High Quality Content by WIKIPEDIA articles! In physics, in the area of electrodynamics, the Larmor formula is used to calculate the total power radiated by a nonrelativistic point charge as it accelerates. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of light. When accelerating or decelerating, any charged particle (such as an electron) radiates away energy in the form of electromagnetic waves. The full derivation can be found here. Here is an explanation which can help understanding the above page. This approach is based on the finite speed of light. A charge moving with constant velocity has a radial electric field Er (at distance R from the charge), always emerging from the future position of the...

ISBN: 978-6-1311-5017-3
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 Lasker-Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be written as an intersection of finitely many primary ideals. The theorem was first proven by Emanuel Lasker for the special case of polynomial rings and convergent power series rings, and was proven in its full generality by Emmy Noether. The Lasker-Noether theorem is an extension of the fundamental theorem of arithmetic, and more generally the fundamental theorem of finitely generated abelian groups to all Noetherian rings. It has a straightforward extension to modules stating that...

ISBN: 978-6-1337-1741-1
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Lateral thinking is a term coined by Edward de Bono in the book New Think: The Use of Lateral Thinking published in 1967; it refers to solving problems through an indirect and creative approach. Lateral thinking is about reasoning that is not immediately obvious and about ideas that may not be obtainable by using only traditional step-by-step logic.Critical thinking is primarily concerned with judging the true value of statements and seeking errors. Lateral thinking is more concerned with the movement value of statements and ideas. A person would use lateral thinking when they want to move from one known idea to creating new ideas. Edward de Bono Данное издание не...

ISBN: 978-6-1311-8361-4
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High Quality Content by WIKIPEDIA articles! The terms lattice graph, mesh graph, or grid graph refer to a number of categories of graphs whose drawing corresponds to some grid/mesh/lattice, i.e., its vertices correspond to the nodes of the mesh and its edges correspond to the ties between the nodes. A common type of a lattice graph (known under different names, such as square grid graph) is the graph whose vertices correspond to the points in the plane with integer coordinates, x-coordinates being in the range 0,..., n, y-coordinates being in the range 1,...m, and two vertices are connected by an edge whenever the corresponding points are at distance 1. In other words, it is a unit distance graph for the described point set....

ISBN: 978-6-1326-3831-1
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In logic, the law of identity states that an object is the same as itself: A ? A. Any reflexive relation upholds the law of identity. When discussing equality, the fact that "A is A" is a tautology.Parmenides the Eleatic (circa BCE. 490) formulated the principle Being is (eon emmenai) as the foundation of his philosophy. Aristotle, by contrast, took the Principle of contradiction as his first principle, and does not refer explicitly to the Law of Identity, although the law is often attributed to him (particularly by the proponents of Ayn Rand's writings). Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1311-8370-6
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High Quality Content by WIKIPEDIA articles! In numerical analysis, the Lax equivalence theorem is the fundamental theorem in the analysis of finite difference methods for the numerical solution of partial differential equations. It states that for a consistent finite difference method for a well-posed linear initial value problem, the method is convergent if and only if it is stable. The importance of the theorem is that while convergence of the solution of the finite difference method to the solution of the partial differential equation is what is desired, it is ordinarily difficult to establish because the numerical method is defined by a recurrence relation while the differential equation involves a differentiable function...

ISBN: 978-6-1318-2082-3
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The lazy caterer's sequence, more formally known as the central polygonal numbers, describes the maximum number of pieces of a circle that can be made with a given number of straight cuts. For example, three cuts across a pancake will produce six pieces if the cuts all meet at a common point, but seven if they do not. This problem can be formalized mathematically as one of counting the cells in an arrangement of lines; for generalizations to higher dimensions, see arrangement of hyperplanes. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1340-0745-0
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Дата выхода: июль 2011

Learning theory is the mathematical foundation of machine learning. In this book we are interested in learning multi-scale structures of data and functions from examples. Our main goal is to give solid mathematical foundations to three families of concrete learning algorithms generated by means of the scaling operator. The main motivation for introducing scaling to learning theory is to learn function features or information with different frequency components when the scaling parameter changes, as done for signal processing or image compression in wavelet analysis. Since the scaling parameter varies, learning algorithms provide richer information but the analysis becomes more involved. In this book, we mainly consider three algorithms...

ISBN: 978-3-6391-9022-9
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Дата выхода: июль 2011

This work addresses the problem of recognizing objects in images. Representation, detection, and learning are the main issues that need to be tackled in designing an object recognition system. This work proposes a framework for the statistical representation of visual features classes. The model combines several key concepts that have been developed in computer vision, machine learning, and computational neuroscience; spatial relations between features, graphical models, and hierarchies of complex cells. This results in a compositional hierarchy of visual feature classes. Its strength is to provide a coherent and generic model by representing both local and global aspects through the combination of shape and appearance modalities....

ISBN: 978-3-6391-8002-2
Издательство: Книга по требованию
Дата выхода: июль 2011

In this work we present a new model for identifying dependencies within a gene regulatory cycle. The model incorporates both probabilistic and temporal aspects, but is kept deliberately simple to make it amenable for learning from the gene expression data of microarray experiments. A key simplifying feature in our model is the use of a compression function for collapsing multiple causes of gene expression into a single cause. This allows us to introduce a learning algorithm which avoids the over-fitting tendencies of models with many parameters. We have validated the learning algorithm on simulated data, and carried out experiments on real microarray data. In doing so, we have discovered novel, yet plausible, biological relationships....

