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Topic: Chebyshev distance

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	Chebyshev Distance
		Chebyshev distance is also called Maximum value distance.
		The Chebyshev Distance between point A and B is
		Chebyshev distance is a special case of Minkowski distance with
	people.revoledu.com /kardi/tutorial/Similarity/ChebyshevDistance.html (70 words)

	Distance geometry Encyclopedia (Site not responding. Last check: )
		Distance geometry is the characterization and study of sets of points based only on given values of the distances between member pairs.
		Therefore distance geometry has immediate relevance where distance values are determined or considered, such as in surveying, cartography and physics.
		Therefore the distance from A to B is no bigger than the length of the straight-line path from A to C plus the length of the straight-line path from C to B.
	www.hallencyclopedia.com /topic/Distance_geometry.html (502 words)

	Pafnuty Chebyshev - Encyclopedia, History, Geography and Biography
		Chebyshev is known for his work in the field of probability, statistics and number theory.
		Chebyshev's inequality is used to prove the weak law of large numbers.
		Chebyshev is considered one of the founding fathers of Russian mathematics.
	www.arikah.net /encyclopedia/Pafnuty_Chebyshev (1004 words)

	Pafnuty Chebyshev - Biocrawler (Site not responding. Last check: )
		He was born in western Russian city Okatovo, in the family of Agrafena Ivanova Pozniakova and Lev Pavlovich Chebyshev with 9 children.
		Chebyshev's inequality says that the probability that the outcome of a random variable is no less than a standard deviations away from its mean is no more than 1/a
		Chebyshev's inequality is used to prove the weak law of large numbers and the Bertrand-Chebyshev theorem (1845
	www.biocrawler.com /encyclopedia/Chebyshev (263 words)

	Chebyshev
		In 1841 Chebyshev was awarded the silver medal for his work "calculation of the roots of equations" which had already been finished in 1838.
		In Russia a famine broke out, Chebyshev's parents were forced to leave the city and were not able to support their son anymore.
		In 1847, Chebyshev defended his dissertation pro venia legendi "About integration with the help of logarithms" at St Petersburg University and thus obtained the right to teach there as a lecturer.
	www.brainyencyclopedia.com /encyclopedia/c/ch/chebyshev.html (1071 words)

	long distance calling card
		A TACAN system is still used today, callint card distance long unlimited even though it is only one card e), long distance calling card the pot with another player, calling canada card distance long that may be dealt face up on the 180 degree mark.
		Other distances, based on lengths of human body parts, calling card discount distance long the distance between two distant objects, one imagines that one can generate two triangles with two distinct types of stars in them.
		Contrast this to a discrepancy of around 38 microseconds per day, calling card distance free long when observed from the 5 are in pliance, whereas in District 3, in northcentral California in the convention center at the poles, and having an of 6372.795 km.
	long-distance-calling-card.onlineus.info (946 words)

	Distance Summary
		One might attempt to define the distance between two non-empty subsets of a given set as the infimum of the distances between any two of their respective points, which would agree with the every-day use of the word.
		Distance is a scalar quantity, containing only a magnitude, whereas displacement is an equivalent vector quantity containing both magnitude and direction.
		The distance covered by a vehicle (often recorded by an odometer), person, animal, object, etc. should be distinguished from the distance from starting point to end point, even if latter is taken to mean e.g.
	www.bookrags.com /Distance (3719 words)

	NationMaster - Encyclopedia: Pafnuty Chebyshev
		In this contribution Chebyshev derived an approximating algorithm for the solution of algebraic equations of nth degree based on Newton's algorithm.
		In a plane, the Chebyshev distance between the point P1 with coordinates (x1, y1) and the point P2 at (x2, y2) is This concept is named after Pafnuty Chebyshev.
		Pafnuty Lvovich Chebyshev (Пафнутий Львович Чебышёв) (1821-1894) was a Russian mathematician.
	www.nationmaster.com /encyclopedia/Pafnuty-Chebyshev (2859 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: )
		One might attempt to define the distance between two non-empty subsets of a given set as the infimum of the distances between any two of their respective points, which would agree with the every-day use of the word.
		Distance is a scalar quantity, containing only a magnitude, whereas displacement is an equivalent vector quantity containing both magnitude and direction.
		The distance covered by a vehicle (often recorded by an odometer), person, animal, object, etc. should be distinguished from the distance from starting point to end point, even if latter is taken to mean e.g.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=distance (778 words)

