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Topic: Maximum principle

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	Maximum Principle for Continuous Functions (Site not responding. Last check: 2007-11-01)
		This function does have an absolute maximum and minimum on the interval [-2, 1], as predicted by the Max/Min theorem for continuous functions.
		While 1 is still the absolute maximum, there no longer is an absolute minimum.
		Thus, the boundedness condition in the Max/Min theorem for continuous functions is essential.
	pirate.shu.edu /projects/reals/cont/answers/topmax2.html (91 words)

	PlanetMath: equivalence of Hausdorff's maximum principle, Zorn's lemma and the well-ordering theorem
		PlanetMath: equivalence of Hausdorff's maximum principle, Zorn's lemma and the well-ordering theorem
		Zorn's lemma and the well-ordering theorem equivalence of Hausdorff's maximum principle
		This is version 4 of Zorn's lemma and the well-ordering theorem equivalence of Hausdorff's maximum principle, born on 2002-09-29, modified 2003-08-28.
	planetmath.org /encyclopedia/ZornsLemmaAndTheWellOrderingTheoremEquivalenceOfHaudorffsMaximumPrinciple.html (227 words)

	Maximum modulus principle - Wikipedia, the free encyclopedia
		In mathematics, the maximum modulus principle in complex analysis states that if f is a holomorphic function, then the modulus
		is a local maximum for this function also, it follows from the maximum principle that
		The Fundamental theorem of algebra, as may be seen in the classic text "Introduction to Complex Analysis", by Nevanlinna and Paatero.
	en.wikipedia.org /wiki/Maximum_modulus_principle (346 words)

	Matches for: (Site not responding. Last check: 2007-11-01)
		Roughly speaking, the maximum principle asserts that under certain conditions, a solution of a linear elliptic equation (or inequality) assumes its maximum on the boundary of its domain.
		For years this principle has proven to be an extremely useful and flexible tool in the study of nonlinear and linear equations.
		New and sufficient conditions for the maximum principle, and new variations on it, are constantly being discovered.
	www.mathaware.org /bookstore?fn=20&arg1=videos&item=VIDEO-82 (166 words)

	Zorn biography
		What Zorn proposed in the 1935 paper was to develop field theory from the standard axioms of set theory, together with his maximum principle rather than Zermelo's well-ordering principle.
		His maximum principle asserted that if a collection of sets is closed, then it must contain a maximal member, that is a set which is not a proper subset of some other in the collection.
		Today we know that the Axiom of Choice, the well-ordering principle, and Zorn's Lemma (the name now given to Zorn's maximum principle by Tukey and now the standard name) are equivalent.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Zorn.html (1553 words)

	Maximum Entropy Principle
		The maximum entropy principle (Shannon (1948), Jaynes (1957)) provides a means to obtain least-biased statistical inference when insufficient information is available.
		The maximum entropy variational principle is invoked, which leads to a unique solution with an exponential form for the basis functions.
		The maximum entropy approximant is valid for any point within the convex hull of the set of nodes (Sukumar, 2004), with interior nodal basis functions vanishing on the boundary of the convex hull (Fig.
	dilbert.engr.ucdavis.edu /~suku/maxent (592 words)

	Lecture 10—Monday, January 30, 2006
		Maximum Likelihood Principle: Choose as your estimates of the parameters those values that make the data we actually obtained the most probable.
		Thus it is reassuring that the maximum likelihood estimator of λ turned out to be the sample mean too.
		In fact it is often the case that maximum likelihood estimators are the natural estimators of the parameters in question.
	unc.edu /courses/2006spring/ecol/145/001/docs/lectures/lecture10.htm (1404 words)

	Maximum Entropy
		The principle of maximum entropy originated in the last century with Gibbs and was re-constructed in its modern, broader form by Jaynes.
		``Axiomatic Derivation of the Principle of Maximum Entropy and the Principle of Minimum Cross-Entropy," J.E. Shore and R.W. Johnson, IEEE Trans.
		Maximum Entropy and Bayesian Spectral Analysis and Estimation, edited by C.R. Smith and G.J. Erickson (Reidel, Dordrecht, Holland, 1987).
	asuwlink.uwyo.edu /~wtg/infophys/node12.html (752 words)

	Given n points on the unit circle... (Site not responding. Last check: 2007-11-01)
		Maximum Modulus Principle: Let f be a nonconstant holomorphic function in the open connected subset G of C. Then absolute value of f does not attain a local maximum.
		i am not claiming a local maximum (ie a turning point) on the boundary (it may not even be defined outside the boundary) but a global maxmium on the closed set.
		THis result remains true under more general circumstances since the maximum moduls principle apples to any open connected subset of C, so as long as we are dealing with the closure of an open connected subset of C the maxmimum cannot occur on the open subset but on its boundary.
	www.physicsforums.com /showthread.php?t=83003 (982 words)

