I have multiple accounts under different banks for different purposes, which should I present? Does the visa officer want to check if I have enough money in my savings maintained consistently over a period or to see my day to day expenses and transactions showing flight/accommodation bookings? My accounts are: Bank 1 - Payroll Account Where my salary is deposited. I transfer some money every month to another bank account for saving purposes, and into another bank account for everyday transactions. I saved some balance in this account too and rarely shows funds being transferred out because i use this only to save. Bank 2 - Saving account This account only used for savings. I always transfer some of my salary here every payday. It shows funds transferred in and rarely shows funds being transferred out because i only use this to save my money Bank 3 - Everyday transactions I transfer money here from Savings for my daily expenses such as foods, consumtive purposes and any cash withdrawals. I do not keep any balance in this account because i used this purely for consumption. In addition to my bank accounts, i also have stock investments which my portfolio and account statements are being sent to my personal email each month. I feel as I should present every single bank accounts to show the full picture of my expenses and i would also wanted to present my stock investments portfolio. I plan to explain the movement in my cover letter. But i feel like i should mark the movement such as funds transfer between accounts with different colored markers for each movement type (such as salary payments, savings, transfers, etc.) but i am concerned if the visa officers would get confused and reject my application. Would the officers reject it stating they can't determine how money got into it? Would it be better if i transfer all my savings to one of my accounts? Any help and advises would be greatly appreciated

The UK Visas and Immigration Directorate publishes  that provides helpful tips that can result in successful visa applications. Section 2 of this guidance opens is entitled "other documents you may want to provide" (emphasis mine).  Section 2: other documents you may want to provide – all visitors This section provides guidance on the types of documents that you may want to provide to help us consider your application against the Immigration Rules. Previous travel documents/passports, which show previous travel. Financial documents showing that you have sufficient funds available.  These must clearly show that you have access to the funds, such as:  bank statements building society book proof of earnings such as a letter from employer confirming employment details (start date of employment, salary, role, company contact details) where a third party (who is either in the UK or will be legally in the UK at the time of your visit) is providing financial support to you e.g. a business, a friend or a relative, documents to show that they have sufficient resources to support you in addition to themselves and any dependant family should be provided   The first item is "bank statements" and this ties in with the , which says...  evidence that you can support yourself during your trip, eg bank statements or payslips from the last 6 months  (Note 'eg' is a Latin abbreviation meaning "for example"; this appears to be optional rather than a fixed requirement.) Question: How should someone interpret this such that the chances of success are maximized? How many statements should I submit? What are they looking for and what do my bank statements tell about me?


Tried to run a python command today and it opened up the page to install Python from the Windows Store for some reason. Somehow a zero-byte "program" called python.exe got installed here and it has precedence over the actual Python installation in the $PATH?  PS C:\> where.exe python C:\Users\me\AppData\Local\Microsoft\WindowsApps\python.exe C:\Users\me\AppData\Local\Programs\Python\Python36\python.exe   Contents of the folder:  Mode                LastWriteTime         Length Name ----                -------------         ------ ---- d-----        11/3/2019   3:02 AM                Microsoft.DesktopAppInstaller_8wekyb3d8bbwe d-----       10/10/2019   8:06 PM                Microsoft.MicrosoftEdge_8wekyb3d8bbwe d-----       10/24/2019   3:59 AM                Microsoft.WindowsTerminal_8wekyb3d8bbwe d-----       10/25/2019   2:36 PM                Microsoft.XboxGamingOverlay_8wekyb3d8bbwe -a---l       10/25/2019   2:36 PM              0 GameBarElevatedFT_Alias.exe -a---l       10/10/2019   8:06 PM              0 MicrosoftEdge.exe -a---l        11/3/2019   3:02 AM              0 python.exe -a---l        11/3/2019   3:02 AM              0 python3.exe -a---l       10/24/2019   3:59 AM              0 wt.exe   I removed it using command prompt, but I'm very curious how it appeared there overnight.

This is strange issue I have observed. I installed Active Python 2.7 on Windows 10 (version 1903).  On typing “python” from search, opens the Python 2.7 prompt but when I type from command prompt window, it triggers the Microsoft Store.  Don't know how to fix it and this never happened on previous versions of Windows (RS5, RS4…)  Edit 2: Please suggest the solution to turn this off: either via command prompt or using answer file to get this after unattended installation.


I'm trying to write a for loop in bash so that I can iterate numbers from 1 to a number larger than 10. In the cases where the number has only one digit, a zero should be added to its left (as in 01).  The solution I found for that was this:  for i in 0{1..9} {10..43}; do         echo "stuff$i.txt" done   This works, but I wanted to have the upper limit as a variable, so I tried this:  max_test=43  for i in 0{1..9} {10..$max_test}; do         echo "stuff$i.txt" done   When running this, the script prints out  stuff01.txt  stuff02.txt  ...  stuff09.txt  stuff{10..43}.txt  I found , but in my situation I'd need 2 for loops due to that one-digit number condition. What is the best way to do what I want?  Thank you in advance

How do I iterate over a range of numbers in Bash when the range is given by a variable?  I know I can do this (called "sequence expression" in the Bash ):   for i in {1..5}; do echo $i; done   Which gives:     1    2    3    4    5   Yet, how can I replace either of the range endpoints with a variable? This doesn't work:  END=5 for i in {1..$END}; do echo $i; done   Which prints:     {1..5}


When one uses the Extra Attack class feature, must it be done with only one weapon?  If I had, for example, one throwing axe and sword, couldn't I throw the axe and attack with the sword as part of the same "extra attack action"?

The fighter's  feature (PHB, p. 72) says:     Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn.   Assuming I am holding two different weapons, and don't want to spend my bonus action on Two-Weapon Fighting, can I attack once with each weapon?


I'm new to programming, so this could be a complete oversight on my part. But I can confirm (down below) that the two values in the If tag are equivalent, but it is not returning my value.  public static LANGUAGESTRING toLangString(String text) {      for (LANGUAGESTRING lang : LANGUAGESTRING.values()) {         String langStr = lang.toString();         System.out.println(langStr);         System.out.println(text);         if (text == langStr) {             return lang;         }     }     return null; }   Here is what was printed out. This is not my entire LANGUAGESTRING enum, but you can get the point from here. It should return the languagestring, right? Seeing as how the 5th and 6th line are the same? And even if it was returning it, it would break the loop, right?  [14:41:45] GodToBelieverPrayerWhenNoItemNeed [14:41:45] GodToBelieverPrayingWeak [14:41:45] GodToBelieverPrayerTooSoon [14:41:45] GodToBelieverPrayingWeak [14:41:45] GodToBelieverPrayingWeak [14:41:45] GodToBelieverPrayingWeak [14:41:45] EnterHolyLandInfoYourGod [14:41:45] GodToBelieverPrayingWeak

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?


Yesterday, the the DeepWeb.SE proposal went into private beta. I knew this because I got the following notification:     private beta invitation   This proposal has entered private beta. Click here to join.   So I visited the site, created my account there and started participating. However, I had not commited to the site or followed the proposal on area51. As you can see in , the Deep Web proposal doesn't show up in the Current Commitment or the Followed section.  According to all sources on the topic I found around here, the only way to access a private beta is having commited to the site prior to the beta or receiving an invitation from a commited member. I don't know any of the active participants of the Deep Web private beta, and I didn't get an invitation email either, but only the notification. So I doubt someone personally invited me.  So how did I get into that private beta?

Apparently, I missed the email that one of the sites I committed to went to public beta.  Why? Because Email sucks as a workflow tool! [Citation (not) needed]  Valiantly, SE sent me a followup email (Titled "Having trouble accessing XYZSite? - Area 51 - Stack Exchange"). Which I also missed, for a while.  Well, DVK, do you have anything constructive to say, or are you just whining here?  Proposal: when a site you committed to goes to private beta, it should send a notification about it in SE notification tool.   Specific tool could be Inbox, or Achievements list, or even a small banner on top of the site. Small variations could be to add the sites you follow (not just commit) and public beta and not just private beta (or even full live status).   Side note: this should be in addition to email, not instead of it - because some people who commit on Area51 may not be active current SE users.


I need to send out an invite for a group to attend a training programme which will be held soon. I intend to know which is the right choice of word "specially" or "especially".  Is this sentence correct for the above request.  "Please ensure you attend this session as it is organized specially for you".

When should I use specially and when especially?


Prove that [x] + $\frac{[2x]}{2} + ..... \frac{[nx]}{n}$ $ \le $ $[nx]$ $x \in R^+$ Where [.] is the greatest integer function. - USAMO 1981. Usually, we can find the solutions of USAMO problems pretty easily but all solutions of this i found were wrong. My attempt: I went on with induction and reached [kx +k] $\ge$ [kx] + $\frac{[kx+x]}{k+1} $ but turns out this wasn't true. So inequality must be very weak. I am absolutely baffled by this problem, any solution would be really appreciated. Thanks! I AM LOOKING FOR A NON CALCULUS solution

Is true that $\displaystyle\sum_{k=1}^n\dfrac{[kx]}{k}\leq[nx]$, for every $x\in\mathbb{R}$ and for every $n\in\mathbb{Z}^+$?  My work:  Let $x\in\mathbb{R}$ be given. For every $k=1,\dots,n$, define $i_k\in\{0,1,\dots,k-1\}$ such that  $$ [x]+\frac{i_k}{k}\leq x<[x]+\frac{i_k+1}{k}\hspace{20mm} (*). $$  On one hand, we have that $[kx]=k[x]+i_k$ for every $k=1,\dots,n$.  So  $\displaystyle\sum_{k=1}^n\dfrac{[kx]}{k}=n[x]+\displaystyle\sum_{k=1}^n\dfrac{i_k}{k}=[nx]+\displaystyle\sum_{k=1}^n\dfrac{i_k}{k}-i_n$  Thus  $$\displaystyle\sum_{k=1}^n\dfrac{[kx]}{k}\leq[nx]\Leftrightarrow\displaystyle\sum_{k=1}^n\dfrac{i_k}{k}\leq i_n\,.$$  On the other hand, from $(*)$ is direct that $i_k=[k(x-[x])]$. Thus  $$\displaystyle\sum_{k=1}^n\dfrac{[kx]}{k}\leq[nx]\Leftrightarrow\displaystyle\sum_{k=1}^n\dfrac{[k(x-[x])]}{k}\leq [n(x-[x])]\,.$$  In other words, we can assume that $x\in[0,1)$.   Now the questions is:  Is true that $\displaystyle\sum_{k=1}^n\dfrac{[kx]}{k}\leq[nx]$, for every $x\in[0,1)$ and for every $n\in\mathbb{Z}^+$?  Any simpler approach? Any thoughts?


find the sum if the following series converges:  $$1 + \frac{1}{3} - \frac{1}{2} + \frac{1}{5} + \frac{1}{7} - \frac{1}{4} + ...$$  my attempt:  The series can be grouped into difference of a series of odd terms and a series of even terms.. but how to find sum?

