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Counting Rocks! An Introduction to Combinatorics
  • Language: en

Counting Rocks! An Introduction to Combinatorics

  • Type: Book
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  • Published: 2023
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  • Publisher: Unknown

None

Win-- Women in Numbers
  • Language: en
  • Pages: 298

Win-- Women in Numbers

This volume is a collection of papers on number theory which evolved out of the workshop WIN - Women in Numbers, held November 2nd-7th, 2008, in Alberta, Canada. The book includes articles showcasing outcomes from collaborative research initiated during the workshop.

Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields
  • Language: en
  • Pages: 131

Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields

The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $mathbb F_p(t)$, when $p$ is prime and $rge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $mathbb F_q(t^1/d)$.

Directions in Number Theory
  • Language: en
  • Pages: 351

Directions in Number Theory

  • Type: Book
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  • Published: 2016-09-26
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  • Publisher: Springer

Exploring the interplay between deep theory and intricate computation, this volume is a compilation of research and survey papers in number theory, written by members of the Women In Numbers (WIN) network, principally by the collaborative research groups formed at Women In Numbers 3, a conference at the Banff International Research Station in Banff, Alberta, on April 21-25, 2014. The papers span a wide range of research areas: arithmetic geometry; analytic number theory; algebraic number theory; and applications to coding and cryptography. The WIN conference series began in 2008, with the aim of strengthening the research careers of female number theorists. The series introduced a novel rese...

Łojasiewicz-Simon Gradient Inequalities for Coupled Yang-Mills Energy Functionals
  • Language: en
  • Pages: 138

Łojasiewicz-Simon Gradient Inequalities for Coupled Yang-Mills Energy Functionals

The authors' primary goal in this monograph is to prove Łojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces that impose minimal regularity requirements on pairs of connections and sections.

Arithmetic Geometry: Computation and Applications
  • Language: en
  • Pages: 175

Arithmetic Geometry: Computation and Applications

For thirty years, the biennial international conference AGC T (Arithmetic, Geometry, Cryptography, and Coding Theory) has brought researchers to Marseille to build connections between arithmetic geometry and its applications, originally highlighting coding theory but more recently including cryptography and other areas as well. This volume contains the proceedings of the 16th international conference, held from June 19–23, 2017. The papers are original research articles covering a large range of topics, including weight enumerators for codes, function field analogs of the Brauer–Siegel theorem, the computation of cohomological invariants of curves, the trace distributions of algebraic groups, and applications of the computation of zeta functions of curves. Despite the varied topics, the papers share a common thread: the beautiful interplay between abstract theory and explicit results.

Theory of Fundamental Bessel Functions of High Rank
  • Language: en
  • Pages: 123

Theory of Fundamental Bessel Functions of High Rank

In this article, the author studies fundamental Bessel functions for $mathrm{GL}_n(mathbb F)$ arising from the Voronoí summation formula for any rank $n$ and field $mathbb F = mathbb R$ or $mathbb C$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.

Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties
  • Language: en
  • Pages: 92

Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties

Gromov-Witten theory started as an attempt to provide a rigorous mathematical foundation for the so-called A-model topological string theory of Calabi-Yau varieties. Even though it can be defined for all the Kähler/symplectic manifolds, the theory on Calabi-Yau varieties remains the most difficult one. In fact, a great deal of techniques were developed for non-Calabi-Yau varieties during the last twenty years. These techniques have only limited bearing on the Calabi-Yau cases. In a certain sense, Calabi-Yau cases are very special too. There are two outstanding problems for the Gromov-Witten theory of Calabi-Yau varieties and they are the focus of our investigation.

Applications of Dynamical Systems in Biology and Medicine
  • Language: en
  • Pages: 240

Applications of Dynamical Systems in Biology and Medicine

  • Type: Book
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  • Published: 2015-07-06
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  • Publisher: Springer

This volume highlights problems from a range of biological and medical applications that can be interpreted as questions about system behavior or control. Topics include drug resistance in cancer and malaria, biological fluid dynamics, auto-regulation in the kidney, anti-coagulation therapy, evolutionary diversification and photo-transduction. Mathematical techniques used to describe and investigate these biological and medical problems include ordinary, partial and stochastic differentiation equations, hybrid discrete-continuous approaches, as well as 2 and 3D numerical simulation.

Riemann Surfaces and Algebraic Curves
  • Language: en
  • Pages: 197

Riemann Surfaces and Algebraic Curves

Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.