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	Einstein notation - Wikipedia, the free encyclopedia
		In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention useful when dealing with coordinate formulae.
		Abstract index notation is an improvement of Einstein notation.
		In some fields, Einstein notation is referred to simply as index notation, or indicial notation.
	en.wikipedia.org /wiki/Einstein_notation (882 words)

	Summation Summary
		Temporal summation is the convergence of many rapid-firing signals from a single synapse onto the postsynaptic axon hillock--the part of the axon closest to the cell body.
		Spacial summation is the simultaneous convergence of one signal from several different synapses onto the axon hillock of a single postsynaptic neuron.
		Summation is the addition of a set of numbers; the result is their sum.
	www.bookrags.com /Summation (1083 words)

	PlanetMath: Einstein field equations
		The Einstein field equations are a system of second order coupled nonlinear partial differential equations for a metric tensor on a manifold.
		In order to adress this issue and to be able to treat the Einstein equations much as one would treat other differential equations, a common practise is to supplement the Einstein equations with auxiliary condidtions which serve to define a coordinate system and hence single out a particular element of an equivalence class in diffeomorphism.
		Throughout this entry, we shall use index notation for tensor fields because that is common in the literature (especially physics literature) and is convenient for computation of particular solutions.
	planetmath.org /encyclopedia/EinsteinFieldEquations.html (615 words)

	Bob Gardner's "Relativity and Black Holes" Special Relativity
		Einstein was bothered by what he saw as a dichotomy in the concept of "mass." On one hand, by Newton's second law (F=ma), "mass" is treated as a measure of an objects resistance to changes in movement.
		Einstein summarizes this in his Principle of Equivalence: There is no way to distinguish between the effects of acceleration and the effects of gravity - they are equivalent!
		In our technical exploration of general relativity, we will adopt Einstein's summation notation in which an index of summation appears in each term both as a subscript and as a superscript and the sigma summation symbol is omitted.
	www.etsu.edu /physics/plntrm/relat/general.htm (692 words)

	Kids.Net.Au - Encyclopedia > Einstein summation convention
		In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention useful when dealing with coordinate equations or formulas.
		The real purpose of the Einstein notation is for formulas and equations that make no mention of the chosen basis.
		Perhaps more significantly, the inner product may be a primary object of study that shouldn't be suppressed in the notation; this is the case, for example, in general relativity.
	www.kids.net.au /encyclopedia-wiki/ei/Einstein_summation_convention (1239 words)

	Summation Notation - Info.co.uk Web Search
		Summation notation is used to define the definite integral of a continuous function...
		Be conversant with summation notation and the use of partitioned matrices.
		i the index of summation, n is the lower limit of summation, and m is the...
	search.info.com /infocom.uk/clickit/search?r_fcp=&r_sacop=1&r_cop=aylf&r_coid=302349&rawto=http://web.info.com/infocom.uk/search/web/Summation%2BNotation/1/20/1/-/1/0/1/1/1/1/_blank/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/N/-/-/-/-/-/-/-/-/-/-/-/-/0/302349?engineset=infocom.uk&cmp=KNC-3LS480536328 (448 words)

	MAT 392 Lecture Notes -- Summation and Matrix Notation (Site not responding. Last check: 2007-10-10)
		An innovation due to Einstein, not as famous as E=mc^2 but more widely used, is to decree that whenever an index appears as both a superscript and a subscript we are to sum over all possible values.
		The notation puts more of a burden on the reader, who is now expected to know that the range of values for k runs from 1 to n.
		A consequence of these notations is that when I write two tables of number next to each other there is an implied sum over the columns of the first and rows of the second.
	www.math.princeton.edu /~stalker/392s00/notation.html (538 words)

	Meningar.com om summation. summation, Ewald, temporal mm.
		Summation notation (1 of 4)topofpage() Summation Notation (1 of 4) The Greek letter Σ (a capital sigma) is used to designate summation...
		Summation Summation The firm’s reputation is based upon its knowledge of the substantive law, attentiveness and responsiveness to individ..
		Summation notation is used to define the definite integral of a continuous function of one variable on a closed interval...
	www.meningar.com /summation.html (865 words)

	Dogpile Web Search: Einstein's tensor notation
		Using e1, e2, and e3 instead of i, j, and k, together with Einstein notation, we obtain a concise algebraic presentation of vector and
		It is important to keep in mind that no new physical laws or ideas result from using Einstein notation; rather,...
		Einstein's summation convention involves summing over repeated indices.
	www.dogpile.com /info.dogpl/search/web/Einstein%2527s%2Btensor%2Bnotation (311 words)

	Einstein notation - Wikipedia, the free encyclopedia
		The basic idea of Einstein notation is very simple.
		The value of the Einstein convention is that it applies to other vector spaces built from V using the tensor product and duality.
		The dot product is defined simply as summation over the indices of a and b:
	en.wikipedia.org /wiki/Summation_convention (882 words)

