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Topic: Invariance theorem

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	Noether's theorem
		The formal statement of the theorem derives an expression for the physical quantity (and hence also defines it) that is conserved, from the condition of invariance alone.
		For example, the invariance of physical systems with respect to translation (when simply stated, it is just that the laws of physics don't vary with location in space) translates into the law of conservation of linear momentum.
		Invariance with respect to rotation gives law of conservation of angular momentum, invariance with respect to time gives the well known law of conservation of energy, et cetera.
	www.ebroadcast.com.au /lookup/encyclopedia/no/Noether's_theorem.html (180 words)

	PlanetMath: invariance theorem
		The invariance theorem states that a universal Turing machine provides an optimal means of description, up to a constant.
		The invariance theorem holds likewise for prefix and conditional complexities.
		This is version 4 of invariance theorem, born on 2003-07-04, modified 2006-11-07.
	planetmath.org /encyclopedia/InvarianceTheorem.html (94 words)

	NationMaster - Encyclopedia: Invariance theorem (via CobWeb/3.1 planetlab1.cs.wisc.edu) (Site not responding. Last check: 2007-10-09)
		In algorithmic information theory, the invariance theorem, originally proved by Ray Solomonoff, states that a universal Turing machine provides an optimal means of description, up to a constant.
		Noether's theorem is a central result in theoretical physics that expresses the one-to-one correspondence between the symmetries and the conservation laws.
		When it comes to quantum field theory, the invariance with respect to general gauge transformations also gives the law of conservation of quantities such as electric charge, though there are some subtleties here; the conservation law here is based on the Ward-Takahashi identities for the BRST symmetry.
	www.nationmaster.com.cob-web.org:8888 /encyclopedia/Invariance-theorem (335 words)

	Untitled Document
		These bridge theorems, called 1) the theorem of invariance or position and 2) the theorem of variance or transposition marked different logical perspectives and were not reducible to one another.
		Specifically, it is proposed that the theorem of invariance or position corresponds to the perspective of nursing practice.
		Whereas the translation metaphor forces a linear acceptance of propositions, the parallel approach spans anything from suggestiveness and mild induction to the goal of "coincidence" and recognition that the "flip" phenomenon (the hardest to prove with the translation metaphor) is in fact provable using the parallel case in the calculus.
	art3idea.psu.edu /hoath/hoath_2.html (2076 words)

	Merton Howard Miller
		The intuition behind MM's second invariance theorem, i.e., that dividend policy does not affect the market value of the firm in equilibrium, is also apparent in retrospect.
		As in the case of the first invariance theorem, the mechanism which generates this conclusion is that investors in the capital market can "counteract" changes in firms' financial structure.
		The main message of the MM theorems may be expressed as follows: if there is an optimal capital asset structure and dividend policy for firms, i.e., if the asset structure and dividend policy affect a firm's market value, then this reflects the consequences of taxes or other explicitly identified market imperfections.
	www.jewishvirtuallibrary.org /jsource/biography/MMiller.html (882 words)

	Invariance of domain - Wikipedia, the free encyclopedia
		Invariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space R
		The theorem and its proof are due to L.E.J. Brouwer, published in 1912.
		Open mapping theorem for other conditions that ensure that a given continuous map is open.
	en.wikipedia.org /wiki/Invariance_of_domain (431 words)

	Team-BIPOP
		Based on this theorem, we are then able to propose a Lagrange-Dirichlet theorem for nonsmooth Lagrangian dynamical systems that can be applied through Potential Shaping to the regulation of the position and force of a robotic manipulator [17].
		A key condition for the statement of Lasalle's invariance theorem is the continuity of the trajectories of the systems with respect to initial conditions.
		So we propose in [33] a version of LaSalle's invariance theorem for time-invariant flows that are countinuous with respect to initial conditions.
	www.inria.fr /rapportsactivite/RA2004/bipop2004/uid44.html (760 words)

