Bøker utgitt av Birkhauser

1. Application of Transgenic and Gene-Targeted Mice to Dissect Mechanisms of Lung Disease.- Emphysema.- 2. Models of Genetic Emphysema: The C57B1/6J Mice and their Mutants: Tight-Skin, Pallid and Beige Giuseppe Lungarella, Eleonora Cavarra and.- 3. ?1-Antitrypsin Deficiency.- 4. Recombinant SLPI: Emphysema and Asthma.- 5. Elastase Inhibitors in the Lung: Expression and Functional Relationships.- 6. Regulation of Neutrophil Proteinases.- 7. Control of Connective Tissue Genes.- Infection.- 8. Genetic Models of Bacterial Lung Infection.- 9. Genetics of Bacteria: Role in Pathogenesis of Infection of the Respiratory Tract.- 10. Polymerase Chain Reaction in the Diagnosis of Respiratory Tract Infections.- 11. Cystic Fibrosis.- 12. Respiratory Bacterial Infections in Patients with Cystic Fibrosis: Pathogenicity and Implications for Serine Proteinase Inhibitor Therapy.

On Some Operator Colligations and Associated Reproducing Kernel Spaces.- On the Spectra of Selfadjoint Extensions.- On the Spectrum of Singular Nonselfadjoint Differential Operators.- The Commutant Lifting Theorem for Contractions on Kre?n Spaces.- A Method for Constructing Invariant Subspaces for some Operators on Kre?n Spaces.- Applications of the Furuta Inequality to Operator Inequalities and Norm Inequalities Preserving some Orders.- Quasi-contractions on Kre?n Spaces.- Antitonicity of the Inverse and J-Contractivity.- Unitary Extensions of a System of Commuting Isometric Operators.- Some Generalizations of Classical Interpolation Problems.- The Kobayashi Distance between two Contractions.- The Category of Quotient Bornological Spaces.

1 Preliminary results. Integral transforms in the complex domain.- 1.1 Introduction.- 1.2 Some identities.- 1.3 Integral representations and asymptotic formulas.- 1.4 Distribution of zeros.- 1.5 Identities between some Mellin transforms.- 1.6 Fourier type transforms with Mittag-Leffler kernels.- 1.7 Some consequences.- 1.8 Notes.- 2 Further results. Wiener-Paley type theorems.- 2.1 Introduction.- 2.2 Some simple generalizations of the first fundamental Wiener-Paley theorem.- 2.3 A general Wiener-Paley type theorem and some particular results.- 2.4 Two important cases of the general Wiener-Paley type theorem.- 2.5 Generalizations of the second fundamental Wiener-Paley theorem.- 2.6 Notes.- 3 Some estimates in Banach spaces of analytic functions.- 3.1 Introduction.- 3.2 Some estimates in Hardy classes over a half-plane.- 3.3 Some estimates in weighted Hardy classes over a half-plane.- 3.4 Some estimates in Banach spaces of entire functions of exponential type.- 3.5 Notes.- 4 Interpolation series expansions in spacesW1/2, ?p, ?of entire functions.- 4.1 Introduction.- 4.2 Lemmas on special Mittag-Leffler type functions.- 4.3 Two special interpolation series.- 4.4 Interpolation series expansions.- 4.5 Notes.- 5 Fourier type basic systems inL2(0, ?).- 5.1 Introduction.- 5.2 Biorthogonal systems of Mittag-Leffler type functions and their completeness inL2(0, ?).- 5.3 Fourier series type biorthogonal expansions inL2(0, ?).- 5.4 Notes.- 6 Interpolation series expansions in spacesWs+1/2, ?p, ?of entire functions.- 6.1 Introduction.- 6.2 The formulation of the main theorems.- 6.3 Auxiliary relations and lemmas.- 6.4 Further auxiliary results.- 6.5 Proofs of the main theorems.- 6.6 Notes.- 7 Basic Fourier type systems inL2spaces of odd-dimensional vector functions.- 7.1 Introduction.- 7.2 Some identities.- 7.3 Biorthogonal systems of odd-dimensional vector functions.- 7.4 Theorems on completeness and basis property.- 7.5 Notes.- 8 Interpolation series expansions in spacesWs, ?p, ?of entire functions.- 8.1 Introduction.- 8.2 The formulation of the main interpolation theorem.- 8.3 Auxiliary relations and lemmas.- 8.4 Further auxiliary results.- 8.5 The proof of the main interpolation theorem.- 8.6 Notes.- 9 Basic Fourier type systems inL2spaces of even-dimensional vector functions.- 9.1 Introduction.- 9.2 Some identities.- 9.3 The construction of biorthogonal systems of even-dimensional vector functions.- 9.4 Theorems on completeness and basis property.- 9.5 Notes.- 10 The simplest Cauchy type problems and the boundary value problems connected with them.- 10.1 Introduction.- 10.2 Riemann-Liouville fractional integrals and derivatives.- 10.3 A Cauchy type problem.- 10.4 The associated Cauchy type problem and the analog of Lagrange formula.- 10.5 Boundary value problems and eigenfunction expansions.- 10.6 Notes.- 11 Cauchy type problems and boundary value problems in the complex domain (the case of odd segments).- 11.1 Introduction.- 11.2 Preliminaries.- 11.3 Cauchy type problems and boundary value problems containing the operators $$ {\mathbb{L}_{s + 1/2}}$$ and $$ \mathbb{L}_{s + 1/2}^*$$.- 11.4 Expansions inL2{?2s+1(?)} in terms of Riesz bases.- 11.5 Notes.- 12 Cauchy type problems and boundary value problems in the complex domain (the case of even segments).- 12.1 Introduction.- 12.2 Preliminaries.- 12.3 Cauchy type problems and boundary value problems containing the operators $${{\mathbb{L}}_{s}} $$ and $$ \mathbb{L}_{s}^*$$.- 12.4 Expansions inL2{?2s(?)} in terms of Riesz bases.- 12.5

