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	Kronecker delta - Wikipedia, the free encyclopedia
		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.
		The function is referred to as an impulse, or unit impulse.
		It is important to note that the Kronecker delta is not the result of sampling the Dirac delta function.
	en.wikipedia.org /wiki/Kronecker_delta (336 words)

	Radial basis function - Wikipedia, the free encyclopedia
		Radial basis functions are a means for interpolation in a stream of data.
		A RBF is a function which has built into a distance criterion with respect to a centre.
		Radial basis functions have been applied in the area of neural networks where they are used as a replacement for the sigmoidal transfer function.
	en.wikipedia.org /wiki/Radial_basis_function (652 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)

	Impulses (Site not responding. Last check: 2007-11-02)
		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)

	THE WAVELET TUTORIAL PART III by ROBI POLIKAR (Site not responding. Last check: 2007-11-02)
		The wavelet analysis is done in a similar way to the STFT analysis, in the sense that the signal is multiplied with a function, {\it the wavelet}, similar to the window function in the STFT, and the transform is computed separately for different segments of the time-domain signal.
		The term mother implies that the functions with different region of support that are used in the transformation process are derived from one main function, or the mother wavelet.
		This definition of the CWT shows that the wavelet analysis is a measure of similarity between the basis functions (wavelets) and the signal itself.
	users.rowan.edu /~polikar/WAVELETS/WTpart3.html (5094 words)

	Mathematical Methods Special Functions Legendre’s Equation and Legendre Polynomials
		The development and manipulations of the other special functions are handled in a similar manner (especially the various polynomial relationships - Hermite and Laguerre polynomials, for example).
		Similar manipulations can be performed for the other orthogonal functions (Hermite polynomials, Laguerre polynomials, etc.) and the reader is encouraged to seek out further details as needed for a particular application.
		Note that the choice of the specific orthogonal polynomial for a given application is often dictated by the domain of interest.
	gershwin.ens.fr /vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/math/s8/s8legd/s8legd.html (1033 words)

	[No title]
		A Humbert type of Bessel function $G_{\nu}(z)$ is defined as the hypergeometric function \begin{equation} \begin{aligned} G_{\nu}(z) & = _{0}F_{2}(1/3, \nu + 2/3\,\,(z/3)^3) \\ & = \sum_{n = 0}^{\infty} \frac{\Gamma(1/3)\Gamma(\nu + 2/3)z^{3n}} {3^{3n}\,n!\,\Gamma(n + 1/3)\Gamma(n + \nu + 2/3)} \end{aligned} \end{equation} for $z \in \mathbb{C}$, the complex numbers.
		This addition in terms of hypergeometric functions is an analogue of the addition for Bessel functions presented by Bochner \cite{Boch55}.
		The function $E_{\nu}(x)$ is the $e^{ix}$ in the the $\nu$-calculus associated with $\vartheta_{\nu}$, it is an entire function of order one.
	www.maths.tcd.ie /EMIS/journals/EJDE/Volumes/2003/87/cholewinski-tex (6180 words)

	Tensors and tensor algebra (Site not responding. Last check: 2007-11-02)
		The delta function has the same properties independent of any rotation.
		Note that it is not a scalar because a scalar is a single number whereas the delta function has several elements.
		Clearly the sum or difference of two tensors of the same rank is also a tensor, and similarly if one multiplies all elements of a tensor by a scalar it is still a tensor.
	grus.berkeley.edu /~jrg/ay202/node185.html (790 words)

	Untitled Document
		Both of these functions have known bugs (versions 5.9.0 and earlier) that may manifest if you attempt to use sets with members that are lists or matrices that contain expressions in CRE form.
		The Kronecker delta function; kron_delta(i,j) simplifies to 1 when is(i = j) is true and it simplifies to zero when sign(i - j) is pos.
		This function is similar to both lreduce and rreduce except that xreduce is free to use either left or right associativity; in particular when f is an associative function and Maxima has a built-in evaluator for it, xreduce may use the nary function; these nary functions include addition, multiplication, 'and', 'or', 'max', 'min', and 'append'.
	www.unk.edu /uploadedFiles/facstaff/profiles/willisb/nset.htm (4875 words)

	Maxima Manual - Tensor
		The dummy indices are renamed in the same manner as in the RENAME function.
		is the generalized Kronecker delta function defined in the Tensor package with L1 the list of covariant indices and L2 the list of contravariant indices.
		Tensor package) This function first computes the covariant components LR[i,j] of the Ricci tensor (LR is a mnemonic for "lower Ricci").
	www.ma.utexas.edu /maxima/maxima_27.html (1080 words)

