Digital Commons Network^™

New View Of Some Propositions On Hesitant Fuzzy Set And Its Application In Selecting The Best Person In Any Job, Manar Mohamed Omran Dr., Arafa A. Nasef A.Dr, Reham Abd El-Aziz Abo Khadra Dr., Mahmoud Arafa Nasef Dr.

Journal of Engineering Research

An essential part of uncertainty is played by the hesitant fuzzy set (HFS). So, it can be utilized when making decisions. The suggested use of HFS to choose the best candidate for any post is thoroughly discussed and introduces new HFS concepts

Stochastic Analysis And White Noise Calculus Of Nonlinear Wave Equations With Application To Laser Generation And Propagation, Sivaguru S. Sritharan, Saba Mudaliar

Journal of Stochastic Analysis

No abstract provided.

The Boltzmann-Enskog Equation With Brownian Forcing, Aurora Wallace

LSU Doctoral Dissertations

Interacting particle systems (IPS) are used to rigorously derive partial differential equations modeling macroscopic behavior given by systems of stochastic differential equa- tions in physics, biology, and other sciences. These systems model the time evolution of n interacting particles with desired dynamics. In the n-system studied here, only two parti- cles may interact at a time (binary collisions). The particles are exchangeable; that is, the ordering of the particles does not play a role, and the interaction between the ith particle and the jth particle models an elastic collision. In this thesis, we use the method of inter- acting particle …

Fractional Calculus Approach For Learning Unknown Dynamic System, Haowei(Alice) Chen

USF Tampa Graduate Theses and Dissertations

The rapidly growing interest in data-driven modeling and fractional-order systems highlights a keychallenge in modern science and engineering: capturing long-memory effects and nonlinear behaviors in real-world dynamical processes. Conventional integer-order methods, while powerful, often overlook the history-dependent nature of many phenomena—ranging from viscoelastic materials to anomalous diffusion and hereditary feedback systems. This dissertation addresses that gap by blending fractional calculus with cutting-edge machine learning to create robust, memory-aware modeling and control frameworks.

Beginning with an extension of Dynamic Mode Decomposition (DMD) to fractional-order systems, we introduce Fractional Dynamic Mode Decomposition (F-DMD) as a data-driven tool that leverages Mittag- Leffler functions …

Critical Appraisal Of Multidrug Therapy In The Ambulatory Management Of Patients With Covid-19 And Hypoxemia Part I. Evidence Supporting The Strength Of Association, Eleftherios Gkioulekas, Peter A. Mccullough, Colleen Aldous

School of Mathematical & Statistical Sciences Faculty Publications

This critical appraisal is focused on three published case series of 119 COVID-19 patients with hypoxemia who were successfully treated in the United States, Zimbabwe, and Nigeria with similar off-label ivermectin-based multidrug treatments that may include ivermectin, nebulized nanosilver, doxycycline, zinc, Vitamins C, and Vitamin D, resulting in rapid recovery of oxygen levels. We used a simplified self-controlled case series method to investigate the association between treatment and the existence of hospitalization rate reduction. External controls of hospitalized patients were compared against the subgroup of patients with baseline room air SpO2 ≤ 90% to investigate the association between treatment and …

Critical Appraisal Of Multidrug Therapy In The Ambulatory Management Of Patients With Covid-19 And Hypoxemia. Part Ii: Causal Inference Using The Bradford Hill Criteria, Eleftherios Gkioulekas, Peter A. Mccullough, Colleen Aldous

School of Mathematical & Statistical Sciences Faculty Publications

We continue the critical appraisal of three published case series of 119 COVID-19 patients with hypoxemia, treated in the United States, Zimbabwe, and Nigeria with similar ivermectin-based multidrug treatments, to assess the available evidence supporting a causal relationship between treatment and reduction in hospitalizations and mortality. A narrative review was conducted to assess the Bradford Hill criteria for a causal association. We used a previously proposed refinement of the Bradford Hill criteria that reorganized them into three categories of direct, mechanistic, and parallel evidence. The efficacy of the two most aggressive ivermectin-based multidrug protocols is supported by the Bradford Hill …

