Format: Hardback, 253 pages, height x width: 235x155 mm, weight: 565 g, 36 Illustrations, color;
5 Illustrations, black and white; VIII, 253 p. 41 illus., 36 illus. in color.,
Series: Springer Proceedings in Mathematics & Statistics 336
Pub. Date: 05-Jan-2021
ISBN-13: 9783030574635
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, quasi-interpolation 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.
Time-variant System Approximation via later-time Samples.- C1-quartic Butterfly-spline Interpolation on Type-1 Triangulations.- Approximation with Conditionally Positive Definite Kernels on Deficient Sets.- Non-stationary Subdivision Schemes: State of the Art and Perspectives.- Cubature Rules Based on Bivariate Spline Quasi-interpolation for Weakly Singular Integrals.- On DC based Methods for Phase Retrieval.- Modifications of Pronys Method for the Recovery and Sparse Approximation of Generalized Exponential Sums.- On Eigenvalue Distribution of Varying Hankel and Toeplitz Matrices with Entries of Power Growth or Decay.- On the Gradient Conjecture for Quadratic Polynomials.- Balian-Low Theorems in Several Variables.- Quasi-Interpolant Operators and the Solution of Fractional Differential Problems.- Stochastic Collocation with Hierarchical Extended B-splines on Sparse Grids.- Trivariate Interpolated Galerkin Finite Elements for the Poisson Equation.- Index.
Format: Hardback, 384 pages, height x width: 235x155 mm, 20 Tables, color; 26 Illustrations,
color; 21 Illustrations, black and white; XX, 384 p. 47 illus., 26 illus. in color.
Pub. Date: 24-Jul-2022
Hardcoer ISBN-13: 9783030956820
Paperback ISBN-13: 9783030956851
This open access book is about the shaping of international relations in mathematics over the last two hundred years. It focusses on institutions and organizations that were created to frame the international dimension of mathematical research. Today, striking evidence of globalized mathematics is provided by countless international meetings and the worldwide repository ArXiv. The text follows the sinuous path that was taken to reach this state, from the long nineteenth century, through the two wars, to the present day. International cooperation in mathematics was well established by 1900, centered in Europe. The first International Mathematical Union, IMU, founded in 1920 and disbanded in 1932, reflected above all the trauma of WW I. Since 1950 the current IMU has played an increasing role in defining mathematical excellence, as is shown both in the historical narrative and by analyzing data about the International Congresses of Mathematicians. For each of the three periods discussed, interactions are explored between world politics, the advancement of scientific infrastructures, and the inner evolution of mathematics. Readers will thus take a new look at the place of mathematics in world culture, and how international organizations can make a difference. Aimed at mathematicians, historians of science, scientists, and the scientifically inclined general public, the book will be valuable to anyone interested in the history of science on an international level.
The long 19th century which made the International Mathematical Union, IMU, possible: 1800-1918.- IMU, the first attempt: 1919-1949.- Seventy Years of Globalizations: 1950-2020.
Format: Book, height x width: 235x155 mm, Approx. 740 p. ., 1 Book
Pub. Date: 09-Apr-2022
ISBN-13: 9783031062476
Jamshid al-Kashi’s Mifta? al- isab (Key to Arithmetic) was largely unknown to researchers until the mid-20th century, and has not been translated to English until now. These three volumes finally bring al-Kashi’s groundbreaking textbook to English audiences in its entirety. As soon as it was studied by modern researchers, Miftah changed some false assumptions about the history of certain topics in mathematics. Written as a textbook for students of mathematics, astronomy, accounting, engineering, and architecture, Miftah covers a wide range of topics in arithmetic, geometry, and algebra. By sharing al-Kashi’s most comprehensive work with a wider audience, this book will help establish a more complete history of mathematics, and extend al-Kashi’s influence into the 21st century and beyond.
Researchers and students of the history of mathematics will find this set indispensable in filling in a frequently overlooked time period and region. These volumes will also provide anybody interested in the history of Islamic culture with an insightful look at one of the mathematical world’s most neglected figures.
Volume I: Arithmetic Introduction.- The First Treatise: On Integer Arithmetic.- The Second Treatise: On Arithmetic of Fractions.- The Third Treatise: On the Method of Arithmetic of Astronomers. Volume II: Geometry Introduction.- The Fourth Treatise: On Measurements. Volume III: Algebra Introduction.- The Fifth Treatise: On Extracting Unknowns.
Format: Hardback, 484 pages, height x width: 235x155 mm,
18 Illustrations, black and white; XX, 484 p. 18 illus
Series: Springer Monographs in Mathematics
Pub. Date: 07-Aug-2022
ISBN-13: 9783031054792
This book offers an up-to-date, comprehensive account of determinantal rings and varieties, presenting a multitude of methods used in their study, with tools from combinatorics, algebra, representation theory and geometry. After a concise introduction to Groebner and Sagbi bases, determinantal ideals are studied via the standard monomial theory and the straightening law. This opens the door for representation theoretic methods, such as the Robinson-Schensted-Knuth correspondence, which provide a description of the Groebner bases of determinantal ideals, yielding homological and enumerative theorems on determinantal rings. Sagbi bases then lead to the introduction of toric methods. In positive characteristic, the Frobenius functor is used to study properties of singularities, such as F-regularity and F-rationality. Castelnuovo-Mumford regularity, an important complexity measure in commutative algebra and algebraic geometry, is introduced in the general setting of a Noetherian base ring and then applied to powers and products of ideals. The remainder of the book focuses on algebraic geometry, where general vanishing results for the cohomology of line bundles on flag varieties are presented and used to obtain asymptotic values of the regularity of symbolic powers of determinantal ideals. In characteristic zero, the Borel-Weil-Bott theorem provides sharper results for GL-invariant ideals. The book concludes with a computation of cohomology with support in determinantal ideals and a survey of their free resolutions. Determinants, Groebner Bases and Cohomology provides a unique reference for the theory of determinantal ideals and varieties, as well as an introduction to the beautiful mathematics developed in their study. Accessible to graduate students with basic grounding in commutative algebra and algebraic geometry, it can be used alongside general texts to illustrate the theory with a particularly interesting and important class of varieties.
