks  private void button1_Click(object sender, EventArgs e)     {         MD5 md5hash = MD5.Create();         string inputMD5;         if (openFileDialog1.ShowDialog() == DialogResult.OK)         {             string fileloc = openFileDialog1.FileName;             byte[] block = File.ReadAllBytes(fileloc);             byte[] data = md5hash.ComputeHash(block);             StringBuilder sBuilder = new StringBuilder();             for (int i = 0; i < data.Length; i++)             {                 sBuilder.Append(data[i].ToString("x2"));             }             inputMD5 = sBuilder.ToString();             MessageBox.Show(inputMD5);         }

In my experience it seems that most people will tell you that it is unwise to force a garbage collection but in some cases where you are working with large objects that don't always get collected in the 0 generation but where memory is an issue, is it ok to force the collect?  Is there a best practice out there for doing so?


Somehow I changed the setting from the default double click to single click which makes the right click open the file when I want the right click menu. So I need to know where I did it so I can reverse it.  I've spent the whole night trying to remember how I did it, Please help, Thanks  The setting altered both sides, Solved thanks guys!

I have Ubuntu 13.1 installed with the default window manager and DE.   I am trying to enable single click so I can open files and folders with only one click. I tried googling and all results said to open files, then go to preferences from top bar but my top bar has no options.  picture of desktop:


The trash seems to be empty, but the partition's trash folder (.Trash-1000) shows the deleted files and they keep taking up space. Is this a bug in the new version (16.10) released today? Everything was working fine a few hours ago before upgrading to the new 16.10 edition.

When using a dual-boot Windows and Ubuntu. I see that there is a folder created with the name .Trash-1000  in the NTFS partitions.   Could someone explain to me :   What does this folder mean ? For what it is used? Maybe Trash related?  Is it necessary to keep this folder ?


I am currently using 1 12V 0.95A fan to circulate air in my humidor (coolerator) and using an AC adapter rated class 2 120V 60/60 with an output of 9V 300mA. Can I add 3 more fans with the same power source or do I need to increase power?  2 days later:  I have 4, of the pre stated fans connected to the aforementioned source.  They surge but do not start without spinning them manually and then run very slow.  What do I need to power them up?

Power supplies are available in a wide range of voltage and current ratings.  If I have a device that has specific voltage and current ratings, how do those relate to the power ratings I need to specify?  What if I don't know the device's specs, but am replacing a previous power supply with particular ratings?  Is it OK to go lower voltage, or should it always be higher?  What about current?  I don't want a 10 A supply to damage my 1 A device.


I am looking for a little help. I am sitting at home trying to learn java programming from programmingbydoing.com. I need to make a program called TwentyQuestions. The code is missing something to make it work completely. I have tried to find help other places on the web. That is why the code looks much like other peoples code.  import java.util.Scanner;  public class TwentyQuestions {     public static void main( String[] args )     {         Scanner keyboard = new Scanner(System.in);          String type, size, guess = "";          System.out.println("TWO QUESTIONS!");         System.out.println("Think of an object, and I'll try to guess it.");         System.out.println("");          System.out.println("Question 1) Is it animal, vegetable or mineral?");         System.out.print("> ");         type = keyboard.next();         System.out.println("");          System.out.println("Question 2) Is it bigger than a breadbox?");         System.out.print("> ");         size = keyboard.next();         System.out.println("");          if (type.equalsIgnoreCase("animal"))         {             if (size == "no")             {                 guess = "squirrel";             }             else             {                 guess = "moose";             }         }          else if (type.equalsIgnoreCase("vegetable"))         {             if (size == "no")             {                 guess = "carrot";             }             else             {                 guess = "watermelon";             }         }          else if (type.equalsIgnoreCase("mineral"))         {             if (size == "no")             {                 guess = "paper clip";             }             else             {                 guess = "Camero";             }         }          if (guess == "")         {             System.out.println("The answers provided are not valid. Please try again.");         }          else         {             System.out.println("My guess is that you are thinking of a " + guess + ".");             System.out.println("I would ask you if I'm right, but I don't actually care.");         }   } }   The problem is that the program does not care about the comparisons that are in the nested if-statements. Control always goes to the else and prints that one.

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


I want to insert a wire into my breadboard for prototyping, however the wire is thin so it folds and frays when I try to push it into an open slot.  Is there a particular type of pin I need to use in order bridge the gap?

I bought some single strand wires hoping to prototype on the breadboards. Unfortunately it was too small to properly fit into the breadboard holes.   So my question is which gauge fits well on those small holes of breadboard?


This question is related to:   I want to see the exact difference between cases (1) and (2). It seems they are the same. But they are not!. I want to see where I missed some thing in the analysis.

The Legendre's conjecture states that the inteval $(m^2,(m+1)^2)$ contains a prime $p_n$ for each $m$. I wante to find a negation of it. I have two versions:   (1) There exists an $m$ such that either $p_n≤m^2$ for all $n$, or $p_n≥(m+1)^2$ for all $n$.  or  (2) There is an $m$ such that for all $n$, either $p_n≤m^2$ or $p_n≥(m+1)^2$.  I am not able to choose the right one.


I have a label All Models. On the click of this label i dynamically add ul to div  $("#MetricsTypeYearModelList").append('

');   "MetricsTypeYearModelList" is the id of my div. After this i loop over a JSON object and add li dynamically to this ul  for (var i = 0; i < metricsTypeYearModel.length; i++)     {         var obj = metricsTypeYearModel[i];         if(i == 0)             $("#MetricsTypeYearModelListUl").append('
 '+obj.ModelTypeName+'
');         else             $("#MetricsTypeYearModelListUl").append('
 '+obj.ModelTypeName+'
');     }   After loading this, i want to click the first element of li. $( '#TestClick' ).trigger( "click" ); Problem is that when i click on the label, the div does not show up, but when i remove $( '#TestClick' ).trigger( "click" ); the div shows up. What can be the possible issue.  JS is:  $(document).on('click', 'li.pModel', function (e) {             e.preventDefault();             e.stopPropagation();             var identifier = fetchIdentifier(this);             var iHandle = $("#" + identifier); // fetch container              $(this).siblings().removeClass('active');             $(this).addClass('active');             // $('li.mModel').removeClass('active');              iHandle.find('ul li.mModel').removeClass('active');             iHandle.find('ul li.cModel').removeClass('active');             iHandle.find('ul li.mModel').fadeOut();             iHandle.find('ul li.cModel').fadeOut();              iHandle.find('ul li.mModel[data-parentid="' + $(this).data('id') + '"]').fadeToggle();             iHandle.find('ul li.mModel[data-parentid="' + $(this).data('id') + '"]:first').addClass("active");                iHandle.find('ul li.cModel').fadeOut();             iHandle.find('ul li.cModel[data-parentid="' + iHandle.find('ul li.mModel.active').data('id') + '"]').fadeToggle();         });   I want to call this JS method from the code for the first li element when i click on the label i.e. i want to click the first li element programmatically.

