text:
Cygwin Install Zlib

Decompress DWARF debug sections using zlib. Bring your development under one roof, and get a handle on your company’s open source footprint with our secure, single-tenant, managed service. 0 $rbenv install 2. m32 files use the proper paths, and adjust as necessary. The most recent version of the Cygwin DLL is 3. dll is distributed from zlib. Cygwin; Install Cygwin; Update Cygwin; Search Packages; Licensing Terms; Cygwin/X; Community; Reporting Problems; cygwin32-zlib: zlib for Cygwin 32bit toolchain. Another fix is to remove the system zlib and let libpng use the wgrib2-supplied zlib. apt-cyg install gdb. One other thing to note is that the package mysql in Cygwin is actually MariaDB. Instructions for installing Cygwin from the Cygwin website can be found on the for Ptolemy II Installation Page. Ruby Version Manager (RVM) RVM is a command-line tool which allows you to easily install, manage, and work with multiple ruby environments from interpreters to sets of gems. Spine - Install from the zip distribution into the c:\cacti directory. exe does not install every package. The best way to get a clean installation of PyTorch, is to install the pre-compiled binaries from the Anaconda distribution. Development on Cygwin is quite active. See Using Apache HTTP Server on Microsoft Windows before you begin. While this is nice if you want to compile Tesseract for your own system where you can install Cygwin on your own, compiling with Visual Studio is better. xeyes, xhost, xinit, xlogo, etc. Dear GMT users, I am trying to install gmt5. The easiest way to install external libraries is via Homebrew. On RedHat OS's install the XFree86-devel package. However while "make" of GMT5. The following assumes that you are using Linux as a build environment. On Unix machines, you can package STAF as a tar or tar. We suggest storing it on your computer in a new directory you make named c:\cygwin\download. This is a bit more complicated. Detailed Installation Here is a more detailed discussion for downloading, configuring and installing Phission. In my opinion, the following packages (and their depending packages) are needed:. How to do this will vary from shell to shell. 2): If you download the library, install one or more development packages - whichever compression codecs you want to use with your deployment. PL" and so on within the structure of my cygwin install. We will be setting up a Ruby on Rails development environment on Windows 10. exe" X/Cygwin program. so file in /usr/lib will need to be recreated:. Download the GNU Embedded Toolchain for ARM, an open source suite of tools for C, C++ and Assembly programming for ARM Cortex-M and Cortex-R families. This section assumes that the Default choice is given for all downloads. The Cygwin tools are constantly being updated, for the latest versions, see the Cygwin website. Since cygwin1. This is a new install of cygwin on new Win 2003 Server using: Zlib 1. 本章ではJulius のコンパイルおよびインストールについて仕様を述べる．まずバイナリパッケージについて説明した後、Linux や互換環境(cygwin / mingw)における一般的なコンパイル方法とオプション設定方法について述べる。. Mingw-w64 is an advancement of the original mingw. The normal way to install the package from the repository is simply sudo apt-get install zlib1g-dev: no explicit URL should be involved in the command. Zlib: general purpose data compression / decompression library. Python IDLE is a GUI-based tool for Python. 2-1 Gnupg 1. , Ubuntu Server) under a VM and running gem5 there. RRDTool - Install from the Cacti website. Hi friends: I tried to compile wireshark at WIN7 with CMAKE under 64bit option,however the result is failed I can not figure out the reason,could you help me to have a check. Build and installation instructions for the NoMachine OpenSSH Win32 Port Although it should be possible to build with Visual C++ 2005 and SDK Platform for Windows XP or later, the following instructions refer to compiling the NoMachine OpenSSH portable version with MingW under a Cygwin environment. Installing Subversion. Home >> Madeline 2. Zlib: general purpose data compression / decompression library. If you are using Cygwin version 1. 0 or higher. The result is an opengl32. Change CMAKE_INSTALL_PREFIX to X:\path\to\zlib-x. 13 and libtool 1. zdebug’ instead of ‘. 02 or above), camlp4, pcre, and zlib. Folks, Im forced to use a win7 host for something (Ive been a desktop linux-only for about 15 years). Install Cygwin. If eclipse. Contrary to other VCS tools like CVS or SVN, Git's revision control is considered "distributed" in a sense that your local Git working directory can function as a fully-working repository with complete history and version-tracking capabilities. Continue until you get to the "Select Packages" screen. 1, deselect to install the fonts. Build libpng from its /projects folder and use LIB RELEASE configuration. by Paul Vorbach, 2014-04-10. zlib is designed to be a free, general-purpose, legally unencumbered -- that is, not covered by any patents -- lossless data-compression library for use on virtually any computer hardware and operating system. Hi all! Last night pepesan was the first man on earth to successfully build libgda under windows. The relating packages may work, but we encourage you to install a recent KDE release. 3-4 is also offered in the gcc4 package, but the Cygwin 1. While some Linux distributions (e. Not sure if the function is needed on Cygwin and so if the second solution is a no-go. Hi On brand new MingW (installed by mingw-get): 'mingw-get install zlib' installs the doc, man and lic components only. Detailed Installation Here is a more detailed discussion for downloading, configuring and installing Phission. lib to the. IX Header "SYNOPSIS" This document will help you configure, make, test and install Perl on Cygwin. pip was unusable with both IDP and Miniconda on Windows. CodeLite) 에서 연결됨. PECL is a repository for PHP Extensions, providing a directory of all known extensions and hosting facilities for downloading and development of PHP extensions. 3/XFree86-4. py install "install" is a Distutils command that installs something (typically a Python module or package). To test the results, issue: make check. h,$ apt-file. exe any time you want to update or install a Cygwin package for 64-bit windows. , make installcheck). Here is a way to compile the squashfs-tools, to produce squashfs from windows. Start the Cygwin Installer, in the "Select Package" page, search and install gcc-g++, gdb, make, libncurses, zlib, zlib-devel. The "prefix scheme" is useful when you wish to use one Python installation to perform the build/install (i. dll makes use of the Windows registry for its mount table, one cannot install two Cygwin installations (including Cygwin-Lite) to different. Escolha Install from Internet, para o instalador baixar os pacotes e já instalá-los. "When installing packages for the first time, setup*. Zip To install zip if you don't already have it, do this sudo apt-get install zip The simplest way to create a zip file (archive) is zip myzipfile. yum install libxslt-devel. The file optional-libs. cygwin Makefile edit Makefile. - 유의사항은 패키시 선택 사항에서 autoconf, automake, bison, flex, gcc, make. The normal way to install the package from the repository is simply sudo apt-get install zlib1g-dev: no explicit URL should be involved in the command. i want to install curses/ncurses. apt-cyg install texinfo. Instructions for installing Cygwin from the Cygwin website can be found on the for Ptolemy II Installation Page. I'm trying to install gpg2 on win10. The shared library needs to be moved to /lib, and as a result the. One other thing to note is that the package mysql in Cygwin is actually MariaDB. Copy the contents of the "lib" directory that was created into /lib/mingw 4. 本章ではJulius のコンパイルおよびインストールについて仕様を述べる．まずバイナリパッケージについて説明した後、Linux や互換環境(cygwin / mingw)における一般的なコンパイル方法とオプション設定方法について述べる。. Home >> Madeline 2. 9 or later, you may specify the configure option '--enable-shared' to build Cygwin DLLs. # See http://cygwin. Compile the package: make. Download the GNU Embedded Toolchain for ARM, an open source suite of tools for C, C++ and Assembly programming for ARM Cortex-M and Cortex-R families. How to install GCC compiler on Ubuntu 18. The Q8 version is twice as bad as Q16. Supports Windows, including Cygwin, MinGW, and Visual Studio. Did you install cygwin? Eclipse does not include a toolchain for licensing reasons, you have to install one separately. Nearly every major or even semi-significant open-source Unix package on earth has been ported to Cygwin and is available in pre-built format from the Cygwin website. Install rbenv. To test the results, issue: make check. I tried to build from a /cygwin/z/ drive and didn't have much success this way. Description. This document explains the intricacies of running HBase on Windows using Cygwin as an all-in-one single-node installation for testing and development. I just downloaded cygwin last week so I think all the packages are up to date (gcc, etc). Very important notice The standard configuration adopted by MinGW64 forbids to effectively link libpthread as a static library. 2 on windows 7 home edition using cygwin 6. Watch it together with the written tutorial to deepen your understanding: Installing Python on Windows, macOS, and Linux To get started working with Python 3, you’ll need to have access to the Python interpreter. These instructions assume you want to compile a 64-bit program, but they can easily be modified for 32-bit. To install the latest Also I installed the packages the packages zlib, zlib-devel, icu and libiconv to cygwin. On the next screen you will select the packages that will be downloaded and installed. IX Header "SYNOPSIS" This document will help you configure, make, test and install Perl on Cygwin. OpenSSL is licensed under an Apache-style license, which basically means that you are free to get and use it for commercial and non-commercial purposes subject to some simple license conditions. Note that if you're building on windows using the msvc toolset, you cannot run it from a cygwin terminal, you'll have to run it from a cmd terminal. Looking at the install options now, you can search for both 'hdf' and 'netcdf'. If you installed CygWin into C:\cygwin, open the file C:\cygwin\etc\profile in a text editor. Hello, I am trying to install fenics on cygwin 64bit running on Window 7. Unfortunately, because the cross compilation environment is more complicated and because MSVC has traditionally been the "standard" build environment, none of these packages are as simple to install as "configure; make; make install" on a linux host, nor are they installable by default with cygwin. Once everything is installed, start a cygwin shell. GNU cygwin: if you are compiling with -mno-cygwin, see the GNU mingw32 entry, above. CMake is an open-source, cross-platform family of tools designed to build, test and package software. 11 to build properly on Cygwin. These are "instructions for the impatient": shortcuts for getting Amber installed on popular operating systems. zlibに関してはcygwinからapt-cygコマンドを導入して $apt-cyg zlib でちゃんとインストール出来ました。 調べた結果pillowとzlibとwindowsは相性が悪いような事が書いてありました。. 5 % cp scripts/makefile. yum install freetype-devel. apt-cyg install zlib-devel. The easiest way to install external libraries is via Homebrew. bat and install. Under Windows, a libiconv package is available on cygwin website, cygwin 1. org, a friendly and active Linux Community. dll DLL that you can copy to the folder containing your application's executable to use Mesa LLVMpipe software rendering. below is the environment setting and command. Download the cygwin setup. zip from zlib. If this appeals to you, follow the instructions below to install Cygwin. Append -Dexpl=exp -Dlogl=log to Makefile's default DFLAGS line, such as:. exe tool with the following parameters to install the (build) dependencies:. ZLib If you downloaded the zlib source, you will have to build ZLib first. Building and installing gnustep-make ----- As ususal. To date (2008. Installing zlib Package zlib not found or ambiguous name, exiting Need Help Installing ROS in Cygwin on Windows Here is the camera info message: D: [-0. Compile the package: make. The packaging and distribution system used by PECL is shared with its sister, PEAR. 6 or later). In the MSYS command prompt:. Just open the appropriate solution and build the project zlibstat using the IDE. Rename mingw32-make. Hello, I am trying to install fenics on cygwin 64bit running on Window 7. com/ Devel の gccとmakeを. How to install curl in Cygwin phptuts August 20, 2016 Curl is a tool for transferring files with URL syntax, supporting FTP, FTPS, HTTP, HTTPS, TELNET, DICT, FILE and LDAP. configure to install zlib, hdf5, netcdf ##### export environment export F77=gfortran export FC=gfortran export CC=gcc export CXX=g++ export CFLAGS=-fPIC. I install HMMER on my computer but apparently it is not possible to use it without cygwin. However while "make" of GMT5. What does it do? It creates a database from the regular expression rules that it finds from the config file(s). >> >> I do it because it's easier to install third party packages, those that >> need an external library to run. From time to time, the ImageMagick developers release new versions. py (and sometimes other associated files). 