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Multiple Polylogarithms: An Introduction.- A (Conjectural) 1/3-phenomenon for the Number of Rhombus Tilings of a Hexagon which contain a Fixed Rhombus.- The Influence of Carr's Synopsis on Ramanujan.- A Bailey Lemma from the Quintuple Product.- Little Flowers to G.H. Hardy (07-02-1877-01-12-1947).- Rogers-Ramanujan Type Identities for Burge's Restricted Partition Pairs Via Restricted Frobenius Partitions.- On q-additive and q-multiplicative Functions.- Antimagic Labeling of Complete m-ary Trees.- Some Recent Advances on Symmetric, Quasi-Symmetric and Quasi-Multiple Designs.- On T-core Partitions and Quadratic Forms.- Observations on Some Algebraic Equations Associated with Ramanujan's Work.- On Rapidly Convergent Series for Dirichlet L-function Values Via the Modular Relation.- On a Conjecture of Andrews-II.- Integrity of P2× Pn.- A Note on Cordial Labelings of Multiple Shells.- A Report on Additive Complements of the Squares.- Transcendental Infinite Sums and Some Related Questions.- The Lehmer Problem on the Euler Totient: A Pendora's Box of Unsolvable Problems.- The Problems Solved by Ramanujan in the Journal of the Indian Mathematical Society.- On the gcd and Icm of Matrices Over Dedekind Domains.- The Billiard Ball Motion Problem I: A Markoff Type Chain for the Octahedron in $${{\Re }^{3}}$$.- Hilbert's Seventeenth Problem and Pfister's Work on Quadratic Forms.- Certain Representations of Mock-Theta Functions.- Bi-Graceful Graphs.- Wheels, Cages and Cubes.- Relevance of Srinivasa Ramanujan at the Dawn of the New Millennium.- Number of Solutions of Equations over Finite Fields and a Conjecture of Lang and Weil.- On An Additive Question.- n-Colour Partitions.

1 Some aspects of operator theory and the theory of analytic functions.- 1 On spectral functions of Hermitian operators.- 2. Representation of a simple Hermitian operator whose deficiency index is (1,1).- 3. On the spectrum of self-adjoint extensions of a Hermitian operator whose deficiency index is (1,1).- 4. Some aspects of the theory of analytic functions.- 2 Entire operators whose deficiency index is (1,1).- 1. Quasiregular gauge.- 2. Principal theorem on regular points of fM(z).- 3. u -regular points of a Hermitian operator.- 4. Functions e(z) and ?M(Z).- 5. Entire operators.- 6. R-functions and generalized resolvents of a Hermitian operator.- 7. On distribution functions of a Hermitian operator.- 8. Method of directing functionals.- 9. Operator, entire with respect to a generalized gauge.- 3 Applications of entire operator theory to some classical problems of analysis.- 1. Power moment problem.- 2. Continuation problem for positive definite functions.- 3. Unitary and spiral curves.- Appendix 1 On entire operators whose defect numbers are arbitrary.- Appendix 2 Enture operators represented by differential operators.- Appendix 3 On a difficult problem of operator theory and its relation to classical analysis.- Comments.

1. The Lung and the Immune System.- 2. The Respiratory System in Rheumatic Diseases.- 3. Pulmonary Manifestations of Systemic Vasculitides.- 4. The Lung in Granulomatous Diseases.- 5. The Diagnosis and Treatment of Respiratory Infections in Autoimmune Disease, Excluding Tuberculosis.- 6. Human Immunodeficiency Virus and the Lung.- 7. Lung Cancer: Immunological Disturbances and Clinical Implications.- 8. Asthma.- 9. Cystic Fibrosis.- 10. Role of the Immune System in the Pathogenesis of Cryptogenic Fibrosing Alveolitis.- 11. Drugs and Other Factors.- 12. Overview.

