Format: Hardback, 220 pages, height x width: 235x155 mm, 11 Illustrations, color;
63 Illustrations, black and white; XVI, 258 p. 66 illus., 10 illus. in color.
Pub. Date: 31-May-2024
ISBN-13: 9789819972562
This is the second book of the two volumes covering the advanced statistical methods and analysis. Significant topics include advanced concepts in regression, index numbers, time series, and vital statistics. The book includes useful examples and exercises as well as relevant case studies for proper implementation of the discussed tools. This book will be a valuable text for advanced undergraduate students of statistics, management, economics, and psychology, wanting to gain advanced understanding of statistics and the usage of its various concepts.
1. Advanced Concepts in Regression.- 2. Index Numbers.- 3. Time Series.-
4. Vital Statistics.
Format: Paperback / softback, 191 pages, height x width: 235x155 mm, 9 Illustrations, color;
14 Illustrations, black and white; V, 170 p. 23 illus., 9 illus. in color.,
Series: Compact Textbooks in Mathematics
Pub. Date: 26-Jun-2024
ISBN-13: 9783031549076
This textbook explores applications of linear algebra in data science at an introductory level, showing readers how the two are deeply connected. The authors accomplish this by offering exercises that escalate in complexity, many of which incorporate MATLAB. Practice projects appear as well for students to better understand the real-world applications of the material covered in a standard linear algebra course. Some topics covered include singular value decomposition, convolution, frequency filtering, and neural networks. Linear Algebra in Data Science is suitable as a supplement to a standard linear algebra course.
Format: Hardback, 173 pages, height x width: 235x155 mm, 13 Illustrations, color;
5 Illustrations, black and white; X, 170 p. 16 illus., 11 illus. in color.,
Series: Research Perspectives Ghent Analysis and PDE Center 4
Pub. Date: 05-Jun-2024
ISBN-13: 9783031567315
The principal aim of the volume is gathering all the contributions given by the speakers (mini courses) and some of the participants (short talks) of the summer school "Modern Problems in PDEs and Applications" held at the Ghent Analysis and PDE Center from 23 August to 2 September 2023. The school was devoted to the study of new techniques and approaches for solving partial differential equations, which can either be considered or arise from the physical point of view or the mathematical perspective. Both sides are extremely important since theories and methods can be developed independently, aiming to gather each other in a common objective. The aim of the summer school was to progress and advance in the problems considered. Note that real-world problems and their applications are classical study trends in physical or mathematical modelling. The summer school was organised in a friendly atmosphere and synergy, and it was an excellent opportunity to promote and encourage the development of the subject in the community.
Part I Mini-courses.- The Hardy constant: a review.- Some harmonic
analysis in a general Gaussian setting.- Introduction to hypercomplex
analysis.- Some norm bounds for the spectral projections of the
Heisenberg sublaplacian.- Boundary value problems for elliptic operators
satisfying Carleson condition.- An elementary computation of heat trace
invariants.- Can we divide vectors? - Geometric calculus in Science
and Engineering.- Maximal regularity as a tool for partial differential
equations.- Recent existence results for some critical subelliptic problems.-
Introduction to the Analysis on Manifolds with Conical Singularities.-
Elliptic systems of phase transition type.- Cordes condition, Campanato
nearness and beyond.- Part II Short talks.- Global hypoellipticity on
homogeneous vector bundles: Necessary and sufficient conditions.- On inverse
source problems for space-dependent sources in thermoelasticity.- Symmetric
properties of eigenvalues and eigenfunctions of uniform beams with axial
loads.- Cylindrical and horizontal extensions of critical Sobolev
type inequalities and identities.- Very weak solution of the wave equation
for Sturm-Liouville operator.- Some new multidimensional Cochran-Lee and
Hardy type inequalities.
Format: Hardback, 310 pages, height x width: 235x155 mm, 9 Illustrations, color;
3 Illustrations, black and white; X, 310 p. 10 illus., 8 illus. in color.,
Series: Research Perspectives Ghent Analysis and PDE Center 5
Pub. Date: 04-Jun-2024
ISBN-13: 9783031570049
Since 2019 Ghent Analysis & PDE Center (GAPC) has been organising international workshops, conferences, seminars, and other scientific events covering a wide range of pioneering topics in Analysis and PDEs. In the winter of 2023, the GAPC decided to collect and publish mathematical results presented by women mathematician hosted at the center. This collection, in the form short papers, presented in the current book offers a wide range of state of art in Analysis and PDEs and disseminates the scientific discoveries of GAPCs visitors and members to scientists outside of the center. The short papers published in current volume in the subseries Research Perspectives Ghent Analysis and PDE Center within the book series Trends in Mathematics are peer-reviewed written versions of the talks presented by women at GAPC events and are grouped accordingly. The current volume is strictly speaking in the realm of pure mathematics, but aims to be of interest not only to scientists in the field, butalso to anyone who has an interest to other applied sciences that Analysis and PDEs have applications to. The collection will also include the talks given at the two workshops "Women in Generalised Functions", organised in 2022 and 2023.
