Show $|f(z)| \leq \frac{2A|z|}{1 - |z|}$
Prove inequality using Schwarz's Lemma
Should I sign, watermark or otherwise label a framed print? And if so how? In what cases does the gerund stemming from a transitive verb take the direct object of that verb and when is a prepositional complement used?  For example:    Brown's deft painting of his daughter is a delight to watch (it is a delight to watch while Brown deftly paints his daughter). Painting his daughter is an outlet for his energy. Securing safety for prisoners is the main problem for the penitentiary system. The widely discussed problem of the securing of prisoners' safety was given priority. What does "All things X" mean? The PS4 is now released in the EU, but due to shipment shortages is not available for sale unless pre-ordered a long time ago. Luckily, it seems as though Dualshock 4 controllers are availble for sale in a number of shops already.  I've long decided to buy the PS4 as well as a second Dualshock 4 controller, so I've been considering buying the "second" controller now in order to replace my old Xbox 360 controller, whose D-Pad is useless and whose RB button no longer responds correctly. But before I buy the Dualshock 4 early, I wanted to know how well my PC will support it.  I already know that , but what exactly does work, and what doesn't?  Can I expect the same key-mapping on the PC as on a PS4?  Basically, can I replace my Xbox 360 controller with a Dualshock 4 and still play games like Batman Arkham Asylum/City/Origins as if I were using the old Xbox 360 controller? Is there ever a case where you would want to accept an answer, but not upvote it?  I can't think of a single situation where this would be the case.. So would it not make sense to have the "Accept" button upvote the answer too? When I start a sentence with words like "someone" or "somebody", I don't know how to choose the right pronoun at the end of the sentence.  Examples:      If anybody asks you about the money, tell (Him - Her - It - Them) that it is in my bank account.     I felt that somebody was in the garden but I did not see (Him - Her - It - Them).     Speaker 1: A friend of mine helped me a lot.      Speaker 2: You should thank (Him - Her - It - Them).     Congratulations on your new baby! What's (His - Her - Its - Their) name?    Those are the cases or situations that I can think of. If you have any other different situations, please let me know. I would like to search an entire MS SQL 2000 database for one value. This would be to aid development only. Keep that in mind when considering this question.   This will get all the table names and the column of the data type I'm looking for:  SELECT Columns.COLUMN_NAME, tables.TABLE_NAME FROM INFORMATION_SCHEMA.Columns as Columns  JOIN INFORMATION_SCHEMA.TABLES as tables  On Columns.TABLE_NAME = tables.TABLE_NAME WHERE Columns.DATA_TYPE = 'INT'     I was thinking something like this:  -- Vars DECLARE @COUNTER INT DECLARE @TOTAL INT DECLARE @TABLE CHAR(128) DECLARE @COLUMN CHAR(128) DECLARE @COLUMNTYPE CHAR(128) DECLARE @COLUMNVALUE INT  -- What we are looking for SET @COLUMNTYPE = 'INT' SET @COLUMNVALUE = 3 SET @COUNTER = 0  -- Find out how many possible columns exist SELECT @TOTAL = COUNT(*)   FROM INFORMATION_SCHEMA.Columns as Columns  JOIN INFORMATION_SCHEMA.TABLES as tables  On Columns.TABLE_NAME = tables.TABLE_NAME WHERE Columns.DATA_TYPE = @COLUMNTYPE PRINT CAST(@TOTAL AS CHAR) + 'possible columns' WHILE @COUNTER &lt; @TOTAL BEGIN     SET @COUNTER = @COUNTER +1     -- ADD MAGIC HERE END   Any ideas?  UPDATE I recently found this  that works quite well. What am I doing when I separate the variables of a differential equation? I see an equation like this:  $$y\frac{\textrm{d}y}{\textrm{d}x} = e^x$$  and solve it by "separating variables" like this:  $$y\textrm{d}y = e^x\textrm{d}x$$ $$\int y\textrm{d}y = \int e^x\textrm{d}x$$ $$y^2/2  = e^x + c$$  What am I doing when I solve an equation this way?  Because $\textrm{d}y/\textrm{d}x$ actually means  $$\lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x}$$  they are not really separate entities I can multiply around algebraically.    I can check the solution when I'm done this procedure, and I've never run into problems with it.  Nonetheless, what is the justification behind it?  What I thought of to do in this particular case is write  $$\int y \frac{\textrm{d}y}{\textrm{d}x}\textrm{d}x = \int e^x\textrm{d}x$$ $$\int \frac{\textrm{d}}{\textrm{d}x}(y^2/2)\textrm{d}x = e^x + c$$  then by the fundamental theorem of calculus  $$y^2/2 = e^x + c$$  Is this correct?  