How can I / is there a way that I can make the star behave just like the sprinkles?
Particles rotation not working correct
Leave the door open vs Leave the door opened Is there any subtle difference between:   We need to carry in some stuff so open the door and leave it open. We need to carry in some stuff so open the door and leave it opened.   I mean "leave it like that (in that state)". How to show that Klein four-group is a normal subgroup of the alternating group $A_4$ I want to show that the Klein four-group is a normal subgroup of the alternating group $A_4$.   I am using the information in , that shows explicitly $A_4$, and Klein four-group as a subgroup.  I know that there is the direct way, by definition, but is there a way that does not require actually multiplying so many permutations ? Do we have different set of badges in different SE sites. eg. I don't see any 'Pundit' badge in badges popup in Hinduism SE.  Also, if the above is true, then can we include the left badges in a SE site at a later stage. Ways to get free and legal access to research papers as a researcher I’ve discovered that website like ResearchGate offer the possibility to ask the paper editor to provide his paper for free. Many are collaborating.  Are there any other ways for researchers to obtain free access to papers? Can $\pi$ or $e$ be a root of a polynomial with algebraic coefficients? Since $\pi$ and $e$ are transcendental, neither can be the root of a polynomial with rational coefficients. However, it is easy to construct a polynomial transcendental coefficients (with $\pi$ or $e$ as one of it's roots), namely $(x-\pi)$ and $(x-e)$. However, is it possible to construct a finite polynomial (one of whose roots is $\pi$ or $e$) with only algebraic coefficients? (i.e. something such as $y=x^5-(\sqrt 2 -1)x^2+x$ .) A polynomial with only radical coefficients would be the best.  P.S. The polynomial doesn't necessarily need to have BOTH $\pi$ and $e$ as it's roots, just one is interesting enough. A continuation of .  I'm fighting a page-limit in a single-column layout and I need to put a Figure and a Table side-by-side and provide them with independent captions. However, the style guide for the publishers (LNCS) wants Figure captions below and Table captions above (probably something to do with ).   =======================================================  If I adapt @lockstep's floatrow example from  accordingly to have a Table caption above ...  \documentclass{article}  \usepackage{floatrow} % Table float box with bottom caption, box width adjusted to content  %% ********************************** %% just adding \captop to original example %% ********************************** \newfloatcommand{capbtabbox}{table}[\captop][\FBwidth]  \usepackage{blindtext}   \begin{document}  \blindtext  \begin{figure} \begin{floatrow} \ffigbox{%   \rule{3cm}{3cm}% }{%   \caption{A figure}% } \capbtabbox{%   \begin{tabular}{cc} \hline   Author &amp; Title \\ \hline   Knuth &amp; The \TeX book \\   Lamport &amp; \LaTeX \\ \hline   Knuth &amp; The \TeX book \\   Lamport &amp; \LaTeX \\ \hline   Knuth &amp; The \TeX book \\   Lamport &amp; \LaTeX \\ \hline   \end{tabular} }{%   \caption{A table}% } \end{floatrow} \end{figure}  \end{document}   =======================================================  The problem becomes clear ...    =======================================================  The floatrow doesn't correctly line up the Table and Caption. I reluctantly tried to use vspace to solve the problem, but it didn't work out.  Any suggestions on how to get these two to align? I'm happy to accept any alignment that ensures that the Table and Figure fit within the same "box".  (A similar-ish question was , but specific for subfig and with a very localised problem it seems.) home socket with DC voltage I'm wondering why, in a standard house, instead of using many low power AC-DC rectifier, there isn't a big (like 12V 20~50A) AC-DC rectifier which supplies some wall socket with a DC voltage? In the long run this should be less expensive, given the fact that AC to DC in one big apparatus is done better than in many low-quality transformers, right?  Also, modern chip DC voltage regulators have efficiency of >90%, so smaller (or even larger) voltages are still efficient and possible.  So we could use a 12V socket to charge a phone, desktop computer, laptop, radio etc... and still have an AC socket to move washing machine engine and other things that work better with an AC supply.  Why isn't this done?  edit: real question is: is it convenient, given a standard family (2 laptop, 1 desktop, 4 smarthpone, 1 big tv and some minor electonic) to do so? Why do people buy stocks that pay no dividend? Before recently, Apple Inc. did not give dividend to shareholders.  This makes me curious why people buy Apple Inc. stocks; while it might be due to the expectation of selling stocks at a higher price, this can only be possible if other people are thinking the same, thereby increasing demand. But the stocks themselves do not pay interests - so Apple's amazing revenue/profit records would not matter.... Unmarshal a single element list fails Selenium/PhantomJS raises error I read a comment under :     There are plenty of events that can occur that have zero probability.   This reminds me that I have seen similar saying before elsewhere, and have never been able to make sense out of it. So I was wondering    if zero probability and impossibility mean the same? if an event with zero probability doesn't mean that the event is impossible to occur, how probability theory represents/describes impossibility?   Thanks and regards! Capacitor Voltage Rating How to find the voltage rating of a capacitor after knowing the capacitance value.  Example, For a power supply, If the input voltage is 60V and output is 5V. The input capacitor(C1) value is 100uf and output capacitor value is 1000uf.  What is the voltage rating for both the capacitors and how to find them. How to know if my servers should use jumbo frames (MTU) Can I list the resources in a given package? Ubuntu copy dialogue stops at the last moment for a long time Whenever I try and copy a file to an USB flash disk, the progress bar runs till the end very fast and stops for an indeterminable time before it is complete.  Is there an issue with ubuntu or my flash disk is what I am not able to figure out. All I want is a realistic copy dialogue Angle between 2 points Given the following image:   $\hskip{1.5 in}$   Supposing $A(100, 300)$ and $B(300, 100)$, how can I find the angle $\alpha$ between A and B?  On a side note, what's the main difference between a point and a vector? translating a point to a vector is as simple as Point = Vector? Sometimes I find articles where the terms are interchangable I know on client side (javascript) you can use windows.location.hash but could not find anyway to access from the server side. I'm using asp.net. Deriving the inverse of a 2x2 matrix I hear so many terms involving the word "linear". Linear function, linear equation, linear system, linear operator, linear transformation, linear mapping, linear space, linear algebra, linear electrical circuits, linear filters, linear electrical elements, linear approximation, linear optimization.  I'm getting crazy trying to understand the application of the "linear concept" to all this aspects (function, equation, mapping, system, operator, transformation, algebra, etc.) and I wish to know the one essence that is to be linear. What something has to be to be linear? If I say something is linear, what do I know for sure about that something (no matter what the something is)?       I heard a definition of linearity is by homogeinity (scaling the input results in a scaled output) and addition (summing the inputs results in summing the outputs). Can I apply this simple definition to all the branches (operator, mapping, system, transformation, algebra, ...) I mentioned ? Do they all behave like a line ?  y = ax + b, for example, is a line but doesn't behave like a line because y is not linear. Google Maps Location History is showing an incorrect location