Series: Mathematiques et Applications, Vol. 46
2005, XII, 179 p., Softcover
ISBN: 3-540-25152-9
About this textbook
Par sa nature pluridisciplinaire, ce livre s'adresse a un large
public de mathematiciens, physiciens et ingenieurs s'interessant
aux aspects theoriques des phenomenes periodiques, de meme qu'aux
etudiants en sciences de la vie interesses par les outils
mathematiques de la modelisation. Les oscillations complexes
mises en evidence dans les systemes physiologiques s'analysent
par des modeles. Cet ouvrage se propose de presenter et de
developper les mathematiques necessaires a leur comprehension. On
presente en particulier les notions d'excitabilite, de
bistabilite, de synchronisation et d'oscillations en salves dans
le cadre de l'analyse qualitative.
Table of contents
1. Introduction a la dynamique qualitative et a la theorie des
oscillations.- 2. La theorie de la stabilite.- 3. La theorie des
bifurcations.- 4. La theorie classique des perturbations et la
theorie des perturbations singulieres.- 5. Systemes d’oscillateurs
couples.- 6. Solutions ondes stationnaires et systemes dynamiques.-
7. Electrophysiologie, synchronisation et rythme cardiaque,
oscillations en salves.- Litterature.- Index.
Series: Mathematiques et Applications, Vol. 47
2005, XI, 212 p., Softcover
ISBN: 3-540-25313-0
About this textbook
Systemes multi-echelles est une introduction a la problematique
des systemes multi-echelles du point de vue du mathematicien
applique. Il se compose d'une mosaique d'exemples dont le seul
lien est d'appartenir a la tres grande famille des problemes
issus de la physique au sens large qui presentent pour leur
modelisation et leur simulation cette difficulte essentielle de
comporter en leur sein des echelles de temps ou d'espace tres
differentes.
Table of contents
1.Modeles micro-macro pour les solides.- 2.Techniques
d'homogeneisation.- 3.Simulation moleculaire.- 4.Modeles micro-macro
pour les fluides.- 5.Cinetique chimique.- 6.Vers une unite des
approches.- References.- Index.
Series: Springer Monographs in Mathematics,
2005, XII, 519 p., Hardcover
ISBN: 3-540-25540-0
About this book
Integral Closure gives an account of theoretical and algorithmic
developments on the integral closure of algebraic structures.
These are shared concerns in commutative algebra, algebraic
geometry, number theory and the computational aspects of these
fields. The overall goal is to determine and analyze the
equations of the assemblages of the set of solutions that arise
under various processes and algorithms. It gives a comprehensive
treatment of Rees algebras and multiplicity theory - while
pointing to applications in many other problem areas. Its main
goal is to provide complexity estimates by tracking numerically
invariants of the structures that may occur.
This book is intended for graduate students and researchers in
the fields mentioned above. It contains, besides exercises aimed
at giving insights, numerous research problems motivated by the
developments reported.
Table of contents
Preface.- Introduction.- Numerical Invariants of a Rees Algebra.-
Hilbert Functions and Multiplicities.- Depth and Cohomology of
Rees Algebras.- Divisors of a Rees Algebra.- Koszul Homology.-
Integral Closure of Algebras.- Integral Closure and Normalization
of Ideals.- Integral Closure of Modules.- How To.- References.-
Notation and Terminology.- Index.
Series: Lecture Notes in Mathematics, Vol. 1868
2005, Approx. 200 p., Softcover
ISBN: 3-540-25787-X
About this book
Posn(R) and Eisenstein Series provides an introduction, requiring
minimal prerequisites, to the analysis on symmetric spaces of
positive definite real matrices as well as quotients of this
space by the unimodular group of integral matrices. The approach
is presented in very classical terms and includes material on
special functions, notably gamma and Bessel functions, and
focuses on certain mathematical aspects of Eisenstein series.
Table of contents
GLn (R) actions on Posn(R).- Measures, Integration, and Quadratic
Model.- Special Functions on Posn(R).- Invariant Differential
Operators on Posn(R).- Poisson duality and zeta functions.-
Eisenstein Series: First Part.- Geometric and Analytic Estimates.-
Eisenstein Series: Second Part.
2005, XII, 441 p., Hardcover
ISBN: 0-387-25529-X
About this book
In the spring of 1976, George Andrews of Pennsylvania State
University visited the library at Trinity College, Cambridge, to
examine the papers of the late G.N. Watson. Among these papers,
Andrews discovered a sheaf of 138 pages in the handwriting of
Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's
lost notebook." Its discovery has frequently been deemed the
mathematical equivalent of finding Beethoven's tenth symphony.
The "lost notebook" contains considerable material on
mock theta functions and so undoubtedly emanates from the last
year of Ramanujan's life. It should be emphasized that the
material on mock theta functions is perhaps Ramanujan's deepest
work. Mathematicians are probably several decades away from a
complete understanding of those functions. More than half of the
material in the book is on q-series, including mock theta
functions; the remaining part deals with theta function
identities, modular equations, incomplete elliptic integrals of
the first kind and other integrals of theta functions, Eisenstein
series, particular values of theta functions, the Rogers-Ramanujan
continued fraction, other q-continued fractions, other integrals,
and parts of Hecke's theory of modular forms.
