High Quality Content by WIKIPEDIA articles! In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that they need not be associative. A quasigroup with an identity element is called a loop. There are two equivalent formal definitions of quasigroup with, respectively, one and three primitive binary operations. We begin with the first definition, which is easier to follow. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-4331-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the concept of quasiconformal mapping, introduced as a technical tool in complex analysis, has blossomed into an independent subject with various applications. Informally, a conformal homeomorphism is a homeomorphism between plane domains which to first order takes small circles to small circles. A quasiconformal homeomorphism to first order takes small circles to small ellipses of bounded eccentricity. Intuitively, let :D ? D? be an orientation preserving homeomorphism between open sets in the plane. If f is continuously differentiable, then it is K-quasiconformal if the derivative of f at every point maps circles to ellipses with eccentricity bounded by K. Данное...

ISBN: 978-6-1303-4308-8
Издательство: Книга по требованию
Дата выхода: июль 2011

Quasiconformal homeomorphisms are topological transformations with uniformly bounded distortion. This book concerns different notions of homogeneity; that is the degree of regularity of sets in extended Euclidean n-space which are assumed to have a family (or group) of quasiconformal homeomorphisms acting transitively. This builds on earlier important and interesting work, mainly in two dimensions, of other researchers. The novelty here is the generalisation to higher dimensions, where new tools and methods had to be developed. The techniques are quite complicated both analytically and topologically, because many classification theorems in two dimensions are not readily applicable in three or more dimensions. It is discovered in the book...

ISBN: 978-3-6390-0650-6
Издательство: Книга по требованию
Дата выхода: июль 2011

Notion of convexity plays an important role in Economics and Engineering. The general equilibrium theory is based on convex programming. In classical economics, production and utility functions are assumed to be concave functions and as consequence, demand and cost functions are convex. The firm theory requires to solve the concave maximization problem while consumer theory considers utility maxmization problem. In recent years, generalized convex functions such as quasiconvex functions are found to be useful in Economics. In this book we consider two problems of maximizing and minimizing a quasiconvex function. Both problems belong to a class of global optimization and application of classical conditions has not been successful for...

ISBN: 978-3-8383-0807-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, specifically ring theory, the notion of quasiregularity provides a computationally convenient way to work with the Jacobson radical of a ring. Intuitively, quasiregularity caputures what it means for an element of a ring to be "bad"; that is, have undesirable properties.[2] Although a "bad element" is necessarily quasiregular, quasiregular elements need not be "bad," in a rather vague sense. In this article, we primarily concern ourselves with the notion of quasiregularity for unital rings. However, one section is devoted to the theory of quasiregularity in non-unital rings, which constitutes an important aspect of noncommutative ring theory. Данное издание не...

ISBN: 978-6-1303-4340-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In optimization, quasi-Newton methods (also known as variable metric methods) are well-known algorithms for finding local maxima and minima of functions. Quasi-Newton methods are based on Newton's method to find the stationary point of a function, where the gradient is 0. Newton's method assumes that the function can be locally approximated as a quadratic in the region around the optimum, and use the first and second derivatives (gradient and Hessian) to find the stationary point. In Quasi-Newton methods the Hessian matrix of second derivatives of the function to be minimized does not need to be computed. The Hessian is updated by analyzing successive gradient vectors instead. Quasi-Newton...

ISBN: 978-6-1303-4294-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a quasiconvex function is a real-valued function defined on an interval or on a convex subset of a real vector space such that the inverse image of any set of the form (-infinity,a) is a convex set. A quasiconcave function is a function whose negative is quasiconvex, and a strictly quasiconcave function is a function whose negative is strictly quasiconvex. A (strictly) quasiconvex function has (strictly) convex lower contour sets, while a (strictly) quasiconcave function has (strictly) convex upper contour sets. Optimization methods that work for quasiconvex functions come under the heading of quasiconvex programming. This comes under the broad heading of mathematical...

