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Articles 1 - 30 of 27124

Full-Text Articles in Physical Sciences and Mathematics

(R2165) Two Different Stages With Two Distinct Harvesting Processes, S. Vijaya, Krishika M Dec 2050

(R2165) Two Different Stages With Two Distinct Harvesting Processes, S. Vijaya, Krishika M

Applications and Applied Mathematics: An International Journal (AAM)

This study extends the classical Lotka-Volterra prey-predator model by incorporating a stage structured prey population consisting of juvenile and adult stages, while considering a single predator species governed by a Holling type II functional response. The growth of the juvenile prey depends on the adult prey population and since the juvenile prey has no reproduction capability. Two distinct harvesting strategies are introduced in the model. Constant-yield harvesting is applied to the juvenile stage of the prey population and represents a fixed amount of harvest regardless of population size. Constant effort harvesting is applied to the adult stage of the prey …

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Toward Mapping Multiphase Multicomponent Mixtures With Neural Networks, Kristen L. Hallas, Melissa De Jesus, Christine J. Wu, Jianzhi Li, Jason Bernstein, Philip C. Myint Dec 2026

Toward Mapping Multiphase Multicomponent Mixtures With Neural Networks, Kristen L. Hallas, Melissa De Jesus, Christine J. Wu, Jianzhi Li, Jason Bernstein, Philip C. Myint

School of Mathematical & Statistical Sciences Faculty Publications

Equation of state (EOS) tables are commonly used in hydrodynamic simulations of high-pressure, high-temperature phenomena in fields like planetary science, astrophysics, and high-energy-density science. However, generating and storing EOS tables for multiphase, multicomponent mixtures over a wide range of pressures and temperatures is computationally infeasible due to their memory-intensive nature. To address this issue, we have developed a neural network-based machine learning model to predict new EOS tables for binary mixtures. In particular, a deep feedforward neural network trained on a set of ten EOS tables at particular mixture compositions is able to predict nine new (hold-out) EOS tables at …

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Revisiting Ulam Stability For Boundary Value Problems, Martin Bohner, Snezhana Hristova, Agnieszka B. Malinowska, Ewa Girejko Dec 2026

Revisiting Ulam Stability For Boundary Value Problems, Martin Bohner, Snezhana Hristova, Agnieszka B. Malinowska, Ewa Girejko

Mathematics and Statistics Faculty Research & Creative Works

The main goal of this paper is to apply Ulam stability theory to boundary value problems for dynamic equations, while addressing several common misconceptions found in the existing literature. We identify the key issues that arise when applying Ulam stability to such problems and propose three distinct approaches to overcome them. To enhance clarity and accessibility, we begin with nonlinear ordinary differential equations and subsequently extend the analysis to nonlinear dynamic equations on time scales. Since a time scale is defined as any nonempty closed subset of the real numbers, our results are applicable to dynamic equations on continuous, discrete, …

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A Finite Element Model For Thermomechanical Stress-Strain Fields In Transversely Isotropic Strain-Limiting Materials, Saugata Ghosh, Dambaru Bhatta, S. M. Mallikarjunaiah Nov 2026

A Finite Element Model For Thermomechanical Stress-Strain Fields In Transversely Isotropic Strain-Limiting Materials, Saugata Ghosh, Dambaru Bhatta, S. M. Mallikarjunaiah

School of Mathematical & Statistical Sciences Faculty Publications

This paper presents a comprehensive computational framework for investigating thermo-elastic fracture in transversely isotropic materials, where classical linear elasticity fails to predict physically realistic behavior near stress concentrations. We address the challenge of unphysical strain singularities at crack tips by employing a strain-limiting theory of elasticity. This theory is characterized by an algebraically nonlinear constitutive relationship between stress and strain, which intrinsically enforces a limit on the norm of the strain tensor. This approach allows the development of very large stresses, as expected near a crack tip, while ensuring that the corresponding strains remain physically bounded. A loosely coupled system …

