Show that if $f_1(x_1), f_2(x_2)$ are convex functions then , $(f_1of_2)(x)=\inf \{f_1(x)+f_2(x):x=x_1+x_2\}$ is convex function The definition of a convex function  f is that $$f((1-t)x+ty)\le (1-t)f(x)+tf(y)\tag{1}$$ for all vectors $x,y\in \mathbb{R}^n,t \in [0,1]$ so, $(f_1of_2)((1-t)x+ty)=(f_1of_2)\{((1-t)x_1+ty_1)+((1-t)x_2+ty_2)\}$ $=\inf\{((1-t)x_1+ty_1)+((1-t)x_2+ty_2):x=x_1+x_2,y=y_1+y_2\}$ I am just stuck weather I can use Infimum properties or not someone can help ?
Show that f(x) = inf{g(x1)+h(x2)} is convex subject to x1+x2=x and where g(.) and h(.) are convex functions.  Can I just go about this by using the regular definition of a convex function or which properties should I use? I know that the sum of convex functions is convex, but the infimum part confuses me. Thank you
Convergence to a Uniform Distribution $\newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor} $  Show that if $P(X_n = i/n)=1/n$ for every $i = 1,...,n$, then $X_n$ converges in distribution to a uniformly distributed random variable $X$.  Convergence in distribution is defined as   $$P(X_n \leq x) \rightarrow P(X \leq x)$$  and I have that a uniform distribution with parameters $a$ and $b$ implies that  $$P(X \leq x) = \frac{x-a}{b-a}$$  I cannot go any further however. I feel like I don't know anything about $X_n$ - I don't even know if it is continuous or discrete. What I can just say is that   $$P(X_n \leq x) = \sum_{i=1}^\floor{x} \frac{1}{n}$$  where $\floor{x}$  means rounding $x$ to the closest lower integer. Convert a string to an enum in C# What's the best way to convert a string to an enumeration value in C#? I have an HTML select tag containing the values of an enumeration. When the page is posted, I want to pick up the value (which will be in the form of a string) and convert it to the corresponding enumeration value. In an ideal world, I could do something like this: StatusEnum MyStatus = StatusEnum.Parse(&quot;Active&quot;);  but that isn't a valid code. Fly and Two Trains Riddle Background: I am currently employed by a start-up that, so far, is doing really well. As part of my contract, I have stock options that will come available on a typical vesting schedule. A quarter of my options are set to vest later this year. Also, the company is not public yet, and it may be several years before it is public / I could sell my shares of the company.  My question is, is there any reason I should exercise them as soon as they vest? As far as I know they don't expire as long as I work at my company (if I leave for any reason, then I only have 3 months to exercise).  I don't foresee leaving any-time soon, and if I did, I would have 3 months to make a final decision.  Is there any disadvantage to just letting the option stay an option for a while? Does Thanos' plan apply to higher order beings? We know that Thanos' plan was to       instantly destroy half of all life in the universe    His plan doesn't appear to apply to lower or non sentient life forms      if it did half the trees in the final Wakanda scene would have disintegrated too   Does his plan apply to all beings more powerful than himself? how to get full path from fileupload using Javascript Suppose I have some large datafile, which overflow the screen in both vertical and horizontal direction. How can I browse this file, while the header-lines stay on the screen?  For the moment, I am using less -S, so that I can nicely scroll my file horizontally and vertically. However, when scrolling down, the header lines obviously disappear. Is there a way to keep these using less?  An alternative is using vim in split-screen mode with :set nowrap. However, now if I scroll horizontally, the top window doesn't scroll in the same way (:windo set scrollbind only works for vertical scrolling as far as I know). I need a regular expression to select all the text between two outer brackets.  Example: some text(text here(possible text)text(possible text(more text)))end text  Result: (text here(possible text)text(possible text(more text))) Wi-Fi only works after waking MacBookPro7,1 from sleep Been having some issues with the STA drivers from bcrmwl-kernel-source. While the drivers do function, they only seem to function after putting the laptop to sleep, by either closing the lid, or manually putting it to sleep, and waking it up. The laptop here is a MacBookPro7,1 (Mid 2010 13-inch MacBook Pro), running Ubuntu 17.04.  While the issue isn't bad enough to deter me from using the laptop, it is not an elegant solution, and I believe that there can be a solution found somewhere.  For reference, here are the outputs from the Wireless Info script for both before and after: , . Hopefully these are of some use. If you need additional information about the computer, I will be happy to answer. In linguistics, is there a term describing this phenomenon, i.e., when the syllables of two words are slurred together in the spoken language?  They are not contractions. While contractions are acceptable in any register, this combination of words is very informal and hardly ever found in formal writing.  kinda (kind of)   sorta (sort of)   coulda (could have)   shoulda (should have)   lotta (lot of)   oughta (ought to)   betcha (bet you)   lemme (let me)   tseasy (it's easy)   willya (will you)  Inasmuch as English Language speakers (just like the speakers of any natural language) have a tendency to join word sounds in speech, examples abound and a complete list would be hard to produce. I’m looking for a word or phrase describing this linguistic phenomenon as it occurs in speech. I've bunch of folders in folder A. I want to move files from all those folders to A.  