Can I use a power supply that supply slightly higher current than the rated current from my dc motor?
Choosing power supply, how to get the voltage and current ratings?
I am using ArcMap 10.1. The background: I have an .mxd that I intend to roll out across the company as our default template for all future maps/figure production. This .mxd contains two Data Frames; the first (&quot;Main&quot;) is larger (occupying almost the entire page) and is designed to be used to hold the majority of mapped data whilst the second (&quot;Inset&quot;) is much smaller and is to be used as an overview map. The problem: When choosing to import this new .mxd to an existing .mxd (using the Change Layout button on the Layout toolbar) the wizard automatically selects the smaller (&quot;Inset&quot;) Data Frame to occupy the larger part of the page. The screenshot below shows this interface with a red box indicating the two possible locations of each Data Frame:  Whilst it is possible to manually alter the order of the Data Frames using the Move Up or Move Down buttons, how do I change the default option for this setting (i.e. so that the &quot;Main&quot; Data Frame always appears in the larger space - &quot;2&quot;)? The reasoning is that I would like the process of using this new .mxd template to be as simple as possible, this is especially important as we have a wide range of users with varying abilities. Does anyone know how to choose/change this default setting? It does not appear to be in the Data Frame Properties &gt; Data Frame menu where I would expect it to be. Let $p(x)$ be a polynomial of degree $n$ satisfying $p(x)\geq 0$ for all $x$. That is, for all $x$, $p(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0 \geq 0$, $a_n\neq 0$.  Show that $p(x)+p&#39;(x)+p&#39;&#39;(x)+\cdots+p^{(n)}(x)\geq 0$ for all $x$ where $p^{(i)}(x)$ is the $i^\text{th}$  derivative.  My interest: I know that, we can rewrite the LDE as follows  $$ p(x)+p&#39;(x)+p&#39;&#39;(x)+\cdots+p^{(n)}(x) = Lp(x) $$  where $L := I + D + D^2  + \cdots + D^{(n)}$. Can we say anything about a linear operator of this kind so that it does not change the sign of the input it takes? I can try to solve the question by writing for all the derivatives and factoring them using $p(x)$, but I think there should be a clever way of showing this by the properties of $L$. Can I figure out a solution by just looking at $L$ and the sign of $p(x)$ as in the question? Where should I look for that? Matrix is conjugate to its own transpose Mariano mentioned somewhere that everyone should prove once in their life that every matrix is conjugate to its transpose.  I spent quite a bit of time on it now, and still could not prove it. At the risk of devaluing myself, might I ask someone else to show me a proof? How do I upgrade from 14.04 LTS to 16.04.1 LTS? How to identify hardware performance bottleneck in laptop? Is there any tool that helps to determine the weakest link of my current laptop hardware specification? Any online guide to help me choose nice balanced configuration for the new laptop?    I need to find the answers:  a) which component should be invested to increase overall performance the most? CPU? GPU? RAM?  b) which component may decrease overall performance and work as a bottleneck for the specific configuration?    The question is general and regards both to validating the current hardware usage (and its possible bottlenecks) and estimating the performance (and avoiding possible issues) of specs I'm going to choose and buy.    P.S. For the specific laptop I need to replace, the following software will be in use:    Windows antivirus, firewall, dropbox service running in the background mail app + web browser with a dozen or so tabs open from time to time: libreoffice apps, movies, games (both online and installed). I recently found out that the expectation of a random variable $X$ in a probability space $(\Omega, \mathcal F,  \mathbb P)$, $\mathbb E(X)$, is just the term used in probability theory for the measure of the function $X$; i.e.:  $$ \mathbb E(X)=\mathbb P(X) $$  or, for a real-valued random variable $X:\Omega\to\mathbb R$:  $$ \mathbb E(X)=\int_\Omega X(x)\mathbb P(dx) $$  The thing is, I am also familiar with the definition of the expectation of a random variable $X:\Omega\to\mathbb R$ with probability distribution function $f$ to be:  $$ \mathbb E (X)=\int_\mathbb R xf(x)dx $$  Here, the integral is with respect to the Lebesgue measure on $\mathbb R$.    We can define the function $f$ in the following way: we have $F(x)=\int_\mathbb R f(x)dx$, where $F(x)=\mathbb P(X^{-1}((-\infty,x]))$.    