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CONTENTS
Fractal Dimensions and Dynamical Systems
Hyers-Ulam-Rassias Stability of Functional Equations in
Nonlinear Analysis in Geometry and Topology
Mathematical Analysis and Applications
Complex Analysis in Several Variables
Interactions, Strings and Isotopies
in Higher Order Anisotropic Superspaces
THE GEOMETRY OF HIGHER - ORDER FINSLER SPACES
Approximation Theory and Applications
Nonlinear Mathematical Analysis and Applications
New Frontiers in Hyperstructures
New Frontiers in Algebras, Groups and Geometries
The first part presents contributions in Santilli's
nonlinear, nonlocal and noncanonical isotopies of contemporary
mathematical methods, including advances in:
Hyperbolic Geometry and Barbilian Spaces
Nonassociative Algebras in Physics
Gauge Theory in Jet Manifolds
Hyperstructures and their Representations
Algebraic Hyperstructures and Applications
The Mathematical Legacy of Hanno Rund
A Riemann Legacy Volume
Stability of Mappings of Hyers-Ulam Type
Tomber's Bibliography and Index in Nonassociative Algebras
The Second Edition of 1997 preserves the content of the First Edition in an
updated and improved form, and then adds two new parts, Part II with a
general presentation of the Lie-Santilli isotheory for matter and its
isodual for antimatter, and Part III with a presentation of the latest
application to the Iso-Grand-Unification with the
axiomatically consistent inclusion of gravity in unified gauge
theories of electroweak interactions,
and the Isoselfdual Cosmology with null total characteristics of the universe.
Part I is recommended for a first study of the isotopies; Part II
is suggested for a more advanced study; Part III
requires an advanced technical knowledge in the field.
A REVIEW: On the whole, the author has done a splendid job in making Santilli's
work understandable to a wider audience of theoretical physicists and
mathematicians.
I.I.S. REVIEWS.
1.TITLES FROM HADRONIC PRESS
2.TITLES FROM UKRAINE ACADEMY OF SCIENCES
1. TITLES FROM THE HADRONIC PRESS
Xenofon S. Motsenigos, University of Warwick, Coventry, UK
February 2001, ISBN 1-57485-052-0, pp. 115, hardcover, US$65
One of the problems of interest in Dynamical Systems is the determination of the
asymptotic behaviour of orbits. Often, we are required to find ways to describe
various complicated sets (like attractors or basins of attraction for example) that
are strongly related to this asymptotic behaviour problem. The aim of this book
is to introduce fractal dimensions (Box-counting and Hausdorff dimensions in particular)
as a tool which aids in the description and understanding of these complicated sets and,
therefore, of the related dynamics.
Mathematical Analysis
SOON-MO JUNG, College of Science and Technology, Hong-Ik University, Korea
Monograph in Mathematics
February 2001, ISBN 1-57485-051-2, pp. 260, hardcover, US $ 85
The study of stability problems for various functional equations originated from a
famous talk given by Stanislaw M. Ulam in 1940. In the talk, Ulam discussed a number
of important unsolved mathematical problems. One of them was a question concerning
the stability of homomorphisms. In the following year, 1941, Donald H. Hyers gave a
partial solution to Ulam's question. This was the first signifant breakthrough in
this area. After D. H. Hyers gave an affirmative answer to Ulam's question, a large
number of papers have been published in connection with various generalizations of
Ulam's problem and Hyer's theorem. In particular, Themistocles M. Rassias succeeded
in extending the result of Hyer's theorem by weakening the condition for the Cauchy
difference. This remarkable result of Rassias directed the concern of mathematicians
towards the study of stability problems of functional equations.
Unfortunately, there were no books that gave a comprehensive illustration of the fast
developing field of nonlinear analysis to the mathematicians who were interested in
this field for more than a half century until D. H. Hyers, G. Isac and Th. M. Rassias
published their book, "Stability of Functional Equations in Several Variables."
The present book will complement the book of Hyers, Isac and Rassias by presenting
mainly the results concerning the Hyers-Ulam-Rassias stability. The concept of the
Hyers-Ulam-Rassias stability is a generalization of the Hyers-Ulam stability of
functional equations. The subjects on the Hyers-Ulam-Rassias stability have
been extensively investigated by many mathematicians. This book covers almost all
classical results on the Hyers-Ulam-Rassias stability in an integrated and
self-contained fashion.
