Applied Mathematics Commons^™

Harvesting Modulation In Three Species Food Chains Using A Robust Control Approach, Hector Puebla, Mariana Rodriguez-Jara, Priti Kumar Roy

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematically Modeling How Trapping Specific Crayfish Life Stages Impacts Removal Efficacy, Relena Pattison, Courtney L. Davis

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Improving Infectious Disease Predictions Through The Use Of Metapopulation Sir Modeling And Graph Convolutional Neural Networks, Petr Kisselev, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Insurance Impact On Opioid Addiction, Ihlara K. Williamson, Eli E. Goldwyn

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

On The Work Of Cartan And Münzner On Isoparametric Hypersurfaces, Thomas E. Cecil, Patrick J. Ryan

Mathematics and Computer Science Department Faculty Scholarship

A hypersurface Mⁿ in a real space form Rⁿ⁺¹, Sⁿ⁺¹, or Hⁿ⁺¹ is isoparametric if it has constant principal curvatures. This paper is a survey of the fundamental work of Cartan and Münzner on the theory of isoparametric hypersurfaces in real space forms, in particular, spheres. This work is contained in four papers of Cartan [3]–[6] published during the period 1938–1940, and two papers of Münzner [47]–[48] that were published in preprint form in the early 1970’s, and as journal articles in 1980–1981. These papers of Cartan and Münzner have been the …

Learning Problems Related To Stochastic Differential Equations, Jinpu Zhou

LSU Doctoral Dissertations

Stochastic differential equations (SDEs) are essential for modeling systems influenced by both deterministic dynamics and random fluctuations, with applications in a wide variety of disciplines. This thesis develops a Bayesian framework for nonparametric learning in SDEs, addressing key challenges in inference, particularly when dealing with complex systems and incomplete data. The thesis begins by establishing a theoretical foundation in optimization over Hilbert spaces, including a generalized representer theorem to address infinite-dimensional optimization problems encountered in nonparametric inference. Building on this, we introduce a Bayesian framework with shrinkage priors to learn drift functions from high-frequency data. Bayesian approach incorporates low-cost sparse …

Cp Decomposition Initialization Schemes For Speeding-Up Of Convolutional Neural Networks, Mollee M. Swift

LSU Master's Theses

While machine learning and convolutional neural networks (CNNs) are making strides, a persistent effort remains to optimize classification techniques and target redundancies from a large number of parameters naturally present in CNNs. While CNNs have become more accessible across machine learning, the aim is to make their use optimal for central processing unit (CPU) schemes with varying degrees of computational power. Tensor decomposition methods, specifically canonical polyadic (CP) decomposition, look to reduce parameters by compressing specific layers in a CNN. However, they have certain inconsistencies, and their full potential remains untouched as decomposition research is endless, with many facets one …

An Introduction To The Time-Independent Schrödinger Equation And Methods To Solve It, Vu Giang, Alex Gnech

OUR Journal: ODU Undergraduate Research Journal

The Time-Independent Schrödinger Equation is a linear elliptic PDE that describes quantum-mechanical systems. Its significance in the science of submicroscopic phenomena, particularly quantum mechanics, is as central as Newton’s laws of motion are to classical mechanics. This study uses various methods, including novel neural networks and finite difference schemes, to solve the one-dimensional two-body equation.

Asymptotic Expansion Of A Maier-Saupe Type Potential Near The Nematic-Isotropic Transition Point In Liquid Crystals, Ryan P. Oneill, Giangvuthanh Nguyen, Xiang Xu

OUR Journal: ODU Undergraduate Research Journal

In this paper we study a Maier-Saupe type bulk potential (Maier & Saupe, 1959) in the Landau-de Gennes free energy in the Q-tensor theory modeling nematic liquid crystal configurations. This potential was originally introduced in Katriel et al. (1986), which is considered as a natural enforcement of a physical constraint on the eigenvalues of symmetric, traceless Q-tensors. More specifically, we present a rigorous derivation of the asymptotic expansion of this singular potential near the nematic-isotropic transition point up to the 4-th order.

