I'm not sure if I've phrased this correctly, but I've just purchased two prime lenses:   Nikkor 50mm f1.8/G (FX)  Nikkor 35mm f1.8/G (DX)   I know that the effective focal length of the 50mm FX lens is actually 50 x 1.5 = 75mm, because I'm shooting with an APS-C sensor.   What I'm curious to know is: when I purchased the 35mm DX lens, is that truly a 35mm length or is it 35 x 1.5 = 52.5mm? In other words, when I use a DX lens must I still do the same crop factor calculation as when I use an FX series lens? Would a 35mm FX lens on a full-frame camera "be the same" as a 35mm DX lens on an APS-C camera?  For clarity: FX lenses are Nikon's full frame lenses while DX are their APS-C series of lenses.
I have a Canon 7D, which has a crop factor of 1.6x.  When using a Canon EF-S lens I get the focal length stated on the lens, when using a Canon EF lens I get the focal length times 1.6 when used on the APS-C body. At least that's what I thought.  I just compared two lenses:   Canon EF-S 15-85mm f3.5-5.6 Canon EF 70-200mm f4   .  The top photo is shot with the 15-85, the bottom photo with the 70-200 - both lenses are set to 70mm. Now why do they look the same?  I thought I would get 112-320mm (70mm*1.6 crop factor). What did I misunderstand about the crop factor calculation? Lightroom also displays the photos as having "70mm" and not 112mm.
Inequality: $x^2+y^2+xy\ge 0$ I want to prove that $x^2+y^2+xy\ge 0$ for all $x,y\in \mathbb{R}$.  My "proof":  Suppose wlog that $x\ge y$, so $x^2\cdot x\ge x^2\cdot y\ge y^2\cdot y=y^3$ (because $x^2\ge 0$ so we can multiply both sides by it without changing the inequality sign) giving $x^3\ge y^3$. Substracting we have $x^3-y^3\ge 0$ or $(x-y)(x^2+xy+y^2)\ge 0$. Since $x\ge y$ we can divide by $x-y$ to get $x^2+xy+y^2\ge 0$.  Is it right?  Thanks for your help! Can one explain the different distributions of the Saxon and the analytic (Norman) (periphrastic, 'of') genitive Repeated squaring method How do I use the repeated squaring method to calcualte 2^176 (mod 177)? I'm not sure, but is there something about the fact that 177 is 1 greater than 176 that makes this a problem? Remove all content using pure JS Proof that $A_n$ the only subgroup of $ S_n$ index $2$. I have what seems to me a very simple proof that $A_{n}$ is the only subgroup of $S_{n}$ of index 2.  Since I've seen other people prove it with what feel like really complicated methods (), I'm wondering if I've overlooked something.  Proof: Let $H$ be any subgroup of index 2 in $S_{n}$.  Then $H\cap A_{n}$ is a normal subgroup of $A_{n}$ and since $A_{n}$ is simple, $H$ is either the trivial or the improper subgroup of $A_{n}$.  If it's the trivial subgroup it doesn't have index 2 in $S_{n}$, and otherwise the theorem is proved. I'm training a neural network for regression. The input vector consists of $140$ entries.   For each feature vector entry, I calculate both min and max over the training set. The difference max-min of some entries are smaller than 1e-5. I understand I can normalize such feature entries by say MinMaxScalar. However, if the difference max-min is this small, can I discard such entries since they seem to be so insensitive? What is the preferred way to mention Stack Overflow from Twitter? I wanted to tweet something on the lines of "Stack&nbsp;Overflow is awesome". When I do this kind of stuff, I usually use a username (for example: ) or a hashtag ()  I found , but it seems it is from someone unrelated with Stack&nbsp;Overflow.  Is there a Twitter account I can reference, or should I use a hash-tag? Should I just point to the site?  Thanks!  (Notice: I've seen lots of questions regarding Twitter and Stack&nbsp;Overflow, but those are mostly about integration/login with Twitter for the users accounts; I'm just asking for a single account for Stack&nbsp;Overflow; probably for announcements and PR, which is different) Help with creating a symbolic link I'm confused with how symbolic links work. I hope someone can guide me in the right direction.  I want to put a demo online from our software, which normally only runs locally on a Mac Mini. So I put all the files in the var/www from my Ubuntu 12.04 server installation.  