The discovery of valproate.- The pharmacology of valproate.- Pharmacological effects and mechanisms of action.- Chemistry and biotransformation.- Absorption, distribution and excretion.- Toxicity.- Clinical use of valproate.- Valproate in the treatment of epilepsies in children.- Treatment of epilepsies in adults.- Valproate use in psychiatry: A focus on bipolar illness.- Valproate in the treatment of headache.- Adverse effects and interactions with other drugs.- The future of valproate.

1. Residue Currents in one Dimension. Different Approaches.- 1. Residue attached to a holomorphic function.- 2. Some other approaches to the residue current.- 3. Some variants of the classical Pompeiu formula.- 4. Some applications of Pompeiu's formulas. Local results.- 5. Some applications of Pompeiu's formulas. Global results.- References for Chapter 1.- 2. Integral Formulas in Several Variables.- 1. Chains and cochains, homology and cohomology.- 2. Cauchy's formula for test functions.- 3. Weighted Bochner-Martinelli formulas.- 4. Weighted Andreotti-Norguet formulas.- 5. Applications to systems of algebraic equations.- References for Chapter 2.- 3. Residue Currents and Analytic Continuation.- 1. Leray iterated residues.- 2. Multiplication of principal values and residue currents.- 3. The Dolbeault complex and the Grothendieck residue.- 4. Residue currents.- 5. The local duality theorem.- References for Chapter 3.- 4. The Cauchy-Weil Formula and its Consequences.- 1. The Cauchy-Weil formula.- 2. The Grothendieck residue in the discrete case.- 3. The Grothendieck residue in the algebraic case.- References for Chapter 4.- 5. Applications to Commutative Algebra and Harmonic Analysis.- 1. An analytic proof of the algebraic Nullstellensatz.- 2. The membership problem.- 3. The Fundamental Principle of L. Ehrenpreis.- 4. The role of the Mellin transform.- References for Chapter 5.

This work gives a coherent introduction to isoperimetric inequalities in Riemannian manifolds, featuring many of the results obtained during the last 25 years and discussing different techniques in the area. Written in a clear and appealing style, the book includes sufficient introductory material, making it also accessible to graduate students. It will be of interest to researchers working on geometric inequalities either from a geometric or analytic point of view, but also to those interested in applying the described techniques to their field.

Anti-Inflammatory Drugs in Asthma: The Pathophysiology of Asthma.- Corticosteroids.- Phosphodiesterases in Asthma.- ?2-Agonists.- Mast Cell Stabilizing Drugs.- Anti-Leukotriene Therapy for Asthma.- Immunomodulators.- Immunomodulators.- Mast Cell Proteases as New Targets for Therapeutic Intervention in Asthma.- Cytokine and Adhesion Molecule Antagonists.