Component Order Edge Connectivity, Vertex Degrees, And Integer Partitions, Michael R. Yatauro

Theory & Applications of Graphs

Given a finite, simple graph G, the k-component order connectivity (resp. edge connectivity) of G is the minimum number of vertices (resp. edges) whose removal results in a subgraph in which every component has an order of at most k − 1. In general, determining the k-component order edge connectivity of a graph is NP-hard. We identify conditions on the vertex degrees of G that can be used to imply a lower bound on the k-component order edge connectivity of G. We will discuss the process for generating such conditions for a lower bound of 1 or 2, and we …

Conditional Quantization For Uniform Distributions On Line Segments And Regular Polygons, Pigar Biteng, Mathieu Caguiat, Tsianna Dominguez, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If, in the quantization some of the elements in the support are preselected, then the quantization is called a conditional quantization. In this paper, we investigate the conditional quantization for the uniform distributions defined on the unit line segments and m-sided regular polygons, where 𝑚≥3, inscribed in a unit circle.

Dynamic Mean-Field Theory For Continuous Random Networks, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of generalized Gaussian random variables. The equation controls the time evolution of a macroscopic state interpreted as neural activity, which depends on position and time. Such a network corresponds to a statistical field theory (SFT) given by a momenta-generating functional. Discrete versions of the mentioned networks appeared in spin glasses and as models of artificial neural networks. Each of these discrete networks corresponds to a lattice SFT, where the …

An Operator Information Quantity Of A Semigroup And Associated Differential Equations, Kimiaki Saito, Ryo Inayoshi

Journal of Stochastic Analysis

No abstract provided.

Biquandle Power Brackets Of Oriented Links, Nesli̇han Gügümcü, Sam Nelson

Turkish Journal of Mathematics

In this paper, we introduce biquandle power brackets, an infinite family of invariants of oriented links containing the classical skein invariants and the quandle and biquandle 2-cocycle invariants as special cases. Biquandle power brackets are generalizations of biquandle brackets in which the values of Kauffman states also depend on the biquandle colors they admit. We provide example computations and discuss the relationship between these new invariants and the previous cases.

Order Structure Of Order-To-Topological Continuous Operator, Gül Si̇nem Keleş, Bahri̇ Turan, Bi̇rol Altin

Turkish Journal of Mathematics

Let J be a vector lattice, and W be a topological vector space. An operator K: J → W is called an order-to-topological continuous operator if u_α → 0 in J implies K(u_α) → 0 in W for each net (u_α) in J. In this study, we examine the order structure of the space of order-to-topological continuous operators in general and the order structure of order-to-norm continuous operators in particular. We study the relationships between order-to-topology continuous operators and other classes of operators, such as order weakly compact and order continuous operators. Moreover, we give …

Fractional Equivalent Of Fourth-Order Laguerre And Chebyshev Polynomials, Zahra Kavousi, Kazem Ghanbari

Turkish Journal of Mathematics

Orthogonal polynomials have very useful properties in the solution of mathematical and physical problems. In the last few years, there has been considerable interest in the properties of orthogonal polynomials satisfying differential equations (DE) of order greater than two, their connection to singular boundary value problems, their generalizations, and their classification as solutions of second-order DE. In this paper, we develop a fractional analog of the fourth-order Laguerre differential equation on the interval [0, ∞) and, in addition, we develop a fractional analog of the fourth-order Chebyshev differential equation on a symmetric interval [−α, α], where α is the order …

Continuous Dependence Of Thermoelasticity Problem, Müge Meyvaci, Şevket Gür

Turkish Journal of Mathematics

The current study considers the initial boundary value problem for the thermoelastic model. The model in which heat conduction is given by Green and Naghdi's theory is called Type II. It is increasingly accepted that studying the structural stability of the initial boundary value problem is crucial. This is because even minor changes in the equation or its coefficients can lead to significant variations in the solution of the problem. From this point of view, we analyze the structural stability of the solutions, specifically examining the continuous dependence of the solutions on all the coefficients of the thermoelastic system, using …

A Note On A Novel Type Of Alster Covering Property In Bitopological Setting, Necati̇ Can Açikgöz, Ceren Sultan Elmali

Turkish Journal of Mathematics

In this paper, we introduce a new type of Alster covering property in bitopological setting. We investigate its relations with other existing covering properties. By giving counterexamples, we indicate that our new property is different than other mentioned properties. We also construct some conditions for equivalences of those properties with the corresponding property. We also consider the preservation of this new form of bitopological Alster covering property. We investigate the productivity of bitopological nearly Lindelöfness and bitopological nearly Mengerness.

