Marymount University
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Pennsylvania State University
Toward Mapping Multiphase Multicomponent Mixtures With Neural Networks,
2026
The University of Texas Rio Grande Valley
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 …
Revisiting Ulam Stability For Boundary Value Problems,
2026
Missouri University of Science and Technology
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, …
Quasi-Poisson Analogs Of Regular Poisson Varieties,
2026
Utah State University
Quasi-Poisson Analogs Of Regular Poisson Varieties, Casen Thompson
All Graduate Theses and Dissertations, Fall 2023 to Present
Let G be a complex semisimple linear algebraic group with 𝐶 a conjugacy class of parabolic subgroups of G. In previous work, Dr. Crooks defines 𝑢𝐶→ B𝐶 , a universal flat family of a fine Hamiltonian Lagrangian G-bundles over 𝐶, and shows that 𝑢𝐶 is a family of regular Poisson varieties. This manuscript introduces a natural candidate for a quasi-Poisson analog of Dr. Crooks’s construction, 𝑢𝐶, using the framework of quasi-Poisson geometry established by Alekseev, Kosmann-Scwarzbach, and Meinrenken. It will be shown that this proposed quasi-Poisson analog indeed has a valid quasi-Poisson structure and …
Peakon Solutions And Analytical Properties For The Camassa–Holm-Type Equations With Quadratic Nonlinearities,
2026
The University of Texas Rio Grande Valley
Peakon Solutions And Analytical Properties For The Camassa–Holm-Type Equations With Quadratic Nonlinearities, Yonghong Chen, Zhijun Qiao, Mingxuan Zhu
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we derive the multi-peakon dynamical system of a class of Camassa-Holm-type equations with quadratic nonlinearities. We also consider the analytical properties for the Cauchy problem. Firstly, we establish local well-posedness of solutions in Besov spaces and then provide the blow-up criteria. Subsequently, we impose appropriate sufficient conditions on the initial data to guarantee that the corresponding solution either exists globally or blows up in a finite time. Finally, we prove the ill-posedness in the Besov space B2,∞3/2 by utilizing the non-traveling wave solutions.
A Finite Element Model For Thermomechanical Stress-Strain Fields In Transversely Isotropic Strain-Limiting Materials,
2026
The University of Texas Rio Grande Valley
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 …
Pattern Formation In Quantum Hierarchical Cellular Neural Networks,
2026
The University of Texas Rio Grande Valley
Pattern Formation In Quantum Hierarchical Cellular Neural Networks, Wilson A. Zuniga-Galindo, B. A. Zambrano-Luna, Chayapuntika Indoung
School of Mathematical & Statistical Sciences Faculty Publications
We present a new class of quantum neural networks (QNNs) whose states are solutions of p -adic Schrödinger equations with a non-local potential that controls the interaction between the neurons. These equations are obtained as Wick rotations of the state equations of p -adic cellular neural networks (CNNs). The p -adic CNNs arise as continuous limits of large discrete hierarchical neural networks (NNs). The CNNs are bio-inspired by the Wilson–Cowan model, which describes the macroscopic dynamics of large populations of neurons. We provide a detailed study of the discretization of the new p -adic Schrödinger equations, which allows the construction …
Geometric Puzzles On A Circular Track: A Recreational Introduction To Quantization,
2026
The University of Texas Rio Grande Valley
Geometric Puzzles On A Circular Track: A Recreational Introduction To Quantization, Sayandip Pandit, Amit Priyadarshi, Mrinal Kanti Roychowdhury
School of Mathematical & Statistical Sciences Faculty Publications
Imagine a circular running track with several water stations placed around it. If only a few stations may remain open, or if a few new stations may be built, where should they be located so that runners travel the shortest possible distance to reach one? This simple question leads to a collection of recreational geometry puzzles involving distance, symmetry, optimization, Voronoi regions, and quantization. Quantization is the mathematical problem of replacing a large collection of points by a smaller set of representative points while minimizing the approximation error. Using only elementary mathematics, we investigate several configurations of points on a …
Progress Towards An Analog Of The Darboux-Griffiths Converse Of Abel's Theorem In Characteristic P,
2026
College of the Holy Cross
Progress Towards An Analog Of The Darboux-Griffiths Converse Of Abel's Theorem In Characteristic P, John B. Little
Mathematics and Computer Science Department Faculty Scholarship
In this working paper, we report our recent efforts concerning a possible characteristic p analog of the so-called converse of Abel's theorem discussed by Darboux and Griffiths. The characteristic zero version is used in one proof of the Lie-Wirtinger theorem on double translation manifolds and also in related aspects of the geometry of webs. In informal terms, our results indicate that, apart from some isolated counterexamples, formal power series Abel relations over an algebraically closed field of characteristic p essentially only arise in the (generalized) Jacobians of algebraic curves. The ultimate goal is to complete thevwork started in the author's …
