Applied Mathematics Commons^™

Multilayer Security Of Rgb Image In Discrete Hartley Domain, Umar H. Mir, Deep Singh, D. C. Mishra, Parveiz N. Lone

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we present RGB image encryption and decryption using random matrix affine cipher (RMAC) associated with discrete Hartley transform (DHT) and random matrix shift cipher (RMSC). The parameters in RMAC and RMSC phases act as two series of secret keys whose arrangement is imperative in the proposed algorithm. The computer simulations with results and examples are given to analyze the efficiency of the proposed approach. Further, security analysis and comparison with the prior techniques successfully supports the robustness and validation of the proposed technique.

Approximate Solutions For The Nonlinear Systems Of Algebraic Equations Using The Power Series Method, M. M. Khader, M. Adel

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the approximate solutions for systems of nonlinear algebraic equations by the power series method (PSM) are presented. Illustrative examples have been presented to demonstrate the efficiency of the proposed method. In addition, the obtained results are compared with those obtained from the standard Adomian decomposition method. It turns out that the convergence of the proposed algorithm is rapid.

On Higher-Order Duality In Nondifferentiable Minimax Fractional Programming, S. Al-Homidan, Vivek Singh, I. Ahmad

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider a nondifferentiable minimax fractional programming problem with continuously differentiable functions and formulated two types of higher-order dual models for such optimization problem.Weak, strong and strict converse duality theorems are derived under higherorder generalized invexity.

An Efficient Algorithm For Numerical Inversion Of System Of Generalized Abel Integral Equations, Sandeep Dixit

Applications and Applied Mathematics: An International Journal (AAM)

In this article a direct method is introduced, which is based on orthonormal Bernstein polynomials, to present an efficient and stable algorithm for numerical inversion of the system of singular integral equations of Abel type. The appropriateness of earlier numerical inversion methods was restricted to the one portion of singular integral equations of Abel type. The proposed method is absolutely accurate, and numerical illustrations are given to show the convergence and utilization of the suggested method and comparisons are made with some other existing numerical solution.

Integrated Farm Model For Optimal Allocation Of Resources- A Linear Programming Approach, Mahak Bhatia, Anil Rana

Applications and Applied Mathematics: An International Journal (AAM)

The mathematical model for optimal allocation of farm resources, especially land and water are proposed to optimize the resources that contribute to increase farm revenues. A study is being carried out, to analyze the cropping practice adopted by growers, depending on availability and accessibility of resources. Different crop-combinations and cropping patterns are being analyzed in districts of Rajasthan. Rajasthan has arid topography with varying weather conditions. Thus, a diverse crop variety is being cultivated in a region. Being a state with inadequate water resources, the formulated model proposed different crop combinations alternatives. A crop-mix model is developed to reduce the …

Analysis Of Map/Ph/1 Queueing Model With Breakdown, Instantaneous Feedback And Server Vacation, G. Ayyappan, K. Thilagavathy

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we analyze a single server queueing model with feedback, a single vacation under Bernoulli schedule, breakdown and repair. The arriving customers follow the Markovian Arrival Process (MAP) and service follow the phase-type distribution. When the server returns from vacation, if there is no one present in the system, the server will wait until the customer’s arrival. When the service completion epoch if the customer is not satisfied then that customer will get the service immediately. Under the steady-state probability vector that the total number of customers are present in the system is probed by the Matrix-analytic method. …

Sum Of Cubes Of The First N Integers, Obiamaka L. Agu

Electronic Theses, Projects, and Dissertations

In Calculus we learned that 􏰅Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{􏰅n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at the endpoints a and b. From my recollection, a former instructor informed us to do the value of memorizing these formulas. …

A Collection Of Fast Algorithms For Scalar And Vector-Valued Data On Irregular Domains: Spherical Harmonic Analysis, Divergence-Free/Curl-Free Radial Basis Functions, And Implicit Surface Reconstruction, Kathryn Primrose Drake

