Just a simple issue, one element has to be center horizontally. So, margin:0px auto has been applied. It was centered but other rule to this element doesn't work properly. For example If top-bottom padding is applied,  bottom padding doesn't show any changes. I set height auto, doesn't work. But when I add overflow:hidden, it works. I think adding overflow:hidden isn't best idea in here. To my knowledge, overflow:hidden is used and has to be work in that condition, where element height is less than content and to hide rest of content which cannot be covered within height.    &lt;html&gt; &lt;head&gt; &lt;style&gt; *{   margin:0px;   padding:0px; } article{   width:100%;   background:red;   float:left;   margin-bottom:10px; } .section{   width:93%;   max-width:1400px;   padding:10px 0px;   margin:0px auto;   height:auto; } .section1{   width:93%;   max-width:1400px;   padding:10px 0px;   margin:0px auto;   overflow:hidden; } aside{   float:left;   width:48%;   background:yellow;   height:auto; } aside:first-of-type{   margin-right:10px; }  &lt;/style&gt; &lt;/head&gt; &lt;body&gt; &lt;article&gt;    &lt;!-- Adding overflow hidden --&gt;      &lt;section class="section1"&gt;      &lt;aside&gt;     This is date Section     &lt;/aside&gt;     &lt;aside&gt;     This is lang Section     &lt;/aside&gt;   &lt;/section&gt; &lt;/article&gt;  &lt;article&gt;    &lt;!-- Not addding overflow hidden --&gt;      &lt;section class="section"&gt;     &lt;aside&gt;     This is date Section     &lt;/aside&gt;     &lt;aside&gt;     This is lang Section     &lt;/aside&gt;   &lt;/section&gt; &lt;/article&gt;  &lt;/body&gt; &lt;/html&gt;
I have the age-old problem of a div wrapping a two-column layout. My sidebar is floated, so my container div fails to wrap the content and sidebar.  &lt;div id="container"&gt;   &lt;div id="content"&gt;&lt;/div&gt;   &lt;div id="sidebar"&gt;&lt;/div&gt; &lt;/div&gt;   There seem to be numerous methods of fixing the clear bug in Firefox:   &lt;br clear="all"/&gt; overflow:auto overflow:hidden   In my situation, the only one that seems to work correctly is the &lt;br clear="all"/&gt; solution, which is a little bit scruffy. overflow:auto gives me nasty scrollbars, and overflow:hidden must surely have side effects. Also, IE7 apparently shouldn't suffer from this problem due to its incorrect behaviour, but in my situation it's suffering the same as Firefox.  Which method currently available to us is the most robust?
I had the Facebook and Instagram apps installed on my iPhone (latest iOS). I deleted both apps and checked that there was no data from either app stored on iCloud (I went to Settings - iCloud - Manage storage and there was no mention of them storing anything on iCloud). Then I reinstalled Instagram, opened it, clicked on Login and the page still showed “Login as MYFACEBOOKNAME”.   How is this possible? How can I delete my FB login info once and for all on my iPhone? Let $f_n = \mathbb 1_{[-n,n]}$ for all $n \in \mathbb{N}$   Compute explicitly $f_n \star f_1$ for all $n \in \mathbb{N}$.  Show that $f_n \star f_1$ is the Fourier transform of $g_n = \frac{  \sin{(2\pi x)} \sin{(2 \pi nx)}}{\pi ^2 x^2}$  Show that $\| g_n \|_1 \to \infty$  Deduce that the Fourier transform is not surjective from $\mathcal{L}^1(\mathbb{R})$ to $C_0( \mathbb{R})$    Here, $C_0(\mathbb{R})$ is the space of continuous functions $f : \mathbb{R} \to \mathbb{R}$ that tends to $0$ at $-\infty$ and $+\infty$. I managed to compute 1) and proved 2). But I don't know how to prove 3). Moreover, I don't see how can 1), 2) and 3) prove 4). Can anyone help? How to sail downwind faster than the wind? Recently a  set a record for sailing a wind-powered land vehicle directly down wind, and a speed faster than wind speed. Wikipedia has a  talking about it, but it doesn't explain exactly how it works.  I can imagine some configurations, but I don't get how a system could be set up to push forward with a tailwind (when the cart is moving slower than the wind) and push forward with a head wind (when the cart is moving faster than the wind).  