I was going to post a comment on my own theory about Mars and Jupiter colliding, but I just read the rules and it breaks it...badly. I was looking for informal peer review.  So my question is, has there been any mainstream published work about the possibility of planets colliding or interacting greatly?  (Velikovsky doesn't count obviously, I'm thinking an actual scientist) (besides the Earth-Moon of course)  I can't seem to find any.
One of the pertinent questions about many body systems that causes me much wonder is why the solar system is so stable for billions of years. I came across the idea of "resonance" and albeit an useful concept, it hardly explains the long stability of the solar system. Normally an N body problem with inverse square mutual interaction is an example of a chaotic system. Is there any real progress about this stability issue?
Is there an example of a ring $S$ with identity $1_S$ containing a non-trivial subring $R$ which itself has an identity $1_R$, but $1_R\neq 1_S$ (or equivalently $1_S\notin R$). I'd also like to know under what conditions the identities have to be equal. I know they must be equal if $S$ has no zero divisors, since for every $r\in R$ we have $(1_S-1_R)r=0$  In other words: Is the category of unital rings with identity-preserving morphisms a full subcategory of the category of rings (where morphism are only required to respect addition and multiplication)? How to make the window full screen with Javascript (stretching all over the screen) What is C# analog of C++ std::pair? I'm interested: What is C#'s analog of std::pair in C++? I found System.Web.UI.Pair class, but I'd prefer something template-based.  Thank you! How to merge multiple Internet connections into one? My PC has a total of 4 NICs, 2 wired Gigabit Ethernet network cards and also 2 wireless network cards. (One Broadcom with proprietary drivers and Ralink with open source software, which works much better than Broadcom.)  My cellphone can share its connection wirelessly to my PC, but I also have a wired Internet connection. So I have multiple Internet connections to access the Internet. How can I merge 2 or more connections together and balance them to enjoy one unified Internet experience that it is the sum of all Internet connections connected to it.  For example if I have a modem with an Internet connection of 1024kB/s and another one that offers 512kB/s and one small one that offers 128kB/s, after load balancing and merging all connections (Bonding or Teaming), I could download at a speed of 1664kB/s using all 3 Internet connections as one for example.  This question has always intrigued me. How to access a clicked URL in a URL handler application created in Automator I'm currently trying to modify the default URL handling behavior in OS X. I would like, when clicking on any link outside of a web browser, to copy this URL to the pasteboard instead of opening it in the default web browser – for instance, clicking a link in a Skype conversation should copy this URL to the OS X pasteboard instead of opening it in Firefox (which is currently my default web browser).  I have thought about solutions, but I’m currently unable to implement one. If I can create an application that puts URLs into the pasteboard that are sent to it, and can set this application as the default web browser, I would be able to achieve my goal.  I created an application with Automator that executes the shell command pbcopy and have set this application as my default web browser, but I didn’t get the expected result. I did some testing and I can confirm that the application runs on clicking on a link, however, I cannot get the URL passed to the application / shell script. I tried both stdin or a passed argument, but without success.  Is there a way for an application created with Automator to retrieve a clicked URL and send it to pbcopy, when that application is set as a (default) handler for URLs?  Alternatively, is there a better way to create a fake web browser that takes the input and puts it in the pasteboard than Automator? Or is there any other way that I can achieve my goal without a custom application / script? ListPlot multiple datasets over same x-values Show that any prime divisor of $x^4+x^3+x^2+x+1$, with $x\in\mathbb{N}$, is $5$ or $1$ mod $5$ We can write the "polynomial" as follows: $$x^4+x^3+x^2+x+1=\frac{x^5-1}{x-1}.$$ For even $x=2y$, we have that $x^5-1=(2y)^5-1=32y^5-1\equiv1$ mod $5$.  For odd $x=2y+1$, we have that $(2y+1)^5-1\equiv_532y^5\equiv2$ mod $5$.  I find it hard to believe my computations above. I guess this makes me rather clueless. I was hoping there was some way out with Legendre symbols. Any help is appreciated. I really read many tutorials, but crontab doesn't start notify send.  