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Articles 31 - 60 of 27186
Full-Text Articles in Entire DC Network
Euler's Explorations Of Extremal Ellipses, Jonathan David Evans
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.
Arithmetic Theorems, Demonstrated By A New Method: An English Translation Of E271, Brendon Lasell
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 …
On Double Integral Formulas: An English Translation Of E391, Thomas W. Polaski
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. …
Eulerian Problem Solving, Christopher Goff, Erik Tou
Eulerian Problem Solving, Christopher Goff, Erik Tou
Euleriana
An introduction to the contents in Volume 6 (Issue 2) of Euleriana.
Taut And Dupin Submanifolds (Updated Version), Thomas E. Cecil
Taut And Dupin Submanifolds (Updated Version), Thomas E. Cecil
Mathematics and Computer Science Department Faculty Scholarship
This is an updated version of the paper [29] by the author which originally appeared in 1997. The original paper was a survey of the closely related fields of taut and Dupin submanifolds of Euclidean space, and this updated version includes many results in the field that have appeared since the publication of the original version. The emphasis is on stating results in their proper context and noting areas for future research, and relatively few proofs are given. The important class of isoparametric hypersurfaces is surveyed in detail, as is the relationship between the two concepts of taut and Dupin. …
Fast Computation And Model Order Reduction Of The Friction Stir Welding Process With Pod-Deim, Joshua Kay, Zilong Song
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 …
On The Existence, Uniqueness And Stability Of Solutions Of Sdes With State-Dependent Variable Exponent, Mustafa Avci
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.
Companion Matrices Associated To Stochastic Matrices, Andreas Boukas, Philip Feinsilver
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.
Z+-Valued Additive Processes In Law With Nonnegative Increments, Nadjib Bouzar
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 …
Motivating Second-Order Differential Equation Models Beyond The Spring–Mass System, Katherine E. Rutherford, John C. Borger
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 …
Generalized Spectral Bound For Quasi-Twisted Codes, Buket Özkaya
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 …
A Novel Iterative Algorithm For Approximating Common Fixed Points Of Generalized Α-Nonexpansive Multivalued Mappings In Kohlenbach Hyperbolic Spaces, Makbule Kaplan Özekes
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.
On Families Of Finsler Metrics, İsmai̇l Sağlam, Ken'ichi Ohshika, Athanase Papadopoulos
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, …
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
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.
On The Generalized Cesàro Sequence Spaces And Some Of Their Properties, Uğur Gönüllü, Faruk Polat, Martin Richard Weber
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 …
A Note On The Periodic Orbits Of Wolbachia Spread Dynamics In Mosquito Populations In Periodic Environments, Jose S. Cánovas
A Note On The Periodic Orbits Of Wolbachia Spread Dynamics In Mosquito Populations In Periodic Environments, Jose S. Cánovas
Turkish Journal of Mathematics
We consider the periodic model introduced by B. Zheng and J. Yu, and disprove the conjectures on the number of periodic orbits the model can have. We rebuild the conjecture to prove that for periodic sequences of maps of any period, the number of nonzero periodic trajectories is bounded by two.
Characterizations Of Bi-Riordan Arrays, Nai̇m Tuğlu, Fatma Yeşi̇l Baran
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.
Exponential Stability For A Strongly Damped Wave Equation With Distributed Internal Delay, Manal Alotaibi, Nasser-Eddine Tatar, Waled Al-Khulaif
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 …
Clairaut Conformal Submersions From Ricci Solitons, Murat Polat
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 …
A Delayed Siamr Prostate Cancer Model With Vertical Transmission And Treatment: Stability Analysis And Numerical Simulation, Hüseyi̇n Demir, İnci̇ Çi̇li̇ngi̇r Süngü, İbrahi̇m Keles
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 …
Compact And Am-Compact Orthogonally Additive Operators, Bahri̇ Turan, Bi̇rol Altin
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.
