Bøger udgivet af Birkhauser

I The fixed point theorems of Brouwer and Schauder.- 1 The fixed point theorem of Brouwer and applications.- 2 The fixed point theorem of Schauder and applications.- II Measures of noncompactness.- 1 The general notion of a measure of noncompactness.- 2 The Kuratowski and Hausdorff measures of noncompactness.- 3 The separation measure of noncompactness.- 4 Measures of noncompactness in Banach sequences spaces.- 5 Theorem of Darbo and Sadovskii and applications.- III Minimal sets for a measure of noncompactness.- 1 ø-minimal sets.- 2 Minimalizable measures of noncompactness.- IV Convexity and smoothness.- 1 Strict convexity and smoothness.- 2 k-uniform convexity.- 3 k-uniform smoothness.- V Nearly uniform convexity and nearly uniform smoothness.- 1 Nearly uniformly convex Banach spaces.- 2 Nearly uniformly smooth Banach spaces.- 3 Uniform Opial condition.- VI Fixed points for nonexpansive mappings and normal structure.- 1 Existence of fixed points for nonexpansive mappings: Kirk's theorem.- 2 The coefficient N(X) and its connection with uniform convexity.- 3 The weakly convergent sequence coefficient.- 4 Uniform smoothness, near uniform convexity and normal structure.- 5 Normal structure in direct sum spaces.- 6 Computation of the normal structure coefficients in Lp-spaces.- VII Fixed point theorems in the absence of normal structure.- 1 Goebel-Karlovitz's lemma and Lin's lemma.- 2 The coefficient M(X) and the fixed point property.- VIII Uniformly Lipschitzian mappings.- 1 Lifshitz characteristic and fixed points.- 2 Connections between the Lifshitz characteristic and certain geometric coefficients.- 3 The normal structure coefficient and fixed points.- IX Asymptotically regular mappings.- 1 A fixed point theorem for asymptotically regular mappings.- 2 Connections between the ?-characteristic and some other geometric coefficients.- 3 The weakly convergent sequence coefficient and fixed points.- X Packing rates and ø-contractiveness constants.- 1 Comparable measures of noncompactness.- 2 Packing rates of a metric space.- 3 Connections between the packing rates and the normal structure coefficients.- 4 Packing rates in lp-spaces.- 5 Packing rates in Lpspaces.- 6 Packing rates in direct sum spaces.- References.- List of Symbols and Notations.

1 Childhood and Youth. Road to Science.- 2 In the Leningrad University (1926-1932).- 2.1. Entering the University.- 2.2. The Jazz-Band.- 2.3. The Abbot and his Astronomer Friends.- 2.4. First Works in Astrophysics, Geophysics and Popular Science.- 2.5. At the Shenroks on the Vasiliev Island.- 3 At the Leningrad Physicotechnical Institute.- 3.1. Theoretical Physics in St. Petersburg and Petrograd.- 3.2. The Physicotechnical Institute and Its Seminars.- 3.3. "Quantising Free Electrons in a Magnetic Field".- 3.4. "A New Crisis in the Theory of Quanta".- 3.5. Science and Society.- 3.6. Quantum Mechanics in the Early Thirties.- 3.7. Cosmology in the Early Thirties.- 3.8. The Ether and the Theory of Relativity.- 3.9. Styles and Generations.- 3.10. The Physics of Semiconductors and Nuclear Physics.- 4 Hard Times for the Laws of Conservation and for Theoreticians.- 4.1. Three Attempts to Topple the Law of Conservation of Energy.- 4.2. The Hypothesis of Non-conservation and the Arguments of its Supporters.- 4.2.1. Waiting for a Relativistic Theory of Quanta.- 4.2.2. The Neutrino Alternative.- 4.2.3. Non-conservation of Energy, General Relativity, Cosmology and Astrophysics.- 4.3. Non-Physical Arguments Applied to Physics.- 4.4. A Duel in Sorena.- 4.5. The Death of a Non-conservation Hypothesis.- 5 cG?-Physics in Bronstein's Life.- 5.1. An Unsuitable Thesis.- 5.2. The Roots of Bronstein's Interest in cG?-physics.- 5.2.1. Quantum Gravity before Bronstein.- 5.2.2. "The Relationship Between the Physical Theories and Their Relation to the Cosmological Problem".- 5.2.3. At the Sources of Quantum Relativistic Astrophysics.- 5.3. The Quantum Theory of the Weak Gravitational Field.- 5.4. "The Fundamental Differences Between Quantum Electrodynamics and the Quantum Theory of Gravitational Field". The Quantum Gravitational Limits.- 5.4.1. The Problem of ch Measurability.- 5.4.2. cG? Measurability and GR Quantum Limits.- 5.4.3. The Planck Scales in cGh-physics.- 5.4.4. Reception of the Quantum-Gravitational Limits.- 5.5. Physics and Cosmology.- 5.5.1. Cosmology in the Thirties.- 5.5.2. Bronstein's Attitude to Cosmology.- 5.5.3. Red shift, the Relativity Principle and Polarisation of the Vacuum.- 6 Creative Personality.- 6.1. Perceiving the World.- 6.2. Vocation of a Teacher.- 6.3. Science and Literature.- 6.4. Personality.- Afterword.- Afterword to the English Edition. Half a Century Later.- 1. From the KGB-NKVD Archives.- 2. The Last Days in the Cell.- 3. Subnuclear Physics, Matvei Bronstein and Ettore Majorana.- Chronology.- Notes.- Appendix 1. Extract from M.P.Bronstein's paper "Quantentheorie schwacher Gravitationsfelder", 1936.- Appendix 2. M.P.Bronstein's note "Über den Spontanen Zerfall der Photonen", 1936.- Appendix 3. M.P.Bronstein "Inventors of Radiotelegraph" (First chapters of the book).- Photographs.

