An abbreviation is a shorter form of a word (or a phrase). This need not be unique. Suppose that one abbreviation for Engineering is ENG. Hence, we would say that the abbreviation of Engineering is ENG. What would we call Engineering with respect to ENG? The &quot;abbreviated word&quot; does the job, but is there a more direct way of getting there? Say, the &quot;unabbreviated&quot;?
I can describe "IMHO" as an acronym for "in my humble opinion."  How can I describe the reverse processes of translating the acronym into the actual phrase?  That is to say, if "IMHO" is the acronym, what do we call "in my humble opinion"?
Is there a way to scale up the bevel object on one end of a curve, a little bit over each point?  I notice the vertex "weight" slider will tweak how much influence each vertex has on the others, is there something like this that can scale the bevel object up a little bit?  Preferably with the option to constrain X,Y,Z independently Is it acceptable to change the vid column of a term programmatically in the database? I need to move some terms from one vocabulary to another by retaining all their data: translations, aliases, and node references.  Is it acceptable to change its vid column value directly in the database? The terms don't have hierarchy relationships which needs to be handled. If $f:\mathbb R \to \mathbb R$ satisfies $f'(x) <L$ for some $L<1$, then $f$ has a unique fixed point Assume that $f: \mathbb{R} \rightarrow \mathbb{R}$  is differentiable.  If there exists an $L&lt;1$ such that for each $x \in \mathbb{R}$, $f'(x)&lt;L$, prove that there exists a unique point $x$ such that $f(x)=x$.  So far I have that where I fixed $a$ to be zero and came up with three cases to show existence for  $f(0) = 0$, $f(0) &lt; 0$, and $f(0) &gt; 0$  $f(0)=0$ was fairly trivial following from the mean value theorem but the other two cases I was only able to eliminate half of the possible fixed points by contradiction and I need help showing it explicitly.  Edit as to avoid confusion here is the work I have garnished so far:  From the mean value theorem it follows for some arbitrary $a,b \in \mathbb{R}$ and $a\neq b$ that there exists a point $c$ such that $a&lt;c&lt;b$ or $b&lt;c&lt;a$ then implies that $\frac{f(b)-f(a)}{b-a}=f'(c)$ and this is because it is differentiable on $\mathbb{R}$ and, by convention, is also continuous on $\mathbb{R}$ as well.  Then the result of $\dfrac{f(b)-f(a)}{b-a}=f'(c)$ then follows for $L&lt;1$ such that $\forall x \in \mathbb{R}$ means $f'(x)&lt;1$ from our hypothesis. Which then follows  (*) $\dfrac{f(b)-f(a)}{b-a}=f'(c)&lt;L&lt;1 \Rightarrow f(b)-f(a)&lt;L(b-a)&lt;b-a$  Now without loss of generality choose $a=0$ and let $b$ be some arbitrary value in $\mathbb{R}$ then there are three cases that need to be considered for the value of $f(a)$:  (i) $f(0) = 0$, (ii) $f(0) &lt; 0$, (iii) $f(0) &gt; 0$  (i) For $f(0)=0$   Then $0$ is a fixed point of point of $f(x)$ and it follows from (*) that if $f(0)=a=0$ then $f(b)-f(0)=f(b)&lt;Lb&lt;b$ which shows that $f(b)&lt;b$ thus shows that for any arbitrary value $b\in \mathbb{R}$ that no $f(b)=b$ thus shows that $0$ is the only fixed point if $f(0)=0$  (ii) For $f(0)&lt;0$  Suppose there exists a fixed point $d&gt;0$ then:  $\frac{f(d)-f(0)}{d}&lt;L&lt;1 \Rightarrow d-f(0)&lt; dL&lt;d \Rightarrow -f(0)&lt;d(L-1)&lt;0\Rightarrow 0&lt;-d(L-1)&lt;f(0)$ but this contradicts that $f(0)&lt;0$  thus no other fixed point exists if $d&gt;0$ when $f(0)&lt;0$  (iii) For $f(0)&gt;0$ My daughter is a US Citizen. We (parents)are also planning to permanently settle in US. We will go their as Permanent Resident,as per US Law. We have a house here in India worth Rs.2 Crores.  We want to sell it and take money with us. We have ordinary savings Bank account here in India.  My US Citizen Daughter is a Income Tax payer.  Now your advises are required as under:   What are the routes to take money from India to US and our tax liabilities Can I gift this whole amount to my US Citizen Daughter or what is the maximum limit of Gift amount.  What will be the tax liability on me and on my Daughter in case of Gift   Whether I have to show it in my Income Tax Return or in my Daughter's Tax Return. What US Income Tax Laws says. What will be the procedure to send money as Gift to my Daughter. Will the money will go directly from my Bank Act.to my Daughter's Bank Account. Will there will be wire transfer from bank to bank Can I send money through other money sender Certified Companies also.    