Mathematics Commons^™

The Method Of Particular Solutions Using Trigonometric Basis Functions, Zhaolu Tian, Xinxiang Li, C.M. Fan, Ching-Shyang Chen

Faculty Publications

In this paper, the method of particular solutions (MPS) using trigonometric functions as the basis functions is proposed to solve two-dimensional elliptic partial differential equations. The inhomogeneous term of the governing equation is approximated by Fourier series and the closed-form particular solutions of trigonometric functions are derived using the method of undetermined coefficients. Once the particular solutions for the trigonometric basis functions are derived, the standard MPS can be applied for solving partial differential equations. In comparing with the use of radial basis functions and polynomials in the MPS, our proposed approach provides another simple approach to effectively solving two-dimensional …

Study Of Pseudo Bl–Algebras In View Of Left Boolean Lifting Property, B. Barani Nia, A. B. Saeid

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we define left Boolean lifting property (right Boolean lifting property) LBLP (RBLP) for pseudo BL–algebra which is the property that all Boolean elements can be lifted modulo every left filter (right filter) and next, we study pseudo BL-algebra with LBLP (RBLP). We show that Quasi local, local and hyper Archimedean pseudo BL–algebra that have LBLP (RBLP) has an interesting behavior in direct products. LBLP (RBLP) provides an important representation theorem for semi local and maximal pseudo BL–algebra.

On Refinements Of Hermite-Hadamard-Fejér Type Inequalities For Fractional Integral Operators, Fatma Ertuğral, Mehmet Z. Sarikaya, Hüseyin Budak

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, utilizing convex functions, we first establish new refinements of Hermite- Hadamard-Fejer type inequalities via Riemann-Liouville fractional integral operators. A generalized refinements of Hermite-Hadamard-Fejer type inequalities for fractional integral operators with exponential kernel is also obtained. The results given in this paper would provide extensions of those presented in earlier studies.

A Concise Workbook For College Algebra, Fei Ye

Open Educational Resources

This workbook is mainly based on the author’s worksheets for the college algebra course (MAD-119) at QCC of CUNY. It is intended as a concise introduction to college algebra at the intermediate level.

It contains 25 lessons. Each lesson, corresponding to roughly one class meeting, starts with a page on concepts, formulas and examples, and ends with a list of practice problems that students are expected to be able to solve and complete in class.

Distance Product Of Graphs, H. S. Mehta, U. P. Acharya

Applications and Applied Mathematics: An International Journal (AAM)

In graph theory, different types of product of two graphs have been studied, e.g. Cartesian product, Tensor product, Strong product, etc. Later on, Cartesian product and Tensor product have been generalized by 2-Cartesian product and 2-Tensor product. In this paper, we give one more generalize form, distance product of two graphs. Mainly we discuss the connectedness, bipartiteness and Eulerian property in this product.

Gaussian Processes With Context-Supported Priors For Active Object Localization, Bruno Jedynak

Portland Institute for Computational Science Publications

We devise an algorithm using a Bayesian optimization framework in conjunction with contextual visual data for the efficient localization of objects in still images. Recent research has demonstrated substantial progress in object localization and related tasks for computer vision. However, many current state-of-the-art object localization procedures still suffer from inaccuracy and inefficiency, in addition to failing to provide a principled and interpretable system amenable to high-level vision tasks. We address these issues with the current research.

Our method encompasses an active search procedure that uses contextual data to generate initial bounding-box proposals for a target object. We train a convolutional …

Cox Processes For Counting By Detection, Purnima Rajan, Yongming Ma, Bruno Jedynak

Portland Institute for Computational Science Publications

In this work, doubly stochastic Poisson (Cox) processes and convolutional neural net (CNN) classifiers are used to estimate the number of instances of an object in an image. Poisson processes are well suited to model events that occur randomly in space, such as the location of objects in an image or the enumeration of objects in a scene. The proposed algorithm selects a subset of bounding boxes in the image domain, then queries them for the presence of the object of interest by running a pre-trained CNN classifier. The resulting observations are then aggregated, and a posterior distribution over the …

