The status remained "awaiting for reviewer selection" after 5 months since re-submission
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A regular challenge that I face is balancing two (or more) logos. Whether they need to be equal or one needs to be given priority. Some logos however might be squares, others rectangles, circles, etc...   As a quick sample I snagged a nice high resolution photo from  and pretend its going to be an advertisement that needs to show some footwear brand logos on it. In this case I used Adidas and Saucony.  This is certainly not balanced even though they're height is the same:    Likewise this is not balanced even though they're width is the same:    So then the question becomes when are they in balance, is this balance:    Maybe a little more adjustment, is this balance:    And in these examples I'm only working with two Black Logos. Factor in color and it can get even more difficult to balance. Another issue being when there's tiny text as part of the logo.  So the question is, other than estimating / eye-balling it, what tips, methods or even tools are there to balance different sized logos? I am having trouble comprehending how anyone could come up with this formula:  $$F = \frac{GMm}{d^2}.$$   Could someone walk me through this? Change all @username references in comments when a user changes their name? The fact that a user can change their name at will can lead to some confusion in the comments.  For instance, suppose a user named "foo" changes his name to "bar", all those comments signed by "foo" are now signed by "bar", but responses to "bar"'s comments still start with "@foo".  Could those "@foo" references in comments be changed to "@bar"?    A brief discussion on this has set me straight.  I didn't think it through.  Request withdrawn. com.google.android.trichromelibrary causes many Android apps to crash How can I double the newlines in an output stream I always stumble when using abbreviations in a sentence, as they inherently contain a period in them. How do I use a comma or a semicolon after an abbreviation? How about a period?  E.g. (This is an example of my quandary) Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite. I have seen another post for this same question but it never got an answer. Since I am fairly new, I can't comment on other's posts, therefore I am creating a new one. The question states:  If a, b, and c are positive integers, prove that if $(a + b + c) | (a*b*c)$, then $a+b+c$ is composite.  I do not really know how to approach this.  The link to the post with the same question is: Compute $\iint\limits_R\frac{y}{x+y^2}dA$ where $R=[0,1]\times[1,2]$ Compute $\displaystyle\iint\limits_R\frac{y}{x+y^2}dA$ where $R=[0,1]\times[1,2]$  $\displaystyle\int_0^1\int_1^2\frac{y}{x+y^2}dydx=\int_0^1\int_1^2y(x+y^2)^{-1}dydx$  How do I integrate the denominator if the superscript is $-1$?   Hints are appreciated! How do I get a DOI for a dataset? A DOI is a commonly used digital object identifier to refer to an electronic document. How do I secure a DOI for a research dataset, to help share and identify it? Area is calculating wrong using $area in field calculator (QGIS 2.8.1-Wien) How to find out where an error occurs? Levels or First Differences, VECM or VAR for Ultimate Impulse Response Functions? My final goal is to generate Impulse Response Functions in R.  I have variables that are non stationary when I set k = 5 in a Unit Root test, and they are cointegrated which to my understanding prompts the use of the VECM, from which the Vec2Var argument is used to then generate IRFs. However, my response functions from this methodology do not decay over time and mostly do not revert to the zero line.  Furthermore, I noticed that when I input first differenced variables into the VECM as opposed to level data above, response function do revert to the zero line. Therefore my first question is: 1) is it appropriate to use differenced variables in a VECM model?  Secondly, as an alternative I am considering restricting the number of lags used in the Unit Root tests so that the variables are not all non-stationary; in this case 2) would the use of VECM be void and the VAR with first differences be a more appropriate model? Again, using differenced data is giving me better response functions that revert to zero in the long run. However, 3) is it ok to use the VAR for stationary/non-stationary data in levels where these variables are still cointegrated?  