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Topic: Finite

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	Finite - Wikipedia, the free encyclopedia
		In mathematics, a set is called finite if and only if there is a bijection between the set and some set of the form {1, 2,..., n} where n is a natural number.
		All finite sets are countable, but not all countable sets are finite.
		It is a theorem (assuming the axiom of choice) that a set is finite if and only if there exists no bijection between the set and any of its proper subsets.
	en.wikipedia.org /wiki/Finite (175 words)

	Finite state machine - Wikipedia, the free encyclopedia
		A finite state machine (FSM) or finite automaton is a model of behaviour composed of states, transitions and actions.
		Finite state machines are one type of the automata studied in automata theory and the theory of computation.
		In computer science, finite state machines are widely used in modelling of application behaviour, design of hardware digital systems, software engineering, compilers, study of computation and languages.
	en.wikipedia.org /wiki/Finite_state_machine (1085 words)

	Finite difference - Wikipedia, the free encyclopedia
		In mathematics, a finite difference is like a differential quotient, except that it uses finite quantities instead of infinitesimal ones.
		This means that difference operators, mapping the function f to a finite difference, can be used to construct a calculus of finite differences, which is similar to the differential calculus constructed from differential operators.
		This is often used in numerical analysis, especially in numerical ordinary differential equations and numerical partial differential equations, which aim at the numerical solution of ordinary and partial differential equations respectively.
	en.wikipedia.org /wiki/Finite_difference (309 words)

	[No title]
		Finite automata recognize regular languages and, conversely, any language that is recognized by a finite automaton is regular.
		If the finite automaton is in an accepting state when the input ceases to come, the sequence of input symbols given to the finite automaton is "accepted".
		There is a finite control which determines the state of the automaton and also controls the movement of the head.
	www.cs.odu.edu /~toida/nerzic/390teched/regular/fa/dfa-definitions.html (892 words)

	Sound and Vibration: Finite Element Analysis - A Numerical Tool for Machinery Vibration Analysis
		Finite Element Analysis (FEA) is a numerical technique that can he used to approximate the structural dynamic characteristics of vibrating mechanical systems, the understanding of which is paramount to any root-cause failure study involving excessive vibrations.
		For example, the modal characteristics of a rotor are usually estimated by a finite element analysis of the shaft and impeller.
		The accuracy of the finite element solution is dependent upon the accuracy of the bearing stiffness used in the analysis.
	www.findarticles.com /p/articles/mi_qa4075/is_200405/ai_n9441160 (1412 words)

	Finite Automata
		In a stochastic finite automaton (SFA), f(q,a) and h(q) are random functions and Pr(f(q,a)q,a) and Pr(h(q)) define the state transition and output probabilities respectively.
		In a probabilistic finite automata (PFA), the output in state q is a random function of q, and the state following q is a deterministic function of q and the output in q.
		PFSA is a PFA in which each state in Q has a unique label corresponding to a sequence (string) of outputs and, moreover, the label for f(q,h(q)) is a suffix of the sequence defined by concatenating the output h(q) to the label for q.
	www.cs.brown.edu /research/ai/dynamics/tutorial/Documents/FiniteAutomata.html (1520 words)

	Finite State Machine Minimization
		Finite state machines are best thought of as pattern recognizers, and minimum-size machines correspond to recognizers that require less time and space.
		Finite state machines are best thought of as edge-labeled directed graphs, where each vertex represents one of n states and each edge a transition from one state to the other on receipt of the alphabet symbol that labels the edge.
		Finite state machines are often used to specify search patterns in the guise of regular expressions, which are patterns formed by and-ing, or-ing, and looping over smaller regular expressions.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK5/NODE207.HTM (1255 words)

	Finite State Machine Design (Site not responding. Last check: 2007-10-21)
		Finite state machines are so named because the sequential logic that implements them can be in only a fixed number of possible states.
		More generally, the outputs and next state of a finite state machine are combinational logic functions of their inputs and present state.
		Finite state machines are critical for realizing the control and decision-making logic in digital -systems.
	www2.ele.ufes.br /~ailson/digital2/cld/chapter8/chapter08.doc.html (248 words)

	Finite (Site not responding. Last check: 2007-10-21)
		In mathematics, a set is called finite if and only if there is a bijection between the set and some set of the form {1, 2,., n} with n∈N.
		It is a theorem that a set is finite if and only if there exists no bijection between the set and any of its proper subsets.
		In physics, the term finite is in addition used in the meaning of "non-zero", for instance in a sentence like "if the distance of the two objects is finite.".
	www.yotor.com /wiki/en/fi/Finite.htm (154 words)

	PlanetMath: finite
		is finite if there exists a natural number
		This is version 3 of finite, born on 2001-10-25, modified 2004-02-22.
		Object id is 500, canonical name is Finite.
	planetmath.org /encyclopedia/Finite.html (68 words)