Free radicals and oxidative damage in biology and medicine: An introduction.- Oxidative metabolism in skeletal muscle.- Strategies to assess oxidative stress.- The course of exercise-induced skeletal muscle fibre injury.- Free radical mechanisms in exercise-related muscle damage.- The effects of exercise, ageing and caloric restriction on protein oxidation and DNA damage in skeletal muscle.- Antioxidant enzyme response to exercise and training in the skeletal muscle.- Glutathione: A key role in skeletal muscle metabolism.- Vitamin E and its effect on skeletal muscle.- Differential susceptibility of skeletal muscle proteins to free radical-induced oxidative damage in vitro.- Oxidative stress and Ca2+ transport in skeletal and cardiac sarcoplasmic reticulum.- Oxidative stress in skeletal muscle atrophy induced by immobilization.- Effect of growth hormone on oxidative stress in immobilized muscles of old animals.- The diaphragm and oxidative stress.- Oxidative damage after ischemia/reperfusion in skeletal muscle.- Oxidative damage in rat skeletal muscle after excessive L-tryptophan and atherogenic diets.- Oxidative stress and muscle wasting of cachexia.- Free radicals and antioxidants in the pathogenesis of alcoholic myopathy.- Drug-induced muscle damage.- Free radicals and diseases of animal muscle.- Therapeutic trials of antioxidants in muscle diseases.

In modern ecotoxicology, fish have become the major vertebrate model, and a tremendous body of information has been accumulated. This volume attempts to summarize our present knowledge in several fields of primary ecotoxicological interest ranging from the use of (ultra)structural modifications of selected cell systems as sources of biomarkers for environmental impact over novel approaches to monitoring the impact of xenobiotics with fish in vitro systems such as primary and permanent fish cell cultures, the importance of early life-stage tests with fish, the bioaccumulation of xenobiotics in fish, the origin of liver neoplastic lesions in small fish species, immunocytochemical approaches to monitoring effects in cytochrome P450-related biotransformation, the impact of heavy metals in soft water systems, the environmental toxicology of organotin compounds, oxidative stress in fish by environmental pollutants to effects by estrogenic substances in aquatic systems.

Einführung.- Wissenschaft an den Universitäten des Mittelalters.- Der Philosoph im 17. Jahrhundert. Selbstbild und gesellschaftliche Stellung.- Wissenschaft und Sozietätsbewegung im 18. Jahrhundert.- The Industrial Revolution and the Growth of Science.- Fortschritt durch Wissenschaft. Die Universitäten im 19. Jahrhundert.- Physik und Physiker im Dritten Reich.- Biologie und politische Macht.- Wissenschaft im heutigen Europa: Aussichten und Probleme.- Literaturauswahl (zur Einführung).- Über die Autoren.

This volume collects contributions from participants in the IWOTA conference held virtually at Lancaster, UK, originally scheduled in 2020 but postponed to August 2021. It includes both survey articles and original research papers covering some of the main themes of the meeting.

Chemokines: Attraction of dendritic cells and role in tumor immunobiology.- Chemokine receptors.- Regulation of gene expression of chemokines and their receptors.- Chemokines and T lymphocytes.- Chemokines and mast cells.- Chemokines and eosinophils.- CXC-chemokines - autocrine growth factors for melanoma and epidermoid carcinoma cells.- Expression of chemokines in dermatoses.

