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An Optimal Transportation Theory For Interacting Paths, Rene Cabrera 2022 University of Massachusetts Amherst

An Optimal Transportation Theory For Interacting Paths, Rene Cabrera

Doctoral Dissertations

In this work we study a modification of the Monge-Kantorovich problem taking into account path dependence and interaction effects between particles. We prove existence of solutions under mild conditions on the data, and after imposing stronger conditions, we characterize the minimizers by relating them to an auxiliary Monge-Kantorovich problem of the more standard kind. With this notion of how particles interact and travel along paths, we produce a dual problem. The main novelty here is to incorporate an interaction effect to the optimal path transport problem. This covers for instance, N-body dynamics when the underlying measures are discrete. Lastly ...


Self-Repelling Elastic Manifolds With Low Dimensional Range, Carl Mueller, Eyal Neumann 2022 University of Rochester, Rochester, NY 14627, USA

Self-Repelling Elastic Manifolds With Low Dimensional Range, Carl Mueller, Eyal Neumann

Journal of Stochastic Analysis

No abstract provided.


Induced Matrices: Recurrences And Markov Chains, Philip Feinsilver 2022 Southern Illinois University, Carbondale, Illinois 62901, USA

Induced Matrices: Recurrences And Markov Chains, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.


Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs 2022 University of Nebraska at Omaha

Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs

Student Research and Creative Activity Fair

The University of Omaha math department's Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes.

Now there are three difficulty tiers to POW problems, roughly corresponding ...


(R1517) Asymptotical Stability Of Riemann-Liouville Fractional Neutral Systems With Multiple Time-Varying Delays, Erdal Korkmaz, Abdulhamit Ozdemir 2022 Muş Alparslan University

(R1517) Asymptotical Stability Of Riemann-Liouville Fractional Neutral Systems With Multiple Time-Varying Delays, Erdal Korkmaz, Abdulhamit Ozdemir

Applications and Applied Mathematics: An International Journal (AAM)

In this manuscript, we investigate the asymptotical stability of solutions of Riemann-Liouville fractional neutral systems associated to multiple time-varying delays. Then, we use the linear matrix inequality (LMI) and the Lyapunov-Krasovskii method to obtain sufficient conditions for the asymptotical stability of solutions of the system when the given delays are time dependent and one of them is unbounded. Finally, we present some examples to indicate the efficacy of the consequences obtained.


(R1516) Results On Fekete-Szegö Problem For Some New Subclasses Of Univalent Analytic Functions With Fractional-Order Operators, N. Singha, R. Kumar 2022 Pandit Deendayal Petroleum University

(R1516) Results On Fekete-Szegö Problem For Some New Subclasses Of Univalent Analytic Functions With Fractional-Order Operators, N. Singha, R. Kumar

Applications and Applied Mathematics: An International Journal (AAM)

We introduce some new subclasses of analytic functions which are univalent in an open unit disk by means of fractional calculus. The elemental interest is to explore the significance of fractional-order operators while formulating a few distinct subclasses of univalent analytic functions. Present work establishes the Fekete-Szegö inequality for the proposed subclasses. In addition, some classical Fekete-Szegö problems have also been retrieved and discussed as particular cases of the presented work. To make the suggested work more evident, an extremal function is also provided for which a sharp upper bound is attained.


(R1521) On Weighted Lacunary Interpolation, Swarnima Bahadur, Sariya Bano 2022 University of Lucknow

(R1521) On Weighted Lacunary Interpolation, Swarnima Bahadur, Sariya Bano

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we considered the non-uniformly distributed zeros on the unit circle, which are obtained by projecting vertically the zeros of the derivative of Legendre polynomial together with x=1 and x=-1 onto the unit circle. We prescribed the function on the above said nodes, while its second derivative at all nodes except at x=1 and x=-1 with suitable weight function and obtained the existence, explicit forms and establish a convergence theorem for such interpolatory polynomial. We call such interpolation as weighted Lacunary interpolation on the unit circle.


Data-Driven Analysis Of Drug And Substance Abuse Rates Across The Varying Regions In The United States Of America, Reem Saleh 2022 Portland State University

Data-Driven Analysis Of Drug And Substance Abuse Rates Across The Varying Regions In The United States Of America, Reem Saleh

University Honors Theses

Drugs and substance abuse is one of the leading causes of death for adolescents in the United States. The consequences of using these drugs are profound and can cause both damage to one's physical and psychological health. The rates of drug abuse in the United States continue to increase over the years. This paper analyzes the trends in rates of drug abuse in the four regions in the United States. It looks at the rates in cocaine, cigarettes, marijuana, and tobacco. A preliminary analysis was done to look at the trend in rates followed by an ARIMA time series ...