V: Triangular Representations.- XX. Additive lower-upper triangular decompositions of operators.- XXI. Operators in triangular form.- XXII. Multiplicative lower-upper triangular decompositions of operators.- VI: Classes of Toeplitz Operators.- XXIII. Block Toeplitz operators.- XXIV. Toeplitz operators defined by rational matrix functions.- XXV. Toeplitz operators defined by piecewise continuous matrix functions.- VII: Contractive Operators and Characteristic Operator Functions.- XXVI. Block shift operators.- XXVII. Dilation theory.- XXVIII. Unitary systems and characteristic operator functions.- VIII: Banach Algebras And Algebras Of Operators.- XXIX. General theory.- XXX. Commutative Banach algebras.- XXXI. Elements of C*-algebra theory.- XXXII. Banach algebras generated by Toeplitz operators.- IX: Extension and Completion Problems.- XXXIII. Completions of matrices.- XXXIV. A general scheme for completion and extension problems.- XXXV. Applications of the band method.- Standard references texts.- List of symbols.

"The book under review collects and regroups results on the representation theory of the Jacobi group of lowest degree mostly due to R.Berndt and his coworkers J.Homrighausen and R.Schmidt. The book is very well written and gives an up to date collection of the results known. It will be quite useful for everyone working in the field. The first chapter introduces the Jacobi group GJ, a semi-direct product of SL(2) with a Heisenberg group, and describes different possible coordinates on the group, the Haar measure, the Lie algebra, as well as, over the reals, a (generalized) Iwasawa decomposition and the associated homogeneous space..." ---Zentralblatt Math "This book is an exposition which incorporates results of the authors' research works [that] will be very helpful for those who have some knowledge of the Jacquet-Langlands theory for GL2... Recommended for researchers interested in modular and automorphic forms." ---Mathematical Reviews

Uncertainty principles for time-frequency operators.- 1. Introduction.- 2. Sampling results for time-frequency transformations.- 3. Uncertainty principles for exact Gabor and wavelet frames.- References.- Distribution of zeros of matrix-valued continuous analogues of orthogonal polynomials.- 1. Preliminary results.- 1.1. Matrix-valued Krein functions of the first and second kinds.- 1.2. Partitioned integral operators.- 2. Orthogonal operator-valued polynomials.- 2.1. Stein equations for operators.- 2.2. Zeros of orthogonal polynomials.- 2.3. On Toeplitz matrices with operator entries.- 3. Zeros of mat rix-valued Krein functions.- 3.1 On Wiener-Hopf operators.- 3.2. Proof of the main theorem.- References.- The band extension of the real line as a limit of discrete band extensions, II. The entropy principle.- 0. Introduction.- I. Preliminaries.- II. Main results.- References.- Weakly positive matrix measures, generalized Toeplitz forms, and their applications to Hankel and Hilbert transform operators.- 1. Lifting properties of generalized Toeplitz forms and weakly positive matrix measures.- 2. The GBT and the theorems of Helson-Szegö and Nehari.- 3. GNS construction, Wold decomposition and abstract lifting theorems.- 4. Multiparameter and n-conditional lifting theorems, the A-A-K theorem and applications in several variables.- References.- Reduction of the abstract four block problem to a Nehari problem.- 0. Introduction.- 1. Main theorems.- 2. Proofs of the main theorems.- References.- The state space method for integro-differential equations of Wiener-Hopf type with rational matrix symbols.- 1. Introduction and main theorems.- 2. Preliminaries on matrix pencils.- 3. Singular differential equations on the full-line.- 4. Singular differential equations on the half-line.- 5. Preliminaries on realizations.- 6. Proof of theorem 1.1.- 7. Proofs of theorems 1.2 and 1.3.- 8. An example.- References.- Symbols and asymptotic expansions.- 0. Introduction.- I. Smooth symbols on Rn.- II. Piecewise smooth symbols on T.- III. Piecewise smooth symbols on Rn.- IV. Symbols discontinuous across a hyperplane in Rn × Rn.- References.- Program of Workshop.