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Finite Mathematics: A Course Guide, Angela West Dixon, Hillary Dosser Oct 2026

Finite Mathematics: A Course Guide, Angela West Dixon, Hillary Dosser

Faculty Publications

Finite Mathematics: A Course Guide is a supplement to Mathematics for Business and Social Sciences by Kathryn Bollinger and Vanessa Coffelt. The authors of this Course Guide, Angela Dixon and Hilary Dosser, are instructors of Mathematics at Stephen F. Austin State University in Nacogdoches, Texas. This Course Guide was developed in response to adapting MATH 1324, Finite Mathematics to a zero-cost course, using an Open Educational Resource (OER) implemented in the Fall semester of 2026. According to the Texas Higher Education Coordinating Board’s Academic Course Guide Manual (ACGM), MATH 1324 Mathematics for Business and Social Sciences concerns the application of …

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Study Of A Nonlinear Delayed Parabolic Model For Prion Disease Dynamics With The Unfolded Protein Response, Gangadhara Boregowda, Laurent Pujo-Menjouet, Zhaosheng Feng, Michael R. Lindstrom Oct 2026

Study Of A Nonlinear Delayed Parabolic Model For Prion Disease Dynamics With The Unfolded Protein Response, Gangadhara Boregowda, Laurent Pujo-Menjouet, Zhaosheng Feng, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

Prion diseases are neurodegenerative disorders characterized by the dynamic spread of misfolded toxic proteins in the brain. In this process, the normal cellular prion protein (PrPC) produced by neurons misfolds into a toxic form known as scrapie prion protein (PrPSc). These misfolded proteins propagate through the brain by converting healthy prions into their toxic form. This biological mechanism can be modeled by a system of nonlinear parabolic partial differential equations, accompanied by a nonlinear delayed integral boundary condition. Our primary objective is to establish the existence of nonnegative classical solutions to this system. Furthermore, we derive a priori estimates for …

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Quantum Mechanics, Non-Locality, And The Space Discreteness Hypothesis, Wilson A. Zuniga-Galindo Oct 2026

Quantum Mechanics, Non-Locality, And The Space Discreteness Hypothesis, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

The space discreteness hypothesis asserts that the nature of space at short distances is radically different from that at large distances. Based on the Bronstein inequality, here, we use a totally disconnected topological space X as a model for the physical space at short distances. However, we consider the time as a real variable. In this framework, the Dirac–von Neumann formalism can be used. This discreteness hypothesis implies that given two different points in space, there is no continuous curve (a world line) joining them. Consequently, this hypothesis is not compatible with the theory of relativity. We propose R×(R×X)3 as …

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How Euler Could Have Done It: Euler And An Integral Of Ramanujan, Alexander Aycock Sep 2026

How Euler Could Have Done It: Euler And An Integral Of Ramanujan, Alexander Aycock

Euleriana

We present a derivation of a definite integral discovered by Ramanujan (1887–1920) in his 1915 paper "Some Definite Integrals," from formulas and ideas already developed by Euler (1707–1783). Additionally, it is argued why Euler did not discover Ramanujan's integral himself, although he had all tools required for this task at his disposal.

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A Note On Euler's Definition Of The Sum Of A Divergent Series, Alexander Aycock Sep 2026

A Note On Euler's Definition Of The Sum Of A Divergent Series, Alexander Aycock

Euleriana

We outline Euler's theory of divergent series and present another approach he could have taken to sum his ``factorial series". Finally, we address the contradictions that arise from his concept of a sum of a divergent series.

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Euler's Explorations Of Extremal Ellipses, Jonathan David Evans Sep 2026

Euler's Explorations Of Extremal Ellipses, Jonathan David Evans

Euleriana

In the 1770s, Euler wrote a series of papers (E563, E691 and E692) about finding the ellipse with minimal area or perimeter in the family of all ellipses passing through a fixed set of points. This is a translation of all three papers from the original Latin, together with a commentary which discusses Euler's results and an appendix which addresses a question from E691 which Euler left for others to consider.

