Bitwise Left Shift operator
What are bitwise shift (bit-shift) operators and how do they work?
Continuous function on closed unit ball Take a continuous mapping $f: \bar{B^{n}} \rightarrow \bar{B^{n}}$, where $\bar{B^{n}}$ is a closed unit ball in $\mathbb{R}^{n}$. Assume that $f(x) \neq x$ for every $x \in \bar{B^{n}}$. Define another function $r$ by following the directed line segment from $f(x)$ through $x$ to its intersection with $\partial B^{n}$, and let the intersection point be $r(x)$. Is it immediately evident that $r$ is a continuous function? Is so how does it follow? Thanks. JavaScript open in a new window, not tab I have a select box that calls window.open(url) when an item is selected.  Firefox will open the page in a new tab by default.  However, I would like the page to open in a new window, not a new tab.    How can I accomplish this? When I type $\overset{\circ}{Z}^\lambda$ the lambda is placed slightly above and to the right of the circle. Is there a way to make it appear as a superscript on the Z? I tried $\overset{\circ}{Z^\lambda}$, but then the circle is too high and to the right.  As a bizarre aside: a friend uses the exact same code with no problem. However, when I type it into MathOverflow it looks the same as in my compiler (i.e. bad). In the season 8 episode finale of Game of Thrones the highest important lords met with Grey Worm to free      Tyrion and Jon. While it was pretty clear why they wanted to free Jon it was unclear to me why they also asked for Tyrion.   To make things even more strange, they asked about his opinion of a potential solution which becomes the actual final one in the end      (choose king and nominate someone).   I thought they (besides Sansa and Bran) don't like him and wanted to judge him? Or am I missing something? Expanding code in etoolbox's \ifblank I am trying to use the etoolbox \ifblank (and its cousin \notblank), but I want to expand any macros in its test statement.  For example:  \documentclass{article} \usepackage{etoolbox}  \begin{document}  \newtoggle{longformt} \newcommand{\longform}{\toggletrue{longformt}} \newcommand{\iflong}[2]{\iftoggle{longformt}{#1}{#2}}  \newcommand{\quoteifnotblank}[1]{%     \notblank{#1}{``#1''}{}% }  % Try commenting this line. \longform  This should be completely blank if the form is short: \quoteifnotblank{\iflong{Some long quoted text}{}}  \end{document}   The problem here is that \notblank sees its argument of \iflong{Some long quoted text}{} as a string, not as code to be expanded, so the quotes always appear.  How do I expand arguments before they are passed to \notblank? I have recently installed ubuntu 11.10. But when i try to install a software it tries to 'updating cache' but after a while, it stops, showing:                            Failed to download repository information                           Check your internet connection   so, now i am totally unable to install any software in my ubuntu.  Please,let me know how to solve the problem. How does editing work? I am trying to think/know about something, but I don't know if my base premise is plausible. Here we go.  Sometimes when I'm talking with people about pure mathematics, they usually dismiss it because it has no practical utility, but I guess that according to the history of mathematics, the math that is useful today was once pure mathematics (I'm not so sure but I guess that when the calculus was invented, it hadn't a practical application).  Also, I guess that the development of pure mathematics is important because it allows us to think about non-intuitive objects before encountering some phenomena that is similar to these mathematical non-intuitive objects, with this in mind can you provide me historical examples of pure mathematics becoming "useful"? Setting a fill and border is pretty easy in apps like Illustrator and Gravit Designer but in Blender. I've found it to be more tedious as I can't find anything online to solve this problem.  The picture above is a simple 2d mouth with lips. I would like to be able to move the lips and still have a fill but in Blender I needed to add another path for the mouth. Is there anyway I can move my lips path while having it also take the exact same shape (but not material) as my mouth's path?    (454.2 KB)  I work in Blender 2.79 cause 2.8 doesn’t run well on my laptop at all. apt-get install with '-' (minus / hyphen) removes packages I was looking for some package (nautilus-terminal), and accidentally did this:  $ sudo apt-get install nautilus- Reading package lists... Done                                                                                                                                                                                                  Building dependency tree                                                                                                                                                                                                       Reading state information... Done                                                                                                                                                                                              The following packages were automatically installed and are no longer required:                                                                                                                                                  apturl apturl-common libgail-3-0 linux-headers-4.4.0-57 linux-headers-4.4.0-57-generic linux-image-4.4.0-57-generic linux-image-extra-4.4.0-57-generic                                                                       Use 'sudo apt autoremove' to remove them.                                                                                                                                                                                      The following packages will be REMOVED:                                                                                                                                                                                          gnome-session-flashback nautilus nautilus-sendto nautilus-share ubuntu-desktop                                                                                                                                               0 upgraded, 0 newly installed, 5 to remove and 69 not upgraded.                                                                                                                                                                After this operation, 2 031 kB disk space will be freed.                                                                                                                                                                       Do you want to continue? [Y/n] ^[[^C                                                                                                                                                                                             That's quite dangerous because remove is much harder to mistype than a simple dash from a failed autocompletion.     Is that an equivalent of apt-get remove? I couldn't find any documentation for that. Edit: except for overlooking the man page... Is there any clever method out there to make my executeEveryDayMethod() execute once a day, without having to involve the Windows TaskScheduler? $R$ is commutative, $I$,$J$ are ideals, $I+J=R$, then $IJ=I\cap J$ If $R$ is a commutative ring and $I$ and $J$ are ideals s.t. $I+J=R$ then show that $IJ=I\cap J$.  I've already shown that $IJ \subset I\cap J$, now I need to show the reverse inclusion.   I'm a bit lost, so far i'm just figuring out what pieces I have to work with.  Such as:  $\forall r\in R$ $\exists i\in I ,j\in J$ s.t. $i+j=r$  $\forall ij\in IJ$, $ij=i_1$ and $ij=j_1$ for some $i_1\in I$, $j_1\in J$.  Also, if I let $x\in I\cap J$, then $x=i_2=j_2=i+j$ for some $i_2\in I$, $j_2\in J$  Anyone, having problem getting to the conclusion here, thanks in advance In how many ways can you choose $k$ numbers out of $\{1,2,3,\dots,n\}$ so none of them is consecutive? How to determine exact contrast ratio Because of the recent Web accessibility Law in my region, I need to ensure I'm designing with an appropriate contrast ratio.  WCAG says the value of this ratio is 4.5:1    How do I figure this out in in Photoshop and Illustrator? What to do with random effects correlation that equals 1 or -1? Not so uncommon occurrence when dealing with complex maximal mixed models (estimating all possible random effects for given data and model) is perfect (+1 or -1) or nearly perfect correlation among some random effects. For the purpose of the discussion, let's observe the following model and model summary   Model: Y ~ X*Cond + (X*Cond|subj)  # Y = logit variable   # X = continuous variable   # Condition = values A and B, dummy coded; the design is repeated  #             so all participants go through both Conditions   # subject = random effects for different subjects    Random effects:  Groups  Name             Variance Std.Dev. Corr               subject (Intercept)      0.85052  0.9222                              X                0.08427  0.2903   -1.00                      CondB            0.54367  0.7373   -0.37  0.37                X:CondB          0.14812  0.3849    0.26 -0.26 -0.56 Number of obs: 39401, groups:  subject, 219  Fixed effects:                  Estimate Std. Error z value Pr(&gt;|z|)     (Intercept)       2.49686    0.06909   36.14  &lt; 2e-16 *** X                -1.03854    0.03812  -27.24  &lt; 2e-16 *** CondB            -0.19707    0.06382   -3.09  0.00202 **  X:CondB           0.22809    0.05356    4.26 2.06e-05 ***   The supposed reason behind these perfect correlations is that we have created a model which is too complex for the data that we have. The common advice that is given in these situations is (e.g., Matuschek et al., 2017; ) to fix the overparameterized coefficients to 0, because such degenerate models tend to lower the power. If we observe a marked change in fixed effects in a reduced model, we should accept that one; if there is no change, then there is no problem in accepting the original one.  