9 or later, you may specify the configure option '--enable-shared' to build Cygwin DLLs. Note: I have been unable to build with cygwin according to these instructions. It is easier to get Vega Strike to compile with gcc -mno-cygwin and with all extra libs than in a "pure" cygwin mode since OpenAL and SDL libs require gcc -mno-cygwin for instance. Builds with the normal Cygwin compiler are not supported. Rename mingw32-make. # Here is an example of a debug build. This section assumes that the Default choice is given for all downloads. # Don't build in the QEMU source directory. Pip is a better alternative to Easy Install for installing Python packages. To work with it on Windows, the Cygwin package can be used. x for ARM cross target. Also this installer has g77 which is no longer a part of GNU compiler suite, its replaced by fortran95. Many choose to install into a "Cacti" sub folder. so file in /usr/lib will need to be recreated:. Test: On NT/2000/XP, Cygwin PostgreSQL passes all regression tests (i. Zip and unzip are found in the right place under C:\cygwin\bin. Is this somehow related to #13354?. This will download a GUI installer called setup-x86. For some reason, you might want to build the image libraries liblept uses. Open the xrick. # Start by making sure your system is up-to-date: sudo yum update sudo yum install yum-utils sudo yum groupinstall development # Libraries needed during compilation to enable all features of Python: yum install zlib-devel bzip2-devel openssl-devel ncurses-devel sqlite-devel readline. apt-cyg install zlib-devel. 9 bcftools-1. Download and install libpng. Description. mingw how-to. Building and installing gnustep-make ----- As ususal. Contrary to other VCS tools like CVS or SVN, Git's revision control is considered "distributed" in a sense that your local Git working directory can function as a fully-working repository with complete history and version-tracking capabilities. Leave Install For set to All unless you lack local administrative privileges. It is a completely cross platform distribution that stays true to the feel of vim while providing modern features like a plugin management system, autocomplete, tags and tons more. The gpg2 package is available through the normal Cygwin installer. Requirements. and add some special flags to your configure invocation. yum install gcc make install zlib-devel readline-devel libxml2-devel openssl-devel libmcrypt-devel curl-devel bzip2-devel xml2-config. Builds with the normal Cygwin compiler are not supported. It is now a valuable resource for people who want to make the most of their mobile devices, from customizing the look and feel to adding new functionality. qemu-discuss Advanced zlib check failed > Make sure to have the zlib libs and headers > sudo apt-get install mingw-w64 This is just the mingw cross. When you run the cygwin installer you have the option of installing 2. com When installing packages for the first time, setup*. It is used by video playback software, emulators, and popular games including Valve's award winning catalog and many Humble Bundle games. Add the Cygwin programs path to the list for "Executable files", before /system32, so VS will use cygwin's "find" command ; Confirm the changes. Install the cygwin package, then run easy_install-. Make sure the environment variables INCLUDE, LIB, ZLIB. Install the package: make install. Cygwin *is* a kind of Unix, and package management requirements on Cygwin thus is radically different from those on Windows. This is an example C program illustrating compressing data using zlib. npm Enterprise empowers developers to do what they do best while providing you with industry-leading administrative capabilities. 01 - Install 2. The zlib data format is itself portable across platforms. The following page is a combination of the INSTALL file provided with the OpenSSL library and notes from the field. The Cygwin tools are constantly being updated, for the latest versions, see the Cygwin website. These installation instructions are based on the suggested instructions provided with GNU Autoconf. apt-cyg install gcc-mingw. Many choose to install into a "Cacti" sub folder. h,$ apt-file. It's based on Linux, and allows Linux programs (for the most part) to work under Windows. "configure" and "make install" should work for you as they do on full Unix systems. Watch Now This tutorial has a related video course created by the Real Python team. Select the third option Install from Local Directory and click Next. I do not even know how you did manage to get the case-sensitive-fs check to pass, windows does not provide a case sensitive FS afaik. Install OCaml (4. Notes on installing Cygwin for first-time or beginner Cygwin users It is often recommended to install in a directory rather than the default C:\ location. you need to edit the makefile so the options are like this: Set this variable to either UNIX, MAC or WIN. 2 and later can be compiled on Cygwin following these steps: Step 1a. $chmod a+r /etc/passwd /etc/group$ chmod 777 /var $ssh-host-config -y. install an older version of bison (1. Open a cygwin shell. I recommend using MSYS2 for this kind of thing. Compiling OpenSSH under Windows 2003 Server MinGW I did attempt to compile OpenSSH using MinGW , however, this appears to be a cut down version of Cygwin so the compilation has issues with pwd. When choosing list of packages to install, search for "znc". Build and Install Hadoop 2. For a static build run. For example, if you want to install Julius files under /usr/local, the copy source and destination will be:. Build Ruby 2. OpenGL은 말 그대로 그래픽 라이브러리에 대한 표준이고 어떤 플랫폼에서건 일관적인 사용을 보장하지만 막상 이 컨텍스트를 띄우려면 윈도에서. How to install "readline" and "readline-devel" on Ubuntu ? The "Readline" library provides a set of functions for use by application that allow users to edit command lines as they are typed in. The Cygwin environment is a Win32 port of the popular GNU development tools for Windows NT, 95, and 98. Install rbenv and ruby-build as usual. To compile and run SU2 in Cygwin on a Windows machine, you will need to configure Cygwin with the appropriate packages (listed below), and then continue from within Cygwin as though you were using a linux machine. Open the xrick. Main choice was to build everything from cygwin by using the mingw versions of gcc. FFmpeg can be built with MSVC 2012 or earlier using a C99-to-C89 conversion utility and wrapper, or with MSVC 2013 or later natively. If you install it using this it will be correctly configured. Compiling ScummVM for Bada/Tizen. h to install by ‘apt-get’. Select Root Install Directory インストール先のディレクトリを指定します。デフォルトでは "C:\cygwin" になっており、そのままで構わないでしょう。 4. How to Install OpenSSH to Windows - Р. Very important notice The standard configuration adopted by MinGW64 forbids to effectively link libpthread as a static library. If you want to compile on 32 bit Cygwin, use setup-x86. gcc -mno-cygwin. Install rbenv and ruby-build as usual. 3 from binary(. apt-cyg install gettext-devel. 2 in cygwin. dll is distributed from zlib. sh: sed: command not found exec: --checktag: not found Can't find Qt. Welcome to LinuxQuestions. After you install Homebrew, run:. 0p0 (2015-12-25 revision 53290) [x86_64-cygwin]. Install rbenv. apt-cyg install zlib-devel. Download and install. cygwin下编译zlib源代码的更多相关文章 eclipse下编译hadoop源代码(转) hadoop是一个分布式存储和分布式计算的框架. Ruby Version Manager (RVM) RVM is a command-line tool which allows you to easily install, manage, and work with multiple ruby environments from interpreters to sets of gems. With Cygwin, also put the SDL. 7 source tree. Otherwise, your build may clash with applications that link to the official build. I am on windows 7 64bit machine with the latest cygwin standard installation. 2 on windows 7 home edition using cygwin 6. bashrc' file in the cygwin home folder (Omitting this step will cause an error):. When you have code that you'd like to compile, you'll put it in a subdirectory of HOME. 0 for RPi, but I used a VM running a Linux system. rvm/ If the install script is run as a standard, non-root user, RVM will install into the current users's home directory. Download the GNU Embedded Toolchain for ARM, an open source suite of tools for C, C++ and Assembly programming for ARM Cortex-M and Cortex-R families. To use the UFRaw Gimp plug-in you need first to install Gimp 2. First, go to the Cygwin homepage, download setup. 0$ rbenv rehash To check, run ruby -v. Gfortran 9 increates support for Fortran 2018 features and has more useful warning messages, particularly if you are currently using Gfortran 7 or older. 1) preparation #1 Install required packages using Cygwin's setup. Normally, you don't have to compile zlib yourself as the official precompiled zlib1. zlib-devel 1. 8-4 installation. I am trying to install the postgresql 7. 6 is now installed on your system. By default, the compiled programs will now be in the vcftools/bin/ directory. You will need a package called "CYGWIN" to run Hercules on a Windows box. apt-cyg install nasm. Created attachment 23009 Build log and full copy of zlib and 32/zlib subdirectories in build directory Comment 28 Ralf Wildenhues 2011-01-18 07:10:48 UTC (In reply to comment #26 ) > I'm seeing the same problem with gcc 4. Cacti - Install from the zip distribution and install in the web root or your choice. The following assumes that you are using Linux as a build environment. 1 (intel i5 ) windows using cygwin and I have installed zlib while installing cygwin but I am. Install Cygwin by running setup-x86_64. For Tcl or Java support, or for more full-featured Python integration, you will have to compile VTK from source code using CMake and compiler for your platform. Then, install the very nice tool apt-cyg which makes package management much easier in cygwin. #!/usr/bin/env php ®N wp-cli. I have had a BIG problem with compiling zlib. Mac OS X already has Perl installed. dist is located in that directory as well. PL" and so on within the structure of my cygwin install. How to install GMT on Cygwin. 7 At runtime, zlib1. Install the package: make install. Install Vowpal Wabbit on Windows and Cygwin April 14, 2014 41 Comments There are already instructions on how to install Vowpal Wabbit on other operating systems, but we could not find a clear one for Windows. This document also describes features of Cygwin that will affect how Perl behaves at runtime. 5 SP1) Note: The. you need to edit the makefile so the options are like this: Set this variable to either UNIX, MAC or WIN. All the files in Cygwin-Lite are present in a complete Cygwin install, except the scripts in /src and the HTML man pages in /html. When you have code that you'd like to compile, you'll put it in a subdirectory of HOME. gz), if you haven't already done so. xeyes, xhost, xinit, xlogo, etc. $chmod a+r /etc/passwd /etc/group$ chmod 777 /var \$ ssh-host-config -y. Make sure your spine. The source archive already has the appropriate cygwin patch applied. Introduction. gz cd libewf-20070408. Cygwin Installation. For Non Windows firewall, one still has to do it manually. Download the current source package of LuaJIT (pick the. 3, and most libraries are updated to newer upstream. After you install Homebrew, run:. Windows環境でMacで書かれたプログラムをコンパイルとか実行とかとかの話です。Cygwinに環境を移動したからLinuxに近い環境はそろえてあったんだけど、それでもcurse. There are many important points to consider before you begin compiling Apache HTTP Server (httpd). Anyway if defining the function does not hurt (would it on Linux for example?), then let's take the first solution?. This could take a while. Please refer to the build instructions provided by the library source for actual build instructions. Install samtools in Cygwin Sep 29, 2014. The Cygwin library brings to Windows the Unix system calls and an environment that Unix programs expect. This article describes how to upgrade your Cygwin GCC installation to a. Mingw-w64 is an advancement of the original mingw. x or later, select to install the fonts. When selecting packages click the top checkbox to select all cygwin packages. If you are not happy with configure's choice of compiler, compilation flags, or libraries, you can give 'configure' initial values for variables by specifying them on the configure command line, e. Did you install cygwin? Eclipse does not include a toolchain for licensing reasons, you have to install one separately. lib and SDLmain.