This monograph provides a comprehensive study of a typical and novel function space, known as the $\mathcal{N}_p$ spaces. These spaces are Banach and Hilbert spaces of analytic functions on the open unit disk and open unit ball, and the authors also explore composition operators and weighted composition operators on these spaces. The book covers a significant portion of the recent research on these spaces, making it an invaluable resource for those delving into this rapidly developing area. The authors introduce various weighted spaces, including the classical Hardy space $H^2$, Bergman space $B^2$, and Dirichlet space $\mathcal{D}$. By offering generalized definitions for these spaces, readers are equipped to explore further classes of Banach spaces such as Bloch spaces $\mathcal{B}^p$ and Bergman-type spaces $A^p$. Additionally, the authors extend their analysis beyond the open unit disk $\mathbb{D}$ and open unit ball $\mathbb{B}$ by presenting families of entire functions in the complex plane $\mathbb{C}$ and in higher dimensions. The Theory of $\mathcal{N}_p$ Spaces is an ideal resource for researchers and PhD students studying spaces of analytic functions and operators within these spaces.

to Nitric Oxide Biology.- 1. Nitric Oxide Synthesis and Actions.- 2. Reactive Oxygen and Reactive Nitrogen Species in the Lung.- Role of Endogenous Nitric Oxide in the Lung.- 3. Non-Adrenergic Non-Cholinergic Neurotransmission in the Airways: Role of Nitric Oxide.- 4. Localisation of Nitric Oxide Synthases in the Lung.- 5. Role of Nitric Oxide in the Regulation of Pulmonary Vascular Tone.- 6. Nitric Oxide and Bronchial Hyperresponsiveness.- 7. Bronchodilator Actions of Nitric Oxide and Related Compounds.- 8. Role of Nitric Oxide in Airway Inflammation.- Therapeutic Potential of Inhalded Nitric Oxide and Nitric Oxide Synthase Inhibitors in Lung Disease.- 9. Nitric Oxide in Exhaled Air: Relevance in Inflammatory Lung Disease.- 10. Luminal Nitric Oxide in the Upper Airways: Implications for Local and Distal Sites of Action.- 11. Inhaled Nitric Oxide as a Therapy for Diseases of the Pulmonary Vasculature.- 12. Combinded Use of Nitric Oxide and Nitric Oxide Synthase Inhibitors as a Possible Therapeutic Approach.

1 The Electromagnetic Program for the Synthesis of Physics.- 2 The General Theory of Relativity: The Core of the Program of Unified Field Theories.- 3 Weyl's Theory: The First Truly Geometrized Unified Field Theory.- 4 1921: The Pivotal Year of Unified Geometrized Field Theories.- 5 Einstein's Decade of Hopes and Disappointments.- 6 The Role of Unified Geometrized Field Theories in the Genesis and Development of Quantum Theory.- Concluding Remarks.

1: Pontryagin Spaces and Operator Colligations.- 1.1 Reproducing kernel Pontryagin spaces.- 1.2 Operator colligations.- 1.3 Julia operators and contractions.- 1.4 Extension of densely defined linear relations.- 1.5 Complementation and reproducing kernels.- A. Complementation in the sense of de Branges.- B. Applications to reproducing kernel Pontryagin spaces.- 2: Schur Functions and their Canonical Realizations.- 2.1 Pontryagin spaces ?(S), ?($$ \widetilde{S} $$ ), and D(S).- 2.2 Canonical coisometric and isometric realizations.- 2.3 Canonical unitary realization.- 2.4 Unitary dilations of coisometric and isometric colligations.- 2.5 Classes SK(F, B).- A. Definition and basic properties.- B. Conformally invariant view.- C. Application to factorization of operator-valued functions.- D. A non-holomorphic kernel.- 3: The State Spaces.- 3.1 Invariance under difference quotients.- 3.2 Spaces ?(S).- 3.3 Spaces ?$$ \widetilde{S} $$.- 3.4 Spaces D(S).- 3.5 Examples and miscellaneous results.- A. Rational unitary functions.- B. Symmetry in the state spaces.- C. Some consequences of Leech's theorem.- D. The scalar case: S(z)? ?(S) if and only if $$ \widetilde{S} $$(z) ? ?($$ \widetilde{S} $$).- 4: Structural Properties.- 4.1 Factorization and invariant subspaces.- A. Inclusion of spaces ?(S).- B. Inclusion of spaces D (S).- 4.2 Kre?n-Langer factorization.- A. Existence and properties.- B. Strongly regular representations.- 4.3 The Potapov-Ginzburg transform.- 4.4 Applications to the realization theory.- A. Kre?n space inner and outer spaces F andB.- B. Other base points.- C. Examples.- 4.5 Canonical models.- Epilogue: Open Questions and Directions for Further Work.- Appendix: Some Finite-Dimensional Spaces.- Notes.- References.- Notation Index.- Author Index

