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Topic: Abstract index notation

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	Einstein notation - Wikipedia, the free encyclopedia
		Abstract index notation is an improvement of Einstein notation.
		Sometimes (as in general relativity), the index is required to appear once as a superscript and once as a subscript; in other applications, all indices are subscripts.
		In some fields, Einstein notation is referred to simply as index notation, or indicial notation.
	en.wikipedia.org /wiki/Einstein_notation (882 words)

	Tensor Information - tensor lamps (Site not responding. Last check: 2007-10-29)
		The tensor table lamps notation was developed around 1890 by Gregorio Ricci-Curbastro under the title absolute differential geometry, and was made accessible to many mathematicians by the publication of Tullio Levi-Civita's cumulant tensor decomposition classic text The Absolute Differential Calculus in 1900 (in Italian; translations followed).
		Physicists and engineers are among the first to recognise that vectors and tensors have tensor lamps a physical significance as entities, which goes beyond the (often arbitrary) co-ordinate system in which their components are enumerated.
		Thus, einstein's tensor notation instead of simply having 70 values as indicated in the above example, for a rank 3 tensor field with dimensions <2, 5, 7> every point in the space would have 70 values associated with tensor fascia muscle it.
	www.inanot.com /Ina-Electronics_Topics_T-/Tensor.html (1961 words)

	MAT 200 Lecture Notes -- Summation and Matrix Notation (Site not responding. Last check: 2007-10-29)
		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.
		We can decide that whenever two variables appear together we are to insert a lower index for the first and an upper index for the second, and then sum over all the possible values for this index.
		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/200s00/notation.html (538 words)

	Call for Abstracts, Western Institute of Nursing (Site not responding. Last check: 2007-10-29)
		As appropriate for the abstract, including research, project or theory development/concept analysis projects, the Program Committee asks that you include content related to the specific implications and significance of the study for the discipline of nursing and how the results can be implemented in practice.
		Abstracts for each paper in the symposium are to be submitted as separate forms.
		Individuals who are notified that their abstracts have been accepted for presentation as completed research have two opportunities to have their papers considered for an award.
	www.ohsu.edu /son/win/conference/callforabstracts.shtml (2081 words)

	Tools of Tensor Calculus - Index notation
		However, there are some operations such as the contractions or the raising and lowering indices that are denoted in an easier way using the so called abstract index notation.
		: a lower index in both, a basis element or a component of a tensor, is indicated in TTC by a minus sign.
		If you have a tensor with a lower index and want to raise it, just type the tensor in index notation moving the subscript to the upper position.
	baldufa.upc.es /xjaen/ttc/tutorial/inde.htm (1111 words)

	How the Abstract System Works
		Abstract authors upload their submission, and may make changes to their submission up to the abstract deadline.
		This is especially important in light of the fact that most client authors submit their abstracts within the last 8 hours before the abstract deadline.
		Reviewers identify the review score of each abstract based upon your review scoring specifications, select their choice of presentation mode (podium, etc.), and have the opportunity to provide individual comments.
	www.convenemachine.com /tools/abstractshow.cgi (386 words)

	tensor questions
		Saying that his notation is standard means the interpretation of tensors is dependent on familiarity with penrose's use of notation.
		Yet, there is a great flexibility in the physicist's notation, particularly in the facility with which it can be used to construct new operations that do not come readily withing the scope of the mathematician's specified operations.
		The abstract-index notation is notational convenience for telling which types of hydra one is tryin to tame.
	www.physicsforums.com /showthread.php?p=888724 (2748 words)

	MML: Notation Module
		It could be expressed in the textual format of MML, in the graphic symbol manner as in Western staff notation, expressed as a frequency, or indicated on a piano roll.
		The abstract MML "note" can thus easily be translated into such a graphical representation as it contains al the necessary information for such a translation.
		In MML the notation rest is indicated with the uppercase letter R. For applications such as MIDI a rest is not explicitly indicated.
	www.musicmarkup.info /modules/notation (1748 words)

	CS202 abstraction on Sat Oct 16 06:59:41 PDT 2004 (Site not responding. Last check: 2007-10-29)
		An abstract operation is not implemented in its class but in classes that are derived from it.
		Instead we define pointers that refer to the abstract type but are attached to objects in concrete classes that implement the abstract class.
		The abstract class serves to organize a set of functions that are implemented in many different ways.
	www.csci.csusb.edu /dick/cs202/abstraction.html (1503 words)