Network Specializations, Symmetries, And Spectral Properties, Dallas C. Smith

Theses and Dissertations

In this dissertation, we introduce three techniques for network sciences. The first of these techniques is a series of new models for describing network growth. These models, called network specialization models, are built with the idea that networks grow by specializing the function of subnetworks. Using these models we create theoretical networks which exhibit well-known properties of real networks. We also demonstrate how the spectral properties are preserved as the models grow. The second technique we describe is a method for decomposing networks that contain automorphisms in a way that preserves the spectrum of the original graph. This method …

Symmetric Presentations, Representations, And Related Topics, Adam Manriquez

Electronic Theses, Projects, and Dissertations

The purpose of this thesis is to develop original symmetric presentations of finite non-abelian simple groups, particularly the sporadic simple groups. We have found original symmetric presentations for the Janko group J₁, the Mathieu group M₁₂, the Symplectic groups S(3,4) and S(4,5), a Lie type group Suz(8), and the automorphism group of the Unitary group U(3,5) as homomorphic images of the progenitors 2^*60 : (2 x A₅), 2^{*60 :} A₅, 2^*56 : (2³ : 7), and 2^*28 : (PGL(2,7):2), respectively. We have also discovered the groups 2 …

Modern Cryptography, Samuel Lopez

Electronic Theses, Projects, and Dissertations

We live in an age where we willingly provide our social security number, credit card information, home address and countless other sensitive information over the Internet. Whether you are buying a phone case from Amazon, sending in an on-line job application, or logging into your on-line bank account, you trust that the sensitive data you enter is secure. As our technology and computing power become more sophisticated, so do the tools used by potential hackers to our information. In this paper, the underlying mathematics within ciphers will be looked at to understand the security of modern ciphers.

An extremely important …

Identifying Prevalent Mathematical Pathways To Engineering In South Carolina, Eliza Gallagher, Christy Brown, D. Andrew Brown, Kristin Kelly Frady, Patrick Bass, Michael A. Matthews, Thomas T. Peters, Robert J. Rabb, Ikhalfani Solan, Ronald W. Welch, Anand K. Gramopadhye

Faculty Publications

National data indicate that initial mathematics course placement in college is a strong predictor of persistence to degree in engineering, with students placed in calculus persisting at nearly twice the rate of those placed below calculus. Within the state of South Carolina, approximately 95% of engineering-intending students who initially place below calculus are from in-state. In order to make systemic change, we are first analyzing system-wide data to identify prevalent educational pathways within the state, and the mathematical milestones along those pathways taken by students in engineering and engineering-related fields. This paper reports preliminary analysis of that data to understand …

Double Lie Algebroids And Representations Up To Homotopy, A. Gracia-Saz, M. Jotz Lean, K. C. H. Mackenzie, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

We show that a double Lie algebroid, together with a chosen decomposition, is equivalent to a pair of 2-term representations up to homotopy satisfying compatibility conditions which extend the notion of matched pair of Lie algebroids. We discuss in detail the double Lie algebroids arising from the tangent bundle of a Lie algebroid and the cotangent bundle of a Lie bialgebroid.

On Maxwell-Dirac Isomorphism, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

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.

The Search For The Cyclic Sieving Phenomenon In Plane Partitions, William J. Asztalos

DePaul Discoveries

The efforts of this research project are best understood in the context of the subfield of dynamical combinatorics, in which one enumerates a set of combinatorial objects by defining some action to guide the search for underlying structures. While there are many examples with varying degrees of complexity, the necklace problem, which concerns the possible unique configurations of beads in a ring up to rotational symmetry, is a well-known example. Though this sort of approach to enumeration has been around for a century or more, activity in this area has intensified in the last couple of decades. Perhaps the most …

Survival Analysis Using Archimedean Copulas, Xieyang Jia

Dissertations

This dissertation has three independent parts. The first part studies a variation of the competing risks problem, known as the semi-competing risks problem, in which a terminal event censors a non-terminal event, but not vice versa, in the presence of a censoring event which is independent of these two events. The joint distribution of the two dependent events is formulated under Archimedean copula. An estimator for the association parameter of the copula is proposed, which is shown to be consistent. Simulation shows that the method works well with most common Archimedean copula models.

