fetch content of a file, by giving from and to pointers in php
Read a file backwards line by line using fseek
Given a $k$-manifold $M$, such that $\partial M$ is a $(k-1)$-manifold, there is a standard way in which $\partial M$ inherits the orientation of $M$. So if $M$ is oriented by the form field $\omega$, then $\omega_\partial=\omega(v_{\text{out}},v_1,\dots,v_{k-1})$ orients $\partial M$, where the $v_1,\dots,v_{k-1}$ are basis vectors for a tangent space on a point of the boundary, and $v_\text{out}$ is an outward pointing vector (see here: , which follows the exposition of Hubbard &amp; Hubbard).  In practice I find this very difficult to interpret. How can one find this $v_\text{out}$ in practice?   For instance, take $M$ to be defined by $z=x^2+y^2$ for $x\ge0$ (technically a manifold with boundary, in fact a half-paraboloid). It's a fact that $\partial M$ is defined by the parabola $z=y^2$. If $M$ is oriented by $dx\wedge dy$, how does this induce an orientation on the boundary (in fact we should obtain a 1-form that induces an orientation on the boundary)?   Note: I find the whole discussion of boundary orientation to be rather clumsy in its exposition. In the case of surfaces inducing orientations on boundary curves, I was originally taught to imagine that the normal vector that induces the surface orientation is me walking on the surface. This normal should walk along the boundary such that the surface lies to its left. OK - but how does this translate to the $v_{\text{out}}$ interpretation, so that we can generalize to other dimensions easily?)  Edit: An ideal answer would merge the intuitive approach with the rigorous approach, if possible. I would grateful to anybody who could help order my (at present confused) understanding! TeXstudio not large enough to use on a 4k display Function $f(z)$ such that $|f(z)| > |z|$ for every $z\in\mathbb{C}, 1/f(z)$ I've inherited a Maintenance Plans that does the following:   Cleanup old data Checks DB integrity Performs Database and Transaction Log Backups Reorganizes Our indexes Updates Statistics Delete old backups and Maintenance Plan files   Of the 23 minute Maintenance Plan, Updating the Statistics takes a staggering 13 minutes. During this 13 minute period, access to the database is blocked (or at least, replication from this DB to our others is paused).  My Question Is:  When should we be Updating the Statistics, and why?   This seems like the kind of thing we should do less frequently than every day. I'm trying to get us out of the "just because" mind-set of doing unnecessary Maintenance. Why does a candle blow out when we blow on it? Our breath is 16% oxygen and only 4% CO2 Gnome terminal will not start I just tried to install python 3.6 on my Ubuntu 16.04 system, and now I can't run the terminal from the launcher or from Ctrl + Alt + T. I tried to run gnome-terminal from XTerm and got the following message:  Traceback (most recent call last):   File "/usr/bin/gnome-terminal", line 9, in &lt;module&gt;     from gi.repository import GLib, Gio   File "/usr/lib/python3/dist-packages/gi/__init__.py", line 42, in &lt;module&gt;     from . import _gi ImportError: cannot import name '_gi' Error in sys.excepthook: Traceback (most recent call last):   File "/usr/lib/python3/dist-packages/apport_python_hook.py", line 63, in apport_excepthook     from apport.fileutils import likely_packaged, get_recent_crashes   File "/usr/lib/python3/dist-packages/apport/__init__.py", line 5, in &lt;module&gt;     from apport.report import Report   File "/usr/lib/python3/dist-packages/apport/report.py", line 30, in &lt;module&gt;     import apport.fileutils   File "/usr/lib/python3/dist-packages/apport/fileutils.py", line 23, in &lt;module&gt;     from apport.packaging_impl import impl as packaging   File "/usr/lib/python3/dist-packages/apport/packaging_impl.py", line 23, in &lt;module&gt;     import apt   File "/usr/lib/python3/dist-packages/apt/__init__.py", line 23, in &lt;module&gt;     import apt_pkg ModuleNotFoundError: No module named 'apt_pkg'  Original exception was: Traceback (most recent call last):   File "/usr/bin/gnome-terminal", line 9, in &lt;module&gt;     from gi.repository import GLib, Gio   File "/usr/lib/python3/dist-packages/gi/__init__.py", line 42, in &lt;module&gt;     from . import _gi ImportError: cannot import name '_gi'   How can I fix this error?  It should also be noted that:   My gnome-terminal file is now a python script. The gnome-terminal.real file will open the terminal as expected. python3.5 gnome-terminal will open the terminal as expected. Passcode is required to enable Touch ID This morning I experienced the weirdest thing by my iPhone 6S requiring me to enter my passcode rather than allowing me to use my finger as Touch ID.  