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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.

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.

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.

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.

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.

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.

A Interpolation And Time-Invariant Systems.- I. Interpolation Problems For Operator-Valued Functions.- 1.1. Preliminaries About Notation And Terminology.- 1.2. Nevanlinna-Pick Interpolation.- 1.3. Tangential Nevanlinna-Pick Interpolation.- 1.4. Controllability Operators And Interpolation.- 1.5. Tangential Hermite-Fejer Interpolation.- 1.6. The Nehari Extension Problem.- 1.7. Sarason Interpolation.- 1.8. Nevanlinna-Pick Interpolation Viewed As A Sarason Problem.- 1.9. Two-Sided Nudelman Interpolation.- 1.10. The Two-Sided Sarason Problem.- 1.11. A Filtering Problem.- Notes To Chapter I.- II. Proofs Using The Commutant Lifting Theorem.- II.1. The Commutant Lifting Theorem.- II.2. Proof Of The Standard Left Nevanlinna-Pick Interpolation Theorem.- II.3. Proof Of The Nehari Extension Theorem.- II.4. Proof of the Sarason Theorem.- II.5. Proof of the Two-Sided Nudelman Theorem.- II.6. Proof of the Two-Sided Sarason Theorem.- Notes to Chapter II.- III. Time Invariant Systems.- III.1. State Space Analysis.- III.2. Controllability and Observability.- III.3. Point Evaluation.- III.4. Realization Theory.- III.5. Anticausal Realizations.- III.6. Computing the Hankel form.- III.7. Computing the Projection in the Sarason Problem.- III.8. Explicit Conversion Formulas.- III.9. Connecting Nudelman and Two-Sided Sarason Problems.- III.10. Isometric and Unitary Systems.- Notes to Chapter III.- IV. Central Commutant Lifting.- IV. 1. Minimal Isometric Liftings.- IV.2. The Central Intertwining Lifting.- IV.3. Central Intertwining Lifting Formulas.- IV.4. Central Intertwining Lifting Quotient Formulas.- IV.5. The Central Schur Solution.- IV.6. The Quasi Outer Factor for D2/By.- IV.7. Maximum Entropy.- IV.8. Some Mixed Bounds for the Central Intertwining Lifting.- IV.9. A Mixed Two-Sided Sarason Result.- Notes To Chapter IV.- V. Central State Space Solutions.- V.1. The Central Formula For Nevanlinna-Pick.- V.2. Central Nevanlinna-Pick Solutions.- V.3. The Central Hermite-Fejer Solution.- V.4. The Central Formula For The Sarason Problem.- V.5. Central Nehari Solutions.- V.6. Central Nudelman Solutions.- V.7. The Central Two Block Solution.- V.8. The Four Block Problem.- Notes To Chapter V.- VI. Parameterization Of Intertwining Liftings And Its Applications.- VI.1. The Möbius Transformation.- VI.2. The Schur Parameterization.- VI.3. Recovering The Schur Contraction..- VI. 4. Constructing The Schur Contraction.- VI.5. The Redheffer Scattering Parameterization.- VI.6. The Parameterization for A ?.- VI.7. The Nevalinna-Pick Parameterization.- VI.8. The Nehari Parameterization.- VI.9. The Two Block Parameterization.- Notes To Chapter VI.- VII. Applications to Control Systems.- VII. 1. Feedback Control.- VII.2. The Youla Parameterization.- VII.3. Mixed H? and H2 Control Problems.- VII.4. A Two Block Control Problem.- VII.5. The Multivariable Case.- Notes To Chapter VII.- B Nonstationary Interpolation and Time-Varying Systems.- VIII. Nonstationary Interpolation Theorems.- VIII.1. Nonstationary Nevanlinna-Pick Interpolation.- VIII.2. Nonstationary Tangential Nevanlinna-Pick Interpolation.- VIII.3. Nonstationary Tangential Hermite-Fejer Interpolation.- VIII.4. Nonstationary Nehari Interpolation.- VIII.5. Nonstationary Sarason Interpolation.- VIII.6. Nonstationary Nudelman Interpolation.- VIII.7. Nonstationary Two-Sided Sarason Interpolation.- Notes to Chapter VIII.- IX. Nonstationary Systems and Point Evaluation.- IX.1. Time Varying Systems.- IX.2. Nonstationary Controllability and Observability.- IX.3. Point Evaluation.- IX.4. From Nonstationary Systems to Stationary Systems.- IX.5. A Nonstationary Filtering Problem.- Notes to Chapter IX.- X. Reduction Techniques: From Nonstationary to Stationary and Vice Versa.- X.1. Spatial Features.- X.2. Operator Features.- Notes to Chapter X.- XI. Proofs of the Nonstationary Interpolation Theorems by Reduction to the Stationary Case.- XI.1. The Standard Nonstationary Nevanlinna-Pick Interpolation Theorem.- XI.2. The Nons

