Do I need 50mm lens If I have ef 24-105mm f/4l is usm lens for canon 6d? What should be my next lens? I mostly interested in landscapes.
Everyone I speak to says that a 50mm lens is the best and beats them all as an all-rounder. I was wondering whether to get myself a decent, fast 50mm as well. However I'm still not 100% sure whether I really need such a lens.  I use a Pentax K10D and mainly shoot people (kids, portraits, some street shots). The lens I love and use most is the DA 70mm f/2.4 Limited. I often also use a DA 40mm f/2.8 Limited. They are great little lenses that produce very high quality images but they could be a bit faster.  Is is worth spending 400 quid on a Sigma 50mm f/1.4 in my situation? It seems like a good compromise between the 40mm and 70mm and much faster (in fact, 2 f-stops faster than the DA 70mm f/2.8!). On the other hand would the lens be sufficiently different from my current lenses?
system wide keyboard hook on X under linux How do I call a .NET assembly from C/C++? Suppose I am writing an application in C++ and C#.  I want to write the low level parts in C++ and write the high level logic in C#.  How can I load a .NET assembly from my C++ program and start calling methods and accessing the properties of my C# classes? If $G/Z(G)$ is cyclic, then $G$ is abelian Continuing my work through Dummit &amp; Foote's "Abstract Algebra", 3.1.36 asks the following (which is exactly the same as exercise 5 in ):     Prove that if $G/Z(G)$ is cyclic, then $G$ is abelian. [If $G/Z(G)$ is cyclic with generator $xZ(G)$, show that every element of $G$ can be written in the form $x^az$ for some $a \in \mathbb{Z}$ and some element $z \in Z(G)$]      The hint is actually the hardest part for me, as the quotient groups are somewhat abstract. But once I have the hint, I can write:  $g, h \in G$ implies that $g = x^{a_1}z_1$ and $h = x^{a_2}z_2$, so \begin{align*}gh &amp;= (x^{a_1}z_1)(x^{a_2}z_2)\\\  &amp;= x^{a_1}x^{a_2}z_1z_2\\\ &amp; = x^{a_1 + a_2}z_2z_1\\\ &amp;= \ldots = (x^{a_2}z_2)(x^{a_1}z_1) = hg. \end{align*} Therefore, $G$ is abelian.  1) Is this right so far?  2) How can I prove the "hint"? Best word wrap algorithm? Word wrap is one of the must-have features in a modern text editor.  How word wrap be handled? What is the best algorithm for word-wrap?  If text is several million lines, how can I make word-wrap very fast?  Why do I need the solution? Because my projects must draw text with various zoom level and simultaneously beautiful appearance.  The running environment is Windows Mobile devices. The maximum 600&nbsp;MHz speed with very small memory size.  How should I handle line information? Let's assume original data has three lines.  THIS IS LINE 1. THIS IS LINE 2. THIS IS LINE 3.   Afterwards, the break text will be shown like this:  THIS IS LINE 1. THIS IS LINE 2. THIS IS LINE 3.   Should I allocate three lines more? Or any other suggestions? ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ One of our SQL Server 2014 database transaction logs is growing very fast and I cannot find the root cause for this.  Database in Simple recovery mode. During full backup the log file grows to its limits (800GB) and backup fails.  I checked the transactions during the backup and did not find anything strange.  All transactions are our regular loading and no maintenance jobs (index rebuilds etc.)  I am aware of that backup keep the log from reuse but this mean 800GB changes during the backup period and this does not make any sense.  I had compared this DB to similar DB size, loading and backup duration. The second DB Log is not growing more than 400GB.  DB size is 7TB. Backup time is ~20H. The only time log is growing is during backup. Log_reuse shows correct Backup_Restore. No long running transactions.  The problem is the "speed" of log growth - compared to similar sites with same load and same backup duration, the log is 4 time less. Shell command to sum integers, one per line? I am looking for a command that will accept (as input) multiple lines of text, each line containing a single integer, and output the sum of these integers.  As a bit of background, I have a log file which includes timing measurements. Through grepping for the relevant lines and a bit of sed reformatting I can list all of the timings in that file.  