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


I have a problem with contiunation of the loop. Here is a code of the hangman for Python. Although using the list or just print for each character seem to be easier ways to proceed the task, I would like to know, where is the problem of the presented solution in order to avoid the future troubles.  word='heksakosjokontaheksafobia'  def hangman(input, word_to_guess):     users_guess=input('What is the first letter of your first thought?\n')     print (users_guess)     if users_guess in word_to_guess:         unknown_chararcters='*'*len(word_to_guess) # The creation of a string showing number of uknown characters         print(unknown_characters)         for char in word_to_guess:             if char==users_guess: # Checking whether input is included in word_to_guess                 ind=word_to_guess.index(char)                 unknown_characters=unknown_characters[:ind]+users_guess+unknown_characters[ind+1:] # Substitution of '*' with input             continue         print(unknown_characters) hangman(input, word)   As you can see, the word includes many 'a', however for input==a the output is:  What is the first letter of your first thought? a ************************* ****a********************   How can I force the loop to iterate over the following characters of a string?

How do I access the index in a for loop like the following?  ints = [8, 23, 45, 12, 78] for i in ints:     print('item #{} = {}'.format(???, i))   I want to get this output:  item #1 = 8 item #2 = 23 item #3 = 45 item #4 = 12 item #5 = 78   When I loop through it using a for loop, how do I access the loop index, from 1 to 5 in this case?


I want to show all files with the name "index.php" in a specific area of my machine. For this I wrote this code-line:  -find /iu/cuve/u3 -name "index.php"   I want it to only show the lines witch include "index.php" in it, but this command shows a bunch of other lines witch does not include "index.php". Many of them ends with "Permission denied", maybe thats why I can't see the "index.php" part of the line.  I tried to add a -exec grep command to it, but didn't get the results I'm looking for.

Code   find / -name netcdf   Output  find: `/root/.dbus': Permission denied find: `/root/.gconf': Permission denied find: `/root/.gconfd': Permission denied find: `/root/.gnome': Permission denied find: `/root/.gnome2': Permission denied find: `/root/.gnome2_private': Permission denied


Due to various reason, I have been in need to install Ubuntu on a thumb drive. I have been trying for the last few days or so to install Ubuntu (Not the  "LIVE CD" ) on a flashdrive. Everytime I try to boot, I get either a) an error from my computer's bios saying that it is not a bootable drive; b) a frozen purple or black screen; c) I get to the GRUB menu and when I try to get to login, it freezes midway; or d) I login and the entire thing freezes for what feels like an eternity only to eventually get up and come back after a minute and find the thing is back at the login screen.   I have reinstalled Ubuntu various ways; I have attempted repairing the installs; I have looked high and low. I don't know what is happening. Can someone please help me! I am very new to Linux, and I am completely lost as to what is going on. Here are some technical specs of what I use:   64GB flashdrive (USB 2.0)         i7 2600   8GB RAM   AMD RADEON HD 6***(No idea what it is after that)      Please help. I'm begging.

If you are hurrying to reply, System → Administration → StartUp Disk Creator -- no, that's not what I'm talking about.   I want to try Ubuntu 11.04's Unity without touching my existing Ubuntu install.  To do this, I need to install the nVidia drivers first (sigh).  To do this, I need changes to persist a reboot.  To do this, I need to really install Ubuntu on a USB key.  How do you do that?    What I tried   I tried to make a USB key from , then boot from it, then choose "Install Ubuntu." The installer refused to install to the installation media itself. I tried, from my installed copy of Ubuntu:  sudo kvm /dev/sdb --cdrom .cache/testdrive/iso/ubuntu_natty-desktop-i386.iso   ...but the installer didn't detect the disk properly.


Suppose I have a relatively long module, but need an external module or method only once.  Is it considered OK to import that method or module in the middle of the module?  Or should imports only be in the first part of the module.  Example:  import string, pythis, pythat ... ... ... ... def func():      blah      blah       blah      from pysomething import foo      foo()      etc      etc       etc ... ... ...   Please justify your answer and add links to s or relevant sources

states:  Imports are always put at the top of the file, just after any module comments and docstrings, and before module globals and constants.  However if the class/method/function that I am importing is only used in rare cases, surely it is more efficient to do the import when it is needed? Isn't this: class SomeClass(object):      def not_often_called(self)         from datetime import datetime         self.datetime = datetime.now()  more efficient than this? from datetime import datetime  class SomeClass(object):      def not_often_called(self)         self.datetime = datetime.now()


I have to calculate the order of the ring $\mathbb{Z}[i]/(1+i)$. This is how far I am: If $a+bi\in \mathbb{Z}[i]/(1+i)$ then there are $n,m\in \mathbb{Z}$ such that $a+bi\equiv 0+ni$ or $a+bi\equiv m+0i $. This means that $\mathbb{Z}[i]/(1+i)=\{x\in \mathbb{Z}[i]: Re(x)=0 \text{ or }Im(x)=0\}$. So the order of this ring has to be infinite. I have a feeling I have something wrong, but cant figure what. Is there something wrong in this calculation? Thanks.

A very basic ring theory question, which I am not able to solve. How does one show that    $\mathbb{Z}[i]/(3-i) \cong \mathbb{Z}/10\mathbb{Z}$. Extending the result: $\mathbb{Z}[i]/(a-ib) \cong \mathbb{Z}/(a^{2}+b^{2})\mathbb{Z}$, if $a,b$ are relatively prime.   My attempt was to define a map, $\varphi:\mathbb{Z}[i] \to \mathbb{Z}/10\mathbb{Z}$ and show that the kernel is the ideal generated by $\langle{3-i\rangle}$. But I couldn't think of such a map. Anyhow, any ideas would be helpful.


Suppose we have two surjective homomorphisms $f_1,f_2: F_{n} \rightarrow F_{m} $ of free groups (so $n\ge m$). One can always find homomorphism $g:F_n \rightarrow F_n $ giving a commuting triangle - when can it be enhanced to be an isomorphism?

Let $f:F_n\to F_m$ be an epimorphism ($n\geq m$). Then it is true that there is a basis $X=X_1\sqcup X_2$ in $F_n$ such that $f$ maps $\langle X_1\rangle$ isomorphically onto $F_m$, and maps $X_2$ to identity. One can probably deduce this statement from the Grushko-Neumann theorem, but somehow I cannot get an elegant proof of it.   I can see that by the Grushko-Neumann we can assume that $m=1$, and hence our epimorphism factors through the abelianization. And then an ugly linear algebra appears... Any suggestions how to make the proof slick?


