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	Saddle point - Wikipedia, the free encyclopedia
		In the most general terms, a saddle point for a smooth function (curve, surface or hypersurface) is a point such that the curve/surface/etc. in the neighborhood of this point lies on different sides of the tangent at this point.
		A saddle point is a point of a function (of one or more variables) which is both a stationary point and a point of inflection.
		A saddle point is an element of the matrix which is both the smallest element in its row and the largest element in its column is called saddle point.
	en.wikipedia.org /wiki/Saddle_point (409 words)

	Saddle Fitting - Nine Points to a Perfect Fit
		With the saddle correctly placed on the horse's back--and the horse still standing squarely--Freeze now instructs us to look at the lowest point of the seat, which, in most cases, is centered between the pommel (the front of the saddle) and the cantle (the back of the saddle) as well as level.
		As long as the saddle tree correctly fits the horse (which will become more apparent as you continue to evaluate the points on this checklist), it may be possible to adjust the level with flocking--extra natural or synthetic wool stuffing placed inside the panels.
		The points of the saddle tree determine the saddle's width, and this is probably the most important aspect of evaluating a saddle's suitability for a particular horse.
	equisearch.com /horses_riding_training/tack_apparel/english/eq9points447 (2776 words)

	physics - Saddle point (via CobWeb/3.1 planetlab-2.cs.princeton.edu) (Site not responding. Last check: 2007-11-02)
		In mathematics, a saddle point is a point of a function of two variables which is a stationary point but not a local extremum.
		At such a point, in general, the surface resembles a saddle that curves up in one direction, and curves down in a different direction (like a mountain pass).
		In terms of contour lines, a saddle point can be recognised, in general, by a contour that appears to intersect itself.
	www.physicsdaily.com.cob-web.org:8888 /physics/Saddle_point (237 words)

	Saddle (hypar) Surfaces
		This surface envelops an important point in applied mathematics called the "saddle point" found at its center which appears to be a maximum point in one plane, a minimum point in another plane, and actually is neither.
		These points are the projections on the cosine curve taken from the evernly spaced points along the equator.
		These points are the projections on the cosine curve taken from the 24 evenly spaced points along the equator.
	www.faculty.fairfield.edu /jmac/rs/saddles.htm (1920 words)

	Experimental Matrix Games
		The right hand matrix has no saddle point, since the maximin pay-off of the row player is found in the lower left cell and that of the collumn player in the upper left cell of the matrix.
		It may be noted that a game matrix may have several saddle points - all of them, of course, containing the same pay-offs for the row player and for the collumn player respectively.
		In fact, saddle points can be computed also for zero-sum games without a saddle point, if we not only permit the selection of one of the alternatives on the part of the players, but also random choices according to predetermined probability distributions over the alternatives.
	www.mathpsyc.uni-bonn.de /doc/micko/2c.htm (621 words)

	$NRTSTR Tutorial Example -- Saddle point footnote (Site not responding. Last check: 2007-11-02)
		A "saddle point" is a mathematical inflection point at which the Hessian matrix (second derivatives of energy with respect to pairs of coordinate variables) has exactly one negative eigenvalue.
		At such a point the potential energy surface therefore curves upward in all directions except along the downward-curving reaction coordinate s.
		A familiar example is the top of a mountain pass, where the terrain curves upward toward surrounding mountain peaks, but downward along the unique path of steepest descent connecting the two valleys.
	www.chem.wisc.edu /~nbo5/saddle.htm (82 words)

	PlanetMath: saddle point approximation
		The saddle point approximation can be applied if the function
		Cross-references: exponential, expansion, term, region, dominant, order, clear, point, Taylor expansion, local minima, separated, global minimum, satisfies, function, limit, integral, theory, field, approximation, stationary
		This is version 2 of saddle point approximation, born on 2003-05-14, modified 2003-08-20.
	planetmath.org /encyclopedia/SaddlePointApproximation.html (189 words)

	Predator and Prey
		In the linearization, this equilibrium point is a centre.
		At this point the future of our predator-prey system looks bad: even a very small amount of harvesting causes the eventual extinction of the prey (followed, of course, by the demise of the predator).
		As we have seen, the trajectories entering and leaving the saddle points are often very important.
	www.math.ubc.ca /~israel/m215/predprey/predprey.html (1186 words)

