Problem of points - Factbites

Problem of points - Factbites
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Topic: Problem of points

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In the News (Fri 1 Jan 10)

Northern Trust

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Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Chalkdust Volume 15 - April 2001 - Prince Edward School, Harare, Zimbabwe.
		In the Distance events Forbes came first with 115 points, Selous second with 111 points, Jameson third with 94 points, Rhodes fourth 89 points, Baines fifth with 73 points, Moffat sixth with 68 points, Coghlan seventh with 60 points, and Wilson eighth with 36 points.
		Fuel problems saw Prince Edward having to hire a bus from ZUPCO for the Slazenger Cup.
		It also resulted in the late cancellation of the Peterhouse Relays (one of the traditional 3 major school athletics meetings.) That left the Peterhouse Invitational (Slazenger Cup) and the Inter-School’s Athletics Meeting.
	site.mweb.co.zw /peschool/chalkdust/vol15 (4393 words)

	Encyclopedia: Curve fitting
		Curve fitting is finding a curve which matches a series of data points and possibly other constraints.
		In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points from a discrete set of known data points.
		To define this more precisely, the maximum number of ogee/inflection points possible in a polynomial curve is n-2, where n is the order of the polynomial equation.
	www.nationmaster.com /encyclopedia/Curve-fitting (1438 words)

	Ivars Peterson's MathLand
		In mathematical terms, the problem comes down to finding a new point P such that the total length of the straight lines joining P to each one of three given points, A, B, and C, on a plane has the least possible value.
		Instead of finding Steiner points on a plane in which roads can go in any direction, he looked for them on a grid, meaning that the roads can go only in certain directions.
		"The Steiner point problem with three points, which is a trivial plane geometry problem, becomes enormously complex in discrete geometry, as many close approximations compete to substitute for the simple optimal solution in the Euclidean plane."
	www.maa.org /mathland/mathland_4_8.html (1438 words)

	Mike Westmoreland's Symbolic Computing Home Page
		The problem is to find the curve between two given points which provides the least time of descent for a particle falling along a wire in the shape of that curve under the influence of gravity.
		An instructor may illustrate the brachistochrone problem by first choosing the sequence of points to be along the straight line between two points.
		A common initial response to this problem is that the curve should be the straight line between the two points.
	www.denison.edu /collaborations/fipse/math/westmor.html (347 words)

	A Maximum b-Matching Problem Arising from Median Location Models with Applications to the Roommates Problem
		We consider maximum b-matching problems where the nodes of the graph represent points in a metric space, and the weight of an edge is the distance between the respective pair of points.
		However, we show that in this case the b-matching problem is the dual of a median location problem with respect to the given set of points, in some extended metric space.
		We show that if the space is either the rectilinear plane, or the metric space induced by a tree network, then the b-matching problem is the dual of the (single) median location problem with respect to the given set of points.
	roso.epfl.ch /ismp97/ismp_abs_323.html (347 words)

	Spherical Codes
		If there is a particular dimension and number of points that you are interested in which is not given here, let me know.
		The Problem Place n points on a sphere in d dimensions so as to maximize the minimal distance (or equivalently the minimal angle) between them.
		There is some overlap with the tables of packings in dimensions 3, 4 and 5 mentioned in Part 1 of this file, and with the tables of spherical coverings, spherical t-designs, minimal energy arrangements, minimal volume arrangements, etc.
	www.research.att.com /~njas/packings (1390 words)

	cs327hw3.html
		Missionaries and Cannibals (20 points): Write a program which solves the missionaries and cannibals problem using breadth-first search.
		XOR Neural Net (20 points): Problem 3.4, page 56.
		Different Searches, Different Orderings (10 points): Problem 8.2, page 137.
	www.mathcs.carleton.edu /faculty/rkirchne/cs327/cs327hw/cs327hw3.html (366 words)

	Steiner Tree
		Steiner was apparently one of several mathematicians who worked the general problem for n points, and he was mistakenly credited with the problem.
		Expositions on the proof that the Steiner tree problem for graphs is hard [ Kar72 ] include [ Eve79a ].
		Such a minimum spanning tree can be refined by inserting a Steiner point whenever the edges of the minimum spanning tree incident on a vertex form an angle of less than 120 degrees between them.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE181.HTM (366 words)

	Modelling and solving a matching problem
		We consider a problem defined on a graph, which is a set of points, that may pairwise be connected by an edge or not.
		Formulate - in general - the perfect matching problem on N points, with costs C_ij on the edge between points i and j, as an Integral Linear Programming problem.
		Use the formulation of the problem above and drop the integrality constraints.
	www.win.tue.nl /~wscor/OW/2V300/LP-assignb.html (366 words)

	Curve fitting
		The compound B-spline cubical curve is built on border points of rectangle in ranges X and Y. The rectangle is divided on NxN cells with identical quantity of points.
		The purpose of constructing a line of approximation (fitting) - to discover the best model to describe your data and to show where the appearance of new points is most possible.
		It is built on method of correlation in interval X, Y you selected.
	www.uniphiz.com /findgraph/online_help/source/func.htm (1242 words)

