Dupin Submanifolds In Lie Sphere Geometry (Updated Version), 2020 College of the Holy Cross

#### Dupin Submanifolds In Lie Sphere Geometry (Updated Version), Thomas E. Cecil, Shiing-Shen Chern

*Mathematics Department Faculty Scholarship*

A hypersurface ** M^{n-1}** in Euclidean space

*is proper Dupin if the number of distinct principal curvatures is constant on*

**E**^{n}**, and each principal curvature function is constant along each leaf of its principal foliation. This paper was originally published in 1989 (see Comments below), and it develops a method for the local study of proper Dupin hypersurfaces in the context of Lie sphere geometry using moving frames. This method has been effective in obtaining several classification theorems of proper Dupin hypersurfaces since that time. This updated version of the paper contains the original exposition together with ...**

*M*^{n-1}Numerical Approach To Non-Darcy Mixed Convective Flow Of Non-Newtonian Fluid On A Vertical Surface With Varying Surface Temperature And Heat Source, 2020 Department of Mathematics, College of Engineering and Technology,Bhubaneswar-751029, Odisha, INDIA

#### 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 ...

Heat And Mass Transfer Of Mhd Casson Nanofluid Flow Through A Porous Medium Past A Stretching Sheet With Newtonian Heating And Chemical Reaction, 2020 Veer Surenrda Sai University of Technology, Burla, India

#### 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 ...

What If We Use Almost-Linear Functions Instead Of Linear Ones As A First Approximation In Interval Computations, 2020 University of Texas at El Paso

#### What If We Use Almost-Linear Functions Instead Of Linear Ones As A First Approximation In Interval Computations, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

In many practical situations, the only information that we have about measurement errors is the upper bound on their absolute values. In such situations, the only information that we have after the measurement about the actual (unknown) value of the corresponding quantity is that this value belongs to the corresponding interval: e.g., if the measurement result is 1.0, and the upper bound is 0.1, then this interval is [1.0−0.1,1.0+0.1] = [0.9,1.1]. An important practical question is what is the resulting interval uncertainty of indirect measurements, i.e., in ...

Egyptian Fractions As Approximators, 2020 University of Texas at El Paso

#### Egyptian Fractions As Approximators, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

In ancient Egypt, fractions were represented as the sum of inverses to natural numbers. Processing fractions in this representation is computationally complicated. Because of this complexity, traditionally, Egyptian fractions used to be considered an early inefficient approach. In our previous papers, we showed, however, that the Egyptian fractions actually provide an optimal solution to problems important for ancient Egypt -- such as the more efficient distribution of food between workers. In these papers, we assumed, for simplicity, that we know the exact amount of food needed for each worker -- and that this value must be maintained with absolute accuracy. In this ...

How To Describe Measurement Errors: A Natural Generalization Of The Central Limit Theorem Beyond Normal (And Other Infinitely Divisible) Distributions, 2020 University of Texas at El Paso

#### How To Describe Measurement Errors: A Natural Generalization Of The Central Limit Theorem Beyond Normal (And Other Infinitely Divisible) Distributions, Julio Urenda, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

When precise measurement instruments are designed, designers try their best to decrease the effect of the main factors leading to measurement errors. As a result of this decrease, the remaining measurement error is the joint result of a large number of relatively small independent error components. According to the Central Limit Theorem, under reasonable conditions, when the number of components increases, the resulting distribution tends to Gaussian (normal). Thus, in practice, when the number of components is large, the distribution is close to normal -- and normal distributions are indeed ubiquitous in measurements. However, in some practical situations, the distribution is ...

Global Analysis Of The Shadow Gierer-Meinhardt System With General Linear Boundary Conditions In A Random Environment, 2020 Samford University

#### 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.

Analysis Of Dynamical Systems For Synthesis Of Phenobarbital, 2020 DePauw University

#### Analysis Of Dynamical Systems For Synthesis Of Phenobarbital, Mishal Ali

*Science Research Fellows Posters*

The use of mathematical methods for the analysis of chemical reaction systems is one of the useful tools. Phenobarbital (a barbiturate type medication also called phenobarb) is a prescription drug used to control seizures, relieve anxiety, treat epilepsy (in some countries), and prevent withdrawal symptoms in people dependent on other barbiture drugs. We approaches it with matrix analysis and ODE system. It helps us understand the chemical stoichiometry of these synthesis reactions.

Supervisor: Prof. Seonguk Kim, PhD

Diagonalization Of 1-D Schrodinger Operators With Piecewise Constant Potentials, 2020 The University of Southern Mississippi

#### Diagonalization Of 1-D Schrodinger Operators With Piecewise Constant Potentials, Sarah Wright

*Master's Theses*

In today's world our lives are very layered. My research is meant to adapt current inefficient numerical methods to more accurately model the complex situations we encounter. This project focuses on a specific equation that is used to model sound speed in the ocean. As depth increases, the sound speed changes. This means the variable related to the sound speed is not constant. We will modify this variable so that it is piecewise constant. The specific operator in this equation also makes current time-stepping methods not practical. The method used here will apply an eigenfunction expansion technique used in ...

