What's the difference between find . -name *gz and find . -name &quot;*gz&quot; I sometimes get the same result, other times I don't
find . -name *.rb   doesn't work on my ubuntu  I have to do  find . -name "*.rb"   to get it to work.  Why is that?
I am reading Tom Apostol's Analysis and come across this theorem.   Should $a \leq b$ if $a\leq b+\epsilon$ for all $\epsilon &gt;0$?   I don't doubt the proof in the book but I don't understand the intuition or geometric explanation behind this. Could somebody shed some light on this equation? I just started studying analysis on my own.$\ \ $ Why can't I log into minecraft with a mojang account? Satisfying explanation of Aristotle's Wheel Paradox. The paradox:    We have a circle and there is another circle with smaller radius. They are co-centeric.  If circle make full turn without sliding, both smaller and bigger circle make full turn too. If we assume that the passed road is equal to the circumference of circles. We have got smaller circle's radius is equal to bigger one's.  Unsatisfying Solutions I found:    "Do not assume that smaller circle's circumference is equal to passed road since the surface that contacts to the ground is bigger one. " // Okey but it does not explain the paradox, it explains just what is the wrong assumption (even does not explain why it is a wrong assumption.) It is undeniable that every point on both smaller and bigger circle will contact exactly one and only one point on their path. Therefore we can think that this is a bijective maps and smaller circle is isomorphic to bigger one. (Okey but ....)   Question: What is the true answer? What is wrong with the definition of circumference of a circle and relationship with its taken path. Compute the (multiplicative) inverse of $4x+3$ in the field $\frac {\Bbb F_{11}[x]}{\langle x^2+1 \rangle}$? So I am finding a polynomial $px+q$ ($p,q \in \Bbb F_{11}$) which is multiplicative inverse of $4x+3$ in $\frac {\Bbb F_{11}[x]}{\langle x^2+1 \rangle}$.  i.e. $[(4x+3)+\langle x^2+1 \rangle][(px+q)+\langle x^2+1 \rangle]=1+\langle x^2+1 \rangle$   $\Rightarrow$  $(4x+3)(px+q)+\langle x^2+1 \rangle=1+\langle x^2+1 \rangle$  $\Rightarrow$  $4px^2+(4q+3p)x+3q+\langle x^2+1 \rangle=1+\langle x^2+1 \rangle$.  We see that the remainder,when $(4x+3)(px+q)$ is divided by $x^2+1$, is $1$. So by Division algorithm,  $$ \require{enclose} \begin{array}{r} 4p \\[-3pt] x^2+1 \enclose{longdiv}{4px^2+(4q+3p)x+3q} \\[-3pt] \underline{4px^2+4p} \\[-3pt] (4q+3p)x+(3q-4p) \\[-3pt] \end{array} $$    So I equate $(4q+3p)x+(3q-4p)=1$ and solve the simultaneous linear equations  $4q+3p=0, 3q-4p=1$. I get $p=6,q=1$  Hence $6x+1$ is the required inverse.  I am pretty sure that the answer is correct but is the method to achieve it right? Is there a RSS to the 'Stack Exchange Inbox'? How about to Activity? Just wondering if I'm missing something here. Also, I couldn't find any previous question related to this. Mirror modifier. Mirrored half is not aligned, but rotated I was working on my character's hand when I realized half of the body was suddenly deleted. I am trying to recreate the other half, but it just won't mirror properly in the center. I tried moving the origin to the 3D cursor while it was completely centered, but the mirror modifier is still applied at an angle. Proving any number of the form $2^n$ can't be written as the sum of k consecutive numbers. I think i have proved that any number of the form $2^n$ can't be written as the sum of k consecutive positive integers, but i would be grateful if i could have some clarification as to whether this is a correct and valid proof or not.  Let $g=x+(x+1)+(x+2)+(x+3)+...+(x+(k-1))$, hence g is the sum of k consecutive positive integers.  $g=kx+\sum_{d=1}^{k-1}d$  Hence, $g=kx+\frac{k(k-1)}{2}$  Rearranging for x we find, $x=\frac{g}{k}-\frac{(k-1)}{2}$  So, for certain values of $k$, we can be sure that a positive integer value of $x$ can be found, and hence $g$ can be written as the sum of $k$ consecutive positive integers.There are two cases for $k$ to considor:  Case 1)  $k$ is odd. If $x$ exists, it must be the case $k$ | $g$, as for odd values of $k$, $\frac{(k-1)}{2}$ will alwyas be an integer, and hence $x$ will.  Case 2)  $k$ is even. $k$ does not divide $g$, but $\frac{g}{k}$ must be a multiple of $\frac{1}{2}$, and hence equals $\frac{h}{2}$, for some odd $h$.  Letting $j=2^n$, assume that we can write $j$ as the sum of $k$ consecutive positive integers.  