Published/Copyright: 2025
This book will be published on August 18, 2025
This book is in the series
De Gruyter Textbook
Designed for a broad spectrum of mathematics majors, not only those pursuing graduate school, this book also provides a thorough explanation of undergraduate Real Analysis. Through a developmentally appropriate narrative that integrates informal discussion, motivation, and basic proof writing approaches with mathematical rigor and clarity, the aim is to assist all students in learning more about the real number system and calculus theory.
Presents mathematical arguments but also shows how they are developed.
Makes connections to what students have studied in their calculus courses to motivate interest.
Includes discussion of elementary mathematical proof techniques.
Mathematics
Analysis
Published/Copyright: 2025
This book will be published on September 22, 2025,
This book is in the series
Volume 40 | De Gruyter Series in Nonlinear Analysis and Applications
The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new findings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenberg inequality involving BMO norms is improved and new techniques are covered that will be of interest. This book also provides many open problems suitable for interested Ph.D students.
? Introduces dynamical systems for applications in biology and ecology
? Covers the main components in cross-diffusion systems and coexistence of geometry-affected steady states
? Discussed global existence and persistence of evolution processes
Mathematics
Analysis
Mathematics
Differential Equations and Dynamical Systems
Mathematics
Probability and Statistics
Mathematics
Applied Mathematics
Published/Copyright: 2025
This book will be published on September 1, 2025,
This book is in the series
Volume 103 | De Gruyter Studies in Mathematics
While the Cobordism Hypothesis provides a translation between topological and categorical structures, the subject of fusion categories arising from representations of finite groups has shown the need for a robust theory of duality in monoidal 2-categories. This book intertwines 3-dimensional category theory with enriched and symmetric monoidal 2-categories to present a comprehensive foundation for duals in dimension two. This framework is presented using wire diagrams, a typographical tool that combines the geometric appeal of ordinary string diagrams with the clarity of standard commutative diagrams in category theory. Chapters on enriched 2-categories, closed 2-categories, and compact closed 2-categories build the theory from the ground up and in full detail. Shorter appendices on technical topics from higher category theory such as icons, strictification theorems, and computads provide readers with concise explanations of key results, as well as references for researchers interested in more depth. The book concludes with a chapter of examples from algebra and topology, including a detailed construction for the example of cobordisms.
Focus on detailed diagrammatic methods via wire diagrams
Comprehensive treatment of enriched structures
Strictification theorems provide less complicated algebraic structures
Nick Gurski is currently an Associate Professor in the Department of Mathematics, Applied Mathematics and Statistics at Case Western Reserve University. He received his PhD in 2006 from the University of Chicago under the supervision of Peter May, and he held an NSF Postdoctoral Fellowship at Yale University with Mikhail Kapranov. His work is in two- and three-dimensional category theory, with a particular emphasis on applications in homotopy theory. Recent work has focused on symmetric monoidal structures and invertible objects, including a proof of the two-dimensional stable homotopy hypothesis.
David Yetter is a University Distinguished Professor in the Department of Mathematics at Kansas State University. He received his PhD in 1984 from the University of Pennsylvania under the supervision of Peter Freyd, with whom he was subsequently one of the groups which independently discovered the HOMFLY-PT polynomial invariant of classical knot and links. He is the author of over 50 papers, largely in topological quantum field theory, but covering areas ranging from topos theory to knot theory and from classical geometry to operator algebras.
Juan Orendain is a Visiting Assistant Professor in the Department of Mathematics, Applied Mathematics and Statistics at Case Western Reserve University. He received his PhD in 2014 from the National Autonomous University of Mexico under the supervision of Francisco Raggi and Jose Rios. He has been a postdoctoral fellow at the University of Tokyo, with Yasuyuki Kawahigashi, and the National University of Mexico, with Robert Oeckl. His work is in two-dimensional category theory, with an emphasis on the study of symmetric monoidal equipments, and their applications to mathematical physics. Recent work has focused on categorical models of higher lattice gauge theories and quantum theories.
Mathematics
Logic and Set Theory
Mathematics
Algebra and Number Theory
Mathematics
Geometry and Topology
Language: English
Published/Copyright: 2026
This book will be published on November 3, 2025, when it will be available here for purchase.
This book is in the series
Volume 78 | De Gruyter Expositions in Mathematics
The book summarizes recent results on problems with uni-variate polynomials. The first of them reads: given the signs of the coefficients of a real polynomial (i. e. its sign pattern), for which pairs of prescribed numbers of positive and negative roots (compatible with Descartesf rule of signs) can one find such a polynomial? For each degree greater or equal to 4, there are non-realizable cases. The problem is resolved for degree less or equal to 8. In another realization problem (resolved for degree less or equal to 5), one fixes the pairs (compatible with Rollefs theorem) of numbers of positive and negative roots of the polynomial and its non-constant derivatives. A third problem concerns polynomials with all roots real. One considers the sign pattern and the order in which the moduli of its positive and negative roots are arranged on the positive half-line. There are examples of pairs (sign pattern, order of moduli) compatible with Descartesf rule of signs that are not realizable. And there are various questions about the discriminant of the general family of uni-variate polynomials. The non-trivial answers to these simply formulated problems will give students and scholars a better understanding of uni-variate polynomials.
The book is about recent realization problems inspired by Descartesf rule of signs and Rollefs theorem
It gives only the necessary conditions.
The non-trivial answers to the problems provide a better understanding of uni-variate polynomials.
Vladimir Petrov Kostov is born in 1959 in Bulgaria. He has defended his PhD thesis at the Faculty of Mechanics and Mathematics of Moscow State University in 1990 and has been on a postdoc position at the University of Utrecht in 1990-1991. Since 1991 he is working at the Laboratory of Mathematics of the University of Nice, France. His research fields are:
1) the analytic theory of systems of linear differential equations, the Riemann-Hilbert and the Deligne-Simpson problem (see [1]);
2) uni-variate and in particular hyperbolic polynomials (i.e. polynomials with all roots real, see [2-6]); this includes also realization problems about uni-variate polynomials in the context of Descartesf rule of signs;
3) analytic properties of the partial theta function (see [6-8]).
[1] V.P. Kostov, The Deligne-Simpson problem -- a survey. Journal of Algebra 281 No. 1 (2004) 83 -108.
[2] V.P. Kostov, Topics on hyperbolic polynomials in one variable. Panoramas et Syntheses 33 (2011), vi 141 p. SMF.
[3] J. Forsgard, V.P. Kostov and B.Z. Shapiro, Could Rene Descartes have known this?, Experimental Mathematics vol. 24, issue 4 (2015), 438-448, DOI: 10.1080/10586458.2015.1030051.
[4] V.P. Kostov, On realizability of sign patterns by real polynomials, Czechoslovak Math. J. 68 (143) (2018), no. 3, 853-874.
[5] V.P. Kostov, Hyperbolic polynomials and rigid orders of moduli, Publicationes Mathematicae Debrecen100/1-2 (2022), 119-128 DOI: 10.5486/PMD.2022.9068.
[6] V.P. Kostov and B.Z. Shapiro, Hardy-Petrovitch-Hutchinson's problem and partial theta function, Duke Math. J. 162, No. 5 (2013) 825-861.
[7] V.P. Kostov, On the zeros of a partial theta function, Bull. Sci. Math. 137, No. 8 (2013) 1018-1030.
[8] V.P. Kostov, On the double zeros of a partial theta function, Bull. Sci. Math. 140, No. 4 (2016) 98-111.
Mathematics
Logic and Set Theory
Mathematics
Analysis
Mathematics
Geometry and Topology