Academic Articles & Research Papers

A History of Mathematics: An Introduction

Part I. Ancient Mathematics 1. Egypt and Mesopotamia 1.1 Egypt 1.2 Mesopotamia 2. The Beginnings of Mathematics in Greece 2.1 The Earliest Greek Mathematics 2.2 The Time of Plato 2.3 Aristotle 3. Euclid 3.1 Introduction to the Elements 3.2 ...

Methods of Mathematical Physics

This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors...

A local meshless method for the one-dimensional Fisher’s equation

This study presents a novel local meshless approach for solving one-dimensional Fisher’s equation, combining a local scheme, Gaussian radial basis functions (G-RBF), and a collocation technique. The method leverages the Gaussian basis’s non...

Mathematics as a science of patterns

Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has ...

Mathematics of Physics and Chemistry

Superconformal indices of N $$ \mathcal{N} $$ = 4 Chern-Simons matter theories

Abstract Gaiotto and Witten found that one can construct 3d N $$ \mathcal{N} $$ = 4 Chern-Simons matter theories by using N $$ \mathcal{N} $$ = 4 SCFT whose momentum map of global symmetries satisfy special condition. Usually, one uses free...

New Insights into Cd²⁺/Fe³⁺ Co-Doped BiOBr for Enhancing the Photocatalysis Efficiency of Dye Decomposition under Visible-Light

Uniform flowerlike microspheres Cd2+/Fe3+ co-doped BiOBr were prepared with the aid of the microwave hydrothermal process. The results indicate that the degradation performance of Bi1−xCdxOBr and Bi1−xFexOBr are 1.31 and 2.05 times that of ...

On proof and progress in mathematics

This essay on the nature of proof and progress in mathematics was stimulated by the article of Jaffe and Quinn, "Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics".Their article raises interesting i...

Mathematics, Matter and Method

Introduction 1. Truth and necessity in mathematics 2. The thesis that mathematics is logic 3. Mathematics without foundations 4. What is mathematical truth? 5. Philosophy of physics 6. An examination of Grunbaum's philosophy of geometry 7. ...

Global quantum correlations in finite-size spin chains

We perform an extensive study of the properties of global quantum correlations in finite-size one-dimensional quantum spin models at finite temperature. By adopting a recently proposed measure for global quantum correlations (Rulli and Sara...

Computational Mathematics and Mathematical Physics

The Philosophy of Mathematics

Russell's logical investigations in the foundations of mathematics produced a fund of novel ideas, techniques, and possibilities. His powers of conception and exposition have made the subject an engaging area of study for generations of stu...

Solitons in Mathematics and Physics

The History of the Soliton Derivation of the Korteweg-de Vries, Nonlinear Schrodinger and Other Important and Canonical Equations of Mathematical Physics Soliton Equation Families and Solution Methods The -Function, the Hirota Method, the P...

Equations of Mathematical Physics

Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical phys...

Mathematical Methods for Physicists

This text is designed for an intermediate-level, two-semester undergraduate course in mathematical physics. It provides an accessible account of most of the current, important mathematical tools required in physics these days. It is assumed...

Mathematical Methods for Physicists

Mathematical Methods for Physicists, Third Edition provides an advanced undergraduate and beginning graduate study in physical science, focusing on the mathematics of theoretical physics. This edition includes sections on the non-Cartesian ...

Mathematical Biophysics

Methods of Mathematical Physics

Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intu...

Methods of Mathematical Physics

Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical int...

International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences publishes research across all fields of mathematics and mathematical sciences, such as pure and applied mathematics, mathematical physics, probability and mathematical statistic...