Yoshitomo Baba (Osaka Kyoiku University, Japan) & Kiyoichi Oshiro (Yamaguchi University, Japan)

CLASSICAL ARTINIAN RINGS AND RELATED TOPICS

Quasi-Frobenius rings and Nakayama rings were introduced by T Nakayama in 1939. Since then, these classical artinian rings have continued to fascinate ring theorists with their abundance of properties and structural depth. In 1978, M Harada introduced a new class of artinian rings which were later called Harada rings in his honour. Quasi-Frobenius rings, Nakayama rings and Harada rings are very closely interrelated. As a result, from a new perspective, we may study the classical artinian rings through their interaction and overlap with Harada rings.

The objective of this seminal work is to present the structure of Harada rings and provide important applications of this structure to the classical artinian rings. In the process, we cover many topics on artinian rings, using a wide variety of concepts from the theory of rings and modules. In particular, we consider the following topics, all of which are currently of much interest and ongoing research: Nakayama permutations, Nakayama automorphisms, Fuller's theorem on i-pairs, artinian rings with self-duality, skew-matrix rings, the classification of Nakayama rings, Nakayama group algebras, the Faith conjecture, constructions of local quasi-Frobenius rings, lifting modules, and extending modules. In our presentation of these topics, the reader will be able to retrace the history of artinian rings.

Contents:

• A Theorem of Fuller
  
• Harada Rings
  
• The Structure Theory of Left Harada Rings
  
• Self-Duality of Left Harada Rings
  
• Skew Matrix Rings
  
• The Structure of Nakayama Rings
  
• Modules over Nakayama Rings
  
• Nakayama Algebras
  
• Local QF-rings

Readership: Researchers in algebra.

300pp Pub. date: Aug 2009
ISBN: 978-981-4287-24-1

Mariagrazia Bianchi (University of Milano, Italy) , Patrizia Longobardi (University of Salerno, Italy) , Mercede Maj (University of Salerno, Italy) , & Carlo Maria Scoppola (University of L'Aquila, Italy)

ISCHIA GROUP THEORY 2008
Proceedings of the Conference in Group Theory, Naples, Italy, 1 - 4 April 2008

The volume contains a collection of research articles by leading experts in group theory, and reports of several accessible surveys of recent research in the area. The compilation provide an overview of the diversity of themes and applications that interest today's group theorists. The topics covered in this volume include: character theory, combinatorial group theory, varieties of groups, conjugacy classes, profinite groups, graphs connected with groups, subgroup structure, representation theory.

Contents:

• Some Exceptional Minimal Situations by Finite p-Groups (Z Janko)
  
• Character Tables of Groups Where All Nonlinear Irreducible Characters Vanish Off the Center (M L Lewis)
  
• Large Normal and Characteristic Subgroups Satisfying Outer Commutator Identities and Their Applications (E I Khukhro)
  
• Some Simple Locally (Soluble-by-Finite) Groups (M R Dixon et al.)
  
• Regular Limits of Infinite Symmetric Groups (O H Kegel)
  
• Varieties of Groups and the Restricted Burnside Problem (P Shumyatsky & J Caldeira Silva)
  
• The Fundamental Group of a Connected Non-Direct Profinite Graph (W Herfort)
  
• On Blichfeld's Like Congruences and Other Close Characters ? Conjugacy Classes Analogs (D Chillag)
  
• On Abnormal Maximal Subgroups of Finite Groups (A Ballester-Bolinches et al.)
  
• Some Results and Questions Related to the Generating Graph of a Finite Group (A Lucchini & A Maroti)
  
• Soluble Linear Groups with Some Restrictions on Subgroups of Infinite Central Dimension (L A Kurdachenko et al.)
  
• Restrictions of Brauer Characters and (-Partial Characters (J Sangroniz)
  
• Permutation Groups Defined by Unordered Relations (F Dalla Volta & J Siemons)
  
• Transitivity of Properties of 2-Generator Subgroups (C Delizia et al.)
  
• and other papers

Readership: Researchers in group theory.

300pp Pub. date: Aug 2009
ISBN: 978-981-4277-79-2(pbk)

Jiu Ding (The University of Southern Mississippi, USA)
& Aihui Zhou (Chinese Academy of Sciences, China)

NONNEGATIVE MATRICES, POSITIVE OPERATORS, AND APPLICATIONS

Nonnegative matrices and positive operators are widely applied in science, engineering, and technology. This book provides the basic theory and several typical modern science and engineering applications of nonnegative matrices and positive operators, including the fundamental theory, methods, numerical analysis, and applications in the Google search engine, computational molecular dynamics, and wireless communications.

Unique features of this book include the combination of the theories of nonnegative matrices and positive operators as well as the emphasis on applications of nonnegative matrices in?Perron operators both of which play key roles in the statistical and stochastic studies of dynamical systems.

It can be used as a textbook for an upper level undergraduate or beginning graduate course in advanced matrix theory and/or positive operators as well as for an advanced topics course in operator theory or ergodic theory. In addition, it serves as a good reference for researchers in mathematical sciences, physical sciences, and engineering.

Contents:

• Elementary Properties of Nonnegative Matrices
  
• Perron?Frobenius Theory of Nonnegative Matrices
  
• Stochastic Matrices
  
• Applications of Nonnegative Matrices
  
• General Theory of Positive Operators
  
• Spectral Theory of Positive Operators
  
• Markov Operators
  
• Frobenius?Perron Operators
  
• Composition Operators
  
• Approximations of Markov Operators
  
• Applications of Positive Operators

Readership:

Readers in mathematical sciences, physical sciences, and engineering; advanced undergraduates and graduate students in pure mathematics, applied mathematics, and computational mathematics.

364pp Pub. date: Aug 2009
ISBN: 978-981-283-917-6

Anthony W Leung (University of Cincinnati, USA)

NONLINEAR SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS
Applications to Life and Physical Sciences

The book presents the theory of diffusion-reaction equations starting from the Volterra-Lotka systems developed in the eighties for Dirichlet boundary conditions. It uses the analysis of applicable systems of partial differential equations as a starting point for studying upper-lower solutions, bifurcation, degree theory and other nonlinear methods. It also illustrates the use of semigroup, stability theorems and W2ptheory. Introductory explanations are included in the appendices for non-expert readers.

The first chapter covers a wide range of steady-state and stability results involving prey-predator, competing and cooperating species under strong or weak interactions. Many diagrams are included to easily understand the description of the range of parameters for coexistence. The book provides a comprehensive presentation of topics developed by numerous researchers. Large complex systems are introduced for modern research in ecology, medicine and engineering.

Chapter 3 combines the theories of earlier chapters with the optimal control of systems involving resource management and fission reactors. This is the first book to present such topics at research level. Chapter 4 considers persistence, cross-diffusion, and boundary induced blow-up, etc. The book also covers traveling or systems of waves, coupled Navier-Stokes and Maxwell systems, and fluid equations of plasma display. These should be of interest to life and physical scientists.

Contents:

• Positive Solutions for Systems of Two Equations
  
• Positive Solutions for Large Systems of Equations
  
• Optimal Control for Nonlinear Systems of Partial Differential Equations
  
• Persistence, Upper and Lower Estimates, Blowup, Cross-Diffusion and Degeneracy
  
• Traveling Waves, Systems of Waves, Invariant Manifolds, Fluids and Plasma

Readership:

Academic researchers, postgraduates and graduates in differential equations, biomathematics, mathematical modeling, control theory and optimization, mathematicians, engineers, ecologists, biologists, physicists and chemists.

540pp Pub. date: Aug 2009
ISBN: 978-981-4277-69-3