Table of contents
Preface.- Introduction.- The Rogers?Ramanujan Continued Fraction
and Its Modular Properties.- Explicit Evaluations of the
Rogers?Ramanujan Continued Fraction.- A Fragment on the
Rogers?Ramanujan and Cubic Continued Fractions.- The
Rogers?Ramanujan Continued Fraction and Its Connections with
Partitions and Lambert Series.- Finite Rogers?Ramanujan Continued
Fractions.- Other q-continued Fractions.- Asymptotic Formulas for
Continued Fractions.- Ramanujan’s Continued Fraction for (q2; q3)8/(q;
q3)8.- The Rogers?Fine Identity.- An Empirical Study of the
Rogers?Ramanujan Identities.- Rogers?Ramanujan?Slater Type
Identities.- Partial Fractions.- Hadamard Products for Two q-Series.-
Integrals of Theta-functions.- Incomplete Elliptic Integrals.-
Infinite Integrals of q-Products.- Modular Equations in Ramanujan’s
Lost Notebook.- Fragments on Lambert Series.- Location Guide.-
Provenance.- References.- Index.
Series: Developments in Mathematics, Vol. 14
2005, XVI, 219 p. 13 illus., Hardcover
ISBN: 0-387-24972-9
About this book
This volume focuses on various aspects of zeta functions:
multiple zeta values, Ohno’s relations, the Riemann hypothesis,
L-functions, polylogarithms, and their interplay with other
disciplines.
Eleven articles on recent advances are written by outstanding
experts in the above-mentioned fields. Each article starts with
an introductory survey leading to the exciting new research
developments accomplished by the contributors.
This book will become the major standard reference on the recent
advances on zeta functions.
Table of contents
Preface.- Conference schedule.- List of participants.- Gollnitz-Gordon
partitions with weights and parity conditions.- Partition
Identities for the Multiple Zeta Function.- A perturbative theory
of the evolution of the center of typhoons.- Algebraic Aspects of
Multiple Zeta Values.- On the local factor of the zeta function
of quadratic orders.- Sums involving the Hurwitz zeta-function
values.- Crystal Symmetry Viewed as Zeta Symmetry.- Sum relations
for multiple zeta values.- The Sum Formula for Multiple Zeta
Values.- Zeta functions over zeros of general zeta and L-functions.-
Hopf Algebras and Transcendental Numbers.
Series: Nonconvex Optimization and Its Applications, Vol. 79
2005, XII, 1184 p., Hardcover
ISBN: 0-387-24209-0
About this book
This book discusses a new discipline, variational analysis, which
contains the calculus of variations, differential calculus,
optimization, and variational inequalities. To such classic
branches of mathematics, variational analysis provides a uniform
theoretical base that represents a powerful tool for the
applications. The contributors are among the best experts in the
field.
Table of contents
PART 1
The Work of G. Stampacchia in Variational Inequalities (J.-L.
Lions)
In Memory of Guido Stampacchia (M.G. Garroni)
The Collaboration between Guido Stampacchia and Jacques-Louis
Lions On Variational Inequalities (E. Magenes)
In Memory of Guido Stampacchia (O.G. Mancino)
Guido Stampacchia (S. Mazzone)
Memories of Guido Stampacchia (L. Nirenberg)
In Memory of Guido Stampacchia (C. Sbordone)
Guido Stampacchia, My Father (G. Stampacchia)
PART 2
Convergence and Stability of a Regularization Method for Maximal
Monotone Inclusions and its Applications to Convex Optimization (Ya.
I. Alber, D. Butnariu and G. Kassay)
Partitionable Mixed Variational Inequalities (E. Allevi, A.
Gnudi, I.V. Konnov and E.O. Mazurkevich)
Irreducibility of the Transition Semigroup Associated with the
Two Phase Stefan Problem (V. Barbu and G. Da Prato)
On Some Boundary Value Problems for Flows with Shear Dependent
Viscosity (H. Beirao da Veiga)
Homogenization of Systems of Partial Differential Equations (A.
Bensoussan)
About the Duality Gap in Vector Optimization (G. Bigi and M.
Pappalardo)
Separation of Convex Cones and Extremal Problems (V. Boltyanski)
Infinitely Many Solutions for the Dirichlet Problem via a
VariationalPrinciple of Ricceri (F.Cammaroto, A.Chinni, and B. Di
Bella)
A Density Result on the Space (A.O. Caruso and M.S. Fanciullo)
Linear Complementarity since 1978 (R.W. Cottle)
Variational Inequalities in Vector Optimization (G.P. Crespi, I.
Ginchev and M. Rocca)
Variational Inequalities for General Evolutionary Financial
Equilibrium (P. Daniele)
Variational Control Problems with Constraints via Exact
Penalization (V.F. Demyanov, F. Giannessi and G.Sh. Tamasyan)
Continuous Sets and Non-Attaining Functionals in Reflexive Banach
Spaces (E. Ernst and M. Thera)
Existence and Multiplicity Results for a Nonlinear Hammerstein
Integral Equation (F. Faraci)
Differentiability of Weak Solutions of Nonlinear Second Order
Parabolic Systems with Quadratic Growth and Non Linearity (L.
