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WinError 32 error when trying to delete shapefiles with QGIS python How to elegantly ignore some return values of a MATLAB function How can I add a "C" wire to my thermostat? I've got some lenses of brand X, but I've just got a new camera of brand Y. How can I tell if it's possible to use my lenses on my camera? I accept that I may lose a lot of automatic functionality like autofocus, aperture control and metering when using an adapter to connect the two. Let $f: \Bbb R \to \Bbb R$ be a differentiable function such that $\sup_{x \in \Bbb R}|f'(x)| \lt \infty$. Then (UGC CSIR-2015, DECEMEMBER, MATHEMATICAL SCIENCES)        $f$ maps a bounded sequence to a bounded sequence.   $f$ maps a Cauchy sequence to a Cauchy sequence.   $f$ maps a convergent sequence to a convergent sequence.   $f$ is uniformly continuous.      I choose all of the options as possible answers because the condition $\sup_{x\in \Bbb R}|f'(x)| \lt \infty$ forces $f$ to be uniformly continuous.(Because $f$ becomes Lipschitz and Lipschitz condition implies uniform continuity)  i.e. $\frac {|f(x)-f(y)|}{|x-y|} \le \sup_{x\in \Bbb R}|f'(x)|$ $ \forall x,y$.  Hence all other options are bound to be true.  Am I correct? Is there a quick way to set an HTML text input (&lt;input type=text /&gt;) to only allow numeric keystrokes (plus '.')? I want to write a survey on one emerging research topic in wireless communications (It can be applied to any field!). There are almost 500 papers on this topic as published or in early access. And the publishing rate in this topic is increasing day by day. So, I want to write a survey on this topic keeping in mind that it will get high citation and it will help new scholar who are in struggle with this topic. I found only one survey written by some reputed authors, however it lacks in many ways, like detailed information related to particular direction, it just assembles the papers in a good manner. I want to pick some directions and discuss  important approaches with good connection between them. However, I find it very difficult to proceed with large number of papers. Is there any good way to handle the survey process in a good efficient and quick way? PS. According to me, many people have already started to write this. Is is true &lt;h1&gt; tag should not have more than 1 on every page for SEO?   Every pages on the header, it includes and &lt;h1&gt; tag. Website Name which show an image from logo class, like this:  &lt;div id="header"&gt;   &lt;h1 class="logo"&gt;      &lt;a href="#"&gt;Website Name&lt;/a&gt;   &lt;/h1&gt; &lt;/div&gt;   and I also include &lt;h1&gt; on the contact page, help, etc and article page for example:  &lt;h1&gt;Contact Us&lt;/h1&gt; &lt;h1&gt;Name of the Article Title here&lt;/h1&gt;   On the homepage, it just has one &lt;h1&gt; for the logo Site Name... other pages have 2 &lt;h1&gt; tags Can any one help me with this?  Determine all integer triples $(x,y,z)$ such that $1 ≤ x ≤ y ≤ z$ and $x + y + z + xy + yz + xz = xyz − 1$.  I thought of Vieta's formula but don't let me lead you into a dead end. Any option for mysqldump to ignore databases for backup? Best practices for Feed restructuring in a social app database Pluralizing Noun Phrase? Why do only two sexes exist for animals? Is the word "data" now considered singular? If so, what about "datum"? Use property to show that if $f_n \rightarrow f$ in measure on finite measure set $E$ then $f_n^2 \rightarrow f^2$ in measure on $E$. Consider the following problem:     Let $E$ have finite measure, $\{f_n\} \rightarrow f$ in measure on $E$ and $g$ be a measurable function on $E$ that is finite almost everywhere. Use the fact that $\{f_n \cdot g\} \rightarrow f_n \cdot g$ to prove that $\{f_n^2 \} \rightarrow f^2$ in measure on $E$. Infer from this that if $\{g_n\} \rightarrow g$ in measure on $E$ then $\{f_n \cdot g_n \} \rightarrow f \cdot g$ in measure on $E$.   I'm struggling understand how I can apply the fact that $\{f_n \cdot g\} \rightarrow f_n \cdot g$ in measure to prove that $\{f_n^2 \} \rightarrow f^2$ in measure. I've been able to come up with a proof of the fact that if $\{g_n\} \rightarrow g$ in measure then $\{f_n \cdot g_n \} \rightarrow f \cdot g$ in measure, and this clearly implies the claim that $\{f_n^2 \} \rightarrow f^2$ in measure. Unfortunately my proof doesn't rely on the fact that $\{f_n \cdot g\} \rightarrow f_n \cdot g$ so it doesn't answer the problem since it explicitly asks us to prove it a certain way.  