An Ode-Based Analytical Approach To Rayleigh Flow Of Kelvin–Voigt Fluid,
2025
Texas A&M International University
An Ode-Based Analytical Approach To Rayleigh Flow Of Kelvin–Voigt Fluid, Kamille Garcia, Mahanthesh Basavarajappa
CODEE Journal
We present some results from a project carried out in the Under- graduate Research in Mathematics (MATH 4380) course at TAMIU. The main goal of this study is to demonstrate that analytical solutions for a system of partial differential equations (PDEs) can be obtained using methods typically taught in an undergraduate ordinary differential equations (ODE) course, such as power series, undetermined coefficients, and Laplace transforms. In this study, we provide semi-analytical solutions for Rayleigh flow type problem utilizing the Kelvin-Voigt fluid model, which describes the behavior of vis- coelastic materials by incorporating both elastic and viscous properties. Heat transfer analysis …
A Bdg Inequality For Stochastic Volterra Integrals,
2025
Universite Denis Diderot (Paris VII)
A Bdg Inequality For Stochastic Volterra Integrals, Alexandre Pannier
Journal of Stochastic Analysis
We establish Burkholder-Davis-Gundy-type inequalities for stochastic Volterra integrals with a completely monotone convolution kernel, which may exhibit singular behaviour at the origin. When the supremum is taken over a finite interval, the upper bound depends linearly on the Lγ-norm of the kernel, for any γ > 2. We demonstrate the utility of this inequality in quantifying the pathwise distance between two stochastic Volterra equations with distinct kernels, with a particular emphasis on the multifactor Markovian approximation. For kernels that decay sufficiently fast, we derive an alternative inequality valid over an infinite time interval, providing uniformin- time bounds for mean-reverting stochastic Volterra …
Follow Me Into Math: Near-Peer Influencers Take The Stage,
2025
The University of Texas Rio Grande Valley
Follow Me Into Math: Near-Peer Influencers Take The Stage, Aaron T. Wilson, Sergey Grigorian, Mayra Ortiz Galarza, Xiaohui Wang
School of Mathematical & Statistical Sciences Faculty Publications
Young people like to be entertained, and to entertain others. What if students were to invest enough of their time and effort into learning topics from our mathematics courses to become experts in the eyes of their peers? In this study we positioned college students and high school students as mathematical performers on the stage in front of their nearpeers, for whom they became math influencers, developing and presenting MathShows. The paper shows readers how we positioned students on the stage, using a 7-step MathShow Design Process informed by a Neer-peer Mathematical Mentoring framework. Of import for educators, researchers and …
Rogue Wave Patterns Associated With Adler–Moser Polynomials In The Nonlocal Nonlinear Schrödinger Equation,
2025
The University of Texas Rio Grande Valley
Rogue Wave Patterns Associated With Adler–Moser Polynomials In The Nonlocal Nonlinear Schrödinger Equation, Tingyou Wang, Zhenyun Qin, Gui Mu, Fuzhuang Zheng, Zhijun Qiao
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, novel rogue wave patterns in the nonlocal nonlinear Schrödinger equation (NLS) are investigated by means of asymptotic analysis, including heart-pentagon, oval-triangle, and fan-triangle. It is demonstrated that when multiple free parameters get considerably large, rogue wave patterns can approximately be predicted by the root structures of Adler–Moser polynomials. These polynomials, which extend the Yablonskii–Vorob’ev polynomial hierarchy, exhibit richer geometric shapes in their root distributions. The (x,t)-plane is partitioned into three regions and through a combination of asymptotic results in different regions, unreported rogue wave patterns can be probed. Predicted solutions are compared with true rogue waves in …
Growth Mindset In The Mathematics Classroom: Studying The Effects Of A Growth Mindset Intervention On High School Students In A Geometry Classroom,
2025
Bemidji State University
Growth Mindset In The Mathematics Classroom: Studying The Effects Of A Growth Mindset Intervention On High School Students In A Geometry Classroom, Katelyn Strauss
Mathematics Graduate Theses
Having a growth mindset is crucial to being successful in a mathematics classroom. However, many students believe themselves to be either “mathematics people” or “not mathematics people”. When students believe they are not a mathematics person, they are far less likely to engage in material where they face struggles, and thus they miss out on valuable learning. A review of the literature has show that students have been able to shift their mindset from fixed to growth through a series of interventions. I used a unit in Geometry to see how a growth mindset intervention would affect the mindset of …