Will such a procedure work every time I can find a way to separate variables? Manually clear saved question drafts I've seen lately that new question editing is stored somewhere for later use if we wander off the new question without posting it and then return back to the page. Which is a good functionality addition in it's own right.  What I'd like to also have is the Discard this draft functionality that would clear form data and forget it. Somehow we find an answer in the meantime and the question isn't valid any more.  So having a Discard saved draft or something similar would be a nice contra-functionality to auto-save to remove stored data. The way it's implemented now seems too hidden hidden and unpredictable to users.  Additional edit  When adding hidden auto functionality usually means creating the opposite as well by either giving the possibility to preference of not having automatism at all or giving the possibility to clear what's been auto saved.  Let's see how GMail doesn't work (and I think we all agree that from UX perspective it does the job as expected:   User clicks Compose message User starts writing a new email message User decides to not send the message and checks their inbox User clicks Compose message again A clean form is presented to user (old one being part of drafts)   I'm not suggesting we should have something like Saved drafts but we surely should have the possibility to clear previous question draft.  Since this new functionality was introduced I should point out that I would use the discard functionality more frequently than the saved one. I do welcome saving messages, but discarding of saved drafts is anything but a rare situation one might want to do. It wouldn't be a problem if this was a 1% against 99%. To me it's more like 50/50.  Best possible solution  When providing saved drafts there should (from the UX perspective) be the opposite functionality as well. Namely discarding of it. But first thing we should be asking ourselves is:    do users more frequently need pre-filled saved question draft or do users more frequently need empty form with the possibility to populate it with a saved draft   User testing should provide the usage frequency between the two and the one that's more likely to happen (my guess is that there would be a big difference between the two) should be implemented. So one of these:   Pre-populate question fields with saved draft on question form load, while also providing a button to clear the draft and start writing anew without the need to manually clear all the fields (which would be the optimal solution in case of a single field form) Question form should always load empty while also having a button that would pre-populate it with a saved draft.   I think this would be the best consensus related to saved question drafts and their usage. But as we've seen this issue has been swept under the rug for an indefinite time. Seasonal Loan Amortization How do I use multirow in LaTeX? There is a remote Windows server on a private network which I can connect to via Remote Desktop Connection.  I would like to be able to make TCP/IP connections from my computer to other computers on that server's network.  Remote Desktop Connection makes it possible to share printers, drives, and other local resources through the connection.  Is there any way to "tunnel" a TCP/IP connection via RDC?  I'd like something similar to the port-forwarding provided by SSH.  I don't see any way to do this via RDC, but I'm hoping the capability is there and I just don't know about it. Could anyone provide an example of a nonempty subset $U$ of $R^2$ such that $U$ is closed under scalar multiplication, but $U$ is not a subspace of $R^2$ Lazy Eye in Infants, Preparations for Seeing a Specialist My youngest (14 months) has started showing signs of either strabismus or ambylopia (both commonly referred to as "lazy eye", where one eye seems to track differently than the other when the child is tired or isn't focusing).  We're going to see an ophthalmologist once the pediatrician weighs in and recommends one, and I'm interested in suggestions for what I should look for in an ophthalmologist, and in what we should do to prepare for the visit.  Particularly, how important is it that we find one that specifically mentions these conditions as things they specialize in?  They're fairly common conditions (affecting over 4% of children), so I would expect most pediatric ophthalmologists to have as one of their main purposes helping to diagnose and treat lazy eyes; but many do not mention them in their list of specializations.    