If $k$ is odd, then if a $k$ exists, it must divide $j$, by Case 1. But, $j$ has no odd factors as it is a power of two, hence $k$ could not be odd.  If $k$ is even, by Case 2 it mut be the case $k$ does not divide $j$. Also, $\frac{j}{k}=\frac{h}{2}$, for some odd $h$.  But, this implies $2j$ has an odd factor, $h$. but, as $2j$ is a power of $2$, it can't have odd factors. So, $k$ can't be odd.  Hence, $k$ is neither odd or even, and this is a contradiction to our assumption. Hence no $x$ exists, and hence and number of the form $2^n$ can't be written as the sum of $k$ consecutive positive integers.  Any feedback on this proof would be appreciated. show all my unanswered questions from SE Any way how to get    my all un-answered questions  from across all SE sites? How do I delete one of two Ubuntus on my PC How to put a full stop at the bottom, not mid-line, after an aligned matrix? My change password interface is not working on java eclipse web application I want to know the memory usage of my Python application and specifically want to know what code blocks/portions or objects are consuming most memory. Google search shows a commercial one is  (Windows only).  And open source ones are  and .  I haven't tried anyone, so I wanted to know which one is the best considering:   Gives most details. I have to do least or no changes to my code. Year-Round Hats for Fun and Profit Is there some markup to post tags? I am wondering because I was editing my profile and I though it would be nice to put the languages I know and stuff like tags.  Is it possible to post a tag? If it's not, do you think it's possible to implement on the profile?  For example:  [c#]   Would generate    With tag formatting and link... Sketching base characteristics of first order pde $$xu_{x} - uu_{t} = t$$   with intial data: $u(1,t) = t, −\infty &lt; t &lt; \infty$  So I want to sketch the base characteristics and I'm not too sure what I'm doing.  characteristic equations: $\frac{\partial{x}}{\partial{\tau}}=x$, $\frac{\partial{t}}{\partial{\tau}}=-u$, $\frac{\partial{u}}{\partial{\tau}}=t$  initial conditions:  $x(0)=1$, $t(0)=\xi$, $u(0)=\xi$  $x=e^\tau$ so $\tau=lnx$  Notice that:  $\frac{\partial^2{u}}{\partial{\tau^2}}=\frac{\partial{t}}{\partial{\tau}}=-u$,  This gives me the second order ODE  $\frac{\partial^2{u}}{\partial{\tau^2}}+u=0$  Solving I get:  \begin{align}   u&amp;=c_{1}\cos(\tau) + c_{2}\sin(\tau)\\ t&amp;=c_{1}\sin(\tau) - c_{2}\cos(\tau) \end{align}  From here I don't know what I'm doing? I am looking for the stuff above, so I can make non-duplicate proposals on area 51. Biasing circuit - Voltage follower circuit I am using , which is and Bias controller/sequencer. I am using this for Providing gate voltage and drain voltage to the . In the datasheet, it is mentioned that the module with combination of EVM can be used in two applications. Application Option 1: Fixed negative gate biasing with pulsed drain biasing. Application Option 2: Pulsed negative gate biasing with pulsed drain biasing. I am trying to design both applications on a single board. The second option for future use. For the 1st application option, he has mentioned a few pins as No connection and he has used those NC pins on the 2nd application.  The issue I am facing:- They have used voltage followers for providing a low impedance output path for pin number 3(GCO). I have reverse-engineered the Ckt from the below-attached image, but I am unable to identify the voltage follower they have used. Pin number 2 of the voltage follower has been connected to pin number 2 (NC/GCP) of the Module. There has been no description of this pin number. I am guessing these:-  Pin numbers 1 and 4 are connected together and output is provided through them. Pin number 5 is +Ve supply hence connected to GND(Highest +Ve supply)? Pin number 3 is connected to -8V Pin number 2 is connected to pin number 2 of MABC-001000-DP000L, which I am unable to understand.  I have mailed component manufacturer regarding full schematic, till now I haven't heard from them. Can anybody help me with this? Thanks in Advance. Low-resolution pic of EVM. I don't think it helps in any way.   Layout Image OS X: Blurry Beamer presentations on Sierra / High Sierra Since OS X 10.12 (Sierra), the built-in Preview, but also many other PDF Viewers on OS X (such as Skim) show a number of problems, among them the following rendering issue:   The page is first rendered in low-res  with blurry text and graphics. About one second (!) later, the page is rendered in high fidelity. The display "wobbles", as text and graphics on the high-fidelity page is about one or two pixels up.   