A Preliminary Fuzzy Inference System For Predicting Atmospheric Ozone In An Intermountain Basin, 2024 Utah State University

#### A Preliminary Fuzzy Inference System For Predicting Atmospheric Ozone In An Intermountain Basin, John R. Lawson, Seth N. Lyman

*Mathematics and Statistics Faculty Publications*

High concentrations of ozone in the Uinta Basin, Utah, can occur after sufficient snowfall and a strong atmospheric anticyclone creates a persistent cold pool that traps emissions from oil and gas operations, where sustained photolysis of the precursors builds ozone to unhealthy concentrations. The basin's winter-ozone system is well understood by domain experts and supported by archives of atmospheric observations. Rules of the system can be formulated in natural language ("sufficient snowfall and high pressure leads to high ozone"), lending itself to analysis with a fuzzy-logic inference system. This method encodes human expertise as machine intelligence in a more prescribed …

Fractional Derivative-Based Analysis Of The Heat Transfer Properties Of Fluid Flow Over A Contracting Permeable Infinite-Length Cylinder, 2024 United Arab Emirates University

#### Fractional Derivative-Based Analysis Of The Heat Transfer Properties Of Fluid Flow Over A Contracting Permeable Infinite-Length Cylinder, Anas Saeb Alhasan

*Thesis/ Dissertation Defenses*

Understanding the complex interplay between the contracting behavior of the cylinder and the fluid flow dynamics has implications for the design of porous structures for heat exchange and filtration systems. In this study, we investigate the dynamics and thermal behavior of fluid flow past a contracting permeable infinite cylinder. First, we developed a mathematical model based on the Navier-Stokes equations to describe the fluid dynamics around the contracting permeable infinite cylinder. A new simple well-behaved definition of fractional derivative called conformable fractional derivative introduced by authors Khalil et al. is employed to generalize the PDE’s of momentum and energy. The …

Hierarchical Neural Networks, P-Adic Pdes, And Applications To Image Processing, 2024 The University of Texas Rio Grande Valley

#### Hierarchical Neural Networks, P-Adic Pdes, And Applications To Image Processing, Wilson A. Zuniga-Galindo, B. A. Zambrano-Luna, Baboucarr Dibba

*School of Mathematical and Statistical Sciences Faculty Publications and Presentations*

The first goal of this article is to introduce a new type of *p*-adic reaction–diffusion cellular neural network with delay. We study the stability of these networks and provide numerical simulations of their responses. The second goal is to provide a quick review of the state of the art of *p*-adic cellular neural networks and their applications to image processing.

Q-Rational Functions And Interpolation With Complete Nevanlinna–Pick Kernels, 2024 Chapman University

#### Q-Rational Functions And Interpolation With Complete Nevanlinna–Pick Kernels, Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Baruch Schneider

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

In this paper we introduce the concept of matrix-valued *q*-rational functions. In comparison to the classical case, we give different characterizations with principal emphasis on realizations and discuss algebraic manipulations. We also study the concept of Schur multipliers and complete Nevanlinna–Pick kernels in the context of *q*-deformed reproducing kernel Hilbert spaces and provide first applications in terms of an interpolation problem using Schur multipliers and complete Nevanlinna–Pick kernels.

Euler Archive Spotlight: Ed Sandifer's Influence, 2024 University of Washington – Tacoma

#### Euler Archive Spotlight: Ed Sandifer's Influence, Erik Tou

*Euleriana*

The Euler Archive owes its existence to the work and enthusiasm of C. Edward Sandifer. In this issue, we give a history of Ed's work and influence on the creation and growth of the Euler Archive.

Translating Scientific Latin Texts With Artificial Intelligence: The Works Of Euler And Contemporaries, 2024 University of São Paulo

#### Translating Scientific Latin Texts With Artificial Intelligence: The Works Of Euler And Contemporaries, Sylvio R. Bistafa

*Euleriana*

The major hindrance in the study of earlier scientific literature is the availability of Latin translations into modern languages. This is particularly true for the works of Euler who authored about 850 manuscripts and wrote a thousand letters and received back almost two thousand more. The translation of many of these manuscripts, books and letters have been published in various sources over the last two centuries, but many more have not yet appeared. Fortunately, nowadays, artificial intelligence (AI) translation can be used to circumvent the challenges of translating such substantial number of texts. To validate this tool, benchmark tests have …

On The Vibration Of Strings: An English Translation Of Leonhard Euler’S `Sur La Vibration Des Cordes' (E140), 2024 Adelphi University

#### On The Vibration Of Strings: An English Translation Of Leonhard Euler’S `Sur La Vibration Des Cordes' (E140), Reilly R. Fortune

*Euleriana*

We present an English translation of E140 - 'Sur la Vibration des cordes.'