Variational methods in mechanics and physical models.- Fluid flows in dielectric porous media.- The impact of a jet with two fluids on a porous wall.- Critical point methods in nonlinear eigenvalue problems with discontinuities.- Maximum principles for elliptic systems.- Exponential dichotomy of evolution operators in Banach spaces.- Asymptotic properties of solutions to evolution equations.- On some nonlinear elastic waves biperiodical or almost periodical in mechanics and extensions hyperbolic nonlinear partial differential equations.- The controllability of infinite dimensional and distributed parameter systems.- Singularities in boundary value problems and exact controllability of hyperbolic systems.- Exact controllability of a shallow shell model.- Inverse problem: Identification of a melting front in the 2D case.- Micro-local approach to the control for the plates equation.- Bounded solutions for controlled hyperbolic systems.- Controllability and turbulence.- The H? control problem.- The H? boundary control with state feedback; the hyperbolic case.- Remarks on the theory of robust control.- The dynamic programming method.- Optimality and characteristics of Hamilton-Jacobi-Bellman equations.- Verification theorems of dynamic programming type in optimal control.- Isaacs' equations for value-functions of differential games.- Optimal control for robot manipulators.- Control theory and environmental problems: Slow fast models for management of renewable ressources.- On the Riccati equations of stochastic control.- Optimal control of nonlinear partial differential equations.- A boundary Pontryagin's principle for the optimal control of state-constrained elliptic systems.- Controllability properties for elliptic systems, the fictitious domain method and optimal shape design problems.- Optimal control for elliptic equation and applications.- Inverse problems for variational inequalities.- The variation of the drag with respect to the domain in Navier-Stokes flow, .- Mathematical programming and nonsmooth optimization.- Scalar minimax properties in vectorial optimization.- Least-norm regularization for weak two-level optimization problems.- Continuity of the value function with respect to the set of constraints.- On integral inequalities involving logconcave functions.- Numerical solution of free boundary problems in solids mechanics.- Authors' index

This open access book covers the main topics for a course on the differential geometry of curves and surfaces. Unlike the common approach in existing textbooks, there is a strong focus on variational problems, ranging from elastic curves to surfaces that minimize area, or the Willmore functional. Moreover, emphasis is given on topics that are useful for applications in science and computer graphics. Most often these applications are concerned with finding the shape of a curve or a surface that minimizes physically meaningful energy. Manifolds are not introduced as such, but the presented approach provides preparation and motivation for a follow-up course on manifolds, and topics like the Gauss-Bonnet theorem for compact surfaces are covered.

1 Myc Structure and Function.- 2 The ETS Family of Transcriptional Regulators.- 3 myb Proto-Oncogene Product as a Transcriptional Regulator.- 4 The v-erbA Oncogene.- 5 Rel Proteins and Their Inhibitors: A Balancing Act.- 6 Structure/Function and Oncogenic Conversion of Fos and Jun.