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Arithmetic Theorems, Demonstrated By A New Method: An English Translation Of E271, Brendon Lasell Sep 2026

Arithmetic Theorems, Demonstrated By A New Method: An English Translation Of E271, Brendon Lasell

Euleriana

After defending in general terms the value of arithmetic demonstrations, where, according to Euler, the force of genius shines more brightly than in any other kind of demonstration, he goes on to let the force of his own genius shine forth in demonstrating the fact that, for any pair of relatively prime numbers a and N, aϕ(N) − 1 is always divisible by N, where we anachronistically denote by ϕ(N) the number of numbers less than N that are relatively prime to it. He approaches this theorem by considering the remainders that result when the numbers in an arithmetic …

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On Double Integral Formulas: An English Translation Of E391, Thomas W. Polaski Sep 2026

On Double Integral Formulas: An English Translation Of E391, Thomas W. Polaski

Euleriana

In this paper, Euler investigates the theory of double intergrals to uses them to find areas, volumes and surface areas. He considers transformations of variables in double integrals. After showing that simple multiplication of the transformed differentials is not appropriate, he derives the formula for a change of variables in double integrals. Euler then uses such changes of variables to investigate areas and volumes, and then turns his attention to the so-called ``Florentine problem.'' This problem requires one to remove four equal windows from a hemispherical surface so that the remaining area is equal to the area of a square. …

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Eulerian Problem Solving, Christopher Goff, Erik Tou Sep 2026

Eulerian Problem Solving, Christopher Goff, Erik Tou

Euleriana

An introduction to the contents in Volume 6 (Issue 2) of Euleriana.

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Fast Computation And Model Order Reduction Of The Friction Stir Welding Process With Pod-Deim, Joshua Kay, Zilong Song Sep 2026

Fast Computation And Model Order Reduction Of The Friction Stir Welding Process With Pod-Deim, Joshua Kay, Zilong Song

Mathematics and Statistics Student Research and Class Projects

Friction stir welding (FSW) is a solid-state manufacturing process widely used in joining aluminum and other metal workpieces. The FSW process can be modeled by a coupled system of non-Newtonian Navier–Stokes and heat-transfer equations. However, solving this non-linear system with high accuracy requires significant computational power. This work refines the system by introducing corrected coefficients and new treatments for boundary conditions near the tool. Then, model order reduction, including the Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM), is applied to efficiently solve the FSW system in a low-dimensional space. To enhance accuracy and effectiveness, two novel treatments …

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On The Existence, Uniqueness And Stability Of Solutions Of Sdes With State-Dependent Variable Exponent, Mustafa Avci Sep 2026

On The Existence, Uniqueness And Stability Of Solutions Of Sdes With State-Dependent Variable Exponent, Mustafa Avci

Journal of Stochastic Analysis

We study a time-inhomogeneous nonlinear SDE with drift and diffusion governed by state-dependent variable exponents. This framework generalizes models like the geometric Brownian motion (GBM) and the constant elasticity of variance (CEV), offering flexibility to capture complex dynamics while posing analytical challenges. Using a fixed-point approach, we prove existence and uniqueness, analyze higher-order moments, derive asymptotic estimates, and assess stability. Finally, we illustrate an application where Poisson’s equation admits a probabilistic representation via a timehomogeneous nonlinear SDE with state-dependent variable exponents.

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Companion Matrices Associated To Stochastic Matrices, Andreas Boukas, Philip Feinsilver Sep 2026

Companion Matrices Associated To Stochastic Matrices, Andreas Boukas, Philip Feinsilver

Journal of Stochastic Analysis

Starting with a stochastic matrix, we study the behavior of powers of an associated companion matrix, which has the same characteristic polynomial as the original matrix. In general the companion matrix will have negative entries while maintaining rowsums equal to 1. We will find the growth rate even if the Ces`aro limit of the sums of the companion matrix diverge. Surprisingly, in the irreducible aperiodic case the powers of the companion matrix will converge even though the norm of the matrix exceeds 1 and it has possibly negative entries.