Boise State University Theses and Dissertations

This dissertation addresses problems that arise in a diverse group of fields including cosmology, electromagnetism, and graphic design. While these topics may seem disparate, they share a commonality in their need for fast and accurate algorithms which can handle large datasets collected on irregular domains. An important issue in cosmology is the calculation of the angular power spectrum of the cosmic microwave background (CMB) radiation. CMB photons offer a direct insight into the early stages of the universe's development and give the strongest evidence for the Big Bang theory to date. The Hierarchical Equal Area isoLatitude Pixelation (HEALPix) grid is …

Asymptotic Analysis Of Radial Point Rupture Solutions For Elliptic Equations, Attou Miloua

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Deep Learning With Physics Informed Neural Networks For The Airborne Spread Of Covid-19 In Enclosed Spaces, Udbhav Muthakana, Padmanabhan Seshaiyer, Maziar Raissi, Long Nguyen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modelling And In Silico Experimentation To Estimate The Quantity Of Covid-19 Infected Individuals In Tijuana, México, Karla A. Encinas, Luis N. Coria, Paul A. Valle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

From Wave Propagation To Spin Dynamics: Mathematical And Computational Aspects, Oleksii Beznosov

Mathematics & Statistics ETDs

In this work we concentrate on two separate topics which pose certain numerical challenges. The first topic is the spin dynamics of electrons in high-energy circular accelerators. We introduce a stochastic differential equation framework to study spin depolarization and spin equilibrium. This framework allows the mathematical study of known equations and new equations modelling the spin distribution of an electron bunch. A spin distribution is governed by a so-called Bloch equation, which is a linear Fokker-Planck type PDE, in general posed in six dimensions. We propose three approaches to approximate solutions, using analytical and modern numerical techniques. We also present …

Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation, Anastassiya Semenova

Mathematics & Statistics ETDs

The present work offers an investigation of dynamics and stability of nonlinear waves in Hamiltonian systems. The first part of the manuscript discusses the classical problem of water waves on the surface of an ideal fluid in 2D. We demonstrate how to construct the Stokes waves, and how to apply a continuation method to find waves in close vicinity to the limiting Stokes wave. We provide new insight into the stability of the Stokes waves by identifying previously inaccessible branches of instability in the equations of motion for the fluid. We provide numerical evidence that pairs of unstable eigenvalues of …

A Phase-Field Approach To Diffusion-Driven Fracture, Friedrich Wilhelm Alexander Dunkel

LSU Doctoral Dissertations

In recent years applied mathematicians have used modern analysis to develop variational phase-field models of fracture based on Griffith's theory. These variational phase-field models of fracture have gained popularity due to their ability to predict the crack path and handle crack nucleation and branching.

In this work, we are interested in coupled problems where a diffusion process drives the crack propagation. We extend the variational phase-field model of fracture to account for diffusion-driving fracture and study the convergence of minimizers using gamma-convergence. We will introduce Newton's method for the constrained optimization problem and present an algorithm to solve the diffusion-driven …

Numerical Approach To Non-Darcy Mixed Convective Flow Of Non-Newtonian Fluid On A Vertical Surface With Varying Surface Temperature And Heat Source, Ajaya Prasad Baitharu, Sachidananda Sahoo, Gauranga Charan Dash

Karbala International Journal of Modern Science

An analysis is performed on non-Darcy mixed convective flow of non-Newtonian fluid past a vertical surface in the presence of volumetric heat source originated by some electromechanical or other devices. Further, the vertical bounding surface is subjected to power law variation of wall temperature, but the numerical solution is obtained for isothermal case. In the present non-Darcy flow model, effects of high flow rate give rise to inertia force. The inertia force in conjunction with volumetric heat source/sink is considered in the present analysis. The Runge-Kutta method of fourth order with shooting technique has been applied to obtain the numerical …

Heat And Mass Transfer Of Mhd Casson Nanofluid Flow Through A Porous Medium Past A Stretching Sheet With Newtonian Heating And Chemical Reaction, Lipika Panigrahi, Jayaprakash Panda, Kharabela Swain, Gouranga Charan Dash

Karbala International Journal of Modern Science

An analysis is made to investigate the effect of inclined magnetic field on Casson nanofluid over a stretching sheet embedded in a saturated porous matrix in presence of thermal radiation, non-uniform heat source/sink. The heat equation takes care of energy loss due to viscous dissipation and Joulian dissipation. The mass transfer and heat equation become coupled due to thermophoresis and Brownian motion, two important characteristics of nanofluid flow. The convective terms of momentum, heat and mass transfer equations render the equations non-linear. This present flow model is pressure gradient driven and it is eliminated with the help of potential/ambient flow …