1. Needle Microinjection: A Brief History.- 2. Microinjection of Macromolecules into Mammalian Cells in Culture.- 3. The Use of Plasmid Microinjection to Study Specific Cell Cycle Phase Transitions.- 4. Combining Microinjection with Microanalytical Methods to Investigate Regulation of Metabolic Pathways.- 5. Import of Stably Folded Proteins into Peroxisomes.- 6. Study of the Function of Microtubule Proteins.- 7. Cytoskeleton Regulation by Rho Proteins.- 8. Cytoskeletal Regulation by Rho-p21 Associated Kinases: Analysis of ROK and PAK Function by Plasmid Microinjection.- 9. Use of Microinjection to Study Apoptosis and its Prevention.- 10. Role of the InsP3 Receptor in Intracellular Ca2+ Release and Ca2+ Entry.- 11. Microinjection of Xenopus laevis Oocytes: A Model System.- 12. Xenopus laevis Oocytes as a Model for Studying the Activation of Intracellular Kinases.- 13. Signal Transduction in Xenopus laevis Oocytes by Ras Oncoproteins and Lipid Metabolites.- 14. The Multiple Roles of Mos During Meiosis.- 15. Use of the Xenopus Oocyte System to Study RNA Transport.- 16. Functional Expression of G Protein-Coupled Receptors in Xenopus laevis Oocytes.- 17. Expression of Glucose Transporters in Xenopus laevis Oocytes: Applications for the Study of Membrane Transporter Function and Regulation.- 18. DNA Injection into Xenopus laevis Embryos as a Tool to Study Spatial Gene Activity.- 19. Transformation of Nematodes by Microinjection.- Guide to Solutions.- Guide to Protocols.- Troubleshooting Guide.

Quantile Functions and Spread for Multivariate Distributions.- A New Definition of Multivariate M-quantiles.- A Depth Function and a Scale Curve Based on Spatial Quantiles.- Sample Quantiles for Locally Dependent Processes.- What are the Limiting Distributions of Quantile Estimators?.- New Selection Indices for University Admissions: A Quantile Approach.- Exploring Transition Data Through Quantile Regression Methods: An Application to U.S. Unemployment Duration.- How to be Pessimistic: Choquet Risk and Portfolio Optimization.- Expected Shortfall and Beyond.- Credit Scoring Using Binary Quantile Regression.- Prediction of 0-1-Events for Short- and Long-memory Time Series.- Nonparametric Quantile Regression with Applications to Financial Time Series.- An Algorithm for Optimal Bandwidth Selection for Smooth Nonparametric Quantile Estimation.- Orthogonal L1-norm Estimation.- L1-Derivatives, Score Functions and Tests.- Optimal Bias Robust M-estimates of Regression.- Robust Bootstrap for S-estimators of Multivariate Regression.- M-tests for Detection of Structural Changes in Regression.- Change Point Detection Based on Empirical Quantiles.- A Class of Probability Metrics and its Statistical Applications.- Whose Hare and Whose Tortoise.- Sign and Rank Covariance Matrices: Statistical Properties and Application to Principal Components Analysis.- Multivariate Signed Ranks: Randies' Interdirections or Tyler's Angles?.- L1-Depth, Depth Relative to a Model, and Robust Regression.- Perturbation Properties of Depth Regions.- Multivariate Trimmed Means Based on Data Depth.- Graphs, L1-Metrics and Clustering.- Classification Based on the Support Vector Machine and on Regression Depth.- A Robust Clustering Method and Visualization Tool Based On Data Depth.- The Median Extension of Data Analysis Metric Structures.- Text Classification for Mining Massive Aviation Inspection Reports.- A Comparison Between L1 Markov Random Field-Based and Wavelet-Based Estimators.- Elastic and Plastic Splines: Some Experimental Comparisons.- On the Bitplane Compression of Microarray Images.- Overdispersed Regression Models for Air Pollution and Human Health.- Atmospheric Pollution and Mortality in São Paulo.- Contributors.

Computational fluid-structure interaction (FSI) and flow simulation are challenging research areas that bring solution and analysis to many classes of problems in science, engineering, and technology. Young investigators under the age of 40 are conducting much of the frontier research in these areas, some of which is highlighted in this volume. The first author of each chapter took the lead role in carrying out the research presented. Some of the topics explored includeDirect flow simulation of objects represented by point cloudsComputational investigation of leaflet flutter in thinner biological heart valve tissuesHigh-fidelity simulation of hydrokinetic energy applicationsHigh-resolution isogeometric analysis of car and tire aerodynamicsComputational analysis of air-blast-structure interactionHeart valve computational flow analysis with boundary layer and leaflet contact representationComputational thermal multi-phase flow for metal additive manufacturingThis volume will be a valuable resource for early-career researchers and students - not only those interested in computational FSI and flow simulation, but also other fields of engineering and science, including fluid mechanics, solid mechanics, and computational mathematics - as it will provide them with inspiration and guidance for conducting their own successful research. It will also be of interest to senior researchers looking to learn more about successful research led by those under 40 and possibly offer collaboration to these researchers.