	[No title]
		The Chebyshev expansions of a scaled arctangent are neater, namely: Given k>0, define q = k / (1 + (1 + k^2)^(1/2)), and then arctan(kx) = 2 sum(n=0 to inf.) ((-1)^n * q^(2n+1)/(2n+1)) * T_(2*n+1)(x) In particular, for k=1 and x=1, the series converges (note q=1/(1+sqrt(2))) but the effect is not very spectacular.
		This means that when we use m+1 terms of a Chebyshev expansion of a function f on [-1,1], and then drop the (m+1)st term c_(m+1)*T_(m+1)(x) then we commit an extra (uniformly bounded) error of size exactly abs(c_(m+1)).
		Chebyshev expansions (and other expansions into polynomials satisfying recursive relations) can be evaluated using a "Clenshaw scheme" (see reference).
	www.math.niu.edu /~rusin/known-math/98/cheby.poly (680 words)

	News \| Gainesville.com \| The Gainesville Sun \| Gainesville, Fla. (Site not responding. Last check: )
		In mathematics, the Chebyshev distance (or Tchebychev distance) between two points in a vector space is the greatest of their differences along any coordinate dimension.
		The two dimensional Manhattan distance also has circles in the form of squares, with side length √2r, at an angle of π/4 to the coordinate axes, so the planar Chebyshev distance can be viewed as equivalent by rotation and scaling to the planar Manhattan distance.
		In chess, the distance between squares, in terms of moves necessary for a king, is given by the Chebyshev distance, hence the second name.
	www.gainesville.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Chebyshev_distance (222 words)

	Properties of distributions
		This can be viewed in two equivalent ways: multiplying by 3 stretches all values; it triples the distance between 1/2 and 0, as shown by the arrow at the left pointing from 1/2 to 3/2.
		Chebyshev's theorem is properly a statement about moments of a distribution, so this is the right place to discuss it.
		Chebyshev's inequality is rather crude: in the figure you can see the gray area is much greater than the green area.
	www.quantdec.com /envstats/notes/class_06/properties.htm (2780 words)

	[No title] (Site not responding. Last check: )
		It has the property that distances along any line-of-sight will be accurate within a factor of 2/sqrt(2), and distances along the same line of sight will compare accurately.
		Where the manhattan distance is accurate within 2/sqrt(2), the Chebyshev distance is accurate within sqrt(2)/2.
		Typically you want to use the manhattan distance when it's important not to underestimate and the Chebyshev distance when it's important not to overestimate.
	library.simugraph.com /relview/docs/rpg/levelgeneration/distance_calculation.txt (486 words)

	Speech recognition apparatus (Site not responding. Last check: )
		Matching distances between frames in these input spectrum patterns and spectrum registration patterns are evaluated, so that the feature parameter stored in the registration pattern storing means which is to be a minimum matching distance is provided as a recognition result.
		The distance calculating portion 51 functionally comprises a constant comparison frequency memory 511, a primary interpolation circuit 512 and a parameter temporary storage memory 513 in the input pattern side, a primary interpolation circuit 514 and a parameter temporary storage memory 515 in the registration pattern side and a Chebyshev distance calculation circuit 516.
		When performing pattern matching, a phoneme distance d(i, j) of a spectrum pattern between a frame i on the input pattern and a frame j on the template pattern is required.
	www.stickebana.com /scitech/thermal-optical_recording_head/speech_recognition.html (6724 words)

	variation
		When the data is not bell shaped then we have to use Chebyshev's Theorem to determine how many values fall within k standard deviations of the mean.
		Chebyshev's Theorem says the proportion of any set of data lying within k standard deviations of the mean is always
		Using IQ scores with a mean of 100 and a standard deviation of 15, Chebyshev's Theorem tells us that at least 75% of IQ scores will fall between 70 and 130, and at least 89% of IQ scores will fall between 55 and 145.
	www.ndsu.nodak.edu /instruct/degges/stat330/variation.html (467 words)

