Two Meanings of "To This Day"
Meaning: To This Day
I usually use "at a company" but I have encountered some articles using "in a company", "in XYZ firm" or "in an organization".  Which one is right? Why am I getting black photos when I use the Manual feature on my DSLR? I was taking photos a few days ago, and I had it set to Manual. After about four photos, the rest started coming out black. I could see through my eyepiece clearly, and it took the photo normally, but when I reviewed it they were all black. Is there any connection between a matrix being invertible and being diagonalizable? Let $A$ be an $n\times n$ matrix.  If $A$ is invertible then one of it's eigenvalues is 0.  If $A$ is diagonalizable then it has $n$ linearly independent eigenvectors.   Are these two statements true? Is there any connection between them? May I infer one from the other? Suppose $f:\mathbb{R}\to\mathbb{R}$ is Borel measurable. I want to show that $\displaystyle \int_a^b f(x)\mathrm dx=0$ for all $-\infty&lt;a&lt;b&lt;\infty$ with $a$ and $b$ rational implies that $f=0$ a.e. I'm really not sure how to approach this problem; any help would be welcome. Can't operator == be applied to generic types in C#? I am relatively new to Blender so please excuse me if this is rather amateur!   The bottom of my torus has poor surface quality, I have scaled the vertices down for a smaller (variable) tubular radius all the way around the torus and at the bottom the surface quality is awful, with inaccurate shading. Any ideas as to what is wrong and/or how I could fix this?  Thanks, itsanate Convert ls -l output format to chmod format Say I have the following output from ls -l:  drwxr-xr-x 2 root root 4096 Apr  7 17:21 foo   How can I automatically convert this to the format used by chmod?  For example:  $ echo drwxr-xr-x | chmod-format 755   I'm using OS X 10.8.3. Why does shell Command Substitution gobble up a trailing newline char? $\mathbb R = X^2$ as a Cartesian product I wonder if it is possible to consider $\mathbb R$ as a Cartesian product $X\times X$ for some set $X$. From the point of view of the dimensionality, there are spaces with a Hausdorff dimension $1/2$ (sort of Cantor sets), but I guess there are other problems in this construction  unrelated to the dimension.  Edited: replying on the comment by Asaf. I want that for all $r\in\mathbb R$ there exists a unique representation $r=\langle x,y\rangle$ where $x\in X$ and $y\in X$. Also, what if we want to have $X$ to be a topological space and $h:X\times X\to\mathbb R$ to be a homeomorphism? QR code scanner ISP blocking port 25 My ISP has started blocking port 25 so I can not send email through my dedicated server any more.   I have several options:   Send email through the SMTP server provided by my ISP. Any problems with this? Setup mu server so that it receives email on another port instead of port 25     No one else sends email through my server so it should be OK. How do I do this on a Linux server? Buy a static client IP - these are not being blocked so far.   Which one is preferable? The real fastest gun in the west Are the questions in the about page taken from real posts? If not, who designs them?  Particularly, why does this specific answer have a date from before the question was asked? How to disable all Vim-LaTeX mappings? I like some of the features provided by the Vim-LaTeX suite, but not all of them.  In particular, I dislike all of the mappings like [[ = \left[ \right] and the automatic placeholder stuff with &lt;++&gt;. I am a very fast typist but with that comes more typing mistakes, which I correct almost instantly by pressing backspace. Unfortunately, if something has automatically added a bunch of place-holders or expanded some expression, I then have to move around the document and remove more characters than necessary. For example, if I accidentally press [ twice, instead of only having to delete one character, I have to delete 10.  Having already looked through the documentation, and some of the source, I have managed to disable some of these "features", but not all of them:  In particular:  let g:Tex_SmartKeyBS = 0 let g:Tex_SmartKeyQuote = 0 let g:Tex_SmartKeyDot = 0   (Turn off maps for backspace, double quote and triple dot.)  let g:Imap_UsePlaceHolders = 0   (Turn off &lt;++&gt; placeholder insertion.)  But I can't seem to find a way of turning off the other stuff. Anyone have any suggestions?  Edit: I was able to "disable" some more things by setting:  let g:Tex_Leader = '`tex' let g:Tex_Leader2 = ',tex'   (Which stops some expansions but still not all. It's not really disabling it but just making it less likely that you're going to type in `texa as opposed to the potentially more common `a, for example.)  PS: Personally, I think it is very poor practice to make an optional package that, when installed, greatly changes the default handling of your system. I don't mind some intelligent source highlighting etc, or some new commands (that don't clobber any old ones), but it seems unhelpful to enable this drastic kind of key remapping by default. Functional Analysis: The rank of an operator detemines if it's a compact operator. Importance of Representation Theory Representation theory is a subject I want to like (it can be fun finding the representations of a group), but it's hard for me to see it as a subject that arises naturally or why it is important. I can think of two mathematical reasons for studying it:   The character table of a group is packs a lot of information about the group and is concise. It is practically/computationally nice to have explicit matrices that model a group.   But there must certainly be deeper things that I am missing. I can understand why one would want to study group actions (the axioms for a group beg you to think of elements as operators), but why look at group actions on vector spaces? Is it because linear algebra is so easy/well-known (when compared to just modules, say)?  I am also told that representation theory is important in quantum mechanics. For example, physics should be $\mathrm{SO}(3)$ invariant and when we represent this on a Hilbert space of wave-functions, we are led to information about angular momentum. But this seems to only trivially invoke representation theory since we already start with a subgroup of $\mathrm{GL}(n)$ and then extend it to act on wave functions by $\psi(x,t) \mapsto \psi(Ax,t)$ for $A$ in $\mathrm{SO}(n)$.   claims that if our physical system has $G$ as a symmetry group, then there is a correspondence between particles and representations of $G$. I'm not sure if I understand this correspondence since it seems to be saying that if we act an element of G on a state that corresponds to some particle, then this new state also corresponds to the same particle. So a particle is an orbit of the $G$ action? Anyone know of good sources that talk about this? The calling thread cannot access this object because a different thread owns it How to find string position within another string in C recursively? How to derive $E=mc^{2}$? Is there some way to derive ? I can understand that energy in something is proportional to its mass, but the $c^{2}$ part. I have no idea. It seems like the way the units are going it would end up as $kg*(m/s)^{2}$, which I think is the unit for Newtons, not energy. And why is there no constant of proportionality $k$? Did Einstein just set it up perfectly so that there wouldn't be one? My account has 20 (!) sites associated to it.  I only use it for 3-5 sites.  To reduce clutter, I would like to delete my profiles that I do not use much.  I have went through , but when I enter the profile URL as:  http://russian.stackexchange.com/users/5772/alex   it gives the error message:     oops! this isn't a link to a valid profile   What procedure do I go through to delete my profile only on certain sites? Why does the Euclidean algorithm work for polynomials? What is the proof?