Bøger udgivet af Birkhauser

I Invited Papers.- 1 On Robust and Adaptive Multi-Grid Methods.- 2 A Generalized Multigrid Theory in the Style of Standard Iterative Methods.- 3 Turbulence Modelling as a Multi-Level Approach.- 4 The Frequency Decomposition Multi-Grid Method.- 5 Multiscale Methods for Computing Propagators in Lattice Gauge Theory.- 6 Adaptive Multigrid on Distributed Memory Computers.- 7 Multicomputer-Multigrid Solution of Parabolic Partial Differential Equations.- 8 Multilevel Solution of Integral and Integro-differential Equations in Contact Mechanics and Lubrication.- Contributed Papers.- 1 A Multi-Grid Method for Calculation of Turbulence and Combustion.- 2 On a Multi-Grid Algorithm for the TBA Equations.- 3 A Multidimensional Upwind Solution Adaptive Multigrid Solver for Inviscid Cascades.- 4 Parallel Steady Euler Calculations using Multigrid Methods and Adaptive Irregular Meshes.- 5 Multigrid Methods for Steady Euler Equations Based on Multi-stage Jacobi Relaxation.- 6 Multigrid and Renormalization for Reservoir Simulation.- 7 Interpolation and Related Coarsening Techniques for the Algebraic Multigrid Method.- 8 Parallel Point-oriented Multilevel Methods.- 9 Large Discretization Step (LDS) Methods For Evolution Equations.- 10 A Full Multigrid Method Applied to Turbulent Flow using the SIM-PLEC Algorithm Together with a Collocated Arrangement.- 11 Multigrid Methods for Mixed Finite Element Discretizations of Variational Inequalities.- 12 Multigrid with Matrix-dependent Transfer Operators for Convection-diffusion Problems.- 13 Multilevel, Extrapolation, and Sparse Grid Methods.- 14 Robust Multi-grid with 7-point ILU Smoothing.- 15 Optimal Multigrid Method for Inviscid Flows.- 16 Multigrid Techniques for Simple Discretely Divergence-free Finite Element Spaces.- 17 Grid-independent Convergence Based on Preconditioning Techniques.- 18 A New Residual Smoothing Method for Multigrid Acceleration Applied to the Navier-Stokes Equations.

This book is based on the lectures given at the Oberwolfach Seminar held in Fall 2021. Logarithmic Gromov-Witten theory lies at the heart of modern approaches to mirror symmetry, but also opens up a number of new directions in enumerative geometry of a more classical flavour. Tropical geometry forms the calculus through which calculations in this subject are carried out. These notes cover the foundational aspects of this tropical calculus, geometric aspects of the degeneration formula for Gromov-Witten invariants, and the practical nuances of working with and enumerating tropical curves. Readers will get an assisted entry route to the subject, focusing on examples and explicit calculations.

1. Local integrability of systems of m smooth linearly independent complex vector fields on m + 1 dimensional manifolds.- 2. On asymptotic properties of the one-dimensional Schrödinger equation.- 3. On Qp functions.- 4. On Green's functions for subelliptic operators.- 5. Clifford analysis on Poincaré space.- 6. Unitarily invariant trace extensions beyond the trace class.- 7. L2 results for $$\overline \partial$$ in a conic.- 8. Lie superalgebras of supermatrices of complex size. Their generalizations and related integrable systems.- 9. A new local variant of the Hausdorff-Young inequality.- 10. Spectral asymptotics of the N particle Schrödinger equation when N ? ? and normal forms of the quadratic boson operators.- 11. A survey of Qp spaces.- 12. Hurwitz-type and space-time-type duality theorems for Hermitian Hurwitz pairs.- 13. On the problem of deciding whether a holomorphic vector field is complete.- 14. Variations on a theorem of Severi.- 15. Bergman-Toeplitz and pseudodifferential operators.- 16. The small Hankel operator in several complex variables.- 17. The reproducing kernel Hilbert space and its multiplication operators.- 18. Lie algebras in Fock space.