Obituary.- In memory of Siegfried Prößdorf.- Siegfried Prößdorf - A short review of his scientific career.- On the theory of a singular Vekua system.- Singular integral operators with complex conjugation from the viewpoint of pseudodifferential operators.- Biorthogonal wavelet approximation methods for the heat equation.- Orientable and nonorientable Riemann-Hilbert problems.- Diffraction in periodic structures and optimal design of binary gratings. Part II: Gradient formulas for TM polarization.- A connection between the determinant and characteristic numbers of an operator pencil.- Random walk models approximating symmetric space-fractional diffusion processes.- On qualocation and collocation methods for singular integral equations with piecewise continuous coefficients, using continuous splines on quasi-uniform meshes.- Toeplitz operators and the modelling of oscillating discontinuities with the help of Blaschke products.- Towards H-matrix approximation of linear complexity.- Wavelet Galerkin schemes for 2D-BEM.- On the stability of collocation methods for Cauchy singular integral equations on an interval.- On a new approach for solving Dirac equations with some potentials and Maxwell's system in homogeneous media.- Revisiting a quadrature method for CSIE with weakly singular perturbation kernel.- Fourier projections in weighted L?-spaces.- Maximal Banach algebra in spaces of multipliers between Bessel potential spaces.- Mixed type direct and inverse scattering problems.- On an inverse problem in groundwater filtration and its regularization by the conjugate gradient method.- On a constructive representation of an orthogonal trigonometric Schauder basis for C2?.- Discretization methods for the Lavrent'ev regularization.- On a hierarchical three-point basis in the space of piecewise linear functions over smooth surfaces.- Algebras of approximation sequences: Fractality.- Fast solvers of generalized airfoil equation of index 1.- On plane potential flow past a porous circular cylinder.

5-Hydroxytryptamine (5-HT)4 receptors and central nervous system function: An update.- Chemical teratogenesis in humans: Biochemical and molecular mechanisms.- Recent advances in potassium channel modulation.- Neuronal prostacyclin receptors.- Effects of NSAIDs on the kidney.- G protein coupled receptors as modules of interacting proteins: A family meeting.- Antifungal therapy, an everlasting battle.- Index - Sachverzeichnis - Table des matières, vol. 49.- Index of titles - Verzeichnis der Titel - Index des titres vol. 1-49.- Author and paper index - Autoren- und Artikelindex - Index des auteurs et des articles, vol. 1-49.

I Introductory Articles.- 1 Classification Problems in the Representation Theory of Finite-Dimensional Algebras.- 2 Noncommutative Gröbner Bases, and Projective Resolutions.- 3 Construction of Finite Matrix Groups.- II Keynote Articles.- 4 Derived Tubularity: a Computational Approach.- 5 Problems in the Calculation of Group Cohomology.- 6 On a Tensor Category for the Exceptional Lie Groups.- 7 Non-Commutative Gröbner Bases and Anick's Resolution.- 8 A new Existence Proof of Janko's Simple Group J4.- 9 The Normalization: a new Algorithm, Implementation and Comparisons.- 10 A Computer Algebra Approach to sheaves over Weighted Projective Lines.- 11 Open Problems in the Theory of Kazhdan-Lusztig polynomials.- 12 Relative Trace Ideals and Cohen Macaulay Quotients.- 13 On Sims' Presentation for Lyons' Simple Group.- 14 A Presentation for the Lyons Simple Group.- 15 Reduction of Weakly Definite Unit Forms.- 16 Decision Problems in Finitely Presented Groups.- 17 Some Algorithms in Invariant Theory of Finite Groups.- 18 Coxeter Transformations associated with Finite Dimensional Algebras.- 19 The 2-Modular Decomposition Numbers of Co2.- 20 Bimodule and Matrix Problems.