My phone was locked probably for like 4 hours while charging overnight and as far as my knowledge my phone did not restart during this time since my Stack Exchange app was left open and upon opening it the same content were still there.  I didn't attempt even once to use my Touch ID; if I would've had a faulty Touch ID sensor then I should've seen such similar behavior either prior to this morning or at least afterwards (I'm already on my phone for the past 3 hours plus).  I didn't register or delete any fingerprints for months.  And finally, I don't have any restrictions setup to require the input of my passcode under Settings > General > Restrictions.  I'm running on iOS Version 10.0 beta 3 (14A5309d)  Anyone out there that has also experienced such similar behavior or with any suggestion on what might've caused it? Note: If you're looking for a simple explanation as to why comments aren't required on downvotes, see .   I used to get "upset" (though that is too strong a term) when I got downvoted without comment. If my answer isn't good enough then I'd like to know why. Not only does it improve the answer for the OP but it improves my knowledge too.  Where the down-vote has been explained I've found it useful &amp; it has improved my answer, or forced me to delete the answer if it was totally wrong.  So is there any way we can encourage people to leave a comment? Perhaps they don't lose rep if they explain their down-vote?  I must admit though that I haven't always explained my down-vote either so you could call me a hypocrite. I've also grown a thicker skin over the months of using SO (it seems to have come with the higher rep score ;-)), so I'm less bothered about this now. Fourier transform of $\exp(-t^2)$ using contour integration. Is there an invalid pthread_t id? For what values of $\alpha$, does this integral converge? For what values of $\alpha&gt;0$ this integral converges $$\int_0^{\infty} \frac {\sin x}{x^{\alpha}}dx $$ $P[X=x]=0$ when $X$ is continuous variable I know that for continuous variable $P[X=x]=0$.   But i can't visualize that if $P[X=x]=0$, there is infinite number of possible $x$'s. And also why do their probabilities get infinitely small ? LaTeX Classes or Styles for Schedules and/or Calendars? Maybe TeX isn't the best for this particular problem, but any teachers out there use a particular class or package to plan lessons?  Right now I'm just using a spreadsheet, but I always find myself wishing there was a 'lessonplan.sty' or 'classschedule.sty' file out there somewhere so I could still use the LaTeX for equations, tables, lists etc.    A bit of searching yielded a few results, but there doesn't seem to be a consensus.  Anyone used any of these:        Any recommendations from anyone on best way to make calendar-based class schedules and/or lesson plans? The following code uses the etoolbox package to convert a list a,b,c into an internal list (called \mylist) and then typesets that with colons: a:b:c:.  However, when I load the etextools package (by uncommenting the second line), I get no list output.   \documentclass{minimal} \usepackage{etoolbox} %\usepackage{etextools} \begin{document} A list: \def\mylist{} \forcsvlist{\listadd\mylist}{a,b,c} \def\do#1{#1:} \dolistloop{\mylist} \end{document}   I suspect it is is a bug since etextools claims to depend on etoolbox.  Is this a bug or am I doing something wrong?  In either case, how can I use \dolistloop with  etextools (which I want for goodies like \expandnext)?  Notes   \show\mylist produces the same output a|b|c| in both cases, so the problem is with \dolistloop which expands to \forlistloop\do The \forlistloop command becomes substantially more complicated when etextools is used.  might be relevant (but not obviously). What are the scope restrictions for setting shopt extglob. and other options? My non-interactive bash shell has extglob off. I would like to turn it on in the statement immediately before a command, but I have noticed that when shopt -s extglob is within an if .. then .. else block, it somehow does not register.   The following extglob-dependant command is not valid: syntax error near unexpected token '('.     Where can extglob be set, and why is there a restriction, at all? Does this apply to other options?  ... GNU bash 4.1.5     This works:    shopt -s extglob if true ;then     touch a.bcd; ls a.@(bcd) fi   This fails:    if true ;then     shopt -s extglob     touch a.bcd; ls a.@(bcd) fi ... line 17: syntax error near unexpected token `(' ... line 17: `touch a.bcd; ls a.@(bcd)' This question is a bit more subjective, but I'm hoping to get some new perspective.  I'm so used to designing for certain screen size (typically 1024x768) that I find that size to not be a problem.  Expanding the size to 1280x1024 doesn't buy you enough screen real estate to make an appreciable difference, but will give me a little more breathing room.  