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# Angular Velocity Formula

Angular velocity is a vector quantity and is described as the rate of change of angular displacement which specifies the angular speed or rotational speed of an object and the axis about which the object is rotating. The amount of change of angular displacement of the particle at a given period of time is called angular velocity. The track of the angular velocity vector is vertical to the plane of rotation, in a direction which is usually indicated by the right-hand rule.

It is articulated as

$\omega\,&space;=\frac{d\Theta&space;}{dt}$

Where, d θ is change in angular displacement,

dt is change in time t.

Angular Velocity Formula is given by

$\omega\,&space;=\frac{\Theta&space;}{t}$

Where, θθ is angular displacement and

is the time taken.

The Angular Velocity and Linear Velocity is articulated by the formula

$\omega\,&space;=\frac{v}{r}$

Where,
the linear velocity  is

the radius of circular path is

Angular velocity is articulated in radian per second (rad/s). Angular Velocity formula is used to compute the angular velocity of any moving body.

Angular Velocity Problems

Underneath are given some problems based on Angular velocity which may be helpful for you.

Solved Examples

Problem  1: Calculate the angular velocity of a particle moving along the straight line given by θ = 3t3 + 6t + 2 when t = 5s.
Given: θ = 3t3 + 6t + 2,
time t = 5 s

$The\,&space;angular\,&space;velocity\,&space;is\,&space;given\,&space;by\,&space;\omega\,&space;=\frac{d\Theta&space;}{dt}\,&space;=9t^{2}+6$

$For\,&space;t\,&space;=\,&space;5s,\,&space;the\,&space;angular\,&space;velocity\,&space;is\,&space;\omega\,&space;=\,&space;9(5)^{2}+6\,&space;=\,&space;181\,&space;units/sec.$

Problem 2: Find the angular velocity of the second hand of a clock?
$The\,&space;angular\,&space;velocity\,&space;is\,&space;given\,&space;by\,\,&space;\omega\,&space;\frac{\theta&space;}{t}$
$=\,&space;\frac{2\pi&space;}{60}$
$=\,&space;0.1047\,&space;rad/s.$

format: plain


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# What pattern is this, and should I do it?

I'm making a game in as3 using flash develop and flash cs5. Everything is object oriented. I was wondering, should I have one "gateway" class that has a property-reference to all instantiations of other classes, and I just pass this gateway class to new objects, so they have access to every class. Like so:

 var block:Block = new Block(gateway);

//In the block class:
this.gateway.player.setHealth(100);
//Or:
this.gateway.input.lock();

Is this like a singleton pattern or something? Should I do this?

This is called the context object design pattern, and it is better than the singleton pattern.

• Context objects aid testing, because you can pass mock contexts to functions you want to test. Singletons hinder it, because to mock singletons you need to make them not singletons.
• Context objects makes your "global state" explicit, and therefore easier to reason about. If a function doesn't take a context object, you know it doesn't use any global context state. You have no such guarantee with singletons or global variables.
• Context objects are very slightly slower if you don't use them, because you add another parameter to all your function calls. They can be faster than globals if you do use them, and are nearly always faster than singletons.
• Context objects are easier to implement; usually they live on the heap or stack in a normal way. Singletons have tricky issues involving threading in many languages.

So no, this is not a singleton, it's way better than a singleton.

However, you're still passing around a crapload of state - the fact you're keeping it all in a single local variable makes it more explicit, but still creates major conflation of concerns. Keep in mind the one responsibility rule. It makes some sense for there to be a context that owns the player and the current level - they're related - but why does the same context own your keyboard input?

Consider different levels of contexts, for example:

• GameplayContext - owns the player, enemies, the level geometry, etc.
• InputContext - owns keyboard and mouse handles, input events, etc.
• GraphicsContext - owns textures, the window handle, etc.
• GlobalContext - owns a GameplayContext, a GraphicsContext, and an InputContext. This is where you want to apply the service locator pattern, to be able to swap out some contexts for others as needed. And maybe, for quick iteration and testing, this should be in a real global variable - just realize that whenever you use it, you're building up tech debt.

These contexts still conflate concerns somewhat - maybe some event handler takes a GameplayContext and really only needs the player - but the responsibilities are clearly laid out. You know that something that takes a GameplayContext won't load a texture; something taking an InputContext can't kill a player.

• +1 Good answer. Some of the speed or threading concerns don't really apply in this context though (ActionScript3 doesn't support threading and a lot of speed improving mechanisms that work in C++ don't apply when using AS3). – bummzack Nov 19 '10 at 11:05
• I don't know much about the AS3VM, but in most dynamic languages, the cost of passing/receiving/using a local is still faster (array lookup) than the cost of looking up a global (hash lookup), and much faster than calling a function (craploads of stuff) to get at it. So I think that advice still applies. – user744 Nov 19 '10 at 11:51

This doesn't look like the Singleton pattern. The way I understand it, you're passing an object with references to important game-objects to all of your instances.

If this would be the Singleton pattern, you would have:

AudioManager.getInstance().playSound(XY);

Whereas in your case you might have:

this.gateway.getAudioManager().playSound(XY);

It looks basically the same, but it really isn't. If you would want to replace AudioManager with a new (extended class) like ExtendedAudioManager, you would hit a wall using the Singleton pattern. Your gateway approach will handle that just fine though.

The drawback of your approach is that you'll have to pass around the gateway everywhere. The service locator pattern (proposed by Joe Wreschnig in this thread), looks like a good replacement for your "gateway pattern".

Sometimes it's better to just run with the simple and straightforward method instead of over-designing things though. Especially when it's a small project or a prototype. Maybe you could make that gateway some sort of a global variable.. eg. Game.gateway and run with it.

Most solutions to this problem, including the Singleton pattern, involve the use of static variables. If you'll only ever have one player, you can just have Player be a singleton class, which means you could access the Player instance through something like Player.currentPlayer. Many people rage against Singletons, however. You could also have a ResourceManager or similar class that contains static references to various useful global or pretty-darn-global variables. In your code, you might as well make "Gateway's" variables statically accessible instead of inflating your code by passing it around everywhere.

• The question has changed substantially since I made this answer, enough that it doesn't seem worth it to edit it. – Gregory Avery-Weir Nov 19 '10 at 14:58
• Apart from the title, nothing changed in the question. – bummzack Nov 19 '10 at 17:33
• What? Nothing has changed other than the title. -1 – AttackingHobo Nov 19 '10 at 18:05
• I think I was thinking of the title here; I remember the original title being something like "How should I do this?" It's totally possible that I misread the initial title/question when I made the answer. – Gregory Avery-Weir Nov 22 '10 at 4:17


text:
D02 Chapter Contents
D02 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentD02PVF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

D02PVF is a setup routine which must be called prior to the first call of either of the integration routines D02PCF and D02PDF.

## 2  Specification

 SUBROUTINE D02PVF ( NEQ, TSTART, YSTART, TEND, TOL, THRES, METHOD, TASK, ERRASS, HSTART, WORK, LENWRK, IFAIL)
 INTEGER NEQ, METHOD, LENWRK, IFAIL REAL (KIND=nag_wp) TSTART, YSTART(NEQ), TEND, TOL, THRES(NEQ), HSTART, WORK(LENWRK) LOGICAL ERRASS CHARACTER(1) TASK