Fattorusso)
An Optimization Problem with Equilibrium Constraint in Urban
Transport (P. Ferrari)
Sharp Estimates for Green’s Functions: Singular Cases (M.G.
Garroni)
First-Order Conditions for Constrained Vector Optimization (I.
Ginchev, A. Guerraggio and M. Rocca)
Global Regularity for Solutions to Dirichlet Problem for Elliptic
Systems with Nonlinearity and with Natural Growth (S. Giuffre and
G. Idone)
Optimality Conditions for Generalized Complementarity Problems (S.
Giuffre, G. Idone and A. Maugeri)
Variational Inequalities for Time Dependent Financial Equilibrium
with Price Constraints (S. Giuffre and S. Pia)
Remarks about Diffusion Mediated Transport: Thinking about Motion
in Small Systems (S. Hastings and D. Kinderlehrer)
Augmented Lagrangian and Nonlinear Semidefinite Programs (X.X.
Huang, X.Q. Yang and K.L. Teo)
Optimality Alternative: a Non-Variational Approach to Necessary
Conditions (A.D. Ioffe)
A Variational Inequality Scheme for Determining an Economic
Equilibrium of Classical or Estended Type (A. Jofre, R.T.
Rockafellar and R.J.-B. Wets)
On Time Dependent Vector Equilibrium Problems (A. Khan and F.
Raciti)
On Some Nonstandard Dynamic Programming Problems of Control
Theory (A.B. Kurzhanski and P. Varaiya)
Properties of Gap Function for Vector Variational Inequality (S.J.
Li and G.Y. Chen)
Zero Gravity Capillary Surfaces and Integral Estimates (G.M.
Lieberman)
Asymptotically Critical Points and Multiple Solutions in the
Elastic Bounce Problem (A. Marino and C. Saccon)
A Branch-and-Cut to the Point-to-Point Connection Problem on
Multicast Networks (C.N. Meneses, C.A.S. Oliveira and P.M.
Pardalos)
Variational Inequality and Evolutionary Market Disequilibria: The
Case of Quantity Formulation (M. Milasi and C. Vitanza)
Numerical Approximation of Free Boundary Problem by Variational
Inequalities. Application to Semiconductor Devices (M. Morandi
Cecchi and R. Russo)
Sensitivity Analysis for Variational Systems (B.S. Mordukhovich)
Stable Critical Points for the Ginzburg Landau Functional on Some
Plane Domains (M.K. Venkatesha Murthy)
The Distance Function to the Boundary and Singular Set of
Viscosity solutions of Hamilton-Jacobi Equation (L. Nirenberg)
Lp-Regularity for Poincare Problem and Applications (D.K.
Palagachev)
Minimal Fractions of Compact Convex Sets (D. Pallaschke and R.
Urbanski)
On Generalized Variational Inequalities (B. Panicucci and M.
Pappalardo)
Bounded (Hausdorff) Convergence: Basic Facts and Applications (J.-P.
Penot and C. Zalinescu)
Control Processes with Distributed Parameters in Unbounded Sets.
Approximate Controllability with Variable Initial Locus (G.
Pulvirenti, G. Santagati and A. Villani)
Well Posedness and Optimization Problems (L. Pusillo)
Semismooth Newton Methods for Shape-Preserving Interpolation,
Option Price and Semi-Infinite Programs (L. Qi)
Holder Regularity Results for Solutions of Parabolic Equations (M.A.
Ragusa)
Survey on the Fenchel Problem of Level Sets (T. Rapcsak)
Integral Functionals on Sobolev Spaces Having Multiple Local
Minima (B. Ricceri)
Aspects of the Projector on Prox-Regular Sets (Stephen M.
Robinson)
Application of Optimal Control Theory to Dynamic Soaring of
Seabirds (G. Sachs and P. Bussotti)
On The Convergence of the Matrices Associated to the Adjugate
Jacobians (C. Sbordone)
Quasi-Variational Inequalities Applied to Retarded Equilibria in
Time-Dependent Traffic Problems (L. Scrimali)
Higher Order Approximation Equations for the Primitive Equations
of the Ocean (E. Simonnet, T. Tachim Medjo and R. Temam)
Hahn-Banach Theorems and Maximal Monotonicity (S. Simons)
Concrete Problems and the General Theory of Extremum (V.M.
Tikhomirov)
Numerical Solution for Pseudomonotone Variational Inequality
Problems by Extragradient Methods (F. Tinti)
Regularity and Existence Results for Degenerate Elliptic
Operators (C. Vitanza and P. Zamboni)
Vector Variational Inequalities and Dynamic Traffic Equilibria (X.Q.
Yang and H. Yu)
A New Proof of the Maximal Monotonicity of the Sum using the
Fitzpatrick Function (C. Zalinescu)
Contributors