And, in terms of preparation, do we need to keep track of time or length of lazy eye bouts?  Should we take any videos?  Our pediatrician hasn't noticed this in her periodic checks, but I suspect that he's more focused during these visits (a person he's not that used to, who is talking a lot to him).  I worry the ophthalmologist will have the same problem - not be able to diagnose because of lack of presentation during the visit. Edit:  I foolishly changed my example right before posting this. The following is what I meant to ask.  On the wikipedia page below, it says "a non-zero non-unit element in an integral domain is said to be irreducible if it is not a product of two non-units."   Then, on the wikipedia page below, it says "an irreducible polynomial is, roughly speaking, a non-constant polynomial that cannot be factored into the product of two non-constant polynomials."   The page then gives an example of a polynomial that is irreducible "over the rationals" (I assume it is implied that "the integers" is referring to the ring of polynomials over the field of rationals, right?)  $p(x) = x^2 + 2 = (x+\sqrt{2})(x-\sqrt{2})$  On the Wofram page below, it says "the irreducible polynomials are examples of irreducible elements."   If irreducible polynomials are a subset of irreducible elements, how is $x+\sqrt{2}$ a unit?  What can it be multiplied by to equal the multiplicative identity?  I think I have it right this time (sorry. long day)  ====================================================================  The following is the original post (for those who already responded and those looking at the corresponding responses)  On the wikipedia page below, it says "a non-zero non-unit element in an integral domain is said to be irreducible if it is not a product of two non-units."   Then, on the wikipedia page below, it says "an irreducible polynomial is, roughly speaking, a non-constant polynomial that cannot be factored into the product of two non-constant polynomials."   The page then gives an example of a polynomial that is reducible "over the integers" (I assume it is implied that "the integers" is referring to some sort of ring, right? due to the claim below)  $p(x) = x^2 + 4x + 4 = (x+2)(x+2)$  On the Wofram page below, it says "the irreducible polynomials are examples of irreducible elements."   If irreducible polynomials are a subset of irreducible elements, how is $x+2$ a unit?  What can it be multiplied by to equal the multiplicative identity? What websites or other resources do users of Blender have available to them to report bugs or problems with the program?  I would like to get this issue cleared in Q&amp;A format so that we can link new users with bug-report-style questions to this post. Issues with win key and right alt key after Windows Update (Polish diacritical signs not working) In "Settings" > "SD card &amp; phone storage settings" under "Internal Phone Storage" it lists "Available Space" as 13.78MB.  I'm trying to install an app that is 2.38MB.  Why do I get the "Insufficient storage available" error message?  I clearly have enough space.  If it's relevant, my phone is an LG Optimus V. Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$? A famous exercise which one encounters while doing Complex Analysis (Residue theory) is to prove that the given integral: $$\int\limits_0^\infty \frac{\sin x} x \,\mathrm  dx = \frac \pi 2$$ Well, can anyone prove this without using Residue theory?  I actually thought of using the series representation of $\sin x$: $$\int\limits_0^\infty \frac{\sin x} x \, dx = \lim\limits_{n \to \infty} \int\limits_0^n \frac{1}{t} \left( t - \frac{t^3}{3!} + \frac{t^5}{5!} + \cdots \right) \,\mathrm  dt$$ but I don't see how $\pi$ comes here, since we need the answer to be equal to $\dfrac{\pi}{2}$. What does the term saturating nonlinearities mean? I was reading the paper  and in section 3 were they explain the architecture of their Convolutional Neural Network they explain how they preferred using:     non-saturating nonlinearity $f(x) = max(0, x). $   because it was faster to train. In that paper they seem to refer to saturating nonlinearities as the more traditional functions used in CNNs, the sigmoid and the hyperbolic tangent functions (i.e. $f(x) = tanh(x)$ and $f(x) = \frac{1}{1 + e^{-x}} = (1 + e^{-x})^{-1}$ as saturating).   Why do they refer to these functions as "saturating" or "non-saturating"? In what sense are these function "saturating" or "non-saturating"? What do those terms mean in the context of convolutional neural networks? Are they used in other areas of machine learning (and statistics)?