About The Cases In Which The Formula X^4+Mxxyy+Y^4 Can Be Reduced To A Square, 2024 Oak Ridge National Laboratory

#### About The Cases In Which The Formula X^4+Mxxyy+Y^4 Can Be Reduced To A Square, Georg Ehlers

*Euleriana*

Euler continues a previous study on the title Quartic (E696) with a new approach. His starting point here is the observation that, when the title Quartic is solved for *m*, the resulting fraction becomes an integer when z=ax^2y^2-(x^2±y^2). He provides many quadratic forms for m that allow special solutions, and tables for |*m*|≤200. Even though the tables are known today to be incomplete, they allow an insight into the enormous amount of work that was needed for their compilation.

The interest in the title Quartic predates Euler, and the fact that he resumed the study indicates a …

Ed Sandifer: A Running Mathematician And Mathematical Runner, 2024 Babson College

#### Ed Sandifer: A Running Mathematician And Mathematical Runner, Rick Cleary

*Euleriana*

Historian of mathematics C. Edward Sandifer was an outstanding marathon runner as well as a first rate mathematician. This note is a review of Prof. Sandifer's athletic successes, and a look at the attributes that he brought to both his professional and running careers.

How Ed Did It - A Memorial Conference To Honor Ed Sandifer, 2024 Ramapo College of New Jersey

#### How Ed Did It - A Memorial Conference To Honor Ed Sandifer, Lawrence D'Antonio

*Euleriana*

I look back at the virtual conference from February 2023 that was organized to honor the memory of the historian of mathematics Ed Sandifer, who had died in August 2022. The program of the conference is given at the end of the article.

Looking Back And Looking Forward, 2024 University of the Pacific

#### Looking Back And Looking Forward, Christopher Goff, Erik Tou

*Euleriana*

An introduction to the contents in Issue 2, Volume 4 of *Euleriana*.

The Heat Kernel On A Finite Graph In Different Time-Scales, 2024 TÜBİTAK

#### The Heat Kernel On A Finite Graph In Different Time-Scales, Yang Chen, Jay Jorgenson, Luis Lopez, Lejla Smajlovic

*Turkish Journal of Mathematics*

Let G be a finite, weighted graph, and let [[EQUATION]] be a Time-scale with a fixed point [[EQUATION]] such that sup[[EQUATION]]. In this paper we construct the heat kernel on G in Time-scale [[EQUATION]] in terms of a certain convolution series involving he heat operator acting on a parametrix, which is a fairly general function depending on the vertex set of G and the time variable [[EQUATION]]. We develop some applications by choosing different parametrices and various Time-scales. The results we obtain here do extend, in part, aspects of the recent articles in that the Time-scale considered in this paper …

Φ−Pluriharmonicity And Φ−Invariance Of Pointwise Bislant Riemanniansubmersions, 2024 TÜBİTAK

#### Φ−Pluriharmonicity And Φ−Invariance Of Pointwise Bislant Riemanniansubmersions, Grayson Light, Cem Sayar, Mehmet Aki̇f Akyol

*Turkish Journal of Mathematics*

In this research, we investigate the intriguing realm of pointwise bislant Riemannian submersions, a generalizationof many previous submersions, such as antiinvariant, slant, semislant, pointwise slant, pointwise semislant,and bislant submersions, within the framework of almost product manifolds. After giving an original example, wedelve into the submersion’s integrability conditions and geodesics. We explore the concept of φ−pluriharmonicity andφ−invariance within this context. The study sheds light on the profound interplay between pointwise bislant submersions’fibers and their being either geodesic or mixed geodesic, offering valuable insights into these intriguing mappings’geometric properties.