The influence of V.P. Potapov and M.G. Krein on my scientific work.- 1. My first dissertation.- 2. A tilt toward operator theory.- 3. The results of Potapov's group in network theory.- 4. Darlington method in the general theory of passive systems.- 5. Regular j-inner matrix functions and related generalized bitangential problems.- References.- The development of some of V.P. Potapov's ideas. The geometric theory of operators in spaces with indefinite metric.- References.- On the Potapov theory of multiplicative representations.- References.- An operator approach to the Potapov scheme for the solution of interpolation problems.- I. Potapov's method of solution of interpolation problems.- 1. Some information from j-algebra.- 2. Nevanlinna-Pick problem.- 3. The Schur problem.- II. Operator identities and interpolation problems.- 1. Formulation of the problem.- 2. The fundamental matrix inequality.- 3. The transformed inequality.- 4. The solution of nondegenerate interpolation problems.- 5. Weyl discs.- 6. Degenerate interpolation problems and the method of regularization.- 7. Applications of the general theory.- References.- Description of a class of functions which admit an approximation by rational functions with preassigned poles I.- 2. The class PCNM of pseudocontinuable functions.- 3. The Smirnov class N*.- 4. The weighted space PCH (I+, I-) of pseudocontinuable meromorphic functions with prescribed denominators.- 5. G. Ts. Tumarkin's theorem on functions which admit weighted approximation by a sequence of rational functions with preassigned poles.- 6. Formulation of the main approximation theorem.- 7. A fundamental approximation Lemma.- References.- An analysis and extension of V.P. Potapov's approach to problems with applications to the generalized bi-tangential Schur-Nevanlinna-Pick problem and J-inner-outer factorization.- 1. Potapov's approach to the Nevanlinna-Pick problem.- 2. An analysis of Potapov's approach and the AIP.- 3. The abstract interpolation problem.- 4. The AIP and unitary extensions of an isometry.- 5. The generalized bi-tangential Schur-Nevanlinna-Pick (SNP) problem.- 6. Inner-outer factorization of J-contractive matrix-functions.- References.- On the theory of inverse problems for the canonical differential equation.- References.- Addendum.- Some properties of linear-fractional transformations and the harmonic mean of matrix functions.- References.- Modification of V.P. Potapov's scheme in the indefinite case.- 0. Introduction.- 1. Preliminaries.- 2. Basic propositions.- 3. Extensions of the operator S.- 4. Examples.- References.- Inverse problems for equations systems.- 1. Introduction.- 2. Existence theorems.- 3. Classical examples.- 4. Uniqueness theorems.- References.

Heat equation asymptotics of a generalized Ahlfors Laplacian on a manifold with boundary.- Recurrent versus diffusive quantum behavior for time-dependent Hamiltonians.- Perturbations of spectral measures for Feller operators.- A global approach to the location of quantum resonances.- On estimates for the eigen-values in some elliptic problems.- Quantum scattering with long-range magnetic fields.- Spectral invariance and submultiplicativity for Fréchet algebras with applications to pseudo-differential operators and ?* -quantization.- Décroissance exponentielle des fonctions propres pour l'opérateur de Kac: le cas de la dimension > 1.- Second order perturbations of divergence type operators with a spectral gap.- On the Weyl quantized relativistic Hamiltonian.- Spectral asymptotics for the family of commuting operators.- Pseudo differential operators with negative definite functions as symbol: Applications in probability theory and mathematical physics.- One-dimensional Schrödinger operators with high potential barriers.- General boundary value problems in regions with corners.- Some results for nonlinear equations in cylindrical domains.- Global representation of Langrangian distributions.- Stable asymptotics of the solution to the Dirichlet problem for elliptic equations of second order in domains with angular points or edges.- Maslov operator calculus and non-commutative analysis.- Relative time delay and trace formula for long range perturbations of Laplace operators.- Functional calculus and Fredholm criteria for boundary value problems on noncompact manifolds.- The variable discrete asymptotics of solutions of singular boundary value problems.- Schrödinger operators with arbitrary non-negative potentials.- Abel summability of the series of eigen- and associated functions of the integral and differential operators.- The relativistic oscillator.- On the ratio of odd and even spectral counting functions.- A trace class property of singularly perturbed generalized Schrödinger semi-groups.- Radiation conditions and scattering theory for N-particle Hamiltonians (main ideas of the approach).

His ideas turned the mathematical world on its head. He calculated the currents of liquids, the moment of inertia, developed the calculus of variations and the modern number theory. As a scientist he should be placed on the same level as Newton and Einstein. Engineers all over the world use his formulas every day - whether it be for constructing the hull of the "Alinghi" or for calculating the vibrations of the "Viaduc de Millau", the world's highest motorway bridge. This account of Euler's life and livings is embedded in the great political developments of his time, particularly in Austria, Prussia and Russia. The comic by Elena Pini (illustrations) and Alice and Andreas K. Heyne (text) follows the life of the genius from Basel, who, born 300 years ago, would set out to change the scientific world. The book is completed by a short biography of Euler and relevant data of the most important politicians and contemporaries.

The book provides a first comprehensive overview of both experimental and theoretical research on information processing in insect societies. Its purpose is to make the reader familiar with the methodology and ways of thinking followed by scientists at the leading edge of the field. The book is aimed at postgraduate students and researchers working on social insects and insects that live in groups as well as any reader interested in behavioural ecology, communication and social organization.