	The Diamond Theorem
		Let G be the group of 322,560 permutations of these 16 tiles generated by arbitrarily mixing random permutations of rows and of columns with random permutations of the four 2x2 quadrants.
		The above is an expanded version of Abstract 79T-A37, "Symmetry invariance in a diamond ring," by Steven H. Cullinane, Notices of the American Mathematical Society, February 1979, pages A-193, 194.
		For a discussion of other cases of the theorem, click here.
	diamondtheorem.com (717 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Now, >>by Invariance of Domain, f(S^n) is open in R^n as f is 1-1 and continuous.
		Invariance of Domain is a theorem which states that if f:M->N is a map between n-dimensional manifolds without boundary which is 1-1 and continuous, then f is an open map.
		The one I am using is the theorem that if M and N are topological n-manifolds without boundary, and f:M->N is 1-1 and continuous, then f is open.
	www.math.niu.edu /~rusin/known-math/99/invar_domain2 (671 words)

	Tulane Math Graduate qualifying exam syllabi
		One is not expected to memorize proofs of major theorems such as the homotopy invariance of homology-the emphasis is on knowing the statements and being able to apply the results.
		However, in some cases, you will be expected to be able to sketch the proof of the theorem.
		Below we will distinguish theorems by SSA for "state, sketch the proof, and apply" and SA for "state and apply." This listing of theorems is not intended to be complete but we do try to mention the most important ones.
	www.math.tulane.edu /graduate/qualifying/topology.html (673 words)

	A FEW PUBLICATIONS WITH COMMENTS
		The theorem provides an enlargement of the initial domain of analyticity, which then can be used for the construction of envelopes of holomorphy.
		The Edge of the Wedge theorem, together with the methods of analytic completion, are also of considerabele interest for theories with broken Lorentz invariance.
		The theorem is the basis for a proof that microcausality, and non-negative energy in all frames, imply the standard, invariant energy-momentom relations, even if Lorentz invariance is violated otherwise.
	home.uchicago.edu /~roehme (1870 words)

	Invited Lectures
		Cameron-Martin Theorem for manifolds (Alias: What happens when you blow on perfume diffusing on a manifold.), talk given in the probability seminar at York University, Toronto Canada, Dec. 4, 1992.
		A Cameron-Martin Theorem for manifolds, talk given and University of California at Irvine, in the probability seminar, June 6, 1993.
		The Cameron-Martin Theorem for Brownian motion on a compact Riemannian manifold, June 23, 1998 given at "Seminare de Probabilites," University of Paris VI.
	math.ucsd.edu /~driver/DRIVER/vitae-etc/invited_lectures.htm (2334 words)

	The Invariance Theorem of Brouwer
		This is expressed by the theorem of dimension invariance of Brouwer (Brouwer(1976)):
		A proof of this theorem is given in Brouwer(1976).
		If one wants to avoid Brouwer's theorem, in this regard one has to map an n-dataset to a topological space which therefore must not be a manifold.
	www.dkfz-heidelberg.de /ibios_old/people/volz/Paper_gfkl2002_volz/node2.html (266 words)

	Nöther's Theorem (Site not responding. Last check: 2007-10-09)
		If you have a theory based on a variational principle, Nöther's Theorem furnishes you with conservation laws that come from the invariance of the principle under continuous groups of transformations.
		A similar result is obtained when infinitesimal rotations are considered, and the conserved quantity is the component of the angular momentum along the axis of the rotation.
		In electromagnetism, gauge invariance of the potential, which amounts to adding the gradient of a function to the vector potential, and a time derivative of the function to the scalar potential, which does not change the fields derived from the potentials, gives the conservation of charge.
	www.du.edu /~jcalvert/math/noether.htm (506 words)

