High Quality Content by WIKIPEDIA articles! In geometry, the Cesaro equation of a plane curve is an equation relating curvature (?) to arc length (s). It may also be given as an equation relating the radius of curvature (R) to arc length. (These are equivalent because R = 1 / ?.) Two congruent curves will have the same Cesaro equation. It is named for Ernesto Cesaro. Determining the length of an irregular arc segment—also called rectification of a curve—was historically difficult. Although many methods were used for specific curves, the advent of calculus led to a general formula that provides closed-form solutions in some cases. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1312-2385-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Ceva's theorem is a well-known theorem in elementary geometry.The theorem can be generalized to higher dimensional simplexes using barycentric coordinates. Define a cevian of an n-simplex as a ray from each vertex to a point on the opposite (n-1)-face (facet). Then the cevians are concurrent if and only if a mass distribution can be assigned to the vertices such that each cevian intersects the opposite facet at its center of mass. Moreover, the intersection point of the cevians is the center of mass of the simplex. (Landy. See Wernicke for an earlier result.) Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1312-9493-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, chain complex and cochain complex are constructs originally used in the field of algebraic topology. They are algebraic means of representing the relationships between the cycles and boundaries in various dimensions of some "space". Here the "space" could be a topological space or an algebraic construction such as a simplicial complex. More generally, homological algebra includes the study of chain complexes in the abstract, without any reference to an underlying space. In this case, chain complexes are studied axiomatically as algebraic structures. Applications of chain complexes usually define and apply their homology groups (cohomology groups for cochain complexes); in more...

ISBN: 978-6-1312-4735-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A chain of events is a number of actions and their effects that are contiguous and linked together.A chain reaction is a chain of events where one or more events in the chain causes additional reaction in an earlier stage of the chain. It results in a self-amplification of the chain of events.Determinism is the philosophical proposition that every event, including human cognition and behaviour, decision and action, is causally determined by an unbroken chain of events. With numerous historical debates, many varieties and philosophical positions on the subject of determinism exist from traditions throughout the world. Данное издание не является оригинальным....

ISBN: 978-6-1311-7463-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In computational geometry, Chan's algorithm, named after Timothy M. Chan, is an optimal output-sensitive algorithm to compute the convex hull of a set P of n points, in 2 or 3 dimensional space. The algorithm takes O(n log h) time, where h is the number of vertices of the output (the convex hull). In the planar case, the algorithm combines an O(n log n) algorithm (Graham scan, for example) with Jarvis march, in order to obtain an optimal O(n log h) time. Chan's algorithm is notable because it is much simpler than the ultimate planar convex hull algorithm, and it naturally extends to 3-dimensional space. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1312-1539-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The mathematical concept of a characteristic set was discovered in the late forties by J.F. Ritt. Besides Grobner basis method, it provides an alternative algorithmic way for solving multivariate polynomial equations or differential equations. In the late seventies, the Chinese mathematician Wen-Tsun Wu specialized it with modifications to commutative algebra. He demonstrated its power for mechanical theorem proving.For an ideal I in the ring k[x1,...,xn] over a field k, a (Ritt) characteristic set C of I is composed of a set of polynomials in I, which is in triangular shape: polynomials in C have distinct main variables. (See the formal definition below.) Given a characteristic set C of I, one...

ISBN: 978-6-1311-9273-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, Chebyshev distance (or Tchebychev distance), Maximum metric, or L? metric is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. It is named after Pafnuty Chebyshev. It is also known as chessboard distance, since in the game of chess the minimum number of moves needed by a king to go from one square on a chessboard to another equals the Chebyshev distance between the centers of the squares, if the squares have side length one, as represented in 2-D spatial coordinates with axes aligned to the edges of the board. Данное издание не является оригинальным....