This sequence is a rearrangement of the series $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}...$. Note that at this point in the text we do not have any theorem about the convergence of rearrangements.  Let $\{s_n\}$ be the sequence of partials sums of the series then for $n \ge 0$  $s_{3(n+1)} = \sum ^n _ {k=0} \frac{1}{4k+1} + \frac{1}{4k+3} - \frac{2}{4k+4}$  We can view it as the sequence(on $n$) of partials sums of  $\sum_0 a_n = \sum_0 \frac{1}{4n+1} + \frac{1}{4n+3} - \frac{2}{4n+4}$  Where $|a_n| = a_n = \frac{1}{4n+4}\{\frac{3}{4n+1}+\frac{1}{4n+3}\} \le \frac{1}{4n^2}$.  By the comparison test $s_{3(n+1)}$ converges to some real $\alpha$.  But $s_{3(n+1)+1} = s_{3(n+1)}+ \frac{1}{4n+5}$ and $s_{3(n+1)+2} = s_{3(n+1)}+ \frac{1}{4n+5}+\frac{1}{4n+7} $hence we have a partition of $\{s_n\}$ into subsequences which tend to $\alpha$ and this implies $s_n \rightarrow \alpha$.  Is my proof correct? Any alternative solutions are appreciated.


I have an Object. How to get number of nested objects in a?  a = {     firstNested: {         name: 'George'     }     secondNested: {         name: 'James'     } }   I supposed to use .length which is usually used for arrays. What should I do in this case?

I have a JavaScript object. Is there a built-in or accepted best practice way to get the length of this object? const myObject = new Object(); myObject["firstname"] = "Gareth"; myObject["lastname"] = "Simpson"; myObject["age"] = 21;


Why is $x^2 + 1$ not divisible by $11$ where $x$ is an integer.

I came across this problem and I believe Lagrange's theorem is the key to its solution.  The question is:     Let $p$ be an odd prime. Prove that there is some integer $x$ such that $x^2 \equiv −1 \pmod p$ if and only if $p \equiv 1 \pmod 4$.   I appreciate any help.  Thanks.


I tried to install shutter with the following command, but I am receiving an error:  $ sudo apt-get install shutter Shutter:  Depends: gnome-web-photo but it is not installable Depends: libgnome2-perl but it is not installable Depends: libgnome2-vfs-perl but it is not installable Depends: libgnome2-wnck-perl but it is not installable Depends: libgoo-canvas-perl but it is not installable Depends: libgtk2-imageview-perl but it is not installable Depends: libgtk2-trayicon-perl but it is not installable Depends: libgtk2-unique-perl but it is not installable Depends: libnet-dbus-perl but it is not installable Depends: libproc-processtable-perl but it is not installable Depends: libwww-mechanize-perl but it is not installable Depends: libx11-protocol-perl but it is not installable Depends: libxml-simple-perl but it is not installable Depends: perlmagick but it is not installable Depends: libpath-class-perl but it is not installable Depends: libjson-perl but it is not installable Depends: libjson-xs-perl but it is not installable Depends: libnet-dropbox-api-perl but it is not installable Depends: libfile-which-perl but it is not installable Depends: libproc-simple-perl but it is not installable Depends: libsort-naturally-perl but it is not installable E: Unable to correct problems, you have held broken packages.   How can I fix this?

After upgrading from 10.04 to 12.04 I am trying to install different packages.  For instance ia32-libs and skype (4.0).  When trying to install these, I am getting the 'Unable to correct problems, you have held broken packages' error message.   Output of commands:  sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   After running this:  sudo dpkg --configure -a foo@foo:~$ sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.


Foreword: Firstly I would like to state I am not requesting this feature be added. I am not foolish enough to believe that yet another person asking for it will have any impact on its implementation. Instead, I opt to ask people's opinions on the matter, find out what peoples' reasons are for wanting or not wanting such a feature.  Background: I'm a reasonably active StackOverflow user, I ask questions when I get stuck, I answer questions when I get bored. Recently I found a question from a person that obviously didn't quite understand the way SO works, he was asking for some suggestions on how to learn a specific language and better his programming skills. Unfortunately his question got put on hold, and long story short it got me thinking just why there isn't a private messaging system. So I looked here in meta and the continual debate, but I didn't feel any of these questions were actually targeting people's feelings about such a system, they were all asking to implement it or asking why it isn't implemented - not explicitly asking people's opinions on the matter. So, I'm asking now.  Question: What are your opinions on the lack of a private messaging system?  Do you like it because you like the disassociation and believe that SO serves well as a "programmer's wiki", or would you rather a messaging system be implemented despite accusations that it would drag SO down and make it more akin to a forum or social network?  Discuss.

There has been quite a few times that I wished I could send a message to another user on SO - not ask a question for everyone to see, but just a short message informing them of something or requesting them to do something.  Are there any plans to allow this to happen in the future?  Related:


A double factorial is such that $(2n)!!=(2n)(2n-2)...(2),$ and $(2n-1)!!=(2n-1)(2n-3)...3$. So $8!!=(8)(6)(4)(2)$. More information here:  Determine if the following is true:$\frac{1}{\sqrt{1+x}}=1+\sum_{n=1}^{\infty}(-1)^n\frac{(2n-1)!!}{(2n)!!}x^n$, $-1 < x < 1$. The fraction on the left hand side looks familiar, as $\frac{1}{\sqrt{1+x}}=\frac{1}{(1-(-x))^{\frac{1}{2}}}$. If this can be converted to its series representation then it would be nice, but I only know that $\frac{1}{1-x}=\sum x^n$, and I can't just apply a power of $\frac{1}{2}$ to the series. Since $-1 < x < 1$, the series will never diverge to infinity and would always approach 0. So it does not diverge either. There is also the option of using the binomial theorem with $\frac{1}{\sqrt{1+x}}=(1+x)^{-\frac{1}{2}}$ to check. Can someone help me complete this?

I'm working on my physics master course homework and I'm given the following equation out of nowhere:  $\displaystyle{ 1 + \sum_{n\ =\ 1}^{\infty}{z^n\left(\, 2n - 1\,\right)!! \over 2n!!} ={1 \over \,\sqrt{\,\vphantom{\large A}1 - z\,}\,} }$  Now I don't need to prove it for my Homework, but still im wondering, how one would calculate this series. Of course it is not mentioned in the Homework, that this series doesn't converge for all $z$ ( sloppy physicsy style, I know : ) ). Wolfram Alpha said, It only converges for  $\,{\rm abs}\left(\, z\,\right) < 1$, which is a hint to the geometric series, but I have no idea how to account for the double factiorals.  Any hints?


Moderators can choose an example question for the about page of their site. But we can't choose from all the questions, but only from a limited subset. This leads to the following situation on Skeptics, the full list of available questions is:    This isn't much of a choice, only a single question qualifies for the about page and that one is not really a good example for new users. A very good example for a Skeptics questions usually contains at least one link and a blockquote, and is often a bit longer.   I'd propose to change the criteria which restrict the available questions, but then I was unable to find those criteria in the first place and don't know which would have to be changed.  So what are the exact criteria for a question to be eligible for the about page?

Diamond moderators  . In the second section from the top—entitled "Ask questions, get answers, no distractions"—that takes us to an opportunity to select one of a page full of questions from the site as the example question used on the about page. The selections currently available on physics are a little idiosyncratic. Is there some rhyme or reason to these? I suppose that we want a good example question to:  Be accessible to the intended audience (perhaps even to the newest and most naive person in that audience) Be judged at least decent by the community (positive score) Have more than one answer which are also judged acceptable (again positive score)  What else? How does a question end up on the list?


Location: interior showroom (mixed tungsten and day light from show window) How do you balance the light? please explain  I am an engineering student taking a non technical elective course about cinema.   I am struggling with this lighting assignment since i have no background in lighting at all.   the question is exactly like i typed it above, i wish there was more information to help solving this question   the answer does not have to be very detailed  thank you in advance

I have a dSLR and I often find myself taking pictures of people in 'mixed lighting' environments (e.g. tungsten lighting and daylight, fluorescent and tungsten, or even the ‘nightmare lighting scenario’ of mixed fluorescent, tungsten and daylight). Since white balancing won't work (or at least it won't work completely) to remove the color cast from these sorts of mixed environments, what can I do to manage the multiple types of lighting in my environment?    Asked by :  I was at a wedding recently, and the reception hall had these huge windows that let a lot of sunlight through. The overhead lamps used inside the reception hall had a strong yellow tint to them. Given the two different types of light sources, "white" seems to have a vastly different definition in different parts of the photo. I found that a lot of my photos were near impossible to correct the white balance in post production (I shot in RAW).   Here is an example from the set I shot at the wedding:    If I set the white balance relative to something outdoors, everything inside looks too yellow (as seen). If I set the white balance relative to something indoors, everything that falls in the sunlight looks too blue. Neither looks particularly "good".  So, does anyone have tips for how to handle this sort of situation next time I take a shot? I'll also accept answers that offer post-processing advice.  // As an aside, I'm just an photography hobbyist...not a professional wedding photographer ;)


Is it safe to store a crockpot full of freshly cooked pork sausage breakfast patties overnight?  set on Warm. ? Also do you think this will make them "dry" to eat in the morning?  If it's safe, do you know any tips for making them keep their taste/texture ?

I just bought all the ingredients to make a soup in the crock pot. I was planning on having it cook all day, but I just realized the recipe only calls for it to cook on low for 3-4 hours. If I cook it on low for 3-4 hours, and then put it on warm before I leave for work, will it be a bacteria minefield or will it be warm enough to keep the food safe from bacteria?


Can I claim SS if I live abroad?  Specifically in France or Germany.  Does the answer depend on citizenship?  I am both a US and UK citizen at the moment. I currently reside in California.  I am eligible - I am 60 and have been paying the taxes since 1985.  I receive letters from the government every year or two telling me how much my monthly would be if I retire at 62, 65, etc.  I live in the US now and have done all the time I've been paying social security taxes.  In case it's not clear, I am referring in this question to the Social Security program of the US government intended to help older people that was started in F. D. Roosevelt's administration.  The duplicate pointed to by littleadv contains a link that does answer the question although the questions are not exact duplicates as one explicitly refers to non-citizens whereas this question refers to citizens.  Regardless, thanks for marking it as a duplicate as it led to the correct answer.