Improving Upper Bounds Of Berezin Number Inequalities Using Convex Function, Sana Khan, Mehmet Gürdal, Muhammad Saeed Akram

Turkish Journal of Mathematics

In this research article, new upper bounds are established for the Berezin number of bounded linear operators within the context of functional Hilbert space using the convex function. These bounds are achieved by exploiting an extension of Furuta's inequality and an extension of Kato's inequality. These Berezin number bounds are refinements of already existing bounds found in the literature.

Quantization Dimensions For Inhomogeneous Bi-Lipschitz Iterated Function Systems, Amit Priyadarshi, Mrinal Kanti Roychowdhury, Manuj Verma

School of Mathematical & Statistical Sciences Faculty Publications

Let ν be a Borel probability measure on a d-dimensional Euclidean space R d , d ≥ 1 , with a compact support, and let ( p 0 , p 1 , p 2 , … , p N ) be a probability vector with p j > 0 for 0 ≤ j ≤ N . Let { S j : 1 ≤ j ≤ N } be a set of contractive mappings on R d . Then, a Borel probability measure μ on R d such that μ = ∑ N j = 1 p j μ ∘ S − …

The Product Formula Of Multiple Stochastic Integrals With Respect To The Poisson Space Noise, Yuh-Jia Lee, Hsin-Hung Shih

Journal of Stochastic Analysis

No abstract provided.

American Option Pricing Using Generalised Stochastic Hybrid Systems, Evelyn Buckwar, Sascha Desmettre, Agnes Mallinger, Amira Meddah

Journal of Stochastic Analysis

No abstract provided.

About Fixed Points Of Quantum Channels, Raffaella Carbone

Journal of Stochastic Analysis

No abstract provided.

Stochastic Bundles, New Classes Of Gaussian Processes And White Noise-Space Analysis Indexed By Measures, Daniel Alpay, Palle Jorgensen

Mathematics, Physics, and Computer Science Faculty Articles and Research

Starting from a fixed measure space (X,F,μ), with μ a positive sigma-finite measure defined on the sigma-algebra F, we continue here our study of a generalization W(μ) of Brownian motion, and introduce a corresponding white-noise process. In detail, the generalized Brownian motion is a centered Gaussian process W^(μ), indexed by the elements A in F of finite μ measure, and with covariance function μ(A ∩ B). The purpose of our present paper is to make precise and study the corresponding whitenoise process, i.e., a point-wise process which is indexed by X, and which arises …

Subfitness In Distributive (Semi)Lattices, G. Bezhanishvili, J. Madden, M. A. Moshier, M. Tressl, Joanne Walters-Wayland

Mathematics, Physics, and Computer Science Faculty Articles and Research

We investigate whether the set of subfit elements of a distributive semilattice is an ideal. This question was raised by the second author at the BLAST conference in 2022. We show that in general it has a negative solution, however if the semilattice is a lattice, then the solution is positive. This is somewhat unexpected since, as we show, a semilattice is subfit if and only if so is its distributive lattice envelope.