Global Analysis Of The Shadow Gierer-Meinhardt System With General Linear Boundary Conditions In A Random Environment, Kwadwo Antwi-Fordjour, Seonguk Kim, Marius Nkashama

Mathematics Faculty Publications

The global analysis of the shadow Gierer-Meinhardt system with multiplicative white noise and general linear boundary conditions is investigated in this paper. For this reaction-diffusion system, we employ a fixed point argument to prove local existence and uniqueness. Our results on global existence are based on a priori estimates of solutions.

Mathematical Modeling Of Nonlinear Problem Biological Population In Not Divergent Form With Absorption, And Variable Density, Maftuha Sayfullayeva

Acta of Turin Polytechnic University in Tashkent

В работе установлены критические и двойные критические случаи, обусловленные представлением двойного нелинейного параболического уравнения с переменной плотностью с поглощением в "радиально-симметричной" форме.Такое представление исходного уравнения дало возможность легко построить решения типа Зельдовоч-Баренбатт-Паттл для критических случаев в виде функций сравнения.

Cover Song Identification - A Novel Stem-Based Approach To Improve Song-To-Song Similarity Measurements, Lavonnia Newman, Dhyan Shah, Chandler Vaughn, Faizan Javed

SMU Data Science Review

Music is incorporated into our daily lives whether intentional or unintentional. It evokes responses and behavior so much so there is an entire study dedicated to the psychology of music. Music creates the mood for dancing, exercising, creative thought or even relaxation. It is a powerful tool that can be used in various venues and through advertisements to influence and guide human reactions. Music is also often "borrowed" in the industry today. The practices of sampling and remixing music in the digital age have made cover song identification an active area of research. While most of this research is focused …

Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the …

Matrix Low Rank Approximation At Sublinear Cost, Qi Luan

Dissertations, Theses, and Capstone Projects

A matrix algorithm runs at sublinear cost if the number of arithmetic operations involved is far fewer than the number of entries of the input matrix. Such algorithms are especially crucial for applications in the field of Big Data, where input matrices are so immense that one can only store a fraction of the entire matrix in memory of modern machines. Typically, such matrices admit Low Rank Approximation (LRA) that can be stored and processed at sublinear cost. Can we compute LRA at sublinear cost? Our counter example presented in Appendix C shows that no sublinear cost algorithm can compute …

Binary Neutron Star Mergers: Testing Ejecta Models For High Mass-Ratios, Allen Murray

The Journal of Purdue Undergraduate Research

Neutron stars are extremely dense stellar corpses which sometimes exist in orbiting pairs known as binary neutron star (BNS) systems. The mass ratio (q) of a BNS system is defined as the mass of the heavier neutron star divided by the mass of the lighter neutron star. Over time the neutron stars will inspiral toward one another and produce a merger event. Although rare, these events can be rich sources of observational data due to their many electromagnetic emissions as well as the gravitational waves they produce. The ability to extract physical information from such observations relies heavily on numerical …

Advection-Reaction-Diffusion Model Of Drug Concentration In A Lymph Node, Ting Yan

Mathematics Theses and Dissertations

It is recognized that there exist reservoirs of HIV located outside the bloodstream, and that these reservoirs hinder the efficacy of antiretroviral medication regimens in combating the virus. The prevailing theories regarding these reservoirs point to the lymphatic system. In this work, we discuss a novel computational model of viral dynamics in the lymph node, to allow numerical studies of viral “reservoirs” causing reinfection. Our model consists of a system of advection-reaction-diffusion partial differential equations (PDEs), where the diffusion coefficients vary between species (virus, drugs, lymphocytes) and include discontinuous jumps to capture differing properties of internal lymph node structures. We …

Variable Compact Multi-Point Upscaling Schemes For Anisotropic Diffusion Problems In Three-Dimensions, James Quinlan