## 3  Description

D02PVF and its associated routines (D02PCF, D02PDF, D02PWF, D02PXF, D02PYF and D02PZF) solve the initial value problem for a first-order system of ordinary differential equations. The routines, based on Runge–Kutta methods and derived from RKSUITE (see Brankin et al. (1991)), integrate
 $y′=ft,y given yt0=y0$
where $y$ is the vector of $n$ solution components and $t$ is the independent variable.
The integration proceeds by steps from the initial point ${t}_{0}$ towards the final point ${t}_{f}$. An approximate solution $y$ is computed at each step. For each component ${y}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$, the error made in the step, i.e., the local error, is estimated. The step size is chosen automatically so that the integration will proceed efficiently while keeping this local error estimate smaller than a tolerance that you specify by means of parameters TOL and THRES.
D02PCF can be used to solve the ‘usual task’, namely integrating the system of differential equations to obtain answers at points you specify. D02PDF is used for all more ‘complicated tasks’.
You should consider carefully how you want the local error to be controlled. Essentially the code uses relative local error control, with TOL being the desired relative accuracy. For reliable computation, the code must work with approximate solutions that have some correct digits, so there is an upper bound on the value you can specify for TOL. It is impossible to compute a numerical solution that is more accurate than the correctly rounded value of the true solution, so you are not allowed to specify TOL too small for the precision you are using. The magnitude of the local error in ${y}_{i}$ on any step will not be greater than ${\mathbf{TOL}}×\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left({\mu }_{i},{\mathbf{THRES}}\left(i\right)\right)$ where ${\mu }_{i}$ is an average magnitude of ${y}_{i}$ over the step. If ${\mathbf{THRES}}\left(i\right)$ is smaller than the current value of ${\mu }_{i}$, this is a relative error test and TOL indicates how many significant digits you want in ${y}_{i}$. If ${\mathbf{THRES}}\left(i\right)$ is larger than the current value of ${\mu }_{i}$, this is an absolute error test with tolerance ${\mathbf{TOL}}×{\mathbf{THRES}}\left(i\right)$. Relative error control is the recommended mode of operation, but pure relative error control, ${\mathbf{THRES}}\left(i\right)=0.0$, is not permitted. See Section 8 for further information about error control.
D02PCF and D02PDF control local error rather than the true (global) error, the difference between the numerical and true solution. Control of the local error controls the true error indirectly. Roughly speaking, the code produces a solution that satisfies the differential equation with a discrepancy bounded in magnitude by the error tolerance. What this implies about how close the numerical solution is to the true solution depends on the stability of the problem. Most practical problems are at least moderately stable, and the true error is then comparable to the error tolerance. To judge the accuracy of the numerical solution, you could reduce TOL substantially, e.g., use $0.1×{\mathbf{TOL}}$, and solve the problem again. This will usually result in a rather more accurate solution, and the true error of the first integration can be estimated by comparison. Alternatively, a global error assessment can be computed automatically using the parameter ERRASS. Because indirect control of the true error by controlling the local error is generally satisfactory and because both ways of assessing true errors cost twice, or more, the cost of the integration itself, such assessments are used mostly for spot checks, selecting appropriate tolerances for local error control, and exploratory computations.
D02PCF and D02PDF each implement three Runge–Kutta formula pairs, and you must select one for the integration. The best choice for METHOD depends on the problem. The order of accuracy is $3$, $5$ and $8$ respectively. As a rule, the smaller TOL is, the larger you should take the value of METHOD. If the components THRES are small enough that you are effectively specifying relative error control, experience suggests
 TOL efficient METHOD ${10}^{-2}-{10}^{-4}$ 1 ${10}^{-3}-{10}^{-6}$ 2 ${10}^{-5}-$ 3
The overlap in the ranges of tolerances appropriate for a given METHOD merely reflects the dependence of efficiency on the problem being solved. Making TOL smaller will normally make the integration more expensive. However, in the range of tolerances appropriate to a METHOD, the increase in cost is modest. There are situations for which one METHOD, or even this kind of code, is a poor choice. You should not specify a very small value for ${\mathbf{THRES}}\left(i\right)$, when the $i$th solution component might vanish. In particular, you should not do this when ${y}_{i}=0.0$. If you do, the code will have to work hard with any value for METHOD to compute significant digits, but ${\mathbf{METHOD}}=1$ is a particularly poor choice in this situation. All three methods are inefficient when the problem is ‘stiff’. If it is only mildly stiff, you can solve it with acceptable efficiency with ${\mathbf{METHOD}}=1$, but if it is moderately or very stiff, a code designed specifically for such problems will be much more efficient. The higher the order, i.e., the larger the value of METHOD, the more smoothness is required of the solution in order for the method to be efficient.
When assessment of the true (global) error is requested, this error assessment is updated at each step. Its value can be obtained at any time by a call to D02PZF. The code monitors the computation of the global error assessment and reports any doubts it has about the reliability of the results. The assessment scheme requires some smoothness of $f\left(t,y\right)$, and it can be deceived if $f$ is insufficiently smooth. At very crude tolerances the numerical solution can become so inaccurate that it is impossible to continue assessing the accuracy reliably. At very stringent tolerances the effects of finite precision arithmetic can make it impossible to assess the accuracy reliably. The cost of this is roughly twice the cost of the integration itself with ${\mathbf{METHOD}}=2$ or $3$, and three times with ${\mathbf{METHOD}}=1$.
The first step of the integration is critical because it sets the scale of the problem. The integrator will find a starting step size automatically if you set the parameter HSTART to $0.0$. Automatic selection of the first step is so effective that you should normally use it. Nevertheless, you might want to specify a trial value for the first step to be certain that the code recognizes the scale on which phenomena occur near the initial point. Also, automatic computation of the first step size involves some cost, so supplying a good value for this step size will result in a less expensive start. If you are confident that you have a good value, provide it via the parameter HSTART.

## 4  References

Brankin R W, Gladwell I and Shampine L F (1991) RKSUITE: A suite of Runge–Kutta codes for the initial value problems for ODEs SoftReport 91-S1 Southern Methodist University

## 5  Parameters

1:     NEQ – INTEGERInput
On entry: $n$, the number of ordinary differential equations in the system to be solved by the integration routine.
Constraint: ${\mathbf{NEQ}}\ge 1$.
2:     TSTART – REAL (KIND=nag_wp)Input
On entry: the initial value of the independent variable, ${t}_{0}$.
3:     YSTART(NEQ) – REAL (KIND=nag_wp) arrayInput
On entry: ${y}_{0}$, the initial values of the solution, ${y}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.
4:     TEND – REAL (KIND=nag_wp)Input
On entry: the final value of the independent variable, ${t}_{f}$, at which the solution is required. TSTART and TEND together determine the direction of integration.
Constraint: ${\mathbf{TEND}}$ must be distinguishable from TSTART for the method and the precision of the machine being used.
5:     TOL – REAL (KIND=nag_wp)Input
On entry: a relative error tolerance.
Constraint: .
6:     THRES(NEQ) – REAL (KIND=nag_wp) arrayInput
On entry: a vector of thresholds.
Constraint: ${\mathbf{THRES}}\left(i\right)\ge \sqrt{\sigma }$, where $\sigma$ is approximately the smallest possible machine number that can be reciprocated without overflow (see X02AMF).
7:     METHOD – INTEGERInput
On entry: the Runge–Kutta method to be used.
${\mathbf{METHOD}}=1$
A $2\left(3\right)$ pair is used.
${\mathbf{METHOD}}=2$
A $4\left(5\right)$ pair is used.
${\mathbf{METHOD}}=3$
A $7\left(8\right)$ pair is used.
Constraint: ${\mathbf{METHOD}}=1$, $2$ or $3$.
On entry: determines whether the usual integration task is to be performed using D02PCF or a more complicated task is to be performed using D02PDF.
${\mathbf{TASK}}=\text{'U'}$
D02PCF is to be used for the integration.
${\mathbf{TASK}}=\text{'C'}$
D02PDF is to be used for the integration.
Constraint: ${\mathbf{TASK}}=\text{'U'}$ or $\text{'C'}$.
9:     ERRASS – LOGICALInput
On entry: specifies whether a global error assessment is to be computed with the main integration. ${\mathbf{ERRASS}}=\mathrm{.TRUE.}$ specifies that it is.
Constraint: ${\mathbf{ERRASS}}=\mathrm{.TRUE.}$ or $\mathrm{.FALSE.}$.
10:   HSTART – REAL (KIND=nag_wp)Input
On entry: a value for the size of the first step in the integration to be attempted. The absolute value of HSTART is used with the direction being determined by TSTART and TEND. The actual first step taken by the integrator may be different to HSTART if the underlying algorithm determines that HSTART is unsuitable. If ${\mathbf{HSTART}}=0.0$ then the size of the first step is computed automatically.
Suggested value: ${\mathbf{HSTART}}=0.0$.
11:   WORK(LENWRK) – REAL (KIND=nag_wp) arrayOutput
On exit: contains information for use by D02PCF or D02PDF. This must be the same array as supplied to D02PCF or D02PDF. The contents of this array must remain unchanged between calls.
12:   LENWRK – INTEGERInput
On entry: the dimension of the array WORK as declared in the (sub)program from which D02PVF is called. ( ${\mathbf{LENWRK}}\ge 32×{\mathbf{NEQ}}$ is always sufficient.)
Constraints:
• if ${\mathbf{TASK}}=\text{'U'}$ and ${\mathbf{ERRASS}}=\mathrm{.FALSE.}$,
• if ${\mathbf{METHOD}}=1$, ${\mathbf{LENWRK}}\ge 10×{\mathbf{NEQ}}$;
• if ${\mathbf{METHOD}}=2$, ${\mathbf{LENWRK}}\ge 20×{\mathbf{NEQ}}$;
• if ${\mathbf{METHOD}}=3$, ${\mathbf{LENWRK}}\ge 16×{\mathbf{NEQ}}$;
• if ${\mathbf{TASK}}=\text{'U'}$ and ${\mathbf{ERRASS}}=\mathrm{.TRUE.}$,
• if ${\mathbf{METHOD}}=1$, ${\mathbf{LENWRK}}\ge 17×{\mathbf{NEQ}}$;
• if ${\mathbf{METHOD}}=2$, ${\mathbf{LENWRK}}\ge 32×{\mathbf{NEQ}}$;
• if ${\mathbf{METHOD}}=3$, ${\mathbf{LENWRK}}\ge 21×{\mathbf{NEQ}}$;
• if ${\mathbf{TASK}}=\text{'C'}$ and ${\mathbf{ERRASS}}=\mathrm{.FALSE.}$,
• if ${\mathbf{METHOD}}=1$, ${\mathbf{LENWRK}}\ge 10×{\mathbf{NEQ}}$;
• if ${\mathbf{METHOD}}=2$, ${\mathbf{LENWRK}}\ge 14×{\mathbf{NEQ}}$;
• if ${\mathbf{METHOD}}=3$, ${\mathbf{LENWRK}}\ge 16×{\mathbf{NEQ}}$;
• if ${\mathbf{TASK}}=\text{'C'}$ and ${\mathbf{ERRASS}}=\mathrm{.TRUE.}$,
• if ${\mathbf{METHOD}}=1$, ${\mathbf{LENWRK}}\ge 15×{\mathbf{NEQ}}$;
• if ${\mathbf{METHOD}}=2$, ${\mathbf{LENWRK}}\ge 26×{\mathbf{NEQ}}$;
• if ${\mathbf{METHOD}}=3$, ${\mathbf{LENWRK}}\ge 21×{\mathbf{NEQ}}$.
13:   IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.
On exit: ${\mathbf{IFAIL}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6  Error Indicators and Warnings

If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
${\mathbf{IFAIL}}=1$
 On entry, ${\mathbf{NEQ}}<1$, or TEND is too close to TSTART, or ${\mathbf{TOL}}>0.01$ or , or ${\mathbf{THRES}}\left(i\right)<\sqrt{\sigma }$, where $\sigma$ is approximately the smallest possible machine number that can be reciprocated without overflow (see X02AMF), or ${\mathbf{METHOD}}\ne 1$, $2$ or $3$, or ${\mathbf{TASK}}\ne \text{'U'}$ or $\text{'C'}$, or LENWRK is too small.

## 7  Accuracy

Not applicable.