I'm studying about Quantum Information and Quantum Mechanics. Right off the bat it's stated that we deal with vectors and operators in Hilbert space. But then I see the definition of a Hilbert space and several questions pop up in my head: like why do we need a complete vector space? Why should it have an inner product structure? etc. One way to learn could be to not worry about these questions, accept the mathematical structure at face value and methodically follow the consequences of these assumptions. But I'd prefer to understand the rationale behind each and every assumption about the mathematical structure. Specifically,  Why is it not possible to use a weaker set of assumptions? From the physical point of view what's the point of each assumption, etc.  My question is, how do I go about answering the bulleted questions as I learn QM?

What does the word "complete" means from the physical point of view? I do not understand what it physically means to say that a  is a .


i recently bought lenovo g510(i5,8GB RAM) how to install windows and ubuntu on this without having any crash of os.

I'm absolutely new to Linux. I would like to know how to install Ubuntu alongside the pre-installed Windows 8+ OS.  Should I do it with Wubi, or through the Live USB/DVD?  What steps do I need to take to correctly install Ubuntu?


I am trying to run this script in ubuntu terminal. script.sh #!/bin/bash #Initializing two variables a=10 b=20   #comparing a and b  if [$a == $b]  then     echo "they are equal"  else     echo "they are not equal" fi  Output is - chmod +x script.sh ./script.sh ./script.sh: line 8: [10: command not found they are not equal  Please help me with the issue here.

I am using the below script to move two days back when script runs at starting two days of the year and also check first and second days of every month and move two days back. if [$month="01"] && [$day="01"]; then         date="$last_month/$yes_day/$last_year"         fulldate="$last_month/$yes_day/$last_year" else         if [$month="01"] && [$day="02"]; then                 date="$last_month/$yes_day/$last_year"                 fulldate="$last_month/$yes_day/$last_year"         else                 if [ $day = "01" ]; then                         date="$last_month/$yes_day/$year"                         fulldate="$year$last_month$yes_day"                 else                         if [ $day = "02" ]; then                                 date="$last_month/$yes_day/$year"                                 fulldate="$year$last_month$yes_day"                         else                                 date="$month/$yes_day/$year"                                 fulldate="$year$month$yes_day"                         fi                 fi         fi fi  But my bad am getting the below error message Etime_script.sh: line 19: [06=01]: command not found Etime_script.sh: line 24: [06=01]: command not found


When I used HttpWebRequest and HttpWebResponse classes for an API calling my game suddenly halt for some seconds but as i used same API calling through WWW with coroutine, it didn't halt.   I heard that unity is single thread but why my game not halt as i used WWW with coroutine? and is i am getting right that  HttpWebRequest and HttpWebResponse are not better than WWW?

In the Unity3D game engine, a common code sequence for getting remote data is this:  WWW www = new WWW("http://remote.com/data/location/with/texture.png"); yield return www;   What is the underlying mechanism here?  I know we use the yield mechanism in order to allow the next frame to be processed, while the download is being completed. But what is going on under the hood when we do the yield return www ?   What method is being called (if any, on the WWW class)? Is Unity using threads? Is the "upper" Unity layer getting hold of www instance and doing something?  EDIT:   This question is specifically about Unity3D internals. I'm not interested in explanations of how yield statement works in C#. Instead, I'm looking for an inside view of how Unity deals with these constructions, to allow, for example, to WWW to download a piece of data in a distributed manner across several frames.


Assume $\{x,x_1,x_2,\ldots\}$ is a subset of a given Hilbert space $X$ with norm $||\cdot||$ such that $x_j$ converges to $x$ weakly and $||x_j||$ converges to $||x||$. Prove that $x_j$ converges to $x$ in norm.  For this question, I think that since $X$ is a Hilbert space, then $||x||$ is equal to the root of the inner product $\langle x,x\rangle$, $||x_j||$ is equal to the root of $\langle x_j,x_j\rangle$, so the root of $\langle x_j,x_j\rangle$ converges to root of $\langle x,x\rangle$.  Does this mean $\langle x_j,x_j\rangle$ converges to $\langle x,x\rangle$?   For my main question, I hope to get a counterexample if $\{x,x1,x2,\ldots\}$ is a subset of a Banach space. Thanks a lot.

Assume that $H$ is a $\mathbb K$-Hilbert space, $(x_n)_{n \ge 1}$ a sequence in $H$ and $x ∈ H$.   Show that $x_n → x$ if and only if $x_n \to x$ weakly and $\Vert x_n \Vert → \Vert x \Vert$.   I'm trying to prove this statement.  The $\Rightarrow$ is basically clear, since a  strongly convergent sequence is also weakly convergent. But how can I show the other direction $\Leftarrow$ ?


Find all integer number such as n,which could  be divisor of 2^n+1.I found that n could be power of three, but I can't find all solutions.

I found this problem in a book and while I understand the given solution, I don't quite understand how somebody would arrive at this solution unless they did out the casework and happened to make the right guesses to solve the problem. Any guidance on solving this from scratch would be greatly appreciated!


The GPS is a very handy example in explaining to a broad audience why it is useful for humanity to know the laws of general relativity.  It nicely bridges the abstract theory with daily life technologies!  I'd like to know an analogous example of a technology which could not have been developed by engineers who didn't understand the rules of quantum mechanics.  (I guess that I should say quantum mechanics, because asking for a particle physics application could be too early.)  To bound the question:   No future applications (e.g. teleportation). No uncommon ones (for, who has a quantum computer at home?). A less frequently-cited example than the laser, please. If possible, for sake of simplicity, we'll allow that the quantum theory appears in form of a small correction to the classical one (just like one doesn't need the full apparatus of general relativity to deduce the gravitational red-shift).

Is there a phenomenon visible to the naked eye that requires quantum mechanics to be satisfactorily explained? I am looking for a sort of quantic Newtonian apple.


I created the question , trying to summarise the issue in the title.  The (shortened) error message precisely identifies the specific issue I experience, however the word "problem" is not allowed in the question title, so I resorted to using l33t-speak.  I could have used a more generic description, but that would mean visitors wouldn't conclusively know from the title, if the questions concerns the issue they're experiencing, or a similar issue.  This seems like a silly and counter-productive restriction, which potentially makes perfectly valid questions harder to find by searching.

Recently this Mathematica question was posted,  The reason for the odd split in the word pro-blem is there is a filter preventing its use in titles. For the most part, I can see where this is useful, as almost by definition all questions asked here are about problems. But, this filter prevents a legitimate use of the word that is accepted in the physics and math communities.   Is there a way around this, or is the problem so great that its legitimate use must be suppressed also?