ISBN: 978-6-1312-7170-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Chebyshev center of a bounded set Q having non-empty interior is the center of the minimal radius ball enclosing the entire set Q.Estimation theory is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured/empirical data. The parameters describe an underlying physical setting in such a way that the value of the parameters affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1311-5903-9
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Chern–Weil homomorphism is a basic construction in the Chern–Weil theory, relating for a smooth manifold M the curvature of M to the de Rham cohomology groups of M, i.e., geometry to topology. This theory of Shiing-Shen Chern and Andre Weil from the 1940s was an important step in the theory of characteristic classes. It is a generalization of the Chern–Gauss–Bonnet theorem. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1312-3567-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, Chern–Weil theory computes topological invariants of vector bundles and principal bundles in terms of connections and curvature. That is, the theory forms a bridge between the areas of algebraic topology and differential geometry. It was developed in the late 1940s by Shiing-Shen Chern and Andre Weil, in the wake of proofs of the generalized Gauss–Bonnet theorem. See Chern–Weil homomorphism for more detail. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1312-3556-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the Chern–Simons forms are certain secondary characteristic classes. They have been found to be of interest in gauge theory, and they (especially the 3-form) define the action of Chern–Simons theory. The theory is named for Shiing-Shen Chern and James Harris Simons, co-authors of a 1974 paper entitled "Characteristic Forms and Geometric Invariants," from which the theory arose. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1312-3554-2
Издательство: Книга по требованию
Дата выхода: июль 2011

This book covers the CherryPy library for Python web development from its history and installation through its main features and core concepts to its integration with Python and other products to construct, test, and deploy a sample photoblog application. The author Sylvain Hellegouarch is dedicated to the development of free software projects and has been coordinating and administrating the community efforts around the CherryPy project since 2004. The approach based on an example application introduces many other common Python libraries, providing transferable skills also relevant for non-web Python projects. CherryPy is a Python library for web development that allows developers to build web applications in the same way as any other...

ISBN: 9781904811848
Издательство: Packt Publishing
Дата выхода: январь 2007

High Quality Content by WIKIPEDIA articles! The chicken or the egg causality dilemma is commonly stated as "which came first, the chicken or the egg?" To ancient philosophers, the question about the first chicken or egg also evoked the questions of how life and the universe in general began. Cultural references to the chicken and egg intend to point out the futility of identifying the first case of a circular cause and consequence. It could be considered that in this approach lies the most fundamental nature of the question. A literal answer is somewhat obvious, as opposed to the logical fallacy of the metaphorical view, which sets a metaphysical ground on the dilemma. So, to understand its metaphorical meaning better, it could be...

ISBN: 978-6-1311-7473-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a polytope P is chiral if it has two orbits of flags under its group of symmetries, with adjacent flags in different orbits.In mathematics, an abstract polytope, informally speaking, is a structure which considers only the combinatorial properties of a traditional polytope, ignoring many of its other properties, such as angles, edge lengths, etc.. No concept of space, such as Euclidean space, is required to contain it. The term polytope is a generalisation of polygons and polyhedra into any number of dimensions.A formal definition of an abstract polytope is given below. In fact, this definition is more general than the traditional concept of a polytope, and allows many new...

ISBN: 978-6-1311-5910-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A chord of a curve is a geometric line segment whose endpoints both lie on the curve. A secant or a secant line is the line extension of a chord. In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment is either an edge (of that polygon) if they are adjacent vertices, or otherwise a diagonal. When the end points both lie on a curve such as a circle, a line segment is called a chord (of that curve). Данное издание не является...

ISBN: 978-6-1312-2393-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, and more particularly in the field of algebraic geometry, Chow coordinates are a generalization of Plucker coordinates, applying to m-dimensional algebraic varieties of degree d in Pn, that is, n-dimensional projective space. They are named for W. L. Chow. A Chow variety is a variety whose points correspond to all cycles of a given projective space of given dimension and degree. To define the Chow coordinates, take the intersection of an algebraic variety Z of degree d and dimension m by linear subspaces U of codimension m. When U is in general position, the intersection will be a finite set of d distinct points. Данное издание не является...