Evaluation Of Virtual Distance Learning And Teaching In The Architectural Design Studio Experience Of Professors And Students Of The College Of Architecture And Planning - Qassim University - Kingdom Of Saudi Arabia., Abdulaziz Ibrahim Alhrabi

Journal of Engineering Research

The paper deals with the evaluation of distance learning of the architectural design studio during the Corona pandemic, and the extent to which distance learning and teaching were achieved between the professor and the student. The paper aims to share and evaluate the experience of distance learning and teaching of the architectural design studio, in the College of Architecture and Planning at Qassim University. The research problem is that the Corona virus crisis generates many ideas for educational programs and media, but there is a deficiency in knowledge of many programs that achieve the continuity of the educational process remotely, …

Nano Topology And Decision Making In Medical Applications, Samir Mukhtar, Mohamed Shokry, Manar Omran

Journal of Engineering Research

Nano Topology is one of the essential topics that receive special attention from some athletes in the field of General Topology, Operations Research, and Computer Science, because it has a vital role in the generalizing most of the various mathematical concepts. Recently, many efforts have been made to study many types of Nano Topology, as the previous studies lacked real applications in Engineering, Medicine, Pharmacy, and Social Sciences. In this paper, we present some different applications of these studies. The paper is divided into two parts: Firstly, we study the theory of The Nano Topology and investigate its relation with …

Optimal Site Layout Planning For Construction Projects Over Waterways, Rana M. Azzam, Nashwa Mohamed Yossef Prof, Adel I. Eldosouky Prof

Journal of Engineering Research

Construction site layout planning is an important part of a project's success. An effective construction layout plan can enhance the performance of the construction process by improving productivity, ensuring safety, and reducing costs. Given the importance of bridges over a waterway and the lack of interest in previous research for planning a construction site over a waterway. This paper concentrates on the problems of site planning for such projects, including the problem of limited site space. The study indicated that constructing an offshore terminal is one of the primary requirements for projects with limited space being carried out on a …

Developing Paths In Areas Of Distinguished Value Between Preservation And Extinction (A Case Study Of The Railway Axis In The Maadi Area), Kamal Mahmoud Elgabalawy

Journal of Engineering Research

Abstract: proportion of the place, and thus the loss of the distinctive general character of the area, which leads to its extinction. These areas are of distinguished value, with all the thought and culture they carry of society over time. Among the areas classified as having distinguished value is the Maadi suburb, which is located in the south of Cairo Governorate, where boundaries and foundations for preserving them have been set through the Central Administration for Studies, Research, and Policies of the National Coordination Organization. The Ministry of Culture, approved by the Supreme Council for Planning and Urban Development by …

Review Of Wood Drying Technologies, Mohamed Salah Elmetwaly, Lotfy Hassan Rabie Saker, Mohamed Sameh Salem

Journal of Engineering Research

Abstract- This article provides a comprehensive review of drying optimization in data centers by examining the limitations of drying methods and discussing advances proposed by scientists through whom we can provide a comparison between different drying systems with an emphasis on improving energy efficiency and thermal performance. Wood drying under atmospheric pressure has many advantages, including the ability to dry at lower temperatures (by reducing the likelihood of some drying defects), significantly reduced drying times, color preservation, increased energy efficiency, better control of volatile organic compound emissions, and the ability to dry very large cross sections. Previous studies have achieved …

"Towards A Methodology For Studying The Impact Of Integrating Motion Systems In The External Envelope Of A Building On Natural Lighting Inside The Building– (An Applied Study On A Government School In Greater Cairo)", Nashwa Youssif

Journal of Engineering Research

يدرك المصمم ما للعناصر البيئية ولا سيما الإضاءة الطبيعية من دور فاعل في الوصول إلى تصميم ناجح يحقق أفضل أداء إستخدامي، فالإضاءة الطبيعية تذهب إلى صميم عمل المعماري فيستعين بها للإيحاء بشكل الفراغات ولونها وملمس سطوحها.