Or  I want to cut all files from child folders and paste them in parent folder.  How to do that? I know from reading about the gravitational waves detected by Ligo, that when an object has angular acceleration, it produces gravitational waves.  I'm wondering if an object creates gravitational waves when only accelerating in one direction, however?   I'm also curious as to how the nature of the waves would differ in this case. Show $R \setminus S$ is a union of prime ideals I'm stuck on the following question:     Let $R$ be a commutative ring with $1$, and $S \subseteq R$ a saturated multiplicative set (that is, $1 \in S$ and $x, y \in S$ if and only if $xy \in S$).  Show that $R \setminus S$ is a union of prime ideals.     Here's my attempt so far.  If $a \in R \setminus S$, then the ideal $Ra$ does not intersect $S$, because if $ra$ were in $S$ for some $r \in R$, then $a$ would have to be in $S$.  Thus, it follows by Zorn's lemma that there exist ideals $I$ of $R$ which are maximal with respect to the property that $I \cap S = \emptyset$.  Let $I$ be any such ideal.  If I can show that $I$ is prime, the conclusion will follow.  Let $xy \in I$.  I want to show that $x$ or $y$ is in $I$.  Suppose $x \not\in I$.  Then $I + Rx$ intersects $S$, so there exists $s \in S, a \in I, r \in R$ such that $s = a + rx$.  Then $sy = ay + rxy \in I$, so $sy$, and hence $y$, cannot be in $S$.  Similarly if $y$ is not in $I$, then $x \not\in S$.  So we are reduced to proving the following is impossible: $xy \in I$, $x$ and $y$ are not in $S$, but they aren't in $I$ either. dd aplied to dev USB before connect corrupt /dev/sdX and dont work I have a USB where I'm coping an ISO of 5 Mb aprox with a small OS with its own grub. If I connect the device and check it sudo fdisk -l I get:  ... Device     Boot Start   End Sectors  Size Id Type /dev/sdb1  *        1  9551    9551  4.7M cd unknown   If I copy with dd the ISO sudo dd if=my_os.iso of=/dev/sdb   14852+0 records in 14852+0 records out 7604224 bytes (7.6 MB) copied, 0.538487 s, 14.1 MB/s   It works perfectly. An boot from BIOS in other PC.  The problem is, sometime I forget to connect the USB after update the BIOS, so I do ff WITHOUT the USB connected,  the output is:  14852+0 records in 14852+0 records out 7604224 bytes (7.6 MB) copied, 0.00987684 s, 770 MB/s   Now, the /dev/sdb register is corrupted, the copy speed (770 MB/s) have no sense, and cannot user again dd until reboot.  I have tried to repair it with ddrescue and it doesn't work  sudo ddrescue /dev/zero /dev/sdb conv=noerror,sync   My question is, what is happening exactly and if is possible, how to repair /dev/sdb to avoid reboot and dd start working again?  Thanks. How does "curved space" explain gravitational attraction? They say that gravity is technically not a real force and that it's caused by objects traveling a straight path through curved space, and that space becomes curved by mass, giving the illusion of a force of gravity.  That makes perfect sense for planetary orbits, but a lot less sense for the expression of gravity that we are the most familiar with in our day-to-day lives: "what goes up must come down."  Imagine that I hold a ball in my hand, several feet off the ground, with my fingers curled around it, and my hand is above the ball.  Then I open my fingers, releasing my grip on it, being very careful to not impart any momentum to the ball from my hand as I do so.  An object at rest remains at rest unless acted upon by an outside force.  If the ball is not moving (relative to my inertial reference frame), it has no path to travel that's any different from the Earth's path through space.  It should remain at rest, hanging there in the air.  And yet it falls, demonstrating that an outside force (gravity) did indeed act upon it.  How does curved space explain this? Make all footnotes numbered subsequently, but one with a symbol The Density of Clouds What is the difference between re.search and re.match? What is the difference between the search() and match() functions in the ?  I've read the  (), but I never seem to remember it.  I keep having to look it up and re-learn it.  I'm hoping that someone will answer it clearly with examples so that (perhaps) it will stick in my head.  Or at least I'll have a better place to return with my question and it will take less time to re-learn it. Excel text alignment with custom formatting Is there anything in a custom formatted formula which defines the text alignment?  I know the different parts of the formula is numbers, negative numbers and so on, but I need to set the alignment.  Example:  _*# ##0_;_*(# ##0)_;_*"-"??_;_@_ Here is my script:  #!/bin/bash  echo "Digite o local em que deseja instalar o IGRAFU(pressione enter para  instalar em  ${HOME}/IGRAFO):" read caminho if test -z $caminho then caminho="${HOME}/IGRAFO" fi echo "O IGRAFU será instalado no diretório: $caminho" mkdir -pv $caminho  mv -v ./* $caminho echo "Pronto!"   At 'read caminho' I may receive from the user a path like ~/somefolder. When the script receives that kind of path both mv and mkdir won't make tilde expansion, so it will try to create a ~/somefolder and not /home/username/somefolder and therefore fail.  How do I ensure that the tilde will be converted into the HOME variable?