Regulation of the inducible nitric oxide synthase (iNOS) gene.- Superoxide anion release from inducible nitric oxide synthase.- Direct and indirect modulation of the inducible nitric oxide synthase by nitric oxide: feedback mechanisms in inflammation.- Nitric oxide regulation of eicosanoid production.- Local and systemic inflammation: role of poly (ADP-ribose) synthetase activation by reactive nitrogen species.- Nitric oxide regulation of leukocyte adhesion molecule expression.- Nitric oxide and leukocyte recruitment.- Nitric oxide regulation of lymphocyte function.- Role of nitric oxide and reactive oxygen species in arthritis.- Role of nitric oxide in chronic gut inflammation.- Nitric oxide and inflammatory disorders of the skin.- Roles of nitric oxide, superoxide, and peroxynitrite in myocardial ischemia-reperfusion injury and ischemic preconditioning.- Nitric oxide and myocarditis.- Nitric oxide in shock: sepsis and hemorrhage.- Nitric oxide as a mediator of interleukin-2 induced cardiovascular toxicity and antitumor activity.

Metallothionein nomenclature and structure.- Nomenclature of metallothionein: Proposal for a revision.- Metallothionein: Molecular evolution and classification.- Structural and biological studies on native bovine Cu, Zn-metallothionein-3.- Circular dichroism, emission, and exafs studies of Ag(I), Cd(II), Cu(I), and Hg(II) binding to metallothioneins and modeling the metal binding site.- Metallothionein structure update.- Simulation of Zn/Cd binding in mammalian metallothionein domains.- The growth inhibitory activity of metallothionein-3 correlates with its novel ? domain sequence rather than metal binding properties.- Recombinant synthesis and metal-binding abilities of mouse metallothionein 1 and its ?- and ?-domains.- Biochemical characterization of monomeric and dimeric cadmium-substituted metallothionein-3.- Chemical and analytical aspects of metallothionein.- Mammalian metallothionein sub-isoform separation by RP-HPLC with on-line UV and electrochemical detection.- Characterisation of mammalian Cd, Zn metallothioneins using differential pulse polarography.- Comparison of CZE and MECC separations of MT isoforms.- Synthetic peptides and domains of metallothionein for structure function studies: rabbit liver peptide MT-IIA 49-61 and lobster MT ?N ?C and ?C?N domains.- Voltammetric methods in isolation and identification of plant metallothioneins from alga Chlorella.- Characterization of isometallothioneins in Chang liver cells and the transient accumulation of metallothionein and glutathione during cell proliferation.- Quantification of cytosolic metallothionein contents by a developed assay system using immobilized antibody.- Protein engineering of metallothionein to study on the metal-binding ability.- Metal binding proteins: Molecular engineering of improvements in metal specificity.- Molecular splicing of metallothionein - study on domains of metallothionein.- Metallothionein in non-mammalian tissues.- Involvement of metallothionein in female squirrelfish reproduction.- Accumulation of untranslated metallothionein mRNA in antarctic hemoglobinless fish (icefish).- Structure and function of metallothionein isoforms in terrestrial snails.- Functional and regulatory aspects of teleost metallothionein.- Metallothionein induction in mussels exposed to a metal mixture.- Synthesis and properties of class III metallothioneins of Schizosaccharomyces pombe in response to cadmium and zinc.- Phytochelatins (class III metallothioneins) and their desglycyl peptides induced by cadmium in root cultures of Rubia tinctorum L..- Chemical and spectroscopic properties of copper metallothionein from the copper resistant fungus Beauveria bassiana.- Transcription factors.- Metallothionein facts and frustrations.- Liver degeneration and embryonic lethality in mouse null mutants for the metal-responsive transcriptional activator MTF-1.- New insights into the mechanisms of cadmium regulation of mouse metallothionein-I gene expression.- Activation of mouse metallothionein I promoter by cadmium in human neuroblastoma cells.- Transcription factors involved in heavy metal regulation of the human metallothionein-IIA gene.- Transcriptional regulation of the gene encoding mouse metallothionein-3 and its expression in the organs of the reproductive system.- Dynamic regulation of yeast metallothionein gene transcription via metalloregulatory signaling factors.- Metal regulation of mammalian metal responsive element (MRE) binding proteins.- Metallothionein and hormone responsiveness.- Synergistic activation of mouse metallothionein-I gene by interleukin-6 and glucocorticoid.- Hammerhead ribozymes mediated down-regulation of rat metallothionein mrnas expression.- Inactivation of metal-induced metallothionein gene expression by protein kinase C inhibitor.- Cadmium-induced metallothionein expression and metallothionein mRNA in mice.- Role of metallothionein in reproduction, development and cell proliferation.- The nuclear-cytoplasmic presence of metallothion..

