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Topic: Delta function

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	[No title]
		In distribution theory, the derivative of the delta function (at zero) is the distribution which assigns to each smooth function f with compact support the value -f'(0).
		Delta, which is a singular distribution, is not termed a function, not even for convenience.
		The "physics" definition of the delta function as a functions such that integral(from -inf to inf) of delta(x)f(x) dx= f(0) is such a definition.
	www.math.niu.edu /~rusin/known-math/00_incoming/delta2 (1547 words)

	The Dirac Delta Function (Site not responding. Last check: 2007-10-24)
		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.
		It is important to emphasize that as defined, the delta function is not a function in the usual sense.
	www.chm.uri.edu /urichm/chm532/delta/node4.html (558 words)

	Delta - Wikipedia, the free encyclopedia
		In mathematical finance delta, δ, is one of "The Greeks"; delta measures the sensitivity of the value of a derivative to changes in the price of its underlying instrument.
		In particle physics, the delta particle is a short lived resonance of the proton.
		In information technology, delta compression is a process that produces a file recording only the changes (or diff) between versions.
	en.wikipedia.org /wiki/Delta (324 words)

	Encyclopedia: Dirac delta function (Site not responding. Last check: 2007-10-24)
		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 Î´(x) that has the value of infinity for x = 0, the value zero elsewhere.
		In mathematics and in particular, functional analysis, convolution is a mathematical operator which takes two functions f and g and produces a third function that in a sense represents the amount of overlap between f and a reversed and translated version...
		is the characteristic function of the nascent delta function Î´(a,x).
	www.nationmaster.com /encyclopedia/Dirac-delta-function (2813 words)

	Delta Function Potentials p.1 (Site not responding. Last check: 2007-10-24)
		The result is a "function" that is zero almost everywhere, but is infinite at the one point (x=0) where the barriers have been centered.
		For physicists, the delta function is well designed to represent, for example, the charge density of a point particle: there is some total charge on the particle, but since the particle is point-like, the charge density is zero except at the single location of the particle.
		A delta function potential causes no force, except at the one point the potential is non-zero.
	www.physics.csbsju.edu /QM/delta.01.html (452 words)

	PlanetMath: Dirac delta function
		is not a true function since it cannot be defined completely by giving the function value for all values of the argument
		can also be defined as a normalized Gaussian function (normal distribution) in the limit of zero width.
		This is version 2 of Dirac delta function, born on 2002-01-19, modified 2002-07-04.
	planetmath.org /encyclopedia/DiracDeltaFunction.html (81 words)

	Dirac delta
		This is associated with the fact that the Dirac delta is not a function in the usual technical sense, since infinity is not a number in the usual sense.
		However, this also means that the delta function by itself can't represent a point charge's charge density function; the integral over all space of a charge density is the total charge, not a number.
		A delta function with some other form of argument still satisfies the description that it is zero unless the argument is zero (whether the zero vector or the number zero), and that it is infinite when the argument is zero.
	physics.tamuk.edu /~cox/WEBEM/NOTES/deltafcn.htm (1619 words)

	delta - Definitions from Dictionary.com
		Deltas form when a river flows into a body of standing water, such as a sea or lake, and deposits large quantities of sediment.
		The term delta is often used, once epsilon has been mentioned, to mean a quantity that is slightly bigger than epsilon but still very small.
		The jargon usage of delta and epsilon stems from the traditional use of these letters in mathematics for very small numerical quantities, particularly in `epsilon-delta' proofs in limit theory (as in the differential calculus).
	dictionary.reference.com /browse/delta (1649 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?t=27517 (1406 words)

	Learn more about List of mathematical functions in the online encyclopedia. (Site not responding. Last check: 2007-10-24)
		Elliptic functions: The inverses of elliptic integrals; used to model double-periodic phenomena.
		Bessel functions: Defined by a differential equation; useful in astronomy, electromagnetism, and mechanics.
		Ackermann function: in the theory of computation, a recursive function that is not primitive recursive.
	www.onlineencyclopedia.org /l/li/list_of_mathematical_functions.html (396 words)