1 Groebner bases, initial ideals and initial algebras.- 2 More on Groebner deformations.- 3 Determinantal ideals and the straightening law.- 4 Groebner bases of determinantal ideals.- 5 Universal Groebner bases.- 6 Algebras defined by minors.- 7 F-singularities of determinantal rings.- 8 Castelnuovo-Mumford regularity.- 9 Grassmannians, flag varieties, Schur functors and cohomology.- 10 Asymptotic regularity for symbolic powers of determinantal ideals.- 11 Cohomology and regularity in characteristic zero.
Format: Paperback / softback, 118 pages, height x width: 235x155 mm, weight: 209 g, 1
Illustrations, black and white; X, 118 p. 1 illus.
Series: JSS Research Series in Statistics
Pub. Date: 02-Jun-2022
ISBN-13: 9789811927072
This book focuses on multiple comparisons of proportions in multi-sample models with Bernoulli responses. First, the author explains the one-sample and two-sample methods that form the basis of multiple comparisons. Then, regularity conditions are stated in detail. Simultaneous inference for all proportions based on exact confidence limits and based on asymptotic theory is discussed. Closed testing procedures based on some one-sample statistics are introduced. For all-pairwise multiple comparisons of proportions, the author uses arcsine square root transformation of sample means. Closed testing procedures based on maximum absolute values of some two-sample test statistics and based on chi-square test statistics are introduced. It is shown that the multi-step procedures are more powerful than single-step procedures and the Ryan?Einot?Gabriel?Welsch (REGW)-type tests. Furthermore, the author discusses multiple comparisons with a control. Under simple ordered restrictions of proportions, the author also discusses closed testing procedures based on maximum values of two-sample test statistics and based on Bartholomew's statistics. Last, serial gatekeeping procedures based on the above-mentioned closed testing procedures are proposed although Bonferroni inequalities are used in serial gatekeeping procedures of many.
Theoretical Basics in One-Sample and Two-Sample Models.- Simultaneous Inference for All Proportions.- All-Pairwise Comparison Tests.- Multiple Comparison Tests with a Control.- Simultaneous Confidence Intervals.- All-Pairwise Comparisons under Simple Order Restrictions.- Comparisons with a Control and Successive Comparisons under Simple Order Restrictions.- Comparisons with a Control and Successive Comparisons under Simple Order Restrictions.- Hybrid Serial Gatekeeping Procedures for Multiple Comparisons With a Control.
Format: Paperback / softback, 124 pages, height x width: 235x155 mm,
19 Illustrations, color; 11 Illustrations, black and white; XII, 124 p. 30 illus., 19 illus. in color
Series: SpringerBriefs in Mathematics
Pub. Date: 24-Jul-2022
ISBN-13: 9783031068324
This book offers a structured algebraic and geometric approach to the classification and construction of quantum codes for topological quantum computation. It combines key concepts in linear algebra, algebraic topology, hyperbolic geometry, group theory, quantum mechanics, and classical and quantum coding theory to help readers understand and develop quantum codes for topological quantum computation.
One possible approach to building a quantum computer is based on surface codes, operated as stabilizer codes. The surface codes evolved from Kitaev's toric codes, as a means to developing models for topological order by using qubits distributed on the surface of a toroid. A significant advantage of surface codes is their relative tolerance to local errors. A second approach is based on color codes, which are topological stabilizer codes defined on a tessellation with geometrically local stabilizer generators. This book provides basic geometric concepts, like surface geometry, hyperbolic geometry and tessellation, as well as basic algebraic concepts, like stabilizer formalism, for the construction of the most promising classes of quantum error-correcting codes such as surfaces codes and color codes.
The book is intended for senior undergraduate and graduate students in Electrical Engineering and Mathematics with an understanding of the basic concepts of linear algebra and quantum mechanics.
[ preliminary]1 An Overview on Quantum Codes1.1 Previous Results1.2 Goals1.3 Some Classes of Quantum Error-Correcting Codes1.4 Quantum Error-Correcting Codes1.4.1 Formalism of Stabilizer Codes1.5 Topological Quantum Codes1.5.1 Topological Stabilizer Codes1.6 CSS Codes1.7 Surface Codes1.8 Toric Quantum Code, g = 11.9 Hyperbolic Surface Codes, g 21.10 Color Codes 2 Preliminaries2.1 Upper Half-Plane Model2.2 Unit Open Disc Model2.3 Geometrical Properties in H2 and [ Delta]2.4 Tessellations in Euclidean and Hyperbolic Planes 3 Surface Codes 293.1 Toric Codes, g = 13.2 Projective Plane Codes, g = 03.3 Homological Quantum Codes, g = 13.4 g-Toric Codes, g 2 4 Color Codes4.1 Quantum Color Codes4.2 Hyperbolic Color Codes4.3 Polygonal Color Codes