	Chebyshev distance - Biocrawler (Site not responding. Last check: )
		In a plane, the Chebyshev distance between the point P
		In chess, the distance between squares for kings and queens is measured in Chebyshev distance.
		Except that they can only reach half the squares on a chessboard, bishops also measure distance Chebyshev-style.
	www.biocrawler.com /encyclopedia/Chebyshev_distance (68 words)

	Batching strategies
		The distance between the depot and the first location of the most left aisle is 2 meter.
		The order addition rules, which select a candidate order when the sum of the distances between every item of the seed order and the nearest item in the candidate order are minimized, are using a metric to determine the distance between two locations.
		Alternative metrics are the Euclidian metric, the Rectilineair metric, the Chebyshev metric and the metric based on the distance between the aisles where the item locations are.
	www.fbk.eur.nl /OZ/LOGISTICA/batch.html (1769 words)

	Distance: Encyclopedia II - Distance - Formal definition
		A distance between two points P and Q in a metric space is d(P,Q), where d is the distance function that defines the given metric space.
		Alternatively, the distance between sets may indicate "how different they are", by taking the supremum over one set of the distance from a point in that set to the other set, and conversely, and taking the larger of the two values (Hausdorff distance).
		The (Euclidean) distance, d, between two points expressed in Cartesian coordinates equals the square root of the sum of the squares of the changes of each coordinate.
	www.experiencefestival.com /a/Formal_definition/id/1288893 (591 words)

	Distance Tutorial
		Once the ranks are normalized, the distance can be computed as quantitative variables.
		To deal with pure rank data, you may use other distance such as Spearman Distance, Kendall Distance, Cayley Distance, and Hamming Distance for ordinal variables, Ulam Distance, and Chebyshev /Maximum Distance for ordinal variable.
		The Euclidean distance between park A and park B is
	people.revoledu.com /kardi/tutorial/Similarity/Normalized-Rank.html (307 words)

	Tapered anechoic chamber - Patent 6437748
		Using this Chebyshev layout around the test zone, the test zone fields will be very clean of stray signals and the polarization will be dictated by the feed horn.
		The front wall is positioned parallel to, and separated a distance from the back wall, and is of a smaller dimension than the back wall.
		The planar front wall is positioned parallel to and separated a distance from the back wall, the front wall having a dimension smaller than the back wall.
	www.freepatentsonline.com /6437748.html (4770 words)

	direction distance travel - (Site not responding. Last check: )
		At distances of 1,500 miles or more, only 15 percent of trips...
		distance personal vehicle trips use a different mode in the opposite travel direction.
		Longer distance travel can be arranged, but may involve using another mode of...
	www.israeltravel.info /travel/direction-distance-travel (168 words)

	Genome Biology \| Full text \| Detection of evolutionarily stable fragments of cellular pathways by hierarchical ... (Site not responding. Last check: )
		Species themselves can be seen as vectors in the COG space, and distances between such vectors can be used to build the species' phylogeny [26]; this aspect is not considered in the current work, except for illustrative purposes (Figure 2, tree at the top).
		Apparently, however, correlation distance is more accurate in assigning to genes to metabolic pathways as defined in the COG database than to larger KEGG charts (Figure 3a and G.V.G. and A.R.M., unpublished data).
		It has been noted that a high 'co-occurrence score' (essentially, the distance between phyletic patterns based on the complement of mutual information) is less indicative of a functional link than chromosomal proximity of genes or translational fusion of domains [28].
	genomebiology.com /2004/5/5/R32 (6724 words)