Consider the matrix   $$ M=\left(\begin{matrix} 0&0&0&1\\ 0&0&0&0\\ 0&0&0&0\\ 0&0&0&0\\ \end{matrix}\right). $$   For which ${n\in{\Bbb Z}}$ does there exist a matrix $P\in{\Bbb C}^{4\times 4}$ such that $P^n=M$?     Since $P$ must be not invertible, one must have $n\geq 1$. For $n=1$, it is trivial.  When $n=3$, we have (thanks to answers to this ) $P^3=M$ where $P$ is the $4\times 4$ Jordan black with $\lambda=0$: $$ P=\left(\begin{matrix} 0&1&0&0\\ 0&0&1&0\\ 0&0&0&1\\ 0&0&0&0\\ \end{matrix}\right). $$ How can I deal with the general cases?

Consider the matrix $$ M=\left(\begin{matrix} 0&0&0&1\\ 0&0&0&0\\ 0&0&0&0\\ 0&0&0&0\\ \end{matrix}\right). $$ Is there a matrix $P\in{\Bbb C}^{4\times 4}$ such that $P^n=M$ for some $n>1$?    One obvious fact is that if such $P$ exists, then $P$ must be nilpotent. However, I have no idea how to deal with this problem. Furthermore, what if $M$ is an arbitrary nilpotent matrix with index $k$?


I have a windows partition mounted in linux (setup with pysdm) with following options:  nls=iso8859-1,umask=000,gid=users,user,uid=my_user   I can access the data on the partition, write/read files, but when I try to run a shell script I get permission denied. The script has:  -rwxrwxrwx 1 my_user users 8419 Aug 11 14:06 test.sh   How can I please setup the partition so that I can read/write files (like now) and run scripts under my user as well as my cron/anacron jobs also being able to run commands writing to this windows partition? (i.e. full extent of functionality as my native linux partition?)   Thank you!

I have this problem: I'm used to compile and run .c files with CodeBlocks. If I do that from my Desktop (ext4 partition) it works without problems, but doing this from my secondary hard drive (NTFS partition) makes CodeBlocks to say permission denied while running a .c file.  I have read it's because of the partition type is it correct? But I don't know how to solve it. I tried to edit fstab (sudo gedit /etc/fstab) adding this line:   /dev/sda /media/Dati ntfs user,exec 0 1   but after rebooting Ubuntu I had a warning on boot about a problem mounting a drive, that's because I set KDE to auto mount my Dati drive on boot.   So I should auto mount my NTFS drive with execute permission? How can I do that?


How do faculty search committees evaluate candidates  for faculty or post-doc positions?   I am a PhD student I found that there is no fixed algorithm to judge a journal. But candidates publish in various journals in their PhD.  How will a researcher know where to publish his PhD so that he can get a Post-Doc or faculty position?  If a candidate does not understand which journal is good/average/bad,how will one decide where to publish?  This question is somewhat related to   NOTE:I am in search of a journal for my first ever manuscript.So I am asking a lot of questions,sorry for that

A colleague and I recently submitted a paper to a journal with an impressive-sounding name, the "International Journal of Artificial Intelligence and Computational Research". According to ,      IJAICR is a referred [sic] journal in the field of computer science, artificial intelligence and soft computing methods.   It was accepted two days after we submitted it. That's too fast. We were suspicious. Although the journal said that all papers are peer-reviewed, we could not see how that was done in two days. Plus, we received no comments from the reviewers. Also, the submission guidelines didn't ask for a "blind" copy (without our names or any references to who we were).   But wait, there's more.  The acceptance letter asked us to send them US$300 to publish it. We did not. We've withdrawn our submission and will submit a new version of the paper to a more reputable journal in the coming months.  How might we make a better choice of respectable journals before we submit next time?


I have 10 content types and they all have page view. These content type have similar fields and the difference is just their name, that is why I don't want to create the following files for every one of them:   views-view--VIEWNAME--page.tpl.php views-view-fields-VIEW_NAME--page.tpl.php   One of the views is called sabk_zendegi, and the following code belongs to views-view--sabk_zendegi--page.tpl.php.
<img src="<?php print $directory; ?>/image/view_tpl_file/top_border.png" />
 <?php print $rows; ?>  <?php print $pager; ?>
<img src="<?php print $directory; ?>/image/view_tpl_file/bottom_border.png"/>
   This is not a good idea to repeat the same code for 10 files which the only difference is just their name. I have the same problem for views-view-fields--sabk_zendegi--page.tpl.php; this code belongs to views-view-fields--sabk_zendegi--page.tpl.php.

     <?php print $fields['field_sabk_zendegi_photo']->content; ?>

     <li style="list-style-image: url('<?php print $directory; ?>/image/view_tpl_file/list_item.png')">     <?php print $fields['field_sabk_zendegi_titr']->content; ?>

         <?php print $fields['field_summary']->content; ?>

     As you can see this code is the same for all the views but the difference is just the $fields fields. (It can be replaced by a variable that is already assigned in template files.)  Is there any preprocess/template function in Drupal 7 that calls one page for views-view--VIEWNAME--page.tpl.php and one page for views-view-fields--VIEWNAME--page.tpl.php and it assigns the relevant variables inside it?   Instead of using $field['fields_summary'], I should be able to use $summary in this new general page, and these variables have their values already assigned by template/preprocess function according to the view.

I have 8 content types and 4 of them are the same and the difference is just their name. they all have a page view and the way I display them on screen is the same. instead of having 8 pages. (VIEWNAME_i stands for the i-th view.)   views-view--VIEWNAME_i--page.tpl views-view-field--VIEWNAME_i--page.tpl   I need a template function to reduce these 8 pages into 2. I want to define a general page for views-view--VIEWNAME_i--page.tpl. I would assign every view's variables in this function. I also want to do the same for fields page.


I would like to know why the menu button has been removed from Android in Android 6 and 7 mobile phones, hosting an apps button instead. Thanks.  (I remember long pressing the home button on Android 4 to get to the apps list.)

I'm fairly new to android development, but am I long time android user. Phones used to have a "hardware" menu button, which I have since seen is emulated in software, but only when I'm running an 'old' app on my phone ("three dots stacked on top of each other that appears to the right of all the other buttons)  Why is writing apps that make use of the button discouraged?  Is it not supported by most phones?  Is it a bad user experience? ('swipe down from top to access soft buttons', etc..)


I have got ajax result with new element on page.  Checkbox is:  <input type="checkbox" checked="checked" uid="933518636168122368" class="flag">   How I can select him?  my code is not working, selector object is empty:  $(document).ready(function(){     if ($('.flag').is(':checked')) {         alert('checkit');     }      $('.flag').click(function(){         alert('checkit');     }); });   What I must to do?