1 Schrödinger and Dirac operators.- Discrete spectrum of the periodic Schrödinger operator for non-negative perturbations.- The discrete spectrum in a gap of the continuous one for compact supported perturbations.- Schrödinger operators with strong local magnetic perturbations: Existence of eigenvalues in gaps of the essential spectrum.- Regularity of the nodal sets of solutions to Schrödinger equations.- Results in the spectral theory of Schrödinger operators with wide potential barriers.- Stark ladders and perturbation theory.- Singular potentials: algebraization.- Asymptotic behavior of the resolvent of the Dirac operator.- Discrete spectrum of the perturbed Dirac operator.- 2 Generalized Schrödinger operators.- The spectrum of Schrödinger operators in Lp(Rd) and in C0(Rd).- On spectral properties of generalized Schrödinger operators.- A Fermi-type rule for contact embedded-eigenvalue perturbations.- A simple model for predissociation.- Scattering on several solenoids.- Hall conductance of Riemann surfaces.- 3 Stochastic spectral analysis.- Framework and results of stochastic spectral analysis.- Occupation time asymptotics to the decay of eigenfunctions.- Holomorphic semigroups and Schrödinger equations.- Some problems on submarkovian semigroups.- Smoothness estimates and uniqueness for the Dirichlet operator.- Trace ideal properties of perturbed Dirichlet semigroups.- Quantum dynamical semigroups.- 4 Many-body problems and statistical physics K.B. Sinha.- Limits of infinite order, dimensionality or number of components for random finite-difference operators.- Atoms at finite density and temperature and the spectra of reduced density matrices.- Quantum fluctuations in the many-body problem.- General Hamiltonians and model Hamiltonians.- Poisson fields representations in the statistical mechanics of conitinuous systems.- Exact ground states for quantum spin chains.- The spectrum of the spin-boson model.- A survey of Wigner-Poisson problems.- 5 Chaos.- Classical d'Alembert field in an one-dimensional pulsating region.- Irregular scattering in one-dimensional periodically driven systems.- Relatively random unitary operators.- 6 Operator theory and its application.- A trace formula for obstacles problems and applications.- Propagation in irregular optic fibres.- Singular perturbations, regularization and extension theory.- Adiabatic reduction theory. Semiclassical S-matrix for N-state one-dimensional systems.- The functional structure of the monodromy matrix for Harper's equation.- Eigenfunction expansion of right definite multiparameter problems.- Singularly perturbed operators.- Some problems of p-adic quantum theory.

Feller Semigroups, Bernstein type Operators and Generalized Convexity Associated with Positive Projections.- Gregory's Rational Cubic Splines in Interpolation Subject to Derivative Obstacles.- Interpolation by Splines on Triangulations Oleg Davydov.- On the Use of Quasi-Newton Methods in DAE-Codes.- On the Regularity of Some Differential Operators.- Some Inequalities for Trigonometric Polynomials and their Derivatives.- Inf-Convolution and Radial Basis Functions.- On a Special Property of the Averaged Modulus for Functions of Bounded Variation.- A Simple Approach to the Variational Theory for Interpolation on Spheres.- Constants in Comonotone Polynomial Approximation - A Survey.- Will Ramanujan kill Baker-Gammel-Wills? (A Selective Survey of Padé Approximation).- Approximation Operators of Binomial Type.- Certain Results involving Gammaoperators.- Recent research at Cambridge on radial basis functions.- Representation of quasi-interpolants as differential operators and applications.- Native Hilbert Spaces for Radial Basis Functions I.- Adaptive Approximation with Walsh-similar Functions.- Dual Recurrence and Christoffel-Darboux-Type Formulas for Orthogonal Polynomials.- On Some Problems of Weighted Polynomial Approximation and Interpolation.- Asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights. Some new theorems and applications.- List of participants.

