Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a number of integers arranged in a n x n x n pattern such that the sum of the numbers on each row, each column, each pillar and the four main space diagonals is equal to a single number, the so-called magic constant of the cube, denoted M3(n). Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1328-5557-2
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Father Magnus J. Wenninger OSB (born Park Falls, Wisconsin, October 31, 1919) is a mathematician who works on constructing polyhedron models, and wrote the first book on their construction. Born to German immigrants in Park Falls, Wisconsin, Joseph Wenninger always knew he was going to be a priest. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1316-3707-0
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High Quality Content by WIKIPEDIA articles! The Majorana equation is a relativistic wave equation similar to the Dirac equation but includes the charge conjugate ?c of a spinor ?.If a particle has a spinor wavefunction ? which satisfies the Majorana equation, then the quantity m in the equation is called the Majorana mass. If ? = ?c then ? is called a Majorana spinor. Unlike Weyl spinors or Dirac spinors, the Majorana spinor is a real representation of the Lorentz group, so it is permitted to include both the spinor and its "complex conjugate" in the same equation. Actually, there is another way (like matrices in Dirac spinor, Imbalzano's clarification) of writing a Majorana spinor in terms of four real components, which shows why the...

ISBN: 978-6-1311-5049-4
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Дата выхода: июль 2011

As post secondary institutes use online learning environments, education has molded into hybrid experiences. Data was gathered from an undergraduate mathematics course designed for students seeking a bachelor’s degree in elementary education. Synergies of quantitative and qualitative data were evaluated to assess the impact of written and video help tutorials in online quizzes on student achievement. Data analysis revealed students were persistent and motivated to retake similar quizzes multiple times until a high or perfect score was obtained. After missing a problem, students selected written help tutorials more often than video help tutorials to identify mistakes and understand how to solve the particular problem. The proportion of...

ISBN: 978-3-6392-2787-1
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A non-associative algebra (or distributive algebra) over a field (or a ring) K is a K-vector space (or more generally a module) A equipped with a K-bilinear map A times A rightarrow A. There are left and right multiplication maps L_a : x mapsto ax and R_a : x mapsto xa. The enveloping algebra of A is the subalgebra of all K-endomorphisms of A generated by the multiplication maps.An algebra is unital or unitary if it has a unit or identity element I with Ix = x = xI for all x in the algebra.The best-known kinds of non-associative algebras are those that are nearly associative—that is, in which some simple equation constrains the differences between different ways of associating multiplication...

ISBN: 978-6-1311-1974-3
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Malliavin calculus, named after Paul Malliavin, is a theory of variational stochastic calculus. In other words it provides the mechanics to compute derivatives of random variables. The original motivation for the development of the subject was the desirability to provide a stochastic proof that Hormander's condition is sufficient to ensure that the solution of a stochastic differential equation has a density. The calculus also allows important regularity bounds to be obtained for this density. While this original motivation is still very important the calculus has found numerous other applications; for example in stochastic filtering. A useful feature is the ability to perform integration...

ISBN: 978-6-1327-5885-9
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Maxwell's Equations, when converted to cylindrical coordinates, and with the boundary conditions for an optical fiber while including birefringence as an effect taken into account, will yield the coupled nonlinear Schrodinger equations. After employing the Inverse scattering transform (a procedure analogous to the Fourier Transform and Laplace Transform) on the resulting equations, the Manakov system is then obtained. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1337-4128-7
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In statistics, the Mann–Whitney U test is a non-parametric test for assessing whether two independent samples of observations come from the same distribution. It is one of the best-known non-parametric significance tests. It was proposed initially by Frank Wilcoxon in 1945, for equal sample sizes, and extended to arbitrary sample sizes and in other ways by H. B. Mann and Whitney (1947). MWW is virtually identical to performing an ordinary parametric two-sample t test on the data after ranking over the combined samples. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1303-3512-0
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics and related technical fields, the term map or mapping is a synonym for function. Thus, for example, a partial map is a partial function, and a total map is a total function. Related terms like domain, codomain, injective, continuous, etc. can be applied equally to maps and functions, with the same meaning. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1329-1584-9
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The concept of a lattice arises in order theory, a branch of mathematics. The Hasse diagram below depicts the inclusion relationships among some important subclasses of lattices. In mathematics, a lattice is a partially ordered set (also called a poset) in which any two elements have a unique supremum (the elements' least upper bound; called their join) and an infimum (greatest lower bound; called their meet). Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1338-1791-3
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High Quality Content by WIKIPEDIA articles! In mathematics, specifically algebraic topology, the mapping cylinder of a function f between topological spaces X and Y is the quotient. the mapping cylinder Mf is obtained by gluing one end of X x [0,1] to Y via the map f. Notice that the "top" of the cylinder is homeomorphic to X, while the "bottom" is the space Y. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1338-1304-5
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, more specifically in differential geometry and topology, various types of functions between manifolds are studied, both as objects in their own right and for the light they shed. Just as there are various types of manifolds, there are various types of maps of manifolds. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1337-9334-7
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High Quality Content by WIKIPEDIA articles! En mathematiques et en physique theorique, une marche au hasard est un modele mathematique d'un systeme possedant une dynamique discrete composee d'une succession de pas aleatoires, ou effectues « au hasard ». On emploie egalement frequemment les expressions marche aleatoire, promenade aleatoire ou random walk en anglais. Ces pas aleatoires sont de plus totalement decorreles les uns des autres ; cette derniere propriete, fondamentale, est appelee caractere markovien du processus, du nom du mathematicien Markov. Elle signifie intuitivement qu'a chaque instant, le futur du systeme depend de son etat present, mais pas de son passe, meme le plus proche. Autrement dit, le systeme « perd la...