	Intro to Einstein Summation
		Introduction to the Einstein Summation Notation for Cartesian Tensors
		Al Barr, Caltech CS The Einstein summation notation is an algebraic short-hand which allows multidimensional Cartesian quantities to be expressed, manipulated, and simplified in a compact and unambiguous manner.
		With this notation, it is convenient to manipulate tensor expressions involving determinants, rotations, multidimensional derivatives, matrix inverses, cross products, and a variety of other multicomponent mathematical entities.
	www.gg.caltech.edu /~barr/stc/esn/esntalk.html (65 words)

	A Hybrid Mathematican's/Physicist's Notation (was: Einstein summation co
		A Hybrid Mathematican's/Physicist's Notation (was: Einstein summation convention)
		What happened is that Einstein took a body of already existing literature (Riemannian geometry) and devised a workable everyday notation and convention for it to allow you to work with it on a practical basis.
		All contractions are expressed via Einstein's summation convention; which was the original advantage of the Physicist's index notation.
	www.lns.cornell.edu /spr/2003-05/msg0051494.html (1059 words)

	Isaac Newton - Wikipedia, the free encyclopedia
		Newton and Gottfried Leibniz developed calculus independently, using their own unique notations (as most great mathematicians do.) Although Newton had worked out his method years before Leibniz, he published almost nothing about it until 1693, and did not give a full account until 1704.
		He discovered Newton's identities, Newton's method, classified cubic plane curves (polynomials of degree three in two variables), made substantial contributions to the theory of finite differences, and was the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations.
		He approximated partial sums of the harmonic series by logarithms (a precursor to Euler's summation formula), and was the first to use power series with confidence and to revert power series.
	en.wikipedia.org /wiki/Isaac_Newton (4976 words)

	Einstein summation convention
		The product C of two matrices A and B is defined as c_(ik)==a_(ij)b_(jk), where j is summed over for all possible values of i and k and the notation above uses the Einstein summation convention.
		In the following equations, we will use Einstein’s summation convention such that whenever an index is repeated in a term, once as a subscript and once as a superscript, it signifies that that...
		The same sum with the Einstein summation convention is c k x k.
	www.logicjungle.com /wiki/Einstein_summation_convention (301 words)

	AMS Glossary
		—A special notation for writing vector equations using the scalar components of vectors rather than the vectors themselves.
		This notation has found widespread use in the study of atmospheric turbulence, where the many vector and tensor components of a governing equation can be concisely represented by a much smaller number of terms.
		The key to this notation is the use of indices (subscripts) i, j, and k, which can each take on the values of 1, 2, or 3 to represent the three Cartesian directions (x, y, z).
	amsglossary.allenpress.com /glossary/search?id=einstein-s-summation-notation1 (123 words)

	Isaac Newton (Site not responding. Last check: 2007-10-10)
		Newton discovered Newton's identities, Newton's method, classified polynomials of degree 3 in 2 variables, made substantial contributions to the theory of finite differences, and was the first to use fractional indices and to employ coordinate geometry to derive solutions to diophantine equations.
		Newton's conceptions of gravity and mechanics, though not entirely correct in light of Einstein's Theory of Relativity, still represent an enormous step in the evolution of human understanding of the universe.
		For this reason, he is generally considered one of history's greatest scientists, ranking alongside such figures as Einstein, Galileo and Carl Friedrich Gauss.
	www.brainyencyclopedia.com /encyclopedia/i/is/isaac_newton.html (5109 words)

	Quantum Mechanics and General Relativity: Incomplete Working Notes
		While I am going to pay attention to some notational details, I do not intend this to be a mathematically rigorous presentation.
		The first equation, when applied to a photon, is simply Einstein's equation for photon energy.
		So g (as we have been using it) is g as in classical mechanics [as we have been misusing the notation prior to now].
	www.zaimoni.com /Notes_GR_QM.htm (2841 words)

	Seek 'Summation' related info here. (Site not responding. Last check: 2007-10-10)
		Summation provides a full range of qualitative and quantitative research services, on-site research for retailers and businesses.
		Here, then, is a summation of the evaluation data I collected, and my thoughts on what this all means.
		By Summary: This is a summation of the concepts used in three different speach sythesis programs.
	www.netinfoseek.com /?q=summation (724 words)

	No Title
		Here the primed frame is moving in the +z direction away from the unprimed and the two coordinate frames are coincident at t=0.
		C Note that we use greek letters as indices that run from 0(t) to 3(z) and we omit an implicit summation sign when indices are repeated up and down.
		This notation "Einstein Summation" is standard, some authors reserve latin indices (i,j,k) for spatial x,y,z markers (others invert this convention - like Landau and Lifshitz).
	www.ifa.hawaii.edu /users/kuhn/ast640/notes1.html (1095 words)

	Primary Math Education
		summations, Goldbach's conjecture, and the Fundamental Theorem of Arithmetic.
		The summation notation looks more complicated than it is. The upper case Greek letter sigma
		Explain the notation, show how to write the series, and ask the student to add the numbers.
	www.members.aol.com /MathObservations/primehall.html (2063 words)

