Mathematics

Pythagorean Theorem Area Proofs, Rachel Morley

Mathematics Undergraduate Theses

This composition is intended to walk the reader through four proofs of the pythagorean theorem that are based on area. It could be used in a classroom to solidify the pythagorean theorem after studying Neutral and Euclidean Geometries.

Go to article

The Evolution Of Psychological Altruism, Gualtiero Piccinini, Armin Schulz

Philosophy Faculty Works

We argue that there are two different kinds of altruistic motivation: classical psychological altruism, which generates ultimate desires to help other organisms at least partly for those organisms’ sake, and nonclassical psychological altruism, which generates ultimate desires to help other organisms for the sake of the organism providing the help. We then argue that classical psychological altruism is adaptive if the desire to help others is intergenerationally reliable and, thus, need not be learned. Nonclassical psychological altruism is adaptive when the desire to help others is adaptively learnable. This theory opens new avenues for the interdisciplinary study of psychological altruism.

Go to article

On Nonnegatively Curved Hypersurfaces In Hyperbolic Space, Vincent Bonini, Shiguang Ma, Jie Qing

In this paper we prove a conjecture of Alexander and Currier that states, except for covering maps of equidistant surfaces in hyperbolic 3-space, a complete, nonnegatively curved immersed hypersurface in hyperbolic space is necessarily properly embedded.

Go to article

Optimal Control Methods For Chagas Disease, Francis Mastrome

Mathematics Theses - Archive

Chagas disease is the world's most neglected tropical disease. Having a lack of cure makes the primary focus on the disease preventing it and controlling it. This study takes into account three different control measures: bed nets, low-volume insecticide spraying, and improving housing conditions, analyzes their cost effectiveness compared to each other, and determines which combination of the three control measures prevents the most T. cruzi infections in a rural Latin American village over a decade. It was shown that there is a a hierarchical importance in the control measures when preventing the spread of Chagas disease. In order of …

Go to article

Euclidian Geometry: Proposed Lesson Plans To Teach Throughout A One Semester Course, Joseph Willert

Mathematics Undergraduate Theses

Overview We provide several engaging lesson plans that would aid in the teaching of geometry, specifically targeting Euclidian Geometry, towards students of high school age. The audience of this piece would be high school or college students who have not yet had an introduction to geometry, but have completed the standard mathematical courses leading up to this point (i.e. algebra, elementary math, etc.). This being the case the lessons and concepts realized in Chapter 1 target a basic understanding of what Euclidian Geometry is and the subsequent chapters aim specifically at underlying properties of a geometry. The main source of …

Go to article

Functional Central Limit Theorem For Additive Functionals Associated To The Generalized Nelson Hamiltonian, Soumaya Gheryani, Achref Majid, Habib Ouerdiane

Communications on Stochastic Analysis

No abstract provided.

Go to article

Stochastic Differential Equations With Anticipating Initial Conditions, Hui-Hsiung Kuo, Sudip Sinha, Jiayu Zhai

Communications on Stochastic Analysis

No abstract provided.

Go to article

Topological Properties Of A 3-Rung Möbius Ladder, Rebecca Woods

Electronic Theses and Dissertations

In this work, we discuss the properties of the 3-rung Möbius ladder on the torus. We also prove ℤ₂ is an orientation preserving topological symmetry group of the 3-rung Möbius ladder with sides and rungs distinct, embedded in the torus.

Go to article

Different Estimation Methods For The Basic Independent Component Analysis Model, Zhenyi An

Arts & Sciences Graduate Student Theses and Dissertations

Inspired by classic cocktail-party problem, the basic Independent Component Analysis (ICA) model is created. What differs Independent Component Analysis (ICA) from other kinds of analysis is the intrinsic non-Gaussian assumption of the data. Several approaches are proposed based on maximizing the non-Gaussianity of the data, which is measured by kurtosis, mutual information, and others. With each estimation, we need to optimize the functions of expectations of non-quadratic functions since it can help us to access the higher-order statistics of non-Gaussian part of the data. In this thesis, our goal is to review the one of the most efficient estimation methods, …

Go to article

Stochastic Lagrangian Formulations For Damped Navier-Stokes Equations And Boussinesq System, With Applications, Kazuo Yamazaki

Communications on Stochastic Analysis

No abstract provided.

Go to article

Generalized Random Fields And Lévy's Continuity Theorem On The Space Of Tempered Distributions, Hermine Biermé, Olivier Durieu, Yizao Wang

Communications on Stochastic Analysis

No abstract provided.

Go to article

On A Stochastic 2d Simplified Liquid Crystal Model Driven By Jump Noise, T. Tachim Medjo

Communications on Stochastic Analysis

No abstract provided.

