Applied Mathematics Commons^™

Numerical Ruin Probability In The Dual Risk Model With Risk-Free Investments, Sooie-Hoe Loke, Enrique Thomann

Mathematics Faculty Scholarship

In this paper, a dual risk model under constant force of interest is considered. The ruin probability in this model is shown to satisfy an integro-differential equation, which can then be written as an integral equation. Using the collocation method, the ruin probability can be well approximated for any gain distributions. Examples involving exponential, uniform, Pareto and discrete gains are considered. Finally, the same numerical method is applied to the Laplace transform of the time of ruin.

Non-Locality, Precognition & Spirit From The Physics Point Of View, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

There are various supernatural phenomena which can hardly be explained by the existing mainstream science, for instance non-local interactions (e.g. ESP) and also precognitive interdictions. And there are other problems such as how to include the Spirit in the framework of physics. For example, it has been known for long time that intuition plays significant role in many professions and human life, including entrepreneurship, government, and also in detective or law enforcement activities. Despite these examples, such a precognitive interdiction is hardly accepted in mainstream science. In this paper, we discuss non-local interactions and advanced solutions of Maxwell equations, and …

The Philosophical Foundations Of Plen: A Protocol-Theoretic Logic Of Epistemic Norms, Ralph E. Jenkins

Dissertations, Theses, and Capstone Projects

In this dissertation, I defend the protocol-theoretic account of epistemic norms. The protocol-theoretic account amounts to three theses: (i) There are norms of epistemic rationality that are procedural; epistemic rationality is at least partially defined by rules that restrict the possible ways in which epistemic actions and processes can be sequenced, combined, or chosen among under varying conditions. (ii) Epistemic rationality is ineliminably defined by procedural norms; procedural restrictions provide an irreducible unifying structure for even apparently non-procedural prescriptions and normative expressions, and they are practically indispensable in our cognitive lives. (iii) These procedural epistemic norms are best analyzed in …

Galois Groups Of Differential Equations And Representing Algebraic Sets, Eli Amzallag

Dissertations, Theses, and Capstone Projects

The algebraic framework for capturing properties of solution sets of differential equations was formally introduced by Ritt and Kolchin. As a parallel to the classical Galois groups of polynomial equations, they devised the notion of a differential Galois group for a linear differential equation. Just as solvability of a polynomial equation by radicals is linked to the equation’s Galois group, so too is the ability to express the solution to a linear differential equation in "closed form" linked to the equation’s differential Galois group. It is thus useful even outside of mathematics to be able to compute and represent these …

Predicting Impacts Of Chemicals From Organisms To Ecosystem Service Delivery: A Case Study Of Endocrine Disruptor Effects On Trout, Valery E. Forbes, Steve Railsback, Chiara Accolla, Bjorn Birnir, Randall J.F. Bruins, Virginie Ducrot, Nika Galic, Kristina Garber, Bret C. Harvey, Henriette I. Jager, Andrew Kanarek, Robert Pastorok, Richard Rebarber, Pernille Thorbek, Chris J. Salice

Department of Mathematics: Faculty Publications

We demonstrate how mechanistic modeling can be used to predict whether and how biological responses to chemicals at (sub)organismal levels in model species (i.e., what we typically measure) translate into impacts on ecosystem service delivery (i.e., what we care about). We consider a hypothetical case study of two species of trout, brown trout (Salmo trutta; BT) and greenback cutthroat trout (Oncorhynchus clarkii stomias; GCT). These hypothetical populations live in a high-altitude river system and are exposed to human-derived estrogen (17α‑ethinyl estradiol, EE2), which is the bioactive estrogen in many contraceptives. We use the individual based model in STREAM …

Yelp’S Review Filtering Algorithm, Yao Yao, Ivelin Angelov, Jack Rasmus-Vorrath, Mooyoung Lee, Daniel W. Engels

SMU Data Science Review

In this paper, we present an analysis of features influencing Yelp's proprietary review filtering algorithm. Classifying or misclassifying reviews as recommended or non-recommended affects average ratings, consumer decisions, and ultimately, business revenue. Our analysis involves systematically sampling and scraping Yelp restaurant reviews. Features are extracted from review metadata and engineered from metrics and scores generated using text classifiers and sentiment analysis. The coefficients of a multivariate logistic regression model were interpreted as quantifications of the relative importance of features in classifying reviews as recommended or non-recommended. The model classified review recommendations with an accuracy of 78%. We found that reviews …