Ecosystem structure and trophic interactions.- Habitat partitioning by zooplankton and the structure of lake ecosystems.- New Zealand mountain stream communities: Stable yet disturbed?.- Complex trophic interactions in freshwater benthic food chains.- Prey dispersal and predator impacts on stream benthic prey.- Aspects of life-history evolution.- Rotifer life history strategies and evolution in freshwater plankton communities.- The evolution and genetics of maturation in Daphnia.- Optimal energy allocation tactics and indeterminate growth: Life-history evolution of long-lived bivalves.- Population biology and reproductive modes.- Ecology and genetics of interspecific hybridization in Daphnia.- Population biology, genetic structure, and mating system parameters in freshwater snails.- Evolution and ecological correlates of uniparental and biparental reproduction in freshwater snails.- Genetic similarity, parasitism, and metapopulation structure in a freshwater bryozoan.- Evolutionary processes following colonizations.- Evolutionary consequences of postglacial colonization of fresh water by primitively anadromous fishes.

Physicochemical basis of the universal genetic codes - quantitative analysis.- Enzymatic generation of complex peptides.- The role of apoptosis in neurodegenerative diseases.- Viral quasispecies and the problem of vaccine-escape and drug-resistant mutants.- Immunotherapy for brain diseases and mental illnesses.- Natural products and their derivatives as cancer chemopreventive agents.- Dopamine receptor diversity: Molecular and pharmacological perspectives.- Novel and unusual nucleosides as drugs.- Index Sachverzeichnis Table des matières, Vol. 48.- Index of titles Verzeichnis der Titel Index des titres Vol. 1-48.- Author and paper index Autoren- und Artikelindex Index des auteurs et des articles, Vol. 1-48.

Erster Teil Die übliche Auffassung von der Mathematik und ihre Widerlegung.- 1 Die Rolle von Anschauung und Erfahrung.- 2 Die Rolle der Voraussetzungen.- 3 Die Nichtuntrüglichkeit des mathematischen Schliessens.- Zweiter Teil Die landläufige Auffassung von der Physik und ihre Berichtigung.- 4 Physikalische Begriffsbildungen.- 5 Die Gesetze der Physik und ewige Naturgesetze.- 6 Die Beziehung zwischen Theorie und Experiment.- Dritter Teil Fragen philosophischen Charakters.- 7 Physikalische Gesetzlichkeit und Kausalität.- 8 Naturgeschehen und Wahrscheinlichkeit.- 9 Die Rolle von idealen Gebilden.

Présence de l'oeuvre de P. Lelong dans les grands thèmes de recherche d'aujourd'hui.- Bibliographic de P. Lelong.- Wiener's type sufficient conditions in ?N.- On the Ohsawa-Takegoshi-Manivel L2 extension theorem.- A geometrical application of the product of two positive currents.- Hypoellipticity: geometrization and speculation.- Moment problems for weighted Bergman kernels.- On the Bergman metric near a plurisubharmonic barrier point.- On the vanishing order of a holomorphic germ along a complex analytic germ in ?n.- Stationary curves and complete integrability in the complex domain.- The Malgrange vanishing theorem with support conditions.- Mesures orthogonales à support compact de longueur finie et applications.- Convexity and Hartogs' theorem in some open subset of a projective manifold.- Pointwise support functions for convex domains of finite type.- Un exemple d'obstruction géométrique à l'extension des fonctions holomorphes bornées.- Potential theory on complex dynamics: regular polynomial mappings of ?k.- Boundaries of Levi-flat hypersurfaces of ?2.- Une démonstration directe de la densité des cycles répulsifs dans l'ensemble de Julia.- Embeddings for 3-dimensional CR-manifolds.- List of Problems.