If ${\mathbf{TASK}}=\text{'C'}$ then the value of the parameter TEND may be reset during the integration without the overhead associated with a complete restart; this can be achieved by a call to D02PWF.
It is often the case that a solution component ${y}_{i}$ is of no interest when it is smaller in magnitude than a certain threshold. You can inform the code of this by setting ${\mathbf{THRES}}\left(i\right)$ to this threshold. In this way you avoid the cost of computing significant digits in ${y}_{i}$ when only the fact that it is smaller than the threshold is of interest. This matter is important when ${y}_{i}$ vanishes, and in particular, when the initial value ${\mathbf{YSTART}}\left(i\right)$ vanishes. An appropriate threshold depends on the general size of ${y}_{i}$ in the course of the integration. Physical reasoning may help you select suitable threshold values. If you do not know what to expect of $y$, you can find out by a preliminary integration using D02PCF with nominal values of THRES. As D02PCF steps from ${t}_{0}$ towards ${t}_{f}$ for each $i=1,2,\dots ,n$ it forms ${\mathbf{YMAX}}\left(i\right)$, the largest magnitude of ${y}_{i}$ computed at any step in the integration so far. Using this you can determine more appropriate values for THRES for an accurate integration. You might, for example, take ${\mathbf{THRES}}\left(i\right)$ to be  times the final value of ${\mathbf{YMAX}}\left(i\right)$.


text:
# Superintegrability of geodesic motion on the sausage model

@article{Arutyunov2017SuperintegrabilityOG,
title={Superintegrability of geodesic motion on the sausage model},
author={G. E. Arutyunov and Martin Heinze and Daniel Medina-Rincon},
journal={Journal of Physics A},
year={2017},
volume={50},
pages={244002}
}
• Published 17 May 2017
• Physics
• Journal of Physics A
Reduction of the eta-deformed sigma model on AdS(5) x S-5 to the two-dimensional squashed sphere (S-2)eta can be viewed as a special case of the Fateev sausage model where the coupling constant v i ...
2 Citations
Spinning strings in the eta-deformed Neumann-Rosochatius system
• Mathematics
• 2017
The sigma model of closed strings spinning in the η deformation of AdS_(5) × S^(5) leads to an integrable deformation of the one-dimensional Neumann-Rosochatius mechanical system. In this article we

## References

SHOWING 1-10 OF 61 REFERENCES
Integrable deformation of the AdS5×S5 superstring action.
• Physics
Physical review letters
• 2014
An integrable deformation of the type IIB AdS5×S5 superstring action is presented and the original psu(2,2|4) symmetry is expected to become q deformed.
Integrability of the $\eta$-deformed Neumann–Rosochatius model
• Mathematics
• 2016
An integrable deformation of the well-known Neumann-Rosochatius system is studied by considering generalised bosonic spinning solutions on the eta-deformed AdS(5) x S-5 background. For this integra
Jordanian deformations of the AdS5 × S5 superstring
• Geology
• 2014
A bstractWe consider Jordanian deformations of the AdS5 × S5 superstring action. These deformations correspond to non-standard q-deformations. In particular, it is possible to perform a partial
Deformed Neumann model from spinning strings on (AdS5 × S5)η
• Mathematics
• 2014
A bstractWe show that bosonic spinning strings on the η-deformed AdS5 × S5 background are naturally described as periodic solutions of a novel finite-dimensional integrable system which can be viewed
S-matrix for strings on η-deformed AdS5 × S5
• Physics
• 2014
A bstractWe determine the bosonic part of the superstring sigma model Lagrangian on η-deformed AdS5 × S5, and use it to compute the perturbative world-sheet scattering matrix of bosonic particles of
An integrability primer for the gauge-gravity correspondence: an introduction
• Physics
• 2016
We introduce a series of articles reviewing various aspects of integrable models relevant to the anti-de Sitter (AdS)/conformal quantum field theory (CFT) correspondence. Topics covered in these re
On integrability of the Yang–Baxter σ-model
We prove that the recently introduced Yang–Baxter σ-model can be considered as an integrable deformation of the principal chiral model. We find also an explicit one-to-one map transforming every


text:
# Question

In a national survey conducted by the Centers for Disease Control to determine college students’ health-risk behaviors, college students were asked, “How often do you wear a seatbelt when driving a car?” The frequencies appear in the following table:
Response ........ Frequency
Never ........ 118
Rarely ........ 249
Sometimes ..... 345
Most of the time .... 716
Always ........ 3093
(a) Construct a probability model for seatbelt use by a driver.
(b) Is it unusual for a college student to never wear a seatbelt when driving a car? Why?

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Views38


text:
1

### JEE Main 2016 (Online) 9th April Morning Slot

A uniformly tapering conical wire is made from a material of Young’s modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3 R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal :
A
L $\left( {1 + {2 \over 9}{{Mg} \over {\pi Y{R^2}}}} \right)$
B
L $\left( {1 + {1 \over 3}{{Mg} \over {\pi Y{R^2}}}} \right)$
C
L $\left( {1 + {1 \over 9}{{Mg} \over {\pi Y{R^2}}}} \right)$
D
L $\left( {1 + {2 \over 3}{{Mg} \over {\pi Y{R^2}}}} \right)$

## Explanation

Here r = 3R $-$ ${{2R} \over L}$ x

$\therefore$   Extension in the wire of length dx,

dl = ${{Fdx} \over {AY}}$

= ${{Mg\,dx} \over {\pi {r^2}\,Y}}$

= ${{Mg\,dx} \over {\pi {{\left( {3R - {{2R} \over L}x} \right)}^2}Y}}$

$\therefore$   Change in wire length,

$\Delta$L = $\int\limits_0^L {dl}$

= $\int\limits_0^L {{{Mg\,dx} \over {\pi {{\left( {3R - {{2R} \over L}x} \right)}^2}Y}}}$

= ${{Mg} \over {\pi Y}}\int\limits_0^L {{{dx} \over {{{\left( {3R - {{2R} \over L}x} \right)}^2}}}}$

= ${{Mg} \over {\pi Y}}\left[ { - {1 \over {\left( {3R - {{2R} \over L}x} \right)}} \times \left( { - {L \over {2R}}} \right)} \right]_0^L$

= ${{Mg} \over {\pi Y}}$ $\left[ {\left( {{L \over {2{R^2}}} - {L \over {6{R^2}}}} \right)} \right]$

= ${{Mg} \over {\pi Y}}\left( {{{2L} \over {6{R^2}}}} \right)$

= ${{MgL} \over {3\pi {R^2}Y}}$

$\therefore$   The equilibrium extended length of the wire,

= L + $\Delta$L

= L + ${{MgL} \over {3\pi {R^2}Y}}$

= L (1 + ${1 \over 3}$ ${{Mg} \over {\pi {R^2}Y}}$)
2

### JEE Main 2016 (Online) 9th April Morning Slot

A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at T=0oC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is $\alpha$ then the value of S is :
A
$\alpha$
B
${\alpha \over 2}$
C
2$\alpha$
D
${1 \over \alpha }$

## Explanation

Change of length of wire with temperature,

$\Delta $$\ell = \alpha \ell \Delta \theta Time period of pendulum at temperature \theta , T\theta = 2\pi$$\sqrt {{{\ell + \Delta \ell } \over g}}$

= 2$\pi$$\sqrt {{{\ell \left( {1 + \alpha \Delta \theta } \right)} \over g}}$

= $2\pi \sqrt {{\ell \over g}} {\left( {1 + \alpha \Delta \theta } \right)^{{1 \over 2}}}$

= $2\pi \sqrt {{\ell \over g}} {\left( {1 + {{\Delta \ell } \over \ell }} \right)^{{1 \over 2}}}$

$\simeq$  T0 $\left( {1 + {{\Delta \ell } \over {2\ell }}} \right)$

Here T0 = time period at temperature 0oC.

$\therefore$   Change in time period,

$\Delta$T = T$\theta$ $-$ T0

= ${{{T_0}\Delta \ell } \over {2\ell }}$

= ${{{T_0}\left( {\alpha \ell \Delta \theta } \right)} \over {2\ell }}$

$\therefore$   ${{\Delta T} \over {\Delta \theta }}$ = ${{{T_0}\alpha } \over 2}$

Given that T0 = 2,

$\therefore$   ${{\Delta T} \over {\Delta \theta }}$ = ${{2\alpha } \over 2}$ = $\alpha$

${{\Delta T} \over {\Delta \theta }}$ is the shape of $\Delta$T and ${\Delta \theta }$

curve = S (given)

$\therefore$   S = $\alpha$
3

### JEE Main 2016 (Online) 9th April Morning Slot

Which of the following option correctly describes the variation of the speed v and acceleration ‘a’ of a point mass falling vertically in a viscous medium that applies a force F = − kv, where ‘k’ is a constant, on the body ? (Graphs are schematic and not drawn to scale)
A
B
C
D

## Explanation

Equation of motion for the mass,

ma = mg $-$ kv

$\Rightarrow$    ${{dv} \over {dt}} = {{mg - kv} \over m}$

$\Rightarrow$   $\int\limits_0^v {{{dv} \over {mg - kv}}} = {1 \over m}\int\limits_0^t {dt}$

$\Rightarrow$   $- {1 \over k}\left[ {\ln \left( {mg - kv} \right)} \right]_0^v = {t \over m}$

$\Rightarrow$   $\ln \left( {{{mg - kv} \over {mg}}} \right) = - {{kt} \over m}$

$\Rightarrow$   $1 - {{kv} \over {mg}} = {e^{ - {{kt} \over m}}}$

$\Rightarrow$   ${{kv} \over {mg}} = 1 - {e^{ - {{kt} \over m}}}$

$\Rightarrow$   $v = {{mg} \over k}\left( {1 - {e^{ - {{kt} \over m}}}} \right)$

ma $=$ mg $-$ k $\times$ ${{mg} \over k}$ (1 $-$ e$^{ - {{kt} \over m}}$)

$=$  mg $-$ mg + mge$^{ - {{kt} \over m}}$

a $=$ g e$^{ - {{kt} \over m}}$
4

### JEE Main 2016 (Online) 9th April Morning Slot

Consider a water jar of radius R that has water filled up to height H and is kept on astand of height h (see figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then :
A
$x = r\left( {{H \over {H + h}}} \right)$
B
$x = r{\left( {{H \over {H + h}}} \right)^{{1 \over 2}}}$
C
$x = r{\left( {{H \over {H + h}}} \right)^{{1 \over 4}}}$
D
$x = r{\left( {{H \over {H + h}}} \right)^{{2}}}$

## Explanation

v1 = velocity of water when it leak from hole

v2 = velocity of water when it reach the ground.

From Bernoulli's principle,

${1 \over 2}\rho {v_1}^2 + \rho gh$ = ${1 \over 2}\rho {v_2}^2$

$\Rightarrow$   ${v_1}^2$ + 2gh = ${v_2}^2$

From Torricelli's theorem,

v1 = $\sqrt {2gH}$

$\therefore$   ${v_2}^2$ = 2gh + 22gH

From continuity equation,

${A_1}{v_1}$ = ${A_2}{v_2}$

$\Rightarrow$   $\pi {r^2} \times \sqrt {2gH}$ = $\pi {x^2}\sqrt {2g\left( {h + H} \right)}$

$\Rightarrow$   x2  =  r2$\sqrt {{H \over {H + g}}}$

$\Rightarrow$   x = r ${\left( {{H \over {H + g}}} \right)^{{1 \over 4}}}$


text:
# Setting up php in apache2

There is probably a very simple solution for this particular issue, alas I ether have yet to find it or understand the solution if I did find it.

Our server is Ubuntu 12.04. Apache2 is set up and currently hosting a number of websites without an issue, none use php. Now I am attempting to add a new website that is run on php.

