Combinatorics of Spreads and Parallelisms

Combinatorics of Spreads and Parallelisms
Author: Norman Johnson
Publisher: CRC Press
Total Pages: 674
Release: 2010-06-03
Genre: Mathematics
ISBN: 1439819475

Combinatorics of Spreads and Parallelisms covers all known finite and infinite parallelisms as well as the planes comprising them. It also presents a complete analysis of general spreads and partitions of vector spaces that provide groups enabling the construction of subgeometry partitions of projective spaces.The book describes general partitions

The Ultimate Challenge

The Ultimate Challenge
Author: Jeffrey C. Lagarias
Publisher: American Mathematical Society
Total Pages: 360
Release: 2023-04-19
Genre: Mathematics
ISBN: 1470472899

The $3x+1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then “multiply by three and add one”, while if it is even then “divide by two”. The $3x+1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem, which verify its truth for $x < 5.4 cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000.

Geometry Of Biharmonic Mappings: Differential Geometry Of Variational Methods

Geometry Of Biharmonic Mappings: Differential Geometry Of Variational Methods
Author: Hajime Urakawa
Publisher: World Scientific
Total Pages: 349
Release: 2018-12-06
Genre: Mathematics
ISBN: 9813236418

'The present volume, written in a clear and precise style, ends with a rich bibliography of 167 items, including some classical books and papers. In the reviewer’s opinion, this excellent monograph will be a basic reference for graduate students and researchers working in the field of differential geometry of variational methods.'zbMATHThe author describes harmonic maps which are critical points of the energy functional, and biharmonic maps which are critical points of the bienergy functional. Also given are fundamental materials of the variational methods in differential geometry, and also fundamental materials of differential geometry.

Mathematical Constants II

Mathematical Constants II
Author: Steven R. Finch
Publisher: Cambridge University Press
Total Pages: 783
Release: 2003
Genre: Mathematics
ISBN: 1108470599

Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 ..., and the natural logarithm base, e = 2.718 .... Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson-Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl-Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton-Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

The Search for a Theory of Cognition

The Search for a Theory of Cognition
Author: Stefano Franchi
Publisher: Rodopi
Total Pages: 397
Release: 2011
Genre: Computers
ISBN: 9401207151

Preliminary Material -- LIFE, DEATH, AND RESURRECTION OF THE HOMEOSTAT /Stefano Franchi -- THE ONTOLOGY OF THE ENEMY: NORBERT WIENER AND THE CYBERNETIC VISION /Peter Galison -- COMPUTERS AS MODELS OF THE MIND: ON SIMULATIONS, BRAINS, AND THE DESIGN OF COMPUTERS /Peter Asaro -- AT THE PERIPHERY OF THE RISING EMPIRE: THE CASE OF ITALY (1945-1968) /Claudio Pogliano -- PROCESSING CULTURES: “STRUCTURALISM” IN THE HISTORY OF ARTIFICIAL INTELLIGENCE /Patrice Maniglier -- ARTIFICIAL INTELLIGENCE WITH A NATIONAL FACE: AMERICAN AND SOVIET CULTURAL METAPHORS FOR THOUGHT /Slava Gerovitch -- THE CARTESIAN-LEIBNIZIAN TURING TEST /Francesco Bianchini -- TURING COMPUTABILITY AND LEIBNIZ COMPUTABILITY /Maurizio Matteuzzi -- LOGICAL INSTRUMENTS: REGULAR EXPRESSIONS, AI, AND THINKING ABOUT THINKING /Christopher M. Kelty -- GÖDEL, NAGEL, MINDS, AND MACHINES /Solomon Feferman -- ENTANGLING EFFECTIVE PROCEDURES: FROM LOGIC MACHINES TO QUANTUM AUTOMATA /Rossella Lupacchini -- TURING 1948 VS. GÖDEL 1972 /Giorgio Sandri -- WORKS CITED -- INDEX -- ABOUT THE CONTRIBUTORS -- VIBS.

Gems, Computers, and Attractors for 3-manifolds

Gems, Computers, and Attractors for 3-manifolds
Author: S¢stenes Lins
Publisher: World Scientific
Total Pages: 468
Release: 1995
Genre: Mathematics
ISBN: 9810219075

This book is about dealing with 3-manifolds using computers. Its emphasis is on presenting algorithms which are used for solving (in practice) the homeomorphism problem for the smallest of these objects. The key concept is the 3-gem, a special kind of edge-colored graph, which encodes the manifold via a ball complex. Passages between 3-gems and more standard presentations like Heegaard diagrams and surgery descriptions are provided. A catalogue of all closed orientable 3-manifolds induced by 3-gems up to 30 vertices is included. In order to help the classification, various invariants are presented, including the new quantum invariants.

Functional Analysis and Economic Theory

Functional Analysis and Economic Theory
Author: Yuri Abramovich
Publisher: Springer Science & Business Media
Total Pages: 301
Release: 2012-12-06
Genre: Business & Economics
ISBN: 3642722229

In July of 1996, the conference Nonlinear Analysis and its Applications in Engineering and Economics took place on the Greek island of Samos, the birthplace of Pythagoras. During this conference, a special session was held on th the occasion of the 50 birthday of the well known mathematician and math ematical economist Professor Charalambos Aliprantis, who, by his numerous friends, is usually called Roko. The story behind this nickname is not quite clear yet; it will be investigated further and will be made public prior to his th 60 birthday. (At this moment we have already found out that it has nothing to do with the famous movie Rocco and his Brothers even though Roko does have two brothers. ) Roko was born on the Greek island of Cephalonia on May 12,1946, and his elementary and secondary school education took place there. At 18 he entered the Mathematics Department at the University of Athens. Upon graduation from the University of Athens he proceeded with his graduate studies at Cal tech, where in 1973 he completed his Ph. D. degree in Mathematics under the supervision of Professor W. A. J. Luxemburg. His research career can be divided into two periods. The first one, till 1981, was devoted entirely to pure mathematics. The other one, after 1981, has been subdivided between pure mathematics and mathematical economics. The main objects of Roko's work in pure mathematics are spaces with order structure (Riesz spaces) and operators acting on them.

Groups of Lie Type and Their Geometries

Groups of Lie Type and Their Geometries
Author: William M. Kantor
Publisher: Cambridge University Press
Total Pages: 324
Release: 1995-01-12
Genre: Mathematics
ISBN: 052146790X

Silk Hope, NC is a buoyant and moving parable in which two good women find, among the hidden, forgotten virtues of the past, a sustenance to carry them into the future.