I can't see any way to show that these two definitions are equal to one another.  The only transformation between integrals with respect to different measures that I know is that $\mu(f^{-1}(g))=\mu(g\circ f)$, which gives that $\mathbb E(g)=\mu_X(g)$, where $\mu_X$ is the image measure $\mathbb P\circ X^{-1}$, but that doesn't seem to help.  Why can we write $\mathbb E(X)=\int_\mathbb R xf(x)dx$?  Why are these two definitions consistent? How does the four card limit work? I'm new to the game and trying to make my first constructed deck. My understanding of the card rule is I can only have four cards of one kind.  What does this precisely mean?  For instance, does this mean I can only have four rat cards total or four rat cards of several kinds? If two different cards do the same thing (like  and ), can I have four of each? How do I diagnose the source of focus problem in a camera? Probably a novice question, but how do I correctly diagnose from a photo for what reason that camera wasn't able to focus properly?  It can be any 1 of the following   Unsteady hand Lens issue Metering Re-Calibration required in camera or ...   Is there a set of unsaid protocols that needs to be followed by a photographer?  Goal is to get a sharp and crisp image prior to editing.  [PS: I own a Nikon D5200.] How can I add custom '.desktop' application launchers to Ubuntu Dock? Laws and theories What is a , a , and what is the relationship among them?  I know this is a very basic question, so any reference to epistemology will be greatly appreciated :) I remember reading a while back about arithmetics with only a single operator that did all the work of the familiar $+ - \times /$ operators. If there is such a thing, could someone point me to it?  As background: I have a side project where I'm playing with neural nets and genetic search algorithms. Right now it's the good old kind, with matrix multiplication and addition. I thought it would be interesting to implement a sort of neural network that used a combined or "all in one" operator.  I've googled like heck and can't pick up the trail of where I thought I saw that before.  Is there study in that area, or am I mis-remembering, or worse, just making it up? I'd appreciate any pointers. Per the kernel documentation:  This control is used to define how aggressive the kernel will swap memory pages.  Higher values will increase aggressiveness, lower values decrease the amount of swap.   However this is kind of vague. I'm trying to figure out exactly what the parameter ultimately controls. I know it adjusts how aggressively the kernel tries to swap out pages, but what decision making process in the kernel code does it affect?  Does it adjust how long ago a page must have been accessed before the kernel swaps it out? If so what does the default value of 60 represent? And how much is changed by a increment/decrement of 1 (a formula would be nice)? Or does it swap out pages based on their access frequency? Or something else? Why does the Taylor expansion of $e^x$ satisfy exponential properties? How to do vlookup and fill down (like in Excel) in R? Of all the people we know, in the books, who were sent to Azkaban, the majority are Death Eaters (Dolohov, Lucius, Crouch Jr, Bellatrix and so on) or suspected to be involved with them (Sirius, Stan, et cetera). They were imprisoned for using the Unforgivable Curses, as well as for being accomplices of a seriously dark wizard. What other crimes are Azkaban-worthy, in normal circumstances? I'm looking for anything that's been stated in the books, or on Pottermore (basically, anything 'canon'), or anything one can conclude from information in the books. I think smaller crimes are punished by imposing a fine, but what about bigger ones? Surely murder and torture (i.e. crimes against humanity) aren't the only ones punishable by imprisonment? That certainly isn't the case in contemporary Muggle society. My thoughts Off the top of my head, I can name these crimes:  Being an unregistered Animagus1 That was what Hermione threatened Skeeter with.  Trespass and robbery2 That's how Sturgis Podmore was imprisoned.   Notes  Several of the arrests in the Half-Blood Prince and the Deathly Hallows were made by an authoritarian (if that's the right word on this case) government, in the time of war. They do not count as normal.  I don't mean that there should be an answer to this question, I was wondering if it was ever addressed in the books. I certainly don't expect a list of all people sent to Azkaban, and the reasons for doing so!     1 &quot;Well, yes,&quot; said Hermione calmly, taking a sip of her drink. &quot;Otherwise, as you very well know, I will inform the authorities that you are an unregistered Animagus. Of course, the Prophet might give you rather a lot for an insider's account of life in Azkaban.