Induced-Minor-Closed Classes Of Matroids, James Dylan Douthitt

LSU Doctoral Dissertations

A graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeated clique-sums. Generalizing this, we consider the class of simple GF(q)-representable matroids that can be built from projective geometries over GF(q) by repeated generalized parallel connections across projective geometries. We show that this class of matroids is closed under induced minors and characterize the class by its forbidden induced minors, noting that the case when q=2 is distinctive. Additionally, we show that the class of GF(2)-chordal matroids coincides …

The Intricacies Of Pairwise Modular Multiplicative Inverse In Lucas Numbers, Charles Liu

Rose-Hulman Undergraduate Mathematics Journal

Let (p,q) be a pair of relatively prime integers greater than 1. The pairwise modular multiplicative inverse (PMMI) of (p,q) is defined as the unique pair of positive integers (p′, q′) such that p p′ ≡ 1 (mod q), p′ < q, qq′ ≡ 1 (mod p), q′ < p. In this paper, we determine all pairs of Lucas numbers such that their PMMIs are pairs of Lucas numbers.

A Student Guide To Using Ai To Enhance Algebraic Understanding, Karan Puri

Open Educational Resources

This is a step-by-step guide that students can follow to use AI tools to check their understanding of concepts that have been tested in the introductory/college algebra classroom.

Time-Dependent Shear Flows And Their Applications In Parabolic–Parabolic Patlak–Keller–Segel Systems*, Siming He

Faculty Publications

In this study, we investigate the behavior of three-dimensional parabolic–parabolic Patlak–Keller–Segel systems in the presence of ambient shear flows. Our findings demonstrate that when the total mass of the cell density is below a specific threshold, the solution remains globally regular as long as the flow is sufficiently strong. The primary difficulty in our analysis stems from the fast creation of chemical gradients due to strong shear advection.

Counting Rotational Sets For Laminations Of The Unit Disk From First Principles, Michael J. Moorman, Gabriel B. Quijano, Matthew C. Williams Jr.

Rose-Hulman Undergraduate Mathematics Journal

By studying laminations of the unit disk, we can gain insight into the structure of Julia sets of polynomials and their dynamics in the complex plane. The polynomials of a given degree, d, have a parameter space. The hyperbolic components of such parameter spaces are in correspondence to rotational polygons, or classes of "rotational sets'', which we study in this paper. By studying the count of such rotational sets, and therefore the underlying structure of these rotational sets and polygons, we can gain insight into the interrelationship among hyperbolic components of the parameter space of these polynomials.

These rotational sets …

Finite Posets As Prime Spectra Of Commutative Noetherian Rings, David T. Alkass

Rose-Hulman Undergraduate Mathematics Journal

We study finite partially ordered sets of prime ideals as found in commutative Noetherian rings. In doing so, we establish that these posets have a bipartite structure and devise a construction for finding ring spectra that are order-isomorphic to many such posets. Specifically, we prove that any finite complete bipartite graph is order-isomorphic to the spectrum of a ring of essentially finite type over the field of rational numbers. Furthermore, we prove that prime spectra of such rings can also depict any finite path or even cycle.

Proportion Of P-Adic Polynomials Which Are Irreducible, Isaac Rajagopal

Rose-Hulman Undergraduate Mathematics Journal

We attempt to quantify the exact proportion of p-adic polynomials of degree n which are irreducible. We find an exact answer to this when n is prime and p != n, and also when n = 4 and p != 2. Our answers are rational functions in p. This relates to previous work done to find exact proportions of p-adic polynomials of degree n which have k roots.

Heart Disease Prediction Using Ensemble Tree Algorithms: A Supervised Learning Perspective, Enoch Sakyi-Yeboah, Edmund F. Agyemang, Vincent Agbenyeavu, Akua Osei- Nkwantabisa, Priscilla Kissi-Appiah, Lateef Moshood, Lawrence Agbota, Ezekiel N.N. Nortey

School of Mathematical & Statistical Sciences Faculty Publications

Heart disease stands as a leading cause of morbidity and mortality globally, presenting a significant public health challenge. Therefore, early prediction and detection are critical, leading to timely and appropriate interventions at early stages. Four ensemble tree-based algorithms were used in this study: adaptive boosting, extreme gradient boosting, random forest, and extremely randomized trees, investigating their ability to predict heart disease. Data related to heart disease clinical features was obtained from the open Kaggle Machine Learning Dataset repository. Adaptive Boosting stands out as the highest performer, achieving an average testing accuracy of 93.70%, precision of 93.71%, recall of 93.70%, and …