About the Mark Krein International Conference.- Mark Grigorevich Krein (A short biography).- The Seminar on Ship Hydrodynamics, Organized by M.G. Krein.- Review Papers: The Works of M.G. Krein on Eigenfunction Expansion for Selfadjoint Operators and their Applications and Development.- M.G. Krein and the Extension Theory of Symmetric Operators. Theory of Entire Operators.- Works by M.G. Krein on Inverse Problems.- Research Papers: The Spectrum of Periodic Point Perturbations and the Krein Resolvent Formula.- The Periodic Choquard Equation.- On the Best Constant in a Poincare-Sobolev Inequality.- On Solutions of Parabolic Equations from Families of Banach Spaces Dependent on Time.- Canonical Systems on the Line with Rational Spectral Densities: Explicit Formulas.- Oscillations in Systems with Periodic Coefficients and Sector-restricted Nonlinearities.- Differential Operator Matrices of Mixed Order with Periodic Coefficients.- Asymptotics of Generalized Eigenvectors for Unbounded Jacobi Matrices with Power-like Weights, Pauli Matrices Commutation Relations and Cesaro Averaging.- Functional Means, Convolution Operators and Semigroups.- The Inverse Spectral Problem for First Order Systems on the Half Line.- Exact Solution of the Marchenko Equation Relevant to Inverse Scattering on the Line.- An Arbitrary Oriented Crack in the Box Shell.- Homogeneity of a String having Three Unperturbed Spectra.- On the Integro-differential Equation of a Torsion of an Elastic Medium Including a Cylindrical Crack.- Green's Formula and Theorems on Isomorphisms for General Elliptic Problems for Douglis-Nirenberg Elliptic Systems.- Sobolev's Problem in Complete Scale of Banach Spaces.- On the Simple Waves with Profiles in the Form of some Special Functions-Chebyshov-Hermite, Mathiev, Whittaker-in Two-phase Media.- Inverse Spectral Problem Related to the N-wave Equation.- Degenerated Hyperbolic Approximations of the Wave Theory of Elastic Plates.- Elliptic Problems with a Shift in Complete Scales of Sobolev-type Spaces.- On the Extremal Regularization of the Variational Inequalities with Multivalued Operators.- Poly-Fock Spaces.- Diffraction of Longitudinal Shear Waves by a Hollow Thick Circular Cylinder which is Situated in the Elastic Halfspace.- On M.G. Krein's Spectral Shift Function for Canonical Systems of Differential Equations.- Table of Contents of Volume II.

Eigenvalue distribution for nonselfadjoint Toeplitz matrices.- Random Hermitian matrices and (nonrandom) Toeplitz matrices.- The extended Fisher-Hartwig conjecture for symbols with multiple jump discontinuities.- A relative Toeplitz-Hausdorff theorem.- Operator-valued Szegö-Widom limit theorems.- The Adamjan-Arov-Krein theorem in general and regular representations of ?2 and the symplectic plane.- Projection method for block Toeplitz operators with operator-valued symbols.- Szegö-Widom-type limit theorems.- (Semi)-Fredholmness of convolution operators on the spaces of Bessel potentials.- Kernels of Toeplitz operators.- A fixed point approach to Nehari's problem and its applications.