Also, I am using growth rate variables, 4) should I still long transform all variables and use logs in all tests?  Thank you for the help! Where is Jon going? From everything I've read about quantum mechanics and quantum entanglement phenomena, it's not obvious to me why quantum entanglement is considered to be an active link. That is, it's stated every time that measurement of one particle affects the other.  In my head, there is a less magic explanation: the entangling measurement affects both particles in a way which makes their states identical, though unknown. In this case measuring one particle will reveal information about state of the other, but without a magical instant modification of remote entangled particle.  Obviously, I'm not the only one who had this idea. What are the problems associated with this view, and why is the magic view preferred? Determine whether $712! + 1$ is a prime number or not Let $n = 712! + 1$ If $n$ was a prime number then, by Wilson's theorem:  $ (712!)! \equiv -1 \pmod{712}$  The double factorial makes it seriously more difficult...  But We can require:  $$712!! + 1 \equiv 0 \pmod{712}$$  $$712 = 2\cdot 356$$   Hence: $712!! = 2^{356} 356!$  Lets compute: $356! \pmod{712}$. Obviously:  $$356! = (356 \cdot 2) \cdot (355!/2)  = 712 \cdot 355!/2$$  Then: $356! \pmod{712} \equiv 0$.   Now, $2^{356} \pmod{712}$  $2^{356} = 2^{6 + 350}$  Nevermind, what should I do? How do i know which wheels will fit my bike? my bike is:  and everything I have came with the bike, only now the axle of the rear wheel bent and the skewer has lost its grooves.  and I would like to replace the rear wheel with the 12 x 142mm version of:   I want to reuse the old casettes and disc break. I was told to buy new rotor bolts, will these do?   Will I be able to migrate all my previous parts onto this new wheel and will the wheel fit onto my bike?  update: A replacement axle would be prefered. What axle would work for my bike? Realtime audio processing using Dynamic Do potions use concentration for their effects? How do I run a program with commandline arguments using GDB within a Bash script? Conjugacy classes in $A_n$. Suppose $n$ is a non negative integer $\geq 4$ and $\sigma\in S_n$ a permutation. Conjugacy classes in $S_n$ are completley determined by the cycle structure of $\sigma$. If we let the alternating group $A_n$.act on $S_n$ by conjugation, the orbits coincide with the conjugacy classes in $S_n$ except for those (even) permutations whose cycle structure is composed of even cycles (which corresponds to cycles of uneven length) of distinct order (fixed points are treated as cycles of length $1$.) See   For instance a $3$-cycle in $A_4$ has cycle structure $[3,1]$ which fits the bill, and a $5$-cycle in $A_5$ or $A_6$ works too, since the cycle structure is $[5]$ and $[5,1]$ respectively. On the other hand, a $3$-cycle in $A_5$ will does not satisfy the criteria as it has cycle structure $[3,1,1]$ with two fixed points.  In this case, the conjugacy class of $\sigma$ inside $S_n$ splits in $2$ orbits of the conjugation action of $A_n$, and if $\tau$ is any odd permutation, for instance $(12)$, then we have $$\mathrm{Conj}_{S_n}(\sigma)=\mathcal{O}(\sigma)\coprod\mathcal{O}(\tau\sigma\tau^{-1})$$  My question is How can we differentiate between the two orbits? Does it have geometric meaning?    I can see that this information can be useful when looking at representations of the alternating groups, since there are as many irreducible representations as conjugacy classes. As for some geometric interpretation, I ask because there is one for the three cycles in $A_4$. If $S_4$ is understood as the group of symmetries of a regular tetrahedron, then $A_4$ is the subgroup of direct symmetries, and a $3$-cycle corresponds to a rotation of angle $\frac{2\pi}{3}$ or $\frac{4\pi}{3}$ with axis passing through one of the vertices. Conjugacy classes inside $A_n$ preserve the angle, and that's how we can tell them apart. In this case the computations are so simple we don't really need this picture, but I think it is a nice way to understand the fact $3$-cycles in are not all conjugate inside $A_4$...