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


So I'm trying to implement a simple class in android studio that takes user input in the form of a spinner and changes the colour of the text accordingly. However, even though the condition has been met, as can be seen by the debugging line, the program will not execute the contents of the if statement.   'import android.content.Intent; import android.graphics.Color; import android.support.v7.app.AppCompatActivity; import android.os.Bundle; import android.view.View; import android.widget.AdapterView; import android.widget.ArrayAdapter; import android.widget.Spinner; import android.widget.TextView; import android.widget.Toast;  public class Colour extends AppCompatActivity {  TextView tv; Spinner mySpinner; ArrayAdapter<CharSequence> adapter; public static final String EXTRA_MESSAGE = "message"; @Override protected void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState);     setContentView(R.layout.activity_colour);     Intent intent = getIntent();     String messageText = intent.getStringExtra(EXTRA_MESSAGE);     tv = (TextView)findViewById(R.id.message);     tv.setText(messageText);     mySpinner = (Spinner) findViewById(R.id.spinner);     adapter = ArrayAdapter.createFromResource(this,R.array.colours,android.R.layout.simple_spinner_item);         adapter.setDropDownViewResource(android.R.layout.simple_spinner_dropdown_item);     mySpinner.setAdapter(adapter);     mySpinner.setOnItemSelectedListener(new     AdapterView.OnItemSelectedListener() {         @Override         public void onItemSelected(AdapterView<?> parent, View view, int position, long id) {             Toast.makeText(getBaseContext(), parent.getItemIdAtPosition(position)+ " selected",Toast.LENGTH_LONG).show();         }          @Override         public void onNothingSelected(AdapterView<?> parent) {          }     });  }  public void change(View v){      String text = mySpinner.getSelectedItem().toString();      if(text == "Red"){         tv.setTextColor(Color.RED);     }     if(text == "Blue"){         tv.setTextColor(Color.BLUE);     }     if(text == "Green"){         tv.setTextColor(Color.GREEN);     } }'    '<TextView     android:textColor="#000000"     android:layout_width="wrap_content"     android:layout_height="wrap_content"     android:id="@+id/message" />  <Spinner     android:layout_width="match_parent"     android:layout_height="wrap_content"     android:entries="@array/colours"     android:layout_centerHorizontal="true"     android:layout_marginTop="16dp"     android:id="@+id/spinner" />  <Button     android:text="HOME"     android:layout_width="wrap_content"     android:layout_height="wrap_content"     android:id="@+id/button"     android:onClick="home"     android:layout_alignParentBottom="true"     android:layout_centerHorizontal="true"     android:layout_marginBottom="52dp" />  <Button     android:text="changeColour"     android:layout_width="wrap_content"     android:layout_height="wrap_content"     android:id="@+id/button4"     android:layout_above="@+id/button"     android:layout_alignStart="@+id/button"     android:layout_marginBottom="101dp"     android:onClick="change" />'

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


I am going to attend my first IEEE conference on Electronic Design/Verification and am feeling quite nervous about my first oral presentation.   I want to make sure to "sell" my point and ensure all questions are being tackled, and so I am looking for advice related to the organization of my slides. For example,   How can the slide material  complement my speaking?  How do I ensure that the end-product is not dry/heavy?  If my work is on for example, SRAM or Post-silicon technologies,is it recommended to begin my presentation with a foil on a collage of the latest news snippets about these topics? This could probably draw their attention rather than picking up some lines from my camera-ready's introduction section.  Also, how many slides should I ideally allocate for each section of my paper?   I am forced to ask such "trivial" questions as my Professor is on a sabbatical currently and has little/no access to mail for the next few weeks.  I have searched the Internet and found some generic advice, like  by David Patterson.  There are some related questions on this site that do not seem to directly address how to organize the content of the slides.  asks about becoming a more effective orator.  asks about effective design elements (not content organization) for slides.

I have been attending a number of academic / professional conferences recently and one thing that really awed me was the flawless and natural way in which the speakers presented on their topics.  Sure, they had the occasional mispronunciations or awkward pauses but they spoke with authority and confidence.   Some of them used powerpoint slides but were not reading from the slides; they were just talking on the points and they had so much to say on each point that I felt they could not do it without notes, but they were not even looking at their notes most of the time.  (The advantages of not looking at their notes too much was that they could maintain eye contact and could use very interesting slides that were not crammed with the dot points of their speeches.)  I hate to think that they had memorised their speech notes but some of the presentations went for more than an hour.  I know rehearsal is important but I wonder how could anyone remember so much in a nervous situation. (Its one thing to know everything on your topic; its another thing to present that 'everything'!)  Question:  What background / foreground things do presenters do that make their presentations flawless and natural?


Good afternoon to everybody  Could you please help to get a closed form of the integral above  where a is a positive real number.  A form based on hypergeometric functions will be also considered as closed form  Best regards

I'm searching a closed form for the integral of the form :  $$ \int_{0}^{\infty}e^{-ax}e^{-x^\frac{\alpha}{2}}dx $$  especially for $\alpha=8$  After several attempts, I find that the general form can be written on the basis of hypergeometric functions. what do you think ?


How to show that  direct product of $\mathbb Z\times\mathbb Z\times\mathbb Z\times...$ is not projective as a $\mathbb Z$ module?  I know that $\mathbb Z$ is a free $\mathbb Z$ module since it has $\{1\}$ as a basis.  An $R-$  module $P$ is said to  projective if $P$ is a direct summand of  a free $R-$  module .Also an $R-$  module is free if it is isomorphic to a direct sum of copies of the underlying ring.  However I cant use these facts to arrive at my proof.How to do it?

Why isn't an infinite direct product of copies of $\Bbb Z$ a free module?   Actually I was asked to show that it's not projective, but as $\Bbb{Z}$ is a PID, so it suffices to show it's not free.   I am stuck here. I saw some questions in SE, but there is no satisfactory answer at all.


While checking if there is a value for a property in an object, I was using if(prop in object) return object[prop] else object[prop] = x (x is some variable outside of this question) to determine if an entry has been made into the object. Should I just use if(object[prop]), because if the property doesn't exist, it will return undefined? Is using the in operator just as fast? The only pitfall caused by changing to check the value is if the value if null, 0, -0, false, or NaN, it will return false when I want a falsy value, is there anything else I should watch out for?

How do I check if an object has a specific property in JavaScript?  Consider:  x = {'key': 1}; if ( x.hasOwnProperty('key') ) {     //Do this }   Is that the best way to do it?


When i type " é " directly with the appointed key, or use a key combination of "´ + e" (where I press the ´ first, the character doesn't show up, and then I pres e and the accent appears) it doesn't show in my pdf when i print for feedback.  i'm using TexMaker and have a AZERTY-keyboard (belgian). I've tried to look at a lot of answers already involving UTC8 and \inputenc but with UTC8 the document lay-out just looks horrible... and with inputenc I only get a lot of weird symbols instead of the accented character.  Any way i can fix this without using \´e?

How to type these special letters from European languages in latex? ä, é, and L'?


trigger SendWelcomeLetter on Account (after insert) {      List<SDOC__SDJob__c> jobList = new List<SDOC__SDJob__c> {};      for(Account acct : Trigger.New) {     SDOC__SDJob__c job =     new SDOC__SDJob__c(SDOC__Start__c=true,                       SDOC__Oid__c=acct.Id,                       SDOC__ObjApiName__c='Account',                       SDOC__SendEmail__c='1',                       SDOC__Doclist__c='Welcome Letter,Email Template');     jobList.add(job);   }   insert jobList;  }  I am using this trigger to generate a sdoc template but I am confused on how to get the test coverage for the same.