This monograph explores the problem of boundary regularity and analytic continuation of holomorphic mappings between domains in complex Euclidean spaces. Many important methods and techniques in several complex variables have been developed in connection with these questions, and the goal of this book is to introduce the reader to some of these approaches and to demonstrate how they can be used in the context of boundary properties of holomorphic maps. The authors present substantial results concerning holomorphic mappings in several complex variables with improved and often simplified proofs. Emphasis is placed on geometric methods, including the Kobayashi metric, the Scaling method, Segre varieties, and the Reflection principle. Geometry of Holomorphic Mappings will provide a valuable resource for PhD students in complex analysis and complex geometry; it will also be of interest to researchers in these areas as a reference.

This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium.The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.

This book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. It splits into three parts. Part one, which is contained in Chapter 1, describes the classical cardinal arithmetic due to Bernstein, Cantor, Hausdorff, Konig, and Tarski. The results were found in the years between 1870 and 1930. Part two, which is Chapter 2, characterizes the development of cardinal arith- metic in the seventies, which was led by Galvin, Hajnal, and Silver. The third part, contained in Chapters 3 to 9, presents the fundamental investigations in pcf-theory which has been developed by S. Shelah to answer the questions left open in the seventies. All theorems presented in Chapter 3 and Chapters 5 to 9 are due to Shelah, unless otherwise stated. We are greatly indebted to all those set theorists whose work we have tried to expound. Concerning the literature we owe very much to S. Shelah's book [Sh5] and to the article by M. R. Burke and M. Magidor [BM] which also initiated our students' interest for Shelah's pcf-theory.

U-50,488 and the K receptor. Part II: 1991-1998.- Quantitative structure-activity relationships of antihypertensive agents.- Combinatorial chemistry: Polymer supported synthesis of peptide and nonpeptide libraries.- From genome to drug - optimising the drug discovery process.- Phosphodiesterase 4 (PDE4) inhibitors in asthma and chronic obstructive pulmonary disease (COPD.- Index Vol. 53.- Index of titles, Vol. 1-53.- Author and paper index, Vol. 1-53.

New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions.This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others.Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.

In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only ?nitely additive measure of total measure one, de?ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at ?rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan's property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related.

Band XIb-2 ist - abgesehen von einigen Erganzungen zu den Banden XIa und XIb-1 - den Sekundarstoffen der Papilionoideae gewidmet und bietet einen wohl einmaligen Uberblick uber die Chemotaxonomie und die sekundaren Inhaltsstoffe dieser Pflanzengruppe. Er ist daher von speziellem Interesse fur Leguminosenforscher, Pharmakologen, Phytochemiker und Ethnobotaniker. Wie die Bande XIa und XIb-1 enthalt auch dieser Band zahlreiche Literaturhinweise und ein Register mit taxonomischem Index und Stichwortverzeichnis. Dieser letzte Band stellt nach etwa vierzigjahriger Arbeit den Abschluss der Chemotaxonomie der Pflanzen von Robert Hegnauer dar. Der erste Band erschien 1962; bei der Aufnahme des Autors in die Leopoldina (1972) waren sechs Bande abgeschlossen, die alle Familien der hoheren Pflanzen mit Ausnahme der Leguminosen berucksichtigten. Diesen Banden folgten drei Nachtragsbande und ein Generalregister sowie drei Bande uber Leguminosen."

This volume collects the proceedings of the International Conference on Recent Developments in Mathematics (ICRDM), held at Canadian University Dubai, UAE, in August 2022. This is the second of two volumes, with this volume focusing on more applied topics, particularly mathematical modeling and scientific computing, and the first covering recent advances in algebra and analysis. Each chapter identifies existing research problems, the techniques needed to solve them, and a thorough analysis of the obtained results. Advances in Mathematical Modeling and Scientific Computing will appeal to a range of postgraduate students, researchers, and industry professionals interested in exploring recent advancements in applied mathematics.