I have looked for a general setup guide for php but thus far have found nothing. I have made sure php module is enabled within apache2, but when I try to load a test PHP file it fails.

PHP5 is installed, apache2ctl configtest shows the syntax is correct.

Can anyone help me with this one?

Edit: It fails by showing a blank screen with the phptest.php file. I have also tried using a helloworld.php test file. Both show blank, I have yet to check the apache log, I will do that asap. Thanks for giving me a lead, ill update this soon.

• How does it fail? – Zypher Apr 24 '14 at 21:41
• If you create a test.php file with contents: <?php phpinfo(); ?> , what does it show on browser? and in apache error.log? – LinuxDevOps Apr 25 '14 at 0:51

OK, so basically you need to install the php5 package through apt-get. When you do that, you need to enable the php5 module by running the following as root:

a2enmod php5

Then open your apache configuration or virtual host configuration and add the line:

 AddType application/x-httpd-php .php

Then restart apache by running the following as root:

 service apache2 restart

If this does not work, you check the logs in /var/log/apache2. Paste last 100 lines of error.log here.


text:
# File System - OOP

I have added an object oriented file system. I am looking for suggestions for how I could improve it further.

package oopdesign.fileSystem;

public abstract  class Entry {

protected Directory parent;
protected long created;
protected long lastUpdated;
protected long lastAccessed;
protected String name;

public Entry(String n, Directory p){
name = n;
parent = p;
created = System.currentTimeMillis();
lastUpdated = System.currentTimeMillis();
lastAccessed = System.currentTimeMillis();
}

public boolean delete(Entry entry){
if(parent == null) return false;
return parent.deleteEntry(this);
}

public abstract int size();

public String getFullPath(){
if( parent == null ) return name;
else return parent.getFullPath() + "/" + name;
}

/* Getter and setter */
public long getCreationTime() { return created; }
public long getLastUpdatedTime() { return lastUpdated; }
public long getLastAccessed() { return lastAccessed; }
public void changeName(String n) { name = n; }
public String getName() { return name; }
}

package oopdesign.fileSystem;

public class File extends Entry {

private String content;
private int size;

public File(String entryName, Directory directory, int size) {
super(entryName, directory);
this.content = content;
this.size = size;
}

public String getContent() {
return content;
}

public void setContent(String content) {
this.content = content;
}

public int size() {
return size;
}

}

package oopdesign.fileSystem;

import java.util.ArrayList;

public class Directory extends Entry {

ArrayList<Entry> fileList;

public Directory(String entryName, Directory directory) {
super(entryName, directory);
fileList = new ArrayList<Entry>();
}

public int size() {
int size = 0;
for (Entry e: fileList) {
size += e.size();
}
return size;
}

public int numberOfFiles() {
int count = 0;
for(Entry e : fileList){
if(e instanceof Directory){
count ++;
Directory d = (Directory) e;
count += d.numberOfFiles();
}else if(e instanceof File){
count ++;
}
}

return count;
}

}

public boolean deleteEntry(Entry entry){
return fileList.remove(entry);
}

protected ArrayList<Entry> getContents() { return fileList; }
}

• Delete function - I don't understand in which case the parent can be null and why it can't be deleted in that case. – shanif Apr 16 '20 at 17:59
• @shanif the root has no parent (excluded volume, mount-point, etc.). It usually can't be deleted. – hc_dev Apr 16 '20 at 18:32
• The problem is that your design does not enforce the Parent-Child relation between directories and entries. You allo insertion of parentless entry to a directory or an entry with conflicting parent. – TorbenPutkonen Apr 17 '20 at 5:27
• I guess this is just a programmer's finger exercise, so never mind. But if you really want to implement a FileSystem with an actual use, you should attempt to write a FileSystem-extension. Have a look at java.nio.file.FileSystems and java.nio.file.spi.FileSystemProvider to get you started. – mtj Apr 17 '20 at 6:29

Seems there is an compilation error in constructor of File:

this.content = content

There is no param content in method signature.

Name params consistently (especially along inheritance hierarchy). You have p (parent) VS directory and n (name) VS entryName. Either they should be consistent throughout the hierarchy (e.g. parent and name seem to fit along) or you should deviate on purpose to highlight special cases (e.g. a future class Alias may have two constructor params with a name: aliasName and targetName).

There could be convenience methods that check for tree-attributes like:

• boolean isLeaf() always true on File, also on empty Directory
• boolean isRoot() always true on root Directory

What about consistent getter for contents:

• the naming differs between File an Directory
• the return type also differs (can this be unified with some generic contents-type?)

Naming convention for packages: avoid camelCase. What about shortening oopdesign.fileSystem to ood.fs (OOD is the abbreviation for object-oriented design) or oo.file.

In reference to the Java API there may be a name collision, because the class File is also used by Java inside package java.io.

Robustness

Your design lacks robustness. I.e. it relies on a specific parent-child relation described with object references but it does not enforce that the relation is sound in the data structure. You allow insertion of parentless entries and entries with different parent to a directory.

Representation of reality

Since this is a representation of a concrete idea, it should reflect the restrictions of the idea in the design. A file does not exist in a void, it always has a parent directory. Note that naming is relevant here, a document may exist as an e-mail attachment or a blob in a database but it becomes a file only when it is placed into a directory tree in a file system. So, you should prevent creation of files that are not attached to a directory by making the Entry class an interface and allowing insertion only via methods in the Directory. E.g.

public class Directory {
public Entry createFile(String name) {
return new ConcreteFile(...);
}
}

With this you are in control of enforcing the integrity of the data structure. Likewise the Directory only exists in a file system. If you remove it, it becomes an archive of documents. It should be an interface and initialized via a FileSystem object.

public clas FileSystem {
public Directory getRoot() {
....
}
}

Methods for manipulating entries (copying, moving and deletion) should then be implemented in the entry, not the directory. When done this way the user is spared the complication of having to obtain a reference to the parent in order to delete an entry.

But how do you create the FileSystem? Well, the FileSystem should be an interface too, created with a FileSystemBuilder. But that's probably a subject of a separate question. :)

Misc

Integer is the wrong type to represent file sizes. It's too small. Use long.

There is no need for us to use long for temporal types anymore. It's a historical artifact from the limitations of long gone hardware. You could very well use java.time.ZonedDateTime and save yourself from a lot of hassle in the future.

For future reference: use a temporal types that include time zones whenever it is possible.

Size is a vague term in this context. In Java's collections it means the number of elements in a collection. For a direcetory I would have to look for documentation about whether it means number of files in it or not. The java.io.File class uses length. I would rename the method to "calculateSize" to signal that it does recursive calculation and can cause a whole lot of IO.

• Like to stress your points by linking the : Robustness depends on constraints. Constraints increase when trying to design for reality (concrete implementation). Though assume OP just exercising with with a simplified model 😉 – hc_dev Apr 17 '20 at 12:40
• BTW: following method name would suggest: public File createFile(String name) together with public Directory createSubDirectory(String name), or is this too concrete (opposed to return abstract Entiry) ? – hc_dev Apr 17 '20 at 12:48

# Missing Implementation

• lastAccessed and lastUpdated are not set beside in the entry constructor.
• a file's size is usually affected by its content.
• addEntry and deleteEntry should affect the parent of entry that was added/removed.
• Validations and error handling. For example, having 2 different files with the same name in the same directory.

# Interfaces

Use interfaces instead of classes so clients will not be affected by the implementation.

I believe that your "implicit interface" aka the public functions are affected by the implementation. I think that if you started your coding with defining an interface, the code would be different.

Here is an example of how the interface should look like:

interface IEntry{

void delete();  //no need to return anything, just perform a command

void changeName(String name);
String getName();

long getSizeInBytes(); // specify the units of size

String getFullPath();

SomeDateTimeClass getCreationTime();
SomeDateTimeClass getLastUpdatedTime();
SomeDateTimeClass getLastAccessed();
}
interface  IDirectory extends IEntry{
int numberOfFiles();

void deleteEntry(IEntry entry);  //no need to return anything, just perform a command

Iterable<IEntry> getContents(); //return the most basic type
}

### Don't use status codes

Returning booleans to indicate if an operation was performed, is a simplified form of status codes. It is better to throw exceptions if the function is misused. for example, delete an entry that doesn't exist.

# Avoiding Nulls

The problem with reference types is that they always can be Null. But how you know if they should be Null.

One solution is to use the Optional class.

Another solution is to design the classes in such a way so you don't need the Null as I described at Root Directory.

# Naming

• Don't use one letter as a name, it cannot mean anything. Also, don't use abbreviations it means too many things.

• I see you wrote this.content = content; so I wonder why not doing the same thing in Entry.

• In Entry you have function changeName and in File you have function setContent. Choose one term and stick to it.

• Directory.fileList contains also directories so it is a confusing name.

# The Root Directory

The root directory is similar to a regular directory but also little different:

• It has no parent
• It cannot be deleted

So I think it should have its own class, let's call it RootDirectory.

## No parent

In your current design, when the parent field is null it means this is the root directory. Based on that you have different logics for getFullPath and delete.

If the root directory doesn't have a parent why it should include this field? writing the specific code for the root directory in RootDirectory class simplifies the code.

## delete

If the root directory cannot be deleted why it should have a delete function?

I suggest splitting the interface to IDeleteable and IEntry. File and Directory should implement IDeleteable, RootDirectory should not.

# Directory

## getContents

You return a reference to fileList which is a member of Directory class. The return type is ArrayList. Let's imagine someone using your classes and wrote the following code:

ArrayList childs = directory.getContents()

the result of this code is that fileList is changed without the Directory class knowing about it. Returning a "read-only type" avoids this problem. Iterable is "read-only type" since it only allows iterating.

I didn't understand why getContents is protected and not public.

## numberOfFiles

You are implicit doing a few things:

• Split between files and directories
• Count the files
• Sum the count of all directories
• Sum the 2 above

I think writing the code in the above way is more readable and using Java Streams it should be very easy.

## size

Using java streams will make the code shorter and more readable.


text:
# Show that $f$ is a homomorphism.

There is a group $G$ of order $p^3$, where $p>2$. Show that $f:G\rightarrow Z(G)$ with $f(x)=x^p$ is a homomorphism.

My attempt:

Case a):

Suppose $|Z(G)|=p^3$. Then $G=Z(G)$, so $G$ is abelian, and $(x_1x_2)^p=x_1^px_2^p$ is obvious.

Case b):

Suppose $|Z(G)|=p^2$. Then $|G/Z(G)|=p$ and is cyclic, so $G$ itself is abelian, which implies that $|G|=|Z(G)|=p^3$. Contradiction.

Case c):

Suppose $|Z(G)|=p$. Then $|G/Z(G)|=p^2$, so $G/Z(G)\cong\mathbb{Z_p}\times\mathbb{Z_p}$(otherwise $G/Z(G)$ is cyclic and $G$ is abelian. So...

I don't even think that it is possible to finish my solution. It seems that there is better one, but this is just my unlucky try.