ISBN: 978-6-1340-5253-5
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the Marcinkiewicz interpolation theorem, discovered by Jozef Marcinkiewicz is a result bounding the norms of non-linear operators acting on Lp spaces. Marcinkiewicz' theorem is similar to the Riesz–Thorin theorem about linear operators, but also applies to non-linear operators. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1327-9098-9
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High Quality Content by WIKIPEDIA articles! Mario Livio (born 1945) is an astrophysicist and an author of works that popularize science and mathematics. He is currently an astronomer and head of public outreach at the Space Telescope Science Institute, which operates the Hubble Space Telescope. He is perhaps best known for his book on the irrational number phi: The Golden Ratio: The Story of Phi, the World's Most Astonishing Number (2002). The book won the Peano Prize and the International Pythagoras Prize for popular books on mathematics. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1325-7281-3
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a Markov chain , named after Andrey Markov is a random process where all information about the future is contained in the present state (i.e. one does not need to examine the past to determine the future). To be more exact, the process has the Markov property, meaning that future states depend only on the present state , and are independent of past states . In other words, the description of the present state fully captures all the information that could influence the future evolution of the process. Being a stochastic process means that all state transitions are probabilistic (determined by...

ISBN: 978-6-1302-9637-7
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Markov's principle, named after Andrey Markov Jr, is a classical tautology that is not intuitionistically valid but that may be justified by constructive means. There are many equivalent formulations of Markov's principle. In the language of computability theory, Markov's principle is a formal expression of the claim that if it is impossible that an algorithm does not terminate, then it does terminate. This is equivalent to the claim that if a set and its complement are both computably enumerable, then the set is decidable. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1318-0648-3
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Markov chain Monte Carlo methods, are a class of algorithms for sampling from probability distributions based on constructing a Markov chain that has the desired distribution as its equilibrium distribution. The state of the chain after a large number of steps is then used as a sample from the desired distribution. The quality of the sample improves as a function of the number of steps.Usually it is not hard to construct a Markov Chain with the desired properties. The more difficult problem is to determine how many steps are needed to converge to the stationary distribution within an acceptable error. A good chain will have rapid mixing—the stationary distribution is reached quickly starting...

ISBN: 978-6-1317-5048-9
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a Markov information source, or simply, a Markov source, is an information source whose underlying dynamics are given by a stationary finite Markov chain. An information source is a sequence of random variables ranging over a finite alphabet ?, having a stationary distribution. A Markov information source is then a (stationary) Markov chain M, together with a function Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1317-9173-4
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High Quality Content by WIKIPEDIA articles! Markov decision processes (MDPs), named after Andrey Markov, provide a mathematical framework for modeling decision-making in situations where outcomes are partly random and partly under the control of a decision maker. MDPs are useful for studying a wide range of optimization problems solved via dynamic programming and reinforcement learning. MDPs were known at least as early as the 1950s (cf. Bellman 1957). Much research in the area was spawned due to Ronald A. Howard's book, Dynamic Programming and Markov Processes, in 1960. Today they are used in a variety of areas, including robotics, automated control, economics and manufacturing. Данное издание не является...

ISBN: 978-6-1317-5059-5
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High Quality Content by WIKIPEDIA articles! In probability theory, Markov's inequality gives an upper bound for the probability that a non-negative function of a random variable is greater than or equal to some positive constant. It is named after the Russian mathematician Andrey Markov, although it appeared earlier in the work of Pafnuty Chebyshev (Markov's teacher), and many sources, especially in analysis, refer to it as Chebychev's inequality or Bienayme's inequality. Markov's inequality (and other similar inequalities) relate probabilities to expectations, and provide (frequently) loose but still useful bounds for the cumulative distribution function of a random variable. An example of an application of Markov's inequality is the...

ISBN: 978-6-1317-7727-1
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In descriptive set theory, the Martin measure is a filter on the set of Turing degrees of sets of natural numbers. Under the axiom of determinacy it can be shown to be an ultrafilter. Let D be the set of Turing degrees of sets of natural numbers. Given some equivalence class [X]in D, we may define the cone (or upward cone) of [X] as the set of all Turing degrees [Y] such that Xle_T Y; that is, the set of Turing degrees which are "more complex" than X under Turing reduction. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1337-6622-8
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Martin L. (Marty) Demaine is an artist and mathematician, the Angelika and Barton Weller artist in residence at the Massachusetts Institute of Technology. Demaine attended Medford High School in Medford, Massachusetts. After studying glassblowing in England, he began his artistic career by blowing art glass in New Brunswick in the early 1970s. The Demaine Studio, located in Miramichi Bay and later at Opus Village in Mactaquac, was the first one-man glass studio in Canada, part of the international studio glass movement. Demaine's pieces from this period are represented in the permanent collections of half a...

ISBN: 978-6-1329-0863-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Maschke's theorem is a theorem in group representation theory which concerns the decomposition of representations of a finite group into irreducible pieces. If (V, ) is a finite-dimensional representation of a finite group G over a field of characteristic zero, and U is an invariant subspace of V, then the theorem claims that U admits an invariant direct complement W; in other words, the representation (V, ) is completely reducible. More generally, the theorem holds for fields of positive characteristic p, such as the finite fields, if the prime p doesn't divide the order of G. It is named after Heinrich Maschke. Данное издание не является оригинальным....

ISBN: 978-6-1339-2316-4
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices. It may also be an entire graph consisting of edges without common vertices. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1328-4646-4
Издательство: Книга по требованию
Дата выхода: июль 2011