Could someone help explain how this is possible? Let $a,b,n$ be integers such that  $\gcd(a,n)=\gcd(b,n)=1$. How to show that $\gcd(ab,n)=1$?   In other words, how to show that if two integers $a$ and $b$ each have no non-trivial common divisor with and integer $n$, then their product does no have a non-trivial common divisor with $n$ either.     This is a problem that is an exercise in my course.   Intuitively it seems plausible and it is easy to check in specific cases but how to  give an actual proof is not obvious. Eevee - Light inside a bulb lamp not passing through glass Using Eevee, I'm trying to simulate a light bulb. I have a sphere with glass material and inside it, I have a Point light. But the light is not passing through the glass:  However, if I disable the sphere object, the light is working:   How to make the light inside a bulb lamp pass through glass (using Eevee)? Here my test project: Prove that a polynomial is irreducible or the field contains a $p$th root An exercise from Lang:  Let $k$ be a field. Let $n$ be a nonnegative integer. Consider the polynomial $x^{p^n}-a \in k[x]$. Assume that $\text{char}(k) = p &gt; 0$. Prove that either the polynomial $x^{p^n}-a$ is irreducible over the field $k$ or there exists a $b\in k$ such that $a = b^p$.  How to prove this statement? I am a little bit confused with this statement. So, say you are a wizard 15/warlock 2. You have the Lance of Lethargy invocation, which pushes an enemy you target with eldritch blast and hit back 10 feet. Say you put a demiplane entrance ~5 feet behind the enemy you target with it. When you hit, you throw the enemy in. Before all this, you had put a Glyph of Warding in there on one of the surfaces. What would be the limit to the trigger for this? Would it be forced to be touch or proximity, or could you base it off something like hostility towards the caster?      ... When you cast this spell, you inscribe a glyph that later unleashes a magical effect ... You decide what triggers the glyph when you cast the spell. For glyphs inscribed on a surface, the most typical triggers include touching or standing on the glyph, ... (PHB 245)   The key word here is "typical". Based on Google's definition, the informal definition of "typical" is     showing the characteristics expected of or popularly associated with a particular person, situation, or thing.   This means, if my assumption is true, that the triggers in the PHB are only the most common ones. Other than the one about being forcibly at maximum 10 feet in diameter in the PHB, I cannot see a limit. Though I probably should assume this would all be DM discretion, (and I know that I sound like a broken record here) but could the trigger be hostility toward the caster, or something else, like being a specific race, gender, from a specific place, etc., or would it be forced to being something from the PHB? Global hotkey in console application What is an "index out of range" exception, and how do I fix it? Reverse Cauchy Schwarz for integrals Let $f,g$ be two continuous positive functions over $[a,b]$ Let $m_1$ and $M_1$ be the minimum and maximum of $f$ Let $m_2$ and $M_2$ be the minimum and maximum of $g$ Prove that $$\sqrt{\int_a^bf^2 \int_a^b g^2}\leq \frac{1}{2}\left(\sqrt{\frac{M_1M_2}{m_1m_2}}+\sqrt{\frac{m_1m_2}{M_1M_2}}\right)\int_a^bfg$$  I can't make any significant progress on this one... Thanks for any hint. Why am I still getting a password prompt with ssh with public key authentication? I'm working from the URL I found here:    My ssh client is Ubuntu 64 bit 11.10 desktop and my server is Centos 6.2 64 bit. I have followed the directions. I still get a password prompt on ssh.  I'm not sure what to do next. Review filter appears to be broken When browsing questions for a given tag, a review indicator has recently started showing up that links to the open review tasks for that tag.  For example, this is what I see when viewing :    The number 187 in the screenshot above would link to    However, clicking on that often opens review tasks that do not have the tag in question.  