ISBN: 978-3-6391-9779-2
Издательство: Книга по требованию
Дата выхода: июль 2011

Students at a Swedish university were subjects in a study about learning limits of functions. The students were enrolled in their first university course in mathematics. They studied algebra and calculus. Students solve problems and work with theory to learn mathematics. There are many possible problems for the students to handle including the notion of function, the formal definition and limits as unattainable values for functions. The students’ perceptions were investigated in terms of traces of concept images through interviews and problem solving. The results imply that most students’ foundations were not sufficiently strong for them to understand the concept of limit well enough to be able to form coherent concept images. Many...

ISBN: 978-3-6390-2550-7
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. Least mean squares (LMS) algorithms are a class of adaptive filter used to mimic a desired filter by finding the filter coefficients that relate to producing the least mean squares of the error signal (difference between the desired and the actual signal). It is a stochastic gradient descent method in that the filter is only adapted based on the error at the current time. It was invented in 1960 by Stanford University professor Bernard Widrow and his first Ph.D. student, Ted Hoff. Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1337-3647-4
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. Least absolute deviations (LAD), also known as Least Absolute Errors (LAE), Least Absolute Value (LAV), or the L1 norm problem, is a mathematical optimization technique similar to the popular least squares technique that attempts to find a function which closely approximates a set of data. In the simple case of a set of (x,y) data, the approximation function is a simple "trend line" in 2D Cartesian coordinates. The method minimizes the sum of absolute errors (SAE), or sum of "residuals" between points generated by the function and corresponding points in the data. Данное издание не...

ISBN: 978-6-1328-9411-3
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Дата выхода: июль 2011

In mathematics, Lebesgue integration refers to both the general theory of integration of a function with respect to a general measure, and to the specific case of integration of a function defined on a sub-domain of the real line or a higher dimensional Euclidean space with respect to the Lebesgue measure. This article focuses on the more general concept. Lebesgue integration plays an important role in real analysis, the axiomatic theory of probability, and many other fields in the mathematical sciences. The integral of a non-negative function can be regarded in the simplest case as the area between the graph of that function and the x-axis. The Lebesgue integral is a construction that extends the integral to a larger class of functions...

ISBN: 978-6-1307-1988-3
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ISBN: 978-6-1311-1414-4
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High Quality Content by WIKIPEDIA articles! Imagine that you have a secret key X that has n uniform random bits, and you would like to use this secret key to encrypt a message. Unfortunately, you were a bit careless with the key, and know that an adversary was able to learn about t < n bits of that key, but you do not know which. Can you still use your key, or do you have to throw it away and choose a new key? The leftover hash-lemma tells us that we can produce a key of almost n ? t bits, over which the adversary has almost no knowledge. Since the adversary knows all but n ? t bits, this is almost optimal. Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1327-3093-0
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the Lehmer–Schur algorithm (named after Derrick Henry Lehmer and Issai Schur) is a root-finding algorithm extending the one-dimensional bracketing used by the bisection method to find the roots of a function of one complex variable inside any rectangular region of the function's holomorphicity (i.e., analyticity). Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1341-0269-8
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High Quality Content by WIKIPEDIA articles! En mathematiques et plus precisement en algebre lineaire, le lemme de Schur est un lemme technique utilise particulierement dans la theorie de la representation des groupes. Il a ete demontre en 1907 par Issai Schur (1875-1941) dans le cadre de ses travaux sur la theorie des representations d'un groupe fini, Ce lemme est a la base de l'analyse d'un caractere d'une representation d'un groupe fini. il permet, par exemple de caracteriser les groupes abeliens finis. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1318-8966-0
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High Quality Content by WIKIPEDIA articles! En mathematiques le lemme d'Euclide est un resultat d'arithmetique elementaire qui correspond a la Proposition 30 du Livre VII des Elements d'Euclide. Il enonce que : Theoreme — Si un nombre premier p divise le produit de deux nombres entiers b et c, alors p divise b ou c. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1341-4436-0
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Lennard-Jones potential (also referred to as the L-J potential, 6-12 potential or, less commonly, 12-6 potential) is a mathematically simple model that describes the interaction between a pair of neutral atoms or molecules. A form of the potential was first proposed in 1924 by John Lennard-Jones. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1326-8955-9
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Leonhard Paul Euler, ne le 15 avril 1707 a Bale et mort le 18 septembre 1783 a Saint-Petersbourg, est un mathematicien et physicien suisse, qui passa la plus grande partie de sa vie en Russie et en Allemagne. Euler fit d'importantes decouvertes dans des domaines aussi varies que le calcul infinitesimal et la theorie des graphes. Il introduisit egalement une grande partie de la terminologie et de la notation des mathematiques modernes, en particulier pour l'analyse mathematique, comme pour la notion d'une fonction mathematique. Il est egalement connu pour ses travaux en mecanique, en dynamique des fluides, en optique et en astronomie. Данное издание не является...

ISBN: 978-6-1318-3736-4
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Дата выхода: июль 2011

ISBN: 978-6-1317-4468-6
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the Lerch zeta-function, sometimes called the Hurwitz–Lerch zeta-function, is a special function that generalizes the Hurwitz zeta-function and the polylogarithm. It is named after Mathias Lerch. For ? rational, the summand is a root of unity, and thus may be expressed as a finite sum over the Hurwitz zeta-function Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1318-2175-2
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In applied mathematics, the Leslie matrix is a discrete, age-structured model of population growth that is very popular in population ecology. It was invented by and named after P. H. Leslie. The Leslie Matrix is one of the best known ways to describe the growth of populations, in which a population is closed to migration and where only one sex, usually the female, is considered. The Leslie Matrix is used in ecology to model the changes in a population of organisms over a period of time. In a Leslie Model, the population is divided into groups based on age classes. A similar model which replaces age classes...

ISBN: 978-6-1307-6995-6
Издательство: Книга по требованию
Дата выхода: июль 2011

ISBN: 978-6-1325-7574-6
Издательство: Книга по требованию
Дата выхода: июль 2011