ISBN: 978-6-1303-3813-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Quasiperiodicity is the property of a system that displays irregular periodicity. Periodic behavior is defined as recurring at regular intervals, such as "every 24 hours". Quasiperiodic behavior is a pattern of recurrence with a component of unpredictability that does not lend itself to precise measurement. It is different from the mathematical concept of an almost periodic function, which has increasing regularity over multiple periods. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1305-1524-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Quasi-empiricism in mathematics is the attempt in the philosophy of mathematics to direct philosophers' attention to mathematical practice, in particular, relations with physics, social sciences, and computational mathematics, rather than solely to issues in the foundations of mathematics. Of concern to this discussion are several topics: the relationship of empiricism with mathematics, issues related to realism, the importance of culture, necessity of application, etc. A primary argument with respect to Quasi-empiricism is that whilst mathematics and physics are more frequently being considered as closely linked fields of study, this may reflect human cognitive bias. It is claimed that,...

ISBN: 978-6-1303-4282-1
Издательство: Книга по требованию
Дата выхода: июль 2011

ISBN: 978-6-1325-8468-7
Издательство: Книга по требованию
Дата выхода: июль 2011

This monograph studies an important generalisation of the Cauchy integral formula, called the Dbar formula. In particular, it investigates the physical significance of this formula, its extension to three, four and higher dimensions and the applications of the relevant formalism to: (i) The solution of boundary value problems for linear partial differential equations ; (ii) The evaluation of real integrals; (iii) The construction of nonlinear integrable equations starting from the corresponding linear equations. A large part of this monograph is devoted to the theory of quaternions. It is shown that quaternions provide the proper generalisation of complex numbers. The book offers a pedagogical introduction to the theory of quaternions...

ISBN: 978-3-6391-1533-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, a quaternion algebra over a field F is a central simple algebra A over F[1][2] that has dimension 4 over F. Every quaternion algebra becomes the matrix algebra by extending scalars (=tensoring with a field extension), i.e. for a suitable field extension K of F, A otimes_F K is isomorphic to the 2x2 matrix algebra over K. The notion of a quaternion algebra can be seen as a generalization of the Hamilton quaternions to an arbitrary base field. The Hamilton quaternions are a quaternion algebra (in the above sense) over F = mathbb{R} (the real number field), and indeed the only one over R apart from the 2x2 real matrix algebra, up to isomorphism. Данное издание не...

ISBN: 978-6-1303-4367-5
Издательство: Книга по требованию
Дата выхода: июль 2011

Quaternion. Cayley– Dickson Construction, Quaternion Variable, Quaternions and Spatial Rotation, Rotation Operator (Vector Space), Quaternion Algebra, Quaternion Group, Split-Quaternion, Biquaternion, Hurwitz Quaternion, Hurwitz Quaternion Order, Hyperbolic Quaternion, Associative Algebra, Exterior Algebra, Clifford Algebra, Article Sources and Contributors, Image Sources, Licenses and Contributors Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1300-4855-6
Издательство: Книга по требованию
Дата выхода: июль 2011

Quaternions and Spatial Rotation. Quaternion, Slerp, Rotation Representation (Mathematics), Rotation, Rotation Group, Rotation Matrix, Rotation (Mathematics), Conversion between Quaternions and Euler Angles, Matrix (Mathematics), Space (Mathematics), Celestial Sphere, Charts on SO(3), Article Sources and Contributors, Image Sources, Licenses and Contributors Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1300-4920-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In group theory, the quaternion group is a non-abelian group of order 8, isomorphic to a certain eight-element subset of the quaternions under multiplication. It is often denoted by Q or Q8, and is given by the group presentation Q = langle -1,i,j,k mid (-1)^2 = 1, ;i^2 = j^2 = k^2 = ijk = -1 rangle, ,! where 1 is the identity element and ?1 commutes with the other elements of the group. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-4378-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A quantum bit or qubit (pronounced /?kju?b?t/) is a unit of quantum information. It is the quantum analogue of the classical bit. It is described by a state vector in a two-level quantum-mechanical system, which is formally equivalent to a two-dimensional vector space over the complex numbers. A bit is the basic unit of computer information. Regardless of its physical realization, a bit is always understood to be either a 0 or a 1. An analogy to this is a light switch— with the off position representing 0 and the on position representing 1. A qubit has some similarities to a classical bit, but is overall very different. Like a bit, a qubit can have two possible values—normally a 0 or a 1....

