Is the first book to systematically study the weak systems of mereology
Presents a critical analysis on topics related to mereology
Constructs systems of mereology with weak sum existence axioms
Discusses a non-standard system of mereology without the transitivity axiom
This is the first book to systematically study the weak systems of mereology. In its chapters,
the author critically analyzes and explains core topics related to mereology, such as parthood
without antisymmetry, non-existence of the zero element, and Leniewski's notion of class and
set. The book also delves into three theories of parthood: two concern the sum existence
axioms, and the third contends with transitivity of parthood. This is the first systematic analysis
of systems of mereology of its kind and is suitable for students, scholars, logicians, and
mathematicians who wish to further their knowledge of mereology. Original polish publication
gPodstawy teorii czcih by The Nicolaus Copernicus University Press
1st ed. 2020, XXIII, 285 p.
729 illus., 4 illus. in color.
Hardcover
ISBN 978-3-030-36532-5
Product category : Monograph
Series : Trends in Logic
Softcover
ISBN 978-3-030-36535-6
Philosophy : Analytic Philosophy
Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and
Topological Groups
Features a new chapter on the classical sequence and function spaces,
offering an unconventional approach which highlights the main examples and
theorems without the need to delve into complicated measure theoretic
notions.
Offers a survey of mathematical structures related to Hilbert space theory
Includes a new final chapter that incorporates the material of the previous
chapters into a coherent introduction to Hilbert space theory and applications
This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for
non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all
addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an
introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory
itself, lies in the strenuous mathematics demands that even the simplest physical cases entail.
Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and
operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly,
compromises must be found between full rigor and the practical use of the instruments. Based
on one of the authorsfs lectures on functional analysis for graduate students in physics, the
book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with
a more practical attitude. It also includes a brief introduction to topological groups, and to
other mathematical structures akin to Hilbert space. Exercises and solved problems accompany
the main text, offering readers opportunities to deepen their understanding. The topics and
their presentation have been chosen with the goal of quickly, yet rigorously and effectively,
preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the
Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited
for use in upper undergraduate and lower graduate courses, both in Physics and in
Mathematics.
Due 2021-04-23
2nd ed. 2021, XXII, 328 p. 19 illus.
Hardcover
ISBN 978-3-030-67416-8
Product category : Graduate/advanced undergraduate textbook
Series : UNITEXT for Physics
Physics : Mathematical Methods in Physics
First research monograph devoted to the analysis of the control of singularly
perturbed linear time delay systems
Brings together and further develops the authorfs previous research on the topic
Presents material in a comprehensive, self-contained manner, allowing for
chapters to be studied independently or consecutively
This monograph provides a comprehensive analysis of the control of singularly perturbed time
delay systems. Expanding on the authorfs previous work on controllability of linear systems
with delays in the state and control variables, this volumefs comprehensive coverage makes it a
valuable addition to the field. Each chapter is self-contained, allowing readers to study them
independently or in succession. After a brief introduction, the book systematically examines
properties of different classes of singularly perturbed time delay systems, including linear timedependent
systems with multiple point-wise and distributed state delays. The author then
considers more general singularly perturbed systems with state and control delays. Euclidean
space controllability for all of these systems is also discussed, using numerous examples from
real-life models throughout the text to illustrate the results presented. More technically
complicated proofs are presented in separate subsections. The final chapter includes a section
dedicated to non-linear time delay systems. This book is ideal for researchers, engineers, and
graduate students in systems science and control theory. Other applied mathematicians and
researchers working in biology and medicine will also find this volume to be a valuable
resource.
Due 2021-05-11
1st ed. 2021, VIII, 392 p.
Hardcover
ISBN 978-3-030-65950-9
Product category : Monograph
Series : Systems & Control: Foundations & Applications
Mathematics : Systems Theory, Control
Presents Grobner bases and quiver theories as providers of computing
models for differential equations and systems
Offers a historical background for a better understanding of how theories
developed
Appeals to a wide readership, from graduate students to researchers and
scholars
This edited volume presents a fascinating collection of lecture notes focusing on differential
equations from two viewpoints: formal calculus (through the theory of Grobner bases) and
geometry (via quiver theory). Grobner bases serve as effective models for computation in
algebras of various types. Although the theory of Grobner bases was developed in the second
half of the 20th century, many works on computational methods in algebra were published
well before the introduction of the modern algebraic language. Since then, new algorithms
have been developed and the theory itself has greatly expanded. In comparison, diagrammatic
methods in representation theory are relatively new, with the quiver varieties only being
introduced ? with big impact ? in the 1990s. Divided into two parts, the book first discusses
the theory of Grobner bases in their commutative and noncommutative contexts, with a focus
on algorithmic aspects and applications of Grobner bases to analysis on systems of partial
differential equations, effective analysis on rings of differential operators, and homological
algebra. It then introduces representations of quivers, quiver varieties and their applications to
the moduli spaces of meromorphic connections on the complex projective line. While no
particular reader background is assumed, the book is intended for graduate students in
mathematics, engineering and related fields, as well as researchers and scholars.