Go to article

New Filters For The Calibration Of Regime Switching Beta Dynamics, Robert J. Elliott, Carlton Osakwe

Communications on Stochastic Analysis

No abstract provided.

Go to article

Non-Continuous Double Barrier Reflected Bsdes With Jumps Under A Stochastic Lipschitz Coefficient, Mohamed Marzougue, Mohamed El Otmani

Communications on Stochastic Analysis

No abstract provided.

Go to article

A Plausible Resolution To Hilbert’S Failed Attempt To Unify Gravitation & Electromagnetism, Florentin Smarandache, Victor Christianto, Robert Neil Boyd

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we explore the reasons why Hilbert’s axiomatic program to unify gravitation theory and electromagnetism failed and outline a plausible resolution of this problem. The latter is based on Gödel’s incompleteness theorem and Newton’s aether stream model.

Go to article

Some New Nonlinear Second-Order Boundary Value Problems On An Arbitrary Domain, Ahmed Alsaedi, Mona Alsulami, Ravi P. Agarwal, Bashir Ahmad

Mathematics and System Engineering Faculty Publications

In this paper, we develop the existence theory for nonlinear second-order ordinary differential equations equipped with new kinds of nonlocal non-separated type integral multi-point boundary conditions on an arbitrary domain. Existence results are proved with the aid of fixed point theorems due to Schaefer, Krasnoselskii, and Leray–Schauder, while the uniqueness of solutions for the given problem is established by means of contraction mapping principle. Examples are constructed for the illustration of the obtained results. Ulam-stability is also discussed for the given problem. A variant of the problem involving different boundary data is also discussed. Finally, we introduce an associated boundary …

Go to article

Dispersion Analysis Of Hdg Methods, Jay Gopalakrishnan, Manuel Solano, Felipe Vargas

Mathematics and Statistics Faculty Publications and Presentations

This work presents a dispersion analysis of the Hybrid Discontinuous Galerkin (HDG) method. Considering the Helmholtz system, we quantify the discrepancies between the exact and discrete wavenumbers. In particular, we obtain an analytic expansion for the wavenumber error for the lowest order Single Face HDG (SFH) method. The expansion shows that the SFH method exhibits convergence rates of the wavenumber errors comparable to that of the mixed hybrid Raviart–Thomas method. In addition, we observe the same behavior for the higher order cases in numerical experiments.

Go to article

Predicted Deepwater Bathymetry From Satellite Altimetry: Non-Fourier Transform Alternatives, Maxsimo Salazar

Dissertations

Robert Parker (1972) demonstrated the effectiveness of Fourier Transforms (FT) to compute gravitational potential anomalies caused by uneven, non-uniform layers of material. This important calculation relates the gravitational potential anomaly to sea-floor topography. As outlined by Sandwell and Smith (1997), a six-step procedure, utilizing the FT, then demonstrated how satellite altimetry measurements of marine geoid height are inverted into seafloor topography. However, FTs are not local in space and produce Gibb’s phenomenon around discontinuities. Seafloor features exhibit spatial locality and features such as seamounts and ridges often have sharp inclines. Initial tests compared the windowed-FT to wavelets in reconstruction of …

Go to article

Hartogs Domains And The Diederich-Fornæss Index, Muhenned Abdulameer Abdulsahib

Graduate Theses and Dissertations

The Diederich-Fornss Index has played a crucial role in studying regularity of the Bergman projection on pseudoconvex domains in Sobolov spaces as is shown by Kohn, Harrington, Pinton and Zampieri and others. In this work, we discuss the Diederich-Fornss Index on Hartogs domains, and its relation to other properties connected to regularity of the Bergman projection. An upper and lower bound for the Diederich-Fornss Index is calculated for Hartogs domains and computed sharply for worm domains. Related conditions for the existence of a strong Stein neighborhood basis for Hartogs domains are introduced.

Go to article

Simplifying Coefficients In A Family Of Ordinary Differential Equations Related To The Generating Function Of The Laguerre Polynomials, Feng Qi

Applications and Applied Mathematics: An International Journal (AAM)

In the paper, by virtue of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Laguerre polynomials.

Go to article

Conformable Derivative Operator In Modelling Neuronal Dynamics, Mehmet Yavuz, Burcu Yaşkıran

Applications and Applied Mathematics: An International Journal (AAM)

This study presents two new numerical techniques for solving time-fractional one-dimensional cable differential equation (FCE) modeling neuronal dynamics. We have introduced new formulations for the approximate-analytical solution of the FCE by using modified homotopy perturbation method defined with conformable operator (MHPMC) and reduced differential transform method defined with conformable operator (RDTMC), which are derived the solutions for linear-nonlinear fractional PDEs. In order to show the efficiencies of these methods, we have compared the numerical and exact solutions of fractional neuronal dynamics problem. Moreover, we have declared that the proposed models are very accurate and illustrative techniques in determining to approximate-analytical …

Go to article

Coincidence Point With Application To Stability Of Iterative Procedure In Cone Metric Spaces, Ismat Beg, Hemant K. Pathak

Applications and Applied Mathematics: An International Journal (AAM)

We obtain necessary conditions for the existence of coincidence point and common fixed point for contractive mappings in cone metric spaces. An application to the stability of J-iterative procedure for mappings having coincidence point in cone metric spaces is also given.