This volume contains the proceedings for the Second Annual Maple Summer Workshop and Symposium held at the University of Michigan, Ann Arbor, on June 28-30, 1993. The goal of this conference was to encourage innovative applications of the Maple V mathematical computation system.

/ Contents.- Perspective and the Plan and Elevation Technique, in particular in the Work by Piero della Francesca.- Hilda Geiringer: ihre ersten Jahre in Amerika.- Adrianus Romanus and the Trigonometric Tables of Georg Joachim Rheticus.- The Influence of Weierstrass's Analytical Methods in Italy.- Der Tabit b. Qurra zugeschriebene Zusatz I, 462 zu Euklid I, 46 in MS Leiden 399,1.- The Arithmetica of Jordanus Nemorarius.- The "Pythagorean Theorem" and Chinese Mathematics. Liu Hui's Commentary on the (Gou-Gu) Theorem in Chapter Nine of the Jiu Zhang Suan Shu.- La théorie des équations différentielles à la limite des XVIIIe - XIXe siècles.- The XVth Century Timurid Mathematician Ghiy?th al-D?n Jamsh?d al-K?sh? and his Computation of the Qubba.- Über eine Auseinandersetzung um den Mathematikunterricht an thüringischen Gymnasien aus dem Jahre 1843.- Non-Mathematica im Briefwechsel Leonhard Eulers mit Johann Bernoulli.- Conrad Landvogt, ein bisher unbekannter Algebraiker um 1500.- On the Axiomatization of Group Theory by American Mathematicians: 1902-1905.- Scientific Revolutions as Convolutions? A Sceptical Enquiry.- Jacobi and the Birth of Lie's Theory of Groups.- The Babylonian Cellar Text BM 85200 + VAT 6599. Retranslation and Analysis.- Zum Stand der westeuropäischen Mathematik zur Zeit der Entdeckung Amerikas.- The Ciphers of the Monks and the Astrolabe of Berselius Reconsidered.- Eulers früheste Studie zum Dreikörperproblem.- Some Remarks on the Almagestum parvum.- The Mathematical Correspondence between Julius Petersen and Ludvig Sylow.- Eléments de la méthode de forcing dans quelques travaux de N.N. Lousin.- Robert Remak and the Estimation of Units and Regulators.- New Light on the Life and Work of Joseph Henry Maclagan Wedderburn (1882-1948).- De 1'histoire du principe variationnel de Dirichlet.- Miszellen zu Leben und Werk des Mathematikers Johann Friedrich Pfaff (22.12.1765-21.4.1825).- Klein, Mittag-Leffler, and the Klein-Poincaré Correspondence of 1881-1882.- The History of Mathematics: Aims, Results, and Future Prospects.- Gauss und die Begründung der "höheren" Geodäsie.- Zur Modernisierung des Studiums der Mathematik in Berlin, 1820-1840.- Einige Bemerkungen zu antiken Konstruktionen.- Ernst August Weiss: Mathematical Pedagogical Innovation in the Third Reich.- Über das Interesse von Mathematikern an der Geschichte ihrer Wissenschaft.- Marx and Engels on the History of Science and Technology.- Felix Klein in Erlangen und München: ein Beitrag zur Biographie.- Contributi Italiani della prima metà del XX secolo alla teoria di Galois.- Anschriften der Autoren / Authors' addresses.

Genetic control of metastasis.- Cytokines in breast cancer cell dyshesion.- Clinical relevance of genetic alterations in lung cancer.- Recent advances in understanding function and mutations of breast cancer susceptibility genes.- Tumour immunology.- Cytokines in the host-tumor interaction.- Gene therapy of cancer.- Antisense strategy for cancer therapy.- Oligonucleotide therapeutics for human leukemia.- Genetic instability and tumor cell variation.

Vladimir Petrovich Potapov, as remembered by colleagues, friends and former students.- On a minimum problem in function theory and the number of roots of an algebraic equation inside the unit disc.- On tangential interpolation in reproducing kernel Hilbert modules and applications.- Notes on a Nevanlinna-Pick interpolation problem for generalized Nevanlinna functions.- The indefinite metric in the Schur interpolation problem for analytic functions, IV.- Bitangential interpolation for upper triangular operators.- Bitangential interpolation for upper triangular operators when the Pick operator is strictly positive.- Integral representations of a pair of nonnegative operators and interpolation problems in the Stieltjes class.- On recovering a multiplicative integral from its modulus.- On Schur functions and Szegö orthogonal polynomials.- Hilbert spaces of entire functions as a J theory subject.- On transformations of Potapov's fundamental matrix inequality.- An abstract interpolation problem and the extension theory of isometric operators.- On the theory of matrix-valued functions belonging to the Smirnov class.- Integral representation of function of class Ka.- On the theory of entire matrix-functions of exponential type.- Analogs of Nehari and Sarason theorems for character-automorphic functions and some related questions.- The Blaschke-Potapov factorization theorem and the theory of nonselfadjoint operators.- Weyl matrix circles as a tool for uniqueness in the theory of multiplicative representation of J-inner functions.- On a criterion of positive definiteness.- Matrix boundary value problems with eigenvalue dependent boundary conditions (The linear case).- Weyl-Titchmarsh functions of the canonical periodical system of differential equations.- On boundary values of functions regular in a disk.