	Finite Square-Well Potential
		In exercise is designed to study the finite square well and to show the shooting method works.
		Although the finite square-well potential problem is more realistic then the infinite well, it is difficult to solve because it yields transcendental equations.
		With the finite potential, it is possible for the particle to be bound or unbound.
	webphysics.davidson.edu /physletprob/ch10_modern/finitewell.html (583 words)

	Amazon.com: Books: Finite Element Procedures (Site not responding. Last check: 2007-10-21)
		It provides not only an introduction to finite element methods and the commonality in the various techniques, but explores state-of-the-art methods as well -- with a focus on what are deemed to become "classical techniques" -- procedures that will be standard and authoritative for finite element analysis for years to come.
		It provides not only an introduction to finite element methods and the commonality in the various techniques, but explores state-of-the-art methods as well — with a focus on what are deemed to become "classical techniques" — procedures that will be standard and authoritative for finite element analysis for years to come.
		Finite element procedures are at present very widely used in engineering analysis, and we can expect this use to increase significantly in the years to come.
	www.amazon.com /exec/obidos/tg/detail/-/0133014584?v=glance (1356 words)

	Finite and Infinite Games
		A finite game is a game that has fixed rules and boundaries, that is played for the purpose of winning and thereby ending the game.
		Finite players try to control the game, predict everything that will happen, and set the outcome in advance.
		Or, you can do everything you do playfully, always knowing you have a choice, having no need to survive the way you are, allowing every element of the play to transform you, taking pleasure in every surprise you meet.
	www.alamut.com /subj/artiface/games/infiniteGames.html (504 words)

	Finite Fields
		Finite fields are the general starting point for the constructions of many combinatorial structures.
		We denote the group of all automorphisms of a field L by G(L) and the subgroup of G(L) that fixes all elements of the subfield K of L by G(L/K).
		When working with finite fields it is convenient to have both of the above representations, since the terms on the left are easy to multiply and the terms on the right are easy to add.
	www-math.cudenver.edu /~wcherowi/courses/finflds.html (3085 words)

	Finite Filter Home Page
		Finite® Filter offers a complete line of compressed air and gas filtration products.
		Finite’s International H-Series is the right solution for most air/gas applications.
		Finite also offers over 2000 competitor interchange elements.
	www.parker.com /ead/cm1.asp?cmid=305 (58 words)

	SPACE.com -- Space Seen as Finite, Shaped Like a Soccer Ball
		After some two millennia of speculation, the scientists involved in the work say, observations may be on the verge of determining whether the universe is infinite or finite.
		A finite amount of matter would generate a finite, or closed universe.
		"The universe is finite," he said, "but there's no boundary to it," implying that there is no beyond, or that if there is, then its nature is left to your imagination and is outside the closed system that astronomers can ever hope to see.
	www.space.com /scienceastronomy/universe_soccer_031008.html (1054 words)

	Finite-State Automata
		In fact, the Type 3 grammars, which are also known as the regular or right-linear grammars, are often identified as the "finite grammars" because of their equivalence to finite automata.
		In the case of an automaton that is equivalent to a finite grammar, as is the case for the transition network illustrated here, the nodes are labelled with the nonterminal symbols of the grammar.
		In a transition network diagram for an automaton that is equivalent to a finite grammar, the arcs are labelled with the words from the terminal vocabulary of the grammar.
	web.uvic.ca /~ling48x/ling484/notes/fsa.html (2176 words)

	Open Directory - Computers: Programming: Languages: Fortran: Source Code: Partial Differential Equations: Finite ...
		Finite Element Analysis Program (FEAP) - General purpose finite element analysis program which is designed for research and educational use.
		Parallel finite element codes for linear/nonlinear solid mechanics and thermal fluid simulations, parallel iterative linear solver library, partitioning subsystem, parallel visualization subsystem and utilities for parallel I/O and coupling of multiple codes.
		PMG employs a non-uniform Cartesian mesh of the user's choice, box-methods or finite element methods for discretization, algebraic (or geometric) construction of lower-dimensional subspace problems, damped-inexact Global Newton methods for nonlinearities, and a jacobian multilevel iteration based on the algebraic (or geometric) subspace hierarchy.
	dmoz.org /Computers/Programming/Languages/Fortran/Source_Code/Partial_Differential_Equations/Finite_Elements (421 words)

	Finite Element and Numerical Methods with Object Oriented Programming in C++ -- for Constrained Optimization, ...
		The variational formulation, finite element approximation, and solution algorithm are the bases for the definition of a numerical problem.
		With fe.lib, students now can be expected to hand in their finite element program assignment at the next class meeting, not at the end of a semester.
		In such a case, fe.lib serves as an example to demonstrate how vs.lib is used in the framework of finite element programming.
	www.vector-space.com (1532 words)

