Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which are easily defined recursively, like Fibonacci or Lucas numbers. One usually distinguishes between Chebyshev polynomials of the first kind which are denoted Tn and Chebyshev polynomials of the second kind which are denoted Un. The letter T is used because of the alternative transliterations of the name Chebyshev as Tchebycheff (French) or Tschebyscheff (German). The Chebyshev polynomials Tn or Un are polynomials of degree n and the sequence of...

ISBN: 978-6-1318-6357-8
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High Quality Content by WIKIPEDIA articles! A chemical equation consists of the chemical formulas of the substances that are mixed (called the reactants), and the chemical formula of the substances that result from the chemical reaction (called the products). The two are separated by an -> —usually read as "yields"— and each chemical formula is separated from others by a plus sign. Sometimes a triangle is drawn over the arrow symbol to denote energy must be added to the substances for the reaction to begin. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1311-4385-4
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Chern classes are characteristic classes. They are topological invariants associated to vector bundles on a smooth manifold. If you describe the same vector bundle on a manifold in two different ways, the Chern classes will be the same. When are two ostensibly different vector bundles the same? When are they different? These questions can be quite hard to answer. But the Chern classes provide a simple test: if the Chern classes of a pair of vector bundles do not agree, then the vector bundles are different.In topology, differential geometry, and algebraic geometry, it is often important to count how many linearly independent sections a vector bundle has. The Chern classes offer some information about this through, for instance, the...

ISBN: 978-6-1306-4676-9
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High Quality Content by WIKIPEDIA articles! A chi- square test is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-square distribution when the null hypothesis is true, or any in which this is asymptotically true, meaning that the sampling distribution (if the null hypothesis is true) can be made to approximate a chi-square distribution as closely as desired by making the sample size large enough. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1327-1949-2
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High Quality Content by WIKIPEDIA articles! Les chiffres dits arabes sont les dix chiffres (1, 2, 3, 4, 5, 6, 7, 8, 9, 0) et le systeme d'ecriture decimale positionnelle qui les accompagne. Ils ont ete inventes en Inde, puis empruntes par la civilisation arabo-musulmane a partir du IXe siecle et decrits dans un ouvrage d'Al-Khawarizmi, puis peu a peu transmis a l'Occident medieval ou ils ont mis plusieurs siecles a s'imposer. Les chiffres arabes ont progressivement remplace les chiffres romains et se sont graduellement imposes dans le monde entier parce qu’ils permettent une notation tres aisee dans le systeme decimal utilise en Occident et facilitent les operations simples sur les grands nombres et les operations complexes....

ISBN: 978-6-1317-8707-2
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High Quality Content by WIKIPEDIA articles! La chimie theorique est l'etude de la chimie a travers un raisonnement theorique fondamental (habituellement a l'aide des mathematiques et de la physique). En particulier, l'application de la mecanique quantique a la chimie a donne naissance a la chimie quantique. Depuis la fin de la seconde guerre mondiale, le progres des ordinateurs a permis le developpement de la chimie numerique (ou computationnelle). Chimie quantique. Application de la mecanique quantique a la chimie. Chimie numerique. Application de codes informatiques a la chimie. Modelisation moleculaire. Application de methodes pour modeliser les structures des molecules sans utiliser necessairement la mecanique quantique. Par exemple,...

ISBN: 978-6-1339-8349-6
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Chinese numerals are characters for writing numbers in Chinese. Today, speakers of Chinese use three numeral systems: the ubiquitous system of Arabic numerals, along with two ancient Chinese numeral systems.One such system is the Suzhou numerals or huama system. It has gradually been supplanted by the Arabic system in writing numbers. It is the only surviving variation of the rod numeral system; this system has been popular only in Chinese markets, such as those in Hong Kong before the 1990s.The other Chinese numeral system is the written numbers system. It is still in use when writing numbers in long form, such as on cheques to hinder forgery. This character system is roughly analogous to spelling out a number in English text. The...