(Si15-022) Five Efficient Cryptography Authentication Schemes With Functional Relation On General Spaces,
2025
Kalasalingam Academy of Research and Education
(Si15-022) Five Efficient Cryptography Authentication Schemes With Functional Relation On General Spaces, L. Sreenivasulu Reddy, S. Lakshmisri
Applications and Applied Mathematics: An International Journal (AAM)
This work addresses the growing demand for diversification in cryptographic schemes to secure communication. This work proposes a novel suite of algorithms, including two block ciphers (TPBlock and TAP-Block), two stream ciphers (TP-Stream and TAP-Stream), and a zero-knowledge proof scheme (F-zero knowledge proof). All schemes leverage functional relations defined over the real number space with a dimension greater than one for encryption, decryption, and key generation, offering an alternative to the number-theoretical aspects and algebraic structures commonly used in existing schemes. The main goal of this work is to introduce and propose these five novel cryptographic schemes to provide authentication …
(Si15-140) Designing Bayesian Double Sampling Plans Based On Zero Inflated Poisson Distribution,
2025
Salem Sowdeswari College
(Si15-140) Designing Bayesian Double Sampling Plans Based On Zero Inflated Poisson Distribution, Priyadharshini R., Shalini K., Hemalatha R., Sangeetha S.
Applications and Applied Mathematics: An International Journal (AAM)
The implementation of attribute-based sampling inspection serves as a quality control technique used across numerous industries to evaluate items or workflow processes. When the data exhibits a substantial number of zero counts, the zero-inflated Poisson (ZIP) distribution serves as an effective model for accommodating this zero-inflation. Double sampling plan (DSP) is a quality check method where the decision to approve or decline a batch comes after examining two samples, providing more conclusive information compared to a single sample plan (SSP). In practice, effective decision-making regarding submitted lots considers both within-lot and between-lot variations, which can be addressed through the use …
(Si15-064) Permutation Pentanomials Over Finite Fields With Even Characteristic,
2025
Himachal Pradesh University
(Si15-064) Permutation Pentanomials Over Finite Fields With Even Characteristic, Shalini Gupta, Sushil Kumar, Ashima .
Applications and Applied Mathematics: An International Journal (AAM)
Permutation polynomials over finite fields constitute an active area of research and play an important role in diverse domains, including finite geometry, combinatorial design, coding theory, and cryptography. The study of these polynomials has a long history, and many results have been obtained in recent years. This paper presents new classes of permutation pentanomials based on permutation over the unit circle of finite fields with even characteristic that contribute to the theoretical development of permutation polynomials.
(Si15-120) Exploring Fractional Difference Equations And Their Applications With Mahgoub-Transform,
2025
Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology
(Si15-120) Exploring Fractional Difference Equations And Their Applications With Mahgoub-Transform, Tharmalingam Gunasekar, Periyasamy Udhayasankar, Prabakaran Raghavendran, Kamalendra Kumar
Applications and Applied Mathematics: An International Journal (AAM)
We discuss the introduction and study of the nabla discrete Mahgoub transform along with its defining properties. The transform of fractional sums and fractional differences are derived, demonstrating the applicability of the transform from the computational viewpoint. Employing the transform, fractional difference equations with initial value problems are solved, thereby enhancing the knowledge of their closed forms. As a side-effect of the Mahgoub-transforms, an attractive connection is established, showing that the discrete Mittag-Leffler function acts as the eigenfunction for the Caputo-type fractional difference operator nabla. These results strengthen the core basis for fractional calculus and herald industrial applications in various …
(Si15-010) On Perturbations Of Gabor Frames,
2025
Delhi Technological University
(Si15-010) On Perturbations Of Gabor Frames, Jamkhongam Touthang
Applications and Applied Mathematics: An International Journal (AAM)
Stability plays a crucial role in frame theory and its applications. The present paper studies the interaction between Gabor frames and perturbations, presenting perturbation results related to small changes of the frame parameters and the window functions both in regular and irregular settings. Examples are provided for illustration. Additionally, the paper briefly discusses algorithms pertinent to Gabor frames under perturbations and highlights challenging areas in the field.