ISBN: 978-6-1309-6269-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Queensland Ambulance Service (QAS) is the chief provider of out-of-hospital emergency care and ambulance transport in the state of Queensland, Australia. It falls under the control of the Queensland government's Department of Community Safety, and is the fourth-largest ambulance service in the world. The service provides a high level of emergency care and transport services to over 4.1 million people in Queensland, covering an area of 1.77 million square kilometres. They provide such services as emergency response, pre-hospital patient care, specialised transport services, coordination of aero-medical services and inter-hospital transfers. Approximately 2,780 paramedics are employed by QAS,...

ISBN: 978-6-1313-9250-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Queen's Gambit Declined (QGD) is a chess opening when after White plays the Queen's Gambit: 1. d4 d5, 2. c4. Black declines the pawn offered by White and plays: 2. ... e6. This is known as the Orthodox Defense of Queen's Gambit Declined. By declining the temporary pawn sacrifice, Black erects a solid position; the pawns on d5 and e6 give Black a foothold in the center. The Queen's Gambit Declined has the reputation as being one of Black's most reliable defenses to 1.d4. Playing 2...e6 releases Black's dark-squared bishop, while obstructing the light-squared bishop. White will try to exploit the passivity of this bishop, and Black will try to release it, trade it, or prove that, while...

ISBN: 978-6-1314-0076-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In queueing theory, a queueing model is used to approximate a real queueing situation or system, so the queueing behaviour can be analysed mathematically. Queueing models allow a number of useful steady state performance measures to be determined, including: * the average number in the queue, or the system, * the average time spent in the queue, or the system, * the statistical distribution of those numbers or times, * the probability the queue is full, or empty, and * the probability of finding the system in a particular state. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд...

ISBN: 978-6-1303-4433-7
Издательство: Книга по требованию
Дата выхода: июль 2011

One of the most disastrous consequences of the actual infinity is the conception of space and time as a continuum infinitely divisible. Basic concepts of physics as motion or velocity were, and continue to be, founded on that assumption. Matter and energy were also initially conceived as a continuum infinitely divisible. But the obstinacy of facts finally revealed that rather than continue, they are discontinue (elementary particle and quanta, respectively). It is now being suggested from different areas of science that space and time could also be of a discrete and finite nature. If that were the case we would have to redefine the foundations of a considerable part of contemporary science. For these reasons it is of capital importance...

ISBN: 978-3-6392-0294-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." Данное издание не является оригинальным....

ISBN: 978-6-1312-6131-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." Данное издание не является оригинальным....

ISBN: 978-6-1312-6137-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Quinary (base-5) is a numeral system with five as the base. A possible origination of a quinary system is that there are five fingers on either hand. In the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100 and sixty is written as 220. Today, the main usage of base 5 is as a biquinary system, which is decimal using five as a sub-base. Another example of a sub-base system, is sexagesimal, base 60, which used 10 as a sub-base. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1329-4910-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A quincunx (IPA) is a geometric pattern consisting of five coplanar points, four of them forming a square or rectangle and a fifth at its center. It forms the arrangement of five units in the pattern corresponding to the five-spot on dice, playing cards, or dominoes. The quincunx was originally a coin issued by the Roman Republic c.211-200 BC, whose value was five twelfths (quinque + uncia) of an as, the Roman standard bronze coin. On the Roman quincunx coins, the value was sometimes indicated by a pattern of five dots or pellets. However, these dots were not always arranged in a quincunx pattern. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1310-1831-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! e–McCluskey algorithm (or the method of prime implicants) is a method used for minimization of boolean functions which was developed by W.V. Quine and Edward J. McCluskey. It is functionally identical to Karnaugh mapping, but the tabular form makes it more efficient for use in computer algorithms, and it also gives a deterministic way to check that the minimal form of a Boolean function has been reached. It is sometimes referred to as the tabulation method. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-4267-8
Издательство: Книга по требованию
Дата выхода: июль 2011