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Z+-Valued Additive Processes In Law With Nonnegative Increments, Nadjib Bouzar Sep 2026

Z+-Valued Additive Processes In Law With Nonnegative Increments, Nadjib Bouzar

Journal of Stochastic Analysis

The goal of this article is to study in depth the subclass of Z+- valued additive processes in law with nonnegative increments. We establish key distributional properties of these processes and obtain some existence results under a variety of conditions. We show that they form a subclass of the family of inhomogeneous Markov chains with spatial homogeneity. We extend the notion of factoring introduced by Sato (2004, [9]) for Rd-valued additive processes in law to their Z+-valued counterparts with nonnegative increments. We give a sufficient condition for the existence of a factoring for these processes. Lastly, we obtain their representation …

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Motivating Second-Order Differential Equation Models Beyond The Spring–Mass System, Katherine E. Rutherford, John C. Borger Sep 2026

Motivating Second-Order Differential Equation Models Beyond The Spring–Mass System, Katherine E. Rutherford, John C. Borger

CODEE Journal

Students in introductory differential equations courses often learn to associate specific equation types with familiar physical systems. While this approach supports procedural fluency, it can inhibit transfer learning: students recognize familiar forms rather than construct models from first principles. This paper presents a modeling-first instructional approach designed to help students recognize the shared structure of second-order differential equations across diverse contexts. Students derive governing equations from fundamental physical laws for multiple systems, including an Inductor, Resistor, and Capacitor (LRC) electrical circuit, a simple pendulum, and viscous pipe flow. Through guided comparison, students identify common components such as inertia, damping, restoring …

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On Families Of Finsler Metrics, İsmai̇l Sağlam, Ken'ichi Ohshika, Athanase Papadopoulos Sep 2026

On Families Of Finsler Metrics, İsmai̇l Sağlam, Ken'ichi Ohshika, Athanase Papadopoulos

Turkish Journal of Mathematics

In this paper, we answer some natural questions concerning symmetrisation and more general combinations of Finsler metrics, with a view to applications to Funk and Hilbert geometries and metrics on Teichmüller spaces. The metrics on Teichmüller space that we consider are the Thurston metric and the earthquake metric, both introduced by Thurston. The first metric has been thoroughly studied over the last couple of decades, and the second over the last few years. The Funk metric and its symmetrisation, the Hilbert metric, are classical metrics that have been investigated in the contexts of hyperbolic geometry and geometric function theory and, …

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On The Monoid Of Partial Order-Preserving Transformations Of A Finite Chain Whose Domains And Ranges Are Intervals, Hayrullah Ayik, Vítor H. Fernandes, Emrah H. Korkmaz Sep 2026

On The Monoid Of Partial Order-Preserving Transformations Of A Finite Chain Whose Domains And Ranges Are Intervals, Hayrullah Ayik, Vítor H. Fernandes, Emrah H. Korkmaz

Turkish Journal of Mathematics

In this paper, we consider the monoid PIOn of all partial order-preserving transformations on a chain with n elements whose domains and ranges are intervals, along with its submonoid PIOn− of order-decreasing transformations. Our main aim is to give presentations for PIOn− and PIOn. Moreover, for both monoids, we describe regular elements and determine their ranks, cardinalities and the numbers of idempotents and nilpotents.

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Stochastic Control Of Inventory And Scheduling Decisions In An Open Network Of Repairables, Erhun Özkan Sep 2026

Stochastic Control Of Inventory And Scheduling Decisions In An Open Network Of Repairables, Erhun Özkan

Turkish Journal of Mathematics

We study maintenance operations for capital goods with repairable components. Because the downtime of a capital good is costly, the maintenance provider keeps an inventory of spare parts to quickly replace broken parts of the capital goods. After the replacement, the broken part is added to the repair facility’s repair queue. Upon a part breakdown, if there is no spare part in the inventory, then the maintenance provider has two options: (i) it can backorder the spare part demand, (ii) it can execute an emergency repair, which is done immediately and quickly, and is followed by a quick installation of …

