Hamming Codes, 2020 University of Washington, Tacoma

#### Hamming Codes, Steve Mwangi, Sterling Quinn

*Access*: Interdisciplinary Journal of Student Research and Scholarship*

We will be looking into the application of Matrix Algebra in forming Hamming Codes. Hamming Codes are essential not just in the detection of errors, but also in the linear concurrent correction of these errors. The matrices we will use, will have entries that are binary units. Binary units are mathematically convenient, and their simplicity permits the representation of many open and closed circuits used in communication systems. The entries in the matrices will represent a message that is meant for transmission or reception, akin to the contemporary application of Hamming Codes in wireless communication. We will use Hamming (7 ...

Applying The Data: Predictive Analytics In Sport, 2020 University of Washington, Tacoma

#### Applying The Data: Predictive Analytics In Sport, Anthony Teeter, Margo Bergman

*Access*: Interdisciplinary Journal of Student Research and Scholarship*

The history of wagering predictions and their impact on wide reaching disciplines such as statistics and economics dates to at least the 1700’s, if not before. Predicting the outcomes of sports is a multibillion-dollar business that capitalizes on these tools but is in constant development with the addition of big data analytics methods. Sportsline.com, a popular website for fantasy sports leagues, provides odds predictions in multiple sports, produces proprietary computer models of both winning and losing teams, and provides specific point estimates. To test likely candidates for inclusion in these prediction algorithms, the authors developed a computer model ...

The Optimum Maximum Allowed Displacement In Monte Carlo Simulation Of One-Component Plasma, 2020 Arab American University

#### The Optimum Maximum Allowed Displacement In Monte Carlo Simulation Of One-Component Plasma, Iyad Suwan

*Journal of the Arab American University مجلة الجامعة العربية الامريكية للبحوث*

In this paper, a periodic One-Component Plasma (OCP) system of N-point particles is simulated by Monte Carlo (MC) technique in three dimensions. Because of the long range nature of the Coulomb potential, no cut-off distance is considered in calculations (i.e, for each particle i, the effect of the other N-1 particles on i, is taken into account). The maximum allowed displacement "dmax" used in MC simulation controls the convergence to the equilibrium state of the system. An optimum maximum allowed displacement, O-dmax, is found and is given by a function of the temperature and the density of the system ...

The Optimum Maximum Allowed Displacement In Monte Carlo Simulation Of Lennard-Jones Potential Point Particles, 2020 Arab American University

#### The Optimum Maximum Allowed Displacement In Monte Carlo Simulation Of Lennard-Jones Potential Point Particles, Iyad Suwan

*Journal of the Arab American University مجلة الجامعة العربية الامريكية للبحوث*

In this paper, periodic systems of N point particles with Lennard-Jones potential are simulated in three dimensional space using Monte Carlo technique. The maximum allowed displacement used in Monte Carlo simulation of any N-particle system controls the convergence of the calculated potential energy to its physical situation. The optimum maximum allowed displacement associated with 50% acceptance rate is found. Since Lennard-Jones potential is a short range one, it is considered to be zero beyond some cut-off radius. The optimum dimensionless cut-off radius in the Lennard-Jones case is 2.5, which is used in simulations. An explicit mathematical formula for the ...

Controlling Aircraft Yaw Movement By Interval Type-2 Fuzzy Logic, 2020 University of Technology, Iraq

#### Controlling Aircraft Yaw Movement By Interval Type-2 Fuzzy Logic, Yamama Shafeek, Laith Majeed, Rasha Naji

*Emirates Journal for Engineering Research*

Aircraft yaw movement is essential in maneuvering; it has been controlled by some methods which achieved tracking but not fast enough. This paper performs the dynamic modeling of aircraft yaw movement and develops PI and PI-like interval type-2 fuzzy logic controller for the model. The mathematical model is derived by inserting the parameters values of single-engine Navion aircraft into standard equations. Using Matlab/ Simulink platform, the controllers' effectivity is tested and verified in two different cases; system without disturbance and when system is disturbed by some wind gust to investigate the system robustness. Simulation results show that PI controller response ...

A Phase-Field Approach To Diffusion-Driven Fracture, 2020 Louisiana State University and Agricultural and Mechanical College

#### 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 ...

Analytical And Computational Modelling Of The Ranque-Hilsch Vortex Tube, 2020 The University of Western Ontario

#### Analytical And Computational Modelling Of The Ranque-Hilsch Vortex Tube, Nolan J. Dyck

*Electronic Thesis and Dissertation Repository*

The Ranque-Hilsch vortex tube (RHVT) is a simple mechanical device with no moving parts capable of separating a supply of compressed fluid into hot and cold streams through a process called temperature separation. The overall aim is to develop models which can be used to assess the temperature separation mechanisms in the RHVT, leading to a better overall understanding of the underlying physics. The introductory chapter contains a thermodynamic analysis and introduction to the flow physics, alongside three miniature literature reviews and critiques identifying research gaps.

The body of the thesis contains three articles. The first article studies the flow ...

Exploring The Potential Of Sparse Coding For Machine Learning, 2020 Portland State University

#### Exploring The Potential Of Sparse Coding For Machine Learning, Sheng Yang Lundquist

*Dissertations and Theses*

While deep learning has proven to be successful for various tasks in the field of computer vision, there are several limitations of deep-learning models when compared to human performance. Specifically, human vision is largely robust to noise and distortions, whereas deep learning performance tends to be brittle to modifications of test images, including being susceptible to adversarial examples. Additionally, deep-learning methods typically require very large collections of training examples for good performance on a task, whereas humans can learn to perform the same task with a much smaller number of training examples.

In this dissertation, I investigate whether the use ...

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 ...

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 ...

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 ...