(Si15-084) Application Of Differentiation Matrices Corresponding To Scaling And Wavelet Functions To Integral Equations,
2025
Hindu College
(Si15-084) Application Of Differentiation Matrices Corresponding To Scaling And Wavelet Functions To Integral Equations, Viresh Kumar, Rakesh Kumar
Applications and Applied Mathematics: An International Journal (AAM)
In the present paper, we have studied the technique by which a differentiation matrix corresponding to scaling and wavelet function is helpful in representing an integral equation in discrete form. In this technique, only finite times continuously differentiable scaling and wavelet functions were used for the differentiation matrix. This method explores the applications of compactly supported wavelets in discretization of Fredholm integral equation and provides us with a bridge for the solution of integral equations via compactly supported finitely differentiable wavelets.
(Si15-017) Modeling Construction Project Uncertainty Using Fuzzy Inference And Nature-Inspired Metaheuristic Knowledge-Based Algorithms,
2025
Jaypee University of Information Technology
(Si15-017) Modeling Construction Project Uncertainty Using Fuzzy Inference And Nature-Inspired Metaheuristic Knowledge-Based Algorithms, M. Kapoor, B. K. Pathak, R. Kumar
Applications and Applied Mathematics: An International Journal (AAM)
Construction projects are influenced by various uncertain factors, including supervisory knowledge, labor expertise, and weather conditions. These uncertain factors have linguistic properties that are challenging to quantify with the help of traditional set theory. To address this, the study applies fuzzy inference systems, specifically the Mamdani fuzzy inference system, to model and evaluate the impact of these uncertainties on construction projects. This fuzzy inference system provides a more nuanced understanding of these factors compared to traditional set theory methods. Experimental results indicate that uncertainties significantly impact construction projects. These findings establish a valuable framework for developing adaptive strategies, enhancing project …
(Si15-142) Selection Of Single Sampling Plans Based On Zero Inflated Binomial Distribution Using Cost Optimization,
2025
Salem Sowdeswari College
(Si15-142) Selection Of Single Sampling Plans Based On Zero Inflated Binomial Distribution Using Cost Optimization, Sangeetha S., Shalini K., Hemalatha R., Priyadharshini R.
Applications and Applied Mathematics: An International Journal (AAM)
Economic design of sampling plans involves creating sampling plans that minimize the total cost associated with the inspection process while ensuring quality. It aims to address the quality risk concerns of both producer and consumer, ensuring product quality while minimizing inspection costs. This article’s objective is to design single sampling plans by attributes based on Zero-inflated Binomial (ZIB) distribution, using cost optimization principles by developing an economic model aimed at achieving optimal total cost by considering the Average Total Inspection (ATI). Numerical illustration is provided to illustrate the selection of single sampling plans under ZIB distribution that minimizes producer’s total …
(Si15-067) Ahp And Moora Decision Making Methods On Bipolar Fuzzy Sets,
2025
Annamalai University
(Si15-067) Ahp And Moora Decision Making Methods On Bipolar Fuzzy Sets, S. Anita Shanthi, R. Preethi
Applications and Applied Mathematics: An International Journal (AAM)
Decision making, in the present contemporary world, has been inherently complicated. Nowadays, the major challenge is the selection of an appropriate option. The arrival of numerous brands and models makes a purchase challenging. Hence, in this paper, four different models of the same branded laptops are considered, for the selection of an appropriate option, using the Analytic Hierarchy Process (AHP) and Multi-Objective Optimization on the basis of Ratio Analysis (MOORA), with bipolar fuzzy sets, which help decision makers arrive at the most logical choice based on their preferences. The bipolar fuzzy Analytic Hierarchy Process efficaciously supports decision making in cases …
Dimension Of Subalgebras Of Fomin-Kirillov Algebras,
2025
DePauw University
Dimension Of Subalgebras Of Fomin-Kirillov Algebras, Taro Ikeda, Sirous Homayouni
Annual Student Research Poster Session
One of the central open problems concerning the Fomin-Kirillov algebras was whether their dimension is finite or infinite. This question was recently resolved in one research by C. Barligea, where it was shown that FK(n) is infinite-dimensional for all n ≥ 6. In our work, we investigate the dimension of a certain subalgebra of FK(6).