Ideals In Semigroups Of Partial Transformations With Invariant Set, 2024 TÜBİTAK

#### Ideals In Semigroups Of Partial Transformations With Invariant Set, Jitsupa Srisawat, Yanisa Chaiya

*Turkish Journal of Mathematics*

This paper explores the ideals and their structural properties in two generalizations of the partial transformationsemigroup. Furthermore, principal, maximal, and minimal ideals within these semigroups are elucidated.

Transmission Eigenvalues Problem Of A Schrödinger Equation, 2024 TÜBİTAK

#### Transmission Eigenvalues Problem Of A Schrödinger Equation, Emel Yildirim, Elgiz Bairamov

*Turkish Journal of Mathematics*

In this paper, transmission eigenvalues of a Schrödinger equation have been studied by constructing a new inner product and using Weyl theory. Necessary conditions for these eigenvalues to be negative, real and finite have been examined. This method has provided a new framework related to transmission eigenvalue problems and investigation of their properties. The conclusions has been verified for special case of the problem.

#### Comprehensive Computational Study On Transient Heat Transfer In Functionally Graded Longitudinal Fins Under Time-Varying Laser Heating, Hüseyi̇n Demi̇r, İnci̇ Çi̇li̇ngi̇r Süngü, İbrahi̇m Keleş

*Turkish Journal of Mathematics*

The present study assumes that the material properties of the fin vary by a force rule in the axial direction, with the exception of the thermal relaxation coefficient, which is assumed to be constant. The temperature distribution in the longitudinal fin with homogeneous cross-section exposed to the laser heat source is numerically investigated. This is because these constraints lead to a linear differential equation with partial solutions that can't be analytically resolved using conventional methods, except for a few elementary order functions. Consequently, a linear or non-linear system of equations as a function of time is obtained by transforming a …

A Short Note On Generalized Robertson Walker Spacetimes, 2024 TÜBİTAK

#### A Short Note On Generalized Robertson Walker Spacetimes, Uday Chand De, Aydin Gezer

*Turkish Journal of Mathematics*

In this article, generalized Robertson Walker spacetimes are investigated in light of perfect fluid spacetimes. First, we establish that a perfect fluid spacetime with non-vanishing vorticity whose associated scalars are constant along the velocity vector field becomes a generalized Robertson Walker spacetime. Among others, it is also shown that a Ricci parallel perfect fluid spacetime is either a generalized Robertson Walker spacetime or a static spacetime. Finally, we acquire that in a conformally semi-symmetric generalized Robertson Walker spacetime of dimension $4$, the scalar curvature vanishes and the spacetime is locally isometric to the Minkowski spacetime, provided the electric part of …

Individual Stability Of Representations Of Abelian Semigroups, 2024 TÜBİTAK

#### Individual Stability Of Representations Of Abelian Semigroups, Heybetkulu Mustafayev

*Turkish Journal of Mathematics*

Let S be a suitable subsemigroup of a locally compact abelian group and let T={T(s)}s(-S be a bounded and strongly continuous trepresentation of S on a Banach space X. In this note, we study the spectral conditions on T and the ergodic conditios on x in X which will imply that T(s)x-->0 strongly as s--> infinity through S.

A Non-Newtonian Conics In Multiplicative Analytic Geometry, 2024 TÜBİTAK

#### A Non-Newtonian Conics In Multiplicative Analytic Geometry, Aykut Has, Beyhan Yilmaz

*Turkish Journal of Mathematics*

In this study, conics (circle, ellipse, hyperbola) are characterized by taking into account basic multiplicationoperations in multiplicative space. For this purpose, firstly multiplicative axes and regions are introduced. Additionally,the multiplicative cone definition is given and visualized on the figure. General definitions and theorems of non-Newtonianconics are given. Additionally, examples were given and drawings were made to make the resulting characterizations andtheorems more memorable.

On The Connection Between Σϵ(A1 ⊗ A2) And Σϵ(A1), Σϵ(A2) For Certain Specialoperators, 2024 TÜBİTAK

#### On The Connection Between Σϵ(A1 ⊗ A2) And Σϵ(A1), Σϵ(A2) For Certain Specialoperators, Fati̇h Yilmaz

*Turkish Journal of Mathematics*

In this paper, the connection between the ϵ -pseudospectrum of the tensor product operator A1 ⊗ A2 andthe ϵ -pseudospectrums of operators A1 and A2 has been investigated and some results are given about this connectionunder certain conditions.