I would like to work out the total. I can pipe this intermediate output to any command in order to do the final sum.  I have always used expr in the past, but unless it runs in RPN mode I do not think it is going to cope with this (and even then it would be tricky).  How can I get the summation of integers? Console.WriteLine and generic List I frequently find myself writing code like this:  List&lt;int&gt; list = new List&lt;int&gt; { 1, 3, 5 }; foreach (int i in list) {     Console.Write("{0}\t", i.ToString()); } Console.WriteLine();   Better would be something like this:  List&lt;int&gt; list = new List&lt;int&gt; { 1, 3, 5 }; Console.WriteLine("{0}\t", list);   I suspect there's some clever way of doing this, but I don't see it. Does anybody have a better solution than the first block? $f,g$ continuous from $X$ to $Y$. if they are agree on a dense set $A$ of $X$ then they agree on $X$ Problem:      Suppose $f$ and $g$ are two continuous functions such that $f: X \to Y  $ and $g : X \to Y $. $Y$ is a a Hausdorff space. Suppose $f(x) = g(x)  $ for all $x \in A \subseteq X $ where $A$ is dense in $X$, then $f(x)  = g(x) $ for all $x \in  X $.   Attempt at a solution:  Put $h(x) = f - g $. Therefore, $h: X \to Y $ is continuous and $Y$ is Hausdorff by hypothesis. Also we know $h(x) = 0 $ for all $x \in A $ such that $A$ is dense in $X$. I want to show that $h(x)$ vanishes everywhere in $X$. We can show $h(x) = 0 $ for all $x \in X \setminus A $. Suppose $h(x) &gt; 0 $ on $X \setminus A$. Pick points $y_1,y_2 \in Y $. Since $Y$ is Hausdorff, can find open set $O_1, O_2 \subseteq Y $ which are disjoint such that $y_1 \in O_1$ and $y_2 \in O_2$. By continuity, $f^{-1}(O_1), f^{-1}(O_2)$ are open in $X$.   I know that if I can show that one of the $f^{-1}(O_i)$ lies in $X \setminus A $, then we would have a contradiction since we have non-empty open set in $X \setminus A$ and this implies $A$ cannot be dense in $X$. But this is the part I am stuck. Any help would greatly be appreciated.  Also, Would be be possible to prove this without using the Hausdorff condition on $Y$? I would like to say something like     The boy, Adam's, favorite toy was a bike.   What is the proper way to say this? Folding a cube (animation) I'm trying to fold a cube with an animation. I've tried inverse kinetics with no luck. Here are some images that explain what I'm trying to do. I'm trying to make this so that    when the upper bone is pushed down, the box is folded to the ground. when the upper bone is pulled up, it unfolds the box. What are the colored/highlighted edges in edit mode? There are red and pink edges on my mesh.  What do these colored edges mean? How can I use them? Why isn't persistence working on Lubuntu 12.04 Live-USB? Show that all horses are of the same color. Im trying to understand the solution about this, and all the other solutions are.. a bit weird for me and dont answer all my questions!  Reference :   Im using the answer there as reference, but my understanding is a bit different!     Find the error in the following proof that all horses are the same   color. CLAIM: In any set of h horses, all horses are the same color.      PROOF: By induction on h.      Basis: For h = 1. In any set containing just one horse, all horses   clearly are the same color. Induction step: For k > I assume that the   claim is true for h = k and prove that it is true for h = k + 1. Take   any set H of k + 1 horses. We show that all the horses in this set are   the same color. Remove one horse from this set to obtain the set H1   with just k horses. By the induction hypothesis, all the horses in H,   are the same color. Now replace the removed horse and remove a   different one to obtain the set H2 . By the same argument, all the   horses in H2 are the same color. Therefore all the horses in H must be   the same color, and the proof is complete.   Here's what i have come up with :  Suppose a set of 1 horse. $H_a = { horse_{1} }$  Obviously, all the horses in set $H_a$ are the same, since theres just 1 horse.  So using that as the Basis of the induction we can proceed and try to prove its true for $N$ horses.  -- I dont fully understand the part below   As an example : set $H_0$ :   $H_0 = { horse_{1}, horse_{2}, horse_{3}... horse_{n} }$  In my understanding, its because, I can make a subset  formed by 1 horse :  $K_1  = {horse_{1}}$ $K_2  = {horse_{2}}$ ...  I don't get it. I clearly know that this proof is a lie.  And for me, its because you cant claim theres a relation on a set with size $&gt;= 2$ , since :  $H_1 = { horse_{1}, horse_{2}}$  Theres nothing that says $horse_{1}$ equals $horse_{2}$. The basis was for one horse. But that alone is not a proof.  So what should I do ? Filling a conical tank I have been working on this problem for about 2 hours and I can't seem to get it, here is exactly what the question reads. "Water is poured into the top of a conical tank at the constant rate of 1 cubic inch per second and flows out of an opening at the3 bottom at a rate of .5 cubic inches per second. The tank has a height of 4 inches, and a radius of 2 inches at the top. How fast is the water level changing when the water is 2 inches high?" Old post apocalyptic cartoon where the main character has red hair and lives with a nomadic group I am looking for an animated TV series which was probably made in the '80s or '90s.  The main character had red hair.  The cartoon is set in a post apocalyptic environment and the character lives with his mother and an old man —his mentor I guess— with a nomadic group.  In one early episode, one of the group is wounded in an ambush, he is taken back to the camp where the mentor performs surgery which is revealed he learned during the war. The wound is caused by a bullet, then the mentor is surprised saying that guns were lost and forgotten.  In another episode the main character is captured and sent to a prison. Then after he escapes with other prisoners, they look outside the gate and see grass and soil which they either didn't see in their lives or were in the prison for a long time.  The main character later finds a sword like Excalibur which can cause some sort of electrical disruptions.  I think his mother was kidnapped in the beginning. Serial voteup someone you learn from Suppose that $X_1,X_2,...,X_n$ is a random sample from a normal distribution, $X_i\sim N(\mu,9)$.  Find the UMVUE (uniformly minimum variance unbiased estimator) of $P(X\le c)$ where $c$ is a known constant.  Do this by finding the conditional distribution of $X_1$ given $\bar{X}={\bar{x}}$ and apply the Rao-Blackwell theorem with $T=u(X_1)$, where $u(x_1)=1$ if $x\le c$ and zero otherwise.  So clearly the parameter that we're trying to estimate given the problem description can be written as $\Phi\left( \frac{c-\mu}{3} \right)$ where $\Phi$ represents the CDF of the standard normal distribution.  However, I get stuck when I need to try and find the conditional distribution.  Without knowing the joint distribution or the other conditional distribution, how can I possibly find the conditional distribution of $X_1$ given $\bar{X}={\bar{x}}$? Which statistics to use? If $$\tan(\frac{\pi}{4}+\frac{\theta}{2})=\tan^3(\frac{\pi}{4}+\frac{\alpha}{2})$$, then prove that $$\sin \theta=\frac{3 \sin \alpha+\sin^3 \alpha}{1+3\sin^2 \alpha}$$  I tried using the fact that  $\frac{\cos A}{1-\sin A}=\tan(\frac{\pi}{4}+\frac{A}{2})$ but now not able to eliminate $\cos \alpha$ and $\cos \theta$. How should I proceed? Pipelined Sed does not work on found filename inside Bash command substitution when invoked from Find "-exec" It looks like 'find', 'bash' and 'sed' in some cases does not work as one expects.  The following example should first create file 'sample.txt', then find the file and finally process it by '-exec' command. The executed command prints found filename, test specimens, and modified filename. The 'sed' command itself is used to replace 'txt' to 'TXT'.  touch sample.txt find ./ -maxdepth 1 -name "*.txt" -exec echo {} $(echo Specimen_before.txt {} Specimen_after.txt |sed -e "s/txt/TXT/g") \;   The expected output is:     ./sample.txt Specimen_before.TXT ./sample.TXT Specimen_after.TXT   Instead it produces:     ./sample.txt Specimen_before.TXT ./sample.txt Specimen_after.TXT   (the example has been tested also with old-school command substitution through backquotes '`' with the same result)  What am I doing wrong?