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Topic: Extremum

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global extremum

maximal extremum

absolute extremum

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	Stationary point - Wikipedia, the free encyclopedia
		a minimal extremum (minimal turning point or relative minimum) is one where the derivative of the function changes from negative to positive;
		a maximal extremum (maximal turning point or relative maximum) is one where the derivative of the function changes from positive to negative;
		If f''(x) = 0, the nature of the stationary point must be determined by way of other means, often by noting a sign change around that point provided the function values exist around that point.
	en.wikipedia.org /wiki/Extremum (716 words)

	Concavity -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-09-17)
		If a convex (i.e., concave upward) function has a "bottom", any (The precise location of something; a spatially limited location) point at the bottom is a (additional info and facts about minimal extremum) minimal extremum.
		If a concave (i.e., concave downward) function has an "apex", any point at the apex is a (additional info and facts about maximal extremum) maximal extremum.
		Contrary to the impression one may get from a calculus course, differentiability is not essential to these concepts; see (additional info and facts about convex) convex.
	www.absoluteastronomy.com /encyclopedia/c/co/concavity.htm (420 words)

	[No title]
		In this case, the extremum point (vertex) of the parabola is on the y - axis, AND, the curve is symmetric with respect to the y - axis:
		Therefore, the extremum point (vertex) of the parabola is at the origin (0, 0).
		The extremum point of the parabola is on the y - axis AND the parabola is symmetric with respect to y - axis
	jwilson.coe.uga.edu /EMAT6680/Caglayan/HW2/hw2.htm (787 words)

	Experimental Application of Extremum Seeking on an Axial-Flow Compressor - Wang, Yeung, Krsti'c (ResearchIndex) (Site not responding. Last check: 2007-09-17)
		Abstract: We show an application of the method of extremum seeking to the problem of maximizing the pressure rise in an axial flow compressor.
		First we apply extremum seeking to the Moore-Greitzer model and design a feedback scheme actuated through a bleed valve which simultaneously stabilizes rotating stall and surge and steers the system towards the equilibrium with maximal pressure.
		Wang, S. Yeung and M. Krsti'c, "Experimental application of extremum seeking on an axial-flow compressor," Proceedings of the 1998 ACC, Philadelphia, PA, TM09-1.
	citeseer.ist.psu.edu /29032.html (389 words)

	The FORMAFLUENS language
		A continuation on an extremum exists when the process which acted on the extremum continues without changing the nature of the critical points.
		If the extremum exits from the allowable zone, a nearby extremum will change its type: this is not allowed by the continuation rule and cannot be admitted.
		A variation on the extremum B m+ is shown in figure 2.4: the squashing m+ becomes an indentation m-.
	iride.unipv.it /formafluens/formafluens97/formaflu.htm (956 words)

	Finding Minimums and Maximums
		For the Lower Bound, arrow to the left of the extremum and press enter.
		The x is where the extremum occurs and the y is the minimum or maximum value.
		You should make sure there is only one extremum in the interval specified or you won't know which one it is going to give you.
	www.richland.edu /james/ti82/minmax (694 words)

	UniDimensionalSolver (WebCab Optimization v2.6 (J2EE Edition))
		A local extremum is a point such that the object function is known to obtain its highest (in the case of maximization) or lowest (in the case of minimization) value within a given sub-region of the entire domain over which the optimization problem is considered.
		A global extremum is the point at which the (object) function takes it maximum or minimum value over the entire domain for which the optimization problem is considered.
		Unless you particular wish to fine tune the optimization algorithms for your given problem at hand we strongly advise that when wishing to find the local or global extremum over an interval that the algorithms with a preset default set of bracketing and locate algorithms are used.
	www.webcabcomponents.com /ejb/optimization/JavaDocs/com/webcab/ejb/math/optimization/unidimensional/UniDimensionalSolver.html (1042 words)

	MultiDimensionalSolver Class
		A global extremum is the point at which the (object) function takes its maximum or minimum value over the entire domain for which the optimization problem is considered.
		However, in practice it is often the global extremum which is sort and often a (local) extremum found will not turn out to be a global extremum for the given optimization problem at hand.
		minimum or maximum) is just the extremum in a neighborhood of a point, where as the global extremum is the extremum on the whole domain over which the optimization problem is considered.
	www.webcabcomponents.com /dotNET/dotnet/optimization/API/COM/WebCab.COM.Math.Optimization.MultiDimensional.MultiDimensionalSolver.html (1970 words)

	A Bayesian Interpretation of Extremum Estimators (ResearchIndex) (Site not responding. Last check: 2007-09-17)
		Abstract: Extremum estimation is typically an ad hoc semi-parametric estimation procedure which is only justified on the basis of the asymptotic properties of the estimators.
		For a fixed finite data set, consider a large number of investigations using different extremum estimators to estimate the same parameter vector.
		The resulting empirical distribution of point estimates can be shown to coincide with a Bayesian posterior measure on the parameter space induced by a minimum information procedure.
	citeseer.ist.psu.edu /el-gamal97bayesian.html (422 words)

