Caps Shield can withstand most projectiles and absorb quite a bit of force (Hulks fist, Thors Hammer to name two of the tougher ones). Wouldn't it make sense for Stark to use the same material for his suit?  If this was already answered somewhere, I am sorry, but I didn't find it...
In the movie Iron Man 2, Tony Stark figured out how to synthesize Vibranium. Why didn't he use it to make a new Iron Man armor?
How to check if a macro value is empty or will not create text with plain TeX conditionals? I have a macro which holds some text value, e.g. \macro{some text}. If it is empty, I would like for nothing to appear in the document, but it has some content of any kind which would produce text displayed in the document, I would like a message to appear, "Text: some text".   \macro{} would be considered empty. \def\somedata{}, \macro{\somedata} would be considered empty. \macro{0} would be considered not empty.   I have tried making a TeX conditional which can check if the value is not empty, but nothing I tried works, e.g.:  \ifx #1 {} \else     Text: #1 \fi  \ifx#1{} \else     Text: #1 \fi  \ifx #1 \nil \else     Text: #1 \fi  \ifx#1!="" \else     Text: #1 \fi   What is the correct syntax for creating a conditional in plain TeX with checks if a value is not empty? Java Command line arguments External arrows in tables How to achieve similar arrows as in the picture?    The main issue cause of arrow   a(2,1) -> a(1,3), a(3,1) -> a(1,4), etc. Or at least how to make them on top of the table, but to make it look readable.  \documentclass[border=10mm]{standalone} \usepackage{tikz} \usetikzlibrary{matrix}  \begin{document} \begin{tikzpicture}[&gt;=stealth] \matrix (A) [matrix of nodes,row sep=3mm,column sep=3mm,nodes in empty cells] {   $a_{11}$ &amp; $a_{12}$ &amp; $a_{13}$ &amp; $a_{14}$ &amp; $a_{15}$ &amp;  $\dots$ \\   $a_{21}$ &amp; $a_{22}$ &amp; $a_{23}$ &amp; $a_{24}$ &amp; $a_{25}$ &amp;          \\   $a_{31}$ &amp; $a_{32}$ &amp; $a_{33}$ &amp; $a_{34}$ &amp; $a_{35}$ &amp;          \\   $a_{41}$ &amp; $a_{42}$ &amp; $a_{43}$ &amp; $a_{44}$ &amp; $a_{45}$ &amp;          \\   $a_{51}$ &amp; $a_{52}$ &amp; $a_{53}$ &amp; $a_{54}$ &amp; $a_{55}$ &amp;          \\   $\vdots$ &amp;          &amp;          &amp;          &amp;          &amp; $\ddots$ \\ };  \begin{scope}[thick,black,-&gt;] \draw (A-1-1)--(A-1-2); \draw (A-1-2)--(A-2-2); \draw (A-2-2)--(A-2-1); %\draw (A-2-1)--(A-1-3); \draw (A-1-3)--(A-2-3); \draw (A-2-3)--(A-3-3); \draw (A-3-3)--(A-3-2); \draw (A-3-2)--(A-3-1); %\draw (A-3-1)--(A-1-4); % etc. \end{scope} \end{tikzpicture} \end{document} Is it OK to reduce the charging current for a Li-ion 18650 battery? I am using NCR18650 batteries with the tp4056 charging module.  When I connect the charger at 2.8&nbsp;V (fully discharged), the tp4056 IC is getting hot at a 1&nbsp;A charge current. Is it OK to reduce this charge current by changing the charge current selecting resistor? So the tp4056 IC heat would be reduced, wouldn't it?  For my application I don't need a quick charge. With a low current, charging time will be increased, but it does not matter for my application.  Will reducing the charge current affect the battery's lifetime? Or will it damage the battery?  I am trying to reduce the heat of the tp4056 IC by reducing the charging current, maybe from 1&nbsp;A to 500&nbsp;mA or less. The 18650 battery never heats for a 1&nbsp;A charge current. What is an observer in quantum mechanics? Define a linear operator $T:C[0,1] \to C[0,1]$ as follows: $$Tf(x) = f(x) + \int_0^x f(u)du$$ It is easy to show that $T$ is a bounded linear operator. The statement also (1) claims that $T$ is one-to-one and onto, and (2) asks to compute $T^{-1}$. (Hence $T$ is an isomorphism due to a corollary of Open Mapping Theorem)  I need help to prove $T$ is onto: given any $g \in C[0,1]$, how to decompose it into a sum between a continuous $f$ and its antiderivative. I have trouble decomposing $g(x)=|x|$, not to mention bizarre functions like Weierstrass function. It seems impossible.  Thanks in advance for help! Doubts on the axiom of union? I'm reading Guerino Mazzolla's Comprehensive Mathematics for Computer Scientists 1:     Axiom 3 (Axiom of Union) If $a$ is a set, then there is a set      $$\{x| \text{ there exists an element } b \in a \text{ such that } x\in b \}$$      This set is denoted by $\cup a$ and is called the union of $a$.    This axiom seems to take elements from inside of a set of sets, for example in the set: $a=\{\{u_1,u_2 \},\{u_3,u_4 \} \}$, there are two elements $b\in a$, then the mentioned set created by the axiom is $\{u_1,u_2,u_3,u_4 \}$.           The axiom seems to imply that the set $a$ must have a set inside of it for it to work, what if it  have an element that is not a set? (I'm not sure if this is possible, but I remember of having read something about the difference of sets and elements).         