Investigating The Influence Of Instructional Strategies On The Development Of Procedural And Conceptual Knowledge In Advanced Algebra Ii Students,
2025
University of South Carolina
Investigating The Influence Of Instructional Strategies On The Development Of Procedural And Conceptual Knowledge In Advanced Algebra Ii Students, Maura Frances Yinger
Theses and Dissertations
This mixed-methods action research study investigated the influence of instructional strategies shown to improve students’ procedural and conceptual understanding in a rational expressions and equations unit in Advanced Algebra II. The instructional strategies used in the study include comparing, self-explaining, and exploring before instruction. The students (N=27) completed a pre-test and a post-test, both of which were followed by questions asking students to justify their responses on two questions. All students also responded to six digital self-explanation journal prompts. Randomly selected students were placed into three homogenous groups to participate in performance task observations. Analysis of the data …
Coefficients Of The Characteristic Polynomial Of A Hypergraph And Their Combinatorial Properties,
2025
University of South Carolina
Coefficients Of The Characteristic Polynomial Of A Hypergraph And Their Combinatorial Properties, Utku Okur
Theses and Dissertations
We investigate the combinatorial properties of the characteristic polynomial $\phi_\mathcal{H}\ev{t}$ of a hypergraph $\mathcal{H}$, in particular, its coefficients. Due to a classical result of Jacobi, the generating function of closed walks at a vertex $u$ in a graph $G$ is determined by the rational function $\phi_{G-u}(t) / \phi_G(t)$. The connection between closed walks of $G$ and its characteristic polynomial has a known elegant proof via an application of Viennot's Heaps of Pieces framework, where cycles are taken as pieces and the concurrence relation is sharing a vertex. Here, we prove a bijection between heaps with a unique maximal piece containing …
Art Forms: Born Out Of Necessity,
2025
CUNY New York City College of Technology
Art Forms: Born Out Of Necessity, Urmi Duttagupta
Publications and Research
This collection of artworks expresses the artist’s profound passion for mathematics and life’s complex balance. As a female mathematician, she uses artistic expression and intricate patterns to evoke mathematical beauty and feminine strength, celebrating the presence and resilience of women in mathematics.
Memoir On A General Property Of A Very Extensive Class Of Transcendental Functions,
2025
College of the Holy Cross
Memoir On A General Property Of A Very Extensive Class Of Transcendental Functions, Niels Henrik Abel 1802--1829, John Little
Mathematics and Computer Science Department Faculty Scholarship
We present this new commentary and translation anticipating the 200th anniversary of the work, commonly known as Abel's ``Paris memoir.'' This is recognized today as one of Abel's most original and influential works. It is significant mostly because it marked the first appearance of a form of a result in the theory of algebraic curves and Riemann surfaces that has come to be known as ``Abel's theorem.'' However, Abel's original understanding of the meaning and context of his result was quite different from the typical modern formulation and the development of the modern understanding has been a long and tortuous …
Packing Independent Cliques Into Planar Graphs,
2025
Department of Mathematics, University of Louisville, Louisville, KY 40292, USA; and Centro de Investigación en Matemática Pura y Aplicada, Universidad de Costa Rica, San José, Costa Rica
Packing Independent Cliques Into Planar Graphs, Csaba Biró, Gabriel Collado, Oscar Zamora
Theory & Applications of Graphs
The indeque number of a graph is largest set of vertices that induce an independent set of cliques. We study the extremal value of this parameter for the class and subclasses of planar graphs, most notably for forests and graphs of pathwidth at most $2$.