I paid SS tax for 40 quarters when I was a permanent resident of US. Now I live abroad. Will I be eligible for getting social security benefits?   Most likely the answer is no but why not ask? :-)


A line is drawn through the point $A(1,2)$ to cut the line $2y=3x-5$ in $P$ and the line $x+y=12$ in $Q$. If $AQ=2AP$, find the coordinates of $P$ and $Q$.  From: Mathematics, The Core Course for A-level, Bostock and Chandler. Chapter 4 Q15.  The answer is $(4,3.5)(7,5)$or$(0.4,-1.9)(2.2,9.8)$  I have no idea where to begin with this question.  I've tried letting $P=(x,12-x)$ and $Q=(x,\frac{3}{2}x-\frac{5}{2})$ and then used the distance formula to try and equate $|AQ|=2|AP|$ but didn't get anywhere.  How should I approach this problem?

A line is drawn through the point $A(1,2)$ to cut the line $2y=3x-5$ in $P$ and the line $x+y=12$ in $Q$. If $AQ=2AP$, find the coordinates of $P$ and $Q$.  I found the lengths of the lines $AQ$ and $AP$ in terms of $x$ and $y$ and used $AQ=2AP$ to get this equation $11x^2-40x-16=0$  Working: $AP=\sqrt{(x-1)^2+(\frac{3}{2}x-\frac{9}{2})^2}=\sqrt{\frac{1}{4}(13x^2-62x+85)}$  $AQ=\sqrt{(x-1)^2+(-x+10)^2}=\sqrt{2x^2-22x+101}$  $AQ=2AP\Rightarrow \sqrt{2x^2-22x+101}=2\sqrt{\frac{1}{4}(13x^2-62x+85)}$  $\Rightarrow 2x^2-22x+101=13x^2-62x+85\Rightarrow 11x^2-40x-16=0$  Using the quadratic formula I found $x=4,x=-\frac{4}{11}$  I then substituted these values into the two equations in the question to get the coordinates $(4,\frac{7}{2}),(-\frac{4}{11},-\frac{15}{11})$ or $(4,8),(-\frac{4}{11},\frac{136}{11})$  But the answers in the book are $(4,\frac{7}{2}),(7,5)$ or $(\frac{2}{5},-\frac{19}{10}),(\frac{11}{5},\frac{49}{5})$  I don't know where I went wrong in my method.  Edit: Found some errors in my method and calculation.  Using $x=4$ in $2y=3x-5$ gives $P(4,\frac{7}{2})$  Line with points $AP$ has equation $y-2=\frac{\frac{7}{2}-2}{3}(x-1)\Rightarrow y=\frac{1}{2}x+\frac{3}{2}$  $Q$ lies on the same line. Therefore, the intersection between $y=\frac{1}{2}x+\frac{3}{2}$ and $y+x=12$ is the point $Q$. Working: $\frac{1}{2}x+\frac{3}{2}=-x+12\Rightarrow x=7$ Therefore, $y=-7+12=5$. Point Q has coordinates $(7,5)$.  But $x=-\frac{4}{11}$ is not the other $x$ coordinate of $P$ according to the answers in the book. I have no idea where I went wrong at this point.


Let $d$ be a square free integer. Show that $\mathbb{Z}[\sqrt{d}]$ is an integral domain.   Here $1+0\sqrt{d}$ is identity of $\mathbb{Z}[\sqrt{d}]$. Also commutative property can be shown easily. But I can't show that $\mathbb{Z}[\sqrt{d}]$ has no zero divisor with $d$ is square free. Could you please help?

In self studying abstract algebra and I've come upon the following problem which I could not solve directly. For any $d\in \mathbb{Z}$ we are asked to show that $\mathbb{Z}[\sqrt d]=\{a+b\sqrt{d} ~\colon a,b\in \mathbb{Z} \}$ is an integral domain. This reduces to showing that the ring has no zero divisors which I tried to do through algebraic manipulation.  I have seen two solutions to this problem that use higher level techniques. One defines conjugate and norm and proves the claim using simple consequences of these definitions. The other says that since the given ring is a subring of the field $\mathbb{C}$ it can have no zero divisors.  I don't like either approach because the first uses ideas that haven't been introduced in the text and isn't a natural place to start (for me). The second, while both true and simple, is not satisfying to me. That $\mathbb{C}$ is a field has not been established and assuming it just makes the problem trivial.   My question is whether or not naive tactics like algebraic manipulation are capable of demonstrating the result. Am I lacking in cleverness or is such an approach impossible?


[FindsBy(How = How.XPath, Using = "//input[@id='Username']")] private IWebElement txtUsername;  public void EditTxtUsername(string text) {     txtUsername.Clear();     txtUsername.SendKeys(text); }   Is there a way in C# to chain the two actions into txtUsername.Clear().SendKeys(text);?

When interacting with different elements and applying multiple actions it  may be quite convenient in some situations if we could do:  WebElement myInput = driver.findElement(By.id("my-input-id")); myInput.clear().sendKeys("test");   Instead of:  WebElement myInput = driver.findElement(By.id("my-input-id")); myInput.clear() myInput.sendKeys("test");   But, the problem is , sendKeys() and other "action" methods cannot be chained as is - they return void and not the current WebElement.  What would be the easiest way to achieve chaining multiple actions?


Perhaps I am missing something really obvious, but what I do know is that  for some $p,q\in\mathbb{Z}$ such that  $r=p/q$ with $q\neq0$, we have that $r^2=p^2/q^2$.   Furthermore, the only way $p^2/q^2$ can be an integer is if $q^2 \mid p^2$; thus, there exists $k\in\mathbb{Z}$ such that $p^2/q^2=k$.  If we prove that such $k$ is a perfect square (except when $r=0$, which is a trivial case) then we are finished.   Is there another way to prove this or is it possible to prove that $k$ is in fact a perfect square?

It is well known that $\sqrt{2}$ is irrational, and by modifying the proof (replacing 'even' with 'divisible by $3$'), one can prove that $\sqrt{3}$ is irrational, as well.  On the other hand, clearly $\sqrt{n^2} = n$ for any positive integer $n$.  It seems that any positive integer has a square root that is either an integer or irrational number.        How do we prove that if $a \in  \mathbb N$, then $\sqrt a$ is an integer or an irrational number?      I also notice that I can modify the proof that $\sqrt{2}$ is irrational to prove that $\sqrt[3]{2}, \sqrt[4]{2}, \cdots$ are all irrational.  This suggests we can extend the previous result to other radicals.        Can we extend 1? That is, can we show that for any $a, b \in \mathbb{N}$, $a^{1/b}$ is either an integer or irrational?


At its height, The Almohad Caliphate controlled much of the Iberian Peninsula and Northwest Africa.  or  At its height, The Almohad Caliphate controlled much of the Iberian Peninsula and Northwestern Africa.

My girlfriend, who is not a native English speaker, asked me this yesterday: why are some geographical regions prefixed with the nouns North, South, East and West, but others are prefixed with the adjectives Northern, Southern, Eastern and Western?  For example, it's far more common (to my British ear at least) to hear people talking about "Eastern Europe" and "Southeast Asia" than the alternatives "East Europe" and "Southeastern Asia."  Why is this the case? I couldn't think of a convincing explanation. Is there a hidden logic that I can't fathom, or is it just one of those wierd idiomatic things?


I'm building this javax.json.JsonObject into a method. But when I try to get the values into aditionalParams for some reason I get null. Then, when I try to use a value inside this object I get:  NullPointerException   private JsonObject renderImage(String id, String brand) {         return Json.createObjectBuilder()                 .add("id", id)                 .add("brand", brand)                 .add("type", "image")                 .add("credit", "This is a credit")                 .add("description", "This is a description")                 .add("aditionalParams", Json.createObjectBuilder()                         .add("source", "this is a source")                         .add("photographer", "leon_s_kenndy@gmail.com")                         .add("date", "2021/01/01")                         .add("comments", "These are some comments")                         .add("cost", "500").build())                 .build();     }  The implementation is like this:     JsonObject image = renderImage("363725", "Televisa");    . . .     saveImageCost(image.asJsonObject().getJsonObject("aditionalParams").getString("cost")); //Getting NPE  Any idea guys? Thanks

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


Did Michael ever get revenge on the guys who killed his wife back in Sicily in The Godfather? I have been unable to locate this on any message boards.

Did Michael Corleone ever get revenge against those who killed his wife?   I just watched the 3 Godfather movies again and I was not able to figure out who made the attempt on his life and in the process killing his wife with the car bomb Sicily in the first movie. I know it was one of his body guards that planted the bomb, but I could not get who was actually behind it. I am guessing it was probably the Barzini crime family for the killing of Virgil Sollozzo, but I am just making an assumption there and if in fact it was the Barzini crime family then obviously he did get his revenge. I was hoping someone could back this assumption up, or not.  So did Michael Corleone ever get revenge against those who killed his wife?


If $p,q$ are distinct primes and $a$ is not divisible by $p$ or $q$, then $\gcd(a, pq)=1$.   I want to show this using linear combinations, so that a linear combination of $a$, and $py$ will give $1$. So for some $x,y,x',y'$:  $ax+py = 1 = ax'+qy'$, and  $a(x-x')+py-qy'=1-ax'-qy'$.   Not sure where to go from here. Hints appreciated.

As stated in the title, the problem to prove is  Let $a,b,c \in \mathbb{Z}$. If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$.  I think I've proved it, but I would like a second opinion. Here goes:  PROOF Suppose $\exists d \neq 1 \in \mathbb{Z}$ s.t $\gcd(ab,c)=d$. It follows then that $d|ab$ and $d|c$. Now, if $d|a$ but not $b$, then since $d|c$, by linearity we have $d|\gcd(a,c)$. But $\gcd(a,c)=1$ so then $d=1$. The argument for $d|b$ is similar, resulting in $d=1$. Thus, since both cases lead us to $d=1$, we have a contradiction on our hands $\implies$ $ab$ and $c$ must be relatively prime $\implies \gcd(ab,c)=1$. $Q.E.D$  The question: was this a valid argument or do you think I should provide more?


I did a bit of research, but I don't think this has been asked elsewhere.  I added a comment to , and the formatting broke. The "code" part consisted of multiple backslashes: \  -> \\\, \\.  Interestingly, the formatting doesn't seem to be broken in the questions/answers. There is a comment right below this question to show the issue.  This is another example of why we need preview for comments.

I'm trying to write a single backslash in a comment as code formatted by backtick. Like this:  `\`   but it escapes the backtick and doesn't close the "inline code block".  I've read  but couldn't figure out.  How do I format a single backslash in comment as code?


In terms of evaluating how well a neural network performs in a classification task with the number of classes greater than 2 (for example, classifying an observation into one of the 4 classes), which would be a better measure to use: (i) error-based measures such as the cross entropy loss, or (ii) strict accuracy rate? And what would be the advantage(s) of one measure over the other? The previous posts on this topic only discusses about the case of binary classification. Thank you.

This is a general question that was asked indirectly multiple times in here, but it lacks a single authoritative answer. It would be great to have a detailed answer to this for the reference.  , the proportion of correct classifications among all classifications, is very simple and very "intuitive" measure, yet it may be a . Why does our intuition misguide us here and are there any other problems with this measure?