Edited by THEMISTOCLES M. RASSIAS, National Technical University of Athens, Greece
Collection of original refereed papers
August 2000, ISBN 1-57485-048-2, pp. 295, hardcover, US$85
Nonlinear Analysis in Geometry and Topology is devoted to recent progress in nonlinear
analysis and its applications to the solution of problems in geometry and topology.
Some of the topics dealt with in this volume include: convexity and metric fixed point
theory, multiple solutions of nonlinear equations via Nielsen fixed point theory,
solvability of quasi variational inclusions, boundary properties for two-dimensional
semiflows, nonlinear planar sprays, nonlinear Hodge structures in vector bundles,
Mobius transformations of the ball, applications of non-Euclidean nonlinear methods,
second order differential equations on total spaces of fiber bundles with connections,
super Darboux-Egoroff equations and solutions, and finite-dimensional reductions of smooth
functionals.
Edited by THEMISTOCLES M. RASSIAS, National Technical University of Athens, Greece
Collection of original refereed papers
June 2000, ISBN 1-57485-045-8, pp. 380, hardcover, US$89
This volume presents works devoted to recent progress in both linear and nonlinear
analysis in the context of approximation theory, partial differential equations,
topological analysis, function theory and a variety of applications.
Some of the topics dealt with include: New results and open problems on the theory of
functions with minimal critical set, Marcinkiewicz inequalities, maximum modulus of
polynomials, variational inequalities, generalizations of Ky Fan minimax inequality,
hypergeometric series, operational techniques and their applications in analytic and
univalent function theory, non linear boundary value problems, a higher order neutral
difference equation, vector analogues of Sturm-Liouville operators, on a generalized
Sobolev space, gyrovector spaces in the service of hyperbolic geometry, applications
of Cartanšs method, a topological generalization of the theorems of Gale-Nikaido
and Mas Colell.
Edited by Themistocles M. Rassias, National Technical University of Athens, Greece
Collection of original refereed papers
Dec. 1988, ISBN 1-57485-43-1, pp. 200, US$65.
In this volume we present articles devoted to recent progress in both linear
and nonlinear analysis in the context of approximation theory, partial differential
equations, topological analysis, function theory and a variety of applications.
functions with minimal critical set, Marcinkiewicz inequalities on maximum modulus
of polynomials, variational inequalities, generalizations of Ky Fan minimax
inequality, hypergeometric series, operational techniques and their applications
in analytic and univalent function theory, non linear boundary value problems,
a higher order neutral difference equation, vector analogues of Sturm-Liouville
operators, on a generalized Sobolev space, gyrovector spaces in the service of
hyperbolic geometry, applications of Cartans method, a topological generalization
of the theorems of Gale-Nikaido and Mas Colell.
SERGIU ION VACARU, Academy of Sciences of Moldova, Republic of Moldova and
The Institute for Basic Research, U.S.A.
Dec. 1998, ISBN 1-57485-032-6, pp. 450, US$85
This is the first monograph on the geometry of locally anisotropic physics.
The main subjects are the theory of field interactions, strings and diffusion
processes on spaces, superspaces and isospaces with higher order anisotropy
and inhomogeneity. The approach proceeds by developing the concept of higher order
anisotropic (super)space which unify the logical and mathematical aspects of
modern Kaluza-Klein theories and generalized Lagrange and Finsler geometry
and leads to modelling of physical processes on higher order fiber (super) bundles
provided with nonlinear and distinguished connections and metric structures.
The view adopted is that a general field theory should incorporate all possible
anisotropic and stochastic manifestations of classical and quantum interactions, and,
in consequence, a corresponding modification of basic principles and mathematical
methods in formulation of physical theories. This book can be also considered as
a pedagogical survey on the mentioned subjects.
RADU MIRON , Univ. Al.I.Cuza Iasi, Romania;
Romanian Academy of Sciences and
The Institute for Basic Research, Italy and U.S.A.
1998, ISBN 1-57485-033-4, pp. 230, US$65
The Miron's monograph is devoted to the geometry of higher-order
Finsler spaces F(k)n. Whole of his theory is based on the fundamental ideas
from the higher order Lagrangian dynamics. Therefore in this book are
studied:
Variational problems for the Lagrangians of higher order, Lagrange
equations, Noether theorems, Jacobi-Ostrogradski momenta,Hamilton-Jacobi
equations, higfher order energies, laws of conservation, canonical k-spray,
nonlinear connection, linear connections and them structure equations, the
geometrical model of a higher order Finsler space
and a theory of subspaces. Here appear, for the firat time a correct
definition of the notion of higher order Finsler space and a systematical
study of its geometry. Also, is given the solution of the famous problem
of prolongation of Riemann spaces to the jet bundle of higher order and the
same problem for the prolongation of the Finsler spaces. In this way one
obtains the most interesting examples of higher order Finsler spaces,
extremlly useful in the construction of geometrical models for theoretical
physics, higher order analytical mechanics, engineering, biology etc.