وهناك العديد من الأساليب الحديثة التي تساعد المعماري علي إتخاذ قراراته التصميمية الخاصة بتصميم المبنى وكيفية الإستفادة من الإضاءة الطبيعية داخل المباني، وهذه الأساليب تهدف إلى زيادة إحترام البيئة وتفترض تحسينات في النظم البيئية من العزل الحراري وإستغلال مصادر الطاقة الطبيعية والإهتمام بنظم الإضاءة الطبيعية والمواد البنائية.

وتعد تقنية دمج الأنظمة الحركية بالغلاف الخارجي للمبنى مع الإستفادة من الإضاءة الطبيعية داخل هذا …

An Efficient Fourier Caching Algorithm For Walk On Spheres, Zihong Zhou

Dartmouth College Master’s Theses

Walk on Spheres (WoS) is a grid-free Monte Carlo method for solving elliptic partial differential equations (PDEs).
Rather than discretizing the domain, WoS leverages the mean-value principle to obtain Monte Carlo estimates by recursively averaging the solution over the largest contained sphere, terminating upon reaching the boundary.
Unfortunately, WoS requires many independent estimates to achieve noise-free results.

We propose an acceleration technique for WoS, inspired by irradiance caching methods, that computes the solution at a sparse set of locations, and extrapolates these cached values to local neighborhoods. A key insight is that WoS can be extended to compute not only …

Production Box Cost Estimating Relationships For Dod Avionics, Carla J. Cisneros, Edward D. White, Brandon M. Lucas, Jonathan D. Ritschel, Robert D. Fass, Shawn M. Valentine

Faculty Publications

The authors use historical information obtained from the Cost Assessment Data Enterprise to estimate recurring production unit cost for DoD avionics via cost estimating relationships (CERs). The specific modeled responses include mean unit cost, median unit cost, and the 100th production unit cost (T100) utilizing learning curve theory. For T100, the authors adopt both a multiplicative and an additive error for CER comparison. Recommended CERs consist of the mean unit cost and the T100 utilizing a multiplicative error. Moreover, results reveal that weight has a significant effect on cost as well as a potential underaccounting of real price change or …

(Si13-07) Optimal Range For Value Of Two-Person Zero-Sum Game Models With Uncertain Payoffs, Sana Afreen, Ajay Kumar Bhurjee

Applications and Applied Mathematics: An International Journal (AAM)

Game theory deals with the decision-making of individuals in conflicting situations with known payoffs. However, these payoffs are imprecisely known, which means they have uncertainty due to vagueness in the data set of most real-world problems. Therefore, we consider a two-person zero-sum game model on a larger scale where the payoffs are imprecise and lie within a closed interval. We define the pure and mixed strategy as well as value for the game models. The proposed method computes the optimal range for the value of the game model using interval analysis. To derive some important results, we establish some lemmas …

(Si13-09) Numerical Methods For Solving Nonlinear Fisher Equation Using Backward Differentiation Formula, Vikash Vimal, Rajesh Kumar Sinha, Liju Pannikkal

Applications and Applied Mathematics: An International Journal (AAM)

This paper examines the numerical solution of the nonlinear Fisher equation that is used to find the growth of tumour cells in the brain. By employing new methods that transform nonlinear partial differential equations (PDE) into nonlinear ordinary differential equations (ODE) through spatial discretization. The stability of the resulting nonlinear system is evaluated using Lyapunov’s criteria. Implicit stiff solvers, including various orders of backward differentiation formulas, are used to address the ODE system. The efficiency of these numerical methods is demonstrated through two examples, and a comparison with existing methods from the literature is conducted. Compared to traditional methods, the …

(Si13-06) Analysis Of Some Unified Integral Equations Of Fredholm Type Associated With Multivariable Incomplete H And I-Functions, Rahul Sharma, Vinod Gill, Naresh Kumar, Kanak Modi, Yudhveer Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this research paper, we examine various effective methods for addressing the problem of solving Fredholm-type integral equations. Our investigation commences by applying the principles of fractional calculus theory. We employ series representations and products of multivariable incomplete H-functions and multivariable incomplete I-functions to solve these integrals. The outcomes derived from our analysis possess a general nature and hold the potential to yield numerous results.