0 Basic Facts.- 1 Hey's Theorem and Consequences.- 2 Siegel-Weyl Reduction Theory.- 3 The Tamagawa Number and the Volume of G(?)/G(?).- 3.1 Statement of the main result.- 3.2 Proof of 3.1.- 3.3 The volume of G(?)/G(?).- 4 The Size of ?.- 4.1 Statement of results.- 4.2 Proofs.- 5 Margulis' Finiteness Theorem.- 5.1 The Result.- 5.2 Amenable groups.- 5.3 Kazhdan's property (T).- 5.4 Proof of 5.1; beginning.- 5.5 Interlude: parabolics and their opposites.- 5.6 Continuation of the proof.- 5.7 Contracting automorphisms and the Moore Ergodicity theorem.- 5.8 End of proof.- 5.9 Appendix on measure theory.- 6 A Zariski Dense and a Free Subgroup of ?.- 7 An Example.- 8 Problems.- 8.1 Generators.- 8.2 The congruence problem.- 8.3 Betti numbers.- References.

1. Die Sprache der Wahrscheinlichkeiten.- 2. Ereignisse.- 3. Wahrscheinlichkeitsräume.- 4. Diskrete Wahrscheinlichkeiten. Abzählungen.- 5. Zufallsvariable.- 6. Bedingte Wahrscheinlichkeit. Unabhängigkeit.- 7. Diskrete Zufallsvariable. Gebräuchliche Verteilungen.- 8. Erwartungswerte. Charakteristische Werte.- 9. Erzeugende Funktionen.- 10. Stieltjes-Lebesgue-Masse. Integrale von reellen Zufallsvariablen.- 11. Erwartungswerte. Absolut stetige Verteilungen.- 12. Zufallsvektoren. Bedingte Erwartungswerte. Normalverteilung.- 13. Erzeugende Funktionen der Momente. Charakteristische Funktionen.- 14. Die wichtigsten (absolut stetigen) Wahrscheinlichkeitsverteilungen.- 15. Verteilungen von Funktionen einer Zufallsvariablen.- 16. Stochastische Konvergenz.- 17. Gesetze der grossen Zahlen.- 18. Zentrale Rolle der Normalverteilung. Zentraler Grenzwertsatz.- 19. Gesetz vom iterierten Logarithmus.- 20. Anwendungen der Wahrscheinlichkeitsrechnung.- Lösungen der Übungsaufgaben.

Alfonso Vignoli - the Researcher, Teacher, and Friend.- How to Make Use of the Solution Set to Solve Boundary Value Problems.- On the Unique Solvability of Hammerstein Integral Equations with Non-Symmetric Kernels.- The Invariance of Domain for C1Fredholm Maps of Index Zero.- Positive Eigenfunctions for Some Unbounded Differential Operators.- Some Geometrical Properties of Rearrangement Invariant Spaces.- Strong Surjections and Nearness.- On the Vanishing Viscosity Approximation of a Time Dependent Hamilton-Jacobi Equation.- Some Remarks on a Nonlinear Model of Competitive Equilibrium.- Almost Discrete Convergence.- Nonlinear Stability of Eigenvalues of Compact Self-Adjoint Operators.- A Bifurcation Theorem for Lagrangian Intersections.- La valutazione di opzioni implicite nei mutui bancari.- Continuity of Near-Duality Maps and Characterizations of Ideal Spaces of Measurable Functions.- A Spectral Theory for Semilinear Operators and its Applications.- Feedback Stability of Closed Sets for Nonlinear Control Systems.- Two Mechanical Systems and Equivariant Degree.- On the Semilinear Dirichlet Problem for a Class of Nonlocal Operators Generating Dirichlet Forms.- Bifurcation for One-Parameter Families of Scalar Maps: A Geometric Viewpoint.- Mountain Pass and Linking Type Solutions for Semilinear Dirichlet Forms.- Self-Similar Measures in Quasi-Metric Spaces.- C1-Fredholm Maps and Bifurcation for Quasilinear Elliptic Equations on$${\mathbb{R}^n} $$.

