(C++) Dont use header files
Why have header files and .cpp files?
Is there an uncountable family of infinite parts of $\mathbb N$ with two to two intersection finite? I followed  to create a soccer ball.  Now I want to texture it in a way that every pentagon has an image inside itself and the exagons are white, but I also want everything to be a little glossy. I managed to successfully UV Map the ball and paint the texture in photoshop but now I am having big problems in applying the texture material to the mesh.    I've created a new material in Blender Render mode with Diffuse and the texture applied to it. I also set the Texture mapping to UV. I've gone in edit mode, selected all the mesh and applied the material. Unfortunately in Texture View Mode I see just a white ball and while rendering I see everything's black.      If I try to do this in Cycles Render and use a Mix Shader with the FAC set to the texture image I get what I want in the Texture View Mode but while rendering I just see everything black and white of my colored images.        I hope I've been clear enough and that someone will help me in this easy/difficult task! Thank you in advance I am looking for an intuitive explanation as to why/how row rank of a matrix = column rank. I've read the proof at  and I understand the proof, but I don't "get it". Can someone help me out with this ?   I find it hard to wrap my head around the idea of how the column space and the row space is related at a fundamental level. I have a scene below where I am wanting to get an HDRI image to come in through the windows and light the scene in the window areas and have a god ray like effect.  I want to do this with a volumetric effect and have the HDRI lighting create throw patterns in the scene.  Is this possible?  To have volumetric lighting where the HDRI creates throw patterns?  Thanks for the help Origins of Tension First of all, I have a confusion about the definition and idea of Tension. For example, in my Physics Textbook, the idea of tension is written like this: &quot;Let's say there is a wire with a cross-section area of A and its length is $L_o$. If I hang the wire from a point and hang a weight of W on the other end of the wire, it will generate a repulsive force of T. This T is called the Tension Force.&quot; For me, this only explains to me what force will we call tension force, but it doesn't quite explain to me what is exactly this Tension force or where it originates from. Also, I have been doing pulley problems (Figuring out the acceleration of weights hanging from pulleys)  by first labeling all of the tension forces by $T_1$, $T_2$, and then doing some math with them to get my answer. But It bugs me that I am using these tension force values without even knowing where they came from or what they are. My idea was, maybe Tension force comes from the intermolecular bonds between the molecules of the rope, rubber or wire, etc. But even then, I have some different situational questions. For example:  Why you can't push a rope, copper wire against a wall?  What happens when I pull on two ends of a wire with 2 different forces?  Does the force increase proportionally to the applied force? Why does the wire break after a certain amount of force is exceeded.?  Does the idea of tension apply to everyday objects,(for example, a coffee mug, glass pane, etc). If it does, can I use something like a heat map or 3D equation to describe the tension in every point of the object? [Edit: more concisely, is there a mathematical way to show the various amounts of tension forces on a 2D (like a metal sheet) and 3D objects (like a football ) instead of a 1D object(like a string)].  If I take a metallic object like a paperclip or a thin wire. I can bend It multiple times and it eventually breaks into two pieces. I used to do this to pull of capacitors from old circuit boards. But does it happen with things like ropes or paper? If not, why it doesn't happen? ( Maybe it has something to do with intermolecular forces and the various internal stresses?)  Let's say I have an iron bar and I have thrown it out into space. Does that iron bar have equal stress distribution or still uneven or will the stress on all points become zero? (Is there even such thing as zero stress?) Run a command without making me wait Taking a screenshot (within X) How can I take a screenshot in X.org?  I am unsure if the Print Screen button will "just work" and I don't know how I would go about testing it. Permalinks: custom post type -> custom taxonomy -> post I am having trouble working with WordPress rewrite rules, and could use some help.  I have a custom post type called _shows_.  All shows have a single custom taxonomy category _show-category_. A _show_ will never have more than one _show-category_.  I would like my urls to route in this manner:  www.mysite.com/shows/  =&gt;  archive-shows.php  www.mysite.com/shows/%category%/ =&gt; taxonomy-show-category.php  www.mysite.com/shows/%category%/%postname%/ =&gt; single-shows.php   So as a real world example, lets say we have a _show-category_ "Foo" and a _show_ post titled "Bar" that has "Foo" as it's _show-category_. I would expect my WordPress app to look like this:  www.mysite.com/shows/foo/ =&gt; shows all posts under the foo category www.mysite.com/shows/foo/bar =&gt; shows the indivual post   I try to avoid plugins when possible, but am open to any solution. Ubuntu 14.04, problem when install gstreamer1.0-libav, unmet dependencies Suddenly my Ubuntu stopped playing video. When I open a video, the player suggests that I install  gstreamer1.0-libav. However, it fails to install.  