Understanding modifiers in Java
What is the difference between public, protected, package-private and private in Java?
Partial Sums of Geometric Series In .NET, what's the best way to prevent multiple instances of an app from running at the same time? And if there's no "best" technique, what are some of the caveats to consider with each solution? I am trying to prove:     $a\mid b \land b\mid c \Rightarrow a\mid c $   $a\mid b$ means that a divides b if there is an integer k, that $b=k\cdot a$  Please give me a hint on how to start, because I have no idea. Topological/Geometrical justification for $\text{CFT}_2$ being special It is known as a fact that conformal maps on $\mathbb{R}^n \rightarrow \mathbb{R}^n$ for $n&gt;2$ are rotations, dilations, translations, and special transformations while conformal maps for $n=2$ are from a much wider class of maps, holomorphic/antiholomorphic maps. I was wondering to know if there is any topological or geometrical description for this.   To show what I mean, consider this example: in $\mathbb{R}^n$ for $n&gt;2$ interchanging particles can only change the wave function to itself or its minus. It is related to the fundamental group of $\mathbb{R}^n-x_0$ ($x_0$ is a point in $\mathbb{R}^n$ and $\pi_1(\mathbb{R}^n-\{x_0\})=e$ for $n&gt;2$) but this is not true for $n=2$.   I want to know whether exists any topological invariant or just any geometrical explanation that is related to the fact that I mentioned about conformal maps on $\mathbb{R}^n$. Prove that functions map countable sets to countable sets One of my homework problems asks to prove that if $f:X\to Y$ is a function and $A$ is a countable subset of $X$, then $f(A)$ is countable.  I believe I have a valid proof by partitioning the set A into equivalency classes based in image under $f$. Then using that partition as domain for a choice function $C_f$ back to $A$. So now the function $f$ restricted to the domain (range $C_f$) $f|_{range(C_f)}$ maps to $f(A)$ 1-1 and onto. Therefore  $$|f(A)|=|range(C_f)|\leq |A|=\aleph_0$$ $\therefore f(A)$ is a countable set. $\quad \blacksquare$  My problem is that I used the axiom of countable choice $AC_\omega$ in my proof but that isn't a part of the course I am taking. Does anyone have a simpler proof or one that does not involve Choice? Why modules with no variables? I have a bunch of client point of sale (POS) systems that periodically send new sales data to one centralized database, which stores the data into one big database for report generation.  The client POS is based on PHPPOS, and I have implemented a module that uses the standard XML-RPC library to send sales data to the service. The server system is built on CodeIgniter, and uses the XML-RPC and XML-RPCS libraries for the webservice component. Whenever I send a lot of sales data (as little as 50 rows from the sales table, and individual rows from sales_items pertaining to each item within the sale) I get the following error:  Fatal error: Allowed memory size of 134217728 bytes exhausted (tried to allocate 54 bytes)   128M is the default value in php.ini, but I assume that is a huge number to break. In fact, I have even tried setting this value to 1024M, and all it does is take a longer time to error out.  As for steps I've taken, I've tried disabling all processing on the server-side, and have rigged it to return a canned response regardless of the input. However, I believe the problem lies in the actual sending of the data. I've even tried disabling the maximum script execution time for PHP, and it still errors out. Switching languages in bibliography with biblatex I would like to have a bibliography with both Cyrillic and Latin and the main document language being English. How can I make biblatex to automatically switch between languages? (without using XeTeX as suggested by some) The minimal example returns an error if the main language is English. However, with the main language being Russian the document works.  \documentclass{article}  \usepackage[utf8]{inputenc} \usepackage[russian,english]{babel}  \usepackage[backend = biber,babel=other]{biblatex} \usepackage{csquotes} \addbibresource{library.bib}  \begin{document} %\selectlanguage{russian} %if the main document language is Russian the bibliography is compiled without any problem. This is a test. \parencite{Bara2006,Baranov2001}  \printbibliography  \end{document}   The .bib entries are  @book{Bara2006, address = {New York}, author = {Bara, Judith}, publisher = {Routledge}, title = {{English Citation entry}}, year = {2006} }  @book{Baranov2001, address = {Санкт-Петербугр}, author = {Баранов, Николай А}, title = {{Эволюция взглядов}}, year = {2001} } I need to print an image at a certain size. What dimensions and resolution should I use? (This question is meant to be a resource to direct others to given that this is a common question.)  Given the task of creating an image that will be printed at a certain size, what pixel dimensions and resolution should I be setting my file at? When a/an precedes a parenthetical aside (sometimes seen in informal/conversational writing), should the vowel rule depend on the first word in parentheses, or the next word in the "regular" flow of the sentence?     