Spring cron job runs every minute
Using crontab to execute script every minute and another every 24 hours
If HTML, CSS, and Javascript are client-side, why are they components of a PHP file? Are continuous self-bijections of connected spaces homeomorphisms? I hope this doesn't turn out to be a silly question.  There are lots of nice examples of continuous bijections $X\to Y$ between topological spaces that are not homeomorphisms.  But in the examples I know, either $X$ and $Y$ are not homeomorphic to one another, or they are (homeomorphic) disconnected spaces.    My Question: Is there a connected topological space $X$ and a continuous bijection $X\to X$ that is not a homeomorphism?    For the record, my example of a continuous bijection $X\to X$ that is not a homeomorphism is the following.  Roughly, the idea is to find an ordered family of topologies $\tau_i$ ( $i\in \mathbb Z$) on a set $S$ and use the shift map to create a continuous bijection from $\coprod_{i\in \mathbb Z} (S, \tau_i)$ to itself.  Let $S = \mathbb{Z} \coprod \mathbb Z$.  The topology $\tau_i$ is as follows: if $i&lt;0$, then the left-hand copy of $\mathbb Z$ is topologized as the disjoint union of the discrete topology on $[-n, n]$ and the indiscrete topology on its complement, while the right-hand copy of $\mathbb Z$ is indiscrete.  The space $(S, \tau_0)$ is then indiscrete.  For $i&gt;0$, the left-hand copy of $\mathbb Z$ is indiscrete, while the right-hand copy is the disjoint union of the indiscrete topology on $[-n, n]$ with the discrete topology on its complement.  Now the map $\coprod_{i\in \mathbb Z} (S, \tau_i)\to \coprod_{i\in \mathbb Z} (S, \tau_i)$ sending $(S, \tau_i) \to (S, \tau_{i+1})$ by the identity map of $S$ is a continuous bijection, but not a homeomorphism. PDF of product of variables Could anyone please indicate a general strategy (if there is any) to get the PDF (or CDF) of the  product of two random variables, each having known distributions and limits?   My particular need is the following: Let $w :=u \cdot v$. The PDF of $u$ is $$\frac{1}{\pi u}\frac{1}{\sqrt{u^2-0.25}},$$ for $z&gt;0.5$ and the PDF of $v$ is $$\exp\left(-\frac{v}{v_0}\right),$$ for $v_1&lt;v&lt;v_2$. What's the PDF of $w$? Why does blowing on someone who is wet feel colder than on someone who is dry? Regular Expressions: Is there an AND operator? Obviously, you can use the | (pipe?) to represent OR, but is there a way to represent AND as well?  Specifically, I'd like to match paragraphs of text that contain ALL of a certain phrase, but in no particular order. Recently, I am trying to create 3D models for my own game project. However, when I do some researches on game models, I come up with the term - game-ready models and I could not find any clear definition online. Could anyone tell me about what exactly is game-ready models and how to know if my 3D models (created by Blender mainly) is suitable for games.  From what I know by far, quad topology is preferred in Blender. However, for most of the game engine, triangle topology is preferred (Please correct me if I am wrong). Does it mean I have to manually change the models in Blender from quad topology to triangle topology before importing to the game engine?  Thanks for any helps. Publicity badges might be taking internal links into account? I was reading French's Vibrations &amp; Waves where he discusses Huygens-Frensel Principle.   The principle talks about how secondary sources give rise to secondary wavelets to form the displaced wavefront. However, any secondary source can form two wavelets one moving forward &amp; other towards the original source as pointed by French:     [...] The Huygen's construction would define two subsequent wavefronts , not one. In addition to a new wavefront farther away from the source, there would be another one corresponding to a wavefront back toward the surface, But we know this does not happen.    Then he writes:     If the Huygens way of visualizing wave propagation is to be acceptable, it must introduce the unidirectional property of a traveling wave. This can be achieved by requiring that the disturbance  starting out from a given point in the medium at a given instant is not equal in all directions. Specifically, if $O$ is the true original source ,&amp; $S$ is the origin of Huygens wavelet, &amp; $P$ is the point at which the disturbance is being recorded, then the effect at $P$ due to the region near $S$is a function of $f(\theta)$ of the angle $\theta$ between $OS$ &amp; $SP$.     I am not understanding how his reasoning actually averts the possiblity of formation of back-waves. Can anyone help me visualise what he is talking? How does his reasoning maintain the unidirectional propagation of waves? Can anyone explain his argument? In the current era of cricket, we see batsmen using switch hits to play a ball. That is, while playing a ball they change their batting side (left to right handed and vice versa) just before the ball comes to them.  