Scattering matrices for microschemes.- 1. General expressions for the scattering matrix.- 2. Continuity condition.- References.- Holomorphic operators between Krein spaces and the number of squares of associated kernels.- 0. Introduction.- 1. Realizations of a class of Schur functions.- 2. Positive squares and injectivity.- 3. Application of the Potapov-Ginzburg transform.- References.- On reproducing kernel spaces, the Schur algorithm, and interpolation in a general class of domains.- 1. Introduction.- 2. Preliminaries.- 3. B(X) spaces.- 4. Recursive extractions and the Schur algorithm.- 5. H?(S) spaces.- 6. Linear fractional transformations.- 7. One sided interpolation.- 8. References.- The central method for positive semi-definite, contractive and strong Parrott type completion problems.- 1. Introduction.- 2. Positive semi-definite completions.- 3. Contractive completions.- 4. Linearly constrained contractive completions.- References.- Interpolation by rational matrix functions and stability of feedback systems: The 4-block case.- 1. Preliminaries.- 2. A homogeneous interpolation problem.- 3. Interpolation problem.- 4. Parametrization of solutions.- 5. Interpolation and internally stable feedback systems.- References.- Matricial coupling and equivalence after extension.- 1. Introduction.- 2. Coupling versus equivalence.- 3. Examples.- 4. Special classes of operators.- References.- Operator means and the relative operator entropy.- 1. Introduction.- 2. Origins of operator means.- 3. Operator means and operator monotone functions.- 4. Operator concave functions and Jensen's inequality.- 5. Relative operator entropy.- References.- An application of Furuta's inequality to Ando's theorem.- 1. Introduction.- 2. Operator functions.- 3. Furuta's type inequalities.- 4. An application to Ando's theorem.- References.- Applications of order preserving operator inequalities.- 0. Introduction.- 1. Application to the relative operator entropy.- 2. Application to some extended result of Ando's one.- References.- The band extension of the real line as a limit of discrete band extensions, I. The main limit theorem.- 0. Introduction.- I. Preliminaries and preparations.- II. Band extensions.- III. Continuous versus discrete.- References.- Interpolating sequences in the maximal ideal space of H? II.- 1. Introduction.- 2. Condition (A2).- 3. Condition (A3).- 4. Condition (A1).- References.- Operator matrices with chordal inverse patterns.- 1. Introduction.- 2. Entry formulae.- 3. Inertia formula.- References.- Models and unitary equivalence of cyclic selfadjoint operators in Pontrjagin spaces.- 1. The class F of linear functionals.- 2. The Pontrjagin space associated with ? ? F.- 3. Models for cyclic selfadjoint operators in Pontrjagin spaces.- 4. Unitary equivalence of cyclic selfadjoint operators in Pontrjagin spaces.- References.- The von Neumann inequality and dilation theorems for contractions.- 1. The von Neumann inequality and strong unitary dilation.- 2. Canonical representation of completely contractive maps.- 3. An effect of generation of nuclear algebras.- References.- Interpolation problems, inverse spectral problems and nonlinear equations.- References.- Extended interpolation problem in finitely connected domains.- I. Matrices and transformation formulas.- II. Disc Cases.- III. Domains of finite connectivity.- References.- Accretive extensions and problems on the Stieltjes operator-valued functions relations.- 1. Accretive and sectorial extensions of the positive operators, operators of the class C(?) and their parametric representation.- 2. Stieltjes operator-valued functions and their realization.- 3. M.S. Livsic triangular model of the M-accretive extensions (with real spectrum) of the positive operators.- 4. Canonical and generalized resolvents of QSC-extensions of Hermitian contractions.- References.- Commuting nonselfadjoint operators and algebraic curves.- 1. Commuting nonselfadjoint operators and the discriminant curve.-...

The abbacus was a thorough and complete system of arithmetical calculations, which saw its dawn in the Indian and Arabic tradition of the Middle Ages, but which was developed in its fully fledged aspects especially in Italy, between Genoa, Milan, Venice and the region of Umbria. In this monograph, Høyrup explores how the abbacus tradition has developed in Europe, with a focus on Italy and Germany between the 14th and the 17th Century. With the analysis of texts from Fibonacci, Pacioli, and Stifel to name but a few, this book offers a critical historical analysis of the development and diffusion of a tradition of calculus that has deeply influenced the way in which mathematics has developed in the West. The primary purpose of the book is to present a fairly detailed portrait of the abbacus tradition as it developed historically; as will be argued, Fibonacci was much less important for the emergence of this tradition than mostly assumed - but since his importance isbroadly taken for granted, that argument needs to be made, for which reason Fibonacci's Liber Abbaci is also described and analyzed in some depth. A secondary purpose is to show how the adoption of abbacus mathematics in German lands gave rise to the creation of a different tradition. The end of the book investigates the interplay of abbacus algebra with other intellectual currents which turned the whole mathematical undertaking upside-down in the 17th Century.​