I have:   string turtle = "turtle" var charArray = turtle.ToCharArray()   When I do:  var distinct = charArray.Distinct().ToArray() // distinct = ["t","u","r","l","e"]   My question is:  How do I save the characters that got deleted from charArray when I called Distinct on it? How do I get the variable distinct to equal "t" (the character that was removed)  Thanks!

If I have the following string:  string s = "abcdefghab";   Then how do I get a string (or char[]) that has just the characters that are repeated in the original string using C# and LINQ. In my example I want to end up with "ab".  Although not necessary, I was trying to do this in a single line of LINQ and had so far come up with:  s.ToCharArray().OrderBy(a => a)...


Others will say we can reduce traffic without damaging the environment. For example, public transportation could be improved, reducing the cars on the roads.  What is the subject of "reducing"? a) public transportation b) public transportation could be improved (i.e. the previous whole clause) I cannot decide which one is right. It seems to me that all of them make sense. If one is a definite answer, I want to know why the other one is not.

Researchers suspect that early exposure to pets carrying bacteria on their fur may encourage the proper functioning of the immune system, helping it to attack only harmful things.  I'm really confused about these.  What is the subject of "helping"? If one thing is right, why are the others not? I cannot refute the ideas myself. a) early exposure to pets carrying bacteria on their fur b) early exposure to pets carrying bacteria on their fur may encourage the proper functioning of the immune system(the whole of the previous clause, if this is the subject we can rephrase the sentence as follows: "~ immune system, and this(or it) helps it to attack only harmful things") c) the proper functioning of the immune system  What does "it" after "helping" indicate? Is it "the immune system"? Am I right?


Let $P$ denote the quotient space obtained by the action of $\mathbb{Z}\backslash2\mathbb{Z}$ by the map $z\mapsto\frac{1}{z}$ on the riemann sphere $\hat{\mathbb{C}}$ (identified here with $\mathbb{C}\cup\left\{\infty\right\}$). I identify $P$ with the set:  $Q=\left\{ z\in\mathbb{C}:\left|z\right|<1\right\} \cup\left\{ e^{it}:0\leq t\leq\pi\right\} $   that is to say, I use elements of $Q$ as the representatives for the equivalence classes in $P$. Note that this is a valid identification, seeing as every element of the orbit space of $z\mapsto\frac{1}{z}$ on $\hat{\mathbb{C}}$ is attested to by exactly one point in $Q$. I need a formula for a function $f:Q\times Q\rightarrow[0,\infty)$ such that $f$ is a metric on $P$. Just to be clear, I do not want an explanation of how to get such a formula; I want the formula.   An analogy for you if I have yet to make myself clear: suppose I was asking for the area of a square with side length $s$. The answers I have received so far for my question are akin to saying "multiply $s$ by itself" or "use the area formula for a square". The answer I am looking for is akin to saying "$s^{2}$". I need the formula. And please, no expressions with differentials, nor matrices, or any of that. I need to know how to compute the metric by using the complex numbers in the indicated set that I have identified with $P$.  As an aside, I found something called the "Fubini-Study metric" on wikipedia. I feel as if this might be close to what I need, but unfortunately, the use of notations and conventions of differential geometry and multilinear algebra makes the wikipedia article virtually unintelligible to me. If someone could give me a formula for how to compute this metric using the complex numbers in the set $Q$, it would be much appreciated—assuming that this Fubini-Study metric is even close to what I am actually asking for.   This is not for homework or anything. I am doing research (in analytic number theory), and I need to know a formula for such a metric so that I can go ahead and show whether or not a certain map is a contraction. I have been making stellar progress with my research, and so it is extremely frustrating to have my work ground to a halt for want of a simple formula.   For your answers, assume that I know nothing of differential geometry, riemannian geometry, tensors, riemannian metrics, pullbacks, metric tensors, projective geometry, multilinear algebra, differential forms, tangent spaces, tangent bundles, covering maps, stereographic projections (and so on). This is (obviously) not true, but I say so because I want to be absolutely certain that a prospective responder to my question understands the kind of answer I am looking for. Dumb it down.  If there is no such formula, then try to explain what I need to do as methodically and algorithmically as possible, and please, do not leave out any steps.   Please... help.

Let $P$ denote the quotient space obtained by the action of $\mathbb{Z}\backslash2\mathbb{Z}$ by the antipodal map $z\mapsto\frac{1}{z}$ on the riemann sphere $\hat{\mathbb{C}}$ (identified here with $\mathbb{C}\cup\left\{\infty\right\}$). I identify $P$ with the set:  $\left\{ z\in\mathbb{C}:\left|z\right|<1\right\} \cup\left\{ e^{it}:0\leq t\leq\pi\right\} $   that is to say, I use elements of the above set as the representatives for the equivalence classes in $P$. I am looking for formula for a function $f:P\times P\rightarrow[0,\infty)$ such that $f$ is a metric on $P$. Specifically, I would like a formula for $f$ that I can evaluate by plugging in representative elements in the above set (or something like that, more or less).  Thanks in advance.  Edit: forgive me for sounding desperate, but I cannot make due with an explanation of how to obtain such a formula. I want the formula.   An analogy for you if I have yet to make myself clear: suppose I was asking for the area of a square with side length $s$. The answers I have received so far for my question are akin to saying "multiply $s$ by itself" or "use the area formula for a square". The answer I am looking for is akin to saying "$s^{2}$". I need the formula. And please, no expressions with differentials, nor matrices, or any of that. I need to know how to compute the metric by using the complex numbers in the indicated set that I have identified with $P$.


I would like to know I can remove yammer appearing in SP search.

I have a heavily branded site I'm working on and can't find where the "Search on Yammer" link is being populated from. It appears within the search refiner/filter web part in the left column but none of the display templates reference this.   I'd like to be able to customize the link, placement on the page, etc. without resorting to jQuery to move elements around the page.     And the markup coming through looks like this. The refiners themselves come through a series of display templates but the Yammer link is nowhere that I can see in any of them.

                     Search on Yammer

             ... refiners populated through display templates ...


I am presently writing a shell function and it would help me in writing it to be able to remove a . from the start of a folder name (changing the folder name from that of a hidden folder to that of a non-hidden folder). The folder name is stored in the variable $CWD, which itself is evaluated using:  CWD=${PWD##*/}   I would like to call the variable that equals $CWD without the . at its start $GWD. Presently I am trying to do this using sed, but I am open to any solution to this problem. This is what I have been trying:  GWD=$(sed -i 's/.*//' $CWD)   I have also tried substituting ' in this expression with " and I have tried substituting -i with -e. But this keeps returning the error:  sed: can't read .atom: No such file or directory   where CWD='.atom' for me at the moment.

I'm quite confused about the following regular expressions I found in a shell script:  ${0##*/} ${0%/*}   How do they work?


I have been taught that we can use either of "to INF" or "Verb-ing" at the beginning of the sentence as a subject, which leads me to a point of confusion.    Here is my confusion:     A: To smoke is not good for all.   B: Smoking is not good for all.   These two sentences both mean the same thing to me.  Could you guys explain the difference and then can we use that explanation to demonstrate  other such sentences with?

As a native speaker of English, the gerund version of this sentence sounds better:  infinitive:     When used together in chains,   extension methods are an unprecedented   tool to produce extremely concise   code.   gerund:     When used together in chains,   extension methods are an unprecedented   tool for producing extremely concise   code.   But how can I explain to someone learning English how to decide in situations like these whether to use the infinitive or the gerund?


I'm going to Brazil from Canada, but I have a layover in Chicago. When I do my check-in, do I use my Brazilian passport or my Canadian? Can I show the Canadian passport when going to Chicago and show the Brazilian passport when going to Brazil, since in Chicago I will have to check in my luggage again? I'm confused and I called the place bought my tickets from and they said I can't use 2 passports. Has anyone done it?

I am a citizen of two different countries, and have two passports.  How should I use my passports when traveling?


Assume that you fixed a speaker to an inclined pipe as well the torch. You can hear sound from the other end of the pipe, but can't see the light from other end of the pipe, why?

If I'm sitting in the den with my door slightly cracked, I can hear my wife washing dishes in the kitchen down the hall. But why can't I also 'see' images of her washing dishes if, say, I looked up on my wall?   Broken down:   Sound waves bounce off things.   Light waves bounce off things.  You can hear sound of someone washing dishes in the next room.  Why don't you can't see the light (visuals) from them?


I encountered a problem:  More than one teacher is/are going to bring the students to a trip.  Can you help me with this? Any help would be appreciated.

While adding to an Answer to  question, I needed to use the above phrase, and I suddenly realised I was unsure whether to write "is" or "are".   There is more than one way to skin a cat. If there are more than one species of cat, we will flay each species differently.   I don't think that second example above sounds quite right to me (disregarding the meaning - sorry!), but in my original Answer I felt "is" would have been even worse.  Is "are" always wrong here? If so, what exactly is the rationale? If not, is there a case where it's unquestionably preferred – and why is that?    Note that in both the problematic Answer and my example attempting to mimic the same context more briefly, the writer doesn't know how many there are. There may be one, more, or even none.  Getting even more specific, the writer might have an opinion on how many there might be, and wish to convey his leanings by choice of verb form if language allows this to be done succinctly.


I'm working on airsoft website using woocommerce. One of my client's needs is to prevent a user to register if his name or mail is in a blacklist (I don't know yet if I'll use a csv file, a json or a simple array).  So I have to execute some validations before insert the user to the database. But I didn't succeed in finding the good hook.

I want to limit registration based on the domain associated with their email address. I was looking at the user_register action hook, but it fires after the user is already inserted, which, although it could be hacked into working, is less than ideal. I want to preempt rather than retroactively remove invalid users.  I've looked through the source in wp-includes/user.php, but nothing in there looks to be helpful. I did notice the pre_user_email filter, but that doesn't seem to offer any options for doing anything useful since I can't see a way to do anything with that.


I have a clean 18.04 install (not update from previous version), the icons in desktop and Show Applications are huge, how can I reduce it. I've tried to go to Nautilus, but I couldn't reduce it to below 50%, I found a solution, but it's for 16.04 (), is it the same for 18.04? Will this solution reduce only icons in Show Applications? TIA.

