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The court poet al-Buhturi (d. 897) composed an unusual, but intense poem. In it, he leaves behind haughty patrons and the urban setting of Samarra and ventures out to the ruins of a Sasanian palace at Ctesiphon,

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{\displaystyle V} . In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related to the concepts of open set and interior. <span>Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount away from that point without leaving the set. Contents [hide] 1 Definitions 1.1 Neighbourhood of a point 1.2 Neighbourhood of a set 2 In a metric space 3 Examples 4 Topology from neighbourhoods 5 Uniform neighbourhoo

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Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount away from that point without leaving the set.

{\displaystyle V} . In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related to the concepts of open set and interior. <span>Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount away from that point without leaving the set. Contents [hide] 1 Definitions 1.1 Neighbourhood of a point 1.2 Neighbourhood of a set 2 In a metric space 3 Examples 4 Topology from neighbourhoods 5 Uniform neighbourhoo

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Integral equation From Wikipedia, the free encyclopedia (Redirected from Integral equations) Jump to: navigation, search For equations of integer unknowns, see Diophantine equation. <span>In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way. See, for example, Green's function, Fredholm theory, and Maxwe

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rview 2 Numerical solution 3 Classification 4 Wiener–Hopf integral equations 5 Power series solution for integral equations 6 Integral equations as a generalization of eigenvalue equations 7 See also 8 References 9 External links Overview<span>[edit source] The most basic type of integral equation is called a Fredholm equation of the first type, f ( x ) = ∫ a b K ( x , t ) φ ( t ) d t . {\displaystyle f(x)=\int _{a}^{b}K(x,t)\,\varphi (t)\,dt.} The notation follows Arfken. Here φ is an unknown function, f is a known function, and K is another known function of two variables, often called the kernel function. Note that the limits of integration are constant: this is what characterizes a Fredholm equation. If the unknown function occurs both inside and outside of the integral, the equation

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In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign.

Integral equation From Wikipedia, the free encyclopedia (Redirected from Integral equations) Jump to: navigation, search For equations of integer unknowns, see Diophantine equation. <span>In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way. See, for example, Green's function, Fredholm theory, and Maxwe

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In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign.

Integral equation From Wikipedia, the free encyclopedia (Redirected from Integral equations) Jump to: navigation, search For equations of integer unknowns, see Diophantine equation. <span>In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way. See, for example, Green's function, Fredholm theory, and Maxwe

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The most basic type of integral equation is where φ is an unknown function, f is a known function, and K is another known function of two variables, often called the kernel function.

rview 2 Numerical solution 3 Classification 4 Wiener–Hopf integral equations 5 Power series solution for integral equations 6 Integral equations as a generalization of eigenvalue equations 7 See also 8 References 9 External links Overview<span>[edit source] The most basic type of integral equation is called a Fredholm equation of the first type, f ( x ) = ∫ a b K ( x , t ) φ ( t ) d t . {\displaystyle f(x)=\int _{a}^{b}K(x,t)\,\varphi (t)\,dt.} The notation follows Arfken. Here φ is an unknown function, f is a known function, and K is another known function of two variables, often called the kernel function. Note that the limits of integration are constant: this is what characterizes a Fredholm equation. If the unknown function occurs both inside and outside of the integral, the equation

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t)\,dt.} In all of the above, if the known function f is identically zero, the equation is called a homogeneous integral equation. If f is nonzero, it is called an inhomogeneous integral equation. Numerical solution[edit source] <span>It is worth noting that integral equations often do not have an analytical solution, and must be solved numerically. An example of this is evaluating the Electric-Field Integral Equation (EFIE) or Magnetic-Field Integral Equation (MFIE) over an arbitrarily shaped object in an electromagnetic scatterin

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Home Subscribe Free trial Learn Getting Started with TypeScript [imagelink] Andrew Chalkley <span>TypeScript is JavaScript with optional typing. TypeScript is a compiled language, it’s not interpreted at run-time. The TypeScript compiler takes TypeScript files (.ts) and compiles them in to JavaScript files (.js). If you want to know why you should be interested in TypeScript and a little more about it you should check out my other post Why TypeScript is Hot Now, and Looking Forward. In this

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o have Node.js and NPM installed. Check out the following posts for help if you haven’t done so already Installing Node.js and NPM on Windows How to Install Node.js and NPM on Linux How to Install Node.js and NPM on a Mac Installation <span>TypeScript can be installed through the NPM package manager. npm install -g typescript The -g means it’s installed on your system globally so that the TypeScript compiler can be used in any of your projects. Test that the TypeScript is installed correctly by typing tsc -v in to your terminal or command prompt. You should see the TypeScript version print out to the screen. For help on

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cript is installed correctly by typing tsc -v in to your terminal or command prompt. You should see the TypeScript version print out to the screen. For help on possible arguments you can type tsc -h or just tsc . Command Line Usage <span>You can use the tsc command in several different ways. Here’s a couple of helpful common usages. Run and Compile The following command will compile a single .ts file in to a .js file: tsc app.ts This will result in an app.js file being created. To compile multiple

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js and someMore.js . You can also use wildcards too. The following command will compile all TypeScript files in the current folder. tsc *.ts All TypeScript files will compile to their corresponding JavaScript files. Joining Files <span>You can also compile all your TypeScript files down to a single JavaScript file. This can reduce the number of HTTP requests a browser has to make and improve performance on HTTP 1.x sites. To do this use the --out option like so: tsc *.ts --out app.js Watcher Instead of running the tsc command all the time you can use the option --watch . tsc *.ts --out app.js --watch Every time there’s an update to a TypeScript file it’

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s created since running the tsc command won’t get compiled, you need to stop the watcher and start again. Syntax Now on to the good stuff – the stuff that makes you less error prone and more productive – it’s syntax. Optional Typing <span>When there’s a variable or an argument in a function or method call, you can annotate your code with types. To annotate, follow the variable or argument with a colon and followed by it’s type. var myName: string = "Andrew"; function printName(name: string) { console.log(name); } When you try and call the function with the missing or wrong types of parameter it warns us. Also it helps with autocompletion since every variable’s type is known and it suggests an

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TypeScript is clever enough to know the type of the myName variable. Interfaces Interfaces are great ways to set up agreements on the shape of object literals. Sometimes you just need to know the structure of a thing as a data store. <span>In this code we want every object pushed in to the addressBook array to conform to the Contact interface. When this is compiled to JavaScript this disappears, but this is helpful in development. interface Contact { name: string, email: string, phone: string } var addressBook: Contact[] = []; It can warn me in the method call of push if I don’t define the type on line 9. Or if I specify the type on the variable declaration, it could warn me on line 9 that I’m missing