	Guide Introductions: Congressional Research Service–Index and Abstract Samples
		Documents are indexed to the most specific applicable subject terms and usually not also to broader or narrower terms that do not reflect as well the subject of the document.
		For example, a document focusing specifically on strikes would be indexed to "Strikes and lockouts" and not also to the more general term "Labor-management relations." When the focus of a document is equally upon the more general and the more particular subject term, we place index entries under both terms.
		However, the wording of a notation of content for a single document may be different for each of the index terms under which it appears.
	www.lexisnexis.com /academic/guides/crs/indexes.asp (816 words)

	Abstract Preparation Guidelines (Symposia)
		When preparing abstracts for submission to ISPO symposia, please follow these guidelines.
		Author listings on abstracts are the basis for the computer-generated author index in the program and abstracts volume.
		A positive notation in no way affects whether or not an abstract is accepted or how it will be scored by reviewers.
	www.cancerprev.org /Meetings/Guidelines/Abstracts (437 words)

	Chart research - PublicWiki
		This page is for the development of the chart notation and its computational models.
		The state of a program is not a single point that follows a directed graph with decision making at the vertices; rather, execution occurs at a vertex when all of its inputs are fulfilled, so (in our standard model) every vertex executes as the course of the program proceeds.
		Dataflow can be represented with charts, but charts are meant to be a more general notation: they are not at all an architectural model (as dataflow tends to be).
	abstract.cs.washington.edu /wiki/index.php/Chart_research (518 words)

	Publication-Abstracts by Martin Erwig
		The visual notation can be used directly as a visu al query interface to spatio-temporal databases, or it can provide predicate specifications that can be integrated into textual query languages leading to heterogeneous l anguages.
		The extension to indexed data types enables the development of specific recursion schemes, which are, in particular, suited to express a large class of graph algorithms.
		Particularly attractive is the use of visual expressions for the description of domain-specific data structures in combination with textual notations for abstract control structures.
	web.engr.oregonstate.edu /~erwig/papers/abstracts.html (10910 words)

	Diagrams 2000 Programme - Abstracts
		The notation is based upon the concept of a mathematical graph consisting of nodes and edges.
		Items in the target notation are modelled as "node objects" and the "rules" of the target notation such as connectivity between elements are expressed as edges between the node objects.
		The specific notations we use in the system are based closely on the diagrams typically used for teaching introductory programming, but the framework is general enough to account for and express many uses of diagram sequences.
	www.cl.cam.ac.uk /Diag2000/abstracts.html (7301 words)

	Abstract index notation - Wikipedia, the free encyclopedia
		Abstract index notation is a mathematical notation for tensors and spinors that uses indices to indicate their types.
		Thus the index is not related to any coordinate system and does not take numerical values.
		It was designed by Roger Penrose to compensate for the difficulty in describing contractions in modern abstract tensor notation, without losing the intrinsically geometric viewpoint.
	en.wikipedia.org /wiki/Abstract_index_notation (148 words)

	Abstract index notation
		We shall use a notation, the abstract index notation.
		The idea is not to introduce a basis but use a notation for tensors that mirrors the expression for their basis components.
		We can also use the index notation to express symmetries of a tensor.
	www.ikp.liu.se /usr/tobol/master/html/node10.html (153 words)

	MAGIC 2002, Abstracts
		Abstract: Splitting method for the approximation of the exponential is used in many applications.
		Abstract: In this talk, we show how to obtain a priori estimates for the global error of a numerical integrator.
		Abstract: EinSum is a C++ package which understands index notation including the Einstein summation convention.
	www.ii.uib.no /~anto/MAGIC/2002/abstracts.html (505 words)

	History overview
		The best known is probably the notation for the calculus used by Leibniz and Newton.
		Leibniz's notation lead more easily to extending the ideas of the calculus, while Newton's notation although good to describe velocity and acceleration had much less potential when functions of two variables were considered.
		Realising that there are abstract properties 2 and 3 which apply to every sets with 2 and 3 elements and that 2 + 3 = 5 is a general theorem which applies whether they are sets of apples, books or trees moves from counting into the realm of mathematics.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/History_overview.html (1886 words)

	Amazon.com: General Relativity: Books: Robert M. Wald (Site not responding. Last check: 2007-10-29)
		The abstract index notation is introduced to deal with the plethora of indices involved in manipulating tensors.
		In the treatment of geodesics, the author shows that it is sufficient to consider curves that are affinely parametrized, and the geodesic equation is derived in a coordinate basis.
		However, there is a practical issue with a geometric approach, the notation used in some books is such that it's very difficult for a reader to write the equations down on a piece of paper.
	www.amazon.com /General-Relativity-Robert-M-Wald/dp/0226870332 (2670 words)