• Also I've showed that the image of homomorphism lies in center in the case "c".That's all Jul 26, 2015 at 13:25
• In case $c$, you can use the fact that since $G / Z(G)$ is isomorphic to $\mathbb{Z}_p \times \mathbb{Z}_p$, each of its elements is of order $p$ or $1$. Jul 26, 2015 at 13:48

For any $a,b\in G$ $$[a,b] := aba^{-1}b^{-1}$$ Since $G/Z(G)$ is abelian, one can see that $$[a,b] \in Z(G) \quad\forall a,b\in G$$ Hence, $[a,b]^p = e$ for all $a,b\in G$. Now for any $x,y\in G$, note that $$(xy)^p = x^py^p[x,y^{-1}]^{p(p-1)/2} = x^p y^p ([x,y^{-1}]^p)^{(p-1)/2} = x^py^p$$
• You still need to prove that the range of $f$ is in $Z(G)$. Jul 26, 2015 at 14:12
• is it a proof only for case "c"? Otherwise could you explain why $G/Z(G)$ is abelian? Jul 26, 2015 at 14:42
• It's a theorem that a $p$-group has a non-trivial center, Jul 27, 2015 at 12:13
Since $G/Z(G)$ is abelian, for any $x,y \in G$, the commutator $[x,y]=x^{-1}y^{-1}xy$ is in $Z(G)$.
Now $yx=xy[y,x]$. To transform $(xy)^p$ to $x^py^p$ we have to carry out this transformation a total of $p(p-1)/2$ times, which is a multiple of $p$ because $p$ is odd.. So, using $[y,x] \in Z(P)$, we get $$(xy)^p = x^py^p[y,x]^{p(p-1)/2} = x^py^p,$$ which proves the result.


text:
Periodic solutions of forced Kirchhoff equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 8 (2009) no. 1, pp. 117-141.

We consider the Kirchhoff equation for a vibrating body, in any dimension, in the presence of a time-periodic external forcing with period $2\pi /\omega$ and amplitude $\epsilon$. We treat both Dirichlet and space-periodic boundary conditions, and both analytic and Sobolev regularity. We prove the existence, regularity and local uniqueness of time-periodic solutions, using a Nash-Moser iteration scheme. The results hold for parameters $\left(\omega ,\epsilon \right)$ in a Cantor set with asymptotically full measure as $\epsilon \to 0$.

Classification: 35L70,  45K05,  35B10,  37K55
Baldi, Pietro 1

1 Dipartimento di Matematica e Applicazioni, “R. Caccioppoli”, Università degli Studi di Napoli, “Federico II”, Via Cintia, Monte S. Angelo, 80126 Napoli, Italia
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title = {Periodic solutions of forced {Kirchhoff} equations},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {117--141},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 8},
number = {1},
year = {2009},
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Baldi, Pietro. Periodic solutions of forced Kirchhoff equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 8 (2009) no. 1, pp. 117-141. http://www.numdam.org/item/ASNSP_2009_5_8_1_117_0/

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text:
Exercises for 2.3: Simple inferential statistics

Preliminaries

• load the driving.Rdata file.
• type head( driving ) to look at the first few observations
• load the following packages: lsr
load( "~/Work/Research/Rbook/workshop_dsto/datasets/driving.Rdata")
head( driving )
library(lsr)

Exercise 2.3.1: Confidence intervals

• use ciMean() to calculate the 95% confidence interval for the mean age
• use ciMean() to calculate the 99% confidence interval for the mean age
• use ciMean() to calculate 95% confidence intervals for all variables
• use aggregate and ciMean to calculate 95% confidence intervals for the mean age separately for each distractor type

Exercise 2.3.2: Independent samples t-test

• Run a t-test comparing the number of errors (at time 1) for the peak hour group versus the non peak hour group.
• Calculate Cohen’s d.

Exercise 2.3.3: Paired samples t-test

• Run a paired samples t-test to see if the number of errors made at time 2 differs from the number of erros people made at tie 1

Exercise 2.3.4: Chi-square goodness of fit tests

• Run a chi-square goodness of fit to see if the number of females vs males differs significantly from chance

Exercise 2.3.5: Chi-square tests of association

• Run a chi-square test of association to see if there is a significant association between gender and distractor type
• Calculate Cramer’s V for the association

Exercise 2.3.6: Testing the significance of a single correlation

• use cor.test to see if the Pearson correlation between errors and RT at time 1 is significant
• again using cor.test, see if the Spearman correlation between errors and RT at time 1 is significant

Exercise 2.3.7: Testing all pairwise correlations

• use correlate to test the significance of all pairwise correlations among (numeric) variables in driving


text:
# Task 6: GDP, economic growth, unemployment and inflation - Mr Lee is a previously self-employed...

Task 6: GDP, economic growth, unemployment and inflation
1. Mr Lee is a previously self-employed man with an income of $4500. He decided to become an employee of a manufacturing company with a salary of$4000. In closing down his business,
two of his employees were dismissed, each previously receiving a salary of $1000. Each of his employee will now receive unemployment benefits worth$1000 per annum. The change in
National income as a result was________. Explain (2 marks).– Word Count 100
The following table sets out the CPI index for each quarter from March 2009 to March 2018. Use
this information to answer questions 2, 3 and 4 below.
Document Preview:

Written Assessment ECO10004 Economic Principles Part C Due Date – See Canvas under the assessment tab All work must be submitted using the turnitin link (see below for more instructions) Please do not attach a coversheet to your assignment. Also, do not include a copy of the questions in your document. You can insert pictures in your document but they must be low resolution pictures. If your file is larger than 20 MB then convert your file to pdf and upload this into turnitin. Marking Scheme and word count • The total marks for the written assessment is 50 and represents 50% of your total mark for the unit. Part A is worth 12; Part B is worth 20 and Part C is worth 18. • Each question is worth either 1, 2 or 4 marks as indicated (at the end of each question). • A word count is set for each question (at the end of each question). Answers should not be larger than the word count (they can be smaller but you should ensure that you have addressed all aspects of the question).Task 6: GDP, economic growth, unemployment and inflation 1. Mr Lee is a previously self-employed man with an income of $4500. He decided to become an employee of a manufacturing company with a salary of$4000. In closing down his business, two of his employees were dismissed, each previously receiving a salary of $1000. Each of his employee will now receive unemployment benefits worth$1000 per annum. The change in National income as a result was________. Explain (2 marks).– Word Count 100 The following table sets out the CPI index for each quarter from March 2009 to March 2018. Use this information to answer questions 2, 3 and 4 below. Quarter Consumer price index; All groups - Quarterly Mar-2009 92.5 Jun-2009 92.9 Sep-2009 93.8 Dec-2009 94.3 Mar-2010 95.2 Jun-2010 95.8 Sep-2010 96.5 Dec-2010 96.9 Mar-2011 98.3 Jun-2011 99.2 Sep-2011 99.8 Dec-2011 99.8 Mar-2012 99.9 Jun-2012 100.4 Sep-2012 101.8 Dec-2012 102.0 Mar-2013...

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text:
## Tohoku Mathematical Journal

### Weighted Hamiltonian stationary Lagrangian submanifolds and generalized Lagrangian mean curvature flows in toric almost Calabi-Yau manifolds

Hikaru Yamamoto

#### Abstract

In this paper, we generalize examples of Lagrangian mean curvature flows constructed by Lee and Wang in $\mathbb{C}^m$ to toric almost Calabi-Yau manifolds. To be more precise, we construct examples of weighted Hamiltonian stationary Lagrangian submanifolds in toric almost Calabi-Yau manifolds and solutions of generalized Lagrangian mean curvature flows starting from these examples. We allow these flows to have some singularities and topological changes.

#### Article information

Source
Tohoku Math. J. (2), Volume 68, Number 3 (2016), 329-347.

Dates
Received: 22 April 2014
Revised: 24 October 2014
First available in Project Euclid: 23 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1474652263

Digital Object Identifier
doi:10.2748/tmj/1474652263

Mathematical Reviews number (MathSciNet)
MR3550923

Zentralblatt MATH identifier
1361.53052

#### Citation

Yamamoto, Hikaru. Weighted Hamiltonian stationary Lagrangian submanifolds and generalized Lagrangian mean curvature flows in toric almost Calabi-Yau manifolds. Tohoku Math. J. (2) 68 (2016), no. 3, 329--347. doi:10.2748/tmj/1474652263. https://projecteuclid.org/euclid.tmj/1474652263

#### References

• T. Behrndt, Generalized Lagrangian mean curvature flow in Kähler manifolds that are almost Einstein, Complex and Differential Geometry, Springer Proceedings in Mathematics, 8, 65–79, Springer-Verlag, 2011.
• T. Behrndt, Mean curvature flow of Lagrangian submanifolds with isolated conical singularities, arXiv:1107.4803v1, 2011.
• K. A. Brakke, The motion of a surface by its mean curvature, Mathematical Notes, Princeton University Press, 1978.
• V. Guillemin, Moment maps and combinatorial invariants of Hamiltonian $T^n$-spaces, Progress in Mathematics, 122, Birkhäuser Boston, Inc., Boston, MA, 1994.
• R. Harvey and H. B. Lawson, Jr., Calibrated geometries, Acta Math. 148 (1982), 47–157.
• D. Joyce, Special Lagrangian $m$-folds in $\mathbb{C}^m$ with symmetries, Duke Math. J. 115 (2002), no. 1, 1–51.
• D. Joyce, Conjectures on Bridgeland stability for Fukaya categories of Calabi–Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow, EMS Surv. Math. Sci. 2 (2015), no. 1, 1–62.
• Y. I. Lee and M.-T. Wang, Hamiltonian stationary cones and self-similar solutions in higher dimensions, Trans. Amer. Math. Soc. 362 (2010), no. 3, 1491–1503.
• A. Mironov, On new examples of Hamiltonian-minimal and minimal Lagrangian submanifolds in $\mathbb{C}^m$ and $\mathbb{CP}^m$, Sb. Math. 195 (2004), no. 1, 85–96.
• A. Mironov and T. Panov, Hamiltonian-minimal Lagrangian submanifolds in toric varieties, Russian Math. Surveys 68 (2013), no. 2, 392–394.
• A. Strominger, S.-T. Yau and E. Zaslow, Mirror symmetry is $T$-duality, Nuclear Phys. B 479 (1996), nos. 1–2, 243–259.
• R. P. Thomas and S.-T. Yau, Special Lagrangians, stable bundles and mean curvature flow, Comm. Anal. Geom. 10 (2002), no. 5, 1075–1113.
• H. Yamamoto, Special Lagrangians and Lagrangian self-similar solutions in cones over toric Sasaki manifolds, New York J. Math. 22 (2016), 501–526.


text:
# The challenge:

Given four coordinates, each in x y form, your job is to find out whether or not the given coordinates form a rectangle, and output a truthy/falsey.