There's also an extension of my proposal, In the same book (and also in others) I've seen that the natural numbers are defined as:   $$\begin{eqnarray*}   {0}&amp;=&amp;{\emptyset} \\    {1}&amp;=&amp;{\{\emptyset\}} \\    {2}&amp;=&amp;{\{ \{\emptyset\}\}} \\    {3}&amp;=&amp;{\{ \{ \{\emptyset\}\}\}} \\   {\vdots}&amp;=&amp;{\vdots} \end{eqnarray*}$$  Then the singleton $\{ 3\}$ could be seen as $\{ \{ \{ \{\emptyset\}\}\}\}$, which could mean that   $$\cup \{ 3 \}=\cup\{ \{ \{ \{\emptyset\}\}\}\}= \{ \{ \{\emptyset\}\}\}=\{2 \}$$          Then the union could also be seen as the antecessor of a number?            Using the framework I provided, I see some ambiguity, look:   $$\{ \{ \{\emptyset\}\}\}=\{2 \}$$          I decided to interpretate it this way, but from the notation it's not clear in which pair of brackets I should stop, I guess that $\{ \{ \{\emptyset\}\}\}=\{2 \}$ but it could also be the case that $\{ \{ \{\emptyset\}\}\}=3$. I could want a singleton with a $2$ inside of it and a $3$ outside a set, no? Explanation of finite correction factor I presented the following problem to some of my students recently (from Senior Mathematical Challenge- edited by Gardiner)  In the Fibonacci sequence $1, 1, 2, 3, 5, 8, 13, 21, 34, 55,\ldots$ each term after the first two is the sum of the two previous terms. What is the sum to infinity of the series: $$\frac{1}{2} + \frac{1}{4}+ \frac{2}{8} + \frac{3}{16} + \frac{5}{32} +\frac{8}{64} + \frac{13}{128} +\frac{21}{256} +\frac{34}{512}+ \frac{55}{1024} + \cdots$$  Now, I solved this using an infinite geometric matrix series (incorporating the matrix version of the relation $a_n= \frac{a_{n-1}}{2}+ \frac{a_{n-2}}{4}$), and my students, after much hinting on my part, googled the necessary string to stumble across Binet's formula (which allows one to split the series into two simple, if rather messy, geometrics). Both of these are good methods, but neither really seems plausible for a challenge set for 15-18 year olds under exam conditions. So how is one supposed to do it? A union of two subspaces not equal to the vector space. How can you get the "real" HttpContext within an ASP.NET MVC application? A Russian girl is asking for 500 euros to get a passport in Russia. Is this a realistic amount of money for a passport fee? How to pop-up alert to a user when he/she navigate away from page without saving the Records in custom visual force page? This week I've read two news stories about two different camera lenses that can magnify things that are very far away.  The first is the , which is a point-and-shoot camera that costs $600, has an 83x optical superzoom lens ("the same field of view as a 2,000mm lens on a full-frame camera"), and lets you see the craters of the moon.  The second is the , which weighs 36 pounds, costs $180,000, and can take portraits of people a half mile away.  A non-photographer might ask, "Why would somebody spend their life savings on a gigantic telescope of a lens when you could take far away pictures with a handheld camera for 1/300th the price?"  Well, I am basically a non-photographer, and I would like to ask that question. What does the big one give you that the little one doesn't provide? I understand that small changes in lenses can make a big difference in size and price, but this seems to be of a different scale entirely.   What is going on with the optics of the lenses that makes the small one able to be so small and the big one have to be so...big?   I'm trying to get a basic intuition for what makes lenses different, and I realize I don't understand enough about how lenses work to even know how to compare these apples and watermelons. Zero divisor in $R[x]$ Let $R$ be commutative ring with no (nonzero) nilpotents. If $f(x) = a_0+a_1x+\cdots+a_nx^n$ is a zero divisor in $R[x]$, how do I show there's an element $b \ne 0$ in $R$ such that $ba_0=ba_1=\cdots=ba_n=0$? Where can I get a device with 'Ubuntu for phones' pre-installed? Canonical has recently announced , which is Ubuntu with a specific interface for mobile devices.  Where can I get phones with this version of Ubuntu pre-installed? If no devices are available yet, where can I pre-order one? A continuous function that attains neither its minimum nor its maximum at any open interval is monotone Let $f: \mathbb R\to \mathbb R$ be a continuous function such that $f$ attains neither its minimum nor its maximum at any open interval $I \subseteq  \mathbb R$ , then how to prove that $f$ is monotone ? How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$? there is a similar thread here , but I'm only looking for a simple linear algebra proof. Graph editor for shape key animation I have animation where object changes his shape using shape keys, and I want to make some animation smoothing with graph editor. Is there a way to use graph editor for shape key animation? Find lines from a file which are not present in another file