	[No title]
		During the summer of 1992 10-m transects were established at each of the Niwot Ridge Saddle grid points, with the exception of grid points 1, 13, 30A, 37, 41, 42, 63, and 71.
		The weight assigned to the "dead" category (59.290 g) for 1993 Saddle grid point 53 was excluded from data entry because it was accompanied by the comment "This was mostly organic soil".
		It was assumed that a second sample was collected at grid point 70A in that year and the data were entered for 70A; thus, the dual entries for that grid point in 1993.
	culter.colorado.edu:1030 /exec/.extracttoolA?saddbiom.mw (2274 words)

	travel.doc
		SADDLE ------ After the input-path has been read-in, it is necessary to flag any points along the path that have already been refined to saddle-points.
		The output is also a chain with three points, the second of which is the unmodified saddle-point, while the two surrounding points are now located closer to the saddle and to the bottom of the adiabatic valley.
		It smoothes an existing path and brings it closer to the bottom of the adiabatic valley by synchronously minimizing all its points, under the constraint that the points move within hyper-planes orthogonal to the path.
	www.lobos.nih.gov /Charmm/c28b2/travel.html (4905 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-02)
		The fact that these two eigenvalues have different signs identify the equilibrium point as a saddle.
		If they were complex conjugates with positive real parts, the point would be a spiral repellor.
		The nature of the point depends on the type of eigenvalues.
	mathforum.org /library/drmath/view/65596.html (288 words)

	A guide to the saddle point method
		Often the starting point is different from (123), but can nevertheless be brought into this form after a change of variable.
		A necessary condition for the use of the saddle point method is that
		In many cases the relevant integral may not be given in as in (123), but by a simple transformation it can be brought to this form.
	www.nbi.dk /~polesen/borel/node13.html (349 words)

	Monkey saddle - Wikipedia, the free encyclopedia
		It it belongs to the class of saddle surfaces and its name derives from the observation that a saddle for a monkey requires three depressions: two for the legs, and one for the tail.
		The term horse saddle is used, by contrast with monkey saddle, to designate a saddle point that is a minimax, that is to say a local minimum or maximum depending on the intersecting plane used.
		The monkey saddle will have a local maximum along certain planes, but it won't be a local minimum along others —just a point of inflection.
	en.wikipedia.org /wiki/Monkey_saddle (152 words)

	Saddle Point Group (Site not responding. Last check: 2007-11-02)
		A saddle point is the critical point of balance between two extremes.
		It marks the point of inflection in a business relationship where partners seek to identify and meet each other’s interest.
		At the Saddle Point Group, we view each transaction as a joint effort.
	www.saddlepointgroup.com (64 words)

	Saddle Point assignment
		A saddle point in a numerical array is a number that is larger than or equal to every number in its column, and smaller than or equal to every number in its row.One simple result is that if the game has a saddle point, then players should always choose the row/column containing that saddle point.
		If these are equal, print that you have a saddle point, and print the row and column number in which it occurs.
		If these two numbers are unequal, print a message saying that there is no saddle point.
	www.cis.upenn.edu /~matuszek/cit591-2003/Assignments/03-saddle-point.html (554 words)

	stirling.html (Site not responding. Last check: 2007-11-02)
		The starting point for all these asymptotic expansions is the bivariate generating function of the Stirling numbers of the second kind:
		This method relies on using an integral along a closed contour in the complex plane chosen in such a way as to pass through a special point called the saddle-point.
		The integral is concentrated in the neighborhood of the saddle-point and good asymptotic estimates are obtained from a local expansion there.
	pauillac.inria.fr /algo/libraries/autocomb/stirling-html/stirling1.html (855 words)

	Asymptotic description of separatrix crossing near a saddle-center point (via CobWeb/3.1 planetlab-2.cs.princeton.edu) (Site not responding. Last check: 2007-11-02)
		This problem may be considered as a separatrix crossing in confluent point.
		The separatrix crossing for the second order equations in the confluent point was considered in a preliminary fashion by R.Haberman in 1979 and D.C.Diminnie and R.Haberman in 2000 in more detail.
		The asymptotic solution crossing the separatrix in the confluent point was constructed by O.M.Kiselev in 1999,2001 for the Painlevé-2 equation.
	ok.on.ufanet.ru.cob-web.org:8888 /andr100/andrtalk.html (814 words)

	Page 2 - Where do you point your saddle? (Site not responding. Last check: 2007-11-02)
		as the saddle, perhaps a bit lower, used to be near 3 INCHES HIGHER than the bar.
		saddle doesn't fit exactly has a lot to do with that, i'm sure.
		saddles tipped way up...then I noticed a similar thing on pix of a few downhill bikes in a mag.
	www.cyclingforums.com /t-39503-15-2.html (2100 words)

