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	Dirac delta function - Wikipedia, the free encyclopedia
		The Dirac delta function, sometimes referred to as the unit impulse function and introduced by the British theoretical physicist Paul Dirac, can usually be informally thought of as a function δ(x) that has the value of infinity for x = 0, the value zero elsewhere.
		The Dirac delta function was named after the Kronecker delta, since it can be used as a continuous analogue of the discrete Kronecker delta.
		The Dirac delta is not a function; but it can be usefully treated as a distribution, as well as a measure.
	en.wikipedia.org /wiki/Dirac_delta_function (911 words)

	Paul Dirac - Wikipedia, the free encyclopedia
		Paul Adrien Maurice Dirac, OM (August 8, 1902 – October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics.
		This work led Dirac to predict the existence of the positron, the electron's antiparticle, which he interpreted in terms of what came to be called the Dirac sea.
		Dirac was Lucasian professor of mathematics at Cambridge from 1932 to 1969.
	en.wikipedia.org /wiki/Paul_Dirac (1037 words)

	Encyclopedia: Dirac delta function (Site not responding. Last check: 2007-10-08)
		The Dirac delta function, sometimes referred to as the unit impulse function and introduced by the The United Kingdom of Great Britain and Northern Ireland is a country in western Europe, and a member of the British Commonwealth and European Union.
		Paul Dirac, can usually be informally thought of as a In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range).
		The Dirac Delta function may be interpreted as a In mathematics, a probability density function (pdf) serves to represent a probability distribution in terms of integrals.
	www.nationmaster.com /encyclopedia/Dirac-delta-function (4328 words)

	PlanetMath: construction of Dirac delta function (Site not responding. Last check: 2007-10-08)
		The Dirac delta function is notorious in mathematical circles for having no actual realization as a function.
		However, a little known secret is that in the domain of nonstandard analysis, the Dirac delta function admits a completely legitimate construction as an actual function.
		This is version 2 of construction of Dirac delta function, born on 2002-04-19, modified 2002-04-21.
	planetmath.org /encyclopedia/ConstructionOfDiracDeltaFunction.html (136 words)

	The Dirac Delta Function (Site not responding. Last check: 2007-10-08)
		The Dirac delta function, invented by P.A.M. Dirac for his important formulations of quantum mechanics, is a continuous analog of the Kronecker delta.
		To appreciate the connection between the Kronecker delta and the delta function, it is important to recognize that subscripts are a kind of function.
		The Kronecker delta extracts a single element from an infinite sum, and the delta function extracts the value of a function at a single point from an integral.
	www.chm.uri.edu /urichm/chm532/delta/node4.html (558 words)

	Kronecker delta - Wikipedia, the free encyclopedia
		This property is similar to one of the main properties of the Dirac delta function:
		The Kronecker delta is used in many areas of mathematics.
		Kronecker Delta is also a German Lager brewed in the UK.
	en.wikipedia.org /wiki/Kronecker_delta (212 words)

	ipedia.com: Dirac delta function Article (Site not responding. Last check: 2007-10-08)
		Technically speaking, the Dirac delta is not a function but a distribution — a mathematical expression that is well defined only when integrated.
		The Fourier transform of the Dirac delta is the constant function, and the convolution of δ with any distribution S yields S.
		The Dirac delta function is a distribution whose indefinite integral is the function
	www.ipedia.com /dirac_delta_function.html (534 words)

	sciforums.com - Delta Function
		I got the impression that the function of the delta 'function' was to overcome the problem that the calculation of the density of a point in space leads to infinities.
		One important thing about the delta function that hasn't been mentioned is that it is the continuous analog of the Kroneker delta matrix, which is the n-dimensional unit matrix, and that operations with it are equivalent to operations with matrices.
		Just kinda know that the Dirac delta function is equal to infinity at some point and zero everywhere else, and if you integrate over all the area, the infinity at that one point offsets the zeros and it is equal to one.
	www.sciforums.com /showthread.php?p=424886 (1415 words)

	Delta article - Delta Greek alphabet delta (letter) river delta Nile Egypt Mediterranean - What-Means.com (Site not responding. Last check: 2007-10-08)
		Delta article - Delta Greek alphabet delta (letter) river delta Nile Egypt Mediterranean - What-Means.com
		A Greek dairy producer and manufacturer, See Delta S.A. 1st SFOD-Delta, a US counterterrorist unit.
		This is a disambiguation page; that is, one that points to other pages that might otherwise have the same name.
	www.what-means.com /encyclopedia/Delta (162 words)

	The Mathematica Book Online: Advanced Mathematics in Mathematica \| Calculus
		Inserting a delta function in an integral effectively causes the integrand to be sampled at discrete points where the argument of the delta function vanishes.
		Dirac delta functions can be used in DSolve to find the impulse response or Green's function of systems represented by linear and certain other differential equations.
		Related to the multidimensional Dirac delta function are two integer functions: discrete delta and Kronecker delta.
	documents.wolfram.com /mathematica/book/section-3.5.13 (374 words)

	Chapter 2 Notes
		Hence, the area under the "curve" defined by the Dirac delta, or impulse function is unity.
		The unit-step and the Dirac delta function are derivative and anti-derivative of one another.
		This means that the Dirac delta function is only useful to describe impulsive forces when integrated over the applicable independent variable.
	web.umr.edu /~stutts/Laplace/Laplace.html (2927 words)