	Tensors (Site not responding. Last check: 2007-11-02)
		Many of the functions in CTENSR will be displayed for the standard metric as examples.
		L1, L2 is the generalized Kronecker delta function defined in the Tensor package with
		function with arguments which would yield that indexed object if the differentiation were carried out.
	starship.python.net /crew/mike/maxima/html/macref/node108.html (1789 words)

	"Lori's Engineering Page"
		When analyzing an LTI circuit in the frequency domain, the impulse function comes out in the math too (specifically it can happen when the order of the numerator polynomial is greater than or equal to the order of the denominator).
		That is, we may take the Laplace transform of the response functions of each component, generate an equivalent circuit in the fequency domain, and treat the components as usual.
		A function is stable if it converges to zero in the time domain (it is semi-stable if it converges to some constant value).
	www.geocities.com /iamlad/engrmain.html (8447 words)

	Photoelectric Effect in Hydrogen
		function is tricky for excitation into the continuum: just how many of these plane wave states satisfy
		The integral is now a Fourier transform of the hydrogen ground state wave function, and is straightforward: choose the
		Appendix: the Golden Rule Delta Function and the Density of States
	galileo.phys.virginia.edu /classes/752.mf1i.spring03/PhotoelectricEffect.htm (1172 words)

	Predicting protein functions with message passing algorithms -- Leone and Pagnani 21 (2): 239 -- Bioinformatics
		Upper boxes are sets of all functions of all the classified proteins neighboring a given unclassified one.
		and intracluster functional overlaps as in Equations (6) and
		Bar heights (ranks) are proportional to the logarithm of the probability of having a given function for all the functions ordered on the horizontal axis.
	bioinformatics.oxfordjournals.org /cgi/content/full/21/2/239 (4604 words)

	DELTA (Microsoft Office 97 Visual Basic Programmer's Guide)
		Use this function to filter a set of values.
		For example, by summing several DELTA functions you calculate the count of equal pairs.
		This function is also known as the Kronecker Delta function.
	msdn.microsoft.com /archive/en-us/office97/html/SEB85.asp?frame=true (140 words)

	FINAL EXAM REVIEW QUESTIONS
		Explain the following statement: The far-field diffraction pattern of an aperture is the Fourier transform of its transmittance function.
		When a lens of focal length f is used to bring in a far-field pattern to a convenient range, what is the relation between the radial distance r from the optic axis of a point in the Fourier transform, and the spatial frequency this location represents if the parallel coherent illuminating beam has wavelength
		Link the following aperture types with the appropriate mathematical form of their Fourier transforms: rectangular slit, circular aperture, sine wave; Bessel function, sinc function, Kronecker delta function.
	www.marquette.edu /~matthysd/FinalReviewQuestions.htm (741 words)

	PHY425B CORE LESSONS & OUTPUT SKILLS, Summer '99 (Site not responding. Last check: 2007-11-02)
		Graph periodic functions when given the algebraic form of the function over one period and the period.
		Also, test whether a function is even or odd, given an algebraic or graphical statement of the function.
		Classify the singularities of a given function according to whether they are isolated singularities, poles (give orders n), branch points, removable singularities, or essential singularities.
	physnet2.pa.msu.edu /home/courses/425B/425Bcorelessons.html (957 words)

	Partial Differential Equations
		In studying ordinary differential equations, we were motivated by the fact that many of the basic equations encountered in nature are cast in a form where the rate of change in the function depends on the function itself.
		are generalized coordinates, and a, b and g are known functions of these coordinates.
		Fortunately, the Kronecker delta function is defined at the limit of a number of functions.
	physics.tamuk.edu /~suson/html/4390/PDE.html (2397 words)

	Number theory algorithms
		We call "number-theoretic" any function that takes integer arguments, produces integer values, and is of interest to number theory.
		The first algorithm used to compute this function uses the Rademacher-Hardy-Ramanujan (RHR) theorem and is efficient for large n.
		are functions that do the same as the above functions, except they do not consider the number n as a divisor for itself.
	homepage.mac.com /yacas/manual/Algochapter2.html (3947 words)

	The Kronecker Delta Function Song
		But he did something else, and it equals one or zero--
		A little delta and a tiny m- n !
		If the subscripts are equal, the value is just one,
	www.haverford.edu /physics-astro/songs/kronecker.htm (64 words)