	Symmetric Multistep Methods for the N-Body Problem
		n consecutive impulses of 1 translates into a change in velocity of 1 between all points, that is, a smooth change in velocity of 1.
		An escape of n means that when simulating a moon orbiting a world, at least n sample points must be taken per orbit or the method will fail to keep the moon in orbit.
		An accuracy of n means that at least n sample points must be taken per orbit in order to maintain an accuracy of position of 1 part per million per orbit.
	burtleburtle.net /bob/math/multistep.html (2478 words)

	Johnny Torrio and the Dream of Real Organized Crime
		Again a call went back to the New York Five Points Gang, to send someone that could be trusted to take care of the problem.
		The “Five Points” gang was noted for contracting out some of its people to carry out the type of work Big Jim wanted.
		In 1909 Big Jim was threatened by some “Black Handers,” and to keep a war from breaking out by using his own men to handle the problem, he called on some on some of his friends in New York to provide the support he needed.
	www.suite101.com /article.cfm/organized_crime/20722 (523 words)

	Glossary
		Each generation of sires is worth 16 points, divided up by the amount of sires, i.e., the immediate sire is worth 16 points while the four sires four generations back are worth four points apiece.
		Joint problem that has progressive degeneration of joint cartilage and the underlying bone.
		A horse's height is measured in hands and inches from the top of the shoulder (withers) to the ground, e.g., 15.2 hands is 15 hands, 2 inches.
	www.countrylifefarm.com /Training/terms.cfm (6922 words)

	AMERICA
		But this extreme problem of identity isn’t just a problem for China: it is a problem for the world.
		Since World War I, the story of the world is to come to America.
		The USSR tried to be a floodgate against the course of history, it tried to be a floodgate against the course of the world.
	america-is.com /bw_preview.html (713 words)

	Math Trek: Squaring Circles, Science News Online, Oct. 30, 2004
		Mathematicians who studied Tarski's circle problem strongly suspected there is no way to cut up a circle to make a square without losing even a single point out of the circle.
		General interest in the problem was so great and the number of proposed but erroneous proofs so voluminous that, in 1775, the Paris Academy found it necessary to pass a resolution stating that no more purported solutions to the circle-squaring problem would be examined.
		A circle and a square have equal areas only if the ratio of a square's side to a circle's radius equals the square root of pi.
	www.sciencenews.org /articles/20041030/mathtrek.asp (1156 words)

	520_midterm.html
		General comment: on many problems there are lots of right answers
		Criteria: If the procedure shows that he/she knows what is resolution refutation, he/she would receive at least 12 points; else if the procedure shows that he/she mixed resolution refutation with other techniques, he/she would receive at most 12 points; Otherwise, less than 5 points would be given.
		Yes: 1) concern only with leaf node; 2) efficiency due to lack of redundant paths (if view as state space there are many paths to each state)
	www.cs.rutgers.edu /~fzeng/520_midterm.html (458 words)

	Problem
		Correct output consists of a set of lines (one for each problem solution) where each line consists of: Black points> White points> newline.
		Each position consists of nine lines of nine characters: X for black stones, O for white stones and a ‘.’ (a dot) for empty intersections.
		There is no empty line separating each problem set.
	acm.uva.es /p/v8/852.html (413 words)

	Brachistochrone curve - Wikipedia, the free encyclopedia
		A Brachistochrone curve, or curve of fastest descent, is the curve between two points that is covered in the least time by a body that starts at the first point with zero speed and passes down along the curve to the second point, under the action of constant gravity and ignoring friction.
		Hence, the brachistochrone curve is simply the trajectory of a beam of light in a medium where the speed of light increases following a constant vertical acceleration (that of gravity g).
		Four of the solutions (excluding l'Hôpital's) were published in the May 1697 edition of the same publication.
	en.wikipedia.org /wiki/Brachistochrone_curve (623 words)

	JAKOB STEINER
		Steiner Chain, Steiner Construction, Steiner's Ellipse, Steiner's Hypocycloid (i.e., the Deltoid), Steiner-Lehmus Theorem, Steiner Points (in addition to the Steiner point already mentioned), Steiner's Porism, Steiner's Problem, Steiner Quadrulple System, Steiner's Segment Problem, Steiner Set, Steiner Surface, Steiner System, Steiner's Theorem, Steiner Triple System, and Poncelet-Steiner Porism.
		Steiner remained at the University of Berlin until his last years, which he spent in his native Switzerland.
		Among the well known objects in triangle geometry are the Steiner point and Steiner ellipse, named in honor of Jakob Steiner.
	faculty.evansville.edu /ck6/bstud/steiner.html (623 words)

