Digital Commons Network^™

A Jump-Diffusion Process For Asset Price With Non-Independent Jumps, Yihren Wu, Majnu John

Journal of Stochastic Analysis

No abstract provided.

Hamilton Cycles In Bidirected Complete Graphs, Arthur Busch, Mohammed A. Mutar, Daniel Slilaty

Mathematics and Statistics Faculty Publications

Zaslavsky observed that the topics of directed cycles in directed graphs and alternating cycles in edge 2-colored graphs have a common generalization in the study of coherent cycles in bidirected graphs. There are classical theorems by Camion, Harary and Moser, Häggkvist and Manoussakis, and Saad which relate strong connectivity and Hamiltonicity in directed "complete" graphs and edge 2-colored "complete" graphs. We prove two analogues to these theorems for bidirected "complete" signed graphs.

Quantization Of The Monotone Poisson Central Limit Theorem, Yungang Lu

Journal of Stochastic Analysis

No abstract provided.

Mitigation Impact Of Statewide Non-Pharmaceutical Policies On Covid-19: An Application Of Infectious Disease Transmission Model And Partially Observed Markov Process To New Mexico, Xingya Ma

Mathematics & Statistics ETDs

This thesis is an application of epidemiological models for infectious disease transmission and the use of partially observed Markov process (POMP) for model fitting. It focuses on COVID-19 pandemic in the state of New Mexico. The analysis covered March 2020 to June 2021. Daily data of COVID19 cases and deaths and a daily index of eleven statewide government non-pharmaceutical intervention (NPI) policies were collected from six public sources and were validated. These data were integrated through the Susceptible-Exposed-Infected-Removed (SEIR) model. Estimated daily transmission rates between the model compartments quantify the impact of the mitigation policies, and show that transmission rates …

Geometry And Dynamics Of Rolling Systems, Bowei Zhao

Arts & Sciences Graduate Student Theses and Dissertations

Billiard systems, broadly speaking, may be regarded as models of mechanical systems in which rigid parts interact through elastic impulsive collision forces. When it is desired or necessary to account for linear/angular momentum exchange in collisions involving a spherical body, a type of billiard system often referred to as no-slip has been used. Previous work indicated that no-slip billiards resemble non-holonomic systems, specifically, systems consisting of a ball rolling on surface. In prior research, such connections were only observed numerically and were restricted to very special surfaces. In this thesis, it is shown that no-slip billiard and rolling systems are …

Preferential Stiffness And The Crack-Tip Fields Of An Elastic Porous Solid Based On The Density-Dependent Moduli Model, Hyun C. Yoon, S. M. Mallikarjunaiah, Dambaru Bhatta

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study the preferential stiffness and the crack-tip fields for an elastic porous solid of which material properties are dependent upon the density. Such a description is necessary to describe the failure that can be caused by damaged pores in many porous bodies such as ceramics, concrete and human bones. To that end, we revisit a new class of implicit constitutive relations under the assumption of small deformation. Although the constitutive relationship \textit{appears linear} in both the Cauchy stress and linearized strain, the governing equation bestowed from the balance of linear momentum results in a quasi-linear partial …

Interactive White Boards In A Secondary Mathematics Classroom, Leann Bolhuis

Mathematics Graduate Theses

"A Formal Portfolio Submitted to the Faculty of the DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE In Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE IN MATHEMATICS".

Applications Of A Superposed Ornstein-Uhlenbeck Type Processes, Santatriniaina Avotra Randrianambinina, Julius Esunge

Journal of Stochastic Analysis

No abstract provided.

