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1. Flows and Cascades.- 2. Equivalence Relations.- 3. Spaces of Systems of Differential Equations and of Diffeomorphisms.- 4. Hyperbolic Rest Point.- 5. Periodic Point and Closed Trajectory.- 6. Transversality.- 7. The Kupka-Smale Theorem.- 8. The Closing Lemma.- 9. Necessary Conditions for Structural Stability.- 10. Homoclinic Point.- 11. Morse-Smale Systems.- 12. Hyperbolic Sets.- 13. The Analytic Strong Transversality Condition.- Appendix. Proof of the Grobman-Hartman Theorem.- References.

On the spectral theory of degenerate quadratic operator pencils.- Two-sided tangential interpolation for Hilbert-Schmidt operator functions on polydisks.- Nonstationary analogs of the Herglotz representation theorem: realizations centered at an arbitrary point.- Characteristic functions of maximal sectorial operators.- Similarity between Krein space bicontractions and Hilbert space contractions.- Classification of cyclic invariant subspaces of Jordan operators.- Elliptic spectral problems of higher order with eigenparameter dependent boundary conditions.- About scattering on the ring.- Dilation of generalized Toeplitz kernels on lexicographic ? × R.- On Riccati equations and reproducing kernel spaces.- A status report on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities.- On the spectrum of unbounded off-diagonal 2 × 2 operator matrices in Banach spaces.- Multithreshold spectral phase transitions for a class of Jacobi matrices.- Positive extensions and diagonally connected patterns.- Parametrized Furuta inequality and its applications.- J-symmetric factorizations and algebraic Riccati equations.- Scattering of waves by periodic gratings and factorization problems.- Corner of numerical ranges.- On some classes of extensions of sectorial operators and dual pairs of contractions.- Liftings of intertwining operators.- Some estimates for the resolvent and for the lengths of Jordan chains of an analytic operator function.- The Parrott problem for singular values.- Unconditional decompositions and Schur-type multipliers.- Scattering in a loop-shaped waveguide.- Pseudospectra of operator polynomials.

This monograph highlights the connection between the theory of neutron transport and the theory of non-local branching processes. By detailing this frequently overlooked relationship, the authors provide readers an entry point into several active areas, particularly applications related to general radiation transport. Cutting-edge research published in recent years is collected here for convenient reference. Organized into two parts, the first offers a modern perspective on the relationship between the neutron branching process (NBP) and the neutron transport equation (NTE), as well as some of the core results concerning the growth and spread of mass of the NBP. The second part generalizes some of the theory put forward in the first, offering proofs in a broader context in order to show why NBPs are as malleable as they appear to be. Stochastic Neutron Transport will be a valuable resource for probabilists, and may also be of interest to numerical analysts and engineersin the field of nuclear research.

I. Introduction.- 1. Encountering Random.- 2. Specimens of Stochastic Reasoning.- II. Markovian Dynamics.- 1. Finite-state Markovian dynamical systems.- 2. The convex set of stochastic matrices.- 3. The asymptotic behavior of Pn: some special cases.- 4. Asymptotic behavior of P, P2, ...: the method of invariant sets.- III. Discrete Probability Spaces.- 1. The Notion of a Discrete Probability Space (DPS).- 2. Obtaining New Probability Spaces from Given Ones.- 3. Independence.- IV. Independent Identically Distributed (IID) Random Variables.- 1. Addition of independent RVs.- 2. Expectation and Variance.- 3. The Weak Law of Large Numbers (WLLN).- 4. The Central Limit Theorem (CLT) I.- 5. The Central Limit Theorem (CLT) II.- 6. Outlook.- V. Statistics.- 1. Specimens of Statistical Reasoning.- 2. The Game-Theoretical Framework of Statistical Theory.- 3. Tests.- 4. Outlook.- VI. Markov Processes.- 1. Conditional Probabilities.- 2. Markov Processes.- VII. Elements of Information Theory.- 1. Combinatorial and Algebraic Coding Theory.- 2. Source Coding.- 3. Noisy Channels.- VIII. Fluctuation Theory.- 1. The Combinatorial Arcsin Law of Erik Sparre Andersen.- 2. Arcsin.- 3. Symmetrically Distributed Random Variables.- 4. Fluctuations of Random Walks.- 5. The Andersen-Spitzer Formula.- 6. Outlook.- IX. Optimal Strategies in Casinoes: Red and Black.- 1. Strategies and Their Probability of Success.- 2. Some Properties of BOLD.- 3. The Optimality of BOLD for p ? 1/2 ? r.- 4. Non-Optimality of BOLD if p ? 1/2 ? r Fails.- X. Foundational Problems.- 1. The Theory of Randomness.- 2. Subjective Probabilities.- 3. Belief ("bel") Functions.- Appendix A: The Marriage Theorem.- Appendix B: Markovian Semigroups.- Appendix C: One-parameter semigroups of stochastic matrices.