References.- Animals at the cell-aggregate body organization.- Porifera.- Humoral immunity.- Cellular immunity.- Conclusions.- References.- Diblastic animals.- Coelenterata.- Humoral immunity.- Cellular immunity.- The immune phenomena characteristics.- Conclusions.- References.- Protostomes.- Annelida.- The evolutionary significance of metamery and the coelom.- The cells.- The origin.- Humoral immunity.- Adaptive humoral immunity.- Cellular immunity.- Phagocytosis.- Cytotoxic reactions.- Transplantation reaction.- Adaptive cellular defense reactions.- Conclusions.- References.- Arthropoda.- References.- Chelicerata.- The cells and structures engaged in the immune reactions.- Humoral immunity.- Cellular immunity.- References.- Crustacea.- Hemopoitic structures.- Humoral immunity.- Cellular immunity.- References.- Insecta.- Blood cells.- Hemopoietic structures and their possible relevance to immunity.- Humoral immunity.- Inducible antibacterial peptides.- Cellular immunology.- Phagocytosis.- Encapsulation.- Transplantation immunity.- References.- Mollusca.- The hemopoietic tissues and organs.- The gastropods.- The bivalves.- The cephalopods.- Humoral immunity.- Cellular immunity.- Conclusions.- References.- Deuterostomes.- Echinodermata.- The coelomic derivatives of echinoderms and their possible role in immunity.- The immune significance of coelomic tubular and perivisceral systems.- The water vascular, hemal and perihemal systems.- Perivisceral coelom.- Other structures engaged in the immunity.- Humoral immunity.- Cellular immunity.- Regeneration.- Conclusions.- References.- Chordates/Urochordata.- The anatomical features of ascidians in regard to their possible immune significance.- The immune significance of the pharyngeal region.- Other structures engaged in the immunity.- The lymph nodules.- Body wall.- The neural gland.- Humoral immunity.- Cellular immunity.- Conclusions.- References.- Chordates/Vertebrates/Agnatha.- Origin.- The immunocompetent tissues and organs.- The possible thymus equivalent lymphoid structures of pharyngeal region.- The gut-associated lymphoid structures considered to be equivalent to the spleen.- Lymphoid tissues with the poietic capability supposed to be equivalent to bone marrow.- Other lymphohemopoietic tissues.- Humoral immunity.- Specific humoral immunity.- Cellular immunity.- References.- Chordates/Vertebrates/Chondrichthyes.- Origins.- The immunocompetent tissues and organs of chondrichthyans.- The thymus.- The spleen.- The gut-associated lymphoid tissue.- The immunocompetent tissues and organs of chondrichthyans comparable to the bone marrow.- The Leydig's organ.- Epigonal organs.- The lymphomyeloid structures of cranial region.- The kidney.- Development of lymphohemopoiesis in elasmobranchs.- Humoral immunity.- Specific humoral immunity.- Cellular immunity.- Specific cellular immunity.- Conclusions.- References.- Chordates/Vertebrates /Osteichthyes.- Origins.- The immunocompetent tissues and organs of osteichthyans.- The thymus.- The spleen.- The gut-associated lymphoid tissue.- The immunocompetent tissues and organs of osteichthyans comparable to the bone marrow.- The kidney.- Other structures.- Cells.- B Lymphocytes.- T Lymphocytes.- MHC Antigens.- Nonspecific humoral immunity.- Specific humoral immunity.- Nonspecific cellular immunity.- Cytokines.- Transplantation.- Cytotoxicity.- Cellular cooperation.- Conclusions.- References.- General conclusions.- References.

I. Sonja Kovalevsky.- Curriculum Vitae.- Scientific publications.- Sophie Kovalevsky.- Sonja Kovalevsky: Her life and professorship at Stockholm.- Rigid bodies and the Bordin Prize.- The limitations of the Cauchy-Kovalevsky theorem.- II. Research papers.- On integrability of many-body problems with point interactions.- Generalized point models in boundary contact value problems of hydroelasticity.- Some spectral properties of the Heun differential equation.- On the approximation of the solution of the Schrodinger equation by superpositions of stationary solutions.- Lyapunov exponents in continuum Bernoulli-Anderson models.- Families of spectral measures with mixed types.- Singular point-like perturbations of the Laguerre operator in a Pontryagin space.- Realizations of Herglotz-Nevanlinna functions via F-systems.- Integral equations of relativistic bound state theory and Sturm-Liouville problem.- The non-relativistic scattering problem for a superposition of ä-potentials.- On the periodic magnetic Schrodinger operator in Rd. Eigenvalues and model functions.- The Laplace operator, null set perturbations and boundary conditions.- Ergodicity in the p-adic framework.- On the resolvent estimates for the generators of strongly continuous groups in the Hilbert spaces.- Supersymmetry of the Sturm-Liouville and Korteveg-de Vries operators.- Resonance triadic quantum switch.- The Hamilton operator and quantum vacuum for nonconformal scalar fields in the homogeneous and isotropic space.- Boundary conditions for singular perturbations of self-adjoint operators.- Asymptotical and topological constructions in hydrodynamics.- Spectral aspects of a class of differential operators.- Spectral properties of Jacobi matrices with rapidly growing power-like weights.- Kovalevskaya's dynamics and Schrodinger equations of Henn class.- Effective quantum number for centrally symmetric potentials.- List of participants.- List of lecture titles.