Developments In Multivariate Post Quantum Cryptography., Jeremy Robert Vates

Electronic Theses and Dissertations

Ever since Shor's algorithm was introduced in 1994, cryptographers have been working to develop cryptosystems that can resist known quantum computer attacks. This push for quantum attack resistant schemes is known as post quantum cryptography. Specifically, my contributions to post quantum cryptography has been to the family of schemes known as Multivariate Public Key Cryptography (MPKC), which is a very attractive candidate for digital signature standardization in the post quantum collective for a wide variety of applications. In this document I will be providing all necessary background to fully understand MPKC and post quantum cryptography as a whole. Then, I …

On Some Metaphysical Problems Of Many Worlds Interpretation Of Quantum Mechanics, Florentin Smarandache, Victor Christianto, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

Despite its enormous practical success, many physicists and philosophers alike agree that the quantum theory is full of contradictions and paradoxes which are difficult to solve consistently. Even after 90 years, the experts themselves still do not all agree what to make of it. The area of disagreement centers primarily around the problem of describing observations. Formally, the socalled quantum measurement problem can be defined as follows: the result of a measurement is a superposition of vectors, each representing the quantity being observed as having one of its possible values. The question that has to be answered is : how …

Developing Optimization Techniques For Logistical Tendering Using Reverse Combinatorial Auctions, Jennifer Kiser

Electronic Theses and Dissertations

In business-to-business logistical sourcing events, companies regularly use a bidding process known as tendering in the procurement of transportation services from third-party providers. Usually in the form of an auction involving a single buyer and one or more sellers, the buyer must make decisions regarding with which suppliers to partner and how to distribute the transportation lanes and volume among its suppliers; this is equivalent to solving the optimization problem commonly referred to as the Winner Determination Problem. In order to take into account the complexities inherent to the procurement problem, such as considering a supplier’s network, economies of scope, …

Fast Adjustable Npn Classification Using Generalized Symmetries, Xuegong Zhou, Lingli Wang, Peiyi Zhao, Alan Mishchenko

Mathematics, Physics, and Computer Science Faculty Articles and Research

NPN classification of Boolean functions is a powerful technique used in many logic synthesis and technology mapping tools in FPGA design flows. Computing the canonical form of a function is the most common approach of Boolean function classification. In this paper, a novel algorithm for computing NPN canonical form is proposed. By exploiting symmetries under different phase assignments and higher-order symmetries of Boolean functions, the search space of NPN canonical form computation is pruned and the runtime is dramatically reduced. The algorithm can be adjusted to be a slow exact algorithm or a fast heuristic algorithm with lower quality. For …

Masked Instability: Within-Sector Financial Risk In The Presence Of Wealth Inequality, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We investigate masked financial instability caused by wealth inequality. When an economic sector is decomposed into two subsectors that possess a severe wealth inequality, the sector in entirety can look financially stable while the two subsectors possess extreme financially instabilities of opposite nature, one from excessive equity, the other from lack thereof. The unstable subsector can result in further financial distress and even trigger a financial crisis. The market instability indicator, an early warning system derived from dynamical systems applied to agent-based models, is used to analyze the subsectoral financial instabilities. Detailed mathematical analysis is provided to explain what financial …

Building Long-Term Support For Faculty Through Graduate Student Instructor Professional Development, Nathan Wakefield, Karina Uhing, Mitchell Hamidi

Department of Mathematics: Faculty Publications

Improving university-level instruction is an important step to improving instruction at all levels, and in order to improve university-level instruction, instructors need to master more effective models of instruction and be able to draw on education literature as they continue to develop as instructors. Well-trained, informed instructors are well equipped to be agents of change when they take on faculty positions. However, this mastery requires training and practice.

An Accelerate Process For The Successive Approximations Method In The Case Of Monotonous Convergence, A. Laouar, I. Mous

Applications and Applied Mathematics: An International Journal (AAM)

We study an iterative process to accelerate the successive approximations method in a monotonous convergence framework. It consists in interrupting the sequence of the successive approximations method produced at the kth iteration and substituting it by a combination of the element of the sequence produced at the iterate k + 1 and an extrapolation vector. The latter uses a parameter which can be calculated mathematically. We illustrate numerically this process by studying a freeboundary problems class.