ISBN: 978-6-1302-0788-5
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Дата выхода: июль 2011

Mathematics in China emerged independently by the 11th century BC.The Chinese independently developed very large and negative numbers, decimals, a decimal system, a binary system, algebra, geometry, trigonometry.Many believe that Chinese mathematics and the mathematics of the ancient Mediterranean world had developed more or less independently up to the time when the The Nine Chapters on the Mathematical Art reached its final form, while the Writings on Reckoning and Huainanzi preceded it. It is often suggested that some Chinese mathematical discoveries predate their Western counterparts. One example is the Pythagorean theorem. There is some controversy regarding this issue and the precise nature of this knowledge in early China. The...

ISBN: 978-6-1307-0109-3
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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In the mathematical area of graph theory, a graph is chordal if each of its cycles of four or more nodes has a chord, which is an edge joining two nodes that are not adjacent in the cycle. An equivalent definition is that any chordless cycles have at most three nodes. Chordal graphs are a subset of the perfect graphs. They are sometimes also called triangulated graphs. A perfect elimination ordering in a graph is an ordering of the vertices of the graph such that, for each vertex v, v and the neighbors of v that occur later than v in the order form a clique. A graph is chordal if and only if it has a perfect elimination ordering (Fulkerson...

ISBN: 978-6-1304-2189-2
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High Quality Content by WIKIPEDIA articles! Christian Huygens, ou Christian Huyghens, tel qu'il est connu dans les lettres francaises depuis le Grand Siecle, (en neerlandais Christianus Huygens, en latin Christianus Hugenius, en neerlandais moderne Christiaan Huygens) (14 avril 1629, La Haye — 8 juillet 1695 dans la meme ville) est un mathematicien, un astronome et un physicien neerlandais. Il est le fils de Constantin Huygens. Huygens est generalement credite pour son role fondamental dans le developpement du calcul moderne, en particulier pour avoir developpe les techniques de sommation et d'integration necessaires a la decouverte de l'isochronisme de la cycloide. Il s'est oppose a Leibniz, a la fin de sa vie, dans la mesure ou il...

ISBN: 978-6-1326-3932-5
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High Quality Content by WIKIPEDIA articles! En mathematiques, une integrale de surface est une integrale definie sur toute une surface qui peut etre courbe dans l'espace. Pour une surface donnee, on peut integrer sur un champ scalaire ou sur un champ vectoriel. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа. High Quality Content by WIKIPEDIA articles! Christian Mission Service (CMS) is the English name of the Christlicher Missionsdienst (CMD), a non- denominational protestant child-care charitable organisation. The CMD was founded in Germany in 1957 by Emil Richter after he...

ISBN: 978-6-1341-8798-5
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For a century, one of the most famous problems in mathematics was to prove the Four-colour theorem. In a paper Birkhof proposed a way of tackling the four-colour problem by introducing a function P(M,?), to be the number of proper colourings of a map M. It turns out that P(M,?) is a polynomial in ?, called the chromatic polynomial of M. In 1968, Read asked: What is the necessary and sufficient condition for two graphs to be chromatically equivalent; i.e. to have same chromatic polynomial? A graphs is said to be unique if no other graphs share its chromatic polynomial. The question of chromatic equivalence and uniqueness is termed the chromaticity of graphs. In chapter 5 we will prove that the Jahangir graph is chromatically unique for p...

ISBN: 978-3-6392-5612-3
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! William Smith Monroe (September 13, 1911–September 9, 1996) was an American musician who helped develop the style of music known as bluegrass, which takes its name from his band, the "Blue Grass Boys," named for Monroe's home state of Kentucky. Monroe's performing career spanned 60 years as a singer, instrumentalist, composer and bandleader. He is often referred to as The Father of Bluegrass. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа. In computability theory the Church–Turing thesis (also known as the Church-Turing conjecture,...

ISBN: 978-6-1307-6516-3
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High Quality Content by WIKIPEDIA articles! In mathematics, a circle map is a member of a family of dynamical systems on the circle first defined by Andrey Kolmogorov. Kolmogorov proposed this family as a simplified model for driven mechanical rotors specifically, a free-spinning wheel weakly coupled by a spring to a motor. The circle map equations also describe a simplified model of the phase-locked loop in electronics. The circle map exhibits certain regions of its parameters where it is locked to the driving frequency phase-locking or mode-locking in the language of electronic circuits, these are referred to as Arnold tongues, after Vladimir Arnold. Among other applications, the circle map has been used to study the dynamical...