I just upgraded to 18.04 (with GNOME 3.28) from 16.04. I am using gnome-shell, gnome-ubuntu-desktop. After upgrading the icon size on desktop are very large.  I am unable to find my option to decrease the size in preferences. How do I decrease it?


sorry for the language. I just can't understand why it wont enter the first while loop and goes straight to the end. The while starts with a boolean but it just wont proceed.  I could use some help :) Thanks in advance. Now its at its (half) full. It doesn't have anything to do with equaling strings. Thanks again.  package guessTheNumber;  import java.util.Random; import java.util.Scanner;  public class Main {      public static void main(String[] args) {          //Opening of the scanner.         Scanner guess = new Scanner (System.in);          //Entry - what the player will see before he starts.         System.out.println("Hello.");         System.out.println("Wellcome to the Guess the number game");         String enter = guess.nextLine();         System.out.println("I choose a nember and you have to guess what it is.");         enter = guess.nextLine();         System.out.println("Ready?");         System.out.println("I don't care... Type NEW to start");          String startGame = guess.nextLine();          while (startGame == "NEW" || startGame == "New" || startGame == "new"){              //generates new number             Random newNumber = new Random();             int newRandom = newNumber.nextInt();             //here the player can guess the number             System.out.println("I chose a number between 1-bitch. what number am I thinking of? ");           //if the player chooses to end the game         System.out.println("See you later mother ******.");      }  }

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?


When determining the centripetal force on an object on a banked curve, it is stated that the banking angle for a given speed and radius is found by :  tanθ = v^2/rg   It is found as follows:  The normal force on the object is resolved into components. The x-component (the one providing the centripetal force) is:   N*sinθ = mv^2/r   Then, the y component is set equal to mg:  N*cosθ = mg =>N = mg/cosθ  Dividing Nsinθ by Ncosθ, we get  :   tanθ = v^2/rg  I'm fine with that.   Here is where I'm confused. When resolving the forces of an object resting on an inclined plane: The component down and parallel to the plane due to gravity is:   mg*sinθ.  The component representing the force of gravity into (perpendicular) to the plane is:  mg*cosθ.   The normal force is equal to this component into the plane by Newton's 3rd Law, so,  N =mg*cosθ.    Why in the first scenario (banked curve) is   N=mg/cosθ,   HOWEVER, in the second (inclined plane)   N=mg*cosθ ?  How can this be? There are two different values for N?  Is the normal force in the first scenario (banked curve) greater than mgcosθ because:   a) the normal force also is responsible for the centripetal acceleration, so it needs to be greater?   Or,   b) the car is not sliding down the curve, so the normal force is greater because of the translational equilibrium requirement? The textbook that I have (Resnick, Fundamentals of Physics) seems to suggest (b), since they use the equation for equilibrium in the Y direction. But if that is the case, then what is PHYSICALLY CREATING this "extra" normal force as compared to the second scenario (inclined plane)?

Normally, if an object of mass $m$ is inclined to the horizontal at an angle $b$, we set the reaction force of the object on the inclined plane as $R = mg\cos{b}$ (if we resolve the force of gravity so the line of action coming out of the plane is perpendicular to it).  However in circular motion*. it's assumed that $R\cos{b} = mg$. In the example above, one would have to do this in order to arrive to the correct answer, instead of $R = mg\cos{b}$. Using $R = mg\cos{b}$ seems natural enough, as I am resolving vertically, however, both equations would produce two different values for $R$. Why is this?   To show what I mean: If we set the reaction force in this question as $mg\cos{a}$, then the centripetal force will be $mg\cos{b}\cos(\pi/2-b) = mg\cos{b}\sin{b} = \frac{1}{2}mg\sin(2b)$   Whereas If we use $R\cos{b} = mg$, $R = mg\sec{b}$ and the centripetal force will be $mg\sec{b}\sin{b} = mg\tan{b}$. This will end up with two different values for the radius of the circular motion, and hence two different final answers.  *In the circular motion questions I've seen in my mechanics module


os version:  ➜  showlink sw_vers ProductName:    Mac OS X ProductVersion: 10.13.1 BuildVersion:   17B35a   before exec the script:   ➜ showlink tree --inodes . . └── [9628588]  test     ├── [9628740]  link.js     └── [9628707]  src  2 directories, 1 file   nodejs script :  const fs = require('fs') const path = require('path') const src = path.resolve(__dirname, './src') //i try to the dist at the same dir with src, but failed  const dist = path.join(__dirname, '../dist') fs.link(src, dist, (err) => console.log(err))   after:  ➜  showlink tree --inodes  . . ├── [9628707]  dist └── [9628588]  test     ├── [9628740]  link.js     └── [9628707]  src  3 directories, 1 file   add some file  ➜  showlink touch test/src/demo{1..3}   now:  ➜  showlink tree --inodes  . . ├── [9628707]  dist │   ├── [9629200]  demo1 │   ├── [9629201]  demo2 │   └── [9629202]  demo3 └── [9628588]  test     ├── [9628740]  link.js     └── [9628707]  src         ├── [9629200]  demo1         ├── [9629201]  demo2         └── [9629202]  demo3  3 directories, 7 files   when i search google 'hard-link' ,all answer show me that: the dir can't make a hard link . but ... node.js create the dir's hard-link (the number in Brackets is i-node number). what happened? Thanks

How do you create a hardlink (as opposed to a symlink or a Mac OS alias) in OS X that points to a directory? I already know the command "ln target destination" but that only works when the target is a file. I know that Mac OS, unlike other Unix environments, does allow hardlinking to folders (this is used for Time Machine, for example) but I don't know how to do it myself.


$$\frac{\cos 10^\circ \cos 50^\circ\cos 70^\circ}{\cos 30^\circ} = ?$$ I use double sine formula $$\sin2A=2\sin A \cos A$$ But isn't help to reduce any fraction but more degree of $\sin 40^\circ$  How should I do after that?

I should prove this trigonometric identity. I think I should get to this point : $\cos(3x) = 4\cos^3 x - 3\cos x $ But I don't have any idea how to do it (I tried solving $\cos(x+60^{\circ})\cos(x-60^{\circ})$ but I got nothing)


Find the ring of algebraic integers in $K=\mathbb Q(\sqrt[3]{2})$.   So, I know that $K=\{a+b\sqrt[3]{2}+c\sqrt[3]{2}^2 \mid a,b,c \in \mathbb Q\}$.   My professor has done very little on this topic. I know that an algebraic integer is the root of a monic polynomial with integer coefficients.   I have no clue on where to start with this question. Any help is much appreciated!

This seems to be one of those tricky examples. I only know one proof which is quite complicated and follows by localizing $\mathbb{Z}[\sqrt[3]{2}]$ at different primes and then showing it's a DVR. Does anyone know any simple quick proof?


I have many special dragons and I can't figure out how to level them past ten.

I have been able to level up half my elemental dragons past level 10. I don't know how to level my epic dragons past level 10, though.


Ran in to this deployment issue error "Cannot deploy InstalledPackage in Package Manifest with any other types!" the only solutions i can find is to roll back from v28 to v27... but i cant find a copy for mac or pc any suggestions on rolling back?    Thanks

I'm a bit of a force.com IDE newbie - still learning. I'm trying to migrate a simple custom object (no fields) from one sandbox to another and I'm running into this error:  # Deploy Results:    File Name:    package.xml    Full Name:  package.xml    Action:  NO ACTION    Result:  FAILED    Problem: Cannot deploy InstalledPackage in Package Manifest with any other types!   Any help would be greatly appreciated.  Thanks!


These are the mutations I've already heard of:   Aspear + Leppa = Hondew Chesto + Persim = Kelpsy Iapapa + Mago = Pomeg Oran + Pecha = Qualot Sitrus + Lum = Tamato Hondew + Yache = Petaya Kelpsy + Wacan = Apicot   I wanted to know if there were any others that I don't already have. Help?    Plus... I've gotten these by accident. Do I put one plant on Surprise Mulch and the other on another type or do they both need to be on the Surprise Mulch?

So I planted some berries at that farm just before the bridge with Snorlax on it, in the hope of expanding my supply. I watered them, came back the next day and each tree had sprouted nicely. However, some of them had an oddly-coloured berry, which (upon picking) I found out was a berry of an entirely different type altogether.  Some scientist then came up to me, and told me she was 'researching berry mutations' and that I should tell her what mutations I find.  My mutation was a Qualot Berry, which (according to the scientist) was made from Oran and Pecha Berries. But how did this happen?  Is it something to do with the way the bushes are planted next to each other, or in a line? Or Is it completely random?  Further to this, What other Berry Mutations can I find?


I’m a native English speaker, so I understand that     It’s.   is not a complete sentence, whereas the sentence     It is.   is a complete sentence.  What linguistic mechanism prevents “It’s.” from being a complete sentence in English?

I heard this lyric in a song the other day and it just sounded so wrong that I assumed it must be incorrect grammar, but I can't find any specific prohibition that applies.     That's what it's.    That rolls off your tongue with the grace of a moose in a tutu, but I can't figure out why.  There is clearly no problem with ending other sentences with a contraction. These sound fine.     I thought I could, but I can't.   Stop touching that, it will fall off if you don't.   You say that the sky is green, but it isn't.   Also, it sounds just fine if you remove the contraction:     That's what it is.   So what's up with this construction? Should it be avoided?


Please am studying about switching power supplies, starting from the simple ones. I've just concluded on joule thief and blocking oscillator, now am progressing to Self oscillating flyback converter(or RCC) and am finding a bit difficulty on how the transistor switches OFF. It seems the transistor switch off concept is quite complex than the switch ON process. Some say the operating principle is very much the same to that of blocking oscillator, but i think the are some contrast.  Here I only understand that a small current flows through the startup resistor to the base of the transistor, to initiate the turn on process. As the transistor is partially ON(active region), collector current will flow and energize the primary winding, as a result, a same polarity voltage will be induce in the feedback winding which will create a positive regenerative feedback and conduct more current to the base of the transistor, and the transistor turn on fully(saturation). That's all I know. I don't know how the transistor will switch OFF. I might make some assumptions based on my knowledge of the joule thief circuit, but am not sure. I don't also know how RC circuit can affect the switching frequency.

I am trying to derive the equation of small signal vout/d for a CCM flyback converter. In order to do this, I need the small-signal average model. I am having difficulty seeing how the small signal model for the flyback (or buck-boost) is derived from the flyback converter:    I recognize that the Vout/Vin for the flyback and buck-boost include a D in the numerator like a buck converter, and a 1-D in the denominator like that boost converter, and that is why the small signal model has a buck type stage (1:D) and a boost type stage ((1-D):1). I just wish to be able to be able to derive the small signal model directly from the normal circuit schematic.


I need to know if an application is requesting one beacon via an image or  request.  Manually I test it via the network tab in  or monitoring the proxied requests in other browsers...  Searching I see several references to  captureNetworkTraffic but none of my Selenium instances have this command.  I'm using the Firefox IDE 1.9.1 and Stand Alone server 2.25.0.  What should I be using to have that captureNetworkTraffic command available? Also, where is it officially documented?

If yes, how is it called, or where can I find more info about it? (I'm not talking about using WebDriverBackend.)  If not, what alternatives are there?