Please advise. If there is something more on the subject to make me understand, please advise. Thanks, Nested roots sequence, how to prove it's monotone and bounded? Let $a\ge1$ and define the sequence $(x_n)$ recursively by: $$x_1 = \sqrt{a}$$ $$x_{n+1}= \sqrt{a+x_n}$$  Here's what I did:  Plugging in some values makes it seem as if the sequence is increasing. I first solve the equation $t=\sqrt{a+t}$, equivalently $t^2 -t -a =0$, to get an idea what's going on. The roots are $$t_{1,2}= \frac{1 \pm \sqrt{1+4a} }{2}.$$ Therefore, between the roots, that is for $$t\in \left( \frac{1 - \sqrt{1+4a} }{2}, \frac{1 + \sqrt{1+4a} }{2}\right)$$  we have $t^2-t-a \le 0 \iff t \le \sqrt{a+t}$. Here's my attempt at showing inductively that $$\forall n\in \mathbb{N}, \ x_n \le \frac{1 + \sqrt{1+4a} }{2}$$  For $n=1$, the statement is true (simple arithmetic). Suppose it's true for $n$. Consider  $$x_{n+1}= \sqrt{a+x_n}\le \sqrt{a+\frac{1 + \sqrt{1+4a} }{2}}=\frac{1 + \sqrt{1+4a} }{2},$$  because $\frac{1 + \sqrt{1+4a} }{2}$ satisfies $x=\sqrt{x+a}$.  So this establishes the sequence $(x_n)$ is bounded. Now, by induction again, I try to show it's monotonically increasing. The base case $x_1\le x_2$ is obvious. Assume (strong induction) $x_{n-1}\le x_n$ for all $n&gt;1$. But since we have $$x_1\le x_n \le \frac{1 + \sqrt{1+4a} }{2}, $$   then $x_n$ lies in the appropriate interval, so $x_n \le \sqrt{a+x_n}=x_{n+1}.$  Is this proof correct? Can the condition on $a$ be relaxed to $a&gt;0$? Maybe even small negative $a$? And could someone provide me with another proof of convergence of $x_n$? I absolutely hate this one! macOS Mojave won't install updates past 10.14.1 due to requirement for APFS formatting I have a MBP 2012 I upgraded from High Sierra to Mojave after it came out as GA. I don't recall if I was asked about upgrading to APFS when Id id that, but at this time the main volume is Mac OS Extended (Journaled).  My current About This Mac...version is Mojave 10.14.1 (18B75). Now, when updates are advertised from the App Store, I'm unable to upgrade because 10.14.3 is required.  No OS updates show in the App Store, and when I searched for the updaters (10.14.2 Combo, etc), I can't install because the installer reports "macOS 10.14.2 Update can't be installed on this disk. This Mac can only install macOS on APFS-formatted drives."  I tried the search results recommending to boot in Recovery Mode and use Disk Utility, but APFS is not available as a type.  I have good backups and I can reformat the boot volume if I need to, but I have not done this before. Should I get a 10.14.3 installer to do this and boot from an external drive? The only guies and message boards I've found just keep saying to install 10.14.3 (I can't) or convert the disk in Recovery Mode (APFS is not available as an option.)  Any known-good ways to get my 10.14.1 upgraded so I can keep getting App Store updates? If I'm given a complex number (say $9 + 4i$), how do I calculate its square root? undelete big files - mission impossible? I've accidentaly deleted outlook.pst (6.7GB) file, while there was only 400MB free space left on primary NTFS partition (winxp).  I've tried several recovery tools to get this file back. "Ontrack Easy Recovery Pro" found 0 pst files (complete scan mode), while "Recover My Files" in sector scan mode found 5 pst's, but 4 of them of sizes from 3 to 28 KB, while the 5th one - 1Gb.  I've managed to succesfuly recover 1Gb pst file, which was 1 year old copy (the one used after the latest windows reinstall).  Now, I'm frustrated and confused   Why 1 year old file was succesfuly recovered if there were only 400MB left on primary partition? Where's 6.7GB file gone? I did some reading (), and it seems that there's almost no probability to retrieve the file I'm looking for, but wait - none of recovery tools i've used found zero-sized pst file, moreover - if due to fragmentation a file might be corrupted - we could use scanpst.exe to fix some errors and survive with 10 or 100 emails missing - whatever. Could you please recommend some more sophisticated recovery tools for this particular task?   Appretiate your help - thanks in advance How do I craft command blocks? I went to my friends house, and he was playing Minecraft on the PC. He showed me a command block, but when I went home and opened Minecraft pocket edition, I went to the crafting table but I could not find any command blocks to craft.  