If a lens is designated by manufacturer as "designed for crop sensor" (i.e. DC in Sigma, DX in Nikon, DT in Sony), how would that affect the calculation of practical focal length (equivalent focal length for a full frame sensor)?  For example, if I were to purchase a 50mm lens designed for a crop sensor camera, would that given/advertised focal length already be adjusted for the size of the crop sensor, or would I still multiply by 1.5 (so that the 50mm design for crop sensor lens is actually effectively 50*1.5=75mm) to get the effective focal length?
So, I mount a 200mm lens on my Canon 450D. It effectively becomes a 320mm lens. Is this the equivalent of 320mm on a full frame camera? That is, from what I've figured out I get an equivalent field of view but nothing I've read is indicating that I get the magnification to go along with it.  So as my question says in the title, does my crop sensor camera really turn my lens into a longer one (in terms of magnification), or does it just look like it based on the reduced field of view I get?
What is safe to exclude for a full system backup? I'm looking for a list which paths/files are safe to exclude for a full system/home backup.   Considering that I have a list of installed packages.   /home/*/.thumbnails /home/*/.cache /home/*/.mozilla/firefox/*.default/Cache /home/*/.mozilla/firefox/*.default/OfflineCache /home/*/.local/share/Trash /home/*/.gvfs/ /tmp/ /var/tmp/ not real folders but can cause severe problems when 'restoring'   /dev /proc /sys    What about...   /var/ in general? /var/backups/ - can get quite large /var/log/ - does not require much space and can help for later comparison /lost+found/ Convergence of the series $ \sum_{n=1}^{+ \infty } \frac{1}{n \cdot \ln(n) \cdot (\ln(\ln(n)))^{a}} $ I have a problem with a convergence of the series $ \sum_{n=1}^{+ \infty } \frac{1}{n \cdot \ln(n) \cdot (\ln(\ln(n)))^{a}}$ depending on the parameter $a$. I know that  $\frac{1}{n} \rightarrow 0$, $\frac{1}{\ln(n)} \rightarrow 0$, but I don't know how to deal with $\frac{1}{\ln(\ln(n)))^{a}}$ and how to get to the final answer. So far I solved tasks with  $\frac{1}{n ^{a}}$ and I know that $a&gt;1  \Leftrightarrow \sum_{n=1}^{+ \infty }\frac{1}{n ^{a}}$ is convergent, but in this task I cannot use it. Can you help me? Send urgent mail in Gmail Is it possible to set the "urgent" flag in Gmail for outgoing mail? I'd like to be able to flag time-sensitive emails as such. Best compiler warning level for C/C++ compilers? When you discard cards at the beginning of the game, where do they go? The appearance is that they get shuffled back into the deck. However, after discarding key cards and not receiving them the whole game, I am now wondering if they get put in the bottom of the deck. Where do they go after being discarded? \numcases with \tag I would like to label some cases with specific tags, and was hoping for something like  \begin{numcases}{A = } \frac{r}{a} &amp; r &gt; a \tag{G} \\ \frac{a}{r} &amp; r &lt; a \tag{H} \end{numcases}   utilizing the numcasesenvironment from the cases package, and \tag from amsmath. However, the two don't seem to be compatible:     ! Package amsmath Error: \tag not allowed here.   Is there any alternatives that would do what I hope to accomplish? How can I transition height: 0; to height: auto; using CSS? There are some .exe and .dll files belonging to some programs on my laptop which communicate with the internet without my permission (for self-update generally). I want to prevent those files one by one from accessing the internet. I don't want to install any external firewalls. I'm using Windows 7 Home Pro and if this can be done by Windows Firewall, it's OK. I took a look at Windows Firewall but couldn't find a setting to disable file access. Why is the mol a fundamental physical quantity? I am starting to study physics in detail and as I read about physical quantities, I was puzzled why mol (amount of substance) is taken as a physical quantity.  A physical quantity is any quantity which we can measure and has a unit associated with it. But a mol represents the amount of substance by telling the number of particles (atoms, molecules, ions, etc.) present. So it is a pure number and numbers are dimensionless. So mol should not be considered a physical quantity.  Also, fundamental physical quantities should be independent of each other. I am wondering whether mass and mol are independent. This is so as they surely affect each other as we can evidently see while calculating the number of moles and using the mass of that sample for calculation.  So how is the mol a fundamental physical quantity and independent of mass? Rotating clears selected tags Changing the orientation of your device within the tag selection view while asking a question removes all selected tags and clears the textbox.     Steps to reproduce:     Ask a question (does not happen when editing) Edit tags Enter some text in the box  Select a tag from the suggestion list Repeat the previous two steps as many times as you care to Rotate the device (source / target orientation doesn't matter, just need to change it) All selected tags and text typed in the textbox are gone and must be re-entered   I've reproduced this using version 1.0.63 of the SE app on two devices:     HTC One E8 m2ss (the Hong Kong version) rooted and running stock 5.0.2 ATT Galaxy S3 i747, rooted and sim unlocked, running Slimkat 4.4.2.build.4.1.official ROM on Android 4.4.2 Putting char into a java string for each N characters I have a java string, which has a variable length.   I need to put the piece "&lt;br&gt;" into the string, say each 10 characters.   For example this is my string:  `this is my string which I need to modify...I love stackoverlow:)`   How can I obtain this string?:  `this is my&lt;br&gt; string wh&lt;br&gt;ich I nee&lt;br&gt;d to modif&lt;br&gt;y...I love&lt;br&gt; stackover&lt;br&gt;flow:)`   Thanks How to prove this limit composition theorem? Number after list name I'm sure this is a really simple setting I'm having trouble finding. If I delete a web part then add it again, there is a number in brackets after the title that goes up by 1 each time. How do I get rid of this? Nullable type issue with ?: Conditional Operator Could someone explain why this works in C#.NET 2.0:      Nullable&lt;DateTime&gt; foo;     if (true)         foo = null;     else         foo = new DateTime(0);   ...but this doesn't:      Nullable&lt;DateTime&gt; foo;     foo = true ? null : new DateTime(0);   The latter form gives me an compile error "Type of conditional expression cannot be determined because there is no implicit conversion between '&lt;null&gt;' and 'System.DateTime'."  Not that I can't use the former, but the second style is more consistent with the rest of my code. Evaluating string "3*(4+2)" yield int 18 Object on curve wont stay flat! Is it possible to build a .dmg file (for distributing apps) from a non-Mac platform? And if yes, how? Fitting a plane to a set of points in 3D using PCA I am trying to estimate a midplane of a 3D model using the midpoints of paired landmarks, in order to reconstruct missing data (midplane refers here to the middle/saggital plane of the cranium which cuts the skull into two symmetrical halves, left and right).  I therefore need to estimate a plane from 27 points in 3D. I need to get the equation of the plane as $$ax+by+cz=d.$$  I have looked into orthogonal regression and principal component analysis (PCA) as methods, however I didn't take maths past A-levels and am struggling. I know I can supposedly use the eigenvectors to get the equation of the plane of best fit, but need someone to explain exactly how. I am using R for the PCA but am not great at R either.  Alternatively, if there's a better way to estimate the plane I would be glad to hear it! Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space? I have a non homework related question from a text and require a nice clear proof/disproof please  Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space?  my ideas:  if $H$ is the subset of the topological space $X$  if the subset is closed in the closed subspace, the complement is open in the subspace, which means the complement is of form $U\cap H$ for some $U$ open in $X$  if the subspace is closed the complement is open which means complement of $H=U$ for some open $U$ in $X$  kind thanks Find all solutions to the functional equation $f(x) +f(x+y)=y+2 $