Instability in the Spectral and the Fredholm Properties of an Infinite Dimensional Dirac Operator on the Abstract Boson-Fermion Fock Space.- Well-Posedness of Nonlinear Parabolic Equations of Viscous Hamilton-Jacobi Type.- Non-Convex Minimization - the Case of Vector Fields.- On the One Dimensional Behaviour of Atoms in Intense Homogeneous Magnetic Fields.- Semi-Classical Resolvent Estimates and Spectral Asymptotics for Trapping Perturbations.- Semiclassical Pseudodifferential Operators with Double Discontinuous Symbols and their Application to Problems of Quantum Statistical Physics.- A Free Boundary Value Problem Arisen in Unsteady Compressible Flow.- Some New Results on the Nonlinear Singular Partial Differential Equations.- A Unified Approach to the Theory of Fundamental Solutions, Non-degenerate Case.- Fourier Integral Operators in SG Classes: Classical Operators.- A Semigroup Criterion for the Completeness of Scattering Systems.- Parameter-Elliptic Boundary Value Problems and their Formal Asymptotic Solutions.- Solutions of q-Deformed Equations with Quantum Conformal Symmetry.- On the Regularization and Stabilization of Approximation Schemes for C0-Semigroups.- Pseudodifferential Operators with Symbols in Weighted Function Spaces of Quasi-Subadditive Type.- Spectral Analysis of Quantum Field Models with a Particle Number Cutoff.- On the Norm Convergence of the Trotter-Kato Product Formula with Error Bound.- Nonperturbative Techniques in the Investigation of the Spectral Properties of Many-Channel Systems.- Essential Self-Adjointness of n-Dimensional Dirac Operators with a Variable Mass Term.- Towards the Spectral Analysis of Schrödinger Operator with Fractal Perturbation.- On $$\mathcal{H}_{ - 4} - $$-4 -Perturbations of Self-Adjoint Operators.- Global Attractor for Generalized 2D Ginzburg-Landau Equation.- Local Asymptotic Properties of Multifractional Brownian Motion.- Strong Uniqueness for Dirichlet Operators with Singular Potentials.- Hardy Type Inequalities, Mourre Estimate and A-priori Decay for Eigenfunctions.- Surgery and the Relative Index in Elliptic Theory.- Propagation of Wave Packets and its Applications.- Gevrey and Analytic Properties of the Solutions of Several Classes of Partial Differential Equations.- Periodic Manifolds, Spectral Gaps, and Eigenvalues in Gaps.- Stability of Inverse Operators of Boundary Value Problems in Non-Smooth Expanding Domains.- Local Algebra of a Non-Symmetric Corner.- The Integrated Density of States for a Random Schrödinger Operator in Strong Magnetic Fields. II. Asymptotics near Higher Landau Levels.- Partial Differential Operators with Multiple Symplectic Characteristics.- On the Homotopy Classification of Elliptic Boundary Value Problems.- Bosons in a Trap: Asymptotic Exactness of the Gross-Pitaevskii Ground State Energy Formula.- Eigenfunction Expansions Associated with Relativistic Schrödinger Operators.- The Time-Dependent Approach to Inverse Scattering.- Cone Conormal Asymptotics.- List of Participants.- List of Talks.

Heinz Langer and his work.- On the spectra of some class of quadratic operator pencils.- Special realizations for Schur upper triangular operators.- On the defect of noncontractive operators in Kre?nin spaces: a new formula and some applications.- Positive differential operators in the Krein space L2(M?n).- Singular values of positive pencils and applications.- Perturbations of Krein spaces preserving the nonsingularity of the critical point infinity.- An analysis of the block structure of jqq-inner functions.- Selfadjoint extensions of the orthogonal sum of symmetric relations, II.- Some interpolation problems of Nevanlinna-Pick type. The Krein-Langer method.- On the spectral representation for singular selfadjoint boundary eigenvalue problems.- Some characteristics of a linear manifold in a Kre?nn space and their applications.- Riggings and relatively form bounded perturbations of nonnegative operators in Krem spaces.- Norm bounds for Volterra integral operators and time-varying linear systems with finite horizon.- The numerical range of selfadjoint matrix polynomials.- Spectral properties of a matrix polynomial connected with a component of its numerical range.- Lyapunov stability of a multiplication operator perturbed by a Volterra operator.- Multiplicative perturbations of positive operators in Krein spaces.- On the number of negative squares of certain functions.- Factorization of elliptic pencils and the Mandelstam hypothesis.- An inductive limit procedure within the quantum harmonic oscillator.- Canonical systems with a semibounded spectrum.