My question is, can a bowler bowl a switch ball? Meaning, can a left hand bowler bowl right handed to a batsman? If it is not permitted, then is it not unfair to the bowlers that batsmen can change their batting style but not the bowlers? Or are there are any rules against a switch hit? I'm trying to recall a story I read in the 1960s or 1970s, but which I suspect was older than that.  It was about a quasi-immortal family in the twentieth century who lived in a rural area and kept a low profile. It was a stand-alone story and only the family, and perhaps distant relatives, had unusual powers. I don't think they were aliens, just some offshoot of humanity.   They were of varying ages, ranging from relatively young to thousands of years old. They had lived in Europe before immigrating to the American colonies. Each person had a distinctive set of psi powers, ranging from the grandpa, pa, ma and son. I believe the youngest, just called Baby, was the most powerful and least human looking, and lived in the attic. He slept most of the time.  Nothing remains in my memory of the plot.  As I recall, the story had a Theodore Sturgeon feeling to it, with a humorous, ironic touch, but it probably wasn't his. I haven't been able to identify it from looking at a list of his works.  I probably read it in an anthology, but I might have seen it in an old magazine. I'm just not sure.  If anyone can help me identify it, I'd be grateful. Then I can scratch that mental itch. C++ Struct Pointer Segfault Merging two incoming broadband lines for faster Internet Why is angular velocity of any point about any other point of a rigid body always the same? I have the following question regarding an ideal rigid body.  Firstly, is it always true without any exceptions that the angular velocity of any point about any other point on a rigid body is always the same?  If so, what happens in case of precession, in which two different angular velocities are predefined? When transiting Moscow (SVO), citizens of which countries need a transit visa? When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$ When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$, where $f_{xy}$ and $f_{yx}$ denote the mixed (second) partial derivatives of a multivariable function $z=f(x,y)$. polytopes as inequalities sistem solutions in R3 (x-y-z) cartesian space i'm here to ask if there's a TikZ/pgf support to draw areas resulting from a system of linear inequalities, into a xyz cartesian space. i found examples of my needs for xy plan at , but i also need to draw some 3d polytopes.  the problem is coordinate system as i found in pgfmanual.pdf seems not suited for R3: only (,) support but i need something like (,,).  As an example, i need to do drawings like this:    but i also need to get a colored surface with a 50% transparent color.  The system which generated that polytope is quite simple and is a linear programming problem:  x_1 + x_2 + x_3 &lt;= 4 x_1             &lt;= 2             x_3 &lt;= 3     3*x_2 + x_3 &lt;= 6 x_1             >= 0       x_2       >= 0             x_3 >= 0    Can you advise me some url/article/doc which can help me, or make me some example to lead me to learn how to reach my target?  Thank you for your attention Can graduated Stack Exchange sites get closed too? Calculating p-values for two tail test for population variance A sporting goods manufacturer claims that the variance of string tensions for any decent tennis racquet should be about 9 pounds. The string tensions of 18 randomly selected tennis racquets produced a variance of 8.13 pounds. Find the p-value to test the manufacturer's claim (assume the population is normally distributed).  I tried attempting the question as follows: ${H_o}: {\sigma ^2} = 9$ ${H_1}: {\sigma ^2} \ne 9$ We are also given the following: $n=18$ $s^2 = 8.13$ Test Statistics: $\chi^2 = {{(n-1)S^2}\over{\sigma^2}}$ Calculating Test Statistics under $H_o$ gives us: $\chi^2 = {{(18-1)8.13}\over 9} = 15.35667$  For calculating the p-value I proceeded as follows: $p-value = 2\min\{P[\chi^2&gt;15.35667],\ P[\chi^2&lt;15.35667]\}\ =2\times 0.430192 = 0.860384$  I am not certain if my method for calculating the p-value is correct or not. Can someone please tell if the above process is valid?  Thanks in advance! How can I keep Ubuntu updated automatically? I want help to  make Ubuntu 'update &amp;&amp; upgrade' itself automatically, select the settings for this automatic system.  How can I do it? Please advice about  where to find the menu (GUI) or file (command line) to do it, what settings that can be recommended (if different from the default).  As a bonus, please describe how different types of program packages are treated,  program packages from Ubuntu repositories and PPAs snap packages flatpak packages other kinds of programs/packages. Is there a one-liner that allows me to create a directory and move into it at the same time? I find myself repeating a lot of:  mkdir longtitleproject cd longtitleproject   Is there a way of doing it in one line without repeating the directory name? I'm on bash here.