I sort of discovered by accident that  &lt;?php ... ?&gt;   can be shortened to  &lt;? ... ?&gt;   Is this a bad idea? In some cases? What cases are they? Are there anymore shorthand examples? I am aware of shorthand examples involving conditional statements but I don't find them easier to read.  Please link me if this has been answered elsewhere, but I could not find it via a search. Maybe I'm not using the right keywords.
Here's the information :     There are four different pairs of   opening and closing tags which can be   used in PHP. Two of those, &lt;?php ?&gt;   and &lt;script language="php"&gt; &lt;/script&gt;,   are always available. The other two   are short tags and ASP style tags, and   can be turned on and off from the   php.ini configuration file. As such,   while some people find short tags and   ASP style tags convenient, they are   less portable, and generally not   recommended.   In my experience most servers do have short tags enabled. Typing  &lt;?=   is far more convenient than typing  &lt;?php echo    The programmers convenience is an important factor, so why are they not recommended?
Why is it considered good practice to mark method parameters as final? A good approximation of $(1+x)^n$ is $1+xn$ when $|x|n &lt;&lt; 1$.  Does this approximation have a name?  Any leads on estimating the error of the approximation? An epimorphism from $S_{4}$ to $S_{3}$ having the kernel isomorphic to Klein four-group Exercise $7$, page 51 from Hungerford's book Algebra.     Show that $N=\{(1),(12)(34), (13)(24),(14)(23)\}$ is a normal subgroup   of $S_{4}$ contained in $A_{4}$ such that $S_{4}/N\cong S_{3}$ and   $A_{4}/N\cong \mathbb{Z}_{3}$.   I solved the question after many calculations. I would like to know if is possible to define an epimorphism $\varphi$ from $S_{4}$ to $S_{3}$ such that $N=\ker(\varphi)$.  Thanks for your kindly help. A classic exponential inequality: $x^y+y^x>1$ This is a classic problem, but I haven't seen it on the site before.     Suppose $x$ and $y$ are real numbers that both lie in the interval   $(0,1)$. Prove  $$x^y+y^x&gt;1.$$   The following spoiler box contains a hint that indicates the solution I know. Does anyone know a more natural solution?       Use Bernoulli's inequality to show $$x^y\ge \frac{x}{x+y}.$$   Edit: I recently learned the source is the 1996 French math olympiad. Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$ Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$. Further Show that $v_0$ is the solution of some differential equation with appropriate boundary conditions. Compute $v_0$ explicitly.   Let $f: H^1(0,1) \to \mathbb{R}$ be defined by $f(u)=u(0)$. Then I showed that $f$ is linear and continuous. Hence there exists $v_0 \in H^1(0,1)$ such that $u(0)=\int_{0}^1u'v_0'+\int_{0}^1uv_0$  The differential equation is given by $f=-u''+u$ with the conditions $u'(0)=u'(1)=0$.   How do I compute $v_0$ explicitly?? Let $f_1 , f_2: I\mapsto \mathbb{R}$ bounded functions. Show that $L(f_1)+L(f_2)\leq L(f_1+f_2)$ (Riemann integral) Let $f_1 , f_2: I\mapsto \mathbb{R}$ bounded functions. Show that $L(f_1)+L(f_2)\leq L(f_1+f_2)$ where $L(F)$ is the supremum of the lower sums of the Riemann integral.  I tried to by contradicction $L(f_1)+L(f_2)&gt; L(f_1+f_2)$ and isoleting $L(f_1)&gt; L(f_1+f_2)-L(f_2)$ and usig the definition of sup.  I also tried to use $\sup(A)+\sup(B)=\sup(A+B)$ but it din't work.  Thanks. Force alt + tab to switch only on current workspace in GNOME shell For example how come $\zeta(2)=\sum_{n=1}^{\infty}n^{-2}=\frac{\pi^2}{6}$. It seems counter intuitive that you can add numbers in $\mathbb{Q}$ and get an irrational number. There are so many questions on this website. There is so many questions on this website.  The former &quot;sounds right,&quot; but the contracted form of the latter does as well:  There's so many questions on this website.  Which is correct? How to get the ASCII value of a character What is the distance a creature or player can travel if they have multiple types of movement speeds? What is the distance a creature or player can travel if they have multiple types of movement?  