I need a (memorable) idiom (preceding an m word; use a)   or     I need an (memorable) idiom (preceding an i word; use an) What are the rules about using an underscore in a C++ identifier? It's common in C++ to name member variables with some kind of prefix to denote the fact that they're member variables, rather than local variables or parameters. If you've come from an MFC background, you'll probably use m_foo. I've also seen myFoo occasionally.  C# (or possibly just .NET) seems to recommend using just an underscore, as in _foo. Is this allowed by the C++ standard? Making an invisible pressure plate I'm trying to build a teleporter. I want the player to be teleported from the first sign(left) to the right sign(right). So, when the player steps on the red wool on the left, he will automatically be teleported to the red wool on the right. I do not want to use any pressure plats.It might work with the testfor comment, but I didn't figure out, put that only works with a radius. BTW I'm in 1.10.2 bou I could probably change the version if necessary.     The testfor command block should activate the teleport command block,when the player is detected. Now, I'm not really the expert, so I know non of the commands that you would need to build this construction. Please help, I would highly appreciate it! If you need any more details, ask me! Program counter goes to the end of code and 8051 Restarts I have an 8051 MCU which I use keil to program it with C. My problem is that the micro-controller restarts at the end of some functions while they should return.  Using a debugger I tried to check it line by line. And I figured out the the MCU is not restated right after the end of the function. The PC(progam counter) goes to somewhere else (sometime somewhere that there is not any code to execute) and then it increases one by one until the end of code. It is very strange for me because I write my code in C and never seen the type of error previously.    I think this problem might be related to the compiler settings and thus I post the settings here:   Assembler settings: XR GEN DB EP NOMOD51  Compiler settings:  DB OE BR LARGE OPTIMIZE(11, SIZE) DEFINE(SILABS_PLATFORM_WMB912) DEFINE(SILABS_WMCU_SI106x)  Linker settings: CODE REMOVEUNUSED CLASSES(BIT(0x20.0-0x2F.7), DATA(D:0-D:0x7F), IDATA(I:0-I:0xFF), XDATA(X:0-X:0xFFF), CODE(C:0-C:0xFBFF), CONST(C:0-C:0xFBFF))  I tried both large and small settings but the problem remains. Kindly help me if you know the reason. I downloaded the Upwork desktop App on ubuntu 18.04. When I open it with Gdebi package installer I saw this error:    I tried to install gksu manually via sudo apt install gksu but I got this error  Building dependency tree        Reading state information... Done Package gksu is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'gksu' has no installation candidate   How can I install this software on ubuntu 18.04 (I download it yesturday so it is the most recent version on upwork website) ? I am using ArcMap 10.2 and I'm looking for a way to add  a table containing certain fields from select elements from a featureclass to my map. Ive tried the add table option from the attribute table, but it doesn't quite give what I want (the table must be editable to look a certain way).   Are there any options out there for 10.2 like arcpy.mapping.tableview or will upgrading to 10.3 so I can get access to the "graphic table element" function be best? I want to install the latest Firefox on my Ubuntu (64bit) box.  What is the best way to do this? Is there a specific update site or should I download the binaries manually? If doing manually, in which directory should I put the files? In my home directory, or is there a better place? Can I get a rebate after using my HSA? How to prove $a^3 + b^3 +c^3 - 3abc =1 $, If a,b,c are infinite series as given in the description box below? How do I prove that $$ a^3+b^3+c^3−3abc = 1 $$ if   $ a = 1+\frac{x^3}{3!}+\frac{x^6}{6!}......$ , $b=x+\frac{x^4}{4!}+\frac{x^7}{7!}....$ , $c=\frac{x^2}{2!}+\frac{x^5}{5!}+\frac{x^8}{8!}......$ ?  I have tried the following :-  I discovered that $a+b+c=e^x$ and that $a=\frac{d(b)}{dx}$, $b=\frac{d(c)}{dx}$, $c=\frac{d(a)}{dx}$ . But I am unable to proceed further with these information. Why do physicists think that the electron is an elementary particle? When we first discovered the proton and neutron, I'm sure scientists didn't think that it was made up of quark arrangements, but then we figured they could be and experiments proved that they were.  So, what is it about the electron that leads us to believe that it isn't a composite particle? What evidence do we have to suggest that it it isn't? I get double question marks when referring to labels inside figures I have some charts embedded in figures, and I want to be able to refer to them easily using the "Figure x" notation. I'm doing it like this (in this order):  \documentclass[12pt,letterpaper]{article}  ...  \section*{Results} ...we performed a linear regression to obtain a standard curve  (Figure~\ref{0:stdcurve})....  \pagebreak \section*{Results (Graphs)} \subsection*{Construction of Standard Graph for PNP} \begin{figure}[h]   % Figure 1     \centering     \includegraphics[scale=1]{kinematics-res/graph0-1}     \caption{The standard curve for PNP.}     \label{0:stdcurve} \end{figure}   However, instead of getting the output "...to obtain a standard curve (Figure 1)...", I just get "...to obtain a standard curve (Figure ??)..."  I also noticed that the PDFLaTeX compiler is generating warnings saying that it couldn't find the reference of the name 0:stdcurve. Why am I getting these warnings?