Basically, I just expand my "grid size" and the same basic design for the slightly smaller screen still works.  However, in the last couple of projects, my clients were all using 1080p (1920x1080) screens and they wanted solutions to use as much of that real estate as possible.  1920 pixels across provides just under twice the width I am used to, and the widescreen makes some of my old go to design approaches not to work as well.  The problem I'm running into is that when presented with so much space, I'm confronted with some major problems.   How many columns should I use?  The wide-format lends itself to a 3 column split with a 2:1:1 split (i.e. the content column bigger than the other two).  However, if I go with three columns what do I do with that extra column? How do I make efficient use of the screen real estate?  There's a temptation to put everything on the screen at once, but too much information actually makes the application harder to use.  White space is important to help make sense of complex information, but too much makes related concepts look too separate. I'm usually working with web applications that have complex data, and visualization and presentation is key to making sense of the raw data.  When your user also has a large screen (at least 24"), some information is out of eyesight and you need to move the pointer a long distance. How do you make sure everything that's needed stays within the visual hot points? Simple sites like blogs actually do better when the width is constrained, which results in a lot of wasted real estate.  I kind of wonder if having the text box and the text preview side by side would be a big benefit for the admin side of that type of screen? (1:1 two-column split).   For your answers, I know almost everything in the design is "it depends".  What I'm looking for is:   General principles you use How your approach to design has changed   I'm finding that I have to retrain myself how to work with this different format.  Every bump in the resolution I've worked through to date has been about 25%: 640 to 800 (25% increase), 800 to 1024 (28% increase), and 1024 to 1280 (25% increase).  However, the jump from 1280 to 1920 is a good 50% increase in space--the equivalent from jumping from 640 straight to 1024.  There was no commonly used middle size to help learn lessons more gradually.    To help focus the question a little bit, I had a project that was somewhat similar to Atlassian JIRA, an issue management system.  There were about six different types of records the client wanted to keep, all of them could potentially be related to each other.  Gathering data wasn't the core problem, although it did play a part.  The more important side of the problem was creating a system which would suggest potential relationships between the records and helped the analysts recognize patterns in the reported incidents.  There were different types of analysts that focused on the different problem domains, and due to the nature of their exploratory type of work, they didn't know what they wanted.  They just knew they had to make sense of a lot of data, draw correlations, and characterize classes of issues.    (Originally asked here: , but told that this might be more appropriate)    For the bounty: Stretch your minds a bit.  The pat answer "Make everything bigger" has a limit to how useful the answer is.  We are talking about users who have to make sense of a lot of data and find relationships between records.  If I simply bump up the size on everything they are going to be very limited in what they can see on the screen--particularly because the vertical is so constrained. iPhone 6s with iOS 12.4 not connecting to MacBook Pro mid2015 with macOS 10.14.6 Choosing research ideas to include in a statement of purpose The functions of each pair are inverse to each other. For each pair, check that both compositions give the identity function.  $F: \mathbb{R} \to \mathbb{R}$ and $F^{−1}:\mathbb{R} \to \mathbb{R}$ are defined by $F(x)=3x+2$ and $F^{−1}(y)=\dfrac{y−2}{3}$. for all y ∈ R  My attempt:     Inverse Function  For each particular but arbitrarily chosen $y \in \mathbb{R}$, according to the definition of $f^{-1}$, $f^{-1}(y) = \dfrac{y-2}{3}$ is a unique real number $x$ such that $f(x) = y$. \begin{align*} F(x) &amp; = y\\ 3x + 2 &amp; = y\\ x &amp; = \frac{y-2}{3} \end{align*} Therefore, $f^{-1}(y) = \frac{y-2}{3}$.  Compositions of Functions  The functions $g \circ f$ and $f \circ g$ are defined as follows: $$(g \circ f)(x) = g(f(x)) = g(3x + 2) = 3x + 2$$  for all $x \in \mathbb{Z}$. Possible Duplicate:          I would like to know if when I'm writing about a "user" (in the broad sense), what do I use? Example: "from the user’s perspective, saving a file is very easy; ? only needs..."  What is correct: she, he, she or he, or they.