	3.4.4 The Joint Distribution of a Sample Mean and an Extremum, With Applications to Quality Control
		In some industrial applications one compares a sample mean and minimum, or a mean and maximum, to reference values, and determines if the lot from which the sample was taken is acceptable, or if further investigation of this lot is indicated.
		And means and maxima of power loss of sampled motors have been recently proposed for use in testing whether manufactured motors comply with labeled motor efficiencies.
		Because the exact joint distribution of an extremum and the mean of a sample is usually complicated, establishing these reference values using statistical considerations typically involves crude approximations or simulation, even under the assumption of normality.
	www.itl.nist.gov /div898/pubs/ar/ar1998/node39.html (304 words)

	Extremum Growth
		When a spacing is adopted which gives this maximum velocity, growth is said to be occurring under extremum conditions.
		This is also the spacing of which, for a fixed velocity, growth would be taking place with the minimum interfacial undercooling.
		In practice, most eutectic systems tend to solidify at the extremum.
	www.matter.org.uk /solidification/eutectic/extremum_growth.htm (118 words)

	AIPS HELP file (version 31DEC05) for MAXFIT
		MAXFIT: Verb to find coordinates and value of an image extremum DOCUMENTOR: E.B.Fomalont (NRAO/VLA) RELATED PROGRAMS: IMFIT, MOMFT, IMVAL PURPOSE MAXFIT is a verb which fits a quadratic function to a specified 3x3 map area in order to determine the location and intensity of an extremum.
		An area as large as 16x16 can be specified in IMSIZE to search for the extremum, although the fit will only be made on the 3x3 area surrounding the extremum.
		The verb is useful for communicating the location and intensity of the extremum to other verbs and tasks.
	www.aoc.nrao.edu /cgi-bin/aips/ZXHLP2.PL?MAXFIT (451 words)

	Scale-Space-Time of a Dynamic Image (Site not responding. Last check: 2007-09-17)
		For temporal-scales much smaller than the time delay, the extremum value increases rapidly and the extremum location converge to the time delay and the Q scale-time converges asymptotically to the Gaussian scale-time.
		For temporal-scales of the same order as the time delay and greater, the extremum value decrease and the extremum location gradually shift to 0.
		For temporal-scales much greater than the time delay the extremum value increase and the extremum location asymptotically converges towards 0.
	www.ensc.sfu.ca /people/grad/brassard/personal/THESIS/node78.html (353 words)

	Example for the Simple Pendulum with Moving Support (Site not responding. Last check: 2007-09-17)
		Extremum of theta occurred at time t = 2.271451 second.
		Extremum of theta occurred at time t = 3.044601 second.
		Extremum of theta occurred at time t = 4.004322 second.
	www.ualr.edu /~dcwold/phys3311/pendulum/example.html (220 words)

	CLiki : EXTREMUM (Site not responding. Last check: 2007-09-17)
		extremum returns -the element of sequence that would appear first if the subsequence of sequence specified by start and end were ordered according to sort using predicate and key.
		extremum determines the relationship between two elements by giving keys extracted from the elements to the predicate.
		That is weird; it would be reasonable to expect one of the minimal elements to be returned.
	www.cliki.net /EXTREMUM (804 words)

	Technometrics: Lot acceptance and compliance testing using the sample mean and an extremum. (Site not responding. Last check: 2007-09-17)
		Technometrics: Lot acceptance and compliance testing using the sample mean and an extremum.
		In industry, one sometimes compares a sample mean and minimum, or a mean and maximum, to reference values to determine whether a lot should be accepted.
		The purpose of this article is to use the saddlepoint method to develop a fairly simple and very accurate...
	www.findarticles.com /p/articles/mi_go2243/is_200208/ai_n6321095 (206 words)

	Gravity - Open Encyclopedia (Site not responding. Last check: 2007-09-17)
		Assuming that the masses are smaller than the distances divided by the constant above, the time dilation is tiny, but it is enough to cause Newtonian gravity as we know it.
		Because of the same form of both equations, the path of the object that takes an extremum of proper time while traveling, and by this taking a geodesic in spacetime, is the same (with accuracy to the negligible in this case curvature of space) as the Newtonian orbit of this object around the mass.
		So it looks as if the path of the object were bent by some "force of attraction" between the object and the mass.
	open-encyclopedia.com /Gravity (3709 words)

	[No title] (Site not responding. Last check: 2007-09-17)
		Local extremum: The value f(c) is local maximum for f(x) if there exists an interval (m,n) containing c such that EMBED Equation.3 for all x in (m,n).
		The quantity f(c) is called a local extremum if it is either a local maximum or a local minimum.
		A turning point is a point on a graph where a local extremum occurs.
	math.boisestate.edu /~liljanab/m160F04/m160-12.doc (480 words)