However, let's presume that we are not interested only in fixed effects controlled for RE (random effects), but also in the RE structure. In the given case, it would be theoretically sound to assume that Intercept and the slope X have non-zero negative correlation. Several questions follow:   What to do in such situations? Should we report the perfect correlation and say that our data is not "good enough" to estimate the "real" correlation? Or should we report the 0 correlation model? Or should we maybe try to set some other correlation to 0 in hope that the "important" one will not be perfect anymore? I don't think there are any 100% correct answers here, I would mostly like to hear your opinions. How to write the code which fixes the correlation of 2 specific random effects to 0, without influencing the correlations between other parameters? How do you set password-hash for OpenLDAP? number of subsets of even and odd When I use the mobile app to vote for an answer that was awarded a bounty,  the bounty is no longer shown until I reload the answers. I  want to download free app in my iPod touch device and i have the following doubts.  Kindly resolve me doubts.   when i try to download it asks my credit card security number. since i am trying to download free app , why do i need to provide my credit card security code? Will i be debited for downloading the free app from app store?   I cant able to find any information regarding this on apple.  Please provide me some references about this from apple and please resolve my doubts.  Thanks a lot. I have two sites that were originally migrated from SPS2003.  It worked well in SharePoint 2007 and even on SharePoint 2010,  however when we migrated it to SharePoint 2013,  the home page throws following errors on the ULS Log.     5/24/2013 09:57:46.62  w3wp.exe (0x0D50)   0x1D24  SharePoint Foundation   Files   ak8dj   High   UserAgent not available, file operations may not be optimized.    at Microsoft.SharePoint.SPFileStreamManager.CreateCobaltStreamContainer(SPFileStreamStore spfs, ILockBytes ilb, Boolean copyOnFirstWrite, Boolean disposeIlb)     at Microsoft.SharePoint.SPFileStreamManager.SetInputLockBytes(SPFileInfo&amp; fileInfo, SqlSession session, PrefetchResult prefetchResult)        05/24/2013 09:57:46.62 w3wp.exe (0x0D50)   0x1D24  SharePoint Foundation   Cobalt  ajoii   Medium   Mapping Store error to Cobalt error. [Store Error: System.NullReferenceException: Object reference not set to an instance of an object.     at Microsoft.SharePoint.CoordinatedStreamBuffer.SPCoordinatedStreamBufferFactory.CreateFromDocParams(SqlSession session, Guid guidSiteId, Int32 cbContent, Nullable1 parentId, Guid docId, Nullable1 level, SPChunkedArray`1 rgbContent, Byte[] rgbRbsId, Int64 bsn, Byte partition, Int32 pageSize, Boolean bStartFilling)        05/24/2013 09:57:46.62 w3wp.exe (0x0D50)   0x1D24  SharePoint Foundation   Cobalt  aintx   High    Failed in CobaltStream.LockBytes: ErrorException --- Error: Unknown (Win32=0x80004003) --- Error message: System.NullReferenceException: Object reference not set to an instance of an object.     at Microsoft.SharePoint.CoordinatedStreamBuffer.SPCoordinatedStreamBufferFactory.CreateFromDocParams(SqlSession session, Guid guidSiteId, Int32 cbContent, Nullable1 parentId, Guid docId, Nullable1 level, SPChunkedArray`1 rgbContent, Byte[] rgbRbsId, Int64 bsn, Byte partition, Int32 pageSize, Boolean bStartFilling)     at         05/24/2013 09:57:46.64 w3wp.exe (0x0D50)   0x1D24  SharePoint Foundation   Files   ak8dj   High    UserAgent not available, file operations may not be optimized.    at Microsoft.SharePoint.SPFileStreamManager.CreateCobaltStreamContainer(SPFileStreamStore spfs, ILockBytes ilb, Boolean copyOnFirstWrite, Boolean disposeIlb)     at Microsoft.SharePoint.SPFileStreamManager.SetInputLockBytes(SPFileInfo&amp; fileInfo, SqlSession session, PrefetchResult prefetchResult)     at         05/24/2013 09:57:46.64 w3wp.exe (0x0D50)   0x1D24  SharePoint Foundation   Database    ab1a9   High    Failed to get document content data. System.NullReferenceException: Object reference not set to an instance of an object.     at Microsoft.SharePoint.CoordinatedStreamBuffer.SPCoordinatedStreamBufferFactory.CreateFromDocParams(SqlSession session, Guid guidSiteId, Int32 cbContent, Nullable1 parentId, Guid docId, Nullable1 level, SPChunkedArray`1 rgbContent, Byte[] rgbRbsId, Int64 bsn, Byte partition, Int32 pageSize, Boolean bStartFilling)     at   I could not find any materials related to this on the internet,  I am not even sure if it has to do something with SPS2003 compatibility.  Any help pointers?