There are a lot of hardcoded links in the software which point to /Applications/XAMPP/xamppfiles/htdocs/narrowcasting  Of course, I could change all these code on my html/php files in /var/www, but that would be quite annoying. I hope I can fix this by creating a symbolic link. For example, I have a directory called thumb in /var/www/thumb. The PHP code is trying to put an image in /Applications/XAMPP/xamppfiles/htdocs/narrowcasting/thumb.   Can anyone give me a tip how to achieve this with a symbolic link? Theoretically if I were able to build some sort of device that let me sit 1 foot away from the surface of the Sun (or any star for that matter) without being vaporized, would a star produce any sort of audible sound at that distance?   From my understanding, sound waves need a medium to propagate through (air, water, etc).   Does this mean that all stars are completely silent (in the audible spectrum of frequencies at least) as they fuse  hydrogen into helium?   I know stars emit radio, xray, infrared, ultraviolet electromagnetic waves, but how about audible (20 Hz to 20Khz) frequencies?   For some reason it seems like this process would produce some sort of sound. Can one create a video from sequence of meshes that you already have using blender? If I have a sequence of .obj (or any other readable format) files created from my own simulation code (say cloth simulation), can I use the rendering capabilities of blender to generate a video?   Is there a way to set the material properties for frame 1 and use the same or rest of the frames while the corresponding meshes are imported afresh from that ones I provide? Sql Server Indexes Include Primary Key? In his 1984 paper , Paul Holland raised one of the most fundamental questions in statistics:     What can a statistical model say about   causation?   This led to his motto:     NO CAUSATION WITHOUT MANIPULATION   which emphasized the importance of restrictions around experiments that consider causation.  Andrew Gelman makes :     "To find out what happens when you change something, it is necessary to change it."...There are things you learn from perturbing a system that you'll never find out from any amount of passive observation.   His ideas are summarized in .  What considerations should be made when making a causal inference from a statistical model? Formula for the $n$th term of $1, 2, 2, 3, 3, 3, 4, 4 ,4, 4, 5, ...$ Please be kind, I am an electronics nub.  This is in reference to getting an LED to emit photons.  From what I read (Getting Started in Electronics - Forrest Mims III and Make: Electronics) electrons flow from the more negative side to the more positive side.  In an example experiment (involving a primary dry cell, a SPDT switch, a resistor and an LED) it states that the resistor MUST be connected to the anode of the LED.  In my mind, if the electrons flow from negative to positive, wouldn't the electron flow run through the LED before the resistor; thereby making the resistor pointless? Determining the characteristic of a field If $\mathbb{F}=\{ 0,1,x,y\}$ is a field with four elements, why is the characteristic 2?   In a field with four elements, the characteristic is 2 or 3(since it has to be a prime). Is there any way to determine precisely the characteristic of this field, and in general any finite field? Cardinality and infinite sets: naturals, integers, rationals, bijections Integer reciprocals in arithmetic progression Let $m_1,m_2,\ldots,m_k$ be $k$ positive integers such that their reciprocals are in AP. Show that $k&lt;m_1+2$. Also find such a sequence.     Whatever way I tried, whichever formula I used, I could not eliminate the $m_k$ term, which I reckon would be the ideal scenario to find the solution. I am exhausted of any further ideas, please help. Thank you. Create unmanaged c++ object in c# How does Cooper get out of the black hole? In the movie Interstellar,  Cooper (played by ) enters a black hole and sends a message to Murph (his daughter). Later, he is found by rangers, but I don't understand how he gets out of the black hole?  As far as I know, nothing can get out of a black hole, as it has extremely high gravity. How do you prove that $e=\sum_{n=0}^{\infty}\frac{1}{n!}$? Here I am assuming $e:=\lim_{n\to\infty}(1+\frac{1}{n})^n$. Do you have any good PDF file or booklet available online on this? I do not like how my analysis text handles this...