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A Full-Scale Watertight Workflow Numerical Study For A Triangular Fin And Tube Heat Exchanger, Hamdi̇ Selçuk Çeli̇k, Bahadir Doğan, Lati̇fe Berri̇n Erbay Sep 2026

A Full-Scale Watertight Workflow Numerical Study For A Triangular Fin And Tube Heat Exchanger, Hamdi̇ Selçuk Çeli̇k, Bahadir Doğan, Lati̇fe Berri̇n Erbay

Turkish Journal of Mathematics

In this study, the thermo-hydraulic characteristics of an air-cooled triangular finned tube heat exchanger were analyzed numerically. The full-scale heat exchanger was modeled using Ansys Fluent watertight workflow, considering water as the primer fluid to precisely investigate the effects of geometrical factors. The effects of fin height, fin width, and fin spacing of the triangular fins on the performance of the heat exchanger were examined using k-ω turbulence model. A basic finned-tube heat exchanger model, which was manufactured as a monolithic structure without tube-fin contact resistance by milling from aluminum 5083 material, was tested in an air tunnel to verify …

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Characterizations Of Bi-Riordan Arrays, Nai̇m Tuğlu, Fatma Yeşi̇l Baran Sep 2026

Characterizations Of Bi-Riordan Arrays, Nai̇m Tuğlu, Fatma Yeşi̇l Baran

Turkish Journal of Mathematics

In this study, we introduce the concept of a bi-Riordan array. As part of this construction, we define new composition and power operations. We then establish an analogue of the well-known fundamental theorem of Riordan arrays (FTRA), which we call the fundamental theorem of bi-Riordan arrays. Next, we show that the product of two bi-Riordan matrices is again a bi-Riordan matrix. Using this product structure, we prove that the set of bi-Riordan matrices forms a monoid.

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​Compact And Am-Compact Orthogonally Additive Operators, Bahri̇ Turan, Bi̇rol Altin Sep 2026

​Compact And Am-Compact Orthogonally Additive Operators, Bahri̇ Turan, Bi̇rol Altin

Turkish Journal of Mathematics

We show that compactness of orthogonally additive operators between Banach lattices is not preserved under taking the modulus by providing a nonlinear analogue of Krengel’s example. In contrast, for operators acting from a Banach lattice into an AM-space, AM-compactness is stable under lattice operations. Moreover, the space of absolutely norm bounded AM-compactorthogonally additive operators from a Banach lattice into an AM-space is a Banach lattice, and on such AM-spaces with the weak Fatou property, norm boundedness coincides with absolute norm boundedness.

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Generalized Spectral Bound For Quasi-Twisted Codes, Buket Özkaya Sep 2026

Generalized Spectral Bound For Quasi-Twisted Codes, Buket Özkaya

Turkish Journal of Mathematics

Minimum distance bounds play a central role in the analysis of algebraic codes. For cyclic and constacyclic codes, several bounds based on their zero set have been developed. However, analogous results for quasi-twisted (QT) codes are comparatively limited. In this paper, we further investigate the spectral theory of QT codes and derive a general spectral bound on their minimum distance. Our bound unifies and generalizes previously known spectral bounds for quasi-cyclic (QC) and QT codes, and contains them as special cases. We present a new proof technique and show that the bound can be formulated with respect to an arbitrary …

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A Novel Iterative Algorithm For Approximating Common Fixed Points Of Generalized Α-Nonexpansive Multivalued Mappings In Kohlenbach Hyperbolic Spaces, Makbule Kaplan Özekes Sep 2026

A Novel Iterative Algorithm For Approximating Common Fixed Points Of Generalized Α-Nonexpansive Multivalued Mappings In Kohlenbach Hyperbolic Spaces, Makbule Kaplan Özekes

Turkish Journal of Mathematics

In this paper, we propose a new iterative scheme involving three multivalued mappings in Kohlenbach hyperbolic spaces. Strong and ∆-convergence theorems are established for approximating common fixed points of nonexpansive multivalued mappings under suitable conditions. A numerical example is also presented to illustrate the efficiency and faster convergence of the proposed method. The results obtained extend and unify several related contributions in the existing literature.