What I've tried:   etc/crontab  added at the end:  15 * * * * notify-send 'crontab' 'test'  with crontab interface:  crontab -e   added at the end:  15 * * * * notify-send 'crontab' 'test' How to cancel a jquery.load()? How can I view all of the flights between two cities across all dates? I believe that the standard routes of carriers between two semi-major US cities always maintain the same route number (e.g. UA3271), and day of the week. I'm looking at planning travel for an interview, so dates are [currently] quite flexible (as in at least one month's range). Since that's the case, there are other constraints that go into my choice of flights. One would be the option to fly out of my home city, land in the interview location, conduct the interview, and fly out in the same day. I figure: if I can view the schedule for flights (i.e. routes) between the two cities, I can make an educated request for days of travel. Yes, I could likely work with the interview scheduler (and I will), but I'd like to be proactive in suggesting some dates to achieve my goal, as well as learn this skill for myself in the future. Thus:  Where can I view the daily routes and times for flights between two cities, on whatever rotating basis (e.g. day of the week) they may be on? What Does it Really Mean to Have Different Kinds of Infinities? Subject/verb agreement when a title ends in a plural 1) "The book 'The Three Musketeers' is a wonderful example of..." Here we have a proper noun, a title that happens to end in a plural, and I have no sense that the verb should be plural. "Musketeers"/is seems proper/natural/correct, and 'are' not at all.   However, such certainty begins to wane in other examples: 2) "'The Heidi Chronicles' is a wonderful example of..." doesn't completely shake my confidence, but it moves the needle, at least a little bit. But, practically speaking, I wouldn't have a second thought about correcting a student who used 'are' instead of 'is'.  Here's the one that really bothers me: 3a) " 'The Basement Tapes' are a wonderful example of..." I don't think this sounds any less proper/natural/correct than 3b) " 'The Basement Tapes' is..." In fact, 3a seems less awkward than 3b.  Why? How can I execute `date` inside of a cron tab job? I want to create a log file for a cron script that has the current hour in the log file name. This is the command I tried to use:  0 * * * * echo hello &gt;&gt; ~/cron-logs/hourly/test`date "+%d"`.log   Unfortunately I get this message when that runs:  /bin/sh: -c: line 0: unexpected EOF while looking for matching ``' /bin/sh: -c: line 1: syntax error: unexpected end of file   I have tried escaping the date part in various ways, but without much luck. Is it possible to make this happen in-line in a crontab file or do I need to create a shell script to do this? Adding Layer Files (.lyr, .lyrx) to QGIS At college we use ArcGIS Desktop 10, but that does not function on my Mac so I have QGIS there instead.  I want to do my exercises with QGIS, but in ArcGIS Desktop we use .lyr files with ArcMap and .lyrx files with ArcGIS Pro, and they are not supported by QGIS.  Does anyone know, how I can connect the *.lyr files to my *.shp files to use them on my Mac with QGIS? Convergence/Divergence of infinite series $\sum_{n=1}^{\infty} \frac{(\sin n+2)^n}{n3^n}$ $$ \sum_{n=1}^{\infty} \frac{(\sin n+2)^n}{n3^n}$$  Does it converge or diverge?   Can we have a rigorous proof that is not probabilistic?   For reference, this question is supposedly a mix of real analysis and calculus. What is a "closed" or "duplicate" question? Laggy viewport in 2.9 when model has a lot vertices I don't know how to prove this example. Let $y(t):\mathbb{R}^+\to \mathbb{R}$ be a nonincreasing function. Assume that there is a constant $A&gt;0$ such that \begin{equation} \int_{s}^{+\infty}y(t)dt \leq Ay(s), \quad 0\leq s&lt;+\infty \end{equation} Then $y(t)\leq y(0)e^{1-\frac{t}{A}}$, for all $t&gt;0$. Lifting idempotents modulo a nilpotent ideal The problem is this:      Suppose $I \subseteq R$ is a nilpotent ideal and there is $r \in R$ with $r \equiv r^2 \pmod I$. Show $r \equiv e \pmod I$ for some $e \in R$ idempotent.   I have spent a few hours rolling around in abstracta with no destination. I believe that if I could write down a concrete example of this, the example could guide me through the abstract definitions and show me where to look for an idempotent in $R$. I have looked at 2x2 matrices and could not find any such examples. Might anybody have one? Regression for an outcome (ratio or fraction) between 0 and 1 I am thinking of building a model predicting a ratio $a/b$, where $a \le b$ and $a &gt; 0$ and $b &gt; 0$. So, the ratio would be between $0$ and $1$.  I could use linear regression, although it doesn't naturally limit to 0..1.  I have no reason to believe the relationship is linear, but of course it is often used anyway, as a simple first model.  I could use a logistic regression, although it is normally used to predict the probability of a two-state outcome, not to predict a continuous value from the range 0..1.  Knowing nothing more, would you use linear regression, logistic regression, or hidden option c?