	DCMI Abstract Model
		Each property may be related to one or more other properties by a refines (sub-property) relationship (where the two properties share some semantics such that whenever a resource is related to a value by the sub-property, it follows that the resource is also related to that same value by the property).
		The DCMI abstract model for resources and descriptions is represented as UML class diagrams [UML] in figures 1 and 2.
		A syntax encoding scheme indicates that the value string is formatted in accordance with a formal notation, such as "2000-01-01" as the standard expression of a date.
	dublincore.org /documents/abstract-model (4224 words)

	Abstract Classes and Subtyping
		Abstract class names must be entirely uppercase and must begin with a dollar sign
		; this makes it easy to distinguish abstract type specifications from other types, and may be thought of as a reminder that operations on objects of these types might be more expensive since they may involve dynamic dispatch.
		In order to motivate the notion of abstract classes, we will start by considering different implementations of a data structure.
	www.gnu.org /software/sather/docs-1.2/tutorial/abstract.html (617 words)

	Abstract Schemas Object Model (Site not responding. Last check: 2007-10-29)
		The abstract schema referenced in these use cases/requirements is an abstraction and does not refer solely to DTDs or XML Schemas.
		To begin with, an abstract schema is a generic structure that could contain both internal and external subsets.
		The namespace URI of the notation being declared.
	www.w3.org /TR/2002/NOTE-DOM-Level-3-AS-20020725/abstract-schemas.html (3829 words)

	Abstract Data Type
		Abstract data types were first formulated in their pure form in CLU:
		For me the Abstract part of AbstractDataType refers to their hidden implementation, not to their lack of mutable state.
		Conventional mathematical notation may have no explicit support for mutability, but it is possible to model mutability and "side-effects" without too much difficulty.
	c2.com /cgi/wiki?AbstractDataType (2455 words)

	Representing Music Using XML - Abstract
		Abstract for a Poster Session presented at the
		These include its lack of representation of musical concepts such as rests and enharmonic pitches (distinguishing Db from C#), as well as notation concepts such as stem direction and beaming.
		It represents common western musical notation from the 17th century onwards, including both classical and popular music.
	www.recordare.com /musicir2000/abstract.html (926 words)

	Conway Notation - Knot Atlas (Site not responding. Last check: 2007-10-29)
		Conway notation was introduced by J.H. Conway in 1967 (see [Conway]).
		For higher values of N a notation is used in which the first number is the number of crossings, and the next is the ordering number of polyhedron (e.g., 101, 102, 103* for N = 10 denoting 10, 10, 10*, respectively, and 111, 112, 113 for N = 11 denoting 11, 11, 11**, respectively, etc.).
		However if you try to draw some knots or links from their Conway symbols the obtained projection might be non-isomorphic with the one given in Rolfsen, for example knot 9_15 denoted in Conway notation as 2 3 2 2 gives projection with 5, and not 4 digons.
	katlas.math.toronto.edu /wiki/Conway_Notation (850 words)

	Euclidean Tensors
		The advantages of vector notation are then lost, and the student is enveloped in coordinate algebra that makes it difficult to understand the subject clearly.
		When an index is repeated, as j is here, we assume a sum of terms for each possible value of j.
		An index that is summed over on the right-hand side of an equation cannot appear on the left-hand side.
	www.du.edu /~jcalvert/math/eucltens.htm (5403 words)

	Viktor's Home Page: Curved Spacetime
		Multiplying a covariant (indicated by a subscripted index) and a contravariant vector's components and summing the result yields a scalar quantity that is independent of the coordinate system:
		When an index appears in an expression twice, as a contravariant (upper) and covariant (lower) index, it is assumed that the expression will be summed over this index:
		For each contravariant index, one term will be added; for each covariant index, one term must be subtracted.
	www.vttoth.com /CURVED/curved.htm (2392 words)

	DeveloperLand.com [Your free search engine – Microsoft Indexing Server]
		But Indexing Server is able to be pointed to a local web site, get the physical path where the files for this web site are located and then index those files and also store the virtual path of those files.
		MS Indexing Server is a separate Windows component which needs to be installed.
		Utilizing the Indexing Service will make searching faster as all the files have been already indexed and the system just needs to search the index instead of the file system itself.
	developerland.com /DotNet/Enterprise/340.aspx (4295 words)

	The Foundations of Relativity
		in tensor notation, a mixed tensor of rank (1,1).
		's is a vector, and thus has an upper index, which I will denote with a dot.
		I gave a short outline of the connection between the abstract multilinear algebra approach to tensors and the transformation approach in this thread.
	www.physicsforums.com /showthread.php?p=875985 (2612 words)

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