6 Preliminaries.- 6.1 The operator of singular integration.- 6.2 The space Lp(?, ?).- 6.3 Singular integral operators.- 6.4 The spaces $$L_{p}^{ + }(\Gamma, \rho ), L_{p}^{ - }(\Gamma, \rho ) and \mathop{{L_{p}^{ - }}}\limits^{^\circ } (\Gamma, \rho )$$.- 6.5 Factorization.- 6.6 One-sided invertibility of singular integral operators.- 6.7 Fredholm operators.- 6.8 The local principle for singular integral operators.- 6.9 The interpolation theorem.- 7 General theorems.- 7.1 Change of the curve.- 7.2 The quotient norm of singular integral operators.- 7.3 The principle of separation of singularities.- 7.4 A necessary condition.- 7.5 Theorems on kernel and cokernel of singular integral operators.- 7.6 Two theorems on connections between singular integral operators.- 7.7 Index cancellation and approximative inversion of singular integral operators.- 7.8 Exercises.- Comments and references.- 8 The generalized factorization of bounded measurable functions and its applications.- 8.1 Sketch of the problem.- 8.2 Functions admitting a generalized factorization with respect to a curve in Lp(?, ?).- 8.3 Factorization in the spaces Lp(?, ?).- 8.4 Application of the factorization to the inversion of singular integral operators.- 8.5 Exercises.- Comments and references.- 9 Singular integral operators with piecewise continuous coefficients and their applications.- 9.1 Non-singular functions and their index.- 9.2 Criteria for the generalized factorizability of power functions.- 9.3 The inversion of singular integral operators on a closed curve.- 9.4 Composed curves.- 9.5 Singular integral operators with continuous coefficients on a composed curve.- 9.6 The case of the real axis.- 9.7 Another method of inversion.- 9.8 Singular integral operators with regel functions coefficients.- 9.9 Estimates for the norms of the operators P?, Q? and S?.- 9.10 Singular operators on spaces H?o(?, ?).- 9.11 Singular operators on symmetric spaces.- 9.12 Fredholm conditions in the case of arbitrary weights.- 9.13 Technical lemmas.- 9.14 Toeplitz and paired operators with piecewise continuous coefficients on the spaces lp and ?p.- 9.15 Some applications.- 9.16 Exercises.- Comments and references.- 10 Singular integral operators on non-simple curves.- 10.1 Technical lemmas.- 10.2 A preliminary theorem.- 10.3 The main theorem.- 10.4 Exercises.- Comments and references.- 11 Singular integral operators with coefficients having discontinuities of almost periodic type.- 11.1 Almost periodic functions and their factorization.- 11.2 Lemmas on functions with discontinuities of almost periodic type.- 11.3 The main theorem.- 11.4 Operators with continuous coefficients - the degenerate case.- 11.5 Exercises.- Comments and references.- 12 Singular integral operators with bounded measurable coefficients.- 12.1 Singular operators with measurable coefficients in the space L2(?).- 12.2 Necessary conditions in the space L2(?).- 12.3 Lemmas.- 12.4 Singular operators with coefficients in ?p(?). Sufficient conditions.- 12.5 The Helson-Szegö theorem and its generalization.- 12.6 On the necessity of the condition a ? Sp.- 12.7 Extension of the class of coefficients.- 12.8 Exercises.- Comments and references.- 13 Exact constants in theorems on the boundedness of singular operators.- 13.1 Norm and quotient norm of the operator of singular integration.- 13.2 A second proof of Theorem 4.1 of Chapter 12.- 13.3 Norm and quotient norm of the operator S? on weighted spaces.- 13.4 Conditions for Fredholmness in spaces Lp(?, ?).- 13.5 Norms and quotient norm of the operator aI + bS?.- 13.6 Exercises.- Comments and references.- References.

This book addresses the issue of uniqueness of a solution to a problem - a very important topic in science and technology, particularly in the field of partial differential equations, where uniqueness guarantees that certain partial differential equations are sufficient to model a given phenomenon. This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establish its uniqueness. This book examines three very fundamental equations: ordinary differential equations, scalar conservation laws, and Hamilton-Jacobi equations. Starting from the standard Gronwall inequality, this book discusses less regular ordinary differential equations. It includes an introduction of advanced topics like the theory of maximal monotone operators as wellas what is called DiPerna-Lions theory, which is still an active research area. For conservation laws, the uniqueness of entropy solution, a special (discontinuous) weak solution is explained. For Hamilton-Jacobi equations, several uniqueness results are established for a viscosity solution, a kind of a non-differentiable weak solution. The uniqueness of discontinuous viscosity solution is also discussed. A detailed proof is given for each uniqueness statement. The reader is expected to learn various fundamental ideas and techniques in mathematical analysis for partial differential equations by establishing uniqueness. No prerequisite other than simple calculus and linear algebra is necessary. For the reader's convenience, a list of basic terminology is given at the end of this book.

Drug discovery: Past, present and future.- Endothelium-derived hyperpolarizing factor - a critical appraisal.- Isoprenoid biosynthesis via the mevalonate-independent route, a novel target for antibacterial drugs?.- Glutamatergic involvement in psychomotor stimulant action.- Polyamines and cerebral ischemia.- The identification and development of antiviral agents for the treatment of hepatitis B virus infection.- Index Vol. 50.- Index of titles, Vol. 1-50.- Author and paper index, Vol. 1-50.

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.

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).