What are command blocks and how do I craft them? How to install a QGIS plugin when offline? Due to various IT policies at my workplace, QGIS is installed on a machine that is not connected to the internet. I wish to install a couple of QGIS plugins on this system.  I have downloaded the required plugins from . How do I install them in QGIS? Did Dolores Umbridge Have Any Association with Voldemort (or Death Eaters) before His Return? I noticed that Dolores Umbridge was born during the first Wizarding War, so it's very likely she wasn't a Death Eater then (but she is pretty evil -- who knows?).  After that Voldemort was not around in a way that could affect many people, and most wouldn't know he was planning to rise again.  During that time, and up through Voldemort's return (in Goblet of Fire), did Umbridge have any connection with the Death Eaters or with Voldemort?  Was she doing what she did on her own, or was it because of an association with Voldemort or his allies? Removing duplicate strings from an array? How to avoid modifications during pg_dumpall Does Class need to implement IEnumerable to use Foreach This is in C#, I have a class that I am using from some else's DLL. It does not implement IEnumerable but has 2 methods that pass back a IEnumerator. Is there a way I can use a foreach loop on these. The class I am using is sealed. How to add chips from Material Components library to input field in android? I am trying to include a figure into LaTeX from a paper originally created using MS Word. I have already converted all the text/equations into LaTeX but I can't figure out how to get the figures over without re-drawing them using LaTeX code (which I do not want to do). The image is a plain box (like a tabular) one row by 7 columns with numbers inside each cell. Then I inserted arrows of varying length above and below the box (several short ones and one much longer).    I am trying to use the  package with the \includegraphics command.   I copied the figure (box and arrows) from my original article into a blank Word doc. The figure only takes up the first 4 or 5 lines of the blank document. I then selected/highlighted the image and printed the selection using 'PDFCreator'. This allowed me to save the image as a .eps file. I then copied and pasted the eps file into the folder where all my .tex files are saved.  When I compile the document using pdftexify there is a blank space where the image should be. In the console I get the following message when I compile the document:  [27] &lt;Fig3-eps-converted-to.pdf, id =105, 391.4625pt x 74.2774pt&gt; &lt;use Fig3-eps-converted-to.pdf&gt; Overfull \hbox 1.46153pt too wide) in paragraph at lines 511--516 []   My code looks like this:  \documentclass[12pt]{article}  \usepackage{graphicx} \usepackage{epstopdf} \begin{document}  %Text  \includegraphics{fig3.eps}  %text  \end{document}   I have read the sections on graphics in 'LaTeX: A Document Preparation System' and 'The Not So Short Introduction to LaTeX2e' but I still can't figure this out. Should I maybe use a PNG image since it is a pretty basic figure? Any advice on how to properly transfer images from a word doc to .eps format and/or how to get those .eps files into LaTeX properly would be a huge help. The use of imaginary and complex values comes up in many physics and engineering derivations. I have a question about that: Is the use of complex numbers simply to make the process of derivation easier, or is it an essential ingredient, without which it would be impossible to derive some results?   I can identify two different settings where the answer may be different:   It doesn't look like it is mandatory for results in Newtonian mechanics, General Relativity and classical electrodynamics. Can we say the same thing about quantum mechanics either way for sure?   Could this be a difference in quantum mechanics over the classical picture? Add the ability to lock a question against edits What is the function of "do" in this sentence? Why does US Robotics destroy Lanning's house? Shortly after the death of Dr. Lanning, Detective Spooner travels to the doctor's house to look for clues.  While he is searching the house a demolition bot (which had been programmed to demolish the house the next day) goes on a rampage and destroys the house with Detective Spooner in it.   The house is fully furnished and appears to be in good condition. Why would US Robotics want to destroy the house with everything in it? Why not sell the house and everything inside?