Applied Mathematics Commons^™

On N Satisfying, N Dividing Φ(N)Σ(N)+1, Hussain Abdulkader Al-Aidroos

Hadhramout University Journal of Natural & Applied Sciences

Let denotes the sum of the positive divisors of the positive integer and be the Euler’s totient function([1],page25). Cleary, divides if is a prime. Then, the question is there a composite that divides ? Considering this problem Yang-Gao Chen and Jin-Hui Fang [5] have proved that , where as usual is the number of distinct prime factors of. and , .We devoted the study of this problem where we prove that every in is odd and that , from which it follows that for any composite in the least prime factors is . Also, we obtained lower bounds for and …

Under Pressure: A Case Study Of The Effects Of External Pressure On Mlb Players Using Twitter Sentiment Analysis, Jonathan Huntley

Honors Projects in Mathematics

Performance under pressure and psychological momentum are well-documented topics in sports psychology, but most research focuses on “in-game” pressure. This study views pressure more broadly to examine how the external pressure of fans, quantified using the sentiment of tweets mentioning the players, can affect how MLB players perform. Although external pressure is intangible, it can impact a player’s psyche and performance. This investigation focuses on players Chris Sale and David Price. A new process was developed leveraging the Vader package in Python that can generate tweet sentiment to compare to several performance metrics from Baseball Reference. Results proved to be …

A Method Of Presenting Experimental Dependencies In Solving Inverse Problems, Anatoliy Fyodorovich Verlan, Miraziz Vorisovich Sagatov

Chemical Technology, Control and Management

Scientific interest in the creation, research and application of methods and means for solving inverse problems is determined by the need for the development of new methods of signal processing, as well as the increased complexity of inverse problems in relation to direct problems, since the latter are not correct from a mathematical point of view and have a number of peculiarities. Since the input information in inverse problems is experimental data determined with a certain error, the resulting solution can differ greatly from the exact solution. An arbitrary discretely given function of time can be approximated with a predetermined …

Multi-Valued Solutions For The Equation Of Motion, Darcy-Jordan Model, As A Cauchy Problem: A Shocking Event, Chandler Shimp

Master's Theses

Shocks are physical phenomenon that occur quite often around us. In this thesis we examine the occurrence of shocks in finite amplitude acoustic waves from a numerical perspective. These waves, or jump discontinuities, yield ill-behaved solutions when solved numerically. This study takes on the challenge of finding both single- and multi-valued solutions.

The previously unsolved problem in this study is the representation of the Equation of Motion (EoM) in the form of the Darcy-Jordan model (DJM) and expressed as a dimensionless IVP Cauchy problem. Prior attempts to solve have resulted only in implicit solutions or explicit solutions with certain initial …

The Phase Transition Of Discrepancy In Random Hypergraphs, Calum Macrury, Tomáš Masarík, Leilani Pai, Xavier Perez Gimenez

Department of Mathematics: Faculty Publications

Motivated by the Beck-Fiala conjecture, we study the discrepancy problem in two related models of random hypergraphs on n vertices and m edges. In the first (edge-independent) model, a random hypergraph H₁ is constructed by fixing a parameter p and allowing each of the n vertices to join each of the m edges independently with probability p. In the parameter range in which pn ⟶ ∞ and pm ⟶ ∞, we show that with high probability (w.h.p.) H₁ has discrepancy at least Ω(2^-n/m √pn) when m = O(n …

Exploring Optimal Lockdown Policies During The Covid-19 Pandemic, Cameron Bundy

Symposium Of University Research and Creative Expression (SOURCE)

COVID-19 has impacted public and economic health worldwide. To bolster the economy and maintain human life, economic and epidemiological research is vital. Nations have implemented lockdowns intent on slowing the spread of the virus. This research examines how lockdown parameter adjustments can help control a nations fatalities. The study incorporated an SIRD disease model that is simulated over a 200 day period. The goal of the research is to take the SIRD model and use it to create a minimization function that analyzes dynamics that best produce minimal loss of GDP as well as low loss of life in a …