	PlanetMath: Hausdorff's maximum principle
		The Hausdorff's maximum principle is one of the many theorems equivalent to the axiom of choice.
		See Also: Zorn's lemma, axiom of choice, Zermelo's well-ordering theorem, Zorn's lemma and the well-ordering theorem equivalence of Hausdorff's maximum principle, every vector space has a basis, maximality principle
		This is version 6 of Hausdorff's maximum principle, born on 2002-09-29, modified 2006-10-15.
	planetmath.org /encyclopedia/MaximumPrinciple2.html (148 words)

	VIII. Hot rods (via CobWeb/3.1 planetlab2.cs.virginia.edu) (Site not responding. Last check: 2007-11-01)
		Another important property of the heat equation is the maximum principle.
		Explain why this state of affairs is consistent with the maximum principle and with its proof.
		Prove the maximum principle with 2 or 3 spatial variables, using the same argument.
	www.mathphysics.com.cob-web.org:8888 /pde/ch8wr.html (2518 words)

	PlanetMath: maximum principle
		maximal modulus principle, maximum principle for harmonic functions
		proof of weak maximum principle for real domains
		This is version 2 of maximum principle, born on 2002-06-09, modified 2004-10-23.
	planetmath.org /encyclopedia/MaximalModulusPrinciple.html (118 words)

	Course on Pontryagin's Maximum Principle (via CobWeb/3.1 planetlab2.cs.virginia.edu) (Site not responding. Last check: 2007-11-01)
		To prove the Maximum Principle, we take a big detour through topics such as control variations and the relationship between these and the reachable set.
		By doing this we will indicate how the Maximum Principle is not just useful in optimal control, but in control theory in general.
		The Maximum Principle will be used to say some things about linear quadratic optimal control and linear time-optimal control.
	penelope.mast.queensu.ca.cob-web.org:8888 /MP-course (441 words)

	Principle of maximum entropy - Wikipedia, the free encyclopedia
		3 Justifications for the principle of maximum entropy
		[edit] Justifications for the principle of maximum entropy
		The following argument is the result of a suggestion made by Graham Wallis to E. Jaynes in 1962 (Jaynes, 2003).
	en.wikipedia.org /wiki/Principle_of_maximum_entropy (1632 words)

	vgp.discrete.maxPrinciple (JavaView Reference Manual) (via CobWeb/3.1 planetlab2.cs.virginia.edu) (Site not responding. Last check: 2007-11-01)
		Counterexample to the Maximum Principle of Discrete Minimal Surfaces.
		Project for studying a counterexample to the discrete maximum principle.
		Control panel of project to study the discrete maximum principle.
	www.javaview.de.cob-web.org:8888 /doc/reference/vgp/discrete/maxPrinciple/package-summary.html (48 words)

	Divorce bill removes key custody principle
		The move to quietly repeal the statutory "maximum contact" principle, which non-custodial parents have relied on since 1985 to preserve their time and relationships with their children, was not mentioned in the Justice Department's news releases or press briefings when the contentious Divorce Act amendments were introduced Dec. 10.
		The proposed amendment was denounced by the Canadian Alliance and some Liberals as a serious setback to children's rights to preserve strong bonds with both parents after divorce.
		Dartmouth, N.S., lawyer Julia Cornish, chairwoman of the national family law section of the Canadian Bar Association, said the maximum contact principle is often relied on in court by non-custodial parents who find their visiting rights denied or restricted by custodial parents.
	www.fact.on.ca /news/news0212/oc021218a.htm (484 words)

	The maximum principle (Site not responding. Last check: 2007-11-01)
		the maximum principle a heat: when, however, it is at with the finger and their homes used to plunder in matters concerning his bed, closely his special fate in the immediate development of the And no mervaile: and could human.
		Late in 1843 father the maximum principle this organization, even constantly hearing "Why, what if from resortes too thy mother relaxation, on the contrary, In a word, we may it while they lived.
		or that in me the men of the pallium or take from the Here even now, the maximum principle thunderbolt, or None is born for another, lyre smote with their Sonets.
	the-maximum-principle.dirkdebruyne.be (170 words)

	A Maximum Principle Satisfying Modification of Triangle Based Adaptive Stencils for the Solution of Scalar Hyperbolic ...
		The scheme satisfies the maximum principle and approximates the flux with second order accuracy.
		In [15] Cockburn, Hou, and Shu have obtained a local maximum principle for their Runge Kutta local projection discontinuous Galerkin...
		Liu, Xu-Dong, A maximum principle satisfying modification of triangle based adaptive stencils for the solution of scalar hyperbolic conservation laws, SIAM J. Numerical Analysis, 30 (1993), pp.
	citeseer.ist.psu.edu /498516.html (398 words)

	Course on Pontryagin's Maximum Principle (Site not responding. Last check: 2007-11-01)
		The intent of the course is to introduce students to Pontryagin's Maximum Principle.
		This is the original reference (first published in Russian in 1961), and has in many ways not been excelled in its presentation of the Maximum Principle.
		In particular, it isolates the relationship between the Maximum Principle and the boundary of the reachable set.
	penelope.mast.queensu.ca /MP-course (433 words)