ISBN: 978-6-1316-0630-4
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High Quality Content by WIKIPEDIA articles! The circumference is the distance around a closed curve. Circumference is a special perimeter.The circumference of an ellipse is more problematic, as the exact solution requires finding the complete elliptic integral of the second kind. This can be achieved either via numerical integration (the best type being Gaussian quadrature) or by one of many binomial series expansions.In graph theory the circumference of a graph refers to the longest cycle contained in that graph. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1311-5938-1
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ISBN: 978-3-8383-0325-3
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Дата выхода: июль 2011

Over the last decade, statistical learning theory has achieved rapid progress due to the introduction and research of classification algorithms including support vector machines and boosting. Along with their successful applications in practice, theoretical performance of these algorithms becomes well understood in terms of margin bounds, Bayes risk consistency, and asymptotic rate analysis. This monograph provides further investigation of these algorithms within regularization frameworks and from an approximation theory point of view. Error analysis frameworks by error decomposition techniques are fully developed for two classes of regularization schemes which cover the support vector machines, regularized boosting, and support vector...

ISBN: 978-3-6391-9835-5
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Дата выхода: июль 2011

The field of Differential Geometry is one of the most important and beautiful parts of modern Mathematics. It has inspired a lot of studies and is a theoretical support for a lot of applications. Structures can be easy defined now on manifolds and also sub-structures may be observed and described. The present book has the intention to present a small part of this universe, lighting up several particular properties of submanifolds of manifolds with geometric structures. Starting from different types of ambient manifolds, the author includes here several results obtained for CR-submanifolds, QR-submanifolds and other particular submanifolds. A special attention is given to the substructures in contact metric manifolds with some nullity...

ISBN: 978-3-6391-4417-8
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Дата выхода: июль 2011

This book considers the development, based solely on reading research, of the recent amendment of U.S. law for funding the remediation of learning disabilities. The issue is whether, given recent research into the classification, prediction, and prevention of mathematics learning disabilities, these reading-based amendments of the learning disability identification procedures are equally appropriate for math disabilities. Given the findings of current mathematics disability research, the book suggests otherwise. Unlike learning to read, which involves practicing just one skill set (the matching of phonemes to graphemes), mathematics learning is cumulative, requiring multiple skill sets and continuing instruction. However, little is yet...

ISBN: 978-3-8383-2523-1
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Дата выхода: июль 2011

ISBN: 978-3-8383-3758-6
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ISBN: 978-3-8383-0278-2
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Дата выхода: июль 2011

Continuous functions are of utmost importance in mathematics and applications. However, not all functions are continuous. If a function is not continuous at a point in its domain, one says that it has a discontinuity there. The set of all points of discontinuity of a function may be a discrete set, a dense set, or even the entire domain of the function. This article describes the classification of discontinuities in the simplest case of functions of a single real variable taking real values. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1311-0578-4
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Дата выхода: июль 2011

ISBN: 978-3-8383-4580-2
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Claude Gaspard Bachet de Meziriac (* 9. Oktober 1581 in Bourg-en-Bresse; † 26. Februar 1638) war ein franzosischer Mathematiker. Er war ein Schuler und Freund des Jesuiten-Mathematikers Jacques de Billy (1602–1679) in der Jesuiten-Hochschule von Reims und schrieb eine interessante Sammlung von arithmetischen Tricks und Fragen aus der Unterhaltungsmathematik, die Problemes plaisants et delectables, qui se font par les nombres, deren erste Ausgabe 1612, die zweite und erweiterte Ausgabe 1624 erschien. Eines der Ratsel war z. B.: "Wie mussen die Masse der vier Standardgewichte einer Balkenwaage lauten, um alle...

ISBN: 978-6-1332-0334-1
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Clausius theorem (1854) states that in a cyclic process. The equality holds in the reversible case and the '<' is in the irreversible case. The reversible case is used to introduce the function state entropy. This is because in cyclic process the variation of a state function is zero. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1318-6619-7
Издательство: Книга по требованию
Дата выхода: июль 2011