New Directions in 4-Manifold Theory.- Lecture 1: Donaldson and Seiberg-Witten Invariants.- Lecture 2: The Immersed Thorn Conjecture.- Lecture 3: Intersection Forms of Smooth 4-Manifolds.- References.- On the Regularity of Classical Field Theories in Minkowski Space-Time E3+1.- 1 Relativistic Field Theories.- 2 The Problem of Break-down.- 3 Energy estimates and the Problem of Optimal Local Well Posedness.- 4 Proof of the Null Estimates.- 5 The Proof of Theorem 4.- 6 Conclusions.- Static and Moving Vortices in Ginzburg-Landau Theories.- Lecture 1.- 1 Background and Models.- 2 The Work of Bethuel-Brézis-Hélein and Others.- 3 Some Generalizations.- Lecture 2.- 1 Renormalized Energy.- 2 A Technical Result.- 3 Proof of Theorem A.- 4 Proof of Theorem B.- Lecture 3: The Dynamical Law of Ginzburg-Landau Vortices.- 1 Gor'kov-Eliashberg's Equation.- 2 Uniqueness of Asymptotic Limit.- 3 Vortex Motion Equations.- References.- Wave Maps.- 1 Local existence. Energy method.- 1.1 The setting.- 1.2 Wave Maps.- 1.3 Examples.- 1.4 Basic questions.- 1.5 Energy estimates.- 1.6 L2-theory.- 1.7 Local existence for smooth data.- 1.8 A slight improvement.- 1.9 Global existence, the case m = 1.- 2 Blow-up and non-uniqueness.- 2.1 Overview.- 2.2 Regularity in the elliptic and parabolic cases.- 2.3 Regularity in the hyperbolic case.- 3 The conformai case m = 2.- 3.1 Overview.- 3.2 The equivariant case.- 3.3 Towards well-posedness for general targets.- 3.4 Approximation solutions.- 3.5 Convergence.- References.

This volume collects the proceedings of the International Conference on Recent Developments in Mathematics (ICRDM), held at Canadian University Dubai, UAE, in August 2022. It is the first of two volumes, this first volume focuses on recent advances in algebra and analysis, and the second volume covers more applied topics. Each chapter identifies existing challenges in these theoretical areas, and highlights the importance of establishing new theorems and algorithms to address them. Recent Developments in Algebra and Analysis will appeal to a range of postgraduate students and researchers who are interested in exploring more on these areas and play an integral role in modern science.

