The work done to fullfil the requirements of the PhD program through this dissertation cannot be considered as complete. There are many areas of study that needed redress. The ideas of incorporating the resultant theory to solve a fifth order eigenvalue problem are challenging, yet needing proper documentation and full proof. Matlab programs that were used to obtain solutions may not be the best or efficient programs. But this research endevour provides some alternative approach towards resolution of equations and system of equations with many parameter values. Introduction of a third species that has a choice on food source is an idea that must be explored often in this world of genetic modified food technologies. We believe that this...

ISBN: 978-3-6391-2496-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Dot and the Line: A Romance in Lower Mathematics is a book written and illustrated by Norton Juster, first published by Random House in 1963. In 1965, famed animator Chuck Jones and the MGM Animation/Visual Arts studio adapted The Dot and the Line into a 10-minute animated short film for Metro-Goldwyn-Mayer, narrated by Robert Morley. The Dot and the Line won the 1965 Academy Award for Animated Short Film. It was entered into the Short Film Palme d'Or competition at the 1966 Cannes Film Festival. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1311-6915-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics is a 1989 book by mathematical physicist Sir Roger Penrose.Penrose presents the argument that human consciousness is non-algorithmic, and thus is not capable of being modeled by a conventional Turing machine-type of digital computer. Penrose hypothesizes that quantum mechanics plays an essential role in the understanding of human consciousness. The collapse of the quantum wavefunction is seen as playing an important role in brain function. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1311-6919-9
Издательство: Книга по требованию
Дата выхода: июль 2011

Vectorial Boolean functions are used in cryptography, in particular in block ciphers. An important condition on these functions is a high resistance to differential and linear cryptanalysis, which are the main attacks on block ciphers. The functions which possess the best resistance to the differential attack are called almost perfect nonlinear (APN). Almost bent (AB) functions are those mappings which oppose an optimum resistance to both linear and differential attacks. Before this work, only a few classes of APN and AB functions had been known and all these classes happened to be extended affine equivalent (EA- equivalent) to power functions. In this work we construct the first classes of APN and AB polynomials EA-inequivalent to power...

ISBN: 978-3-8364-9410-6
Издательство: Книга по требованию
Дата выхода: июль 2011

It is known that the ordinary least squares (OLS) estimates in the regression model are efficient when the errors have mean zero, constant variance and are uncorrelated. In time series, it is often the errors are correlated. It is known that OLS may not be optimal in this context. We have proved that the relative efficiency of the variance of the generalized least squares (GLS) to that of OLS is invariant to scaling and shifting of the design vectors. We have derived explicit formulae for the relative efficiencies of the GLS to that of OLS in some important special cases. We consider both linear and quadratic design vectors in the presence of AR(1) errors and show some asymptotic properties of the estimators. Additionally, using computer...

ISBN: 978-3-6390-8690-4
Издательство: Книга по требованию
Дата выхода: июль 2011

The reflection group H_4 encodes the symmetries of the regular polytope called the 600-cell, which is a four-dimensional analogue of the icosahedron. The structure of H_4 has many interesting relations to a variety of topics of mathematics and physics. This book outlines the ideas behind the classification of finite reflection groups, giving a context for H_4 as the largest exceptional noncrystallographic reflection group. Different constructions of H_4 and its root system, which have thus far been published in pieces throughout the mathematics literature, are then described and compared. The book also examines a construction of the character table of H_4, which uses information about the group and root system structure. Finally, an...

ISBN: 978-3-6390-3162-1
Издательство: Книга по требованию
Дата выхода: июль 2011

A fullerene is a carbon molecule where each carbon atom is chemically bonded to three other carbon atoms and the atoms form pentagonal and hexagonal rings and this molecule can be viewed as a finite connected trivalent plane graph, all of whose faces are pentagons and hexagons. Some research has focused on the graph theoretical properties of fullerenes and in some cases trying to determine a relationship between a graph theoretical property and chemical properties of the molecule. In this research we will focus on the graph theoretical property of a graph being l_1-embeddable and discuss the face consistency of a particular class of fullerenes. This class is the hexagonal orange peel fullerenes with the symmetry group D_{6h} and the...

ISBN: 978-3-6392-0660-9
Издательство: Книга по требованию
Дата выхода: июль 2011

In recent years, graph theory has been used as a tool to study rings in the form of several different graphs, many of which are based on the zero divisor structure of the ring. We de?ne here the annihilator graph of a ring to try to harness the best possible graphical representation of a ring. This paper lays the foundation for the theory of annihilator graphs and the extension of them to a more general form, the Grobner annihilator graph. We will study the relationships between the algebraic properties of a ring, and the graph theoretic properties of the Grobner annihilator graph of that ring. We will state some concise results while also formally stating areas in which the author feels further research is needed. This work is an...