This monograph presents an original method to unify the mathematical theories of well-posed problems and contact mechanics. The author uses a new concept called the Tykhonov triple to develop a well-posedness theory in which every convergence result can be interpreted as a well-posedness result. This will be useful for studying a wide class of nonlinear problems, including fixed-point problems, inequality problems, and optimal control problems. Another unique feature of the manuscript is the unitary treatment of mathematical models of contact, for which new variational formulations and convergence results are presented. Well-Posed Nonlinear Problems will be a valuable resource for PhD students and researchers studying contact problems. It will also be accessible to interested researchers in related fields, such as physics, mechanics, engineering, and operations research.

A semigroup formulation of a nonlinear size-structured distributed rate population model.- Damage detection and characterization in smart material structures.- Optimality conditions for non-qualified parabolic control problems.- Convergence of trajectories for a controlled viscous Burgers' equation.- Optimality conditions for boundary control problems of parabolic type.- Pontryagin's principle for optimal control problems governed by semilinear elliptic equations.- Invariance of the Hamiltonian in control problems for semilinear parabolic distributed parameter systems.- Rate distribution modeling for structured heterogeneous populations.- A model for a two-layered plate with interfacial slip.- Numerical solution of a constrained control problem for a phase field model.- Uniform stabilizability of nonlinearly coupled Kirchhoff plate equations.- Boundary temperature control for thermally coupled Navier-Stokes equations.- Adaptive estimation of nonlinear distributed parameter systems.- Decay estimates for the wave equation with internal damping.- On the controllability of the rotation of a flexible arm.- Modeling and controllability of interconnected elastic membranes.- On feedback controls for dynamic networks of strings and beams and their numerical simulation.- Various relaxations in optimal control of distributed parameter systems.- Convergence of an SQP-method for a class of nonlinear parabolic boundary control problems.- Conditional stability in determination of densities of heat sources in a bounded domain.- Boundary stabilization of the Korteweg-de Vries equation.- Controllability of the linear system of thermoelasticity: Dirichlet-Neumann boundary conditions.

This volume contains a collection of articles on state-of-the-art developments in the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Seventeenth International Conference on Integral Methods in Science and Engineering, held virtually in July 2022, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical, electrical, and petroleum engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential working tool.

Basic Research Overview.- Cellular and molecular mechanisms of Alzheimer's disease inflammation.- Clinical Research Overview.- Anti-inflammatory agents as possible protective factors for Alzheimer's disease: Analysis of relevant epidemiological studies.- Topics of Special Interest.- Role and regulation of early complement activation products in Alzheimer's disease.- Complement mediator systems in Alzheimer's disease.- Amyloid ? peptide interactions with the classical pathway of complement.- Physiology and biochemistry of the interleukin-6 receptor complex. Implications for CNS disorders and Alzheimer's disease.- Interactions of ?2-macroglobulin and amyloid ? peptide.- Proinflammatory actions of derivatives of the ? amyloid precursor protein.- The involvement of glial cell-derived reactive oxygen and nitrogen species in Alzheimer's disease.- The role of cyclooxygenase in Alzheimer's disease neurodegeneration.- Microglia.- Neurons.- The gero-inflammatory manifold.

Alternative medicine: Herbal drugs and their critical appraisal - Part II.- Virus population dynamics, fitness variations and the control of viral disease: an update.- Applications of yeast in drug discovery.- Sympathetic nervous system and experimental diabetes: role of adrenal medullary hormones.- From outer to inner space: Traveling along a scientific career from astrochemistry to drug research.- Index Vol. 57.- Index of titles, Vol. 1-57.- Author and paper index, Vol. 1-57.