ISBN: 978-6-1311-9282-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a Cohen–Macaulay ring is a particular type of commutative ring, possessing some of the algebraic-geometric properties of a nonsingular variety, such as local equidimensionality. They are named for Francis Sowerby Macaulay, who proved the unmixedness theorem for polynomial rings in Macaulay (1916), and for Irvin S. Cohen, who proved the unmixedness theorem for formal power series rings in Cohen (1946). (All Cohen–Macaulay rings have the unmixedness property.) Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1311-9289-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Chu spaces generalize the notion of topological space by dropping the requirements that the set of open sets be closed under union and finite intersection, that the open sets be extensional, and that the membership predicate (of points in open sets) be two-valued. The definition of continuous function remains unchanged other than having to be worded carefully to continue to make sense after these generalizations.Understood statically, a Chu space (A, r, X) over a set K consists of a set A of points, a set X of states, and a function r : A x X ? K. This makes it an A x X matrix with entries drawn from K, or equivalently a K-valued binary relation between A and X (ordinary binary relations being...

ISBN: 978-6-1311-7493-3
Издательство: Книга по требованию
Дата выхода: июль 2011

ISBN: 9781849519564
Издательство: Packt Publishing

High Quality Content by WIKIPEDIA articles! The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane whose interiors are disjoint. A circle packing is a connected collection of circles (in general, on any Riemann surface) whose interiors are disjoint. The intersection graph (sometimes called the tangency graph or contact graph) of a circle packing is the graph having a vertex for each circle, and an edge for every pair of circles that are tangent. If the circle packing is on the plane, or, equivalently, on the sphere, then its intersection graph is called a coin graph. Coin graphs are always connected, simple, and planar. Данное...

ISBN: 978-6-1311-5930-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In geometry, the circle of antisimilitude (also known as mid-circle) of two circles ? and ? is a circle for which ? and ? are inverses of each other. If ? and ? are non-intersecting or tangent, there exists one circle of antisimilitude; if ? and ? intersect at two points, there exist two circles of antisimilitude. When ? and ? are congruent, the circle of antisimilitude is degenerate; it becomes a line of symmetry, in which ? and ? are reflections of each other. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1312-6952-3
Издательство: Книга по требованию
Дата выхода: июль 2011

ISBN: 9781849694407
Издательство: Packt Publishing

High Quality Content by WIKIPEDIA articles! In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation F(x, y) = 0, where F is a polynomial with real coefficients and the highest-order terms of F form a polynomial divisible by x2 + y2. More precisely, if F = Fn + Fn?1 + ... + F1 + F0, where each Fi is homogeneous of degree i, then the curve F(x, y) = 0 is circular if and only if Fn is divisible by x2 + y2. Equivalently, if the curve is determined in homogeneous coordinates by G(x, y, z) = 0, where G is a homogeneous polynomial, then the curve is circular if and only if G(1, i,0) = G(1, ?i,0) = 0. In other words, the curve is circular if it contains the circular points at infinity, (1, i ,0) and...

ISBN: 978-6-1312-1078-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon. The center of this circle is called the circumcenter. A polygon which has a circumscribed circle is called a cyclic polygon. All regular simple polygons, all triangles and all rectangles are cyclic. A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it. Not every polygon has a circumscribed circle, as the vertices of a polygon do not need to all lie on a circle, but every polygon has unique minimum bounding circle, which may be constructed by a linear time algorithm. Данное...

ISBN: 978-6-1312-8751-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In geometry, a cissoid is a curve generated from two given curves C1, C2 and a point O (the pole). Let L be a variable line passing rough O and intersecting C1 at P1 and C2 at P2. Let P be the point on L so that OP = P1P2. (There are actually two such points but P is chosen so that P is in the same direction from O as P2 is from P1.) Then the locus of such points P is defined to be the cissoid of the curves C1, C2 relative to O. Slightly different but essentially equivalent definitions are used by different authors. For example, P may be defined to be the point so that OP = OP1 + OP2. This is equivalent to the other definition if C1 is replaced by its reflection through O. Or P may be defined...

ISBN: 978-6-1312-2466-9
Издательство: Книга по требованию
Дата выхода: июль 2011