	Bell's Theorem (Stanford Encyclopedia of Philosophy)
		That Quantum Mechanics admits of such entangled states was discovered by Erwin Schrödinger (1926) in one of his pioneering papers, but the significance of this discovery was not emphasized until the paper of Einstein, Podolsky, and Rosen (1935).
		This reformulation is important because it diminishes the force of Bohr's (1935) rebuttal of Einstein, Podolsky, and Rosen on the grounds that one is not entitled to draw conclusions about the existence of elements of physical reality from considerations of what would be seen if a measurement other than the actual one had been performed.
		constitute a polarization basis for photon j (j =1, 2), the former representing (in Dirac's notation) a state in which the photon 1 is linearly polarized in the x-direction and the latter a state in which it is linearly polarized in the y-direction.
	plato.stanford.edu /entries/bell-theorem (12693 words)

	PlanetMath: summation
		Anyone with an account can edit this entry.
		This is version 17 of summation, born on 2004-10-12, modified 2006-08-20.
		Object id is 6361, canonical name is Summation.
	planetmath.org /encyclopedia/Summation.html (265 words)

	New System for Indicial Computation and Its Applications in Gravitational Physics -- from Mathematica Information Center
		The package automatically handles dummy indices and Einstein's summation notation, enables one to define new indexed objects and to assign symmetries to that objects.
		Other important features of EinS are the ability to perform an automatically "3+1" split of implicit summations, printing expressions in a natural 2-dimensional form and exporting them into plain TEX or LATEX with user-controllable alignment commands.
		As a typical application of EinS, the problem of constructing of a local reference system for a massive extended body in the framework of the Parametrized Post-Newtonian formalism is briefly described.
	library.wolfram.com /infocenter/Articles/2278 (189 words)

	Title display page
		The basic concepts of Cartesian analysis are developed along with the application of tensor notation to engineering analysis.
		Tensor notation (the Einstein summation convention) is introduced to give the reader exact component equations and to demonstrate its value in multi-variable analysis.
		By applying the summation notation in the analysis, the author believes that a more complete description of the dynamic problems of aerospace vehicle motion can be offered, and that this approach is already finding applications in aerospace engineering technologies.
	www.eurospan.co.uk /eurospan/display.asp?K=900000000468559&pdmtex=_O_&m=1&dc=15&sort=IMPRINT&mw=2&st_01=20051117:20060516&sf_01=sort_date;&st_02=PB*&sf_02=BIC_SUBJ_CODE (285 words)

	Advanced Physics Forums - Generalized Lorentz Transformation for an Accelerated Frame of Reference (Site not responding. Last check: 2007-10-10)
		I\'m pretty sure what you want is just equations 9 from the paper, which appears to be the most general form for velocity and acceleration being collinear (being in 1+1 dimension) and lacking any rotation.
		Perhaps it would be better to ask any questions you may have about the notation of those equations.
		And the use of Einstein summation notation, which is when you sum over all three spatial dimensions when you see one raised Roman letter and one lowered Roman letter, as described here.
	www.advancedphysics.org /forum/printthread.php?t=1260 (282 words)

	ASP: Books of Note Archives
		Beautifully written and illustrated, this is an elegant, informative, magisterial summation of one of the twentieth century's greatest cultural achievements.
		Parker also discusses Einstein's reluctant connection with atomic weapons, his pacifist philosophy, his quest for the elusive unified field theory, and the relationship of his work to the recent "hot" area of superstrings.
		This episode of Big Ideas is a homage to Albert Einstein, the man and his legacy, focusing on the attempts by physicists, mathematicians and theorists to derive a unifying theory to explain all the forces of nature in the same terms.
	www.astrosociety.net /books/archive1.html (8052 words)

	A package for computation with indexed objects within Mathematica and its applications to metric gravity theories (Site not responding. Last check: 2007-10-10)
		The package automatically handles Einstein's summation notation, generates dummy indices, enables one to define new indexed objects and assign symmetries to that objects.
		Other important features of EinS are the ability to perform automatically "3+1" split of implicit summations, printing expressions in a natural 2-dimensional form and exporting into plain T
		Several typical applications of EinS are described: computation of the Landau-Lifshits pseudotensor in a rotating reference system, the problem of constructing of a local reference system of a massive extended body in the framework of the parametrized post-Newtonian formalism.
	www.math.unm.edu /ACA/1998/sessions/gr/klioner (147 words)

	General relativity:Einstein Summation Notation - Research Area
		But that summation sign, do we really want to write it over and over and over and over.
		Here are some more examples of the Einstein summation notation being used:
		Used material from the Wikibooks article "General relativity:Einstein Summation Notation - Research Area" (see Copyrights for details)
	www.researcharea.org /books/General_relativity:Einstein_Summation_Notation (474 words)

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