Edited by Themistocles M. Rassias, National Technical University
of Athens, Athens, Greece
Collection of original refereed papers
Dec. 1998, ISBN 1-57485-041-5, pages 200, US$65
In this volume we present articles involving theory and applications of
approximations in a variety of contexts.
Some of the topics dealt with include: exact inequalities for norms of
intermediate derivatives of half-integer order and some of their applications,
asymptotic approximation by entire functions with positive coefficients,
bounds for orthogonal polynomials and other families of special
functions, spline interpolation via matrix factorization , optimal
oscillation points for polynomials of restricted growth on the
real line, special Lagrange and Hermite interpolation processes,
analytic continuation of the generalized hypergeometric series near
unit argument with emphasis on the zero- balanced series,on a class
of analytic functions with negative coefficients for operator on
Hilbert space, Hyers-Ulam-Rassias stability of functional equations
in approximation theory, a new abstract approximation theorem, as
well as best approximation and coincidence theorems in topological spaces.
Edited by Themistocles M. Rassias, National Technical University of Athens, Greece
Dec. 1998, ISBN 1-57485-044-X, pages 320, US $ 70
Nonlinear Mathematical Analysis and Applications is devoted to recent
advances in pure and applied analysis in the context of nonlinear partial
differential equations, special aspects of nonlinear functional analys
approximation theory, inequalities and topics in mathematical physics.
Subjects dealt with in this volume include : nonlinear transforms
and analyticity of functions, some classes of multilinear and multilateral
generating functions, optimality conditions for approximation problems,
some multi-dimensional integral inequalities, variational inequalities,
iterative methods for nonlinear problems, fixed point theory, monotone
sequences, generalized topological characteristics of nonlinear Fredholm
and monotone maps and solvability of operator inclusions, minimal
surfaces, approximation and numerical solution for nonlinear free
boundary problems, the local conservation laws basis for one-dimensional
gas dynamics, Hamiltonian symmetries, Euler-Darboux equation, asymptotic of
viscoelastic model solution when viscous coefficient tends to zero,
as well as existence theorems in Nelsonšs stochastic mechanics
on Riemannian manifolds and space-times of general relativity.
Edited by T. VOUGIOUKLlS (Democritos Univ., Trace, Greece.
and IRB, Monteroduni, Italy)
Proceedings of the First International Workshop on New
Frontiers in Hyperstructures held at the IBR, Castle Prince
Pignatelli , Monteroduni (IS), Molise, Italy, August 1995
1996, ISBN 1-57485-008-3, 236 pages, US$70
Hyperstructures are some of the most advanced mathematical structures
conceived until now. This collection of original, refereed articles
presents for the first time a formulation of hyper-structures with an
invariant hyperunit which permits their first applications on record in
other branches of mathematics, physics, theoretical biology and all
quantitative sciences in general. The first hyperextension on record of
the Lie-Santilli iso- and geno-algebras is also presented. This
momentous collection includes a variety of advances in conventional
lines of research in hyperstructures, such as: hyperstructures
associated with character algebras; construction of hypergroups,
W-hypergroups and H<sub V>- hyperstructures; very thin
hyper-structures; quotient of P-H<sub V> rings; and other advanced
topics. This title is recommended to all scholars interested in the most advanced
mathematical methods currently available.
Edited by C. T. TSAGAS (Aristotle Univ., Greece, and IRB Monteroduni,
Italy, and Palm Harbor, USA)
Proceedings of the First International Workshop on New Frontiers in
Mathematics held at the IRB, Castle Prince Pignatelli , Monteroduni
(IS), Molise, Italy, August 1995
1996, ISBN 1-57485-009-1, 455 pages, US$80
This is a collection of original refereed articles on the ultimate
frontiers of contemporary knowledge in algebras, groups, geometries and
related fields.