This book both articulates and responds to increasing scholarly interest in the materiality of the book. Taking as its base the unique collection of mathematical books in the Russell Library at Maynooth, it addresses questions related to printing techniques and print culture, book production, provenance, and reading practices. It considers the histories of individual items of the Russell Collection, their previous locations and owners, and explores ways in which annotations, underlinings, hand-drawn diagrams, and the like reveal patterns of reading and usage. Finally, it seeks to elicit more information on a previously under-researched topic: the historical role of mathematics in the extensive network of Irish colleges that once covered Catholic Europe, located in places such as Salamanca, Rome, Douai, and Prague. Alongside delivering important new insights into print culture as a medium for transmitting scientific ideas, Mathematical Book Histories is thus also intended to contribute to a broader understanding of the role and significance of mathematics in the context of clerical instruction and more broadly in the academic tradition of Ireland up to the beginning of the twentieth century. Many of the volumes in the Russell Library reflect the remarkably rich book-trade that flourished in seventeenth and early eighteenth century Dublin and which was quite distinct from that in London. Booksellers often bought in their wares directly from abroad, with the result that publications could enter collections that did not enter the purview of contemporary English or Scottish scholars in Britain.

Special lectures.- A tale of protein kinase C and membrane lipid signaling.- Complement, neuroinflammation and neuronal degeneration in Alzheimer disease.- Memory and its impairment.- Neurobiological mechanisms by which emotional arousal influences long-term memory formation.- Amygdalar damage and memory impairment in Alzheimer's disease.- Neural substrate for spatial memory in the monkey hippocampus.- Involvement of CaM kinase II and mitogen-activated protein kinase in hippocampal long-term potentiation.- Pathogenesis of dementia - tau.- Transgenic mice overexpressing the shortest human tau isoform develop a progressive tauopathy.- Tau and neurodegenerative disease: genetics and pathogenetic mechanisms.- Tau mutations altering splicing of tau exon 10 in japanese frontotemporal dementia.- Amyotrophic lateral sclerosis/parkinsonism-dementia complex of the Kii peninsula of Japan (Kii ALS/PDC) may be a familial tauopathy. Epidemiological trends, clinical features, neuropathology and molecular genetics.- Senile dementia of the neurofibrillary tangle type (SD-NFT): a clinical, neuropathological and molecular genetic study.- The dual role of tau in cell polarisation and organelle trafficking.- Rearrangement of microtubule networks by tau bearing missense mutations.- Possible role of tau phosphorylation on ER membrane in Alzheimer pathology.- Pathogenesis of dementia - synuclein.- Pathogenesis of dementia: updating the role of synuclein pathology in sporadic and hereditary Alzheimer's disease.- ?-Synuclein/NACP and neurodegeneration.- ?-Synuclein fibrillogenesis as target for drug development.- Pathogenesis of dementia - presenilin and amyloid.- Genetics of early-onset Alzheimer disease.- Lessons from presenilin domain analysis: endoproteolytic processing and enhanced A?42 production mediated by FAD-linked variants.- Amyloid and presenilins in the pathobiology of Alzheimer's disease.- Role of presenilin in APP processing and A? production.- Impairment of response to ER stress in presenilin 1 mutant.- Mechanism of neuron death in Alzheimer's disease.- Notch3 gene in CADASIL syndrome: mutation frequencies in Japanese and its expression and processing.- Etiological roles of A? and carboxyl terminal peptide fragments of amyloid precursor protein in Alzheimer disease.- Amyloid ?-protein granules in glial cells in Alzheimer's disease brain.- Amyloid ? induces phosphorylation and translocation of MARCKS through tyrosine kinase-activated PKC-? signaling pathway in microglia.- Amyloid ?-protein accumulation in the human brain during aging.- Molecular mechanisms underlying initiation of amyloid fibril formation.- Catabolism of amyloid-? peptide in brain parenchyma.- Diagnosis and therapeutics of dementia.- Lessons in familial Alzheimer's disease.- Biological markers for differential diagnosis of Alzheimer's disease and related disorders.- Dietary factors and the risk of Alzheimer's disease: a low fish consumption and a relative deficiency of ?-3 polyunsaturated fatty acids.- Risk factors for dementia.- New therapeutic approaches to Alzheimer's disease.