I'm upgrading switches in my older (1978) home, putting smart switches in. I have found many "interesting" wiring situations, some I have remedied, some I have just left as-is.  Recently I opened a junction box with a single pole switch, controlling accent lighting above my kitchen cabinets. I was surprised to see a single 12-2 cable feeding the box. The black wire is hot, and the white wire is the load, with the bare ground protecting the switch.   What should be done here? Luckily, I'm able to add a smart dimmer because my brand (Lutron Caseta) doesn't need a neutral.  Is this wiring safe? I believe so. Up to code in Massachusetts? There's got to be a white wire connected to a black or red, somewhere else in the house (I haven't found out where yet) to make this work.  What needs to be done, here? Do I need to label the white wire?

Long time reader, first time poster. Working on updates for our new house and I bought a few lutron caseta switches the other day to wire up in our front entryway. I went with the PD-6ans which requires a neutral wire. I pulled the plate off and looked around and saw a neutral bunch so I thought I was good to go.   Well, like any project I get myself into, things didn't go as planned. The two switches on the left come from one circuit with the neutral bundle, the switch on the right is on a different circuit and there's no neutral.  Can I use the neutral bundle from the other circuit in the box or is that a big no-no? If not, is there any other way to get around it?  I'm thinking I may just need to buy a different switch that doesn't require a neutral (Lutron Caseta PD-5WS).  Here are a few pictures of the three gang box. It's a three way switch on the far right and left, single pole in the middle. For what it's worth, at the other location (in the garage) for the three way on the right there does appear to be a neutral bundle.   Also, there's a ground wire that doesn't go anywhere from that far right switch. Should I pigtail it into the ground wire bundle in the box that is in the other circuit?   Thanks for any help you can provide!


i have created a module to hook Drupal cron system and the function in my module is being executed on every cron run, which is perfect.  I need this hooked cron function to run only once weekly without scheduling the default Drupal cron job . Any help on this ? Thanks

What's the proper way to execute a function every 3 months? Watchdog variables don't seem to be available after a certain time. I could create another table to insert the execute function date to compare, but it doesn't seem to be the best approach.  The functionality of such functions are:   Send an eMail Tag an inactive user


This was what I wanted to say in my previews questions. I need a real life example that can be solved only with linear transformation. I will be verry grateful if you can give me a problem and it' s solution. Bun I really need a "real life application". I cound't find what I wanted anywhere and I hope that maybe this time I was more specific.

Can anyone help me with a practical application of linear transformations? I am very curious about how can be an application in real life that can be solved with a linear transformation.


Named ranges are duplicated when their sheet is duplicated. However, protected ranges are not.  I have 40 protected ranges on a sheet that I need to replicate six times, so I'm not really looking forward to defining 240 ranges.  Is there a way to keep the protected ranges when you replicate a sheet, or otherwise import them to the replicated sheet?

I have created my spreadsheet with protected cells scattered throughout the document in Google Sheets.  Now I want to duplicate the spreadsheet and have the protected cells in the new worksheet keep the same protection. The new spreadsheet would be in the same workbook (tabs). I have tried copy and paste into the new worksheet and everything copies but the protection.  How would I accomplish this task?


Is there a general rule as to how much clearance you should add to through-hole components' holes to allow them to fit easily?  For example, if I have a component with 1mm pin diameter, what should the diameter of the holes for it's pads be?   Using my calipers on a PCB I have handy, it looks like about 0.1mm is added to some holes, but I don't know if that's "normal" or not.

I am making some new through-hole parts in Eagle for components that are not already in the various libraries. I've realized that the drill size needs to be a little larger than the lead diameter, but I'm not sure by how much.  With  , I found the following information:   "It depends" based on whether the component is being hand or machine soldered add 6 mil to the lead diameter 7 to 15 mil (diametric gap) for 63/37 solder 5 to 10 mil (diametric gap) for lead-free/RoHS solder   Is there a rule of thumb or guide to support this information? Someone referred to the  Industry Standard for Printed Board Design (IPC-2221), but the IPC apparently only provides the table of contents of the document unless you .  I'm planning on soldering the components by hand using 63/37 solder.


$\mathbf{Question:}$ Prove that there exists a constant $c>0$ such that for all $x \in [1, \infty)$, $\displaystyle\sum_{n \geq x}\frac{1}{n^2} \leq \frac{c}{x}$  $\mathbf{Attempt:}$ Evidently,   $\displaystyle\bigg[\displaystyle\sum_{n =1}^\infty\frac{1}{n^2}-\sum_{j=1}^{\lfloor x \rfloor} \frac{1}{j^2}\bigg]{\lfloor x \rfloor}\leq x\displaystyle\sum_{n \geq x}\frac{1}{n^2} \leq \displaystyle\bigg[\sum_{n =1}^\infty\frac{1}{n^2}-\sum_{j=1}^{\lfloor x \rfloor} \frac{1}{j^2}\bigg]{\lceil x \rceil} $.   This inequality arises since,   $\displaystyle\bigg[\sum_{n =1}^\infty\frac{1}{n^2}-\sum_{j=1}^{\lfloor x \rfloor} \frac{1}{j^2}\bigg]=\displaystyle\sum_{n \geq x}\frac{1}{n^2}$.  Now, let $\lfloor x\rfloor=m$  $\displaystyle\lim_{m \to \infty}\bigg[\sum_{n =1}^\infty\frac{1}{n^2}-\sum_{j=1}^m \frac{1}{j^2}\bigg]m$  $=\lim_{{m \to \infty},{r\to \infty}}\bigg[\frac{m}{(m+1)^2}+\frac{m}{(m+2)^2}+\frac{m}{(m+3)^2}+...+\frac{m}{(m+r)^2}+...\bigg]=$  $\lim_{{h \to 0},{r\to \infty}}h\bigg[\frac{1}{(1+h)^2}+\frac{1}{(1+2h)^2}+\frac{1}{(1+3h)^2}+...+\frac{1}{(1+rh)^2}+...\bigg]=\displaystyle\int_{x=0}^\infty\frac{1}{(1+x)^2}dx=1$  We have, $\lceil x\rceil=m+1$ and $\displaystyle\lim_{m \to \infty}\bigg[\sum_{n =1}^\infty\frac{1}{n^2}-\sum_{j=1}^m \frac{1}{j^2}\bigg](m+1)=\lim_{m \to \infty}\bigg[\sum_{n =1}^\infty\frac{1}{n^2}-\sum_{j=1}^m \frac{1}{j^2}\bigg]m$  Thereby, we conclude, $\displaystyle \lim_{x\to \infty}x\sum_{n \geq x}\frac{1}{n^2}=1 $.  Therefore, from the definition of limit, $\forall \varepsilon>0$, $\exists G>0$ such that $\bigg|x\displaystyle\sum_{n \geq x}\frac{1}{n^2}-1\bigg|<\varepsilon$ $\forall x>G$. Choosing $\varepsilon =1$, we get $G=G_0$ such that $x\displaystyle\sum_{n \geq x}\frac{1}{n^2}<2$, for any $x> G_0$.   We set $\displaystyle c=\max\bigg\{2, \sup_{x\in [1,G_0]}x\sum_{n \geq x}\frac{1}{n^2} \bigg\}$  Is this procedure valid? Kindly verify.

Prove that there exists a constant $c>0$ such that for all $x \in [1,\infty)$, $$\sum_{n>x} \frac{1}{n^{2}} \leq \frac{c}{x}$$


I have a website on a test directory folder:  www.example.com/tst/   I want to move the whole website a directory up to become live (/root folder).   Is there a fast way to do it rather than wait for filezilla to copy every single file which might take hours??

I want to copy files from one directory to another on the same server using FileZilla. Please guide me how can it be done?


I've had it for a while but haven't used it much because it is not sharp. Suggestions? Can it be sent off and is that expensive?

I use a Canon EOS Rebel T3i (600D) with the kit lens. I have experimented a lot with different settings and modes, but I feel like I have wasted many good shots that could have looked amazing, if only they were a little bit sharper.  I use auto-focus on most of my pictures and make sure to choose the right focus point, but all of my photos are still a little bit out of focus. When I zoom in, I can see that the pixels are not very crisp or well-aligned.  I am not sure if this issue is caused by my equipment or skills.


Nowadays, many papers are based on data that can easily reach several Gigas. It is understandable that these data are not incorporated into the work, nor are hosted with the publisher. What is the more acceptable way of asking them to access this data? Call + email? Email to the publishers? Making a Freedom of information request to the university?

I am working on a mathematical model to help explain some experimental results and generate new hypotheses. Unfortunately, I have neither the resources nor interest to gather experimental data, but in this particular sub-field publishing a model without showing its usefulness on some experimental data is not common.  There are several existing experimental findings that can be explained by my model. However, they are presented in other modeling papers and the raw data is not available with the paper or on the authors' websites. In the papers they only present partially-analyzed data (for instance, they show results averages over participants, but not individual participant's results; or sometimes they only give the results of statistical tests).   I want to contact the authors for their raw data and have 3 related questions:   What is the protocol for contacting by email to ask for authors' raw data? Is this common?  Will the researchers expect to be invited on-board as co-authors? Or is a citation to their papers, and an acknowledgement of the form "AK would like to thank X, Y, Z for providing their raw data" sufficient? If my model (without fits to specific data) is in a pre-print state then should I send a pre-print to the authors I contact? What if the pre-print points out weaknesses in their approach to modeling similar problems?


I am looking for a help with solving this chemical-engineering problem. Is there anybody, who can help?   The task is about this: Concentration profiles $cA,dA$ during extraction of A-component from solvent C into solvent B in countercurrent colony with axial mixing of continual phase of solvent B are described with following diff equations which I have to solve: \begin{align} dA'' &= -(uB/E)\, dA'-kL \,(cA-dA/psi)\\ cA' &= -(kL/uC)\, (cA-dA/psi), \end{align}  where $cA,dA$ represent concentrations of A-component in original and new solvent, $kL$,$uB$,$uC$,$E$ are constants, "psi" is partition coefficient. Then we have following initial and boundary conditions - z=0 m is inlet of feedstock, z=2 m is inlet of extraction agent.   $cA(0) = 100$  $uB* \,dA(2)+E\,* dA'(2) = 0$  $dA'(0) = 0$    Firstly, I have to solve it for $psi = 100$ (at this moment system of diff equations is linear) and find value for $cA(2)$ in raffinate then. Then I have to calculate using shooting method and then use proper Runge-Kutta approximation (using $psi = 10*sqrt(dA)$, for non-physical option $dA$ $=<0$ I have to use $dA/psi = 0$).   Firstly I want understand the problem in general - the final numbers are not important. I want to try it using your advices (or some similar problems which I can use in my solution) and how to use the substition for the diff equation with rate 2, then how to calculate three diff equations with rate 1 with these written conditions for both cases - linear and nonlinear.  Thank you, J.