1st ed. 2020, XI, 371 p. 56
illus., 1 illus. in color.
Hardcover
ISBN 978-3-030-26453-6
Product category : Contributed volume
Series : Algorithms and Computation in
Mathematics : Other renditions
Softcover : ISBN 978-3-030-26456-7
Mathematics : Field Theory and Polynomials
Presents a rigorous mathematical description of statistical methodology for
small area estimation
Compares and contrasts various statistical methodologies
Shows how to apply small area estimation techniques in surveys, providing
the underlying R code
This advanced textbook explores small area estimation techniques, covers the underlying
mathematical and statistical theory and offers hands-on support with their implementation. It
presents the theory in a rigorous way and compares and contrasts various statistical
methodologies, helping readers understand how to develop new methodologies for small area
estimation. It also includes numerous sample applications of small area estimation techniques.
The underlying R code is provided in the text and applied to four datasets that mimic data
from labor markets and living conditions surveys, where the socioeconomic indicators include
the small area estimation of total unemployment, unemployment rates, average annual
household incomes and poverty indicators. Given its scope, the book will be useful for master
and PhD students, and for official and other applied statisticians.
Due 2021-05-09
1st ed. 2021, XX, 599 p.
Hardcover
ISBN 978-3-030-63756-9
Product category : Graduate/advanced undergraduate textbook
Series : Statistics for Social and Behavioral Sciences
Statistics : Statistics for Social Sciences, Humanities, Law
Revised version which completes the first 1996 publication
Presents the state of the art concerning finite volume methods
More examples and details added An expanding field
Excellent up-to-date review of the current research trends in this area
This monograph is devoted to the theory and approximation by finite volume methods of
nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows
directly a previous publication on hyperbolic systems of conservation laws by the same authors.
Since the earlier work concentrated on the mathematical theory of multidimensional scalar
conservation laws, this book will focus on systems and the theoretical aspects which are
needed in the applications, such as the solution of the Riemann problem and further insights
into more sophisticated problems, with special attention to the system of gas dynamics. This
new edition includes more examples such as MHD and shallow water, with an insight on
multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic
preserving schemes, introducing relaxation schemes and addressing problems related to
resonance and discontinuous fluxes while adding details on the low Mach number situation.
Due 2021-05-06
2nd ed. 2021, X, 869 p.
Hardcover
ISBN 978-1-0716-1342-9
Product category : Monograph
Series : Applied Mathematical Sciences
Mathematics : Numerical Analysis
Derives the quantum measurement formalism without postulates about
operators as observables
Enables a better physical understanding of quantum measurement and its
conceptual problems
Introduces the new idea of relativistic consistency, which removes
anthropocentric concepts from the derivation of no signalling conditions in
relativistic quantum theory
This book treats various aspects of the quantum theory of measurement, partially in a
relativistic framework. Measurement(-like) processes in quantum theory are identified and
analysed; and the quantum operator formalism is derived in full generality without postulating
operators as observables. Consistency conditions are derived, expressing the requirement of
Lorentz-frame independence of outcomes of spacelike separated measurements and implying
the impossibility of using quantum nonlocality to send signals faster than light. Local
commutativity is scrutinized. The localization problem of relativistic quantum theory is studied,
including comprehensive derivation of the theorems of Hegerfeld, Malament and ReehSchlieder.
Finally, the quantum formalism is derived from the dynamics of particles with
definite positions in Bohmian mechanics.
Due 2021-04-07
1st ed. 2021, XI, 384 p. 13 illus.
Hardcover
ISBN 978-3-030-67532-5
Product category : Monograph
Series : Fundamental Theories of Physics
Physics : Quantum Physics