1 The Abstract Cauchy Problem.- 1. Well-Posedness of the Differential Cauchy Problem in C(E).- 1. The Cauchy problem in a Banach space E. Definition of well-posedness in C(E).- 2. Examples of well-posed and ill-posed problems in C(E).- 3. The homogeneous equation. Strongly continuous semigroups.- 4. The nonhomogeneous equation. Analytic semigroups.- 5. Well-posedness in C(E) of the general Cauchy problem.- 2. Well-Posedness of the Cauchy Problem inC0?(E).- 1. The homogeneous problem. The space C0?(E).- 2. Well-posedness in C0?(E) of the general Cauchy problem.- 3. Well-Posedness of the Cauchy Problem in Lp(E).- 1. Definition of the well-posedness of the Cauchy problem in LP(E).- 2. A formula for the solution of the Cauchy problem in Lp(E).- 3. Spaces of initial data.- 4. The values of the solution of the Cauchy problem in Lp(E) for fixed t.- 5. The coercivity inequality for the solutions in Lp(E) of the general problem (1.1).- 4. Well-Posedness of the Cauchy Problem in Lp(E?, Q).- 5. Well-Posedness of the Cauchy Problem in Spaces of Smooth Functions.- 1. The space C0ß, ?(E). The nonhomogeneous problem.- 2. Well-posedness of the general problem.- 3. Semigroup estimates.- 4. The coercivity inequality for the general problem.- 2 The Rothe Difference Scheme.- 0. Stability of the Difference Problem.- 1. The difference problem.- 2. Banach spaces of grid functions.- 3. The operator equation in ?(E). Definition of the stability of the difference scheme.- 4. Stability of the difference scheme.- 1. Well-Posedness of the Difference Problem in C(E).- 1. The homogeneous difference problem.- 2. The nonhomogeneous problem. A real-field criterion for analyticity.- 3. An almost coercive inequality in C(E).- 2. Well-Posedness of the Difference Problem in C0?(E).- 3. Well-Posedness of the Difference Problem in Lp(E).- 1. Definition of the well-posedness of the difference problem in LP(E).- 2. Spaces of initial data.- 3. The coercivity inequality for the solutions in LP(E) of the general problem (0.6).- 4. Well-Posedness of the Difference Problem in Lp(E?, Q).- 1. Strongly positive operators and fractional spaces.- 2. Well-posedness of the difference problem in Lp(E'?, q).- 5. Well-Posedness of the Difference Problem in Difference Analogues of Spaces of Smooth Functions.- 1. The space CQ'(E). The nonhomogeneous difference problem.- 2. Well-posedness of the general difference problem.- 3. Estimates for powers of the resolvent.- 4. The coercivity inequality for the general problem.- 3 PadÉ Difference Schemes.- 0. Stability of the Difference Problem.- 1. Padé approximants of the function e-z.- 2. Difference schemes of Padé class.- 1. Well-Posedness of the Difference Problem in C(E).- 1. The homogeneous problem.- 2. The nonhomogeneous problem.- 3. Sufficient conditions for almost-well-posedness. A real-field criterion for analyticity.- 4. Estimates of powers of the operator step.- 2. Well-Posedness of the Difference Problem in C0?(E).- 1. The case of a general space C0?(E).- 2. The case of the special space C0? (E).- 3. Well-Posedness of the Difference Problem in Lp(E).- 1. Definition of the well-posedness of the difference problem in Lp(E). Stability of the difference problem.- 2. Spaces of initial data. Well-posedness of the difference problem.- 3. Estimates of powers of the operator step.- 4. Well-Posedness of the Difference Problem in Lp(E'?, Q).- 1. Stability of the difference problem.- 2. Well-posedness of the difference problem.- 5. Well-Posedness of the Difference Problem in Difference Analogues of Spaces of Smooth Functions.- 1. Well-posedness of the difference problem in C0ß, ? (E).- 2. Estimates of powers of the operator step. The coercivity inequality for the general problem.- 4 Difference Schemes for Parabolic Equations.- 1. Elliptic Difference Operators with Constant Coefficients.- 1. The definition of an elliptic difference operator and properties of its symbol.- 2. A formula for the solution of the resolvent equation.- 3. Point estimat

Taxonomy and phylogeny of the Glomales.- Biodiversity and characterization of arbuscular mycorrhizal fungi at the molecular level.- Characterization of arbuscular mycorrhizal fungi by immunochemical methods.- European Bank of Glomales - An essential tool for efficient international and interdisciplinary collaboration.- Physiological characteristics of the host plant promoting an undisturbed functioning of the mycorrhizal symbiosis.- Recognition and infection process, basis for host specificity of arbuscular mycorrhizal fungi.- Ultrastructural analysis reveals the complex interactions between root cells and arbuscular mycorrhizal fungi.- Impact of mycorrhizal colonisation on root architecture, root longevity and the formation of growth regulators.- Biogeochemical cycling and arbuscular mycorrhizas in the sustainability of plant-soil systems.- Arbuscular mycorrhizas and agrosystem stability.- Hyphal phosphorus transport, a keystone to mycorrhizal enhancement of plant growth.- Approaches to the study of the extraradical mycelium of arbuscular mycorrhizal fungi.- Water relations and alleviation of drought stress in mycorrhizal plants.- Impact of arbuscular mycorrhizal fungi on plant uptake of heavy metals and radionuclides from soil.- Biocontrol of plant pathogens using arbuscular mycorrhizal fungi.- Management of positive interactions of arbuscular mycorrhizal fungi with essential groups of soil microorganisms.- Micropropagated plants, an opportunity to positively manage mycorrhizal activities.