- Dynamical sampling for PDEs.- Mckean-Vlasov SPDES with additive noise
as limits of weighted interacting particle systems.- Strong BirkhoffJames
orthogonality of compact operators on Hilbert spaces.- Constructions of dual
frames compensating for erasures with implementation.- On Differential
Systems in Sobolev spaces with Generic Inhomogeneous Boundary Conditions.-
Amenability of Semihypergroups.- On Pseudo-difference operators on the
Lattice Zn.- Coercive inequalities on step-two Carnot groups.- The Laplace
transform in Dunkl theory.- Asympotic analysis for generalized functions
using frames.- On octonionic harmonic projection operator.- Generalised Fock
spaces.- Time-frequency analysis and metaplectic operators.- A
characterization of compact weighted SG pseudo-differential operators.-
Global analytic solutions and symmetric waves of the 0-equation.- On the
Greens function of the perturbed Laplace-Beltrami operator with a finite
number of punctured points on the two-dimensional sphere.- Mixed boundary
value problems for the Helmholtz equation in a model 2D double angular
domain.- On hyperbolic equations with space-dependent coefficients:
C well-posedness and Levi conditions.- Covering numbers of the unit ball of
reproducing kernel Hilbert space of zonal positive definite kernels.- Recent
examples of hypersemitoric systems and first steps towards a classification:
a brief survey.- The spaces of ultradistributions over Rd+ and the Weyl
calculus of pseudo-differential operators.- Nonlinear Control Problems with
Fractional Derivatives.- Some Generalizations of Fixed Circle.- Investigating
some measurements on the optimal dual frames for erasures.- A Short Essay on
the Special Functions of Fractional Calculus.- Quantum dissipative systems in
infinite dimensions.- Operator semigroups and generators associated to
stochastic processes.- Strong and weak type estimates for the
Littlewood-Paleyoperator g, with non-convolution kernel.- Generalized
holomorphic functions: sketches of a new theory.- On an inverse
time-dependent control function problem for the time-fractional diffusion
equation.- Asymptotic behavior of solutions to the extension problem for the
fractional Laplacian on noncompact symmetric spaces.- A brief excursus on
mixed operators in peridynamics.- On some local and nonlocal variational
problems.- Virus diffusion modeling via fractional stochastic differential
equations.- Acoustic wave propagation through a cluster of hard
upright cylinders: porous media and radiative transfer approach.- A note on
Hardy inequality in metric measure space for the case p = 1.- Coincidence
degree and fixed point theory applied to the study of solutions of a
nonlinear fractional boundary value problem.- Degenerate diffusion equation
with the Hadamard time-fractional derivative.- On the multipliers of Fourier
series in the generalized Haar system.- Hardy Inequalities on metric measure
spaces for different indices p and q.- Geometric Interpolations for Fourier
multipliers on groups.- On scattering for critical NLS on waveguide
manifolds: a short survey.- Exponential growth of solution for a class of
reaction-diffusion equations with memory term.
Format: Hardback, 335 pages, height x width: 235x155 mm, 7 Illustrations, black and white; X, 305 p.,
Series: Developments in Mathematics 79
Pub. Date: 19-May-2024
ISBN-13: 9783031567230
This book provides an overview of the main results and problems concerning Diophantine m-tuples, i.e., sets of integers or rationals with the property that the product of any two of them is one less than a square, and their connections with elliptic curves. It presents the contributions of famous mathematicians of the past, like Diophantus, Fermat and Euler, as well as some recent results of the author and his collaborators. The book presents fragments of the history of Diophantine m-tuples, emphasising the connections between Diophantine m-tuples and elliptic curves. It is shown how elliptic curves are used in solving some longstanding problems on Diophantine m-tuples, such as the existence of infinite families of rational Diophantine sextuples. On the other hand, rational Diophantine m-tuples are used to construct elliptic curves with interesting MordellWeil groups, including curves of record rank with agiven torsion group. The book contains concrete algorithms and advice on how to use the software package PARI/GP for solving computational problems. This book is primarily intended for researchers and graduate students in Diophantine equations and elliptic curves. However, it can be of interest to other mathematicians interested in number theory and arithmetic geometry. The prerequisites are on the level of a standard first course in elementary number theory. Background in elliptic curves, Diophantine equations and Diophantine approximations is provided.
Introduction.- Elliptic curves over the rationals.- Elliptic curves
induced by Diophantine triples.- Integer points on elliptic curves.- Sets
with the property D(n).