	2. Residual Finiteness Results - Residually Finite Groups
		The residual finiteness of free groups was again proven independently by Marshall Hall [MHall49], who in fact proved that free groups have the LERF property, a stronger property which will be discussed in section 4 of this paper.
		A large set of residually finite groups was revealed by Mal'cev's 1940 result [Mal40] that a finitely generated subgroup of a matrix group over a commutative ring with identity is residually finite.
		A and B are finitely generated torsion-free nilpotent and C is closed in A and B. A and B are finitely generated torsion-free nilpotent and C is cyclic (recall that Higman's example [Higm51] shows that one cannot weaken the conditions to A and B residually finite)
	www.math.umbc.edu /~campbell/CombGpThy/RF_Thesis/2_RF_Results.html (3347 words)

	Finite Element Mesh Generation
		Two functions, AddNode() and AddElement(), are employed for the generation of finite element nodal coordinates, and the attachment of finite elements to the nodes.
		When the finite element problem is three-dimensional, coord_vector is a 1x3 matrix containing the [x, y, z] nodal coordinates.
		Aladdin's looping constructs are ideally suited for specification of the finite element nodes in a compact manner, and for the attachment of the two-node finite elements.
	www.isr.umd.edu /~austin/aladdin.d/fe-mesh.html (1255 words)

	Lee Lady: Finite Rank Torsion Free Modules over Dedekind Domains (a book)
		The theory of finite rank torsion free abelian groups is full of results that depend on countability, or on having characteristic zero, or working over a ring whose quotient field is a perfect field, as well as proofs using quite specialized results from number theory.
		And one becomes more aware of the fact that the theory of finite rank torsion free abelian groups is moving away from abelian group theory in general in much the same fashion that abelian group theory has moved away from general group theory.
		Unlike the theory of torsion groups, the theory of finite rank torsion free modules is becoming something that fits in fairly well with the mainstream of commutative ring theory.
	www.math.hawaii.edu /~lee/book (629 words)

	Math Forum - Ask Dr. Math
		If we are restricted to a finite number of monkeys and a finite amount of time, then the answer is no. It is entirely possible that in a finite amount of time a finite number of monkeys may type out nothing but pages upon pages of meaningless drivel.
		If the monkeys are particularly unlucky, you may have to let them run an infinite amount of time before they crank out the desired sonnet, but chances are with this many monkeys on the job you will get results in five years.
		To make a long story short, if you have only a finite number of outcomes and you take an infinite number of trials, you will end up getting the outcome you are looking for.
	mathforum.org /library/drmath/view/55871.html (1047 words)

	Finite Element Circus
		The Spring 2005 Finite Element Circus was held at the University of Delaware on April 29-30, 2005.
		The Spring 2004 Finite Element Circus was held at the University of Pittsburgh on April 16-17, 2004.
		The Finite Element Circus is a regular conference devoted to the theory and applications of the finite element method, and related areas of numerical analysis and partial differential equations.
	math.rutgers.edu /~falk/fecircus (544 words)

	Adding a new Finite Element to Aladdin
		The Aladdin finite element libraray has been designed so that "nearly all" of the code associated with a new element is located in one file.
		Here ARRAY p is a pointer to the working array data structure that transfers information between the ALADDIN database and the finite* element library functions (note this data structure is used for all of the finite elements!), and "isw" is simply a constant for the task to be accomplished.
		In the finite element attributes set called "elmt_attr1", "section1" is the name of the element section attributes, and "material1" is the name of the material attributes.
	www.isr.umd.edu /~austin/aladdin.d/fe-elmts.html (1211 words)

	Carse Rules of Finite and Infinite Games (Site not responding. Last check: 2007-10-21)
		Finite play is limited and the limitations are chosen by the players, however, "no one is under any necessity to play a finite game.
		Finite players "somehow veil" the freedom they have "to step off the field of play at any time.
		Finite play is "contradictory" in that players seek to bring their play to an end.
	www.wvu.edu /~lawfac/jelkins/pmpl99/imagine/carse.html (507 words)

	Open Directory - Science: Technology: Software for Engineering: Finite Element Analysis (Site not responding. Last check: 2007-10-21)
		CAEFEM - A Windows-based finite element analysis system used to perform both linear and nonlinear structural and thermal analyses of design models and assemblies.
		Computer Aided analysis of structures using the Finite Element Method - Free FEA software developed by students of BIST which can be used for analysis of structures like beams, trusses and Plates.
		From the analysis, it is possible to determine the primary and secondary current distribution of the electrochemical cells and it is possible to obtain other data such as over potential of reactions, and coating thickness.
	dmoz.org /Science/Technology/Software_for_Engineering/Finite_Element_Analysis (1651 words)

	Finite
		This is taking as a definition the observation that infinite cycles and chaos are not possible in finite dynamical systems.
		Definition of what it means for a set to be finite is (surprizingly) much more complicated than definition of infinite.
		This particular definition is not one of the standard ones from the literature (which usually uses isomorphism with finite cardinals, though numerous other definitions are also common).
	www.iwu.edu /~lstout/NewTheoremlist/node25.html (93 words)

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