I tried installing it manually, here is the error message:  $ sudo apt-get install gstreamer1.0-libav Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  gstreamer1.0-libav : Depends: libavcodec54 (&gt;= 6:9.1-1) but it is not going to be installed or                                libavcodec-extra-54 (&gt;= 6:9.13) but it is not going to be installed                       Depends: libavformat54 (&gt;= 6:9.1-1) but it is not going to be installed E: Unable to correct problems, you have held broken packages. A question about eigenvalues of $5\times5$ matrix Unable to install "": snap "" has "install-snap" change in progress Where does the term "fun fact" originate?-- namely, not with the compositional meaning but rather with the idiomatic usage to introduce some sort of unusual, esoteric, absurd or otherwise "controversial" fact? Passive aggressive people will sometimes veil insulting, critical, derogatory or generally aggressive comments with humor. The patina of humor makes the comment seem like a joke, not to be taken seriously, all in good fun, and it safeguards the aggressive person. If someone gets offended, they are being too serious, can't take a joke, and so they cannot voice their upset without seeming to be the one escalating the situation, when in fact it was the aggressor who did that.   This behavior seems to lie on a spectrum. On one side are comments which are simultaneously aggressive and genuinely funny (though of course both, especially the latter, are fairly subjective). On the other side would be lame attempts at the behavior, something like "you are fat!... just joking!" in which nothing in the tone or delivery signals a register of humor. In the middle of the spectrum, I imagine, are aggressive statements genuinely delivered as jokes. Their register signals that they are jokes, but they are aggressive rather than funny. They are aggressive comments masquerading as jokes.      A friend once called this "joking on the square", but I have never heard or seen this phrase. This type of comment is both pervasive and psychologically subtle and in my experience there is often an exact word describing such things. If not a word, is there an astute phrase which cuts to the heart of this? For US federal tax, whether a taxpayer is subject to AMT is determined by a complicated way in Instructions for Form 1040, Line 45, which involves an incomprehensible "worksheet to see if you should fill in form 6251".  By simplification and approximation, is there a rule of thumb for an estimate of a salary value of a taxpayer, so that a salary above the value might cause the taxpayer to pay AMT with a big possibility, and a salary below the value might not with a big possibility?  Why do the following two sources seem to differ greatly in estimates of the boundary salary value:    says that  the possible boundary salary value for a single taxpayer  to pay AMT is $53,900.  says that      Taxpayers with small incomes fall within the AMT exemption limits.   That leaves the upper middle class to face the tax, especially those   with incomes between $200,000 and $500,000    Thanks. E2099 Overflow in conversion or arithmetic operation I have two exchange accounts on my iPhone 4. One that connects to my gmail, the other connects to my work's Lotus Notes. There are no overlapping contacts in the two accounts. There are also no contacts saved locally on my phone.   When I enable contacts in both accounts, I get two identical entries for each of the contacts in my gmail. If I disable the Notes exchange account, then there are no more duplicates. If I have Notes contacts enabled, and gmail contacts disabled then I have no contacts at all.  Does anyone know what is going on? Is this a problem with having multiple exchange accounts or is it a Lotus Traveler problem? (I tend to blame Notes for all the trouble in the world, but that is just my bias)  Thanks all. Integral of Sinc Function Squared Over The Real Line Why are there no byte or short literals in Java? I can create a literal long by appending an L to the value; why can't I create a literal short or byte in some similar way? Why do I need to use an int literal with a cast?  And if the answer is "Because there was no short literal in C", then why are there no short literals in C?  This doesn't actually affect my life in any meaningful way; it's easy enough to write (short) 0 instead of 0S or something. But the inconsistency makes me curious; it's one of those things that bother you when you're up late at night. Someone at some point made a design decision to make it possible to enter literals for some of the primitive types, but not for all of them. Why? if $(x_0,y_0)$ is local extrema in $ax^2 + by^2 + cxy + dx + ey + l$ then its global too. An exercise on a book asks me to prove that if a point $(x_0,y_0)$ is a local extrema for the function $$f(x,y) = ax^2 + by^2 + cxy + dx + ey + l$$ then it's also a global extrema.  The exercise asks me to consider that $g(t) = f(x_0+ht,y_0+kt)$ is a parabola, but I couldn't understand how it helps. Maybe since it's a parabola, I know that this derivative has to be $0$ in some point, and also that this function $g(t)$ has a global extrema point, but I couldn't derive anything from this. I also tried to find the derivatives, equal them to $0$ and solve the system. I got:  $$x_0 = -\frac{2 b d - c e}{4 a b - c^2}, y_0 = -\frac{   c d - 2 a e}{-4 a b + c^2}$$  But when I try to find   $$f\left(-\frac{2 b d - c e}{4 a b - c^2},-\frac{   c d - 2 a e}{-4 a b + c^2}\right)$$ so I can try to prove:  $$f(x,y)-f(x_0,y_0)$$  is either greater or less $0$ depending on the case (so I can do $f(x,y) \le f(x_0,y_0)$ and $f(x,y) \ge f(x_0,y_0)$)  things get hairy. How do you unpin and move the form in the Visual Studio designer?