System Reliability Using Generalized Intuitionistic Fuzzy Rayleigh Lifetime Distribution, Ali Ebrahimnejad, Ezzatallah B. Jamkhaneh

Applications and Applied Mathematics: An International Journal (AAM)

Reliability analysis as one of the important research topics in engineering has been researched by a number of authors. Reliability in classical distributions is based on precise parameters. It is usually assumed that parameters of distributions are precise real numbers. However, in the real world, the data sometimes cannot be measured and recorded precisely. In this paper, the concept of fuzzy reliability is extended by the idea of generalized intuitionistic fuzzy reliability. We investigate the reliability characteristics of systems using Rayleigh lifetime distribution, in which the lifetime parameter is assumed to be generalized intuitionistic fuzzy number. Generalized intuitionistic fuzzy reliability, …

A New Approach To Solve Multi-Objective Transportation Problem, Lakhveer Kaur, Madhuchanda \ Rakshit, Sandeep Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a simple approach is proposed to obtain the best compromise solution of linear multiobjective transportation problem (MOTP). Using this approach, we get unique efficient solution. Because unique efficient extreme point obtained by proposed approach directly leads to compromise solution, which is preferred by decision maker. Also this approach is simple to use and less time consuming. For the application of proposed approach, numerical examples are considered from existing literature and are solved with proposed method.

Simulating The Electrical Properties Of Random Carbon Nanotube Networks Using A Simple Model Based On Percolation Theory, Roberto Abril Valenzuela

Physics

Carbon nanotubes (CNTs) have been subject to extensive research towards their possible applications in the world of nanoelectronics. The interest in carbon nanotubes originates from their unique variety of properties useful in nanoelectronic devices. One key feature of carbon nanotubes is that the chiral angle at which they are rolled determines whether the tube is metallic or semiconducting. Of main interest to this project are devices containing a thin film of randomly arranged carbon nanotubes, known as carbon nanotube networks. The presence of semiconducting tubes in a CNT network can lead to a switching effect when the film is electro-statically …

United States Population Future Estimates And Long-Term Distribution, Sean P. Brogan

DePaul Discoveries

The population of the United States has always increased year over year. Even now with decreasing birth rates, the overall population continues to grow when looking at conventional models. The present study specifically examines what would happen to the U.S. population if we were to maintain the current birth and survival rates into the future. By 2050, our research shows that the U.S. population will become much older and cease to grow at all.

A Hybrid Dynamic Modeling Of Time-To-Event Processes And Applications, Emmanuel A. Appiah

USF Tampa Graduate Theses and Dissertations

In the survival and reliability data analysis, parametric and nonparametric methods are used to estimate the hazard/risk rate and survival functions. A parametric approach is based on the assumption that the underlying survival distribution belongs to some specific family of closed form distributions (normal, Weibull, exponential, etc.). On the other hand, a nonparametric approach is centered around the best-fitting member of a class of survival distribution functions. Moreover, the Kaplan-Meier and Nelson-Aalen type nonparametric approach do not assume either distribution class or closed-form distributions. Historically, well-known time-to-event processes are death of living specie in populations and failure of component in …

Herglotz Functions Of Several Quaternionic Variables, Khaled Abu-Ghanem, Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

We first review realizations of Herglotz functions in the unit ball of C^N and provide new insights. Then, we define the corresponding class and prove the extend the results in the case of several quaternionic variables.

Examples Of Solving The Wave Equation In The Hyperbolic Plane, Cooper Ramsey

Senior Honors Theses

The complex numbers have proven themselves immensely useful in physics, mathematics, and engineering. One useful tool of the complex numbers is the method of conformal mapping which is used to solve various problems in physics and engineering that involved Laplace’s equation. Following the work done by Dr. James Cook, the complex numbers are replaced with associative real algebras. This paper focuses on another algebra, the hyperbolic numbers. A solution method like conformal mapping is developed with solutions to the one-dimensional wave equation. Applications of this solution method revolve around engineering and physics problems involving the propagation of waves. To conclude, …

Rapid Generation Of Jacobi Matrices For Measures Modified By Rational Factors, Amber Sumner

Dissertations

Orthogonal polynomials are important throughout the fields of numerical analysis and numerical linear algebra. The Jacobi matrix J for a family of n orthogonal polynomials is an n x n tridiagonal symmetric matrix constructed from the recursion coefficients for the three-term recurrence satisfied by the family. Every family of polynomials orthogonal with respect to a measure on a real interval [a,b] satisfies such a recurrence. Given a measure that is modified by multiplying by a rational weight function r(t), an important problem is to compute the modified Jacobi matrix Jmod corresponding to the new measure from knowledge of J. There …