Format: Hardback, 782 pages, height x width: 235x155 mm, 1 Illustrations, color;
6 Illustrations, black and white; XX, 748 p. 6 illus., 1 illus. in color
Series: Operator Theory: Advances and Applications 296
Pub. Date: 03-Jun-2024
ISBN-13: 9783031567193
The book captures a fascinating snapshot of the current state of results about the operator-norm convergent Trotter-Kato Product Formul? on Hilbert and Banach spaces. It also includes results on the operator-norm convergent product formul? for solution operators of the non-autonomous Cauchy problems as well as similar results on the unitary and Zeno product formul?.After the Sophus Lie product formula for matrices was established in 1875, it was generalised to Hilbert and Banach spaces for convergence in the strong operator topology by H. Trotter (1959) and then in an extended form by T. Kato (1978). In 1993 Dzh. L. Rogava discovered that convergence of the Trotter product formula takes place in the operator-norm topology. The latter is the main subject of this book, which is dedicated essentially to the operator-norm convergent Trotter-Kato Product Formul? on Hilbert and Banach spaces, but also to related results on the time-dependent, unitary and Zeno product formul?.
The book yields a detailed up-to-date introduction into the subject that will appeal to any reader with a basic knowledge of functional analysis and operator theory. It also provides references to the rich literature and historical remark
Part I Preliminaries.- Semigroups and their generators.- Linear
Evolution Equations.- Quasi-sectorial contractions and operator-norm
convergence.- Part II: Trotter-Kato product formul? for self-adjoint
semigroups.- Product approximations of self-adjoint semigroups.- Trotter-Kato
product formul?: strong operator topology.- Trotter-Kato product formul?:
operator-norm topology.- Trotter-Kato product formulae: operator-norm
topology and error bounds.- Part III: Trotter-Kato product formul? for
non-self-adjoint semigroups.- Operator-norm approximation theory `a la Cherno
.- Product formul? for non-self-adjoint semigroups.- Operator-norm Trotter
product formula on Banach spaces.- Part IV: Time-dependent product formul?.
- Time-dependent product formul?: Banach space.- Time-dependent product
formul?: Hilbert space.- Part V: Unitary and Zeno product formul?.- Unitary
product formul?. - Zeno product formul?.
Format: Hardback, 357 pages, height x width: 235x155 mm, 7 Illustrations, black and white; X, 333 p. 7 illus.
Series: Graduate Texts in Mathematics 301
Pub. Date: 03-Jun-2024
ISBN-13: 9783031553677
In addition to covering the essentials, the author’s intention in writing this text is to entice the reader to further study mathematical logic. There is no current “standard text” for a first graduate course in mathematical logic and this book will fill that gap. While there is more material than could be covered in a traditional one semester course, an instructor can cover the basics and still have the flexibility to choose several weeks’ worth of interesting advanced topics that have been introduced. The text can and will be used by people in various courses with different sorts of perspectives. This versatility is one of the many appealing aspects of this book. A list of suggested portions to be covered in a single course is provided as well as a useful chart which maps chapter dependencies. Additionally, a motivated student will have ample material for further reading.
New definitions, formalism, and syntax have been streamlined to engage thereader quickly into the heart of logic and to more sophisticated topics. Part I and Part IV center on foundational questions, while Part III establishes the fundamentals of computability. Part II develops model theory, highlighting the model theory of the fields of real and complex numbers. The interplay between logic and other areas of mathematics, notably algebra, number theory, and combinatorics, are illustrated in Chapters 5, 6, 8, 14, and 16. For most of the text, the only prerequisite is mathematical maturity. The material should be accessible to first year graduate students or advanced undergraduates in mathematics, graduate students in philosophy with a solid math background, or students in computer science who want a mathematical introduction to logic. Prior exposure to logic is helpful but not assumed.
Introduction.- I. Truth and Proof.- 1 Languages, Structures and
Theories.- 2 Embeddings and Substructures.- 3 Formal Proofs.- 4 Godel's
Completeness Theorem.- II. Elements of Model Theory.- 5 Compactness and
Complete Theories.- 6 Ultraproducts.- 7 Quantifier Elimination.- 8 Model
Theory of the Real Field.- III. Computability.- 9 Models of Computation.- 10
Universal Machines and Undecidability.- 11 Computably Enumerable and
Arithmetic Sets.- 12 Turing Reducibility.- IV. Arithmetic and
Incompleteness.-13 Godel's Incompleteness Theorems.- 14 Hilberts 10th
Problem.- 15 Peano Arithmetic and 0.- 16 Models of Arithmetic and
Independence Results. - Appendices.- A Set Theory. - B Unique Readability.
- C Real Algebra. -Bibliography. - Index.