	Springer Online Reference Works
		A function which makes it possible to describe the spatial density of a physical magnitude (mass, charge, intensity of a heat source, force, etc.) which is concentrated or applied at a point
		Thus, the delta-function is not an ordinary function in the sense of the classical theory of functions, and is defined in the theory of generalized functions as a singular generalized function, i.e.
		The Dirac delta-function is the derivative (in the sense of distributions or generalized functions) of the Heaviside function (Heaviside distribution)
	eom.springer.de /d/d030950.htm (228 words)

	Representations of .
		In use, the Dirac delta function is never evaluated without multiplying by a test function and integrating over some domain.
		Equations involving Dirac delta functions without such integrations are a convenient half-way stage that nevertheless have enormous utility.
		Properly speaking, the Dirac delta function is not a function at all (it is a generalized function or a functional), however it can be represented as the limit of a sequence of ordinary functions.
	www.engr.unl.edu /~glibrary/home/whatisG/node7.html (152 words)

	Kronecker delta Summary
		The Kronecker delta is not something that can be proven or disproven--it merely indicates, without a lot of excess verbiage, which of several potential components the mathematician is using.
		In mathematics, the Kronecker delta or Kronecker's delta, named after Leopold Kronecker (1823-1891), is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
		It is important to note that the Kronecker delta is not the result of sampling the Dirac delta function.
	www.bookrags.com /Kronecker_delta (587 words)

	ipedia.com: Dirac delta function Article (Site not responding. Last check: 2007-10-24)
		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)

	Gauss (Site not responding. Last check: 2007-10-24)
		Figure 13 The delta functions in the second derivative are approximated by 1/ht in a 4096 point integration across the region from t=0 to t=128.
		Figure 14 The integral of the delta functions in the fourth derivative leading to the third derivative of the function.
		Figure 34 Black dots are the integral of a delta function. Red line is integral of truncated Gauss function.
	www.phys.ufl.edu /~coldwell/ligo/Gauss.htm (598 words)

	Dirac Delta Function (Site not responding. Last check: 2007-10-24)
		So, er, really it is a function, but it isn't a function from {numbers} to {numbers}; it's a function from {functions} to {numbers}.
		The theory of distributions uses sequences of functions that approach the 'delta function', and defines the resulting limit to be 'the delta function' even though it isn't a function.
		L. integrable functions are a superset of R-S. integrable functions.
	c2.com /cgi/wiki?DiracDeltaFunction (578 words)

	Generalized Functions and Related Objects
		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.
		The unit step function is often used in setting up piecewise continuous functions, and in representing signals and other quantities that become non-zero only beyond some point.
		The Fourier transform of a constant function is a delta function.
	documents.wolfram.com /v4/MainBook/3.5.12.html (266 words)

	CS/EE 545 Class 4
		The Fourier transform of a constant is a delta function.
		This satisfies two of the three properties of the delta function since the limit is infinity 0 or zero depending on whether or not u is zero.
		The real value in understanding transform theory is not in being able to find transforms of some functions, but in understanding the properties of transforms, including those in Table 4.1 in the text.
	www.cs.wpi.edu /~cs545/2002f/classes/class04 (910 words)

	Kronecker delta -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-24)
		and in fact Dirac's delta was named after the Kronecker delta because of this analogous property.
		The Kronecker delta is used in many areas of mathematics.
		This function takes the value 1 if and only if all the upper indices match the corresponding lower one, taking the value zero otherwise.
	www.absoluteastronomy.com /encyclopedia/k/kr/kronecker_delta.htm (247 words)

	Electronics 6
		The Dirac delta function δ(t) is zero for t unequal to zero, but is infinite at t = 0 in such a way that its integral is unity, as shown at the left.
		The frequency domain representation, or Fourier transform, of the DC signal shown in the figure is a delta function at zero frequency, with a coefficient equal to the value of the signal.
		This relation is mutual, since a sharp shock at t = 0, represented by a unit delta function, is represented as a superposition of all frequencies with equal amplitudes, as the figure illustrates.
	www.du.edu /~etuttle/electron/elect6.htm (3364 words)