Stability Analysis Of Krylov Subspace Spectral Methods For The 1-D Wave Equation In Inhomogeneous Media, 2020 The University of Southern Mississippi

#### Stability Analysis Of Krylov Subspace Spectral Methods For The 1-D Wave Equation In Inhomogeneous Media, Bailey Rester

*Master's Theses*

Krylov subspace spectral (KSS) methods are high-order accurate, explicit time-stepping methods for partial differential equations (PDEs) that also possess the stability characteristic of implicit methods. Unlike other time-stepping approaches, KSS methods compute each Fourier coefficient of the solution from an individualized approximation of the solution operator of the PDE. As a result, KSS methods scale effectively to higher spatial resolution. This thesis will present a stability analysis of a first-order KSS method applied to the wave equation in inhomogeneous media.

Why Significant Wave Height And Rogue Waves Are So Defined: A Possible Explanation, 2020 University of Texas at El Paso

#### Why Significant Wave Height And Rogue Waves Are So Defined: A Possible Explanation, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

Data analysis has shown that if we want to describe the wave pattern by a single characteristic, the best characteristic is the average height of the highest one third of the waves; this characteristic is called significant wave height. Once we know the value of this characteristic, a natural next question is: what is the highest wave that we should normally observe -- so that waves higher than this amount would be rare ("rogue"). Empirically, it has been shown that rogue waves are best defined as the ones which are at least twice higher than the significant wave height. In this ...

How To Explain The Relation Between Different Empirical Covid-19 Self-Isolation Periods, 2020 El Paso Community College

#### How To Explain The Relation Between Different Empirical Covid-19 Self-Isolation Periods, Christian Servin, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

Empirical data implies that, to avoid infecting others, an asymptomatic career of Covid-19 should self-isolate for a period of 10 days, a patient who experiences symptoms for 20 days, and a person who was in contact with a Covid-19 patient should self-isolate for 14 days. In this paper, we use Laplace's Principle of Insufficient Reason to provide a simple explanation for the relation between these three self-isolation periods.

How To Separate Absolute And Relative Error Components: Interval Case, 2020 El Paso Community College

#### How To Separate Absolute And Relative Error Components: Interval Case, Christian Servin, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

Usually, measurement errors contain both absolute and relative components. To correctly gauge the amount of measurement error for all possible values of the measured quantity, it is important to separate these two error components. For probabilistic uncertainty, this separation can be obtained by using traditional probabilistic techniques. The problem is that in many practical situations, we do not know the probability distribution, we only know the upper bound on the measurement error. In such situations of interval uncertainty, separation of absolute and relative error components is not easy. In this paper, we propose a technique for such a separation based ...

Mathematical Modeling Of Nonlinear Problem Biological Population In Not Divergent Form With Absorption, And Variable Density, 2020 National University of Uzbekistan

#### 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, 2020 Southern Methodist University

#### 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 ...

On The Solvability Of Hypersingular Equation Of Peridynamics, 2020 National University of Uzbekistan

#### On The Solvability Of Hypersingular Equation Of Peridynamics, Shavkat Alimov, Shukhrat Sheraliev

*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*

The integro-differential equation of peridynamics with hyper-singular kernel is considered. The existence and uniqueness of solution is proved.

Does Transition To Democracy Lead To Chaos: A Theorem, 2020 University of Texas at El Paso

#### Does Transition To Democracy Lead To Chaos: A Theorem, Olga Kosheleva, Vladik Kreinovich

*Departmental Technical Reports (CS)*

When a country transitions to democracy, at first, many political parties appear. A natural question is whether the number of such parties feasible and reasonable -- or whether this is a complete chaos. In this paper, we formulate a simplified version of this question in precise terms and show that the number of parties will be feasible -- i.e., that transition to democracy does not lead to chaos.

Evaluating Performance Of Openmp Tasks In A Seismic Stencil Application, 2020 Stony Brook University

#### Evaluating Performance Of Openmp Tasks In A Seismic Stencil Application, Eric Raut, Jie Meng, Mauricio Araya-Polo, Barbara Chapman

*Department of Applied Mathematics & Statistics Faculty Publications*

Simulations based on stencil computations (widely used in geosciences) have been dominated by the MPI+OpenMP programming model paradigm. Little effort has been devoted to experimenting with task-based parallelism in this context. We address this by introducing OpenMP task parallelism into the kernel of an industrial seismic modeling code, Minimod. We observe that even for these highly regular stencil computations, taskified kernels are competitive with traditional OpenMP-augmented loops, and in some experiments tasks even outperform loop parallelism.

This promising result sets the stage for more complex computational patterns. Simulations involve more than just the stencil calculation: a collection of kernels ...

How To Extend Interval Arithmetic So That Inverse And Division Are Always Defined, 2020 University of California, Merced

#### How To Extend Interval Arithmetic So That Inverse And Division Are Always Defined, Tahea Hossain, Jonathan Rivera, Yash Sharma, Vladik Kreinovich

*Departmental Technical Reports (CS)*

In many real-life data processing situations, we only know the values of the inputs with interval uncertainty. In such situations, it is necessary to take this interval uncertainty into account when processing data. Most existing methods for dealing with interval uncertainty are based on interval arithmetic, i.e., on the formulas that describe the range of possible values of the result of an arithmetic operation when the inputs are known with interval uncertainty. For most arithmetic operations, this range is also an interval, but for division, the range is sometimes a disjoint union of two semi-infinite intervals. It is therefore ...

Matrix Low Rank Approximation At Sublinear Cost, 2020 The Graduate Center, City University of New York

#### 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 ...