Hyers-Ulam And Hyers-Ulam Rassias Stability Of Caputo Fractional Hahn Difference Equations, Karima Mohamed Oraby, Alaa E. Hamza, Afrah Al-Bossly
Hyers-Ulam And Hyers-Ulam Rassias Stability Of Caputo Fractional Hahn Difference Equations, Karima Mohamed Oraby, Alaa E. Hamza, Afrah Al-Bossly
Turkish Journal of Mathematics
In this paper, we investigate Hyers–Ulam and Hyers–Ulam–Rassias stability for fractional linear Hahn difference equations of Caputo Type. To the best of our knowledge, this is the first work concerning Hyers–Ulam type stability in the framework of Caputo fractional Hahn difference equations, thereby filling a significant gap in the literature on fractional stability theory. Our approach is based on establishing an equivalence between the fractional Hahn difference initial value problem and a corresponding fractional integral equation, via the Caputo–Hahn inversion formula. These results lay a strong groundwork for analyzing the stability of Hahn fractional systems, which could be useful in …
Model-Theoretic Arguments In Philosophy, Peter Susanszky
Model-Theoretic Arguments In Philosophy, Peter Susanszky
Dissertations, Theses, and Capstone Projects
This dissertation is on model-theoretic arguments in philosophy, especially those of Quine, Davidson, and Putnam. In the first part, to ground the debate, I give a rigorous introduction to the salient parts of first-order model theory. I start the second part by giving an introduction to Quine's philosophy, and how the model-theoretic arguments fit into it. After considering how Donald Davidson adopted the Quinean lesson, I move on to Putnam's model-theoretic arguments. Putnam's spin on these model-theoretic considerations significantly departs from Quine and Davidson, while retaining many of the core ideas. Most importantly, I argue that the target of Putnam's …
Self-Organized Criticality In Biased Activated Random Walk, Joshua Meisel
Self-Organized Criticality In Biased Activated Random Walk, Joshua Meisel
Dissertations, Theses, and Capstone Projects
We demonstrate many of the conjectured universality and self-organized criticality (SOC) properties of the interacting particle system Activated Random Walk (ARW) in the setting of one-dimensional biased walks, as formulated for instance in Levine and Silvestri’s 2024 survey. Namely, there exists the same limiting critical state for two finite ARW models, as well as for the infinite model as the density approaches its critical value from below. Many of the desired properties hold, including heavy-tailed avalanches, but spatial correlations decay exponentially fast, a deviation from the SOC paradigm. Nonetheless, the obtained decay rate vanishes with the bias. Since the critical …
Braids On The Stranded Cellular Automata Model, Alexa Renner
Braids On The Stranded Cellular Automata Model, Alexa Renner
Mathematical Sciences Technical Reports (MSTR)
The Stranded Cellular Automata (SCA) model is a grid of cells such that each cell can contain 0, 1, or 2 strands, together with two cellular automata that control when and how strands turn and cross. It was developed to study patterns occurring in fiber arts. We define a notion of what it means for a braid, in the sense of an element of a braid group, to be represented by an SCA pattern, and provide several algorithms to determine when a braid has an SCA representation with certain additional properties.
Stochastic Control Of Inventory And Scheduling Decisions In An Open Network Of Repairables, Erhun Özkan
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 …
A Full-Scale Watertight Workflow Numerical Study For A Triangular Fin And Tube Heat Exchanger, Hamdi̇ Selçuk Çeli̇k, Bahadir Doğan, Lati̇fe Berri̇n Erbay
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 …
Generalizations Of The Dirichlet Problem For Bianalytic Functions, William L. Blair
Generalizations Of The Dirichlet Problem For Bianalytic Functions, William L. Blair
Math Faculty Publications and Presentations
We prove the Dirichlet problem for second-order iterated Vekua equations, a natural generalization of the Bitsadze equation, is well-posed when the boundary condition is defined as a product of an exponential function and a polynomial on a non-degenerate conic that is not a circumference. Also, we extend this result, as well as other related results for the Dirichlet problem for polyanalytic and generalized analytic functions from the literature, to their analogues for bicomplex differential equations.
Pseudo-Traveling Waves And Bumps In Quantum And Classical Hierarchical Cellular Neural Networks, Wilson A. Zuniga-Galindo, B. A. Zambrano-Luna, Chayapuntika Indoung
Pseudo-Traveling Waves And Bumps In Quantum And Classical Hierarchical Cellular Neural Networks, Wilson A. Zuniga-Galindo, B. A. Zambrano-Luna, Chayapuntika Indoung
School of Mathematical & Statistical Sciences Faculty Publications
We study the existence of pseudo-traveling waves and bump solutions for two classes of hierarchical cellular neural networks (CNNs) defined over the ring of p-adic integers Zp. The first type is a p-adic CNN described by a reaction-diffusion equation, while the second type is its quantum analog obtained via Wick rotation. The p-adic CNNs are hierarchical versions of the classical Chua-Yang CNNs; these networks have a tree-like hierarchical architecture with infinitely many cells and hidden layers. The states are governed by integro-differential equations on Zp. The p-adic traveling waves behave fundamentally differently from their Archimedean counterparts. A traveling wave restricted …
Fast-Track Ode: A Student-Centered, Game-Based Summer Differential Equations Course, Chamila D. Malagoda Gamage
Fast-Track Ode: A Student-Centered, Game-Based Summer Differential Equations Course, Chamila D. Malagoda Gamage
CODEE Journal
This article describes a student-centered and game-based redesign of an Elementary Differential Equations course taught during a six-week summer session. In this compressed setting, students had to move through the standard course content quickly while still developing procedural fluency, conceptual understanding, and confidence with applications. To support these goals, the course used real-time feedback tools, collaborative problem solving, applications connected to students' fields, and mathematical games. The paper describes the course context, major activities, implementation details, and student feedback. Student responses suggest that the activities were well received and helped students stay engaged, participate regularly, prepare for exams, and see …