Go to article

Induced Hesitant 2-Tuple Linguistic Aggregation Operators With Application In Group Decision Making, Tabasam Rashid, Ismat Beg, Raja N. Jamil

Applications and Applied Mathematics: An International Journal (AAM)

In this article, hesitant 2-tuple linguistic arguments are used to evaluate the group decision making problems which have inter dependent or inter active attributes. Operational laws are developed for hesitant 2-tuple linguistic elements and based on these operational laws hesitant 2- tuple weighted averaging operator and generalized hesitant 2- tuple averaging operator are proposed. Combining Choquet integral with hesitant 2-tuple linguistic information, some new aggregation operators are defined, including the hesitant 2-tuple correlated averaging operator, the hesitant 2-tuple correlated geometric operator and the generalized hesitant 2-tuple correlated averaging operator. These proposed operators successfully manage the correlations among the elements. After …

Go to article

Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

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

Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms …

Go to article

Contact Numbers For Packing Of Spherical Particles, Eduardo Alejandro Ramirez Martinez

Theses and Dissertations

This thesis covers packings of spherical particles. The main object of this investigation is the contact number of a packing. New bounds for contact numbers of certain families of sphere packings in dimension 3 are obtained as the outcome of this research.

Go to article

Generalized &Thetas;-Parameter Peakon Solutions For A Cubic Camassa-Holm Model, Michael Rippe

Theses and Dissertations

In this paper we outline a method for obtaining generalized peakon solutions for a cubic Camassa-Holm model originally introduced by Fokas (1995) and recently shown to have a Lax pair representation and bi-Hamiltonian structure by Qiao et al (2012). By considering an amended signum function—denoted sgn &thetas;(x)—where sgn(0) = &thetas; for a constant &thetas;, we explore new generalized peakon solutions for this model. In this context, all previous peakon solutions are of the case &thetas; = 0. Further, we aim to analyze the algebraic quadratic equation resulting from a substitution of the single-peakon ansatz equipped with our amended …

Go to article

The Mathematical Aspects Of Theoretical Physics, Hassan Kesserwani

Theses and Dissertations

The aim of this thesis is to outline the mathematical machinery of general relativity, quantum gravity, cosmology and an introduction to string theory under one body of work. We will flesh out tensor algebra and the formalism of differential geometry. After deriving the Einstein field equation, we will outline its traditional applications. We then linearize the field equation by a perturbation method and describe the mathematics of gravitational waves and their spherical harmonic analysis. We then transition into the derivation of the Schwarzschild metric and the Kruskal coordinate transformation, in order to set the stage for quantum gravity. This sets …

Go to article

Scheduling Problems, Aamir Kudai

Honors Theses

Manufacturing industry is growing exponentially. The need of using algorithms and computational techniques to enhance processes is increasing every day. Algorithms help us solve almost all kind of computational problems. Not only choosing the right algorithm for a problem is important but also optimizing its time and space efficiency is crucial. BorgWarner Transmission Systems located in Water Valley, Mississippi is one among the leading manufacturing companies. This paper will demonstrate a real-world audit scheduling problem happened at BorgWarner and the techniques used to solve it. A gentle introduction to some of the heuristic algorithms such as Genetic algorithm, Randomized algorithm, …

Go to article

Identities For Partitions Of N With Parts From A Finite Set, Acadia Larsen

Theses and Dissertations

We show for a prime power number of parts m that the first differences of partitions into at most m parts can be expressed as a non-negative linear combination of partitions into at most m – 1 parts. To show this relationship, we combine a quasipolynomial construction of p(n,m) with a new partition identity for a finite number of parts. We prove these results by providing combinatorial interpretations of the quasipolynomial of p(n,m) and the new partition identity. We extend these results by establishing conditions for when partitions of n with parts coming from …

Go to article

Blow-Up Solutions Of Wave Map Equations With Periodic In Time Speed Of Propagation, Nathalie M. Luna-Rivera

Theses and Dissertations

We study the initial value problem for the wave map equation with time-dependent speed of propagation. In particular, for arbitrary, small, and smooth initial data we construct blow-up solutions of the wave map with coefficients that are periodic in time. For the proof we use Lyapunov-Floquet theory and Borg’s theorem.