1 E2Fs and the Retinoblastoma Protein Family.- 2 Signalling to the C-terminus of p53.- 3 Chromosome Translocations Generating Chimeric Transcription Factors, Unique Genetic Events with Pleiotropic Cellular Consequences.- 4 The Runt Domain Transcription Factor, PEBP2/CBF, and its Involvement in Human Leukemia.- 5 EBNA2: A Viral Transcription Factor Essential for the Immortalization of Human B Lymphocytes by the Epstein-Barr Virus (EBV).

This book contains the lecture series originally delivered at the Advanced Course on Limit Cycles of Differential Equations in the Centre de Rechercha Mathematica Barcelona in 2006. It covers the center-focus problem for polynomial vector fields, and the application of abelian integrals to limit cycle bifurcations. Both topics are related to the authors' interests in Hilbert's sixteenth problem, but would also be of interest to those working more generally in the qualitative theory of dynamical systems.

My Life and Mathematics.- List of Publications of Peter Lancaster.- Forty-four Years with Peter Lancaster.- Peter Lancaster, my Friend and Co-author.- The Joint Numerical Range of Bordered and Tridiagonal Matrices.- Iterative Computation of Higher Derivatives of Repeated Eigenvalues and the Corresponding Eigenvectors.- Colligations in Pontryagin Spaces with a Symmetric Characteristic Function.- Logarithmic Residues of Fredholm Operator Valued Functions and Sums of Finite Rank Projections.- Positive Linear Maps and the Lyapunov Equation.- Full-and Partial-Range Completeness.- Spectral Isomorphisms between Generalized Sturm-Liouville Problems.- Existence and Uniqueness Results for Nonlinear Cooperative Systems.- Young's Inequality in Compact Operators.- Partial Indices of Small Perturbations of a Degenerate Continuous Matrix Function.- Finite Section Method for Difference Equations.- Iterative Solution of a Matrix Riccati Equation Arising in Stochastic Control.- Lyapunov Functions and Solutions of the Lyapunov Matrix Equation for Marginally Stable Systems.- Invariant Subspaces of Infinite Dimensional Hamiltonians and Solutions of the Corresponding Riccati Equations.- Inertia Bounds for Operator Polynomials.- A Note on the Level Sets of a Matrix Polynomial and its Numerical Range.

Reprint from GAFA, Vol. 5 (1995), No. 2. Enlarged by a short biography of Mikhail Gromov and a list of publications. In the last decades of the XX century tremendous progress has been achieved in geometry. The discovery of deep interrelations between geometry and other fields including algebra, analysis and topology has pushed it into the mainstream of modern mathematics. This Special Issue of Geometric And Functional Analysis (GAFA) in honour of Mikhail Gromov contains 14 papers which give a wide panorama of recent fundamental developments in modern geometry and its related subjects. CONTRIBUTORS: J. Bourgain, J. Cheeger, J. Cogdell, A. Connes, Y. Eliashberg, H. Hofer, F. Lalonde, W. Luo, G. Margulis, D. McDuff, H. Moscovici, G. Mostow, S. Novikov, G. Perelman, I. Piatetski-Shapiro, G. Pisier, X. Rong, Z. Rudnick, D. Salamon, P. Sarnak, R. Schoen, M. Shubin, K. Wysocki, and E. Zehnder. The book is a collection of important results and an enduring source of new ideas for researchers and students in a broad spectrum of directions related to all aspects of Geometry and its applications to Functional Analysis, PDE, Analytic Number Theory and Physics.