ISBN: 978-3-6391-9605-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Geometry Center was a mathematics research and education center at the University of Minnesota. It was established by the National Science Foundation in the late 1980s and closed in 1998. Its founding director was Al Marden. The focus of the Center's work was the use of computers for research and education in geometry.Much of the work at the Center was of the development of Geomview, a three dimensional interactive geometry program. This focused on mathematical visualization with options to allow hyperbolic space to be visualised. This originally ran on Silicon Graphics machines, and has been ported to run under X11 on unix machines. Geomview can run under Windows using Cygwin and under Mac...

ISBN: 978-6-1311-6995-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Geometer's Sketchpad is a popular commercial interactive geometry software program for exploring Euclidean geometry, algebra, calculus, and other areas of mathematics. It was created by Nicholas Jackiw. It is designed to run on Windows 95 or Windows NT 4.0 or later and Mac OS 8.6 or later (including Mac OS X). It also runs on Linux under Wine with few bugs.Geometer's Sketchpad includes the traditional Euclidean tools of classical Geometric constructions; that is, if a figure (such as the pentadecagon) can be constructed with compass and straight-edge, it can also be constructed using this program. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1311-6980-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Harmful Effects of Algorithms in Grades 1-4 is a research paper published in the NCTM 1998 Yearbook and written by Constance Kamii and Ann Dominick. It argues that that children should not be taught through traditional mathematics methods in elementary school, and should instead be guided to construct their own mathematical reasoning.The paper's data is derived from a sample of 46 low-performing, low-socioeconomic status 1st graders, divided into control and experimental groups - the experimental group was found to perform better on word problems at the conclusion of the school year. Данное издание не является оригинальным. Книга печатается...

ISBN: 978-6-1311-7006-5
Издательство: Книга по требованию
Дата выхода: июль 2011

In this work we deal with the degree of ill-posedness of linear operators in Hilbert spaces, where the operator may be decomposed into a compact linear integral operator with a well-known decay rate of singular values and a multiplication operator. This case occurs, for example, for nonlinear operator equations. Then the local degree of ill-posedness is investigated via the Frechet derivative, providing the situation described above. If the multiplier function has got zeroes, the determination of the local degree of ill-posedness is not trivial. We are going to investigate this situation, provide analytical tools as well as their limitations. By using several numerical approaches for computing the singular values we find that the degree...

ISBN: 978-3-6390-6913-6
Издательство: Книга по требованию
Дата выхода: июль 2011

This book discusses the necessary tools to compute the lower algebraic K-theory of the integral group ring for the pure braid groups on the 2- sphere and on the real projective plane. We begin with the statement of the fibered isomorphism conjecture of Farrell-Jones through the definitions of all necessary ingredients for the actual computations. We illustrate the defnitions with specific examples used later on to discuss the proof of the main results of this work. Consider the 2- sphere or the real projective plane and let PBn(M) and Bn(M) be the pure and the full braid groups on n-strands of M respectively. In this work we show that PBn(M) and Bn(M) satisfy the Farrell-Jones isomorphism conjecture and use this fact to compute the lower...

ISBN: 978-3-6391-0919-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Laws of Thought, more precisely, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, is a very influential 19th century book on logic by George Boole, the second of his two monographs on algebraic logic. It was published in 1854.George Boole was Professor of Mathematics of then Queen's College, Cork in Ireland (now University College Cork, where the Boole Centre for Research in Informatics is named in his honour) Boole's work began the discipline of algebraic logic, and is often, but mistakenly, credited as being the source of what we know today as Boolean algebra. In fact, however, Boole's algebra differs from modern Boolean...

ISBN: 978-6-1311-7042-3
Издательство: Книга по требованию
Дата выхода: июль 2011

In the study of such concepts as fairness and justice, there is a large gap between the ethics literature (where utilitarianism and egalitarianism enjoy wide support) and mathematical bargaining theory (where the Nash bargaining solution has held canonical status ever since its introduction in 1950). This work analyzes the rationale upholding each of the three major ways in which the Nash bargaining solution is justified mathematically (the axiomatic approach, the alternating offers game and dynamic systems) and shows that in every case the basic premises leading to the Nash solution diverge from real-life bargaining scenarios. Furthermore, the book goes on to show that by correcting these premises, the utilitarian solution emerges...

ISBN: 978-3-8383-1804-2
Издательство: Книга по требованию
Дата выхода: июль 2011

A theoretical model for oxygen and substrate transport to tissues within skeletal muscle involving several interacting capillaries has been developed. It involves an elegant technique that discretizes the transport problem in a tissue with large number of capillaries. The technique can be equally applied to other heat transport problems with actual anatomical information. For oxygen, the role of myoglobin and the effect of axial diffusion have been considered. For the myoglobin model, myoglobin facilitates oxygen diffusion into tissue and can prevent hypoxia due to the interaction of the capillaries. The analysis yields a great deal of information about hypoxia, since as shown, a multicapillary model of the type presented here is needed...