For example, it opened the following on successive attempts:   (c)   (java)  It seems that the filters are broken.  A sample screenshot (note the mention of the filter on the review page): Minimum value of $\left(a+\frac{1}{b}\right)^2+\left(b+\frac{1}{c}\right)^2+\left(c+\frac{1}{a}\right)^2$ Given $a,b,c \in \mathbb{R^+}$ such that $a+b+c=12$   Find Minimum value of $$S=\left(a+\frac{1}{b}\right)^2+\left(b+\frac{1}{c}\right)^2+\left(c+\frac{1}{a}\right)^2$$  My Try: By Cauchy Schwarz Inequality we have  $$\left(a+\frac{1}{b}\right)+\left(b+\frac{1}{c}\right)+\left(c+\frac{1}{a}\right)\le \sqrt{3}\sqrt{S}$$  $\implies$  $$\sqrt{3S} \ge 12+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$$  Now by $AM \ge HM $ inequality we have  $$\frac{a+b+c}{3} \ge \frac{3}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}$$ $\implies$  $$\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \ge \frac{3}{4}$$  hence  $$\sqrt{3S} \ge 12+\frac{3}{4}=\frac{51}{4}$$  hence  $$3S \ge \frac{2601}{16}$$  so $$S \ge \frac{867}{16}$$  is this approach correct and any better approach please share. What constitutes protons? When I see pictures, I can't understand. Protons are made of quarks, but some say that they are made of 99% empty space. Also, in this illustration from Wikipedia, what's between the quarks? Copyright of a set of colors? I often see color combinations on webpages, images, posters, products etc. that harmonize really well. Am I allowed to use those colors in my own design?   This is solely about the colors. I will not use images, logos or shapes from that source, and my content is not related to the original color source. I am also far from any commercial aspect here. Image of Jacobson Radical is the Jacobson Radical I'm stuck on the following problem:      Let $R$ be a commutative ring with $1$, and suppose $R$ is semilocal with maximal ideals $\mathfrak m_1, ... , \mathfrak m_s$.  Let $\mathfrak a$ be an ideal of $R$. The problem is to show that under the usual surjection $\pi:R \rightarrow R/\mathfrak a$, the Jacobson radical of $R$ is sent to the Jacobson radical of $R/\mathfrak a$.   My attempt: suppose that $\mathfrak m_1, ... , \mathfrak m_t$ contain $\mathfrak a$, but $\mathfrak m_{t+1}, ... , \mathfrak m_s$ do not.  Then $Jac(R/\mathfrak a) = (\mathfrak m_1/ \mathfrak a) \cap \cdots \cap (\mathfrak m_t/ \mathfrak a)$.  Obviously $\pi Jac(R) \subseteq Jac(R/ \mathfrak a)$, and the converse inclusion is equivalent to the following claim: if $x \in \mathfrak m_1 \cap \cdots \cap \mathfrak m_t$, then there exists a $y \in \mathfrak m_1 \cap \cdots \cap \mathfrak m_s$ such that $x - y \in \mathfrak a$.    This should be some application of the Chinese remainder theorem, but I'm not seeing it.  All I have to go on is that there exist $m_i \in \mathfrak m_i$ ($t+1 \leq i \leq s$) with $m_i \not\in I$.  I also haven't found out a way to use the fact that $\mathfrak m_1 ,... , \mathfrak m_s$ are all the maximal ideals of $R$.  I was also thinking about looking at some explicit maps.  If we let $\Gamma$ be the composition $$\frac{(R/\mathfrak a)}{Jac(R/ \mathfrak a)} \xrightarrow{\cong} \frac{(R/\mathfrak a)}{(\mathfrak m_1/\mathfrak a)} \oplus \cdots \oplus \frac{(R/\mathfrak a)}{(\mathfrak m_t/\mathfrak a)} \xrightarrow{\cong} R/\mathfrak m_1 \oplus \cdots \oplus R/\mathfrak m_t$$ then we have a commutative diagram $$\begin{matrix} R/Jac(R) &amp;  \rightarrow &amp; \frac{(R/\mathfrak a)}{Jac(R/\mathfrak a)} \\ \downarrow &amp; &amp; \downarrow \Gamma \\ R/\mathfrak m_1 \oplus \cdots R/\mathfrak m_s &amp; \rightarrow &amp; R/\mathfrak m_1 \oplus \cdots \oplus R/\mathfrak m_t \end{matrix}$$ where the vertical arrows are isomorphisms, and the horizontal arrows are surjections. Is it possible to add new alphabets to unicode-math? I want to attach a code file to my question, but I am not able to find a link to do it. Is attaching files possible at all? Is it possible to call a function whose name is stored in a string in vbscript? Was The Empire in Star Wars inspired by Nazi Germany?