	The Yacas Book of Algorithms
		When functions are multiplied by constants, that situation is handled by the integration rule that can deal with univariate polynomials multiplied by functions, as a constant is a polynomial of degree zero.
		In the case of one function with one variable, the summation reduces to one term, so this linear set of equations was a lot simpler in that case.
		There are two tasks related to preparation of plots of functions: first, to produce the numbers required for a plot, and second, to draw a plot with axes, symbols, a legend, perhaps additional illustrations and so on.
	homepage.mac.com /yacas/manual/Algo.html (16313 words)

	Letter H
		A linear functional (PL), both defined on a subspace of a vector space and dominated by a sublinear function defined on the vector space, has a linear extension which is also dominated by the sublinear function.
		Bessel function of third kind, Webber function) and linearly combines Bessel functions of first and second kind.
		PL harmonic function, Harnack's Principle, Liouville's Conformability Theorem.
	members.fortunecity.com /jonhays/letterH.htm (3508 words)

	Theory
		is the Kronecker delta function and the sum runs over the N measurements made during the simulation.
		which is the standard expression for the propagation of error in a function of two independent variables [10].
		The error in a thermodynamic quantity like the energy can be obtained simply by replacing f with E in (14).
	www.arches.uga.edu /~amf/papers/histerr/node2.html (802 words)

	Introduction and Notation
		The number of orbitals in the one-particle basis set.
		Kronecker delta function, equal to one if i=j and zero otherwise.
		Usually denotes a single Slater determinant, but may also be a configuration state function (CSF).
	vergil.chemistry.gatech.edu /notes/ci/node2.html (309 words)

	Definition of delta - Merriam-Webster Online Dictionary
		Etymology: Middle English deltha, from Greek delta, of Semitic origin; akin to Hebrew dAleth daleth
		2 : something shaped like a capital Greek delta; especially : the alluvial deposit at the mouth of a river
		For More Information on "delta" go to Britannica.com
	www.m-w.com /cgi-bin/dictionary?book=Dictionary&va=delta (98 words)

	Hartley Transform (Site not responding. Last check: 2007-11-02)
		This applet shows the difference between slow and fast Hartley transforms.
		(They are near kin of the Fourier transform.) A good test is the double-transform of a Kronecker delta function in the specified position; the double transform should recover the original function, and it does so very well.
		The "Hartley Transform" button makes the code print out the entire transform, which might be more than you want to see for size 8192 so in general use the "Double Hartley Transform" button when you play with this applet, since it will only print out the one value that isn't down in the mud.
	www.mindspring.com /~hamill4/hamillnumerics/java/funapplets/hartley/HartleyApplet1.html (227 words)

	Choice of #tex2html_wrap_inline2635# and #tex2html_wrap_inline2637# (Site not responding. Last check: 2007-11-02)
		the space of piecewise constant functions nodally determined at cell centers, taking the basis
		'' here denotes the Kronecker delta function on integer pairs).
		as the space of piecewise bilinear functions of dimension
	www-math.bgsu.edu /latex2html_info/WSS_example/node16.html (208 words)

	[No title]
		In the HYPERLINK "http://www.npac.syr.edu/users/gcf/CPS713STAT/node45.html" proof using moment-generating function, we see that the high-order terms EMBED Equation.3 are gone since first order and second order statistics dominate the value of the moment-generating function as n goes to infinity.
		Intuitively, first order and second order statistics can completely characterize the distribution in the asymptotic region, since the randomness is averaged out; we only need to capture the mean and variance (energy) of the sample mean in the asymptotic domain.
		White Gaussian noise: The auto-correlation function: EMBED Equation.3 .
	www.cs.cmu.edu /~dpwu/books/math/probability/StochasticProcess.doc (1910 words)

	The Wavelet Digest :: Post a reply
		Maybe I have made misunderstanding, please let me know the correct explanation.
		Posted: Mon May 10, 2004 6:01 am Post subject: Others: I am confused with dirac delta and kronecker delta function in sampling theorem
		I am a graduate student, from electrical engineering.
	www.wavelet.org /phpBB2/posting.php?mode=quote&p=5018 (216 words)

	Microsoft Office Assistance: DELTA (Site not responding. Last check: 2007-11-02)
		Assistance > Excel 2003 > Working with Data > Function Reference > Engineering Functions
		If this function is not available, and returns the #NAME?
		The example may be easier to understand if you copy it to a blank worksheet.
	office.microsoft.com /en-us/assistance/HP052090571033.aspx?mode=print (199 words)

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