	Dror Bar-Natan:Classes:2001-02:Algebraic Topology
		Class notes for March 12th (the basic idea of algebraic topology, Brouwer's theorem, the fundamental group, the fundamental group of the circle).
		Ex2-2.png (Van-Kampen's theorem, invariance of the Euler characteristic)
		Class notes for May 9th (homology is a functor, homotopy invariance of homology).
	www.math.toronto.edu /~drorbn/classes/0102/AlgTop/index.html (510 words)

	Laplace's Equation - Dirichlet Problem (Site not responding. Last check: 2007-10-09)
		Theorem 11.2 (N-Value Dirichlet Problem for the Upper Half Plane).
		for which the solution is given by Theorem 11.2.
		Theorem 10.4 guarantees the existence of such a conformal mapping.
	math.fullerton.edu /mathews/c2003/DirichletProblemMod.html (415 words)

	Well-Founded Induction and the Invariance Theorem for Loops - Morris (ResearchIndex) (via CobWeb/3.1 ... (Site not responding. Last check: 2007-10-09)
		Well-Founded Induction and the Invariance Theorem for Loops (1989)
		This is the standard well-founded induction theorem proved, for example, in [2].
		Morris, J. M.: Well-founded induction and the invariance theorem for loops.
	citeseer.ist.psu.edu.cob-web.org:8888 /morris89wellfounded.html (345 words)

	Modal Operators for Coequations (Site not responding. Last check: 2007-10-09)
		We present the dual to Birkhoff's variety theorem in terms of predicates over the carrier of a cofree coalgebra (i.e.
		We then discuss the dual to Birkhoff's completeness theorem, showing how closure under deductive rules dualizes to yield two modal operators acting on coequations.
		We discuss the properties of these operators and show that they commute, and we prove as main result the invariance theorem, which is the formal dual of Birkhoff's completeness theorem.
	www.cs.cmu.edu /Groups/LTC/papers/invariant.html (74 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Abstract: We proof a homotopy invariance theorem for algebraic K-theory of locally convex algebras stabilized by Schatten ideals.
		Action functionals present in literature are structured in such a way to reflect $kappa$-Poincaré invariance, renouncing to invariance under cyclic permutations of the arguments of the action functional.
		We can support this point of veiw by a theorem which states that if for a certain Dirac operator on a unital C-algebra, there is no upper limit for the eigenvalues, while keeping the eigen spaces, then the C-algebra is AF.
	www.stp.dias.ie /events/2004/abstracts.html (2271 words)

	Kolmogorov complexity - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab1.cs.wisc.edu) (Site not responding. Last check: 2007-10-09)
		To prove the theorem, note that the number of descriptions of length not exceeding n − c is given by the geometric series:
		This theorem is the justification for various challenges in comp.compression FAQ.
		It has the desirable properties of statistical invariance (the inference transforms with a re-parametrisation, such as from polar coordinates to Cartesian coordinates), statistical consistency (even for very hard problems, MML will converge to any underlying model) and efficiency (the MML model will converge to any true underlying model about as quickly as is possible).
	en.wikipedia.org.cob-web.org:8888 /wiki/Kolmogorov_complexity (2049 words)

	Donsker's theorem ; invariance principle ; functional central limit theorem
		Donsker's theorem ; invariance principle ; functional central limit theorem
		Donskersches Theorem ; Invarianzprinzip ; funktionaler zentraler Grenzwertsatz
		This Glossary may not be copied, reproduced or retained in any form whatsoever without the express permission of the ISI.
	isi.cbs.nl /glossary/term1014.htm (219 words)

	Dedecker, Rio: On the functional central limit theorem for stationary processes
		Dedecker, Rio: On the functional central limit theorem for stationary processes
		On the functional central limit theorem for stationary processes.
		, Limit theorems for functionals of ergodic Markov chains with general state space, Mem.
	www.numdam.org /numdam-bin/item?id=AIHPB_2000__36_1_1_0 (294 words)

	Johan van Benthem : Current Teaching Activities
		characterization theorem for the modal fragment of FOL
		modal one iff it is invariant for bisimulation
		Extend the invariance theorem to an extended modal language
	staff.science.uva.nl /~johan/AML-2003.html (602 words)