Multivariate Inequalities of Kolmogorov Type and Their Applications.- Monotone Iterative Technique for Impulsive Differential-Difference Equations with Variable Impulsive Perturbations.- Multivariate Cosine Wavelets.- On Almost Interpolation by Multivariate Splines.- Locally Linearly Independent Systems and Almost Interpolation.- Exponential-Type Approximation in Multivariate Harmonic Hilbert Spaces.- Interpolation by Continuous Function Spaces.- Discrete Characterization of Besov Spaces and its Applications to Stochastics.- One-Sided Approximation and Interpolation Operators Generating Hyperbolic Sigma-Pi Neural Networks.- Unconstrained Minimization of Quadratic Splines and Applications.- Interpolation by Translates of a Basis function.- On the Sup-Norm Condition Number of the Multivariate Triangular Bernstein Basis.- Integration Methods of Clenshaw-Curtis Type, Based on Four Kinds of Chebyshev Polynomials.- Tensor Products of Convex Cones.- The Curse of Dimension and a Universal Method for Numerical Integration.- Interpolation by Bivariate Splines on Crosscut Partitions.- Necessary and Sufficient Conditions for Orthonormality of Scaling Vectors.- Trigonometric Preconditioners for Block Toeplitz Systems.- The Average Size of Certain Gram-Determinants and Interpolation on Non-Compact Sets.- Radial Basis Functions Viewed From Cubic Splines.- Wavelet Modelling of High Resolution Radar Imaging and Clinical Magnetic Resonance Tomography.- A New Interpretation of the Sampling Theorem and its Extensions.- Gridded Data Interpolation with Restrictions on the First Order Derivatives.- Affine Frames and Multiresolution.- List of Participants.

This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author¿s extension of the theory will enable researchers to better describe the mechanics of modern materials and biological tissues. The global approach to continuum mechanics also enables the formulation and solutions of practical optimization problems.Foundations of Geometric Continuum Mechanics will be an invaluable resource for researchers in the area, particularly mathematicians, physicists, and engineers interested in the foundational notions of continuum mechanics.

Blending Approximations with Sine Functions.- Quasi-interpolation in the Absence of Polynomial Reproduction.- Estimating the Condition Number for Multivariate Interpolation Problems.- Wavelets on a Bounded Interval.- Quasi-Kernel Polynomials and Convergence Results for Quasi-Minimal Residual Iterations.- Rate of Approximation of Weighted Derivatives by Linear Combinations of SMD Operators.- Approximation by Multivariate Splines: an Application of Boolean Methods.- Lm, ?, s-Splines in ?d.- Constructive Multivariate Approximation via Sigmoidal Functions with Applications to Neural Networks.- Spline-Wavelets of Minimal Support.- Necessary Conditions for Local Best Chebyshev Approximations by Splines with Free Knots.- C1 Interpolation on Higher-Dimensional Analogs of the 4-Direction Mesh.- Tabulation of Thin Plate Splines on a Very Fine Two-Dimensional Grid.- The L2-Approximation Orders of Principal Shift-Invariant Spaces Generated by a Radial Basis Function.- A Multi-Parameter Method for Nonlinear Least-Squares Approximation.- Analog VLSI Networks.- Converse Theorems for Approximation on Discrete Sets II.- A Dual Method for Smoothing Histograms using Nonnegative C1-Splines.- Segment Approximation By Using Linear Functionals.- Construction of Monotone Extensions to Boundary Function

I: Models, concepts, and policy instruments.- Beyond costs and benefits of climate change: A workshop overview.- 1. Introduction.- 2. An increasing scope of integration.- 2.1. Cost and benefit estimates.- Benefits.- Costs.- 2.2. Integrated cost/benefit studies.- 2.3. Towards integrated climate-economy models.- 3. Integrated assessments: Simulation models.- 3.1. Fully integrated models.- 3.2. Partially integrated models.- 4. Integrated assessments: Optimization models.- 4.1. Fully integrated models.- Global single-region, aggregated models.- Global multi-region, aggregated models.- Sectorally disaggregated models.- 4.2. Partially integrated assessments.- 5. Layout for the book.- 6. Closing remarks.- First principles and the economic comparison of regulatory alternatives in global change.- 1. Introduction.- 2. Taxes versus standards versus marketable permits under uncertainty.- 3. Marketable permits versus joint implementation under certainty.- 4. Concluding remarks.- Dynamics of policy instruments and the willingness to participate in an international agreement.- 1. Introduction.- 2. Impacts of different kinds of policy instruments.- 2.1 Taxes.- 2.2 Tradable permits.- 2.3 Joint implementation.- 3. Participation in an international agreement to mitigate greenhouse gases emissions.- 4. Need for future research activities.- Global warming and the insurance industry.- 1. Introduction.- 2. Increasing disaster losses.- 3. Indications of climate change.- 4. Climate change predictions.- 5. Economic effects of climate change.- 6. Conclusions for the insurance industry.- II. Stabilization targets, costs, and technologies.- European stabilization targets: What do they bring, how much do they cost?.- 1. European stabilization targets: The leading climate change policy.- 2. Lack of knowledge about the realistic costs of reducing CO2 emissions.- 3. What are the additional costs of CO2 mitigation in the next 10 to 50 years?.- 4. Final suggestions for research.- Climate protection and the economy of prevention.- 1. Global scenarios: Wide range of conceivable 'energy futures'.- 1.1 Rising energy consumption is not a matter of fate, but political will.- 1.2 Climate protection policies avoid grave future risks - and are cost-effective.- 2. European Union: Risk minimization is financable.- 3. Germany: Room for manoeuvre and deficits in implementation.- 3.1 Business-as-usual versus climate protection and risk minimization: The scenarios of the German Bundestag's Climate Study Commission.- Scenario definition.- Analysis of scenario findings.- 3.2 Instruments of climate protection and risk minimization policy.- 4. Outlook.- The value of advanced energy technologies in stabilizing atmospheric CO2.- 1. Introduction.- 2. The economics of CO2 consideration ceilings.- 3. Energy, agriculture, land-use, and economy.- 4. Implications of stabilizing the atmosphere at 550 ppmv.- 5. The value of enhanced technology.- 6. Technology and protocols to stabilize the atmosphere.- 7. Conclusions.- Policy context: Follow-up of the Berlin climate conference.- 1. Introduction.- 2. The Berlin Conference.- 3. Forthcoming events.- The implications of including sulfate aerosols on scenarios of admissible greenhouse gas emissions.- 1. Introduction.- 2. Climate window - base case.- 3. Climate window including aerosols.- 4. Conclusions.- The tolerable windows approach to climate control: Optimization, risks, and perspectives.- 1. Introduction.- 2. The philosophy of the Tolerable Windows Approach (TWA).- 3. A simple example: The WBGU scenario.- 4. Optimization of cumulative emissions.- 4.1 Mathematics of optimal control.- 4.2 Realization of optimal solutions.- 5. Including uncertainties: Risk analysis.- 6. Conclusions.- Appendix 1: List of participants.- Appendix 2: Workshop program.