Epidemic Conditions With Temporary Link Deactivation On A Network Sir Disease Model, Hannah Scanlon, John Gemmer

Spora: A Journal of Biomathematics

The spread of an infectious disease depends on intrinsic properties of the disease as well as the connectivity and actions of the population. This study investigates the dynamics of an SIR type model which accounts for human tendency to avoid infection while also maintaining preexisting, interpersonal relationships. Specifically, we use a network model in which individuals probabilistically deactivate connections to infected individuals and later reconnect to the same individuals upon recovery. To analyze this network model, a mean field approximation consisting of a system of fourteen ordinary differential equations for the number of nodes and edges is developed. This system …

Using Lie Sphere Geometry To Study Dupin Hypersurfaces In R^N, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

A hypersurface M in Rⁿ or Sⁿ is said to be Dupin if along each curvature surface, the corresponding principal curvature is constant. A Dupin hypersurface is said to be proper Dupin if each principal curvature has constant multiplicity on M, i.e., the number of distinct principal curvatures is constant on M. The notions of Dupin and proper Dupin hypersurfaces in Rⁿ or Sⁿ can be generalized to the setting of Lie sphere geometry, and these properties are easily seen to be invariant under Lie sphere transformations. This makes Lie sphere geometry an effective …

Interpolating With Outer Functions, Javad Mashreghi, Marek Ptak, William T. Ross

Department of Math & Statistics Faculty Publications

The classical theorems of Mittag-Leffler and Weierstrass show that when (λn)n≥1 is

a sequence of distinct points in the open unit disk D, with no accumulation points in

D, and (wn)n≥1 is any sequence of complex numbers, there is an analytic function

ϕ on D for which ϕ(λn) = wn. A celebrated theorem of Carleson [2] characterizes

when, for a bounded sequence (wn)n≥1, this interpolating problem can be solved with

a bounded analytic function. A theorem of Earl [5] goes further and shows that when

Carleson’s condition is satisfied, the interpolating function ϕ can be …

Cohomological Blow Ups Of Graded Artinian Gorenstein Algebras Along Surjective Maps, Anthony Iarrobino, Pedro Macias Marques, Chris Mcdaniel, Alexandra Seceleanu, Junzo Watanabe

Department of Mathematics: Faculty Publications

We introduce the cohomological blow up of a graded Artinian Gorenstein (AG) algebra along a surjective map, which we term BUG (Blow Up Gorenstein) for short. This is intended to translate to an algebraic context the cohomology ring of a blow up of a projective manifold along a projective submanifold. We show, among other things, that a BUG is a connected sum, that it is the general fiber in a flat family of algebras, and that it preserves the strong Lefschetz property. We also show that standard graded compressed algebras are rarely BUGs, and we classify those BUGs that are …

Instabilities Of Overturned Traveling Waves, Tyler B. Pierce

Theses and Dissertations

The instabilities of overturned traveling waves are determined by the use of spectral methods. Two separate numerical methods, Spectral Stability Analysis and Dynamic Stability Analysis, are used to assess the instabilities of branches of waves solved from conformally-mapped Euler equations. The branches of waves with Bond number less than two were found to be spectrally stable to super-harmonic perturbations. The branches of waves with Bond number in [2,3) had some waves that were stable and some that were unstable. All overturned waves with Bond number greater than or equal to two were unstable.

Towards Cnl-Based Verbalization Of Computational Contracts, Inari Listenmaa, Maryam Hanafiah, Regina Cheong, Andreas Kallberg

Centre for Computational Law (2022-2025)

We present a CNL, which is a component of L4, a domain-specific programming language for drafting laws and contracts. Along with formal verification, L4’s core functionalities include natural language generation. We present the NLG pipeline and an interactive process for ambiguity resolution.