Vladimir Maz'ya: Friend and mathematician. Recollections.- On Maz'ya's work in potential theory and the theory of function spaces.- 1. Introduction.- 2. Embeddings and isoperimetric inequalities.- 3. Regularity of solutions.- 4. Boundary regularity.- 5. Nonlinear potential theory.- Maz'ya's works in the linear theory of water waves.- 1. Introduction.- 2. The unique solvability of the water wave problem.- 3. The Neumann-Kelvin problem.- 4. Asymptotic expansions for transient water waves due to brief and high-frequency disturbances.- Maz'ya's work on integral and pseudodifferential operators.- 1. Non-elliptic operators.- 2. Oblique derivative problem: breakthrough in the generic case of degeneration.- 3. Estimates for differential operators in the half-space.- 4. The characteristic Cauchy problem for hyperbolic equations.- 5. New methods for solving ill-posed boundary value problems.- 6. Applications of multiplier theory to integral operators.- 7. Integral equations of harmonic potential theory on general non-regular surfaces.- 8. Boundary integral equations on piecewise smooth surfaces.- Contributions of V. Maz'ya to the theory of boundary value problems in nonsmooth domains.- 1. Maz'ya's early work on boundary value problems in nonsmooth domains.- 2. General elliptic boundary value problems in domains with point singularities.- 3. Boundary value problems in domains with edges.- 4. Spectral properties of operator pencils generated by elliptic boundary value problems in a cone.- 5. Applications to elastostatics and hydrodynamics.- 6. Singularities of solutions to nonlinear elliptic equations at a cone vertex.- On some potential theoretic themes in function theory.- 1. Approximation theory.- 2. Uniqueness properties of analytic functions.- 3. The Cauchy problem for the Laplace equation.- Approximate approximations and their applications.- 1. Introduction.- 2. Quasi-interpolation.- 3. Generating functions for quasi-interpolation of high order.- 4. Semi-analytic cubature formulas.- 5. Cubature of integral operators over bounded domains.- 6. Approximate wavelets.- 7. Numerical algorithms based upon approximate approximations.- Maz'ya's work on the biography of Hadamard.- Isoperimetric inequalities and capacities on Riemannian manifolds.- 1. Introduction.- 2. Capacity of balls.- 3. Parabolicity of manifolds.- 4. Isoperimetric inequality and Sobolev inequality.- 5. Capacity and the principal frequency.- 6. Cheeger's inequality.- 7. Eigenvalues of balls on spherically symmetric manifolds.- 8. Heat kernel on spherically symmetric manifolds.- Multipliers of differentiable functions and their traces.- 1. Introduction.- 2. Description and properties of multipliers.- 3. Multipliers in the space of Bessel potentials as traces of multipliers.- An asymptotic theory of nonlinear abstract higher order ordinary differential equations.- Sobolev spaces for domains with cusps.- 1. Introduction.- 2. Extension theorems.- 3. Embedding theorems.- 4. Boundary values of Sobolev functions.- Extension theorems for Sobolev spaces.- 1. Introduction.- 2. Extensions with preservation of class.- 3. Estimates for the minimal norm of an extension operator.- 4. Extensions with deterioration of class.- Contributions of V.G. Maz'ya to analysis of singularly perturbed boundary value problems.- 1. Introduction.- 2. Domain with a small hole.- 3. General asymptotic theory by Maz'ya, Nazarov and Plamenevskii.- 4. Asymptotics of solutions of boundary integral equations under a small perturbation of a corner.- 5. Compound asymptotics for homogenization problems.- 6. Boundary value problems in 3D-1D multi-structures.- Asymptotic analysis of a mixed boundary value problem in a singularly degenerating domain.- 1. Introduction.- 2. Formulation of the problem.- 3. The leading order approximation.- A history of the Cosserat spectrum.- 1. Introduction.- 2. The first boundary value problem of elastostatics.- 3. The second and other boundary-value problems.- 4. Applications and o...

Resolution of singularities is notorious as a difficult topic within algebraic geometry. Recent work, aiming at resolution of families and semistable reduction, infused the subject with logarithmic geometry and algebraic stacks, two techniques essential for the current theory of moduli spaces. As a byproduct a short, a simple and efficient functorial resolution procedure in characteristic 0 using just algebraic stacks was produced. The goals of the book, the result of an Oberwolfach Seminar, are to introduce readers to explicit techniques of resolution of singularities with access to computer implementations, introduce readers to the theories of algebraic stacks and logarithmic structures, and to resolution in families and semistable reduction methods.

Caco-2 cell permeability vs human gastrointestinal absorption: QSPR analysis.- Pharmacology of appetite suppression.- Serotonin, dopamine and norepinephrine transporters in the central nervous system and their inhibitors.- Neuropeptides in drug research.- Regulation of NMDA receptors by ethanol.- Troglitazone and emerging glitazones: New avenues for potential therapeutic benefits beyond glycemic control.- Applications of developmental biology to medicine and animal agriculture.- Index Vol. 54.- Index of titles, Vol. 1-54.- Author and paper index, Vol. 1-54.