	The Perceptual Binding Problem
		I think that the perceptual binding problem might be solved by looking for neurophysiological changes that correspond to the complexity of the object represented, from the perspective of the animal.
		The interpretation of this study as an instance of perceptual binding seems to have lost sight of the original problem, which is t o show how the activity of cells with different receptive fields are integrated when their prefered stimuli are presented simultaneously as features of the same object.
		Early attempts to solve the perceptual binding problem assumed that complex object-detecting neurons acted as conjunction detectors ("cardinal cells" or "grandmother neurons") that integrated convergent input from lower level cells representing eleme ntary features of the object.
	www.sahs.uth.tmc.edu /jafrederick/pbp.dir/pbp.html (2975 words)

	BBC - h2g2 - Lagrange Points
		Lagrange was one of the first people to study this problem, which is known as the 'three-body problem'.
		Lagrange discovered that there are five points called the Lagrange (or Lagrangian) points where the asteroid can share approximately the same orbit as the planet, with the same orbital period.
		Rumours of a supposed planet at the L3 point, where it would be invisible from the Earth, cannot be true, as the L3 point has a 'stability lifetime' of around 150 years.
	www.bbc.co.uk /dna/ww2/A947333 (2975 words)

	"The application of the boundary integral equation method to numerical solution of Dirichlet's problem in domains with corner points"
		"The application of the boundary integral equation method to numerical solution of Dirichlet's problem in domains with corner points"
		An approach for computing the normal derivative of the solution to the problem is discussed.
		In order to solve this problem numerically, we propose a method with exponential rate of convergence.
	www.srcc.msu.su /num-meth/english/zhurnal/tom_2000/art1_1.html (2975 words)

	Articles - Leonhard Euler
		In 1736 Euler solved, or rather proved insoluble, a problem known as the seven bridges of Königsberg, publishing a paper Solutio problematis ad geometriam situs pertinentis which was the earliest application of graph theory or topology.
		The solution to the seven bridges problem reduced the land masses to points and the bridges to lines (or edges) connecting those points.
		Leonhard Euler was born in Basel, Switzerland, the son of Paul Euler, a Lutheran minister.
	www.gaple.com /articles/Leonhard_Euler (1451 words)

	Solving Chess
		Number of participants 95 (84 with rating - average rating 2320), system of competition 1 round, 12 problems, maximum 55 points / 180 minutes.
		System of competition 2 rounds 12 problems, maximum 60 points/240 minutes.
		IGM Petko Petkov (BUL) compose all 130 fairy chess problems for this competition.
	www.geocities.com /solvingchess (589 words)

	hw5-GradingPolicy.txt
		[5 pts] [2.5 pts] correct explaination of the upward funarg problem.
		[2.5 pts] correct example of the upward funarg problem.
		We did not take off points if you had the wrong information in the return value column (but we did if you omitted the column).
	classes.engr.oregonstate.edu /eecs/fall2002/cs381/hw5-GradingPolicy.txt (140 words)

	PlanetMath: elliptic curve discrete logarithm problem
		The problem is computationally difficult unless the curve has a ``bad" number of points over the given field, where the term ``bad" encompasses various collections of numbers of points which make the elliptic curve discrete logarithm problem breakable.
		The elliptic curve discrete logarithm problem is the cornerstone of much of present-day elliptic curve cryptography.
		This is version 2 of elliptic curve discrete logarithm problem, born on 2003-07-17, modified 2004-02-18.
	planetmath.org /encyclopedia/EllipticCurveDiscreteLogarithmProblem.html (140 words)

	PlanetMath: elliptic curve discrete logarithm problem
		The problem is computationally difficult unless the curve has a ``bad'' number of points over the given field, where the term ``bad'' encompasses various collections of numbers of points which make the elliptic curve discrete logarithm problem breakable.
		The elliptic curve discrete logarithm problem is the cornerstone of much of present-day elliptic curve cryptography.
		This is version 4 of elliptic curve discrete logarithm problem, born on 2003-07-17, modified 2005-03-18.
	planetmath.org /encyclopedia/EllipticCurveDiscreteLogProblem.html (140 words)

	On the Exact Solution of the Euclidean Three-Matching Problem
		We consider the problem where the cost cijk of a triplet is the sum of the lengths of the two shortest edges of the triangle (i, j, k); the reason for this assumption is the nature of the practical problems.
		Three-Matching Problem (3MP) is an NP-complete graph problem which has applications in the field of inserting electronic components on a printed circuit board.
		We give two different integer formulations and several lower bounds of the problem based on the Lagrangian relaxations of the integer programs.
	www.inf.u-szeged.hu /kutatas/actacybernetica/vol14n2/cikk11.xml (140 words)

	[Tutor] Re: Tutor Digest, Vol 8, Issue 67
		> > Kent Hi Kent, Yeah, the problem with points snapping to different grid points occurred to me before I got too far, so I went with just iterating through the list of endpoints searching for near points (I specifically don't want to join any lines by their middles, which makes the task easier).
		There must be some way of sorting the list of points so I don't have to iterate through the entire thing.
		This search is very slow, which is only a bit of a problem, since I don't need to run this script many times once it's working.
	mail.python.org /pipermail/tutor/2004-October/032676.html (347 words)

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In the News (Fri 1 Jan 10)