Ambientes De Inclusión Para El Desarrollo Del Pensamiento Numérico Con Población Con Síndrome De Down, Luisa Valeria Escobar Buitrago, Ingry Yuliana Torres Garzón, Juan David Firigua Bejarano

Educación

La importancia de tratar sobre una educación inclusiva es hacer que la humanidad obtenga la aceptación hacia la diversidad, donde se encuentre un mundo lleno de posibilidades reconociendo todos los tipos de población entre ella las personas con Síndrome de Down, lo cual consiste en que la educación esté centrado en el respeto y la valoración de la diversidad, haciendo un enfoque general en las necesidades que esta población tiene, desarrollando habilidades para su desenvolvimiento tanto personal como laboral en determinada sociedad, por lo tanto el objetivo principal de este trabajo es desarrollar el pensamiento numérico de los estudiantes de …

How The Perceived Value Of Education, Parental Influences, And Students' Perceived Success Affect Post-Graduate Decisions, Valerie Blanchard

Honors Projects in Mathematics

While technical education has been enhanced in many ways over the past few decades, college is still the preferred post-graduate path for many students and is the societal norm. This study will analyze the value that students view in their career path that leads them to make their post-graduate decisions. The goal of this research is to better understand why students pursue college and how these decisions come to be with specific attention paid to the impact of gender, interests, and self-efficacy. This understanding can educate others about the gravity of social norms and can start conversations about how to …

Meertens Number And Its Variations, Chai Wah Wu

Communications on Number Theory and Combinatorial Theory

In 1998, Bird introduced Meertens numbers as numbers that are invariant under a map similar to the Gödel encoding. In base 10, the only known Meertens number is 81312000. We look at some properties of Meertens numbers and consider variations of this concept. In particular, we consider variations of Meertens numbers where there is a finite time algorithm to decide whether such numbers exist, exhibit infinite families of these variations and provide bounds on parameters needed for their existence.

On The Diagonalizability And Factorizability Of Quadratic Boson Fields, Luigi Accardi, Andreas Boukas, Yungang Lu, Alexander Teretenkov

Journal of Stochastic Analysis

No abstract provided.

How To Choose A Law Review: An Empirical Study, Ignacio Cofone, Pierre-Jean G. Malé

Journal of Legal Education

No abstract provided.

A View Into Secondary Education Mathematics, Thomas Krieger Jr.

Honors Theses

Teaching methods, and the effects they can have on students, are important to consider for a classroom because when teaching you should allow for every student to have an opportunity. Every student should feel encouraged in the classroom, however not every method may allow for that. An important task for a teacher is to find out how to reach their students in their classroom; be it adapting methods or choosing when to implement one item over another. This task differs with every student that enters the classroom as no student is the same. Every students’ differences stem from their academic …

One-Parameter Darboux-Deformed Fibonacci Numbers, Stefani C. Mancas, H. C. Rosu

Publications

One-parameter Darboux deformations are effected for the simple ODE satisfied by the continuous generalizations of the Fibonacci sequence recently discussed by Faraoni and Atieh [Symmetry 13, 200 (2021)], who promoted a formal analogy with the Friedmann equation in the FLRW homogeneous cosmology. The method allows the introduction of deformations of the continuous Fibonacci sequences, hence of Darboux-deformed Fibonacci (non integer) numbers. Considering the same ODE as a parametric oscillator equation, the Ermakov-Lewis invariants for these sequences are also discussed.

Predicting The Outcomes Of Internet-Based Cognitive Behavioral Therapy For Tinnitus: Applications Of Artificial Neural Network And Support Vector Machine, Hansapani Rodrigo, Eldré W. Beukes, Gerhard Andersson, Vinaya Manchaiah

School of Mathematical & Statistical Sciences Faculty Publications

Purpose:

Internet-based cognitive behavioral therapy (ICBT) has been found to be effective for tinnitus management, although there is limited understanding about who will benefit the most from ICBT. Traditional statistical models have largely failed to identify the nonlinear associations and hence find strong predictors of success with ICBT. This study aimed at examining the use of an artificial neural network (ANN) and support vector machine (SVM) to identify variables associated with treatment success in ICBT for tinnitus.