How do I write a unit-test / test class for a trigger?  What are my options?   Inline with the trigger?  New Class?


\begin{equation} \text{RMSPE} = \sqrt{\frac{1}{n} \cdot \sum_{i=1}^n \Delta X^2_{\text{rel},i}}\cdot 100\% \end{equation} with  \begin{equation}  \Delta X_{\text{rel},i}=\frac{X_i}{T_i}-1, \end{equation} where $T_i$ is the desired value and $X_i$ is the actual value.  If this error actually exists, then a citable source for it would be greatly appreciated. If it does not exist, then why so?  Thanks in advance.

\begin{equation} \text{RMSRE} = \sqrt{\frac{1}{n}\cdot\sum_{i=1}^n \Delta X^2_{\text{rel},i}} \end{equation} with  \begin{equation}  \Delta X_{\text{rel},i} = \frac{X_i}{T_i}-1, \end{equation} where $T_i$ is the desired value and $X_i$ is the actual value.  If this error actually exists, then a citable source for it would be greatly appreciated. If it does not exist, then why so?  Thanks in advance.


I have several large figures which need their own page. I would like to force the figures to occupy adjacent pages, starting from where I place the code for the first figure.  Regular figure environments take the option [H] from the float package, but this seems to not work with sidewaysfigure. Is there a workaround, or do I just have to settle with my figures being all over the place?

I'm trying to force a sideways figure to be drawn in a specific point of the text, but I haven't found any valid solution. In particular, I need to achieve the following layout:   page 1 - contains only text page 2 - contains the sideways figure page 3 - text and figures   Here the code I'm using.  \begin{sidewaysfigure}[counterclockwise]   \centering     \scalebox{0.99}     {\includegraphics[width=0.99\textwidth]{myfigure}}     \caption{def}     \label{def} \end{sidewaysfigure}   When I compile, myfigure figure is rendered only after page 3, but it's not I want to achieve.  Any suggestions?


I've been having a problem in the software recently, and it's been bothering me a lot.  I accidentally either opened this console or expanded it from the top, (currently empty as I just reopened the file, didn't help, ) and it wont close or shrink.  (see picture below)  I've looked at other guides similar to this, and nothing's helped.  The main problem I've had is that any time I try to merge it, it just creates a new ribbon with file, render, etc., and no guides cover this topic.  I don't know what to do, and can't find any guides, so I hope you can help!

I would like to close some view windows that I opened accidentally.  See the image below:    Edit: another note: I tried searching for the solution, but only found things like "Join Area", which don't seem to work in this situation.


When I run the following SQL command   select payee_id, start_dt,         row_number() over(partition by payee_id order by start_dt) as rn  from xxx  where rn = 1   I got an error :     error Invalid identifier 'rn'   Please advise.

I have restored the Northwind database() from a backup file using SQL Server.   Trying to execute the following query results in error "Invalid column name 'products'.", product is an alias.  SELECT OrderID, COUNT(ProductID) products FROM [NORTHWND].[dbo].[OrderDetails] GROUP BY OrderID HAVING products > 5;   What is the problem?


I really want some Java that randomizes from 1-2 and all that I came up with (Doesn't work either) is:  random.math (int.1+2)   Might actually look stupid to an expert but yeah

How do I generate a random int value in a specific range? I have tried the following, but those do not work: Attempt 1: randomNum = minimum + (int)(Math.random() * maximum);  Bug: randomNum can be bigger than maximum. Attempt 2: Random rn = new Random(); int n = maximum - minimum + 1; int i = rn.nextInt() % n; randomNum =  minimum + i;  Bug: randomNum can be smaller than minimum.


I recently started playing around with Python 3 (or coding, for that matter) and I quickly ran into something that I don't understand. I somehow managed to define a function that not only gives the wrong output, but also unexpectedly changes its input. I'll explain this more precisely on an example.  Say we want to write a function that takes a list/vector   L = [v_0, ..., v_n]   and spits out the following transformed version:  L' = [v_0, v_0+v_1, ..., v_0+...+v_n]   Even if there are better ways, let's try to do it using this algorithm:   Step 0: Set L_0=L as initial data. Step 1: Take L_0=L and add v_0 to L_0[j] for j>1. Call the result L_1. ... Step i: Take L_i and add v_i to L_i[j] for j>i. Call the result L_i. ...   This gives L' in n steps (hopefully...). As I said, there are probably better ways to do it, but let's stick with this approach. Here's what I tried to do:  # problematic function: def Mod(L):     newL = L     for i in range(len(L)-1):         for j in range(i+1,len(V)):             newL[j] = newL[j] + L[i]     return newL  # illustration of problem: L = [1,2,3,4] print(L)        # gives [1,2,3,4], as expected print(Mod(L))   # gives [1,3,7,15], L' would be [1,3,4,10] print(L)        # gives [1,3,7,15] instead of [1,2,3,4]. WHY?!   Again, I'm not looking for better solutions or better algorithms. This is an artificial problem and I've already solved my actual problem in another way. What I want is to understand why this code does not work properly and why it does what it does.  As indicated, there are two things that are going wrong:  (1) First of all, 'Mod' does not do what I want: Mod(L) does not give L'.  (2) More importantly, for some reason running Mod(L) changes the variable L.   I'm seriously stumped by this, especially by (2). I keep going through the loops trying to find out what's wrong, but I seem to be stuck in a loop myself (overlooking the same thing again and again). Somehow the input of Mod must get redefined somewhere in the loops. But I don't see where this would be happening. The only thing that I see getting changed is the local variable 'newL'.  Any pointers as to what I'm missing are highly appreaciated!

I'm trying to understand Python's approach to variable scope. In this example, why is f() able to alter the value of x, as perceived within main(), but not the value of n?  def f(n, x):     n = 2     x.append(4)     print('In f():', n, x)  def main():     n = 1     x = [0,1,2,3]     print('Before:', n, x)     f(n, x)     print('After: ', n, x)  main()   Output:  Before: 1 [0, 1, 2, 3] In f(): 2 [0, 1, 2, 3, 4] After:  1 [0, 1, 2, 3, 4]


I am interested in why this proof is wrong since every proof I have seen uses much more knowledge than this and I can't figure out why it is incorrect.   Suppose $x^3 = x$ for every $x \in R$. Then $x = x^{-1}$ and similarly for every $y  \in R$, $y = y^{-1}$. So then $xy \in R$ and $xy = x^{-1}y^{-1}$. Since $yx(x^{-1}y^{-1}$) = $e$, $(yx)^{-1} = (x^{-1}y^{-1})$. Then $xy = (yx)^{-1}$. Since $R$ is closed under multiplication, $yx \in R$ and so by the discussion above, $yx = (yx)^{-1}$. Therefore, $xy = yx$ for all $x$,$y \in R$ which means that $R$ is commutative.

