Academic Articles & Research Papers

Graded weakly 1-absorbing prime ideals

In this paper, we introduce and study graded weakly 1-absorbing prime ideals in graded commutative rings. Let $G$ be a group and $R$ be a $G$-graded commutative ring with a nonzero identity $1\neq0$. A proper graded ideal $P$ of $R$ is call...

Existence and multiplicity of homoclinic solutions for p(t)-Laplacian systems with subquadratic potentials

By using the genus properties, we establish some criteria for the second-order p(t)-Laplacian system $$ \frac{d}{dt}\big(|\dot{u}(t)|^{p(t)-2}\dot{u}(t)\big)-a(t)|u(t)|^{p(t)-2}u(t) +\nabla W(t, u(t))=0 $$ to have at least one, and i...

Review of Public Opinion Dynamics Models

Social network provides a medium for information dissemination,leading to the rapid development of public opinion.Controlling the development direction of public opinion is one of the core issues of public opinion dynamics.However,the publi...

Mathematics and Computation

Mathematical Statistics

Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. Mathematical Statis...

Mathematical Capabilities of ChatGPT

We investigate the mathematical capabilities of two iterations of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets, as well as hand-crafted ones, using a novel methodology. In...

Mathematics without Numbers

Abstract Develops a structuralist understanding of mathematics, as an alternative to set‐ or type‐theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to abstract entities. Modal logic is ...

Advanced Engineering Mathematics

A long-standing, best-selling, comprehensive textbook covering all the mathematics required on upper level engineering mathematics undergraduate courses. Its unique programmed approach takes students...

Mathematics and the Body

This book explores alternative ways to consider the relationship between mathematics and the material world. Drawing on the philosophy of Gilles Châtelet and the post-humanist materialism of Karen Barad, the authors present an 'inclusive ma...

On Mathematical Problem Posing.

In mathematics classes at all levels of schooling in all countries of the world, students can be observed solving problems. The quality and authenticity of these mathematics problems has been the subject of many discussions and debates in r...

Mathematics for Economists

An abundance of applications to current economic analysis, illustrative diagrams, thought-provoking exercises, careful proofs, and a flexible organization-these are the advantages that Mathematics for Economists brings to today's classroom....

The Mathematics of Financial Derivatives

Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematic...

The Nature of Mathematical Knowledge

Abstract The Nature of Mathematical Knowledge develops and defends an empiricist approach to mathematical knowledge. After offering an account of a priori knowledge, it argues that none of the available accounts of a priori mathematical kno...

The Ethics of Mathematics: Is Mathematics Harmful?

The Handbook of Mathematical Cognition

Part 1: Cognitive Representations for Number and Mathematics. M. Fayol, X. Seron, About Numerical Representations: Insights from Neuropsychological, Experimental and Developmental Studies. M. Brysbaert, Number Recognition in Different Forma...

Introduction to Mathematical Logic.

is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and...

A Mathematical Theory of Evidence

Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probabilit...

Mathematics and Learning Disabilities

Between 5% and 8% of school-age children have some form of memory or cognitive deficit that interferes with their ability to learn concepts or procedures in one or more mathematical domains. A review of the arithmetical competencies of thes...

Robustness of a bisimulation-type faster-than preorder

TACS is an extension of CCS where upper time bounds for delays can be specified. Luettgen and Vogler defined three variants of bismulation-type faster-than relations and showed that they all three lead to the same preorder, demonstrating th...

Wireless Link-Quality Estimation in Smart Grid Environments

Recently, wireless sensor networks (WSNs) have gained great attention from the research community for various smart grid applications, including advanced metering infrastructure (AMI), power outage detection, distribution automation, towers...