ISBN: 978-3-6390-9777-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Music of the Primes (English subtitle: Why an Unsolved Problem in Mathematics Matters; American subtitle: Searching to Solve the Greatest Mystery in Mathematics) is a 2003 book by Marcus du Sautoy, a professor in mathematics at the University of Oxford, on the history of prime number theory. In particular he examines the Riemann hypothesis, the proof of which would revolutionize our understanding of prime numbers. He traces the history of the prime number theorem back through history, highlighting the work of some of the greatest mathematical minds along the way. Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1311-4485-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Mathematical Diary was an early American mathematical journal and mathematics magazine, published between 1825 and 1833.The Mathematical Diary was founded by Robert Adrain at Columbia College (now Columbia University) after two unsuccessful attempts, in 1808 and 1814, to start a more purely academic mathematics journal, The Analyst, or, Mathematical Museum. The Mathematical Diary contained, in addition to some serious mathematics, articles of general interest such as mathematical puzzles aimed at the amateur problem-solver, which may have helped it attract more laypeople as subscribers and contributed to its greater longevity. Данное издание не является...

ISBN: 978-6-1311-7083-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Mathematics Educator (TME) is peer-reviewed journal within the field of mathematics education. TME is produced by students, and it is published by the Mathematics Education Student Association (MESA) in the Department of Mathematics Education at the University of Georgia. MESA is an affiliate of the National Council of Teachers of Mathematics (NCTM). The journal first appeared in 1990, and it has appeared one or two times a year since then. It welcomes different types of manuscripts, like research reports, commentaries, literature reviews, theoretical articles, critiques, mathematical problems, and translations of previously published articles. Данное издание не...

ISBN: 978-6-1311-4274-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! "The Martians" was the name of a group of prominent scientists (mostly, but not exclusively physicists and mathematicians) who emigrated from Hungary to the United States in the early half of the 20th century. They included, among others, Theodore von Karman, Leo Szilard, Eugene Wigner, Edward Teller and Paul Erd?s. They received the name from a fellow Martian John von Neumann who jokingly suggested that Hungary was a front for aliens from Mars. (This is analogous to Enrico Fermi's answer to the question whether extraterrestrial beings exist: "Of course, they are already here among us: they just call themselves Hungarians.") Данное издание не является...

ISBN: 978-6-1311-7071-3
Издательство: Книга по требованию
Дата выхода: июль 2011

Over the last few years, the Mittag-Leffler function is drawn the attention of several special functionalist. In 21st century this is one of the frequently useful functions in the research area of Engineering, Technology and Applied Sciences. This book therefore provides a new generalization of Mittag-Leffler function, its related fractional operators and Decomposition (Chapters-2 Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-3-8383-9976-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Mathematical Institute is the mathematics department at the University of Oxford, England. It forms one of the eight departments of the Mathematical, Physical and Life Sciences Diviion in the University.The Institute is located in a building built in 1966 at the southern end of Banbury Road in central north Oxford. It also has an entrance on Blackhall Road to the east. In addition, the Institute has two annexes, which are also located close to the centre of Oxford. Dartington House is situated on Little Clarendon Street, a short walk from the main building, and the Gibson Building is situated further north, on the site of the Radcliffe Infirmary Данное издание не...

ISBN: 978-6-1311-7095-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Mathematical Experience is a 1981 book by Philip J. Davis and Reuben Hersh that discusses the practice of modern mathematics from a historical and philosophical perspective. It won the 1983 National Book Award in the Science categoryIt is frequently cited by mathematicians as a book that was influential in their decision to continue their studies in graduate school and has been hailed as a classic of mathematical literature. The book drew a critical review from Martin Gardner, who disagreed with some of the authors' philosophical opinions, but was well-received otherwise. Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1311-7089-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 1st century CE. This book is the one of the earliest surviving mathematical texts from China, the first being Suan shu sh? (202 BCE – 186 BCE) and Zhou Bi Suan Jing (compiled throughout the Han until the late 2nd century CE). It lays out an approach to mathematics that centres on finding the most general methods of solving problems, which may be contrasted with the approach common to ancient Greek mathematicians, who tended to deduce propositions from an initial set of axioms. Данное издание не...

ISBN: 978-6-1303-5191-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Quadrature of the Parabola is a treatise on geometry, written by Archimedes in the 3rd century B.C. Written as a letter to his friend Dositheus, the work presents 24 propositions regarding parabolas, culminating in a proof that the area of a parabolic segment (the region enclosed by a parabola and a line) is 4/3 that of a certain inscribed triangle. The proof uses the method of exhaustion. Archimedes dissects the area into infinitely many triangles whose areas form a geometric progression. He computes the sum of the resulting geometric series, and proves that this is the area of the parabolic segment. This represents the most sophisticated use of the method of exhaustion in ancient...

ISBN: 978-6-1303-5206-6
Издательство: Книга по требованию
Дата выхода: июль 2011