	numapprox.html
		The Chebyshev series expansion of f(x) on [0,4] is as follows, where we specify that we want accuracy 1E-8 which means that all terms with coefficients smaller than this magnitude will be dropped.
		If the Chebyshev series was truncated at degree 8, to yield a polynomial with the same degree as the Taylor polynomial approximation considered above, we would find that the maximium error in the Chebyshev series approximation of degree 8 is approximately 0.6E-5.
		The (m,n) Chebyshev-Pade approximation for f(x) is a rational function r[m,n](x) with numerator of degree m and denominator of degree n such that the Chebyshev series expansion of r[m,n](x) agrees with the Chebyshev series expansion of f(x) through the term of degree m+n.
	www.adeptscience.co.uk /maplearticles/f231.html (1514 words)

	Taxicab geometry - Definition, explanation
		Taxicab geometry, considered by Hermann Minkowski in the 19th century, is a form of geometry in which the usual metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the (absolute) differences of their coordinates.
		It is named so because it is the distance a car would drive in a city laid out in square blocks, like Manhattan (discounting the facts that in Manhattan there are one-way and oblique streets and that real streets only exist at the edges of blocks - there is no 3.14th Avenue).
		In chess, the distance between squares for rookss is measured in Manhattan distance; kingss, queenss, and bishopss use Chebyshev distance.
	www.calsky.com /lexikon/en/txt/t/ta/taxicab_geometry.php (255 words)

	The Bell-shaped, Normal, Gaussian Distribution
		The height of the curve represents the probability of the measurement at that given distance away from the mean.
		Chebyshev (1821–1894) was a preeminent Russian mathematician who primarily worked on the theory of prime numbers, although his writings covered a wide range of subjects.
		The general concept of being able to find the mean of a data set and determine how much of it is within a certain distance (number of standard deviations) of the mean is an important one which we will continue in the next lesson.
	www.andrews.edu /~calkins/math/webtexts/stat06.htm (1287 words)

	The Dispatch - Serving the Lexington, NC - News (Site not responding. Last check: )
		It is a consequence of Chebyshev inequalities for the number
		A more precise form is given by the celebrated prime number theorem: the quotient of the two expressions approaches 1 as
		Among his students were Dmitry Grave, Aleksandr Korkin, Aleksandr Lyapunov and Andrei Markov, themselves well known and prolific mathematicians.
	www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Pafnuty_Chebyshev (1014 words)

	CLUSTER_TREE
		The distance between two clusters is defined as the average distance for all pairs of objects between each cluster, weighted by the number of objects in each cluster.
		The distance between two clusters is defined as the distance between the centroids of each cluster.
		If the LINKAGE keyword is equal to 3, the distance between two clusters may be less than the distance between items within one of the clusters.
	www.physics.nyu.edu /grierlab/idl_html_help/C24.html (673 words)

	CLUSTER_TREE
		The distance between two clusters is defined as the average distance for all pairs of objects between each cluster, weighted by the number of objects in each cluster.
		The distance between two clusters is defined as the distance between the centroids of each cluster.
		If the LINKAGE keyword is equal to 3, the distance between two clusters may be less than the distance between items within one of the clusters.
	physics.nyu.edu /grierlab/idl_html_help/C24.html (673 words)

	[No title]
		The scoring function is expanded using the Chebyshev polynomials, for which the coefficients are determined by minimizing the Z-score of native structures in the ensembles of alternate conformations.
		Since the Chebyshev representation is most naturally applied to functions defined on the interval [-1, 1], we transform the functional dependence of E on n as follows: n - 10 E[sub]i[/sub] = E[sub]a[/sub] (------).
		In fact, the Chebyshev approximating polynomial is very nearly the same as the minimax polynomial.
	www.research.ibm.com /journal/rd/453/fain.txt (4030 words)

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