&quot;  The Beetle at Bay, Harry Potter and the Order of the Phoenix     2 Sturgis Podmore, 38, of number two, ... charged with trespass and robbery ... sentenced to six months in Azkaban.  Percy and Padfoot, Harry Potter and the Order of the Phoenix How to remove chromium-browser settings from Ubuntu 14.04? I have already gone through   and I'm really not getting why the solutions given there are not working for me.  What I'm doing is:   sudo apt-get purge chromium-browser   rm -rf ~/.config/chromium     Then reinstalling by running the following command:   sudo apt-get install chromium-browser    This must remove the settings of chromium-browser and do a fresh installation. The browser is uninstalling, but after being installed it is containing the previous settings, moreover it's not signing me out of even Gmail! I have been following  tutorial until I started adding nodes. The problem is that he has completely different nodes than I have. Even nodes that are created at start are different (I have Material and Output and he has Render Layers and Composite). Have I missed something or should I use different nodes than he? Calculate: $$\int_{0}^{2\pi}e^{R{ {\cos t}}}\cos(R\sin t+3t)\mathrm{d}t$$ My try: $\displaystyle\int_{0}^{2\pi}e^{R{ {\cos t}}}\cos(R\sin t+3t)dt\\ \displaystyle \int_{|z|=R}e^{\mathfrak{R\textrm{z}}}\cos(\mathfrak{I\textrm{z}}+3(-i\log z)dz\\ \displaystyle \int_{|z|=R}e^{\mathfrak{R\textrm{z}}}\mathfrak{R\textrm{e}}^{(\mathfrak{I\textrm{z}}+3(-i\log z))i}dz\\ \displaystyle \int_{|z|=R}e^{\mathfrak{R\textrm{z}}}\mathfrak{R\textrm{e}^{\mathfrak{I\textrm{z}}}}z^{3}dz\\ \displaystyle \int_{|z|=R}e^{\mathfrak{R\textrm{z}}}\mathfrak{R\textrm{e}^{\mathfrak{I\textrm{z}}}R}z^{3}dz$ and there is nothing here that is not holomorphic, therefore according to Cauchy theorem it must be exactly $0$. I've heard that in the study of finite fields, and other concepts related to finite fields, mathematicians have found a sort of gap: there are various results and things that seem like they correspond to a field with one element, $\mathbf{F}_1$, even though there is no such field. Of course, there is an object which seems similar to a field with one element: the zero ring, $\mathbf{Z}_1$, defined as having one element, $0$, obeying the equations $$0 + 0 = 0 - 0 = 0 \cdot 0 = 1 = 0.$$ The zero ring seems to behave like a field in every respect, except for the fact that it fails to satisfy $0 \ne 1$. (But the importance of the axiom $0 \ne 1$ isn't clear to me.) However, in any case, there seems to be consensus that the zero ring is not the field with one element. People say that the zero ring &quot;does not behave like a finite field&quot; () or that it &quot;does not have the features that mathematicians need&quot; (). I'm not familiar enough with algebraic geometry to understand the properties that $\mathbf{F}_1$ is expected to have. Is there an elementary, undergraduate-level explanation of  why it seems like a field with one element &quot;ought to exist&quot; in the first place, what properties we expect it to have and why, and how the zero ring fails to satisfy these properties?  Or do I need to study algebraic geometry if I want to have an understanding of any of this? (A side question: do we have a good answer to the question of whether the single element of $\mathbf{F}_1$ ought to be $0$, $1$, both, or neither?) I don't always answer myself, but when I do, I fail to ask a good question Sometimes I'll encounter problems while coding, or sometimes out of simple interest for a question, I'll google for an answer, and most of the time I find that answer is here on stackoverflow.com.   If I can't find an answer, or if it's not enough to satisfy my curiosity, sometimes I expend my own effort to solve those questions. And after I've solved it, I'm happy to make my contribution to the community, and I post them as the Q&amp;A style posts. For example:     It seems relatively easier to ask a question if I didn't already have a solution, and I can put what I have so far in the question body, such as:     The problem to me is, if I have my own solution to my own question, then most of what I have so far becomes part of the solution. It's likely I have failed in making my contribution by asking a question to which I have an answer, for example:     So I'm wondering if there are some guidelines or good practices for Q&amp;A style posts?   How do I do it better?