Go to article

Full-Text Articles in Mathematics

Pythagorean Theorem Area Proofs, Rachel Morley

Mathematics Undergraduate Theses

The Evolution Of Psychological Altruism, Gualtiero Piccinini, Armin Schulz

Philosophy Faculty Works

On Nonnegatively Curved Hypersurfaces In Hyperbolic Space, Vincent Bonini, Shiguang Ma, Jie Qing

Mathematics

Optimal Control Methods For Chagas Disease, Francis Mastrome

Mathematics Theses - Archive

Euclidian Geometry: Proposed Lesson Plans To Teach Throughout A One Semester Course, Joseph Willert

Mathematics Undergraduate Theses

Functional Central Limit Theorem For Additive Functionals Associated To The Generalized Nelson Hamiltonian, Soumaya Gheryani, Achref Majid, Habib Ouerdiane

Communications on Stochastic Analysis

Stochastic Differential Equations With Anticipating Initial Conditions, Hui-Hsiung Kuo, Sudip Sinha, Jiayu Zhai

Communications on Stochastic Analysis

Topological Properties Of A 3-Rung Möbius Ladder, Rebecca Woods

Electronic Theses and Dissertations

Different Estimation Methods For The Basic Independent Component Analysis Model, Zhenyi An

Arts & Sciences Graduate Student Theses and Dissertations

Stochastic Lagrangian Formulations For Damped Navier-Stokes Equations And Boussinesq System, With Applications, Kazuo Yamazaki

Communications on Stochastic Analysis

Generalized Random Fields And Lévy's Continuity Theorem On The Space Of Tempered Distributions, Hermine Biermé, Olivier Durieu, Yizao Wang

Communications on Stochastic Analysis

On A Stochastic 2d Simplified Liquid Crystal Model Driven By Jump Noise, T. Tachim Medjo

Communications on Stochastic Analysis

New Filters For The Calibration Of Regime Switching Beta Dynamics, Robert J. Elliott, Carlton Osakwe

Communications on Stochastic Analysis

Non-Continuous Double Barrier Reflected Bsdes With Jumps Under A Stochastic Lipschitz Coefficient, Mohamed Marzougue, Mohamed El Otmani

Communications on Stochastic Analysis

A Plausible Resolution To Hilbert’S Failed Attempt To Unify Gravitation & Electromagnetism, Florentin Smarandache, Victor Christianto, Robert Neil Boyd

Branch Mathematics and Statistics Faculty and Staff Publications

Some New Nonlinear Second-Order Boundary Value Problems On An Arbitrary Domain, Ahmed Alsaedi, Mona Alsulami, Ravi P. Agarwal, Bashir Ahmad

Mathematics and System Engineering Faculty Publications

Dispersion Analysis Of Hdg Methods, Jay Gopalakrishnan, Manuel Solano, Felipe Vargas

Mathematics and Statistics Faculty Publications and Presentations

Predicted Deepwater Bathymetry From Satellite Altimetry: Non-Fourier Transform Alternatives, Maxsimo Salazar

Dissertations

Hartogs Domains And The Diederich-Fornæss Index, Muhenned Abdulameer Abdulsahib

Graduate Theses and Dissertations

Simplifying Coefficients In A Family Of Ordinary Differential Equations Related To The Generating Function Of The Laguerre Polynomials, Feng Qi

Applications and Applied Mathematics: An International Journal (AAM)

Conformable Derivative Operator In Modelling Neuronal Dynamics, Mehmet Yavuz, Burcu Yaşkıran

Applications and Applied Mathematics: An International Journal (AAM)

Coincidence Point With Application To Stability Of Iterative Procedure In Cone Metric Spaces, Ismat Beg, Hemant K. Pathak

Applications and Applied Mathematics: An International Journal (AAM)

Induced Hesitant 2-Tuple Linguistic Aggregation Operators With Application In Group Decision Making, Tabasam Rashid, Ismat Beg, Raja N. Jamil

Applications and Applied Mathematics: An International Journal (AAM)

Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

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

Contact Numbers For Packing Of Spherical Particles, Eduardo Alejandro Ramirez Martinez

Theses and Dissertations

Generalized &Thetas;-Parameter Peakon Solutions For A Cubic Camassa-Holm Model, Michael Rippe

Theses and Dissertations

The Mathematical Aspects Of Theoretical Physics, Hassan Kesserwani

Theses and Dissertations

Scheduling Problems, Aamir Kudai

Honors Theses

Identities For Partitions Of N With Parts From A Finite Set, Acadia Larsen

Theses and Dissertations

Blow-Up Solutions Of Wave Map Equations With Periodic In Time Speed Of Propagation, Nathalie M. Luna-Rivera

Theses and Dissertations