The present volume contains the proceedings of the International Conference on Ap- plications of Operator Theory held in Winnipeg, Canada (October 2nd to 6th, 1994), which was organized by the Institute of Industrial Mathematical Sciences (IIMS) of the University of Manitoba. At this conference 92 participants representing 15 countries par- ticipated, and 64 papers were presented. This meeting was the second of a linked pair. The first was a program of advanced instruction held at the Fields Institute, Ontario, followed by a research conference. The first of these events gave rise to the volume "Lectures on Operator Theory and its Applications", published by the American Mathematical Society for the Fields Institute in 1995. These two events were the creation of the following Program Committee: M. A. Dahleh (M. I. T. ) P. A. Fillmore (Dalhousie) B. A. Francis (Toronto) F. Ghahramani (Manitoba) K. Glover (Cambridge) I. Gohberg (Tel Aviv) T. Kailath (Stanford) P. Lancaster (Calgary), Chair H. Langer (Vienna) P. N. Shivakumar (Manitoba) A. A. Shkalikov (Moscow) B. Simon (Cal. Tech. ) H. Widom (Santa Cruz) Both events focused on the following main topics: Infinite matrices and projection methods, linear operators on indefinite scalar product spaces, differential operators and mathematical systems theory and control. This volume contains a selection of papers in modern operator theory and its appli- cations. They are dedicated to recent achievements and many are written by leaders in the mentioned fields.

Infinite length modules. Some Examples as Introduction.- Modules with strange decomposition properties.- Failure of the Krull-Schmidt theorem for artinian modules and serial modules.- Artinian modules over a matrix ring.- Some combinatorial principles for solving algebraic problems.- Dimension theory of noetherian rings.- Krull, Gelfand-Kirillov, Filter, Faithful and Schur dimensions.- Cohen-Macaulay modules and approximations.- The generic representation theory of finite fields A survey of basic structures.- On artinian objects in the category of functors between $${{\mathbb{F}}_{2}} $$ -vector spaces.- Unstable modules over the Steenrod algebra, functors, and the cohomology of spaces.- Infinite dimensional modules for finite groups.- Bousfield localization for representation theoretists.- The thick subcategory generated by the trivial module.- Birational classification of moduli spaces.- Tame algebras and degenerations of modules.- On some tame and discrete families of modules.- Purity, algebraic compactness, direct sum decompositions, and representation type.- Topological and geometrical aspects of the Ziegler spectrum.- Finite versus infinite dimensional representations A new definition of tameness.- Invariance of tameness under stable equivalence: Krause's theorem.- The Krull-Gabriel dimension of an algebra Open problems and conjectures.- Homological differences between finite and infinite dimensional representations of algebras