	Andreas Berthold Thom (Site not responding. Last check: 2007-10-09)
		The results include a smooth homotopy invariance theorem of non-positive algebraic K-theory for algebras which are stable with respect to a harmonic operator ideal.
		We study the algebraic K-theory of the tensor product of a sub-harmonic ideal with an arbitrary complex algebra and prove that the obstruction for the periodicity of algebraic K-theory is again cyclic homology.
		The main technical tools we use are the diffeotopy invariance theorem of Cuntz and the second author (which we generalize), and the excision theorem for infinitesimal K-theory, due to the first author.
	www.uni-math.gwdg.de /thom (1148 words)

	Recent advances in invariance principles for stationary sequences, Florence Merlevède, Magda Peligrad, Sergey Utev
		In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences.
		We also describe several maximal inequalities that are the main tool for obtaining the invariance principles, and also they have interest in themselves.
		The classes of dependent random variables considered will be martingale-like sequences, mixing sequences, linear processes, additive functionals of ergodic Markov chains.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.ps/1137162933 (102 words)

	Noether's theorem and Time invariance?
		But in any case I have been reading around about Noether's theorem and about the time invariant nature of general relativity.
		From what I can make out Noether's theorem appears to suggest (among other things) that the first law of thermodynamics agrees with Einstein's theory of General relativity in that it predicts that the first law can be considered as time invariant?
		So this has led me to wonder somewhat if the first law of thermodynamics would apply equally well in reverse as it does when time is considered to be running forward?
	www.physicsforums.com /showthread.php?t=83071 (2456 words)

	Topological Robust Control
		This line of research has been dedicated to putting into use the arsenal of mathematical tools provided by combinatorial, algebraic, and differential topology in robust control problems.
		The boundary behavior of the Nyquist return difference map, as it was introduced by Horowitz in the Quantitative Feedback Theory, is an issue relevant to the celebrated Brouwer domain invariance theorem, the Caratheodory prime end theorem, and the simplicial approximation theorem, the latter being a foundational result of combinatorial, piecewise-linear topology.
		Existence of fast robust stability tests on a subspace of uncertainty is an issue relevant to homotopy theory, obstruction theory, and the Fredholm index approach to K-theory as developed by Michael Atiyah.
	eudoxus.usc.edu /TOPOL/topol.html (879 words)

	Citations: A homotopy invariance theorem in coarse cohomology and K-theory - Higson, Roe (ResearchIndex) (via ... (Site not responding. Last check: 2007-10-09)
		A coarse map from X to Y is a continuous and proper map f : X Y so that for every R 0 there exists S 0 with d(x; x 0) R implying d(f(x) f(x 0) S: A coarse homotopy from X to Y is a continuous and proper....
		QUASI ISOMETRY CLASSIFICATION OF COARSE HADAMARD MANIFOLDS 17 Theorem 2.19.
		Let X be a Hadamard manifold, and let 0 be a fixed point in X. Denote by T the tangent space to X at 0.
	citeseer.ist.psu.edu.cob-web.org:8888 /context/340626/0 (257 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		meeting -- Outline -- * developing loops, an introduction (Cohen's chapter 8) The key idea is figuring out what the predicates are so can go back to calculating the loopless parts before and after * other forms of postconditions Note that the Invariance theorem requires postconditions to have a special form.
		Can use the rule of consequence again, but in general need some intitialization code.
		choose invariant P and guard B so that P /\ !B ==> R 1.
	www.cs.iastate.edu /~leavens/ui181/lectures/loops/loops-intro.txt (233 words)

	Nigel Higson - Research Articles and Lecture Notes
		The residue index theorem of Connes and Moscovici
		A Bott periodicity theorem for infinite-dimensional Euclidean space
		A note on the cobordism invariance of the index
	www.math.psu.edu /higson/ResearchPapers.html (211 words)

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