I need a little help with solving of this system, please.  \begin{align} y'' &= -(a/b)\, y'-c \,(z-y/e)\\ z' &= -(c/f)\, (z-y/e), \end{align}  where $a,b,c,f$ are known constants   $z(0) = 100$ I.C. $a \,y(5)-b\, y'(5) = 0$ B.C. $y'(0) = 0$ I.C.   Firstly, I have to solve it for $e = 100$ as a system of linear diff equations and find value for $z(2)$. Then I have to calculate using shooting method and then use proper Runge-Kutta approximation (using $e = 10*sqrt(y)$, y $=<$ use $y/e = 0$).   Is there anybody who can push me a bit? Or give me a link for similar problem? Thanks.


i have one variable  e.g.   var1="<envpath>/home/genl/jeenk[path]/OT/</envname>"   and having <envpath>/home/genl/jeenk[path]/OT/</envname> entry in file.txt  but if i try to change this by using sed command its not changed.  e.g.  sed -i "s|$var1|/home/genk/g" file.txt   what could be the solution to this, to escape [ & ] in var?

I have a script that reads a text stream and generates a file of sed commands that is later run with sed -f. The generated sed commands are like:  s/cid:image002\.gif@01CC3D46\.926E77E0/https:\/\/mysite.com\/files\/1922/g s/cid:image003\.gif@01CC3D46\.926E77E0/https:\/\/mysite.com\/files\/1923/g s/cid:image004\.jpg@01CC3D46\.926E77E0/https:\/\/mysite.com\/files\/1924/g   Assume the script which generates the sed commands is something like:  while read cid fileid do     cidpat="$(echo $cid | sed -e s/\\./\\\\./g)"     echo 's/'"$cidpat"'/https:\/\/mysite.com\/files\/'"$fileid"'/g' >> sedscr done   How can I improve the script to ensure all regex metacharacters in the cid string are escaped and interpolated properly?


<asp:RadioButtonList ID="rdStatus" onclick="javacript:display();" runat="server" RepeatDirection="Vertical"> <asp:ListItem Text="Temporary Waiver" Value="T" Selected="True"></asp:ListItem>     <asp:ListItem Text="Never Expires" Value="P"></asp:ListItem>     <asp:ListItem Text="Expires after the close of:" Value="W"></asp:ListItem> </asp:RadioButtonList>  function display() {     if(radiobuton is enabled)           //code here      else           //code here }   Please suggest some idea to detect hoe to check radiobutton is disable o enable

I have two radio buttons and want to post the value of the selected one. How can I get the value with jQuery?  I can get all of them like this:  $("form :radio")   How do I know which one is selected?


I've just switched a site from http only to https only (on the same domain name), and have 301 redirects from old to new in place on a page by page basis. How do I now inform Google, using Webmaster Tools or otherwise, of this change of address so as to maintain rank?

Here at Stack Exchange we're working on moving all traffic to SSL. The reason we're not doing logged-in-users only is that one side of the login divide would suffer a redirect from Google every time.  This happens because Google's only going to have http:// or https:// in the results, not both.  Aside from building the SSL infrastructure (), the outstanding question we have is: how do we best transition to SSL?  Here are the relevant bits of our plan (testing on small sites, moving up to stackoverflow.com):   Get SSL ready/enabled (but not linked to) on all domains Start rendering only the <link rel="canonical"> as https:// Start sending a 301 for all http:// requests to https:// (from our domains...of course we can't do anything about all the existing links pointing to us) After a transition period, set all user cookies as secure   So the endgame is having all content delivered over SSL and all HTTP requests redirected.  What we're primarily concerned with is how this will affect PageRank to our sites. We depend a great deal on traffic that comes from Google and want to ensure that doesn't take a dive as we start delivering more security to our users.  The only bits I've found on this that seem to be substantive are  on :     @Frank Yes, I'm certain that Google treats HTTP and HTTPS URLs as separate URLs for crawling, indexing and ranking (I work with the web-search team here at Google). Doing canonicalization with a 301 redirect like you mentioned is a great way to solve this :) –  Oct 23 '10   and the only webmasters video I could find:  The video doesn't have a solid answer, not one I'd base the future of a company on anyway.  Is our transition plan the best way to accomplish an SSL move, at least from an SEO perspective?  If there's other more recent or concrete advice around how a move like this affects Google ranking we'd love to hear about it.


is (F=mg) equal to (F=GmM/r^2)? And what's the difference between them?

Newton's Law of Universal Gravitation tells us that the potential energy of object in a gravitational field is $$U ~=~ -\frac{GMm}{r}.\tag{1}$$  The experimentally verified near-Earth gravitational potential is  $$U ~=~ mgh.\tag{2}$$  The near-Earth potential should be an approximation for the general potential energy when $r\approx r_{\text{Earth}}$, but the problem I'm having is that they scale differently with distance.  $(1)$ scales as $\frac 1r$.  So the greater the distance from the Earth, the less potential energy an object should have.  But $(2)$ scales proportionally to distance.  So the greater the distance from the Earth, the more potential energy an object should have.  How is this reconcilable?


When I have a manual line break in a cell of a tabularx table, then the vertical line goes missing.  \documentclass{article}  \usepackage{tabularx}  \usepackage[sfdefault]{cabin}  % https://tex.stackexchange.com/questions/89166 \newcolumntype{Y}{>{\centering\arraybackslash}X}   \begin{document}  \begin{tabularx}{\textwidth}{lc|l|Y|Y|Y|Y} \hline % Row Text & & & & & & \\ \hline % Row Text\\ Text & & & & & & \\ \hline \end{tabularx}  \end{document}     Related

I have the following code that produces the table that is shown. What I am trying to do is to get the fourth and fifth column titles vertically aligned at the top. Is this possible?  \documentclass{article} \usepackage{multirow} \usepackage{array}  \newcolumntype{x}[1]{% >{\raggedright\hspace{0pt}}p{#1}}%  \begin{document} \centering \renewcommand{\arraystretch}{1.2} \begin{tabular}{| m{2cm} | p{2cm} | p{2cm} | p{2cm} | p{2cm} | p{2cm} |} \hline     \multirow{3}{1.7cm}{Data Set} &%     \multicolumn{3}{c |}{Raw Data} &%     Offline Processing Time &     Index Size (KB)\\ \cline{2-4} %     & %     RDF N3 File SizeKB (sec)    &%     Number of Triples &%     Number of Entities\\    \hline \end{tabular} \end{document}


I already readed lots of guides about how to level archery fast but after my level is hight enough i needs hours to level please help me my archery skill is 51

Furthermore, how does Archery level? Does every successful hit on an enemy reward me with a set amount of experience, or does damage dealt also play a role?  Also, do I receive any experience for a missed shot?


Company name — "Mushroom Joinery" Tag line — "Creation and restoration in wood"  Should capitals be used in the tag line? If so, where?

Are there any concrete rules that say which words (parts of speech) in a title should start with a capital letter? What would be a correct capitalization for the title of this question?


I am a newbie, just started rendering. I am not able to get the final image that I have rendered. When I press F12 I get just a window (the pic below) showing almost nothing. Can someone please tell me where I went wrong or what extra needs to be done? Thank you.

A scene I made is not rendering, at all. This grey screen stays the same and nothing changes.  Here are my settings:  [


This is my first time ever attempting to use class templates (I'm very new to C++)  I'm trying to create a very simple Number class.  To start, I'm creating a ToString method.  As of now, for testing purposes, I just want ToString to return the string "testing".  When I run my code, I get the following error:  Undefined symbols for architecture x86_64:   "Number<int>::ToString()", referenced from:       _main in main.o ld: symbol(s) not found for architecture x86_64 clang: error: linker command failed with exit code 1 (use -v to see invocation) make: *** [build/ml] Error 1  Here is my code, any help is appreciated:  main.cpp  #include "number.h"  int main(int argc, char* argv[]) {     Number<int> x(15);     x.ToString();     return 0; }   number.h  #ifndef _NUMBER_ #define _NUMBER_  #include <iostream>  template <class T>  class Number {     private:         T m_val;     public:         Number(T val) : m_val(val) {};         std::string ToString(); };  #endif   number.cpp  #include "number.h"  template<class T>  std::string Number<T>::ToString() {     return std::string("testing");   }

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


I have a fucntion of $x^3 -x - r=0$ for $r>0$ and I need to find its roots.   How can I do this ..?

I can't seem to find a way to change this equation into its irreducible form to solve it: $$x^{3}-x-2=0.$$   It should have 1 real root and 2 complex roots.


I have a JavaScript function that returns the result of multiplications using decimal values (four digits after dot).  But, in some conditions, the result is a mess like this:  3.9050 * 9 = 35.144999999999996.   What should I do to normalize those results?

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


The Banach-Alaoglu says that the closed unit ball in a dual space $X^*$ of a normed space $X$ is compact in the weak-star topology.  The sequential Banach-Alaoglu says that the closed unit ball in a dual space of a separable normed space is sequentially compact in the weak-star topology.  According to page 71, example 5.3.1 ii) , the assumption of separability cannot be dropped in the sequential Banach-Alaoglu. The proof makes sense to me. However I also reason that the (strong) Banach-Alaoglu covers the sequential Banach-Alaoglu as a special case. So by Banach Alaoglu, shouldn't the sequential Banach Alaoglu theorem still hold true for $X$ inseparable?

I know the following theorem from the lecture:     Let $X$ be a seperable Banachspace. Then $\overline{B(0)}$ is weakly* sequentially compact in $X'$.   Since it is specified that $X$ has to be separable, I want to look at an example where $\overline{B_1(0)}$ is not necessarily weakly* sequentially compact in $X'$, if we choose a Banachspace $X$ that is not separable. I found out from a book that $\overline{B_1(0)}$ is not weakly* sequentially compact in $(l^\infty)'$. $l^\infty$ is not separable ( I showed that already), but how can we now show that $\overline{B_1(0)}$ is not weakly* sequentially compact in $(l^\infty)$'?


What is the simplest and best device (or circuit) to stop the flow of current in a 3.7V (2A) line when current in another 5V (2A) line is present?  Basically I want to make an UPS using a LiPo battery for a SIM800l, I have an SIM800l module attached to A 3.7V wall adapter but I also have connected the SIM800l to a 3.7V LiPo Battery, I want to stop using the battery when there is current from the USB wall charger.   I do not want to use a standard powerbank since these always use the battery.