Beyond Intent: Teacher Capacity, Opportunity To Learn, And The Persistence Of Math Equity Gaps In Tennessee (2000-2025),
2026
Metro Nashville Public Schools
Beyond Intent: Teacher Capacity, Opportunity To Learn, And The Persistence Of Math Equity Gaps In Tennessee (2000-2025), Soso Dede
The Journal of the Research Association of Minority Professors
For a quarter-century (2000–2025), Tennessee pursued mathematics reforms aiming for equity, yet stark racial and socioeconomic achievement gaps endure. Framed by Opportunity to Learn (OTL) and Mathematical Knowledge for Teaching (MKT), this study investigates the intersection of equity, teacher capacity, and policy. By synthesizing assessment data, program evaluations, policy documents, and research literature, this study reveals that systemic OTL inequities—disparate access to quality instruction, adequate resources, and teachers possessing strong MKT—are primary drivers of these enduring gaps. Such inequities deny marginalized students a fair chance at mathematical proficiency. The interplay between OTL and MKT is critical: inadequate OTL constrains knowledgeable …
Exact Formulas For Restricted Coprime Representations Of Even Integers,
2026
Pontificia Universidad Javeriana - Cali
Exact Formulas For Restricted Coprime Representations Of Even Integers, Andres Mauricio Salazar
Communications on Number Theory and Combinatorial Theory
Let p ≥ 5 be prime, and let g(2n,p) denote the number of unordered representations by positive integers 2n = h + k, with h ≤ k and gcd(h,6p) = gcd(k,6p) = 1. Every positive integer coprime to 6 belongs to exactly one of the families 6z + 1 and 6z + 5. In each family, divisibility by p excludes one explicit residue class of z modulo p. We use these two excluded classes to derive an exact formula for g(2n,p) from finite residue counts and nonnegative lift counts. The formula is valid for every positive integer n, including all …
Finite Mathematics: A Course Guide,
2026
Stephen F Austin State University
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 …
Quantum Mechanics, Non-Locality, And The Space Discreteness Hypothesis,
2026
The University of Texas Rio Grande Valley
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 …
Study Of A Nonlinear Delayed Parabolic Model For Prion Disease Dynamics With The Unfolded Protein Response,
2026
The University of Texas Rio Grande Valley
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 …
Implementation Of The Problem-Based Learning Model On The Topic Of The Immune System To Enhance The Critical Thinking Skills Of Grade Xi B Students At Sman 1 Tojo,
2026
Biologi Education Study Program, Universitas Tadulako
Implementation Of The Problem-Based Learning Model On The Topic Of The Immune System To Enhance The Critical Thinking Skills Of Grade Xi B Students At Sman 1 Tojo, Nani Sofyanti, Sutrisnawati Sutrisnawati, Vita Indri Febriani, Mohammad Jamhari, Bustamin Bustamin, Raya Agni
Jurnal Pendidikan Sains
Critical-thinking skills are essential competencies for students in 21st-century learning. Preliminary classroom observations in Class XI B at SMAN 1 Tojo indicated that instruction remained predominantly teacher-centered and provided limited opportunities for students to engage in activities involving interpretation, analysis, evaluation, and inference. This study aimed to improve students’ critical-thinking skills through the implementation of Problem-Based Learning (PBL) on the immune system topic. The study employed a Classroom Action Research (CAR) design conducted over two cycles, involving 28 students in Class XI B. Data were collected using a teacher activity observation sheet and critical-thinking skills tests assessing four indicators: interpretation, …
Modelling Acute Haemorrhagic Conjunctivitis In East Africa: An Integrated Approach To Transmission Dynamics And Outbreak Response Strategies,
2026
Mkwawa University College of Education, University of Dar es Salaam, P.O. Box 2513, Iringa, Tanzania
Modelling Acute Haemorrhagic Conjunctivitis In East Africa: An Integrated Approach To Transmission Dynamics And Outbreak Response Strategies, Geofrey Wingi Sikazwe
Tanzania Journal of Science
Acute hemorrhagic conjunctivitis (AHC) poses a significant global health risk, with the potential for rapid spread during outbreaks. For instance, a localized outbreak in Yunnan Province, China, recorded infection rates of up to 48%, illustrating how transmission can intensify under favourable epidemiological and environmental conditions. Existing mathematical models of AHC transmission overlook seasonal variations, a critical factor in epidemic spread. This study combines species distribution models (SDMs) and epidemiological modelling to analyse key drivers of AHC in East Africa. We use the SEIR type (Susceptible-Exposed-Infected-Recovered - incorporating waning immunity) framework with temperature-dependent infectivity rate as the key driver of an …