	Examples Of Delta Functions -
		Delta Sequence -- from MathWorld Delta Sequence -- from MathWorld A delta sequence is a sequence of strongly peaked functions for which \lim_{n\to \infty} \int_{-\infty}^\infty \delta_n(x)f(x)\,dx = f(0) so that in the limit as n\to\infty,...
		The Fourier transform of the Gaussian function is another Gaussian: Note that the width sigma is oppositely positioned in the arguments of the exponentials.
		Properties of Dirac delta functions' Dirac delta functions aren't really functions, they are "functionals", but...
	functions.faasv.com /index.php?k=examples-of-delta-functions (811 words)

	5.5 Generalized Fourier transform
		The unit impulse function or Dirac delta function is denoted by
		The Dirac delta function is not a function in an ordinary sense, it is a so-called generalized function.
		An important property of Dirac delta function is the so-called sifting property of Dirac delta function, which states that if f(x) is continuous at x=a then
	www.math.ut.ee /~toomas_l/harmonic_analysis/Fourier/node32.html (247 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		A number of analytical expressions of delta function are commonly used in the literature.
		Figure A. Approximated Dirac Delta Function EMBED Word.Picture.6 Note that the smaller EMBED Equation.3 is, the higher the peak will be and the more narrow the peak will become.
		The approximated Dirac delta function is peaked symmetrically and drops quickly towards zero value.
	www.fanginc.com /rdic/texas2.doc (770 words)

	MUG: Dirac - Problem (17.3.99)
		It seems that Maple (version 4.0) cannot handle the Dirac delta functional when its argument is a non-linear function of x.
		The problem with the Dirac delta function is that its definition in Maple is somewhat different from the usual definition in theoretical physics.
		In Maple the Dirac delta function is defined by
	www.math.rwth-aachen.de /mapleAnswers/html/729.html (334 words)

	► » Re: The Dirac Delta? (Site not responding. Last check: 2007-10-08)
		to show the delta is not integrable locally.
		Dirac's Delta is a functional (member of the dual space of a proper
		Dirac's delta is not (look at the common physicist definition
	www.science-chat.org /Re-The-Dirac-Delta-6013985.html (790 words)

	Dirac Delta Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-08)
		Looking For dirac delta - Find dirac delta and more at Lycos Search.
		Find dirac delta - Your relevant result is a click away!
		The Dirac delta function, sometimes referred to as the unit impulse function and introduced by the British theoretical physicist Paul Dirac, can usually be informally thought of as a function δ(x) that has the value of infinity for x = 0, the value zero elsewhere such that the total integral is one.
	www.artisticnudity.com /encyclopedia/Dirac_delta (1044 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		As part of his bra-ket formalism, Dirac introduced the so-called Dirac delta function, a formal entity without a counterpart in the classical theory of functions.
		Four of the most important features of Dirac's formalism are: \begin{enumerate} \item To each element of the spectrum of an observable $A$, there correspond a left and a right eigenvector (for the moment, we assume that the spectrum is non-degenerate).
		The Dirac delta normalization generalizes the orthonormality~(\ref{orthonomr}) of the eigenvectors of a Hermitian matrix.
	www.ma.utexas.edu /mp_arc/papers/05-61 (2663 words)

	simple dirac delta question. - Physics Help and Math Help - Physics Forums
		I have used the three common definitions, with the usual convention that Dirac sequences are symmetric, as is the Dirac delta, and H(0)=1/2.
		The whole point of using Dirac deltas in physical problems is that something is happening on so short a time (or spatial) scale that its precise structure is irrelevant.
		I was saying to let the delta function be in its exact form (or approximated some symmetric function), but define the step function as a limit of continuous functions.
	www.physicsforums.com /showthread.php?threadid=83056 (2636 words)

	Impulses (Site not responding. Last check: 2007-10-08)
		In this applet, the Kronecker delta function is delayed so that it is centered in the visible window.
		The continuous-time case, which is called the Dirac delta function, is mathematically much more difficult to work with.
		The Dirac delta function, of course, cannot be represented precisely, because its infinitely narrow width and infinite height are problematic for the computer.
	ptolemy.eecs.berkeley.edu /eecs20/week11/impulses.html (405 words)

	MUG: Dirac(x) problem (15.8.00)
		The problem is in `int/defDirac` where it is implicitly assumed that the first Dirac in a product is a function of the integration variable.
		My solution is to modify the do command in line 19 to consider only those terms that involve Dirac of the integration variable.
		I am working for some years with maple4s Dirac and Heaviside routines and there were several additional bugs in the derivatives of the Dirac distribution, e.g.
	www.math.rwth-aachen.de /mapleAnswers/html/1090.html (523 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		The Dirac delta is a Borel probability measure on the real line with a unit mass at the origin.
		You may "represent" the Dirac delta function as any ordinary sharply peaked function (such that their integral is normalized to unity) and take the limit where the peak gets infinitely sharp.
		Subject: Dirac delta To: maple-list@scg.math.uwaterloo.ca You are applying the delta function with a singularity at 0 to a distribution (the Heaviside function) with a singularity at 0 too, or multiplying two distributions.
	www.scg.uwaterloo.ca /~maple_gr/Digests/Digest02.08 (6466 words)

	Problem (Site not responding. Last check: 2007-10-08)
		In lecture, we introduced the Dirac delta function in order to be able to write
		The delta function is a generalization of the Kroenecker delta, δ
		The delta function is only a function of the difference between x and x'.
	www.physics.umd.edu /courses/Phys374/fall04/hw/MP27.htm (138 words)

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