Let $R$ be a ring, where $a^{3} = a$ for all $a\in R$. Prove that $R$ must be a commutative ring.


Ok so I'm learning some topics and I'm learning prototypes. I see that this works:  function Person(name) {     this.name = name || 'Luis Felipe Zaguini';      this.sayHi = function() {         console.log(`Hey there, ${this.name}!`);     }      this.sayGoodBye = function() {         console.log(`Good bye, ${this.name}!`);     } }  let me = new Person(); me.sayHi();  let other = new Person('Other'); other.sayGoodBye();   But that also works:  function Person(name) {     this.name = name || 'Luis Felipe Zaguini';      this.sayHi = function() {         console.log(`Hey there, ${this.name}!`);     } }  Person.prototype.sayGoodBye = function() {     console.log(`Good bye, ${this.name}!`); }  let me = new Person(); me.sayHi();  let other = new Person('Other'); other.sayGoodBye();   They end up 'in the same way'. Which version is better? Are there some disadvantages? It seems to me that the first way (defining methods inside the function object) looks clearer. What do you people think?

What's the difference between  var A = function () {     this.x = function () {         //do something     }; };   and  var A = function () { }; A.prototype.x = function () {     //do something };


I'm stuck with this problem :  Let $a,b$ positive integers such that $$a\mid b^2, b^2\mid a^3,\ldots ,a^n\mid b^{n+1},b^{n+1}\mid a^{n+2},\ldots$$ Show that $a=b$.  If were $ b > a $ then $\lim_{n \to \infty}\frac{b^n}{a^n}=0 $ choosing $\epsilon = \frac{1}{a}$ we got a contradiction, but I can't show that $b<a$ can't hold.  Any help is apreciated.

Let $a$ and $b$ be positive integers such that $a | b^2, b^2 | a^3, a^3 | b^4, b^4 | a^5, \cdots $ Prove that $a = b$.  My way is as follows: Let $A=v_p(a), B=v_p(b)$ be the exact power of a prime $p$ dividing $a$ and $b$ respectively. Then by assumption, $(2n-1)A \leq 2nB, n=1,2,3,\cdots.$ Hence $A \leq (2n/(2n-1))B$. Taking limit as $n$ tends to infinite yields $A \leq B.$ Likewise, $2nB \leq (2n+1)A, n=1,2,3,\cdots,$ by a similar argument, we have $B \leq A.$ So that $A=B$ and we are done. But I am rather unsatisfied with the proof because it involves limit. I wanna ask if there is any other alternative proof, thank in advances.


I found out how to get WoW running on Ubuntu using Wine 1.5 and am able to play it (albeit somewhat slow, but that's mostly due to my hardware). It was downloading just fine and I could play without any errors.  But now that it has reached 85.5%. It refuses to download any more. It was stopped at 84.5 but I reloaded the Launcher multiple times and it moved another 1%.   I don't know why it stopped; the only thing I did was close the Launcher to resume it later (which hadn't caused problems until 84.5% downloaded). Everything loads and it seems like it is just lagging (the download speed wont show up and start downloading the game again).   Anyone know what I can do?   (Not using dual-boot with Windows, just straight Ubuntu)

I am looking for a step by step instruction to guide me in the ways of installing, configuring and debugging many of the issues new users have when dealing with Wine in Ubuntu.  What is the recommended way of installing Wine, some of the key issues that it has and how to solve them?  If I have a specific problem with an App in Wine, how do I go about solving it? What are the recommended steps to ensure that I can fix a problem related to an app I wish to use?


Theres an app to find snapchat friends. And there is a guy wanting to be my sugar daddy. We havnt met let alone even talked. And he asks if he can trust me. And i say yes. So he gives me his bank account information to pay of credit in paypal. Im pretty sure its gotta be a scam. But i just wanted to say what you guys think.

This is a really weird situation. A guy contacted me regarding a business I have. He offered far in excess of my stated fees and even told me he could help me financially if I needed it, which I do. He said he was a doctor. Before he even showed up, he gave me his bank account and routing number and full name, which I used to pay some utility bills. All the payments went through. He also sent me $2500 through PayPal, and I received an email that I had received the payment, though it's been 24 hours and it still hasn't shown up in my "recent activity" in my account. But at the time when I met him, I had no reason to doubt the whole thing was real.   So we met, and through conversation he seemed totally legit. Halfway through our session, he abruptly left — he claimed he was being called in to the hospital. He had already received some, but not all, of the services we had agreed to. He said he would come back in a few hours. Oh yeah, and since the PayPal funds hadn't gone through yet, and I needed cash to pay rent, he said his "financial advisor" would be wiring me $800 a couple hours later. Well, I never heard back from him and never got a call about a wire transfer. In retrospect it all seems very obviously a scam, except for the fact that he gave me a bank account number that actually worked as far as paying some bills!  My question is, assuming the PayPal payment never goes through — I never got an email saying that it was cancelled, but it isn't showing up in my payments either. I'm planning on calling PayPal if it hasn't gone through by tomorrow. But assuming that payment doesn't go through, how can I use the bank account info to get the payment he promised me as far as the services I provided? Other than paying all my utilities in advance? You'd think with an account number and routing number and full name, I would be able to withdraw money somehow, but I really have no idea how. And since it isn't under my name, I can't make a payment on my student loans. I wouldn't take more than he owed me, but it would really be nice to at least get that, even if I didn't get the $2500 he had promised me.   You always hear about not letting people see your account number and stuff like that, but it seems impossible to do anything with this info even though I have it! If scamming people with their bank account number is so easy, how do scammers do it? So I'm wondering two things:   What legal way can I take what I am owed from this guy? What illegal way do people use this info if they had it? I don't want to get in trouble, but I'm just curious because you always hear how easy it is.   (Oh, and I never actually saw his ID so I don't know that the name & bank info he gave me was actually his, he could have stolen it from someone, though he really didn't seem like a hacker — he was a middle aged black man who was very smart-sounding, polite, soft spoken, and he seemed to have a lot of knowledge that a real doctor would have. I have a college degree and am very skeptical in general and careful about not being scammed and I've never had an experience even close to this, and the whole time I kept thinking "is this guy for real?" but since the utility stuff had gone through, it seemed legit. And nothing he did sent up a red flag like he might be a criminal or something. But later I googled the name and couldn't find a doctor by that name, at least not in the state he said he lives in. And since he said he would be contacting me last night, and he never did, it seems obvious that he planned the whole thing, but it just makes no sense to me.)