For example, the  has a 40 ft walking speed, a 40 ft climbing speed, and an 80 ft flying speed. Can it move a total of 160 ft in a round using each of those fully, or is there another way this is calculated? Prove: If $a$ and $b$ are odd integers, then $8\mid (a^2-b^2)$  So far I have: $$8\mid \left((2n+1)^2-(2m+1)^2\right)\Longleftrightarrow 8\mid \left(4n^2+4n+1-4m^2-4m-1\right) $$ Is this right so far? Where do I go from here? Step by step explanation please! How are ssl certificates verified? What is the series of steps needed to securely verify a ssl certificate?  My (very limited) understanding is that when you visit an https site, the server sends a certificate to the client (the browser) and the browser gets the certificate's issuer information from that certificate, then uses that to contact the issuerer, and somehow compares certificates for validity.     How exactly is this done?  What about the process makes it immune to man-in-the-middle attacks? What prevents some random person from setting up their own verification service to use in man-in-the-middle attacks, so everything "looks" secure? How can you accelerate without moving? I know this question has been asked in other forms, generally regarding the balance of forces.  This time I want to focus on motion.  I've got a laser accelerometer on my desk.  It tells me that I'm accelerating at $9.8~\rm m/s^2$.  For the first experiment I'm travelling in space.  I pick a nearby star and discover that I move about $490$ meters in $10$ seconds from that star.  For the next experiment I'm on the surface of Earth.  I measure the same acceleration with my laser accelerometer.  I pick a spot (the center of the Earth) and discover I don't move at all in $10$ seconds.  How is acceleration without motion possible? PhD without previous academic degree: truth or myth? Different voltage sources in parallel I realize connecting two different voltage sources in parallel is a contradiction (in an ideal circuit). But if I were to connect this in practice and measure the voltage across points A and B, what value of voltage would it show? And how much current would be sunk by the 5V battery? (Non ideal conditions) Why more (and varying number of) logical reads with read ahead (prefetch)? After creating tpch database in my SQL Server, I tried below query:      set statistics io on     DBCC DROPCLEANBUFFERS;             select top 100 * from dbo.lineitem order by l_partkey;   The table lineitem has a non-clustered index on l_partkey. I issued the above queries for several times and found out that the logical reads vary each time:      Table 'lineitem'. Scan count 1, logical reads 1019, physical reads 4, read-ahead reads 1760, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.     Table 'lineitem'. Scan count 1, logical reads 1007, physical reads 4, read-ahead reads 1720, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.     Table 'lineitem'. Scan count 1, logical reads 1030, physical reads 4, read-ahead reads 1792, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.   From the post here: , I know it could be caused by read ahead behavior.  BUT exactly why read ahead could cause more logical reads? How does it change the SQL Server behavior? Like SQL Server may read more index page since it's in cache anyway?  Anyway, I disabled read ahead and issue the above query again. Now it reports the same amount of logical reads each time. BUT the logical reads is much smaller!!      Table 'lineitem'. Scan count 1, logical reads 404, physical reads 160, read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.   So my question is, why the read ahead feature could cause many more and various logical reads count?  Out of curiosity, I tried another query without the "order by":      select top 100 * from dbo.lineitem   Here's the result without read ahead:      Table 'lineitem'. Scan count 1, logical reads 5, physical reads 3, read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.   Here's the result with read ahead:      Table 'lineitem'. Scan count 1, logical reads 15, physical reads 2, read-ahead reads 3416, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.   The one with read ahead still has more logical reads. So, why? Is there any direct relation among first, third, fourth order moments? We have a view for a type of node that includes a Private File.  We cannot see a way to add an exposed filter, such as "Contains any word", and have it filter based on the file's name.  Are we missing something obvious? How can I filter items with a certain enchantement?