Rescuing a possibly corrupt PDF in Acrobat
How can I fix/repair a corrupted PDF file?
Transaction log reported full but is not :  Not ten minutes ago, I received this error, twice:  And also an &quot;Oops, something bad happened&quot; error.  I'm also getting question posting errors.  Can we fix this, please? Why is "night" spelled with "gh"? I made something like this:    I did this with the Ellipse Tool and the Line Tool.  Now the circle is accurate, but the lines inside are very inaccurate. Is there another tool that does the same thing but with a lot more accuracy? I have a formula in a cell which counts the values in 2 other cells. Normally, after entering in the values in these 2 other cells, the formula cell updates automatically when Enter is pressed or when the cells are clicked out of.  However, for some reason, the value calculated by the formula does not update automatically. I am having to click on the formula bar, then I have to click enter for the formula cell to do its thing.  Why is this happening? I'm trying to understand the UMP of the product functor as right adjoint to the diagonal functor but I'm having difficulties understanding the notation in Steve Awodey's . On page 210 he uses $(f_1, f_2)$, $\langle f_1, f_2 \rangle$ and $(f_1 \times f_2)$ all within one paragraph. What are those? How are these defined and how do they differ? Let $z_1, z_2, z_3,$ ...be a sequence of independent random variables s.t. $P(z_i=1)=P(z_i=-1)=\frac 1 2$. Does this sequence converge almost surely?  My intuition is telling me that the sequence will approach the random variable Z? i.e. $z_n-&gt;Z$ as $n-&gt;\infty$ and Z is just another RV s.t. $P(Z=1)=P(Z=-1)=\frac 1 2$.  Here is my confusion, if a sequence converges almost surely, then $z_i$ should be different for each term s.t. it approaches Z in the end; but in this sequence $z-i$ is the same for every term. So I dont udnersntand. Youtube video lag on 18.04 I just upgrade from Ubuntu 17.10 to Ubuntu 18.04, there is an issue when playing youtube video.The video stops play but audio playing, then I move the cursor &amp; video is playing...... What should I do?? There are several distinct usages:   kernel density estimation   kernel trick   kernel smoothing   Please explain what the "kernel" in them means, in plain English, in your own words. Let $a, b, \&amp; \, m$ be integers. Prove that if $2a + 3b \geq 12m + 1$, then $a \geq 3m + 1$ or $b \geq 2m + 1$.   My Attempt: I don't conceive apace how to contrive, from the one inequality in the antecedent, the two inequalities in the consequent. So a proof by contraposition may be more facile. The contrapositive is: $\text{If }  \color{Green}{a &lt; 3m + 1} \; \&amp; \; \color{#0073CF}{b &lt; 2m + 1}, \text{ then } 2a + 3b &lt; 12m + 1 \tag{*}.$  From $(*)$, $\color{Green}{2a} + \color{#0073CF}{3b} &lt; \color{Green}{6m + 2} \; + \;\color{#0073CF}{6m + 3} = 12m +5$. But this doesn't prove $(*)$.     Given Solution:  Assume that $a &lt; 3m+1$ and $b &lt; 2m+1.$ Since a and b are integers, $a ≤ 3m$ and $b ≤ 2m.$ Therefore, $2a + 3b ≤ 2(3m) + 3(2m) = 12m &lt; 12m+ 1,$ as desired. $\blacksquare$   What went wrong in my attempt? I understand the given solution but I persisted with the more natural and direct green and blue, instead of deviating to weak inequalities. Shouldn't both solutions work?  Source: Problem 4.19 on P102 (related to P90, Result 4.8) of Mathematical Proofs, 2nd ed by Chartrand et al.    $\large{\text{Supplement to Cameron Buie and pritam's Answers :}}$  What overriding, catholic lessons can be extrapolated from this example to generalise about inequalities?   Moreover, in order to circumvent the problem here (ie the loss of information from the weaker inequalities), should I always start with the strictest inequality? If so, should I always rework any weak inequality into the equivalent strict inequality?   For example, define $r \in \mathbb{R} $ and $n \in \mathbb{Z}$ and $g(...) \neq h(...)$. Then $ f(r) &lt; h(r) \require{enclose}      \enclose{updiagonalstrike}{\iff} f(r) \leq g(r).$ But $ f(n) &lt; h(n) \text{ MAY OR MAY NOT }\iff f(n) \leq g(n).$ Gay rights – does Star Trek ever address this issue? I am aware of the picture of the man wearing the 'dress' from TNG, which promotes gender equality, but are gay rights ever addressed in Star Trek at all? (All seasons accepted.) How to turn off Facebook notifications on Mac OS X? So: I have a Gantt chart created with pgfgantt where in order to fit my pages I have included  x unit=1.4cm,y unit chart=6mm   in its preamble.  This means that milestone shapes are spread out horizontally.  How can I change the vertical and horizontal units of a Gantt chart in a way which doesn't affect the aspect ratios of elements like milestones? Given that , I wonder if every intelligent biological species is capable of producing beings that are Force-Sensitive?   Or are there some species characteristics that can make it 100% impossible for them ever to produce a Force-sensitive individual.  NOTE: Let's exclude - if they exist in EU - things like random new-species-creating mutations - e.g. the individual should be 100% the same species, able to interbreed. I did some mathematical induction problems on divisibility   $9^n$ $-$ $2^n$ is divisible by 7. $4^n$ $-$ $1$ is divisible by 3. $9^n$ $-$ $4^n$ is divisible by 5.   Can these be generalized as $a^n$ $-$ $b^n$$ = (a-b)N$, where N is an integer? But why is $a^n$ $-$ $b^n$$ = (a-b)N$ ?  I also see that $6^n$ $- 5n + 4$ is divisible by $5$ which is $6-5+4$ and $7^n$$+3n + 8$ is divisible by $9$ which is $7+3+8=18=9\cdot2$.  Are they just a coincidence or is there a theory behind?  Is it about modular arithmetic? What is a predicate in c#? How can I sort a string of text followed by a number using LINQ Why do you have to use copy_to_user()/copy_from_user() to access user space from the kernel? Addons: Only some .zips will install Why is it that if I go to install an add-on from User Preferences > Add-ons > Install from File... and choose a *.ZIP, some add-ons will install, while others will return me to the User Preferences with nothing having happened (as far as I can tell)?  Is there a specific file structure required in the .ZIP? I get many add-ons from GitHub, using the Download Zip button, and even there installation of the actual Zip file only works some of the time. I was wondering about the reason of the choose of the X as symbol used to represents the "Close application" operation.