D'Alembert Functions On Groups, Jing Wang 2022 University of Windsor

D'Alembert Functions On Groups, Jing Wang

Major Papers

This major paper is devoted to the study of pre-d'Alembert functions and d'Alembert functions on groups.

In this paper, we first study additive and multiplicative Cauchy equations and the sine addition formula on groups. Then we discuss some properties ofpre-d'Alembert functions on groups. In particular, we characterize when a pre-d'Alembert function is abelian, and furthermore get the general form of abelian pre-d'Alembert functions on groups. Finally we achieve our goal: we obtain the structure of the solution by group representation theory.


A New Model For Predicting The Drag And Lift Forces Of Turbulent Newtonian Flow On Arbitrarily Shaped Shells On The Seafloor, Carley R. Walker, James V. Lambers, Julian Simeonov 2022 University of Southern Mississippi

A New Model For Predicting The Drag And Lift Forces Of Turbulent Newtonian Flow On Arbitrarily Shaped Shells On The Seafloor, Carley R. Walker, James V. Lambers, Julian Simeonov

Dissertations

Currently, all forecasts of currents, waves, and seafloor evolution are limited by a lack of fundamental knowledge and the parameterization of small-scale processes at the seafloor-ocean interface. Commonly used Euler-Lagrange models for sediment transport require parameterizations of the drag and lift forces acting on the particles. However, current parameterizations for these forces only work for spherical particles. In this dissertation we propose a new method for predicting the drag and lift forces on arbitrarily shaped objects at arbitrary orientations with respect to the direction of flow that will ultimately provide models for predicting the sediment sorting processes that lead to ...


Data And Algorithmic Modeling Approaches To Count Data, Andraya Hack 2022 Murray State University

Data And Algorithmic Modeling Approaches To Count Data, Andraya Hack

Honors College Theses

Various techniques are used to create predictions based on count data. This type of data takes the form of a non-negative integers such as the number of claims an insurance policy holder may make. These predictions can allow people to prepare for likely outcomes. Thus, it is important to know how accurate the predictions are. Traditional statistical approaches for predicting count data include Poisson regression as well as negative binomial regression. Both methods also have a zero-inflated version that can be used when the data has an overabundance of zeros. Another procedure is to use computer algorithms, also known as ...


Lattice Reduction Algorithms, Juan Ortega 2022 California State University, San Bernardino

Lattice Reduction Algorithms, Juan Ortega

Electronic Theses, Projects, and Dissertations

The purpose of this thesis is to propose and analyze an algorithm that follows
similar steps of Guassian Lattice Reduction Algorithm in two-dimensions and applying
them to three-dimensions. We start off by discussing the importance of cryptography in
our day to day lives. Then we dive into some linear algebra and discuss specific topics that
will later help us in understanding lattice reduction algorithms. We discuss two lattice
problems: the shortest vector problem and the closest vector problem. Then we introduce
two types of lattice reduction algorithms: Guassian Lattice Reduction in two-dimensions
and the LLL Algortihm. We illustrate how both ...


Error Terms For The Trapezoid, Midpoint, And Simpson's Rules, Jessica E. Coen 2022 California State University - San Bernardino

Error Terms For The Trapezoid, Midpoint, And Simpson's Rules, Jessica E. Coen

Electronic Theses, Projects, and Dissertations

When it is not possible to integrate a function we resort to Numerical Integration. For example the ubiquitous Normal curve tables are obtained using Numerical Integration. The antiderivative of the defining function for the normal curve involves the formula for antiderivative of e-x^2 which can't be expressed in the terms of basic functions.

Simpson's rule is studied in most Calculus books, and in all undergraduate Numerical Analysis books, but proofs are not provided. Hence if one is interested in a proof of Simpson's rule, either it can be found in advanced Numerical Analysis books as ...


Some Results About Reproducing Kernel Hilbert Spaces Of Certain Structure, Jesse Gabriel Sautel 2022 University of Tennessee, Knoxville

Some Results About Reproducing Kernel Hilbert Spaces Of Certain Structure, Jesse Gabriel Sautel

Doctoral Dissertations

The theory of reproducing kernel Hilbert spaces has been crucial to the development of many of the most significant modern ideas behind functional analysis. In particular, there are two classes of reproducing kernel Hilbert spaces that have seen plenty of interest: that of complete Nevanlinna-Pick spaces and de Branges-Rovnyak spaces.

In this dissertation, we prove some results involving each type of space separately as well as one result regarding their potential overlap. It turns out that a de Branges-Rovnyak space is also of complete Nevanlinna-Pick type as long as there exists a multiplier satisfying a certain identity.

Further, we extend ...