This monograph develops a theory of continuous and differentiable functions, called monogenic functions, in the sense of Gateaux functions taking values in some vector spaces with commutative multiplication. The study of these monogenic functions in various commutative algebras leads to a discovery of new ways of solving boundary value problems in mathematical physics. The book consists of six parts: Part I presents some preliminary notions and introduces various concepts of differentiable mappings of vector spaces. Part II - V is devoted to the study of monogenic functions in various spaces with commutative multiplication, namely, three dimensional commutative algebras with two-dimensional radical, finite-dimensional commutative associative algebras, infinite-dimensional vector spaces associated with the three-dimensional Laplace equation and infinite-dimensional vector spaces associated with axial-symmetric potential fields. Part VI presents some boundary value problems for axial-symmetric potential fields and develops effective analytic methods of solving these boundary value problems with various applications in mathematical physics. Graduate students and researchers alike benefit from this book.

These lecture notes are dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems appearing in geometry and in various applications, ranging from crystal growth, tumour growth, biological membranes to porous media, two-phase flows, fluid-structure interactions, and shape optimization.We first give an introduction to classical methods from differential geometry and systematically derive the governing equations from physical principles. Then we will analyse parametric approaches to interface evolution problems and derive numerical methods which will be thoroughly analysed. In addition, implicit descriptions of interfaces such as phase field and level set methods will be analysed. Finally, we will discuss numerical methods for complex interface evolutions and will focus on two phase flow problems as an important example of such evolutions.

Table.- Première Partie: Le monde construit par le Tractatus.- Chapitre Premier: La forme cyclique du Tractatus.- Deuxième Chapitre: Ordo et connexio rerum dans la substance du monde.- Troisième Chapitre: La proposition élémentaire.- Quatrième Chapitre: Le fait.- Cinquième Chapitre: Les images d'un fait.- Sixième Chapitre: Les totalités dans le Système du Tractatus.- Septième Chapitre: Le monde comme un Tout limité.- Huitième Chapitre: Les limites du monde.- Neuvième Chapitre: l'ordre du monde du Tractatus.- Duexième Partie: La Nature naturée construite par l'Éthique.- Chapitre Premier: l'Étendue.- Deuxième Chapitre: l'essence d'une chose étendue.- Troisième Chapitre: Le Corps de Dieu.- Quatrième Chapitre: l'attribut de la Pensée.- Cinquième Chapitre: l'attribut X.- Sixième Chapitre: La substance.- Septième Chapitre: Cause, idée et essence.- Huitième Chapitre: La Pensée de Dieu 269.- Neuvième Chapitre: l'homme.- Troisième Partie: Comparaison du monde du Tractatus avec la Nature naturée de l'Éthique.- Chapitre Premier: Le monde wittgensteinien et la nature spinoziste.- Deuxième Chapitre: La vue wittgensteinienne du monde et 1'intuition spinoziste.- Troisième Chapitre: Le système de l'Éthique et le système du Tractatus.- Notes et references.- Première Partie.- Deuxième Partie.- Troisième Partie.- Bibliographie.- Wittgenstein. Oeuvres.- Éditions originals.- Éditions critiques.- Wittgenstein. Études et commentaries.- Spinoza. Oeuvres.- Éditions originals.- Édition critique.- Traductions.- Spinoza. Études et commentaries.

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 ...