Multiple Polylogarithms: An Introduction.- A (Conjectural) 1/3-phenomenon for the Number of Rhombus Tilings of a Hexagon which contain a Fixed Rhombus.- The Influence of Carr's Synopsis on Ramanujan.- A Bailey Lemma from the Quintuple Product.- Little Flowers to G.H. Hardy (07-02-1877-01-12-1947).- Rogers-Ramanujan Type Identities for Burge's Restricted Partition Pairs Via Restricted Frobenius Partitions.- On q-additive and q-multiplicative Functions.- Antimagic Labeling of Complete m-ary Trees.- Some Recent Advances on Symmetric, Quasi-Symmetric and Quasi-Multiple Designs.- On T-core Partitions and Quadratic Forms.- Observations on Some Algebraic Equations Associated with Ramanujan's Work.- On Rapidly Convergent Series for Dirichlet L-function Values Via the Modular Relation.- On a Conjecture of Andrews-II.- Integrity of P2× Pn.- A Note on Cordial Labelings of Multiple Shells.- A Report on Additive Complements of the Squares.- Transcendental Infinite Sums and Some Related Questions.- The Lehmer Problem on the Euler Totient: A Pendora's Box of Unsolvable Problems.- The Problems Solved by Ramanujan in the Journal of the Indian Mathematical Society.- On the gcd and Icm of Matrices Over Dedekind Domains.- The Billiard Ball Motion Problem I: A Markoff Type Chain for the Octahedron in $${{\Re }^{3}}$$.- Hilbert's Seventeenth Problem and Pfister's Work on Quadratic Forms.- Certain Representations of Mock-Theta Functions.- Bi-Graceful Graphs.- Wheels, Cages and Cubes.- Relevance of Srinivasa Ramanujan at the Dawn of the New Millennium.- Number of Solutions of Equations over Finite Fields and a Conjecture of Lang and Weil.- On An Additive Question.- n-Colour Partitions.

This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko's scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.

1 Some aspects of operator theory and the theory of analytic functions.- 1 On spectral functions of Hermitian operators.- 2. Representation of a simple Hermitian operator whose deficiency index is (1,1).- 3. On the spectrum of self-adjoint extensions of a Hermitian operator whose deficiency index is (1,1).- 4. Some aspects of the theory of analytic functions.- 2 Entire operators whose deficiency index is (1,1).- 1. Quasiregular gauge.- 2. Principal theorem on regular points of fM(z).- 3. u -regular points of a Hermitian operator.- 4. Functions e(z) and ?M(Z).- 5. Entire operators.- 6. R-functions and generalized resolvents of a Hermitian operator.- 7. On distribution functions of a Hermitian operator.- 8. Method of directing functionals.- 9. Operator, entire with respect to a generalized gauge.- 3 Applications of entire operator theory to some classical problems of analysis.- 1. Power moment problem.- 2. Continuation problem for positive definite functions.- 3. Unitary and spiral curves.- Appendix 1 On entire operators whose defect numbers are arbitrary.- Appendix 2 Enture operators represented by differential operators.- Appendix 3 On a difficult problem of operator theory and its relation to classical analysis.- Comments.