Emergence Of Purely Elastoplastic Turbulence In Shear Flows,
2026
University of Pennsylvania
Emergence Of Purely Elastoplastic Turbulence In Shear Flows, Muhammad Abdullah, Shravan Pradeep, Doug J. Jerolmack, Becca Thomases, Paulo E. Arratia
Mathematics Sciences: Faculty Publications
Yield-stress fluids only flow above a critical stress. Here, we observe the emergence of a distinct, elasticity-driven flow state in a yield-stress fluid in the absence of inertia. Numerical simulations show that this elastoplastic turbulent state is characterized by non-Gaussian bimodal velocity distribution and a broad spectrum of velocity and stress fluctuations. Results show a nonmonotonic relationship between the volume fraction of the unyielded flow and plasticity. Surprisingly, the system can fluidize near the emergence of the elastoplastic turbulent state. Our results reveal the complex interplay between elasticity and plasticity in simple shear flows, indicating that plasticity can mobilize the …
The Use Of Gadgets And Learning Motivation Among Grade Xi Students In Biology Learning At Sma Negeri 5 Palu,
2026
Tadulako University
The Use Of Gadgets And Learning Motivation Among Grade Xi Students In Biology Learning At Sma Negeri 5 Palu, Yulia Citra, Mohammad Jamhari, Masrianih Masrianih, Lestari M.P Alibasyah, Mursito S. Bialangi, Yulia Windarsih
Jurnal Pendidikan Sains
This study aims to describe the profile of gadget use and learning motivation among Grade XI students in biology learning at SMA Negeri 5 Palu and to explore students’ and teachers’ experiences of gadgets as learning support tools and potential sources of digital distraction. A qualitative descriptive design was employed, supported by descriptive questionnaire profiling. A total of 74 students completed a 50-item questionnaire on gadget use and learning motivation, while 10 students and two biology teachers participated in semi-structured interviews. Questionnaire data were analyzed using frequencies and percentages, while interview data were analyzed thematically. The descriptive findings showed that …
The Application Of The Group Investigation (Gi) Model Of Cooperative Learning To Improve Students’ Understanding Of Biodiversity In Year 10 At Sman 2 Mori Atas,
2026
Tadulako University
The Application Of The Group Investigation (Gi) Model Of Cooperative Learning To Improve Students’ Understanding Of Biodiversity In Year 10 At Sman 2 Mori Atas, Nadia Rosmita Lumako, Mohammad Jamhari, Yulia Windarsih, Lilies Lilies, Rafiqa Rafiqa, Amalia Buntu
Jurnal Pendidikan Sains
Biology instruction at SMAN 2 Mori Atas was predominantly conducted through conventional teaching practices. Preliminary observations revealed that students had difficulty understanding biodiversity concepts, and several students did not meet the minimum passing criterion of 70. These conditions highlighted the need for learning activities that promote active investigation, discussion, and conceptual connections. This classroom action research examined the use of the Group Investigation (GI) cooperative learning model to improve Grade 10 students’ classroom engagement and conceptual understanding of biodiversity, as assessed through Higher-Order Thinking Skills (HOTS) questions based on the Structure of Observed Learning Outcomes (SOLO) taxonomy. The study involved …
The Effect Of The Problem-Based Learning Model On Biology Learning Outcomes In The 8th Grade Science Class At Smp Negeri 19 Palu,
2026
Universitas Tadulako
The Effect Of The Problem-Based Learning Model On Biology Learning Outcomes In The 8th Grade Science Class At Smp Negeri 19 Palu, Delfi Srieviyani, Mursito S. Bialangi, Masrianih Masrianih, Abd Hakim Laenggeng, Vita Indri Febriani, Bustamin Bustamin
Jurnal Pendidikan Sains
Research background: The low student achievement in biology at SMP Negeri 19 Palu specifically regarding the human respiratory system is attributed to the conventional teaching methods still employed by teachers. Purpose and scope of the article: This study examines the effect of the Problem-Based Learning (PBL) model on students’ learning outcomes in biology, specifically regarding the human respiratory system. Method: This study used a quasi-experimental design with a quantitative approach. The research design employed was a nonequivalent control group design using two groups: an experimental group (Class VIII D) consisting of 25 students who received the PBL model, and a …
Generalized Apostol-Bernoulli Functions And The Evaluation Of Character Sums,
2026
CUNY New York City College of Technology
Generalized Apostol-Bernoulli Functions And The Evaluation Of Character Sums, Brad Isaacson
Publications and Research
We introduce two types of generalized Apostol–Bernoulli functions attached to Dirichlet characters and express them by generalized Apostol–Bernoulli numbers. As a corollary, we obtain formulas expressing two families of character sums by generalized Apostol–Bernoulli numbers. These sums are twisted generalizations of sums introduced and studied by Arakawa, Berndt, Ibukiyama, Kaneko, Kim, Ramanujan, and Zaharescu in the context of modular forms and theta function identities.
