Bøger udgivet af Birkhauser

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

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

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

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

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

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

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

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

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

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

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

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

The 39 chapters in this volume consider subjects ranging from genetics, markers, and molecular biology of alcoholism, to clinical observations and treatment. The aim is to integrate pertinent information from the fields of molecular and cell biology with view to establishing a molecular basis of alcohol use and abuse. An initial preview summarizes historical aspects of alcohol use, and subsequent chapters concern novel drugs, pharmacological aspects, gene structures, cloning, and enzymatic properties. Also contributions by "non-traditional" alcohol scientists have been included in this collection, in order to highlight possible interaction and parallels between different fields. Novel results of particular interest include up-dated summaries on receptors, enzymes, and other proteins, as well as corresponding gene structures and regulation, setting the basis for distinguishing markers and pinpointing further possible pharmacological treatments.

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.

This volume is designed as a textbook for an introductory course on wavelet analysis and time-frequency analysis aimed at graduate students or advanced undergraduates in science and engineering. It can also be used as a self-study or reference book by practicing researchers in signal analysis and related areas. Since the expected audience is not presumed to have a high level of mathematical background, much of the needed analytical machinery is developed from the beginning. The only prerequisites for the first eight chapters are matrix theory, Fourier series, and Fourier integral transforms. Each of these chapters ends with a set of straightforward exercises designed to drive home the concepts just covered, and the many graphics should further facilitate absorption. Chapters 10 and 11 consist of original research and are written in a more advanced style. In Chapter 10 it is shown that the structure of Maxwell's equations implies the existence of a wavelet analysis specifically adopted to electromagnetic radiation. The associated "eletromagnetic wavelets" are pulses parameterized by their point of origin and their scale, and can be made arbitrarily short by choosing fine scales. Furthermore, it is shown that every electromagnetic wave can be composed of such localized wavelets. This is applied in Chapter 11 to give a new formulation of radar based on electromagnetic wavelets. Since this theory is fully relativistic, its description of the Doppler effect is exact. In particular, it is three-dimensional, and does not make the usual assumption that the outgoing signal has a narrow bandwidth. Thus it should be useful in the construction of ultra-wideband radar systems.

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.

In 1931 Erwin Schrödinger considered the following problem: A huge cloud of independent and identical particles with known dynamics is supposed to be observed at finite initial and final times. What is the "most probable" state of the cloud at intermediate times? The present book provides a general yet comprehensive discourse on Schrödinger's question. Key roles in this investigation are played by conditional diffusion processes, pairs of non-linear integral equations and interacting particles systems. The introductory first chapter gives some historical background, presents the main ideas in a rather simple discrete setting and reveals the meaning of intermediate prediction to quantum mechanics. In order to answer Schrödinger's question, the book takes three distinct approaches, dealt with in separate chapters: transformation by means of a multiplicative functional, projection by means of relative entropy, and variation of a functional associated to pairs of non-linear integral equations. The book presumes a graduate level of knowledge in mathematics or physics and represents a relevant and demanding application of today's advanced probability theory.

This monograph extends this approach to the more general investigation of X-lattices, and these "tree lattices" are the main object of study. The authors present a coherent survey of the results on uniform tree lattices, and a (previously unpublished) development of the theory of non-uniform tree lattices, including some fundamental and recently proved existence theorems. Tree Lattices should be a helpful resource to researcher sin the field, and may also be used for a graduate course on geometric methods in group theory.

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.

Tendering constitutes the transition from the drawing and planning stage to the construction phase. In addition to its economic and contractual dimension, it is also an essential tool for translating design quality into built quality. This volume presents various ways to put construction works out to tender. In addition, it explains in practical terms how to describe construction work and how to prepare all of the documentation required for a complete invitation to tender.Subjects: Allocating construction work; Different ways to specify construction work; The structure of a work specification; Quantity determination; Using invitations to tender to realize plan quality.