The second part presents
contributions in local-differential geometries including advances in:
The third part presents
contributions in algebras, groups and related fields, including advances
in:
on generalized structurable algebras;
gauge fields;
W. G. BOSKOFF (Univ. Ovidius, Constanta, Romania and IRB,
Monteroduni, Italy)
1996, ISBN 1-57485-007-5. 169 pages, US$60
This is the only original monograph on Barbilian spaces existing in
the mathematical literature, with a short historical perspective and the
most recent results, some of which are original. After pointing out the
contribution of imaginary elements in geometry to create geometrical
transforms, a projective model of Lobacevski's hyperbolic geometry
appears as the proper interpretation of the group of projectivity of the
circle. The Barbilian distance which connects this model by Poincare's
model of the Lobacevski hyperbolic geometry will highlight a general
procedure of metrization with applications in Riemannian spaces.
Generalized Lagrangian spaces, constant curvature geomerry. This
monograph is indispensable to all geometers.
J. LOHMUS, E. PAAL and L. SORGSEPP (Estonian Acad. of Sciences, Tartu;
IRB, Monteroduni, Italy, and Palm Harbor, USA)
Monograph winner of the 1994 Estonia Science Award
1994, ISBN 0-911767-71-1, 260 pages, US$75
This is the only original monograph on nonassociative algebras in
physics existing in the recent literature, with an emphasis on the
historical perspective and the most advanced recent applications. After
due emphasis on the contributions of Sophus Lie, the monograph presents:
This is an
indispensable text for all scientific libraries.
G. A. SARDANASHVILY (Moscow State Univ.Russia)
1993, ISBN 0-911767-60-6, 162 pages, US$60
After appearing in the mathematical literature, jet manifolds and
multisymplectic structures remained lingering for a number of years, but
lately have proved to be of physical interest.
This is one of the very
few books in the field presenting:
This is an interesting book...I heartily recommend this book for
differential geometers and physicists...it will be also very useful for
students beginning their research in the subject. Indeed, the book is
well written and contains many examples.
MATHEMATICAL REVIEWS
T. VOUGIOUKLIS (Democritus Univ. of Thrace, Greece)
1994, ISBN 0-91176-86-X, 190 pages, US$65
This book deals with the advanced field of mathematics known as
classical algebraic hyper-structures (or multivalued algebras) with at
least one hyperoperation (multivalued operation), and includes
semihypergroups, hypergroups, hyperrings, hyperfields, hypermatrices,
etc., with further generalizations in which the conventional axioms of
associativity, commutativity and distributivity are replaced by the weak
ones. The main topic of this book is the study of the representations of
hypergroups via generalized permutations and hypermatrices. The main
tools used in the study are the smallest equivalence relations in
hyperstructures under which the quotient yields a corresponding
structure. Several new classes of hyperstructures are introduced, such
as the very thin hyperstructures, the P-hyperstructures, and others. The
content of this book has direct applications in various branches of
mathematics, including combinatorics, field theory, finite geometry,
cryptography, computer science, etc. This book is highly recommended to
pure and applied mathematicians and graduate students in mathematics.
Edited by M. STEFANESCU (Ovidius Univ., Constanta Rumania)
Proceedings of the Fifth International Congress on Algebraic
Hyperstructures and Applications, held at Al. I. Cuza Univ., Iasi,
Romania,July 1993
1994, ISBN 0-911767-76-2, 300 pages, US$80
This volume contains four review and twenty research papers presented
at the meeting. It identifies the state-of-the-art in algebraic
hyperstructures with advanced applications in
informatics, combinatorics and geometry. The volume is highly
recommended to mathematicians and theoreticians in pure and applied
mathematics.
Edited by J. V. KADEISVILI (Intern. Center for Phys.,
Alma-Ata, Kazakhstan)
Collection of original refereed papers dedicated to Hanno Rund
1994, ISBN 0-911767-80-0, 440 pages, US$90
This is a unique collection of original papers by former graduate
students and colleagues of the late Hanno Rund (1925-1993).
The
collection contains a number of potentially seminal studies, such as:
Analysis Geometry and Groups:
Edited by H. M. SRIVASTAVA (Univ. of Victoria, Canada) and
Th. M. RASSIAS (Univ. of La Verne, Greece)
Collection of original and refereed articles
1993 ISBN 0-911767-59-2, two volumes, 715 pages, US$120 per
set (hard-bound US$180 per set, ISBN 0-911767-85-9)
Geometry, function theory and other fields continue to be influenced
by the everlasting contribution by Georg Friedrich Bernhard Riemann
(1826-1866). The purpose of this collection is to include refereed and
edited, original research and survey articles by eminent and leading
researchers in these areas. Many of the articles provide the
state-of-the-art presentation of their topics. This collection is
recommended to teachers, researchers and graduate students in various
areas of the mathematical and physical sciences.