## Rules:

• For the sake of simplicity, squares, lines (two identical pairs of coordinates) or dots (all four of the coordinates are the same) are all counted as rectangles

• Coordinates for rectangles can be given in any order, for example this:

A----B
|    |
D----C

and this:

A---B
|   |
|   |
|   |
C---D

are both rectangles.

• Rectangles can be rotated, so they won't always be parallel to x and y axis.

• You may take input in any form you like as long as the order for each coordinate is not mixed: [x,x,x,x,y,y,y,y] is not acceptable, where as [x,y,x,y,x,y,x,y] or [(x,y),(x,y),(x,y),(x,y)] is fine.

• Complex numbers are a valid form of input

• This is codegolf, so lowest byte count wins.

## Test cases:

[0,2, 3,2, 3,0, 0,0]      Truthy
[3,5, 2,0, 0,2, 5,3]      Truthy
[6,3, 3,5, 0,2, 3,0]      Falsy
[1,4, 5,2, 4,0, 0,2]      Truthy
[0,0, 0,0, 3,2, 4,0]      Falsy
[1,1, 1,1, 1,1, 1,1]      Truthy
[1,4, 100,1, 100,1, 1,4]  Truthy

• Is [6,3,3,5,0,2,2,0] really a rectangle? – xnor Apr 5 at 9:45
• @Arnauld Good point, spacing it better does make the rectnagles clearer. It looks like the second test case actually has the issue that the points are in the wrong order, making a self-crossing shape. – xnor Apr 5 at 11:49
• @SurculoseSputum I'm understanding it the other way, that the "Coordinates should not be treated like this figure:" means we should always interpret input points as being in cyclic order, so that the second test case wouldn't be a rectangle. I've VTC'ed as unclear. – xnor Apr 5 at 12:34
• @Noodle9 fully approve of your edit, thank you! – Dion Apr 5 at 17:13
• @MitchellSpector, yep – Dion Apr 5 at 17:34

# Python 3, 88 $$\\cdots\$$ 54 43 bytes

lambda l:len({abs(sum(l)/4-z)for z in l})<2

Try it online!

How

Calculates the distances from the quadrilateral's centre of mass to all of its vertices and tests if they're equal.

Input The four vertices as a sequence of complex numbers in any order.
Output True/False

• Oh, I see, that's clever. That should work then in the "in any order" interpretation of the challenge. – xnor Apr 5 at 16:46
• A nice solution! – Mitchell Spector Apr 5 at 16:50
• Here's an argument that convinced me only a rectangle passes your test. Consider the circle on which four points lie. Its center must be the points' center of mass. One way to "average" the four points is to take the midpoint between two points and then midpoint between the other two points, and take the midpoint between those midpoints. To get the center of the circle at the end, the two midpoints must be opposite each inside the circle. (cont'd) – xnor Apr 5 at 17:06
• (continuing) Draw the segment between the two midpoints. We can obtain the pair of points on the circle producing a midpoint by drawing the perpendicular to that segment and intersecting it with the circle. In fact, this the only such of pair of points on the circle. Doing so for both midpoints, we find that central segment is now perpendicular to two equal-length segments whose endpoints are the four corners, so they form a rectangle. (This was all probably confusing without a drawing...) – xnor Apr 5 at 17:08
• Diagram – xnor Apr 5 at 23:11

# Jelly, 6 bytes

A port of Noodle9's Python answer with a slight adjustment for golfing purposes.

×4_SAE

A monadic Link accepting a list of four complex numbers which yields 1 if they form a rectangle or 0 if not.

Try it online! Or see the test-suite.

### How?

Checks that all four coordinates are equidistant from the centre of mass of the uniform density quadrilateral.

×4_SAE - Link: list of complex numbers, C
4     - literal four
×      - (C) multiply (4) (vectorises across C)
S   - sum (of C)
_    - (C×4) subtract (sum(C)) (vectorises across C×4)
A  - absolute value (vectorises)
E - all equal?

Note this still works given an equilateral triangle with a repeated coordinate (it would skew the centre of mass toward the repeated coordinate).

The equivalent change to Noodle9's program would be:

lambda l:len({abs(z*4-sum(l))for z in l})<2

# 05AB1E, 11 bytes

Port of Noodle9's Python answer. 05AB1E doesn't have complex numbers, so it ends up a bit long.

εIøO4/-}nOË

Try it online!

# Python 3, 115108 107 bytes

This solution finds if any permutation of A,B,C,D results in a rectangle. Output is correct for all test cases except test case 3 which is not a rectangle due to corners not equal to 90 degrees.

lambda a,b,c,d:g(a,b,c,d)+g(a,c,b,d)+g(a,b,d,c)
g=lambda a,b,c,d:b+d-a-c==((b-a)*(d-a).conjugate()).real==0

Try it online!

Input: 4 complex numbers representing the 4 coordinates.
Output: a positive integer if input is a rectangle, or 0 if input is not.

105 bytes if output can be 0 for rectangle, and non-zero for non-rectangle.

lambda a,b,c,d:g(a,b,c,d)*g(a,c,b,d)*g(a,b,d,c)
g=lambda a,b,c,d:b+d-a-c or((b-a)*(d-a).conjugate()).real

# APL2: 33 bytes

Yet another port of Noddle9's answer, this time in APL2.

Prerequisites:

1. This is code is ⎕IO-dependant since it uses Partition with axis. This example in ⎕IO=0
2. The list of coordinates is stored in variable C.

D≡⌽D←↑+/(M-+/¨.25×M←⊂[1]⍉4 2⍴C)*2

The result is either 1 for true or 0 for false.

### An example

If C is the vector 3,5,2,0,0,2,5,3 or rather 3 5 2 0 0 2 5 3, then the first thing that happens is that 4 2⍴C turns it into a 4x2 matrix:

3 5
2 0
0 2
5 3

Then ⍉ transposes that matrix and ⊂[1] turns it into a vector of 2 vectors (x & y). This is stored as M: ((3 2 0 5)(5 0 2 3)).

Next M is multiplied with 0.25 and summed element-wise: (this is what +/¨ does)

(2.5 2.5).

Now we subtract this from M and square the differences: (M- ...)*2 (yes, * is "power"). We now have: (0.25 0.25 6.25 6.25)(6.25 6.25 0.25 0.25).

This is summed by the +/ outside the brackets and we get ((6.5 6.5 6.5 6.5)). Sadly we have a 4-element vector inside another structure so we have to "spend" a character to remove the outer shell: ↑.

The inner vector is assigned to variable D. Finally we use ≡ to compare D to its reverse ⌽D thereby checking if all items are equal.

# Ruby, 44 bytes

Input is an array of 4 complex numbers, again.

->l{l.map{|z|(l.sum/4.0-z).abs}.uniq.size<2}

Try it online!

# Bash + GNU utilities, 77 bytes

cat>t;join -j3 t t|xargs -I% dc -e%sDsClD-d*sqlC-d*lq+p|sort|uniq -c|grep 2\

(There's a space at the end, after the backslash.)

Try it online!

Or try the entire test suite online.

The input is in the form:

x1 y1
x2 y2
x3 y3
x4 y4

(with a newline after each point).

The output is the exit code: 0 for falsey, 1 for truthy.

Here's how it works (there are no complex numbers available in bash):

1. The join computes all the pairs of points. There are 4 points, so there are 16 pairs of points. (This includes each pair in both orders, and it even includes pairs where the two points are the same.)

2. The xargs command uses dc to compute the square of the distance between each pair of points. We now have a list of all the squares of the distances between pairs of the points.

3. Now, sort|uniq -c computes how many times each value appears in the list of squared distances.

4. The original four points form a rectangle iff no value appears exactly twice in the list.

# APL (Dyalog Unicode), 25 bytes

{1=≢∪|⍵-+/⍵÷4}

Try it online!

input: complex numbers.

distances from centre of gravity must match.


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 Ufimsk. Mat. Zh.: Year: Volume: Issue: Page: Find

 Ufimsk. Mat. Zh., 2016, Volume 8, Issue 1, Pages 113–126 (Mi ufa318)

Minimal value for the type of an entire function of order $\rho\in(0,1)$, whose zeros lie in an angle and have a prescribed density

V. B. Sherstyukov

National Research Nuclear University MEPhI, Kashirskoe highway, 31 115409, Moscow, Russia

Abstract: In the work we find the minimal value that can be taken by the type of an entire function of order $\rho\in(0,1)$ with zeroes of prescribed upper and lower densities and located in an angle of a fixed opening less than $\pi$. The main theorem generalizes the previous result by the author (the zeroes lie on one ray) and by A. Yu. Popov (only the upper density of zeros was taken into consideration). We distinguish and study in detail the case when the an entire function has a measurable sequence of zeroes. We provide applications of the obtained results to the uniqueness theorems for entire functions and to the completeness of exponential systems in the space of analytic in a circle functions with the standard topology of uniform convergence on compact sets.

Keywords: type of an entire function, upper and lower density of zeroes, uniqueness theorem, completeness of exponential system.

 Funding Agency Grant Number Russian Foundation for Basic Research 13-01-00281-à The work is supported by RFBR (grant no. 13-01-00281-a).

Full text: PDF file (534 kB)
References: PDF file   HTML file

English version:
Ufa Mathematical Journal, 2016, 8:1, 108–120

Bibliographic databases:

UDC: 517.547.22
MSC: 30D15

Citation: V. B. Sherstyukov, “Minimal value for the type of an entire function of order $\rho\in(0,1)$, whose zeros lie in an angle and have a prescribed density”, Ufimsk. Mat. Zh., 8:1 (2016), 113–126; Ufa Math. J., 8:1 (2016), 108–120

Citation in format AMSBIB
\Bibitem{She16} \by V.~B.~Sherstyukov \paper Minimal value for the type of an entire function of order $\rho\in(0,1)$, whose zeros lie in an angle and have a~prescribed density \jour Ufimsk. Mat. Zh. \yr 2016 \vol 8 \issue 1 \pages 113--126 \mathnet{http://mi.mathnet.ru/ufa318} \elib{http://elibrary.ru/item.asp?id=25631807} \transl \jour Ufa Math. J. \yr 2016 \vol 8 \issue 1 \pages 108--120 \crossref{https://doi.org/10.13108/2016-8-1-108} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000411731100009} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84994339080}

• http://mi.mathnet.ru/eng/ufa318
• http://mi.mathnet.ru/eng/ufa/v8/i1/p113

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This publication is cited in the following articles:
1. G. G. Braichev, V. B. Sherstyukov, “Tochnye otsenki asimptoticheskikh kharakteristik rosta tselykh funktsii s nulyami na zadannykh mnozhestvakh”, Fundament. i prikl. matem., 22:1 (2018), 51–97
2. V. B. Sherstyukov, “Asimptoticheskie svoistva tselykh funktsii s zadannym zakonom raspredeleniya kornei”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 104–129
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