Equichordal Tight Fusion Frames And Biangular Orthopartitionable Tight Frames, Benjamin R. Mayo

Theses and Dissertations

An equichordal tight fusion frame (ECTFF) is a sequence of equidimensional subspaces of a Euclidean space that achieves equality in Conway, Hardin and Sloane's simplex bound, and so is a type of optimal Grassmannian code. In the special case where its subspaces have dimension one, an ECTFF corresponds to an equiangular tight frame (ETF); such frames have minimal coherence and so are useful for compressed sensing. More generally, an ECTFF will yield a frame with minimal block coherence when its subspaces are pairwise isoclinic, namely when it is an equi-isoclinic tight fusion frame (EITFF). In this dissertation, we generalize the …

Advances In Modeling Gas Adsorption In Porous Materials For The Characterization Applications, Max A. Maximov

Dissertations

The dissertation studies methods for mesoporous materials characterization using adsorption at various levels of scale and complexity. It starts with the topic introduction, necessary notations and definitions, recognized standards, and a literature review.

Synthesis of novel materials requires tailoring of the characterization methods and their thorough testing. The second chapter presents a nitrogen adsorption characterization study for silica colloidal crystals (synthetic opals). These materials have cage-like pores in the range of tens of nanometers. The adsorption model can be described within a macroscopic approach, based on the Derjaguin-Broekhoff-de Boer (DBdB) theory of capillary condensation. A kernel of theoretical isotherms is …

Modeling Dewetting, Demixing, And Thermal Effects In Nanoscale Metal Films, Ryan Howard Allaire

Dissertations

Thin film dynamics, particularly on the nanoscale, is a topic of extensive interest. The process by which thin liquids evolve is far from trivial and can lead to dewetting and drop formation. Understanding this process involves not only resolving the fluid mechanical aspects of the problem, but also requires the coupling of other physical processes, including liquid-solid interactions, thermal transport, and dependence of material parameters on temperature and material composition. The focus of this dissertation is on the mathematical modeling and simulation of nanoscale liquid metal films, which are deposited on thermally conductive substrates, liquefied by laser heating, and subsequently …

Modeling And Design Optimization For Membrane Filters, Yixuan Sun

Dissertations

Membrane filtration is widely used in many applications, ranging from industrial processes to everyday living activities. With growing interest from both industrial and academic sectors in understanding the various types of filtration processes in use, and in improving filter performance, the past few decades have seen significant research activity in this area. Experimental studies can be very valuable, but are expensive and time-consuming, therefore theoretical studies offer potential as a cost-effective and predictive way to improve on current filter designs. In this work, mathematical models, derived from first principles and simplified using asymptotic analysis, are proposed for: (1) pleated membrane …

Improved Ships Course-Keeping Robust Control Algorithm Based On Backstepping And Nonlinear Feedback, Sirui Wang

Maritime Safety & Environment Management Dissertations (Dalian)

No abstract provided.

Supplementary Files For "Creating A Universal Depth-To-Load Conversion Technique For The Conterminous United States Using Random Forests", Jesse Wheeler, Brennan Bean, Marc Maguire

Browse all Datasets

As part of an ongoing effort to update the ground snow load maps in the United States, this paper presents an investigation into snow densities for the purpose of predicting ground snow loads for structural engineering design with ASCE 7. Despite their importance, direct measurements of snow load are sparse when compared to measurements of snow depth. As a result, it is often necessary to estimate snow load using snow depth and other readily accessible climate variables. Existing depth-to-load conversion methods, each of varying complexity, are well suited for snow load estimation for a particular region or station network, but …

An Upper Bound On The Spectral P-Norms Of Tensors And Matrix Permanent, Killian J. Hitsman, Vehbi E. Paksoy

Mako: NSU Undergraduate Student Journal

No abstract provided.

Simulating Dislocation Densities With Finite Element Analysis, Ja'nya Breeden, Dow Drake, Saurabh Puri

REU Final Reports

A one-dimensional set of nonlinear time-dependent partial differential equations developed by Acharya (2010) is studied to observe how differing levels of applied strain affect dislocation walls. The framework of this model consists of a convective and diffusive term which is used to develop a linear system of equations to test two methods of the finite element method. The linear system of partial differential equations is used to determine whether the standard or Discontinuous Galerkin method will be used. The Discontinuous Galerkin method is implemented to discretize the continuum model and the results of simulations involving zero and non-zero applied strain …