Sequential Deformations Of Hadamard Matrices And Commuting Squares, Shuler G. Hopkins 2022 University of Tennessee, Knoxville

Sequential Deformations Of Hadamard Matrices And Commuting Squares, Shuler G. Hopkins

Doctoral Dissertations

In this dissertation, we study analytic and sequential deformations of commuting squares of finite dimensional von Neumann algebras, with applications to the theory of complex Hadamard matrices. The main goal is to shed some light on the structure of the algebraic manifold of spin model commuting squares (i.e., commuting squares based on complex Hadamard matrices), in the neighborhood of the standard commuting square (i.e., the commuting square corresponding to the Fourier matrix). We prove two types of results: Non-existence results for deformations in certain directions in the tangent space to the algebraic manifold of commuting squares (chapters 3 ...


Applying Data Analytics As An Alternative To Subjective Rankings Of Players In Fantasy Basketball, Christopher Collins 2022 United States Military Academy

Applying Data Analytics As An Alternative To Subjective Rankings Of Players In Fantasy Basketball, Christopher Collins

Mathematica Militaris

This paper demonstrates the ranking of players for fantasy basketball using one of the platforms of Multi Criteria Decision Making (MCDM), the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method. Specially, it compares results of TOPSIS generated fantasy rankings from the 2016-2017 NBA Season against industry fantasy experts’ 2017-2018 NBA pre-season rankings. Fantasy experts combine various techniques to create their rankings. Frequently blending quantitative and qualitative factors in order to project bottom-up rankings, they incongruently mix subjective and objective criterion. Conversely, TOPSIS is a mathematical way of doing literally what its name describes, ranking by a ...


Computational Complexity Reduction Of Deep Neural Networks, Mee Seong Im, Venkat Dasari 2022 United States Naval Academy

Computational Complexity Reduction Of Deep Neural Networks, Mee Seong Im, Venkat Dasari

Mathematica Militaris

Deep neural networks (DNN) have been widely used and play a major role in the field of computer vision and autonomous navigation. However, these DNNs are computationally complex and their deployment over resource-constrained platforms is difficult without additional optimizations and customization.

In this manuscript, we describe an overview of DNN architecture and propose methods to reduce computational complexity in order to accelerate training and inference speeds to fit them on edge computing platforms with low computational resources.


On The Geometry Of Multi-Affine Polynomials, Junquan Xiao 2022 The University of Western Ontario

On The Geometry Of Multi-Affine Polynomials, Junquan Xiao

Electronic Thesis and Dissertation Repository

This work investigates several geometric properties of the solutions of the multi-affine polynomials. Chapters 1, 2 discuss two different notions of invariant circles. Chapter 3 gives several loci of polynomials of degree three. A locus of a complex polynomial p(z) is a minimal, with respect to inclusion, set that contains at least one point of every solution of the polarization of the polynomial. The study of such objects allows one to improve upon know results about the location of zeros and critical points of complex polynomials, see for example [22] and [24]. A complex polynomial has many loci. It ...


Artsy Chaos: The Secret Life Of A Class Of Trigonometric Sums, Kaleb Swieringa, Joelena Brown, Rachael Harbaugh, Francis Nadolny 2022 Ohio Northern University

Artsy Chaos: The Secret Life Of A Class Of Trigonometric Sums, Kaleb Swieringa, Joelena Brown, Rachael Harbaugh, Francis Nadolny

ONU Student Research Colloquium

We start from classical trigonometric sums (of terms such as k^n*cos(k), k^n*sin(k) - where n is a positive integer). These classical sums allow fairly straightforward closed form representations. In our work we considered changing the arguments of the trigonometric factors to powers (so that they get replaced by cos(k^a) and sin(k^a) - for a positive real exponent that may or may not be an integer), while also introducing in any term of such a sum a "rotational" factor of the form omega^k, where "omega" is a complex number of modulus 1 ...


Impact Of Treatment Length On Individuals With Substance Use Disorders In Allegheny County, Cassie DiBenedetti, Kate Rosello 2022 Duquesne University

Impact Of Treatment Length On Individuals With Substance Use Disorders In Allegheny County, Cassie Dibenedetti, Kate Rosello

Undergraduate Research and Scholarship Symposium

Auberle social services is opening the Family Healing Center (FHC), a level 3.5 treatment program in Pittsburgh, PA that provides housing and 24-hour support for families struggling with opioid addiction. We partnered with Auberle to study characteristics of individuals receiving level 3.5 treatment and to determine whether longer treatment lengths correlate with fewer adverse outcomes. We obtained data from the Allegheny County Department of Human Services on 2,016 individuals admitted to level 3.5 treatment in 2019. The data included birth year, race, gender, admittance date, discharge date, and Children Youth and Family (CYF) incidents before and ...


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