Properties And Convergence Of State-Based Laplacians, Kelsey Wells

Department of Mathematics: Dissertations, Theses, and Student Research

The classical Laplace operator is a vital tool in modeling many physical behaviors, such as elasticity, diffusion and fluid flow. Incorporated in the Laplace operator is the requirement of twice differentiability, which implies continuity that many physical processes lack. In this thesis we introduce a new nonlocal Laplace-type operator, that is capable of dealing with strong discontinuities. Motivated by the state-based peridynamic framework, this new nonlocal Laplacian exhibits double nonlocality through the use of iterated integral operators. The operator introduces additional degrees of flexibility that can allow better representation of physical phenomena at different scales and in materials with different …

Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

Dissertations, Theses, and Capstone Projects

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions are …

The Advection-Diffusion Equation And The Enhanced Dissipation Effect For Flows Generated By Hamiltonians, Michael Kumaresan

Dissertations, Theses, and Capstone Projects

We study the Cauchy problem for the advection-diffusion equation when the diffusive parameter is vanishingly small. We consider two cases - when the underlying flow is a shear flow, and when the underlying flow is generated by a Hamiltonian. For the former, we examine the problem on a bounded domain in two spatial variables with Dirichlet boundary conditions. After quantizing the system via the Fourier transform in the first spatial variable, we establish the enhanced-dissipation effect for each mode. For the latter, we allow for non-degenerate critical points and represent the orbits by points on a Reeb graph, with vertices …

The Auxiliary Space Preconditioner For The De Rham Complex, Jay Gopalakrishnan, Martin Neumüller, Panayot S. Vassilevski

Portland Institute for Computational Science Publications

We generalize the construction and analysis of auxiliary space preconditioners to the n-dimensional finite element subcomplex of the de Rham complex. These preconditioners are based on a generalization of a decomposition of Sobolev space functions into a regular part and a potential. A discrete version is easily established using the tools of finite element exterior calculus. We then discuss the four-dimensional de Rham complex in detail. By identifying forms in four dimensions (4D) with simple proxies, form operations are written out in terms of familiar algebraic operations on matrices, vectors, and scalars. This provides the basis for our implementation of …

The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas

Honors Projects

In this project, I unravel various mathematical milestones and relate them to the human experience. I show and explain the solution to the Tautochrone, a popular variation on the Brachistochrone, which details a major battle between Leibniz and Newton for the title of inventor of Calculus. One way to solve the Tautochrone is using Laplace Transforms; in this project I expound on common functions that get transformed and how those can be used to solve the Tautochrone. I then connect the solution of the Tautochrone to clock making. From this understanding of clocks, I examine mankind’s understanding of time and …

Using Random Forests To Describe Equity In Higher Education: A Critical Quantitative Analysis Of Utah’S Postsecondary Pipelines, Tyler Mcdaniel

Butler Journal of Undergraduate Research

The following work examines the Random Forest (RF) algorithm as a tool for predicting student outcomes and interrogating the equity of postsecondary education pipelines. The RF model, created using longitudinal data of 41,303 students from Utah's 2008 high school graduation cohort, is compared to logistic and linear models, which are commonly used to predict college access and success. Substantially, this work finds High School GPA to be the best predictor of postsecondary GPA, whereas commonly used ACT and AP test scores are not nearly as important. Each model identified several demographic disparities in higher education access, most significantly the effects …

On Central Branch/Reinsurance Risk Networks: Exact Results And Heuristics, Florin Avram, Sooie-Hoe Loke

Mathematics Faculty Scholarship

Modeling the interactions between a reinsurer and several insurers, or between a central management branch (CB) and several subsidiary business branches, or between a coalition and its members, are fascinating problems, which suggest many interesting questions. Beyond two dimensions, one cannot expect exact answers. Occasionally, reductions to one dimension or heuristic simplifications yield explicit approximations, which may be useful for getting qualitative insights. In this paper, we study two such problems: the ruin problem for a two-dimensional CB network under a new mathematical model, and the problem of valuation of two-dimensional CB networks by optimal dividends. A common thread between …

Second Order Fully Discrete Energy Stable Methods On Staggered Grids For Hydrodynamic Phase Field Models Of Binary Viscous Fluids, Yuezheng Gong, Jia Zhao, Qi Wang

Mathematics and Statistics Faculty Publications

We present second order, fully discrete, energy stable methods on spatially staggered grids for a hydrodynamic phase field model of binary viscous fluid mixtures in a confined geometry subject to both physical and periodic boundary conditions. We apply the energy quadratization strategy to develop a linear-implicit scheme. We then extend it to a decoupled, linear scheme by introducing an intermediate velocity term so that the phase variable, velocity field, and pressure can be solved sequentially. The two new, fully discrete linear schemes are then shown to be unconditionally energy stable, and the linear systems resulting from the schemes are proved …

Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam

Masters Theses & Specialist Projects

Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of convergence. Different …