MIC-1 and other TGF-? superfamily members in inflammation.- Signal transduction mechanisms for members of the TGF-? family.- The transforming growth factor family and the endothelium.- TGF-? and macrophages in the rise and fall of inflammation.- TGF-? and the cardiovascular system.- Bone morphogenetic proteins and related cytokines.- Biology of glial cell-line derived neurotrophic factor.- TGF-? superfamily cytokines in wound healing.

Airways.- 1 Measurement of lung function in rodents in vivo.- Spontaneous respiration.- Pulmonary manoeuvres.- Material and equipment.- Lung function laboratory.- Methods.- Preparation and calibration.- Pulmonary function testing.- Examples for applications.- Discussion.- Troubleshooting.- References.- 2 The isolated perfused lung.- Advantages and disadvantages of perfused lungs.- Theoretical background.- Vascular resistance.- Respiratory mechanics.- Material and equipment.- Artificial thorax chamber and ventilation.- Perfusion.- Weight measurement.- Gas exchange.- Methods.- Surgery and setting up the lung.- Criteria for viability.- Cleaning the apparatus.- An example application.- Discussion.- Interpretation of the results.- Constant flow (CFP) versus constant pressure perfusion (CPP).- Negative or positive pressure ventilation.- Choice of perfusate.- Recirculating versus non-recirculating perfusion.- Additional experimental options.- Troubleshooting.- Final comments.- References.- 3 Lung explants.- Material and equipment.- Preparation of culture media.- Preparation of agarose.- Preparation of animals.- Preparation of explants.- Image acquisition.- Variations on this technique.- Applications.- Effects of bronchoconstriction.- Measurements of mucociliary clearance.- Measurements of pulmonary vasculature.- Long term explant culture techniques.- Investigations of protein and gene expression.- Troubleshooting.- Discussion.- Acknowledgements.- References.- 4 Tracheal preparations.- Methods.- Guinea pig tracheal preparations.- Immersion techniques.- Tracheal chain.- Spirally cut trachea.- Zig-zag tracheal strip.- Tracheal tube preparations.- Superfusion techniques.- Electrically stimulated trachea.- Epithelium-denuded trachea.- Conclusion.- References.- Vessels.- 5 Intravital microscopy: Airway circulation.- Materials and equipment.- Microscope.- Video equipment.- Peripheral equipment.- Ventilation.- Solutions.- Methods.- Surgery.- Experimental procedure.- Species differences.- Discussion.- References.- 6 The bronchial circulation.- Importance and role of the bronchial circulation.- Postobstructive pulmonary vasculopathy (POPV) and principles of the techniques.- Material and equipment.- Production of POPV in dogs, rats and guinea pigs: Ligation of the left main pulmonary artery.- In situ perfused LLL preparation.- Morphological assessment of the bronchial and pulmonary vasculature using light microscopy and morphometry.- Methods.- Surgical ligation of the left main pulmonary artery in dogs, rats and guinea pigs.- Canine model.- Rat and guinea pig model.- In situ perfused LLL preparation to measure pulmonary and bronchial vascular flows, pressures and resistances using modified AO and VO and bronchial vascular micropuncture.- Procedure for the in situ perfused LLL preparation.- AO and VO measurements.- Modified in situ perfused LLL preparation for bronchial collateral.- vascular pressure measurements by micropuncture.- Morphological assessment of the bronchial and pulmonary vasculature, using light microscopy and morphometry.- Measurement of pulmonary vascular medial thickness and muscularization in lungs injected with pigmented gelatin-barium mixtures.- Fixation and preparation.- Morphometry.- Assessment of proliferation in the bronchial vasculature.- Bronchial vessel number per airway.- Assessment of bronchial vascular endothelial proliferation using bromodeoxyuridine (BrdU) labeling.- Discussion and troubleshooting.- Production of POPV.- In situ perfused left lower lobar preparation.- Morphological assessment of the bronchial and pulmonary vasculature.- Acknowledgements.- References.- 7 Segmental vascular resistance and compliance from vascular occlusion.- Methods.- The lumped parameter RCR model.- The continuous RC distribution.- More distributed lumped parameter models.- The 3C4R model.- The 3C2R model.- Arterial occlusion in vivo.- Acknowledgements.- References.- Edema.- 8 Experimental and clinical measurement of pulmonary ...

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