Edited by Th. M. RASSIAS (Univ. of La Verne, Athens, Greece) and
J. TABOR (Pedagogical Univ., Cracow, Poland)
Collection of original refereed articles
1994, ISBN 0-911767-64-9, 155 pages, US$60
This book provides an account of the most important research results
which have recently been obtained in the new field of nonlinear
mathematics now called 'Hyers-Ulam stability of
mappings'. The articles provide an authoritative and logically balanced
presentation of the different approaches and problems of functional
equations which are connected with the stability of approximate
homomorphisms. The volume, which is dedicated to D. H. Hyers and S. M.
Ulam, the founders of this new field of mathematics, is recommended to
professional mathematicians and students at the graduate and
postgraduate levels.
C. BALTZER et al. (Michigan State Univ., East Lansing, MI)
1984, ISBN 0-911767-30-4, 540 pages, US$50
Gamma Rings
S. KYUNO (Tohoku Gakuin Univ., Japan)
1991, ISBN 0-911767-49-5, 540 pages, US$40
Harmonic Analysis and Homogeneous
Spaces of SO(1,2)
Yi. A. VERDIEV (Azerbaijan Academy of Sciences, Baku)
Foreword by N. Ya. VILENKIN (Russia Academy of Sciences)
1988, ISBN 0-911767-40-1, 150 pages, US$50
Algebras and Differential Equations
S. WALCHER (Techn. Univ., Munchen, Germany)
1991, ISBN 0-911767-48-7, 190 pages, US$50
Lie Algebras and Flexible Lie-Admissible Algebras
H. C. MYUNG (Univ. of Northern Iowa, Cedar Falls)
1982, ISBN 0-911767-01-0, 330 pages, US$50
Advances in Discrete Mathematics and Computer Sciences
Edited by D. F. HSU (Fordham Univ., New York)
VOL. I: Neofields and Combinatorial Designs
1985, ISBN 0-911767-26-6, 400 pages, US$50
VOL. II: Complete Mappings
1986, ISBN 0-911767-38-X, 420 pages, US$50
VOL. III: Gradient Projection Methods in Linear and Nonlinear
Programming,
1988, ISBN 0-911767-47-9, 342 pages, US$60
Proceedings of the Conference on Groups and Geometry
dedicated to R. H. Bruck
Edited by D. W. CROWE, J. M. OSBORN and L. SOLOMON (Univ. of Wisconsin,
Madison)
1985, ISBN 0-911767-44-4, 350 pages, US$40
2. TITLES FROM THE UKRAINE ACADEMY OF SCIENCES, KIEV
Distributed by the HADRONIC PRESS
Available in stock in the USA
Santilli's Isotopies of Contemporary Algebras,
Geometries and Relativities
J. V. KADEISVILI (Div. of Math., Inst. for Basic Research,
Palm Harbor, Florida, USA)
1997 ISBN 0-911767-55-X, 450 pages, US$80
Description of First Edition of 1991: After reviewing the foundations of Santilli's isotopies of fields,
spaces and algebras, the book presents a detailed description of
the isotopies of the symplectic, affine and Riemannian
geometries whlch are nonlinear in the coordinates as well as velocities,
nonlocal-integral in all variables and nonpotential.
The book then presents Santilli's isogeneral,
isospecial and isogalilean relativities for the description of interior
dynamical problems (such as a satellite during re-entry in atmosphere
or a neutron in the core of a neutron star)
while preserving the axioms of the exterior problem in vacuum.
Mathematical Foundations of the Lie-Santilli Theory
D.S.SOURLAS (Univ of Patras, Greece) and C. T. TSAGAS (Univ. of
Thessaloniki, Greece)
1993, ISBN 0-911767-65-7, 230 pages, US$75
The Lie-Santilli theory is a nonlinear, nonlocal-integral and
nonhamiltonian, yet axiom-preserving isotopy of the conventional Lie
theory which, as such, is acquiring a fundamental role in various
branches of science. This first monograph in the field, ever written by
mathematicians, presents:
The book is recommended to all scholars interested in
fundamental mathematical advances and indispensable for all mathematlcs
libraries.
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