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On The Generalized Cesàro Sequence Spaces And Some Of Their Properties, Uğur Gönüllü, Faruk Polat, Martin Richard Weber Sep 2026

On The Generalized Cesàro Sequence Spaces And Some Of Their Properties, Uğur Gönüllü, Faruk Polat, Martin Richard Weber

Turkish Journal of Mathematics

Let Ct = (cnm)n,m∈ℕ denote the generalized Cesàro matrix defined by cnm = tn−m/n for m ≤ n and t ∈ [0, 1], and cnm = 0 otherwise. For each q ∈ [1, ∞), the associated generalized Cesàro sequence spaces cesqt are introduced. These spaces form Banach lattices under the coordinatewise order, equipped with a naturally defined order continuous norm. We prove that cesqt = cesq0 for all t ∈ [0, 1) and q ∈ [1, ∞), implying that the space …

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Exponential Stability For A Strongly Damped Wave Equation With Distributed Internal Delay, Manal Alotaibi, Nasser-Eddine Tatar, Waled Al-Khulaif Sep 2026

Exponential Stability For A Strongly Damped Wave Equation With Distributed Internal Delay, Manal Alotaibi, Nasser-Eddine Tatar, Waled Al-Khulaif

Turkish Journal of Mathematics

This paper investigates the exponential stability of a strongly damped wave equation subject to an internal distributed time delay. Two distinct analytical frameworks are developed: the first employs a modified energy method based on auxiliary functionals, while the second introduces a transformation that rewrites the delay term as the derivative of a convolution integral. Both approaches yield explicit decay conditions and establish exponential convergence of the energy under weaker assumptions on the damping coefficient and the delay kernel. Notably, the transformation method allows for a wider class of admissible delay weights than those permitted by classical techniques. Numerical simulations based …

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Clairaut Conformal Submersions From Ricci Solitons, Murat Polat Sep 2026

Clairaut Conformal Submersions From Ricci Solitons, Murat Polat

Turkish Journal of Mathematics

In this study, we investigate Clairaut conformal submersions in the context of total manifolds that support a Ricci soliton structure. We begin by deriving the scalar curvature and Ricci tensor expressions associated with these manifolds, and we establish criteria under which the fibres can be characterized as almost Ricci solitons or Einstein manifolds. Additionally, we identify the conditions required for the base manifold to admit Ricci soliton and Einstein structures. We also determine the necessary conditions for a vector field ζ to be conformal or Killing. Moreover, we demonstrate that when the potential vector field of the Ricci soliton is …

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A Delayed Siamr Prostate Cancer Model With Vertical Transmission And Treatment: Stability Analysis And Numerical Simulation, Hüseyi̇n Demir, İnci̇ Çi̇li̇ngi̇r Süngü, İbrahi̇m Keles Sep 2026

A Delayed Siamr Prostate Cancer Model With Vertical Transmission And Treatment: Stability Analysis And Numerical Simulation, Hüseyi̇n Demir, İnci̇ Çi̇li̇ngi̇r Süngü, İbrahi̇m Keles

Turkish Journal of Mathematics

​In this paper, we propose and analyse a delayed-compartmental mathematical model of prostate cancer dynamics that incorporates vertical transmission and therapeutic intervention. The population is stratified into five compartments: susceptible (S), infected/virally activated (I), asymptomatic infectious under treatment (A), malignant untreated (M), and recovered (R). A discrete time delay τ > 0 is introduced in the force-of-infection term to model the age-dependent onset of susceptibility in middle-aged adult males. Vertical transmission of viral etiology at a rate qΛ ensures that a fraction of newborns enter the infected compartment directly, rendering the disease persistent regardless of the basic reproduction number R₀. We …

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