I have a Sager NP9150 laptop with an i7-3610QM CPU and a AMD HD 7970m GPU. I get the Grand Theft Auto V has exited unexpectedly  error when I try run the game and it happens in safe mode also. It was mentioned  how someone else got it working. I tried following those steps but could not get it working. Does anyone know any workaround for laptops with an AMD GPU?

I recently ordered the GTA V PC from Steam and when I finished installing and launch the game. It gave me "Grand Theft Auto V has exited unexpectedly". I tried "safe mod" and every option available, but none of them work. I checked some forums and found a lot of people having the same problems. What could be the possible cause? I'm using a laptop with these specs:  CPU: i7 4700m GPU: AMD HD8970M RAM: 8GB  I'm pretty sure my laptop is way beyond the minimum specs. Does someone know how can I enter the game?


I have a script that works when called:  /usr/local/bin/myscript #this works fine   Permissions for the file are:  -rwxr-xr-x 1 root root 155 Jan 27 09:34 myscript   I've added a line to /etc/crontab:  * * * * * root /usr/local/bin/myscript   But cron doesn't seem able to run this.  The crontab has the PATH variable set:  PATH=/usr/local/sbin:/usr/local/bin:/sbin:/bin:/usr/sbin:/usr/bin   The script is a mysqldump to the /var/tmp/ directory:  #!/bin/bash  DAY=`date +%y%m%d` TIME=`date +%k%M` mysqldump test -u john -pxxxxxxx > /var/tmp/$DAY.$TIME.test.sql   I can't think what is wrong with this, but the script isn't running.  Edit: /var/log/syslog shows the following entries:  Jan 27 10:20:01 hector CRON[8286]: (root) CMD (/bin/bash /usr/local/bin/myscript) Jan 27 10:20:01 hector CRON[8285]: (CRON) info (No MTA installed, discarding output)   So I guess it's trying to run the script, but it must be failing somewhere because I don't get the same output as if I ran it with /usr/local/bin/myscript.

This is a  about using cron & crontab.   You have been directed here because the community is fairly sure that the answer to your question can be found below. If your question is not answered below then the answers will help you gather information that will help the community help you. This information should be edited into your original question.  The answer for 'Why is my crontab not working, and how can I troubleshoot it?' can be seen below.  This addresses the cron system with the crontab highlighted.


Why is $(V^\perp)^\perp=\overline{V}$ when $V$ is a subspace of a Hilbert space $H$? I googled about this but only $V$ as a subspace of finite vector space. Any reference or proof or idea are welcome.

So I'm in an advanced Linear Algebra class and we just moved into Hilbert spaces and such, and I'm struggling with this question.   Let $A$ be a nonempty subset of a Hilbert space $H$. Denote by $\operatorname{span}(A)$ the linear subspace of all finite linear combinations of vectors in $A$, and by $\overline{\operatorname{span}(A)}$ the topological closure of $\operatorname{span}(A)$ with respect to $\|\cdot\|$.  Also, let $A^⊥ = \{h ∈ H : \langle h,f \rangle = 0, ∀f ∈ A\}$ and $A^{⊥⊥} = (A^⊥)^⊥$.  Use orthogonal projection to prove that $A^{⊥⊥} =\overline{\operatorname{span}(A)}$.  The thing that trips me up is that we don't know much about $A$, like if I knew a little more, perhaps to show it's closed, then I can do the direct sum decomposition blah blah, but it also confuses me why we're using the complement of $\operatorname{span}(A)$. Is it possible to show that $\operatorname{span}(A)$ is closed, then go from there? I know it might look a bit like a duplicate, but all the questions I find don't refer to orthogonal projection at all. Any hints would be greatly appreciated!


What is a simple way to prove that the point-wise limit of the sequence $\{kx^k\}_{k\in \Bbb N}$ is $0$.  I have proved it using L'hospitals rule, however I want to know if there is a more basic way of proving the result.

If $-1<x<1$ show that $\lim\limits_{n \to \infty}{n\,x^n} = 0$. I don't have idea. I only prove that $n\,x^n$ is decreasing.


$$\lim_{x\to 0}\frac{\sin(\tan x)-\tan(\sin x)}{\arcsin(\arctan x)-\arctan(\arcsin x)}$$ Hopital's rule and Taylor expansion are practically impossible. Is there a better way to do it (mathematica gives the answer $1$). This limit is of the form $$\lim_{x\to 0}\frac{f(x)-g(x)}{g^{-1}(x)-f^{-1}(x)}$$ but first $f$ and $g$ are not monotone on any neighborhood of $0$ and second how to interpret this limit graphically.

The following problem came up at dinner, I know some ways to solve it but they are quite ugly and as some wise man said: There is no place in the world for ugly mathematics.  These methods are using l'Hôpital, but that becomes quite hideous very quickly or by using series expansions.  So I'm looking for slick solutions to the following problem:     Compute $\displaystyle \lim_{x \to 0} \frac{\sin(\tan x) - \tan(\sin x)}{\arcsin(\arctan x) - \arctan(\arcsin x)}$.   I'm curious what you guys will make of this.


Hi Guys sorry i'm ridiculously new to this but I'm attempting to read in a file and place into an array to work out the averages of the data in there, This is my code but every time i'm getting a NullException on "  String[] row = file.readLine().split(" ");"  int nRows =652;  int nCols =7;  double data [][] = new double[nRows][nCols]; char map [][]  = new char[nRows][nCols];  for (int i=1; i < nRows ; i++) {      String[] row = file.readLine().split(" ");     // below here ......     for (int j=1; j < nCols-1 ; j++) {         data[i][j] = Double.parseDouble(row[j]);          //put if no more data then stop.             } }  file.close();  for (int i =0; i < nRows; i++) {      for (int j=0; j< nCols; j++) {         map[i][j] = '0';       } }  for (int i =1; i < (nRows -1); i++) {      for (int j=1; j < (nCols -1); j++) {         double sum = data [i-1] [j] + data [i] [j-1] + data [i][j+1] + data [i+1][j];        double average = sum /4;        System.out.println(average);     } }  for (int i=0; i <nRows; i++) {     for (int j=0; j <nCols; j++) {        System.out.print(map [i][j] + "");     }    for (int h = 1; h < (nRows -1); h++) {     for (int l =1; (l <nCols -1); l++) {            double sum = data [h-1] [h] + data [i] [h-1] + data [i] [h+1] + data [i+1] [h];           // this is average.          double average = sum /4;          System.out.println(average);      } } }  for (int i=0; i <nRows; i++) {  for (int j=0; j <nCols; j++) {      System.out.print(map [i][j] + " ");  }  System.out.println(); } } }

I have a simple setter method for a property and null is not appropriate for this particular property. I have always been torn in this situation: should I throw an , or a ? From the javadocs, both seem appropriate. Is there some kind of an understood standard?  Or is this just one of those things that you should do whatever you prefer and both are really correct?