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**CONTENTS**

1.TITLES FROM HADRONIC PRESS

2.TITLES FROM UKRAINE ACADEMY OF SCIENCES

**Fractal Dimensions and Dynamical Systems**

**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.

**Hyers-Ulam-Rassias Stability of Functional Equations in
Mathematical Analysis**

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.

**Nonlinear Analysis in Geometry and Topology **

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.

**Mathematical Analysis and Applications**

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.

**Complex Analysis in Several Variables**

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.

** Interactions, Strings and Isotopies
in Higher Order Anisotropic Superspaces**

**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.

**THE GEOMETRY OF HIGHER - ORDER FINSLER SPACES**

**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.

**Approximation Theory and Applications**

**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.

**Nonlinear Mathematical Analysis and Applications**

** 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.

**New Frontiers in Hyperstructures**

**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.

New Frontiers in Algebras, Groups and Geometries

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 first part presents contributions in Santilli's nonlinear, nonlocal and noncanonical isotopies of contemporary mathematical methods, including advances in:

The second part presents contributions in local-differential geometries including advances in:

- Globalization of Santilli's isofields, isospaces and isogeometries;
- Lie-Santilli isotheory;
- Classification of Lie- Santilli isoalgebras;
- Isotopies of hypercomplex numbers;
- Integral lifting of the Euclidean, Minkowskian, symplectic affine and Riemannian geometries for the geometrization of nonlocal interior dynamical systems of extended, nonspherical and deformable bodies moving within physical media.
The third part presents contributions in algebras, groups and related fields, including advances in:

- Higher order sprays for the characterization of non-first-order-lagrangian systems;
- The geometry of fluctuations in non-equilibrium statistical mechanics and quantum gravity;
- The geometry of the six-dimensional sphere;
- Principal bundles in gauge theories;
- Fractional calculus; and other topics.

- Semigroups; generalized Knizhnik-Zamolo-dchikov structures;
- Studies

on generalized structurable algebras;- Nonassociative

gauge fields;- Special nilpotent Lie algebras;
- and related studies.

Hyperbolic Geometry and Barbilian Spaces

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.

Nonassociative Algebras in Physics

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.

- The work of Albert, Jordan, Santilli and others,
- Nonassociativity in mathematics and physics,
- Limit transition between algebras, contractions and deformations,
- Cayley-Dikson algebras and their representations,
- Dirac equation and the problem of self- duality in the hypercomplex formalism of octonions and sedenions,
- Moufang-Mal'tsev symmetries and conservation laws.

Gauge Theory in Jet Manifolds

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

- The background notions of fibred manifolds,
- A detailed presentation of first, second and higher order jet manifolds and connections, including differential operators defined on them,
- Lagrangian formalism on jet manifolds,
- The multimomentum Hamiltonian counterpart,
- Detailed description of constraints including hyper-regular, semi- regular and almost regular Lagrangian densities,
- Gauge theories with basic advances in gravitation, spontaneous symmetry breaking Dirac Fermion fields, and other topics.

Hyperstructures and their Representations

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.

Algebraic Hyperstructures and Applications

Edited byM. 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.

The Mathematical Legacy of Hanno Rund

Edited byJ. 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:

- A comprehensive generalization of number theory,
- The initiation of the nonlinear-integral isorepresentation theory,
- Hypersurfaces of quaternionic projective spaces,
- Studies on Hardy space,
- Group properties of local loops and modules,
- Subneofields and finite neofields,
- Studies on the Lotka-Volterra algebras,
- Integral axiom-preserving lifting of Lie's theory and contemporary geometries, and other advances.

Analysis Geometry and Groups:

A Riemann Legacy Volume

Edited byH. 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.

Stability of Mappings of Hyers-Ulam Type

Edited byTh. 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.

Tomber's Bibliography and Index in Nonassociative Algebras

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.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.

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.

- The background isotopies of rings, fields, vector spaces, modules, transformations, algebras and groups,
- The structure of the Lie-Santilli theory, with an in depth study of the nonlinear-nonlocal-noncanonical isotopies of universal enveloping algebras and of the celebrated Lie's First, Second and Third Theorems along their original proposal of 1978,
- The isotopies of manifolds and tensors fields defined on them,
- The geometric counterpart of the Lie-Santilli algebras, the isotopies of exterior forms and of the symplectic geometry,
- The integral isotopies of manifolds, and other basic aspects.

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