So far my best attempt to utilize the fact is as follows. Let $\eta &gt; 0$ then by triangle inequality and monotonicity of measure  \begin{align*}     \lim_{n\rightarrow \infty}\mu\left\{ \left|f_n^2 - f^2\right| &gt; \eta \right\} &amp;\leq \lim_{n\rightarrow \infty}\mu \left\{\left|f_n - f\right|\cdot \left|f_n\right| + \left|f_n - f\right| \cdot \left|f\right| &gt; \eta \right\} \\     &amp;\leq \lim_{n\rightarrow \infty}\mu\left\{\left|f_n - f\right|\cdot \left|f_n\right| &gt; \eta/2 \right\} + \lim_{n\rightarrow \infty}\mu\left\{\left|f_n - f\right| \cdot \left|f\right| &gt; \eta/2 \right\} \end{align*}  By the fact that $\{f_n \cdot f\} \rightarrow f \cdot f$ in measure \begin{equation*} \lim_{n\rightarrow \infty}\mu\left\{\left|f_n - f\right| \cdot \left|f\right| &gt; \eta/2 \right\} = \mu\left\{\left|f_n \cdot f - f\cdot f\right| &gt; \eta/2 \right\} = 0. \end{equation*} I don't see how to deal with the other limit without first proving the most general statement $\{f_n \cdot g_n \} \rightarrow f \cdot g$ in measure.   Any help or advice is greatly appreciated. GNOME 2 allows one to either save the session automatically or manually (i.e. save the session as it looks right now). This is a nice feature because it restores the various desktop states between logins (and system restarts):   which apps were open where (physically) on the desktop were they open what specific window sizes were these apps set to   Looking around, I can't find the feature in GNOME 3? Did I not look hard enough? I've done numerous WP sites, written my own plugins, run my own server, etc etc.  But I have not seen this before. I just installed a fresh 4.7.1 and installed the  and all its plugins.  When I went to add media files, I got:  Maximum upload file size: 2 KB.   I deactivated all plugins one by one...no dice. My PHP memory limit is set to 256MB for this installation via wp_config.php.  Googling the 2 KB limit turned up no results.   Anyone seen this before or know how to fix this limit? In my book, the following are described to be the steps that one must follow if he wishes to find the direction of static friction force acting on an object:  &quot;(1) Draw the F.B.D(free body diagram) of the object in question with respect to the other object on which it is kept. (2) Include the pseudo force also, if the contact surface is accelerating. (3) Decide the direction of the resultant force and resolve this force into two components; one along the surface of contact and the other along the normal to this surface. (4) The direction of static friction is opposite to the component of the result force along the contact surface.&quot;  Firstly, are these steps correct? Will I always obtain the correct answer by following these steps? Secondly, consider the following problem:  In questions like these, when I try to find the resultant force and then assign the direction to static friction, I find that my answer is incorrect! Are there some other steps to follow when I know that the object is definitely accelerating in one direction or another? Edit 1: I approached the above question by doing exactly what my book suggests; first, I identified all the forces acting on the smaller block, being the normal force applied by the block A and its weight mg downward. Adding these two forces, I get another force that actually acts on the body like so:  I wonder if I'm not supposed to take either of the contact forces into consideration when drawing the F.B.D to figure out the direction of static friction acting on the body. Also, are there other steps for finding the direction of kinetic friction? Edit 2: From Judge's answer, I have been able to figure out my mistake, it being that I completely missed step (3) and didn't resolve the resultant force into components! Sheesh. Sorry! Much thanks in advance! :) Regards. Where can I find information on German soldiers from World War I and World War II?   I am curious to find out about my ancestors' role in the wars, i.e. what rank they had, where they where fighting, with whom and anything else. Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$ Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$.   My approach:   Since $p$ is prime, it is of the form $6k+1$ or $6k-1$. Now if $p$ is of the form $6k-1$ then $(p+1)/2 = 3k$ which is not possible as $3|3k$.   So $p$ is of the form $6k+1$. Now $(p-1)/4 = 3k/2$ so $2\mid k$. So $p$ is of the form $12k+1$. But now, how to prove $k=1$?  Please help!