The second part studies the properties of …

Numerical Simulations Of Thin Viscoelastic Films, Valeria Barra

Dissertations

This dissertation is developed in the field of Computational Fluid Dynamics (CFD) and it focuses on numerical simulations of the dynamics of thin viscoelastic films in different settings. The first part of this dissertation presents a novel computational investigation of thin viscoelastic films and drops, that are subject to the van der Waals interaction force, in two spatial dimensions. The liquid films are deposited on a flat solid substrate, that can have a zero or nonzero inclination with respect to the base. The equation that governs the interfacial dynamics of the thin films and drops is obtained within the long-wave …

Instabilities In Nematic Liquid Crystal Films And Droplets, Michael-Angelo Y.-H. Lam

Dissertations

The dynamics of thin films of nematic liquid crystal (NLC) are studied. Nematic liquid crystals are a type of non-Newtonian fluid with anisotropic viscous effects (due to the shape of the molecules) and elasticity effects (due to interacting electrical dipole moments). Exploiting the small aspect ratio in the geometry of interest, a fourth-order non-linear partial differential equation is used to model the free surface of the thin films. Particular attention is paid to the interplay between the bulk elasticity and the preferred orientation (boundary condition) of NLC molecules at the two interfaces: the substrate and the free surface. This work …

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 …

Stratification Of Ovarian Tumor Pathology By Expression Of Programmed Cell Death-1 (Pd-1) And Pd-Ligand- 1 (Pd-L1) In Ovarian Cancer, Maureen L. Drakes, Swati Mehrotra, Monica Aldulescu, Ronald K. Potkul, Yueying Liu, Anne Grisoli, Cara Joyce, Timothy O'Brien, M. Sharon Stack, Patrick J. Stiff

Mathematics and Statistics: Faculty Publications and Other Works

Background

Ovarian cancer is the major cause of death among gynecologic cancers with 75% of patients diagnosed with advanced disease, and only 20% of these patients having a survival duration of five years. Treatments blocking immune checkpoint molecules, programmed cell death (PD-1) or its ligand PD-ligand- I (PD-L1) have produced a beneficial and prolonged effect in a subgroup of these patients. However, there is debate in the literature concerning the prognostic value of the expression of these molecules in tumors, with immunotherapy responsiveness, and survival.

We evaluated the immune landscape of the ovarian tumor microenvironment of patients, by measuring the …

Constructing Surfaces With (1/(K-2)^2)(1,K-3) Singularities, Liam Patrick Keenan

Lawrence University Honors Projects

We develop a procedure to construct complex algebraic surfaces which are stable, minimal, and of general type, possessing a T-singularity of the form (1/(k-2)²)(1,k-3).

The Effect Of Warmer Winters On The Demography Of An Outbreak Insect Is Hidden By Intraspecific Competition, Devin W. Goodsman, Guenchik Grosklos, Brian H. Aukema, Caroline Whitehouse, Katherine P. Bleiker, Nate G. Mcdowell, Richard S. Middleton, Chonggang Xu

Mathematics and Statistics Faculty Publications

Warmer climates are predicted to increase bark beetle outbreak frequency, severity, and range. Even in favorable climates, however, outbreaks can decelerate due to resource limitation, which necessitates the inclusion of competition for limited resources in analyses of climatic effects on populations. We evaluated several hypotheses of how climate impacts mountain pine beetle reproduction using an extensive 9‐year dataset, in which nearly 10,000 trees were sampled across a region of approximately 90,000 km², that was recently invaded by the mountain pine beetle in Alberta, Canada. Our analysis supports the hypothesis of a positive effect of warmer winter temperatures on …

Full Dyon Excitation Spectrum In Extended Levin-Wen Models, Yuting Hu, Alexandra Tebbs, Yong-Shi Wu

Mathematics and Statistics Faculty Publications

In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two-dimensional topological phases, it is relatively easy to describe only single-fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations. To incorporate charged and dyonic excitations in (doubled) topological phases, an extension of the LW models is proposed in this paper. We first enlarge the Hilbert space with adding a tail on one of the edges of each trivalent vertex to describe the internal charge degrees of freedom at the vertex. Then, we study the full dyon spectrum of the extended LW models, including …

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.

Combinatorial Proofs Of Identities Of Alzer And Prodinger And Some Generalizations, John Engbers, Christopher Stocker

Mathematics, Statistics and Computer Science Faculty Research and Publications

We provide combinatorial proofs of identities published by Alzer and Prodinger. These identities include that for integers b, n, and r with b ≥ 1 and n − 1 ≥ r ≥ 0 we have

and for integers b, n, and r with b ≥ 0 and n − 1 ≥ r ≥ 0 we have

Our combinatorial proofs generalize squares to sth powers, and involve generalized Eulerian numbers and generalized Delannoy numbers.