Joint spectrum and discriminant varieties of commuting nonselfadjoint operators.- 1. Introduction.- 2. Joint spectra of commuting operators with compact imaginary parts.- 3. Colligations and vessels.- 4. The discriminant varieties.- References.- On the differential structure of matrix-valued rational inner functions.- 1. Introduction and preliminaries.- 2. The differential structure of Inp.- 3. Charts using Schur algorithm.- 4. Conclusion.- References.- Conservative dynamical systems and nonlinear Livsic-Brodskii nodes.- 1. Conservative systems.- 2. Nonlinear Livsic-Brodskii nodes: models for a given dynamics up to energy preserving diffeomorphic change of variable.- 3. Other partionings of the cast of characters into knowns and unknowns.- References.- Orthogonal polynomials over Hilbert modules.- 1. Introduction.- 2. Orthogonalization with invertible squares.- 3. Preliminaries on inertia theorems for unilateral shifts.- 4. The main result.- References.- Relations of linking and duality between symmetric gauge functions.- 1. Introduction.- 2. Linked symmetric gauge functions.- 3. Quotient of symmetric gauge functions.- 4. Q-norms.- References.- Julia operators and coefficient problems.- 1. Introduction.- 2. Julia operators for triangular matrices.- 3. Multiplication transformations on power series.- 4. Extension problem for substitution transformations.- Appendix. Formal algebra.- References.- Shifts, realizations and interpolation, Redux.- 1. Introduction.- 2. Formulas and facts.- 3. R? variance.- 4. Realizations.- 5. Reproducing kernel spaces.- 6. H(S) spaces.- 7. A basic interpolation problem.- 8. Factorization and recursive methods.- 9. Characteristic functions.- References.- Arveson's distance formulae and robust stabilization for linear time-varying systems.- 1. Introduction.- 2. Preliminaries.- 3. Stabilization and proper representations.- 4. Robust stabilization: Proper representation uncertainty.- 5. Gap metric robustness.- Entire cyclic cohomology of Banach algebras.- 1. Background.- 2. Definitions.- 3. Results.- References.- The bounded real characteristic function and Nehari extensions.- 1. Introduction.- 2. Bounded real functions.- 3. Hankel operators.- 4. State space realizations.- 5. Suboptimal Nehari extensions.- References.- On isometric isomorphism between the second dual to the "small" Lipschitz space and the "big" Lipschitz space.- The Kantorovich-Rubinstein norm.- Completion of the space of measures in the KR norm.- Critical and noncritical metric spaces.- References.- Rules for computer simplification of the formulas in operator model theory and linear systems.- I. Introduction.- II. The reduction and basis algorithms.- III. Operator relations with finite basis for rules.- IV. Operator relations with infinite basis for rules.- V. A new algebra containing the functional calculus of operator theory.- VI. Gröbner basis property.- VII. Summary of practical rules you might use.- References.- Some global properties of fractional-linear transformations.- Preliminaries.- 1. The case of invertible plus-operators.- 2. The general case of a non-invertible operator U.- References.- Boundary values of Berezin symbols.- 1. Introduction.- 2. Compactness criterion.- 3. Continuous Berezin symbols.- 4. Two questions.- References.- Generalized Hermite polynomials and the bose-like oscillator calculus.- 1. Introduction.- 2. Generalized Hermite polynomials.- 3. The generalized Fourier transform.- 4. Generalized translation.- 5. The Bose-like oscillator.- References.- A general theory of sufficient collections of norms with a prescribed semigroup of contractions.- 1. Formulation of the problem.- 2. Notions.- 3. Formulations of results.- 4. Proofs of results.- References.