	Delta Function Potentials p.10
		For scattering from a "one-nuclei" delta function, we found the reflection amplitude:
		Consider a particle in an infinite square well with a repulsive delta function at its center.
		Plot the results as a function of the strength of the delta function.
	www.physics.csbsju.edu /QM/delta.10.html (823 words)

	Source Code For DELTA Function
		The DELTA function returns the change in a value from the previous row.
		If the DELTA function is dependent on the order of a column, or columns, within the query then these columns should be specified on an ORDER BY clause.
		The DELTA function appears to be called prior to the sort resulting in erroneous results.
	www-03.ibm.com /servers/eserver/iseries/db2/db2rpgudfdesc.html (1087 words)

	Tutorial for Green's Functions, Materials Reliability Division, N.I.S.T
		Green's functions play an important role in the solution of linear ordinary and partial differential equations, and are a key component to the development of boundary integral equation methods.
		In elastostatics, the Green's function represents the displacement in the solid due to the application of a unit force.
		In heat transfer, the Green's function represents the temperature at the field point due to a unit heat source applied at the source point.
	www.boulder.nist.gov /div853/greenfn/tutorial.html (1029 words)

	Märklin Trains: DELTA / Digital Multi-train Control
		With DELTA you can operate four or five trains simultaneously and independently on a layout.
		And when you are ready to expand your operating capabilities it's easy to move from DELTA to Digital.
		Although the DELTA and Digital systems can be used to operate trains produced by other manufacturers, the system is designed to easily combine with Märklin's HO, Maxi and 1 Gauge trains for prototypical multi-train operation on the layout.
	www.marklin.com /digital (286 words)

	Fourier Series, Fourier Transforms and the Delta Function (Site not responding. Last check: 2007-10-24)
		Any periodic function of interest in physics can be expressed as a series in sines and cosines—we have already seen that the quantum wave function of a particle in a box is precisely of this form.
		The function is linearly divergent at the origin, and has finite oscillatory behavior everywhere else.
		That is to say, the delta function can be defined as the “narrow limit” of a Gaussian wave packet with total area 1.
	landau1.phys.virginia.edu /classes/751.mf1i.fall02/FourierSeries.htm (2113 words)

	Dirac delta function
		In physics and engineering, we inevitably deal with the notion of "point actions", that is, actions which are highly localized in space and /or time.
		As in the case of the one-dimensional delta function
		may be visualized as the formal limit of a sequence of ordinary functions.
	www.sci.hkbu.edu.hk /msc/full/billy/node5.html (395 words)

	Bayes's Theorem and the Likelihood Function
		What this means, roughly, is that the likelihood function looks like a bell curve with a peak at 1.02 and a width (standard deviation) of 0.02, roughly as shown in Figure 2.
		The likelihood function, by definition, is the probability density of getting the data that we actually observed, as a function of the value of
		The narrow spike is a delta-function (infinitely high and narrow, with a finite area).
	www.richmond.edu /~ebunn/bayes/node4.html (597 words)

	The Delta Function Potential (Site not responding. Last check: 2007-10-24)
		One limiting case of a square well is a very narrow deep well, which can be approximated by a delta function when the range of variation of the wave function is much greater than the range of the potential, so Schrödinger’s equation becomes
		d-function cannot be balanced by the finite right hand side, so the wave function must have a discontinuity in slope at the origin.
		To find the ground state energy, note first that as a one-dimensional attractive potential there will be a bound state: any change in slope is sufficient to connect an exponentially increasing function coming in from -¥ to a decreasing one going to +¥, since the rates of increase and decrease can be arbitrarily slow.
	landau1.phys.virginia.edu /classes/751.mf1i.fall02/DeltaFnPotl.htm (212 words)

	Impulses (Site not responding. Last check: 2007-10-24)
		In this applet, the Kronecker delta function is delayed so that it is centered in the visible window.
		The Dirac delta function is defined to be
		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)

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