Example code:  \documentclass{beamer} \begin{document} \begin{frame}{Duke says}   \begin{itemize}   \item&lt;+-&gt; It don't mean a thing, if it ain't got that swing         \item&lt;+-&gt; (doo-ah, doo-ah, doo-ah, doo-ah, doo-ah, doo-ah, doo-ah, doo-ah)         \item&lt;+-&gt; It don't mean a thing all you got to do is sing         \item&lt;+-&gt; (doo-ah, doo-ah, doo-ah, doo-ah, doo-ah, doo-ah, doo-ah, doo-ah)  \end{itemize}  \end{frame}  \end{document}   While one may consider this acceptable when reading documents on screen, this is a show stopper for presenting beamer presentations with animations. The low-res display and wobbling makes the audience sick, while the 1 second rendering time makes PDF-based animations impossible.  So I am looking for a PDF Viewer for OS X that does not suffer this problems, but that a suitable for presenting beamer-based slide shows. Requirements:   page-wise full-screen/presenting mode with just the page and nothing else on the screen crisp and high-fidelity display quick rendering time   Unfortunately, the root of the problem is in Apple's own PDFKit library that is the base for most PDF viewers on OS X. So I am looking for PDF viewers that are not based on PDFKit, but fulfil the requirements above.  I am aware, of course, of Acrobat Reader DC. However, I do not particularly like its font rendering (Req 2) and I would also prefer something more light weight. I also have PDFExpert, which also is not PDFKit-based, however, does not support a presenting mode (Req 1). Thermodynamics of supercooled water Now that it's been freezing outside for the last few days, I experimented a bit with supercooling. I've left a bottle of clean water outside for a few hours, and behold, when I shook the bottle, the liquid began to freeze rapidly, as expected.   However, not all of the water froze, only about half of it. This got me thinking.  I reasoned that happens because freezing releases heat, and that heat raises the temperature of the ice and remaning water to 0$^\circ$C, at which point the freezing stops.  To try to quantify this, set   $H_f = 334000 \frac{J}{kg}$, the "freezing heat" (enthalpy of fusion) of ice, $c_i = 2110 \frac{J}{kg\cdot K}$, specific heat of ice, $c_w = 4181 \frac{J}{kg\cdot K}$, specific heat of water, $M$, initial mass of supercooled water, $T_0$, initial temperature of supercooled water, $m$, mass of ice at a given moment, $T$, temperature at a given moment.   We suppose that the energy released by the freezing of a $\textrm dm$ mass of ice is used up by raising the temperature of both the already frozen ice ($m$) and the remaining water ($M-m$):  $$ \textrm dm \cdot H_f = c_i m \cdot\textrm dT + (M-m)c_w \cdot\textrm dT$$  By rearranging we get a linear differential equation for $m(T)$:  $$\frac{\textrm dm}{\textrm dT}+\frac{c_w-c_i}{H_f}m = \frac{c_w}{H_f}M$$  The solution of this equation, using the initial condition that at $T=T_0$, $m=0$:  $$ m = M \frac{c_w}{c_w-c_i}\left[ 1-e^{-\frac{c_w-c_i}{H_f}(T-T_0)} \right]$$  This looks neat, however, plugging in the actual values of the constants, $T = 0^\circ$C and $T_0 = -6^\circ$C, I get that little more than 7% of the water should freeze - as opposed to more than half, as I've observed. What's worse, the formula can be used to calculate the starting temperature required to freeze all the supercooled water: $$T_{all} = \frac{H_f \log\frac{c_w}{c_i}}{c_i-c_w}=-110.26^\circ \textrm C$$ which seems absurd.  Where is the error in the calculation above?  I've made a number of assumptions which may or may not hold:   the constants are really constant. I think this is a good approximation for $c_w$, a not that good but still acceptable approximation for $c_i$, and I suppose it holds to $H_f$ to some extent as well. there is no heat transfer with the environment, i.e. the bottle is a closed system. The process seemed fast enough (a few seconds at most) for this to be a good approximation. the system is in a thermal equilibrium at all times and the heat released by the freezing of the ice is distributed evenly in the emerging ice-water mixture. Now this is where I have doubts. Precisely because of the process happening so fast, this might not be true at all. However, acknowledging the presence of temperature variations makes the problem order of magnitudes harder: one has to solve a system of partial differential equations that take heat transfer, the shape of the bottle and \$deity knows what else into account. Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$