A Discrete Mathematical Model For The Aggregation Of Β-Amyloid, Maher A. Dayeh, George Livadiotis, Saber Elaydi

Mathematics Faculty Research

Dementia associated with the Alzheimer's disease is thought to be correlated with the conversion of the β − Amyloid (Aβ) peptides from soluble monomers to aggregated oligomers and insoluble fibrils. We present a discrete-time mathematical model for the aggregation of Aβ monomers into oligomers using concepts from chemical kinetics and population dynamics. Conditions for the stability and instability of the equilibria of the model are established. A formula for the number of monomers that is required for producing oligomers is also given. This may provide compound designers a mechanism to inhibit the Aβ aggregation.

Dynamic Statistical Models For Pyroclastic Density Current Generation At Soufrière Hills Volcano, Robert L. Wolpert, Elaine T. Spiller, Eliza S. Calder

Mathematics, Statistics and Computer Science Faculty Research and Publications

To mitigate volcanic hazards from pyroclastic density currents, volcanologists generate hazard maps that provide long-term forecasts of areas of potential impact. Several recent efforts in the field develop new statistical methods for application of flow models to generate fully probabilistic hazard maps that both account for, and quantify, uncertainty. However, a limitation to the use of most statistical hazard models, and a key source of uncertainty within them, is the time-averaged nature of the datasets by which the volcanic activity is statistically characterized. Where the level, or directionality, of volcanic activity frequently changes, e.g., during protracted eruptive episodes, or at …

Orthogonal Polynomials With Respect To The Measure Supported Over The Whole Complex Plane, Meng Yang

USF Tampa Graduate Theses and Dissertations

In chapter 1, we present some background knowledge about random matrices, Coulomb gas, orthogonal polynomials, asymptotics of planar orthogonal polynomials and the Riemann-Hilbert problem. In chapter 2, we consider the monic orthogonal polynomials, $\{P_{n,N}(z)\}_{n=0,1,\cdots},$ that satisfy the orthogonality condition,

\begin{equation}\nonumber \int_\mathbb{C}P_{n,N}(z)\overline{P_{m,N}(z)}e^{-N Q(z)}dA(z)=h_{n,N}\delta_{nm} \quad(n,m=0,1,2,\cdots), \end{equation}

where $h_{n,N}$ is a (positive) norming constant and the external potential is given by

$$Q(z)=|z|^2+ \frac{2c}{N}\log \frac{1}{|z-a|},\quad c>-1,\quad a>0.$$

The orthogonal polynomial is related to the interacting Coulomb particles with charge $+1$ for each, in the presence of an extra particle with charge $+c$ at $a.$ For $N$ large and a fixed ``c'' this …

Meeting Real World Demands Of The Global Economy: An Employer's Perspective, Doreen Mcgunagle, Laura Zizka

Journal of Aviation/Aerospace Education & Research

Educational programs prepare students theoretically for the workplace, but many programs are still lacking in the real-world skills that the workplace requires. This is especially evident in Science, Technology, Engineering, and Math (STEM) education where today’s graduates hold a fundamental role in advancing science, medicine, sustainability, national security, and the economy, yet the programs to prepare them are falling short of employer expectations. At present, there is a lack of information on the necessary skills for workplace success that is specific to Airline, Aerospace, Defense (A&D) and related Industries’ STEM graduates. This paper attempts to fill this gap by offering …

Mixed Categories Of Sheaves On Toric Varieties, Sean Michael Taylor

LSU Doctoral Dissertations

In [BGS96], Beilinson, Ginzburg, and Soergel introduced the notion of mixed categories. This idea often underlies many interesting "Koszul dualities." In this paper, we produce a mixed derived category of constructible complexes (in the sense of [BGS96]) for any toric variety associated to a fan. Furthermore, we show that it comes equipped with a t-structure whose heart is a mixed version of the category of perverse sheaves. In chapters 2 and 3, we provide the necessary background. Chapter 2 concerns the categorical preliminaries, while chapter 3 gives the background geometry. This concerns both some basics of toric varieties as well …