Commemorates the mathematical achievements of Anthony Joseph, one of Lie
theory’s leading figures
Explores recent advances in topics that Joseph fundamentally influenced
Equips readers with an understanding of various subjects within Lie algebra
and representation theory
This volume, a celebration of Anthony Joseph’s fundamental influence on classical and
quantized representation theory, explores a wide array of current topics in Lie theory by experts
in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of
Representations,” the first of which was held from July 16-18 at the Weizmann Institute of
Science and the second from July 19-23 at the University of Haifa. The chapters in this volume
cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group
actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is
addressed to mathematicians who specialize in representation theory and Lie theory, and who
wish to learn more about this fascinating subject.
1st ed. 2019, XVII, 553 p.
75 illus., 16 illus. in color.
Hardcover
ISBN 978-3-030-23530-7
Product category : Contributed volume
Series : Progress in Mathematics
Softcover
ISBN 978-3-030-23533-8
Mathematics : Topological Groups, Lie Groups
Presents an accessible guide to AC and GF written for engineers to address
engineering problems
Provides theory in an easy to understand manner and application of the
theory to real life projects and solutions
Describes GFs and their applications in a language that is familiar to
engineers, with connections to optimal control and signal processing
The book shows that the analytic combinatorics (AC) method encodes the combinatorial
problems of multiple object tracking?without information loss?into the derivatives of a
generating function (GF). The book lays out an easy-to-follow path from theory to practice and
includes salient AC application examples. Since GFs are not widely utilized amongst the
tracking community, the book takes the reader from the basics of the subject to applications of
theory starting from the simplest problem of single object tracking, and advancing chapter by
chapter to more challenging multi-object tracking problems. Many established tracking filters (e.
g., Bayes-Markov, PDA, JPDA, IPDA, JIPDA, CPHD, PHD, multi-Bernoulli, MBM, LMBM, and MHT)
are derived in this manner with simplicity, economy, and considerable clarity. The AC method
gives significant and fresh insights into the modeling assumptions of these filters and, thereby,
also shows the potential utility of various approximation methods that are well established
techniques in applied mathematics and physics, but are new to tracking. These unexplored
possibilities are reviewed in the final chapter of the book.
1st ed. 2021, XVI, 221 p. 16
illus., 15 illus. in color.
Hardcover
ISBN 978-3-030-61190-3
Product category : Monograph
Engineering : Signal, Image and Speech Processing
Includes survey articles on nonstationary subdivision and Prony’s method
Includes 11 research papers on approximation theory
Covers both theory and applications of approximation theory
These proceedings are based on the international conference Approximation Theory XVI held
on May 19?22, 2019 in Nashville, Tennessee. The conference was the sixteenth in a series of
meetings in Approximation Theory held at various locations in the United States. Over 130
mathematicians from 20 countries attended. The book contains two longer survey papers on
nonstationary subdivision and Prony’s method, along with 11 research papers on a variety of
topics in approximation theory, including Balian-Low theorems, butterfly spline interpolation,
cubature rules, Hankel and Toeplitz matrices, phase retrieval, positive definite kernels,
quasiinterpolation operators, stochastic collocation, the gradient conjecture, time-variant systems, and
trivariate finite elements. The book should be of interest to mathematicians, engineers, and
computer scientists working in approximation theory, computer-aided geometric design,
numerical analysis, and related approximation areas.
1st ed. 2021, VIII, 253 p.
41 illus., 36 illus. in color.
Hardcover
ISBN 978-3-030-57463-5
Product category : Proceedings
Series : Springer Proceedings in Mathematics & Statistics
Mathematics : Approximations and Expansions
Presents a general and rigorous framework of quantum information based on
von Neumann algebras
Makes a comprehensive study of different types of quantum divergences
Updates Petz' previous work on reversibility/sufficiency for quantum
operations
Relative entropy has played a significant role in various fields of mathematics and physics as
the quantum version of the Kullback?Leibler divergence in classical theory. Many variations of
relative entropy have been introduced so far with applications to quantum information and
related subjects. Typical examples are three different classes, called the standard, the maximal,
and the measured f-divergences, all of which are defined in terms of (operator) convex
functions f on (0,) andhave respective mathematical and information theoretical backgrounds.
The -Renyi relative entropy and its new version called the sandwiched -Renyi relative entropy
have also been useful in recent developments of quantum information. In the first half of this
monograph, the different types of quantum f-divergences and the Renyi-type divergences
mentioned above in the general von Neumann algebra setting are presented for study. While
quantum information has been developing mostly in the finite-dimensional setting, it is widely
believed that von Neumann algebras provide the most suitable framework in studying quantum
information and related subjects. Thus, the advance of quantum divergences in von Neumann
algebras will be beneficial for further development of quantum information. Quantum
divergences are functions of two states (or more generally, two positive linear functionals) on a
quantum system and measure the difference between the two states. They are often utilized to
address such problems as state discrimination, error correction, and reversibility of quantum
operations
Due 2021-02-16
1st ed. 2021, X, 194 p. 1 illus.
Hardcover
ISBN 978-981-33-4198-2
Product category : Monograph
Series : Mathematical Physics Studies
Mathematics : Mathematical Physics
Draws on latest historical research and new archival sources to give a
comprehensive picture of Noether’s life and work
Gives a detailed account of Noether’s role in the relativity revolution
Shows how Emmy Noether promoted modern algebra through her school
Provides historical background to the play "Diving into Math with Emmy
Noether"
Although she was famous as the "mother of modern algebra," Emmy Noether’s life and work
have never been the subject of an authoritative scientific biography.Emmy Noether ?
Mathematician Extraordinairerepresents the most comprehensive study of this singularly
important mathematician to date. Focusing on key turning points, it aims to provide an overall
interpretation of Noether’s intellectual development while offering a new assessment of her
role in transforming the mathematics of the twentieth century. Hermann Weyl, her colleague
before both fled to the United States in 1933, fully recognized that Noether’s dynamic school
was the very heart and soul of the famous Gottingen community. Beyond her immediate circle
of students, Emmy Noether’s lectures and seminars drew talented mathematicians from all
over the world. Four of the most important were B.L. van der Waerden, Pavel Alexandrov,
Helmut Hasse, and Olga Taussky. Noether’s classic papers on ideal theory inspired van der
Waerden to recast his research in algebraic geometry. Her lectures on group theory motivated
Alexandrov to develop links between point set topology and combinatorial methods. Noether’s
vision for a new approach to algebraic number theory gave Hasse the impetus to pursue a line
of research that led to the Brauer?Hasse?Noether Theorem, whereas her abstract style clashed
with Taussky’s approach to classical class field theory during a difficult time when both were
trying to find their footing in a foreign country. Although similar toProving It Her Way: Emmy
Noether, a Life in Mathematics, this lengthier study addresses mathematically minded readers.
Thus, it presents a detailed analysis of Emmy Noether’s work with Hilbert and Klein on
mathematical problems connected with Einstein’s theory of relativity
1st ed. 2021, XXI, 339 p.
Hardcover
ISBN 978-3-030-63809-2
Product category : Biography
Mathematics : History of Mathematics