Assume that $f$ is a given real-valued continuous function over $\mathbb{R}$. How to construct an entire function $F$ such that $F(z)$ is real-valued when $z\in \mathbb{R}$ and there exists a real number $a$ such that $f(z)&lt;F(z)$ for all $z&gt;a,z\in \mathbb{R}$.
Does there exist a continuous function $\: f : \mathbf{R} \to \mathbf{R} \:$ such that for   all  functions $\: g : \mathbf{R} \to \mathbf{R} \:$, for all real numbers $x$,  there exists a real number $y$ such that $\: x &lt; y \:$ and $\: g(y) &lt; f(y) \:$?
If $(Tx \mathbin{|} x) = 0$ for all $x$ then $T = 0$ Let $T$ be a linear operator on an inner product vector space $V$. I'd like to prove that if $$(Tx|x)=0 \quad \forall x \in V$$ then $T$ is the null operator. I can't figure out this proof using contradiction, do I have to choose an appropriate vector? How can I set the processor affinity of a process on Linux? How can I set the processor affinity of a process on Linux? What is the sum of $$\sum_{n=0}^{\infty}\frac{1}{2^n(n+1)}$$    I've spent an insane amount of time on this problem. I checked on Wolfram and it gives $ln(4)$, which I assume you get from $2\ln(2)$.   I know that the integral of $\frac{1}{n+1}$ is $\ln(n+1)$. What am I missing?  Thank you! I will be getting a point-and-shoot camera for taking portraits and only portraits.  Specifically portraits with a shallow depth of field.   Groups portraits sometimes.  It's just too much work to add lens blur at post-prod.  I understand that setting a P&amp;S on macro mode gives a shallow focus and DOF.    How do I read P&amp;S camera specs to shortlist those with the shallowest depth of field?   Added: By point-and-shoot, I mean a camera that is easy to use -- Not necessarily compact, inexpensive, or current.  Also, if there are two or three factors/specs to get a shallow depth of field, then which spec contributes the most to bokeh? which is second most contributing? the third, etc.? In an ideal circuit, How can there be a current b/w points a &amp; b, when there is no potential difference and thus no electric field between a &amp; b? If there is no current, then where does current across the resistor come from, because that means no charge is coming from the battery (?). How do I select all the columns in a table that only contain NULL values for all the rows?  I'm using MS SQL Server 2005.  I'm trying to find out which columns are not used in the table so I can delete them. I'm robotic engineer. I'm using OpenSCAD to model robotic components (gears, pulleys, parts, etc). But I need application to model physics and interaction of the components (for i.e. how will robot move if I will rotate current gear).  So, is it possible to import OpenSCAD models into Blender and model interactions in it?  I have models in STL format (for i.e. gears). I need to make reductor from it and see how it moves (if possible - measure rotation speed and torque). Proof that no polynomial with integer coefficients can only produce primes Doing a discrete math review and am trying to solve problem 1.6 in the text found here:  - I believe I've gotten parts (a) and (b) correctly, but (c) is a bit tricky for me. Would appreciate a review of a/b and a hint for c if possible. Restatement here:  For n = 40, the value of polynomial $p(n)::=n^2 + n + 41$ is not prime, as noted in Section 1.1. But we could have predicted based on general principles that no nonconstant polynomial can generate only prime numbers.  In particular, let $q(n)$ be a polynomial with integer coefﬁcients, and let $c::=q(0)$ be the constant term of q.  (a) Verify that $q(cm)$ is a multiple of c for all $m \in Z$  Proof: Since q is a polynomial, it will be of the form: $q(x) = a_nx^n+a_{n-1}x^{n-1} + ... + a_1x + c$  If $x = cm$, then notice that cm will be inside every term of the polynomial, and since the final term is c, c can be factored out of every term. Hence, q(cm) is a multiple of c for all $m \in Z$.  b) Show that if q is nonconstant and c > 1, then as n ranges over the nonnegative integers, $N$, there are infinitely many $q(n) \in Z$ that are not primes.  Proof: Continuing from the result found in (a), it is easy to see that for all $m \in Z$, there will be an infinite number of multiples of c that will be generated by q. Since c > 1, these multiples are guaranteed not to be prime.  c) Conclude that for every nonconstant polynomial, q, there must be an $n \in N$ such that $q(n)$ is not prime. Hint: Only one easy case remains.  c = 0 is trivially easy to prove using the (b) above.  I assume the "easy" case is referring to c = 1, but in this case I'm not sure how to continue, since the result of (a) and (b) don't apply: I can't use them since adding 1 to any even number may make it prime. If the result of the terms not including c is odd, then adding 1 to that result makes it even and it is not prime. However, if the terms add up to an even number, I don't see a way of using the knowledge I have so far to prove conclusively that that number + 1 will NOT in fact be prime. Down Arrow Key is not working Does anyone know of a simple Image Editor, with functionality comparable to ,  for Ubuntu?  I've always found GIMP to be overkill and too complicated for what I want to do. Using Elseif Conditional Statement in QGIS Field Calculator? Relating the union of the power set of a set to the set itself Check whether an array is a subset of another Any idea on how to check whether that list is a subset of another?  Specifically, I have  List&lt;double&gt; t1 = new List&lt;double&gt; { 1, 3, 5 }; List&lt;double&gt; t2 = new List&lt;double&gt; { 1, 5 };   How to check that t2 is a subset of t1, using LINQ? Converting from 7-speed to 10-speed rear wheel My Bridgestone MB-5 currently has a 7-speed rear wheel. I'd like to convert it to a 10-speed. Is this possible? Is it practical? I'm trying to identify a novel about an alien race coming to Earth. They are rabbit-like.    I thought it was Niven or Pournell but I cannot remember the title.  It was Quotzal or something like that. How to Create a Vinyl Plastic Toy Shader? How can I make one of the vinyl toy plastic material like this?    Video: I am on SharePoint 2013 and do not have access to Designer, as a preface.  I am trying to create a list view that filters items by whether or not they were added in the last hour.  I had done this earlier, only with items that were added in the current week, by creating two columns, 'Week Start' and 'Week End', and filtering by Created falling between those two.  Simple enough.  However, filtering list views does not allow for complex functions, nor does the [Today] function recognize time, causing an issue.  Is there any workaround for this?  Thanks. What are valid values for the id attribute in HTML? When creating the id attributes for HTML elements, what rules are there for the value? I solved the Lagrangian of a simple pendulum (with help from online examples as this concept is new to me) and ended with the following: $$\ddot{\theta}+\omega^2\theta=0$$ But in the example I was following, the next line written was this: $$\theta(t) = A\cdot\sin(\omega t + \Phi)$$ And I don't know what steps they took to get there? Is there a way to follow a particular person (or List&lt;Person&gt;) easily? Some people answer the questions in a very educative way, and I don't want to miss them.