Method:

The study involved a secondary analysis of data from 228 individuals who had completed ICBT in previous intervention studies. A 13-point reduction …

Ideals Of Functions With Compact Support In The Integer-Valued Case, Themba Dube, Oghenetega Ighedo, Batsile Tlharesakgosi

Mathematics, Physics, and Computer Science Faculty Articles and Research

For a zero-dimensional Hausdorff space X, denote, as usual, by C(X, ℤ) the ring of continuous integer-valued functions on X. If f ∈ C(X, ℤ), denote by Z(f) the set of all points of X that are mapped to 0 by f. The set C_K(X; ℤ) = {f ∈ C(X; ℤ) | cl_X(X \ Z(f)) is compact} is the integer-valued analogue of the ideal of functions with compact support in C(X). By first working in the category of locales and then interpreting …

The History Of The Enigma Machine, Jenna Siobhan Parkinson

History Publications

The history of the Enigma machine begins with the invention of the rotor-based cipher machine in 1915. Various models for rotor-based cipher machines were developed somewhat simultaneously in different parts of the world. However, the first documented rotor machine was developed by Dutch naval officers in 1915. Nonetheless, the Enigma machine was officially invented following the end of World War I by Arthur Scherbius in 1918 (Faint, 2016).

On Moments Of Certain Families Of L-Functions, Gopal Maiti

Doctoral Theses

In this thesis, I described the notion of moments of L-functions in some families. Then I discussed some problems on estimating moments of L-functions. As applications, I showed some simultaneous non-vanishing and correlation results of certain product L-functions over number fields as well as function fields.

Local Well-Posedness Of The Cauchy Problem For A P -Adic Nagumo-Type Equation, L. F. Chacón-Cortés, C. A. Garcia-Bibiano, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

We introduce a new family of p -adic nonlinear evolution equations. We establish the local well-posedness of the Cauchy problem for these equations in Sobolev-type spaces. For a certain subfamily, we show that the blow-up phenomenon occurs and provide numerical simulations showing this phenomenon.

Congruences For Consecutive Coefficients Of Gaussian Polynomials With Crank Statistics, Dennis Eichhorn, Lydia Engle, Brandt Kronholm

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we establish infinite families of congruences in consecutive arithmetic progressions modulo any odd prime ℓ for the function p ( n , m , N ) , which enumerates the partitions of n into at most m parts with no part larger than N . We also treat the function p ( n , m , ( a , b ] ) , which bounds the largest part above and below, and obtain similar infinite families of congruences.

For m ≤ 4 and ℓ = 3 , simple combinatorial statistics called "cranks" witness these congruences. We prove …

(R1886) Effect Of Aggregation Function In Moma-Plus Method For Obtaining Pareto Optimal Solutions, Alexandre Som, Abdoulaye Compaoré, Kounhinir Somé, Blaise Somé

Applications and Applied Mathematics: An International Journal (AAM)

In this work, we have proposed some variants of MOMA-Plus method that we have numerically tested for the resolution of nonlinear multiobjective optimization problems. This MOMA-Plus method and variants differ from each other by the choice of aggregation functions in order to reduce the number of objective functions. The theoretical results allowing us to use these aggregation functions to transform multiobjective optimization problems into single objective optimization problems are proved by two theorems. This study has highlighted the advantages of each aggregation function according to the type of Pareto front of the optimization problem. Six benchmarks test problems have been …

Which Interval-Valued Alternatives Are Possibly Optimal If We Use Hurwicz Criterion, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, for each alternative i, we do not know the corresponding gain xi, we only know the interval [li,ui] of possible gains. In such situations, a reasonable way to select an alternative is to choose some value α from the interval [0,1] and select the alternative i for which the Hurwicz combination α*ui + (1 − α)*li is the largest possible. In situations when we do not know the user's α, a reasonable idea is to select all alternatives that are optimal for some α. In this paper, we describe a feasible algorithm for such a selection.