The Badgastein Lecture.- The Challenge of the 21st Century.- Neurology, Psychiatry.- First Evaluation in Humans of [123I]PE21: A Selective Radioligand for Visualization of the Striatal Dopamine Transporter Density.- Comparison of Iodine-123 labelled Nor-ß-Cit and ß-Cit as Potential Radioligands for Serotonin Transporter Imaging.- Brain Serotonin and Dopamine Transporters in Depressive Children.- Prognostic Potential of Tc-99m-ECD-SPET within 6 Hours after Onset of Stroke Symptoms.- Brain Perfusion in Patients with Severe Sleep Apnea Syndrome (SAS) before and after n-CPAP-Therapy.- Therapy.- Radioimmunotherapy of Colorectal Cancer in Small Volume Disease: Preclinical Evaluation in Comparison To Equitoxic Chemotherapy and Preliminary Results of an Ongoing Phase-I/II Clinical Trial.- Radioimmunotherapy of Glioblastoma by Using I-131 and Y-90 Labeled Anti-tenascin Monoclonal Antibodies.- I-131-Lipiodol Therapy in Liver Neoplasms.- Individualized Dose Estimation for Sr-89 with the Use of Diagnostic Tc-99m MDP Bone Scintigraphy.- Rhenium-186-HEDP and Strontium-89-Chloride in Treatment of Metastatic Bone Pain.- The Development of Chromatographic 188W/188Re Generators for Therapy.- Radiopharmacology.- Evaluation of mRNA Targeting by Labeled Oligonucleotides for Tumor-Diagnosis.- Synthesis and Evaluation of [123I]-Iodoaminoglutethimide, a Ligand for Visualization of the Aromatase Enzyme by SPECT.- Comparative Analysis of Kinetic Models to Study Glucose Metabolism of the Brain.- Bone Scintigraphy and Palliative Therapy with Multibone Kit.- Pharmaosintigraphic Study of Localization in the G.I. Tract of Controlled Release Tablets Using 153Sm as Marker.- Endocrinology, Thyroid.- On the Use of Routine Preoperative Scintigraphy in Thyroid Carcinoma Patients.- The Value of HMPAO SPECT Scanning in Patients with Congenital Hypothyreosis.- Advanced Stage Thyroid Cancer - Treatment with Isotretinoin.- Is SPECT-Technique Necessary for Preoperative Diagnosis of Parathyroid Adenoma ?.- Oncology, Haematology.- Comparison of Interlesionally and Systemically Administered Radiolabelled Monoclonal Antibodies in Implanted Tumours.- Comparison of MRI and Somatostatin Receptor Scintigraphy (SRS) in Post-surgical Follow-up of Meningioma.- Comparison of Contrast Enhanced MRI, Tc-99m Hydroxymethylene Diphosphonate and Tc-99m Tetrofosmin Scintimammography in Patients with Suspicious Breast Lesions.- Neoadjuvant Treatment of Patients with Breast Cancer under Surveillance of 99mTc-Tetrofosmin Scintigraphy.- 99Tc-Furifosmin Uptake by Melanoma Cells.- Lymphoscintigraphy in Tumors of the Head and Neck Using a Double Tracer Technique.- Clinical PET.- Clinical Application of 18FDG-PET in the Assessment of Head and Neck Tumors.- The Role of FDG-PET and MIBI Investigations in the Restaging of Treated Patients with Malignant Lymphomas.- Assessment of Pulmonary Nodules and Colorectal Cancer Recurrences by FDG Scan on an"Ordinary" Coincidence Gamma Camera (CDET).- Clinical Utility of 18FDG-PET with Molecular Coincidence Detection (MCD) and a Modified SPECT-Camera.- Deoxyglucose Uptake by Apoptosing and Proliferating Colonic Tumour Cells.- Cardiology.- Relation Between Viability, Improvement of LVEF and Heart Failure Symptoms after Revascularization.- Attenuation Corrected Tl-201 SPECT Using a Gd-153 Moving Line Source: Clinical Value and the Impact of Attenuation Correction on the Extent and Severity of Perfusion Abnormalities.- Correlation of EBCT and Tl-201-SPECT Scintigraphy in Patients with Coronary Heart Disease.- Influence of Right Ventricular Stimulation Site on Left Ventricular Function in a Trial Synchronous Pacing.- Varia.- 153Sm-EDTMP for Pain Relief in Malignant and Benign Bone and Joint Diseases.- Tc-99m-Tetrofosmin SPECT Scintigraphy in the Post-operative Follow-up of Microvascular Anastomosed Flaps in Facial Reconstruction.- Long-Term Follow-up Study of Gastric Emptying and Helicobacter Pylori Eradication among Patients with Functional Dyspepsia.- The Valu

Peptidases: a view of classification and nomenclature.- Carboxypeptidases.- Signal peptidases.- Proteasomes.- Cathepsin E and cathepsin D.- Cell-associated metalloproteinases.- Proteinases in parasites.- Cell-surface proteases in cancer.- Insect proteinases.- Alzheimer's disease and proteinases.- Calpains: structure and function of the calpain super family.- Arg-gingipain and Lys-gingipain: a novel class of cysteine proteinases.- Proteinases in apoptosis.- Caspases: cytokine activators and promoters of cell death.- Lysosomal cysteine proteinases: Structure and regulation.

1 Introduction.- 2 Schatten-von Neumann Classes.- 3 Topological Groups.- 4 Haar Measures and Modular Functions.- 5 Unitary Representations.- 6 Square-Integrable Representations.- 7 Wavelet Transforms.- 8 A Sampling Theorem.- 9 Wavelet Constants.- 10 Adjoints.- 11 Compact Groups.- 12 Localization Operators.- 13 Sp Norm Inequalities, 1 ? p ? ?.- 14 Trace Class Norm Inequalities.- 15 Hilbert-Schmidt Localization Operators.- 16 Two-Wavelet Theory.- 17 The Weyl-Heisenberg Group.- 18 The Affine Group.- 19 Wavelet Multipliers.- 20 The Landau-Pollak-Slepian Operator.- 21 Products of Wavelet Multipliers.- 22 Products of Daubechies Operators.- 23 Gaussians.- 24 Group Actions and Homogeneous Spaces.- 25 A Unification.- 26 The Affine Group Action on ?.- References.