Dissertations

Simulation is a useful tool to mitigate risk and uncertainty in subsurface flow models that contain geometrically complex features and in which the permeability field is highly heterogeneous. However, due to the level of detail in the underlying geocellular description, an upscaling procedure is needed to generate a coarsened model that is computationally feasible to perform simulations. These procedures require additional attention when coefficients in the system exhibit full-tensor anisotropy due to heterogeneity or not aligned with the computational grid. In this thesis, we generalize a multi-point finite volume scheme in several ways and benchmark it against the industry-standard routines. …

Exploring Food Deserts And Environmental Impacts On Health In Chicago And Oregon, Sivasomasundari Arunarasu, Paulina Grzybowicz

altREU Projects

Food deserts are defined as, “an impoverished area where residents lack access to healthy foods”. This lack of access can be due to a combination of socioeconomic, geographic, and food-related variables, and has been proven to impact the health of residents in the area. In this project, several statistical and machine learning techniques are used to model the impact of food desserts and various other factors on health outcomes, including diabetes and obesity rates, in both the different neighborhoods in the City of Chicago and the various counties in the state of Oregon. The models are then used to determine …

Combating Covid On College Campuses: The Impact Of Structural Changes On Viral Transmissions, Jared Knofczynski, Aria Killebrew Bruehl, Ben Warner, Ryne Shelton

altREU Projects

One of the most significant issues in the COVID-19 pandemic is the reopening of schools while minimizing the transmission of coronavirus. Opportunities for evaluating the effectiveness of policies that might be utilized at such institutions are limited, as the necessary empirical data has not been gathered yet. Agent-based modeling, where various entities within an environment are simulated as agents, offers an opportunity to examine the effectiveness of various policies in a way that drastically minimizes the health and economic risks involved. Agent-based modeling is common within biology, ecology and other fields; and has seen some use within the coronavirus literature. …

Analyzing Network Topology For Ddos Mitigation Using The Abelian Sandpile Model, Bhavana Panchumarthi, Monroe Ame Stephenson

altREU Projects

A Distributed Denial of Service (DDoS) is a cyber attack, which is capable of triggering a cascading failure in the victim network. While DDoS attacks come in different forms, their general goal is to make a network's service unavailable to its users. A common, but risky, countermeasure is to blackhole or null route the source, or the attacked destination. When a server becomes a blackhole, or referred to as the sink in the paper, the data that is assigned to it "disappears" or gets deleted. Our research shows how mathematical modeling can propose an alternative blackholing strategy that could improve …

An Adaptive Approach To Gibbs’ Phenomenon, Jannatul Ferdous Chhoa

Master's Theses

Gibbs’ Phenomenon, an unusual behavior of functions with sharp jumps, is encountered while applying the Fourier Transform on them. The resulting reconstructions have high frequency oscillations near the jumps making the reconstructions far from being accurate. To get rid of the unwanted oscillations, we used the Lanczos sigma factor to adjust the Fourier series and we came across three cases. Out of the three, two of them failed to give us the right reconstructions because either it was removing the oscillations partially but not entirely or it was completely removing them but smoothing out the jumps a little too much. …

Numerical Approximations Of Phase Field Equations With Physics Informed Neural Networks, Colby Wight

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Designing numerical algorithms for solving partial differential equations (PDEs) is one of the major research branches in applied and computational mathematics. Recently there has been some seminal work on solving PDEs using the deep neural networks. In particular, the Physics Informed Neural Network (PINN) has been shown to be effective in solving some classical partial differential equations. However, we find that this method is not sufficient in solving all types of equations and falls short in solving phase-field equations. In this thesis, we propose various techniques that add to the power of these networks. Mainly, we propose to embrace the …

Optimal Allocation Of Two Resources In Annual Plants, David Mcmorris

Department of Mathematics: Dissertations, Theses, and Student Research

The fitness of an annual plant can be thought of as how much fruit is produced by the end of its growing season. Under the assumption that annual plants grow to maximize fitness, we can use techniques from optimal control theory to understand this process. We introduce two models for resource allocation in annual plants which extend classical work by Iwasa and Roughgarden to a case where both carbohydrates and mineral nutrients are allocated to shoots, roots, and fruits in annual plants. In each case, we use optimal control theory to determine the optimal resource allocation strategy for the plant …