Following on an earlier  I am looking for a circuit where it powers from USB when it is available and uses the battery when USB is not plugged in.  I want voltage drop to be minimal, zero if possible. So using oring diodes is not possible. The mosfet power oring ICs mentioned in the answer are extremely expensive (4$ for 1K) although they have low voltage drop.   I am looking for a discrete solution where I can build with simple switches or even a cheap LDO. I didn't try to build it but I thought I could use the existence of the Vbus to do a simple switch to control LDO's one from VBus, the other from VBat.   UPDATE   Ideally zero drop is wanted however up to 100mV can be tolerated.  My system has 4 AA batteries, so there could be cases where the battery voltage is larger than 5V, that is why I focus on the existence of VBus. The small drop comes from the Operation voltage of one of the ICs, it needs to be 3.5V (min) and the larger voltage drop eats into the battery life. (i.e. 4 battery, 0.9 each, 3.6V, 100mV drop, I can squeeze the batteries). If there is a 0.7V drop, I can not use the full battery power. (I have to shut down the system at some point of time to ensure proper operation but batteries has still a lot of juice left)


What is the up to date correct usage of the H tags?  I was originally told that it was only one H1 tag per page.  Now I am being told that you can use more than one h1 tag as long as it is only one per sectioning root or content section and that it is better than the former way.  What is the correct usage!

Is is true
 tag should not have more than 1 on every page for SEO?   Every pages on the header, it includes and
 tag. Website Name which show an image from logo class, like this:

      Website Name

   and I also include
 on the contact page, help, etc and article page for example:
Contact Us

Name of the Article Title here
   On the homepage, it just has one
 for the logo Site Name... other pages have 2
 tags


Hello this is my first question on here, but after looking around I cant seem to find a fix for my problem.   So here it is, Everytime I start up my PC I get the usual "enter Passcode" Which I do. But after this all I get is a black screen.  I already have the Ubuntu OS installed on my PC perfectly (well not so perfectly). I cant seem to determine what the problem is, and sorry for the lack of any detail. If any is needed I am willing to oblige.

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


I have been using Shift+Space for input source change. MacOS Mojave, however, doesn't allow it. The default shortcut is Ctrl+Space and optionally Capslock. I can customize the shortcut except for Shift+Space.  Am I missing something? Please advise.

Shift + Control + Space doesn't seem to work anymore.


I need to find an explicit expression for a bijection between $[0,1]$ and $(0,1)$. I've seen some between $[0,1]$ and $[0,1]$, but I can't seem to find one between $[0,1]$ and $(0,1)$.  Thanks in advance!

How to define a bijection between $(0,1)$ and $(0,1]$?   Or any other open and closed intervals?   If the intervals are both open like $(-1,2)\text{ and }(-5,4)$ I do a cheap trick (don't know if that's how you're supposed to do it): I make a function $f : (-1, 2)\rightarrow (-5, 4)$ of the form $f(x)=mx+b$ by \begin{align*} -5 = f(-1) &= m(-1)+b \\ 4 = f(2) &= m(2) + b \end{align*} Solving for $m$ and $b$ I find $m=3\text{ and }b=-2$ so then $f(x)=3x-2.$  Then I show that $f$ is a bijection by showing that it is injective and surjective.


How many times do you write the digit 4 when writing all the numbers from 10 to 100?   Is there a way of doing this without having to write down all the numbers?

My homework asks me the following:     If a student writes the integers from 5 to 305 inclusive by hand, how many times will she write the digit 5?   I started out by writing every number that contains 5 and I got 31, but 31 is not among the answers possible:     5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105, 115, 125, 135, 145, 155, 165, 175, 185, 195, 205, 215, 225, 235, 245, 255, 265, 275, 285, 295, 305   I counted 55, 155, and 255 as two each since there are two occurrences of the digit 5 in each.  I can't figure out what I'm doing wrong.  In addition, suppose I were given the numbers 1 and 100,000 - writing them out isn't efficient, and I would assume there's a formula for this but I can't figure that out either.


I'll be travelling to Rio (actually Volta Redonda, 100km north of Rio) for three months for research. I live in Canada.   I am looking for an approximate cost of living per week in Brazil so I may do my finances. Using some sources online mainly Numbeo, I used the estimate of $200 BRL per week with a total of 2400 BRL over 12 weeks. I plan on eating out more and cooking less. Is this too high, too low, or just right?

Disclaimer: The locations are just examples to set up the question and all prices are made up for the sake of the example and question.  Background: Let's say I want to visit London or Busan, and my currency is USD. While comparing the two locations I notice their exchange rates. 1 USD is 0.60 GBP, while 1 USD is 1,200 KRW.   Question: Are there traveler's tips and/or tools when it comes to currency exchanges where I know how much I can get for my "dollar" in a certain travel location? To use the exchange rate above as an example, consider the following. A bottle of water in London costs 0.40 GBP while a bottle of water in Busan costs 2,000 KRW. How would I know the relative value of goods I can get for my "dollar"?  I found  that provides that information but I'm wondering if there are other travel tips or anything to answer my question.   Edit: I replaced Korea with Busan to give it a more precise location and to keep it on the same level as London.


How many integral triplets $(x, y, z)$ satisfy the equation $x^2 + y^2 + z^2 = 1855$ ?  solution:- Note that 1855 = 7 mod 8 while all perfect squares are 0, 1 or 4 mode8. So it is impossible for 3 squares to sum up to 7 mod8. So no solutions are there.  Could anyone please explain how we choose number to take mod with, on both the sides.Here for example, we took mod 8..why not, mod 4?   How we chose 8 here.

I have figured out a (long, and tedious) way to do it. But I was wondering if there is some sort of direct correlation or another path that I completely missed.  My attempt at the program was as follows:   A number of the form, $8k + 7 = 7 (mod 8)$. That is, we are looking for integers a, b, c such that $a^2 + b^2 + c^2 = 7 (mod 8)$.   LONG and TEDIOUS way: $$(8k)^2 = 0 (mod 8)$$ $$(8k+1)^2 = 1 (mod 8)$$ $$(8k+2)^2 = 4 (mod 8)$$ $$(8k+3)^2 = 1 (mod 8)$$ $$(8k+4)^2 = 0 (mod 8)$$ $$(8k+5)^2 = 1 (mod 8)$$ $$(8k+6)^2 = 4 (mod 8)$$ $$(8k+7)^2 = 1 (mod 8)$$  That is, using three of these modulo there is no way to arrive at  $$a^2 + b^2 + c^2 = 7 (mod 8)$$


What is a string method, and how are does their usage differ from using a built-in function?  Can anyone help me with this ?

Can someone provide a simple explanation of methods vs. functions in OOP context?


I am trying to get all installed apps in the computers of my domain but i haven't found a way to get the information in an accurate way first i was trying to achieve this through the registry key:    HKLM:\Software\Wow6432Node\Microsoft\Windows\CurrentVersion\Uninstall\*   but this returned more info than i need like updates installed. So i searched for another way and I found that the wmi class Win32_product contains all installed apps but after trying with this y have found that the info that recolects is incorrect    ¿why there are some apps like google chrome, free proxy, dell system diagnostics, that does not appear when querying the class?  In this link is the answer for this question     ¡there is a way to accurately get all installed applications in windows via powershell or command line?

There are various methods to find installed applications on the system but to my knowledge none returns exactly the same list as control panel item Add Remove Programs. Some of the ways I tried are:   WMI via Win32_Product and Win32Reg_AddRemovePrograms Registry, both x32 and x64 branches   For instance, I have 217 entries in AR and   gwmi  Win32_Product   returns 261 items.  gp HKLM:\Software\Microsoft\Windows\CurrentVersion\Uninstall\*, HKLM:\SOFTWARE\Wow6432Node\Microsoft\Windows\CurrentVersion\Uninstall\* | ? {![string]::IsNullOrWhiteSpace($_.DisplayName) } | select DisplayName   returns 119 items.   (gwmi Win32Reg_AddRemovePrograms) + (gwmi Win32Reg_AddRemovePrograms64) | sort DisplayName -Unique    returns 107 items.  I tried to nail it down with more complex filter that included InstallLocation, InstallSource, InstallDate etc without success.


Here is the connection class   public class ConnectionManager {      Connection cn = null;      public Connection getConnection() throws ClassNotFoundException, SQLException {         String dbPath = "jdbc:mysql://localhost:3306/postjob";         String username = "root";         String password = "root";         Class.forName("com.mysql.jdbc.Driver");          cn = DriverManager.getConnection(dbPath, username, password);         return cn;     }      public void closeConnection() throws SQLException{         cn.close();       } }   Here is my service class  public class UserdetailsServices {      public Connection connection;     public ResultSet resultset; //    private Object resultSet;      public UserdetailsServices() {         try {             connection = new ConnectionManager().getConnection(); //here I am getting connection=null.         } catch (ClassNotFoundException ex) {             Logger.getLogger(UserdetailsServices.class.getName()).log(Level.SEVERE, null, ex);         } catch (SQLException ex) {             Logger.getLogger(UserdetailsServices.class.getName()).log(Level.SEVERE, null, ex);         }     }      /**      *      * @param user      * @return      */     public boolean registerUser(UserModal user) {         try {             java.sql.PreparedStatement psmt = connection.prepareStatement("insert into userdetails(role,name,gender,email,password,cpassword,contact) values(?,?,?,?,?,?,?)");             psmt.setString(1, user.getRole());             psmt.setString(2, user.getName());             psmt.setString(3, user.getGender());             psmt.setString(4, user.getEmail());             psmt.setString(5, user.getPassword());             psmt.setString(6, user.getCpassword());             psmt.setString(6, user.getContact());             int flag = psmt.executeUpdate();             if (flag > 0) {                 return true;             } else {                 return false;             }         } catch (SQLException ex) {              return false;         }     }

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I am writing a thesis and I began write as a article. I thought it is easy convert to beamer. Now I have some problems. In equnarray and $, parenthesis, bracket and \bigoplus don't seem.  \documentclass[12pt]{beamer} \usefonttheme{professionalfonts} \usepackage{siunitx} \usepackage{newtxtext,newtxmath} \usepackage{bm} \mode<presentation>{\usefonttheme{professionalfonts}} \usepackage[turkish]{babel} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsthm} \usepackage{amssymb} \usepackage{tikz} \usepackage[loadonly]{enumitem} \usepackage[shortlabels]{enumerate} \newcommand*\circled[1]{\tikz[baseline=(char.base)]{         \node[shape=circle,draw,inner sep=2pt] (char) {#1};}} \usepackage{mathptmx} \begin{document}     \begin{eqnarray*}         x\bigoplus y=max\left\{x,y\right\}\\         x\bigotimes y=x+y     \end{eqnarray*} \end{document}   In article:  In beamer:

In a LaTeX article, the math characters are more "curvy" than the text characters:  \documentclass[12pt]{article} \begin{document}  $x^2 + y^2 = z^2$ \end{document}     In a beamer presentation, the math characters do not have the same curves:  \documentclass{beamer} \begin{document} \begin{frame}  $x^2 + y^2 = z^2$ \end{frame} \end{document}     Question  How can I get the beamer math to look just like the article math?  I would prefer if the solution was a single line (that I could place at the top of my LaTeX file) as opposed to something that needs to appear next to every piece of math.