	Connectedness and Necessary Conditions for an Extremum (Site not responding. Last check: 2007-09-17)
		Book Description: This monograph is the first book in the study of necessary conditions of an extremum in which topological connectedness plays a major role.
		The synthesis of the well-known Dybrovitskii-Milyutin approach, based on functional analysis, and topological methods permits the derivation of the so-called alternative conditions of an extremum: if the Euler equation has the trivial solution only at an extreme point, then some inclusion is valid for the functionals belonging to the dual space.
		Also, the present approach gives a transparent answer to the question why the Kuhn-Tucker theorem establishes the restrictions on the signs of the Lagrange multipliers for the inequality constraints but why this theorem does not establish any analogous restrictions on the multipliers for the equality constraints.
	isbn.nu /0792349105 (436 words)

	PacParaGeoTess::SetDoubFromSys (Site not responding. Last check: 2007-09-17)
		If an extremum matrix does not exist, a new one is obtained.
		If no extremum matrix exists, and none can be obtained, the value FALSE is returned as the functional result and all further operations are avoided.
		The extremum matrix is given an opportunity to capture any extension of the bounding box represented by the supplied dVal argument.
	www.grc.nasa.gov /WWW/price000/geo/htm/pacparageotess_setdoubfromsys.html (145 words)

	Free extremum downloads: download extremum software
		Graph Plotter is a powerful tool which can help you to plot and analyze different types of graphs.
		In addition it can find asymptotes of function, break points, extremums and calculate limit, define integral, derivative of function and more.
		Third-party products and brand names may be trademarks or registered trademarks of their respective owners.
	www.soft-album.com /free/extremum (87 words)

	IOM Web Site - Instruction
		as the local extremum (that is, it corresponds to the smallest value of the cost functional and thus to the smallest
		(i) Since the penalty functional is quadratic, the local extremum is the global extremum;
		(ii) Since the penalty functional is nonnegative, it is clear that the global extremum is actually a global minimum.
	www.eas.asu.edu /iom/instruction/mod1euler_equa/mod1euler_equa.html (121 words)

	HYBRIDMAGAZINE.COM \| REVIEWS \| Die Form - Extremum
		The mood is such that suspension of disbelief is on full bore and you’re wanting to buy the soundtrack.
		Until, that is, the techno "un-ch un-ch un-ch" starts in out of nowhere and you go flaccid with an outraged "What the fuck?" Excremumoops, Freudian slip, Extremum takes that bad idea all the way to the Roxbury with 14 tracks.
		On a scale of one (1) to five (5): one being Hasselfhoff, and five being Neubauten, "Extremum" is two (2) Horkheimer.
	www.hybridmagazine.com /reviews/0401/dieform.shtml (850 words)

	PacParaGeoTess::operator=
		If the rOth object has an existing parameterization array, a new parameterization array is obtained for the presenting object (through the standard GetClassDesc CreateObject mechanisms) and a loop is executed to replicate the objects so arrayed by the rOth object for the presenting PacParaGeoTess object (again, through standard GetClassDesc CreateObject mechanisms).
		If the rOth object has an existing extremum matrix, a new extremum matrix is obtained for the presenting object (through the standard GetClassDesc CreateObject mechanisms) and the contents of the rOth extremum matrix assigned to it.
		If the rOth object has an existing encountered extremum bitmap, a new encountered extremum bitmap is obtained for the presenting object (through the standard GetClassDesc CreateObject mechanisms) and the contents of the rOth encountered extremum bitmap assigned to it.
	www.lerc.nasa.gov /WWW/price000/geo/htm/pacparageotess_operatorassign.html (275 words)

	sciforums.com - sum over paths
		when the action is at an extremum, all the phases of that exponential add constructively, and when you are far from the extremum, the phases tend to cancel out.
		is extremum like the focus of the photon shooter?
		the extremum of the action occurs along the classical path.
	www.sciforums.com /showthread.php?t=24638 (1391 words)

	No Title (Site not responding. Last check: 2007-09-17)
		The word ``local'' is often used in place of the term ``relative.'' The word ``extremum'' is used to mean ``maximum or minimum''.
		A critical point of f at which f does not have a local extremum is called a saddle point of f.
		If one of them has a relative maximum, relative minimum, or saddle point, then the other also has, respectively, a relative maximum, relative minimum, or saddle point.
	www.math.okstate.edu /~myersr/4013/maxmin/maxmin.html (2469 words)

	Projekt: darkwave - 'Extremum (boxed) - OUT OF PRINT'
		It is also about a look on the past century, the real and the unreal, the manipulations, the barbarity and the (de)construction of the body.
		Extremum represents a sound peak, a mathematical extreme, while XX could be, besides the excess, a representation of the 20th century that ends, the double X of censorship, but also the double place of a crime, a double cross of Saint Andre, the symbol of 20 = 2 + 0 = duality and emergence.
		New hybrid techniques have been used, in order to generate sound textures from enlarged fragments of pictures.
	www.projekt.com /projekt/product.asp?sku=TRN00060&dept_id=20 (293 words)

	Extremum Seeking Control for Discrete-Time Systems
		This technique is used to modify the separation principle and the Kalman—Bucy filtering to wide-band noise driven systems.
		MIROSLAV Krstic, "Extremum Seeking Control for Discrete-Time Systems" (2002).
		However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
	repositories.cdlib.org /postprints/396 (184 words)

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