	Saddle (hypar) Surfaces (via CobWeb/3.1 planetlab-2.cs.princeton.edu) (Site not responding. Last check: 2007-11-02)
		In spherical coordinates these saddle equations become R = cot A csc A sec 2t.
		The saddle as a developable surface can be continuously transformed from a plane two dimensional lamina into a shallow saddle and gradually into a deep saddle.
		This model demonstrates this fact because it is a flexible saddle.
	www.faculty.fairfield.edu.cob-web.org:8888 /jmac/rs/saddles.htm (1920 words)

	HOME
		Saddle Point Publishing produces unique books for both the trade and educational markets.
		We are proud to enlist a team of professionals who have extensive publishing experience.
		Copyright 2006 Saddle Point Publishing. All rights reserved.
	www.saddlepointpublishing.com (35 words)

	Game Saddle Point -- from Wolfram MathWorld
		A necessary and sufficient condition for a saddle point to exist is the presence of a payoff matrix element which is both a minimum of its row and a maximum of its column.
		game may have more than one saddle point, but all must have the same value.
		Dresher, M. "Saddle Points." §1.5 in The Mathematics of Games of Strategy: Theory and Applications.
	mathworld.wolfram.com /GameSaddlePoint.html (120 words)

	Extrema of a function and saddle points. (Site not responding. Last check: 2007-11-02)
		This theorem is proved by use of Taylor's formula (see section 1).
		The function has a critical point at (0,0), but the second derivative test is unconclusive here, as
		You can check that the function has a saddle point at the origin and a local maximum at (-1,-1), equal to -1.
	ndp.jct.ac.il /tutorials/Infitut2/node29.html (236 words)

	How to tell whether it's a max, min or saddle point. (Site not responding. Last check: 2007-11-02)
		You will probably remember that with a function of one variable we looked at the second derivative to establish whether a point was a maximum or a minimum or a point of inflection.
		is NEGATIVE, then the point is neither a max nor a min, it is a SADDLE POINT.
		Finally let's check that the point (0,0) is indeed a saddle point.
	www.ucl.ac.uk /Mathematics/geomath/level2/pdiff/pd9.html (304 words)

	Saddle Point -- from Wolfram MathWorld
		A point of a function or surface which is a stationary point but not an extremum.
		An example of a one-dimensional function with a saddle point is
		SEE ALSO: Game Saddle Point, Hyperbolic Fixed Point.
	mathworld.wolfram.com /SaddlePoint.html (71 words)

	Solution Methods for Saddle Point Systems in Computational Mechanics
		Saddle point systems that arise in exponential integration of the incompressible Navier-Stokes equations
		Saddle Point Problems in Elasticity: Motivation and Methods of Solution
		Algebraic multigrid methods for discretized saddle point problems with application to contact problems
	sccm.stanford.edu /csri (160 words)

	saddle point - BioInformatics Glossary (via CobWeb/3.1 planetlab-2.cs.princeton.edu) (Site not responding. Last check: 2007-11-02)
		A point on a surface that is neither a peak nor a valley, but still has a 0 gradient.
		Saddle points are situated such that moving in one direction takes one uphill, while moving in another direction would be downhill.
		Hence, saddles look like the things that cowboys ride on.
	big.mcw.edu.cob-web.org:8888 /display.php/1785.html (68 words)

	Saddle Point Systems Fastback® dealer for the greater San Francisco Bay Area.
		The PowisPrinter® and the Foilfast™ cover printer provide an exciting way to easily personalize your documents on-demand.
		Saddle Point Systems is the Fastback® dealer for the greater San Francisco Bay Area.
		© Copyright 2001 Saddle Point Systems.All Rights Reserved.
	www.saddlepointsystems.com (144 words)

	eBay Store - South Point Farm Saddle Shop: saddles, Halters, bridles and breastplates (Site not responding. Last check: 2007-11-02)
		Here at South Point we Sell saddles and tack and all that goes with the horse.
		We stock a huge selection and will try our best to meet or beat other,s prices.We are specialists at repairing and restoring saddles and tack including McClelland cavalry 1859 to 1904 models.Restored originals available.
		Use of this Web site constitutes acceptance of the eBay User Agreement and Privacy Policy.
	stores.ebay.com /South-Point-Farm-Saddle-Shop (135 words)

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