Applied Mathematics Research Papers

System 2 Thinking in OpenAI’s o1-Preview Model: Near-Perfect Performance on a Mathematics Exam

The processes underlying human cognition are often divided into System 1, which involves fast, intuitive thinking, and System 2, which involves slow, deliberate reasoning. Previously, large language models were criticized for lacking the de...

Chaotic outbreak in discrete epidemic model with vaccination and quarantine interventions and limited medical resources

The spread of infectious diseases can be analyzed dynamically using a discrete dynamic system. The characteristics of the infectious disease phenomenon are interesting to study as parameters considered in a dynamic system. Some of these inc...

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...

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 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...

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...

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...

MOMENTS OF THE LENGTH OF LINE SEGMENTS IN HOMOGENEOUS PLANAR STIT TESSELLATIONS

Homogeneous planar tessellations stable under iteration (STIT tessellations) are considered. Using recent results about the joint distribution of direction and length of the typical I-, K- and J-segment we prove closed formulas for the firs...

MATHEMATICS AND THE NATURAL SCIENCES

Read: https://www.bookdepository.com/Mathematics-Natural-Sciences-Physical-Singularity-Life-Giuseppe-Longo/9781848166936?ref=grid-view&qid=1628083851263&sr=1-3#Introduction in free access : https://www.di.ens.fr/users/longo/files/BaLoSingBo...

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...

Elements of mathematical ecology

"Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that, for the...

Mathematical Logic

Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas ...

Elements of Mathematical Ecology

Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore mu...