(R1885) Analytical And Numerical Solutions Of A Fractional-Order Mathematical Model Of Tumor Growth For Variable Killing Rate, N. Singha, C. Nahak

Applications and Applied Mathematics: An International Journal (AAM)

This work intends to analyze the dynamics of the most aggressive form of brain tumor, glioblastomas, by following a fractional calculus approach. In describing memory preserving models, the non-local fractional derivatives not only deliver enhanced results but also acknowledge new avenues to be further explored. We suggest a mathematical model of fractional-order Burgess equation for new research perspectives of gliomas, which shall be interesting for biomedical and mathematical researchers. We replace the classical derivative with a non-integer derivative and attempt to retrieve the classical solution as a particular case. The prime motive is to acquire both analytical and numerical solutions …

(R1500) Type-I Generalized Spherical Interval Valued Fuzzy Soft Sets In Medical Diagnosis For Decision Making, M. Palanikumar, K. Arulmozhi

Applications and Applied Mathematics: An International Journal (AAM)

In the present communication, we introduce the concept of Type-I generalized spherical interval valued fuzzy soft set and define some operations. It is a generalization of the interval valued fuzzy soft set and the spherical fuzzy soft set. The spherical interval valued fuzzy soft set theory satisfies the condition that the sum of its degrees of positive, neutral, and negative membership does not exceed unity and that these parameters are assigned independently. We also propose an algorithm to solve the decision making problem based on a Type-I generalized soft set model. We introduce a similarity measure based on the Type-I …

(R1978) Heated Laminar Vertical Jet Of Psudoplastic Fluids-Against Gravity, Manisha Patel, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

A heated laminar jet of Pseudo-plastic fluid flowing vertically upwards from a long narrow slit into a region of the same fluid which is at a rest and at a uniform temperature is considered. The governing non-linear Partial differential equations (PDEs) for the defined flow problem are transformed into non-linear ordinary differential equations using the effective similarity technique-one parameter deductive group theory method. The obtained non-linear coupled Ordinary differential equations are solved and the results are presented by graphs. The effect of the Prandtl number and Grashof number on the velocity and temperature of the jet flow is discussed. Also, …

Data Processing Under Fuzzy Uncertainty: Towards More Accurate Algorithms, Marina Tuyako Mizukoshi, Weldon Lodwick, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Data that we process comes either from measurements or from experts -- or from the results of previous data processing that were also based on measurements and/or expert estimates. In both cases, the data is imprecise. To gauge the accuracy of the results of data processing, we need to take the corresponding data uncertainty into account. In this paper, we describe a new algorithm for taking fuzzy uncertainty into account, an algorithm that, for small number of inputs, leads to the same or even better accuracy than the previously proposed methods.

Non-Localized Physical Processes Can Help Speed Up Computations, Be It Hidden Variables In Quantum Physics Or Non-Localized Energy In General Relativity, Michael Zakharevich, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

While most physical processes are localized -- in the sense that each event can only affect events in its close vicinity -- many physicists believe that some processes are non-local. These beliefs range from more heretic -- such as hidden variables in quantum physics -- to more widely accepted, such as the non-local character of energy in General Relativity. In this paper, we attract attention to the fact that non-local processes bring in the possibility of drastically speeding up computations.

Graph Approach To Uncertainty Quantification, Hector A. Reyes, Cliff Joslyn, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional analysis of uncertainty of the result of data processing assumes that all measurement errors are independent. In reality, there may be common factor affecting these errors, so these errors may be dependent. In such cases, the independence assumption may lead to underestimation of uncertainty. In such cases, a guaranteed way to be on the safe side is to make no assumption about independence at all. In practice, however, we may have information that a few pairs of measurement errors are indeed independent -- while we still have no information about all other pairs. Alternatively, we may suspect that for …

Systems Approach Explains Why Low Heart Rate Variability Is Correlated With Depression (And Suicidal Thoughts), Francisco Zapata, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

Depression is a serious medical problem. If diagnosed early, it can usually be cured, but if left undetected, it can lead to suicidal thoughts and behavior. The early stages of depression are difficult to diagnose. Recently, researchers found a promising approach to such diagnosis -- it turns out that depression is correlated with low heart rate variability. In this paper, we show that the general systems approach can explain this empirical relation.