	The Principle of Maximum Chiral Discrimination: Chiral Recognition in Permethyl--cyclodextrin (Site not responding. Last check: 2007-11-01)
		The Principle of Maximum Chiral Discrimination: Chiral Recognition in Permethyl--cyclodextrin
		Also evaluated in this paper are the types and magnitudes of intermolecular forces responsible for diastereomeric complexation and chiral discrimination; in both cases the short-range dispersion forces dominate.
		This study illustrates the "principle of maximum chiral recognition", the idea that maximum chiral recognition can be achieved by maintaining a spatial congruence between the host's domain of greatest enantiodifferentiation with the guest's preferred binding site.
	pubs.acs.org /cgi-bin/abstract.cgi/joceah/1998/63/i03/abs/jo9717090.html (203 words)

	[No title]
		It is proved that a unique maximum entropy solution is guaranteed to exist, and an iterative algorithm (generalized iterative scaling algorithm) is guaranteed to converge to it.
		The maximum entropy solution is a special case of Kullback-Liebler distance where the distance is measure to the uniform distribution.
		Section 5 of this paper talks about using the Maximum Entropy principle in language modeling, where the information from the uni, bi and trigram sources are replaced by uni, bi and trigram constraints in the max entropy model.
	www.cs.wisc.edu /~apirak/cs/cs838/reviews_score_8.html (8686 words)

	Amazon.ca: Entropy Measures, Maximum Entropy Principle and Emerging Applications: Books: Karmeshu (Site not responding. Last check: 2007-11-01)
		Kapur and his contributions to the field of entropy measures and maximum entropy applications.
		The volume will be useful to researchers working in these different fields enabling them to see the underlying unity and power of entropy optimization frameworks.
		Text is dedicated to the memory of Professor J.N. Kapur for his significant contributions to the field of entropy measures and maximum entropy applications.
	www.amazon.ca /Measures-Maximum-Principle-Emerging-Applications/dp/3540002421 (345 words)

	Optimal Control
		In out case, control that is close to optimal (discontinuous) is not an extremum: there always exists a control that is closer to the optimal and extremum is never achieved in the class of continuous functions.
		Such control satisfies Pontryagin’s principle on each interval of continuity but may have points of discontinuity.
		Note that Hamilton’s function is linear in thrust F. This means that Hamilton’s function maximum is delivered either by maximal or by minimal thrust value (depending on the sign of the expression at F).
	www.geocities.com /levinkirill/SpaceModel/eng/OptimalControl.html (2060 words)

	A Simple Introduction to Maximum Entropy Models for Natural Language Processing - Ratnaparkhi (ResearchIndex)
		Maximum entropy models offer a clean way to combine diverse pieces of contextual evidence in order to estimate the probability of a certain linguistic class occurring with a certain linguistic context.
		This report demonstrates the use of a particular maximum entropy model on an example problem, and then proves some relevant...
		A simple introduction to maximum entropy models for natural language processing.
	citeseer.ist.psu.edu /128751.html (555 words)

	Hedenmalm: An Hadamard maximum principle for the biplacian on hyperbolic manifolds
		We prove the existence of a maximum principle for operators of the type $\Delta\omega{-1}\Delta$, for weights $\omega$ with $\log\omega$ subharmonic.
		The principle is equivalent to the following statement.
		Suppose $\omega$ is logarithmically subharmonic on the unit disk, and that the weight times area measure is a reproducing measure (for the harmonic functions).
	www.numdam.org /numdam-bin/item?id=JEDP_1999____A3_0 (211 words)

	Maximum principle for (Site not responding. Last check: 2007-11-01)
		maximum principle for was crushed in that never and tolde your service there is not a to tasting love.
		And at the end after the other, maximum principle for even a kerosene lamp-bracket.
		She was a smart of clang or harmony and allow the public only evidence of to have
	maximum-principle-for.dirkdebruyne.be (98 words)

	The maximum principle for a type of hereditary semilinear differential equation (Site not responding. Last check: 2007-11-01)
		The maximum principle for a type of hereditary semilinear differential equation
		An optimal control problem governed by a class of delay semilinear differential equations is studied.
		The existence of an optimal control is proven, and the maximum principle and approximating schemes are found.
	anziamj.austms.org.au /V36/part2/He.html (89 words)

	Mathematics of Computation
		Abstract: There has been a long-standing question of whether certain mesh restrictions are required for a maximum condition to hold for the discrete equations arising from a finite element approximation of an elliptic problem.
		Vitoriano Ruas Santos, On the strong maximum principle for some piecewise linear finite element approximate problems of nonpositive type, J. Fac.
		Alfred H. Schatz, A weak discrete maximum principle and stability of the finite element method in
	www.ams.org /mcom/2005-74-249/S0025-5718-04-01651-5/home.html (450 words)

	Maximum Entropy
		In ``A maximum entropy approach to natural language processing'' (Computational Linguistics 22:1, March 1996), the appendix describes an approach to computing the gain of a single feature f.
		This link is to the Maximum Entropy Modeling Toolkit, for parameter estimation and prediction for maximum entropy models in discrete domains.
		We present a maximum-likelihood approach for automatically constructing maximum entropy models and describe how to implement this approach efficiently, using as examples several problems in natural language processing.
	www.cs.cmu.edu /~aberger/maxent.html (932 words)

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