Mathematics Commons^™

The Research On Ship Financing Lease Mode And Risk Prevention, Yang Liu

World Maritime University Dissertations

No abstract provided.

Equidistribution Results For Singular Metrics On Line Bundles, Dan Coman, George Marinescu

Mathematics - All Scholarship

Let L be a holomorphic line bundle with a positively curved singular Hermitian metric over a complex manifold X. One can define naturally the sequence of Fubini-Study currents associated to the space of square integrable holomorphic sections of the p-th tensor powers of L. Assuming that the singular set of the metric is contained in a compact analytic subset of X and that the logarithm of the Bergman kernel function associated to the p-th tensor power of L (defined outside the singular set) grows like o(p) as p tends to infinity, we prove the following:
1) the k-th power of …

Non-Commutative Crepant Resolutions: Scenes From Categorical Geometry, Graham J. Leuschke

Mathematics - All Scholarship

Non-commutative crepant resolutions are algebraic objects defined by Van den Bergh to realize an equivalence of derived categories in birational geometry. They are motivated by tilting theory, the McKay correspondence, and the minimal model program, and have applications to string theory and representation theory. In this expository article I situate Van den Bergh's definition within these contexts and describe some of the current research in the area.

Isomorph-Free Generation Of 2-Connected Graphs With Applications, Derrick Stolee

School of Computing: Technical Reports

Many interesting graph families contain only 2-connected graphs, which have ear decompositions. We develop a technique to generate families of unlabeled 2-connected graphs using ear augmentations and apply this technique to two problems. In the first application, we search for uniquely Kr-saturated graphs and find the list of uniquely K4-saturated graphs on at most 12 vertices, supporting current conjectures for this problem. In the second application, we verify the Edge Reconstruction Conjecture for all 2-connected graphs on at most 12 vertices. This technique can be easily extended to more problems concerning 2-connected graphs.

Omnisculptures., Cihan Eroglu

Electronic Theses and Dissertations

In this thesis we will study conditions for the existence of minimal sized omnipatterns in higher dimensions. We will introduce recent work conducted on one dimensional and two dimensional patterns known as omnisequences and omnimosaics, respectively. These have been studied by Abraham et al [3] and Banks et al [2]. The three dimensional patterns we study are called omnisculptures, and will be the focus of this thesis. A (K,a) omnisequence of length n is a string of letters that contains each of the a^k words of length k over [A]={1,2,...a} as a substring. …

Systems Of General Nonlinear Set-Valued Mixed Variational Inequalities Problems In Hilbert Spaces, Ravi P. Agarwal, Yeolje Cho, Narin Petrot

Mathematics and System Engineering Faculty Publications

In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed) variational inequalities problems, it is clear that it cannot be directly applied to the problems …

Utilizing Induced Voxel Correlation In Fmri Analysis, Daniel B. Rowe, Andrew S. Nencka

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Directional Subdifferentials And Optimality Conditions, Ivan Ginchev, Boris S. Mordukhovich

Mathematics Research Reports

This paper is devoted to the introduction and development of new dual-space constructions of generalized differentiation in variational analysis, which combine certain features of subdifferentials for nonsmooth functions (resp. normal cones to sets) and directional derivatives (resp. tangents). We derive some basic properties of these constructions and apply them to optimality conditions in problems of unconstrained and constrained optimization.

Higher Derivatives Of The Hurwitz Zeta Function, Jason Musser

Masters Theses & Specialist Projects

The Riemann zeta function ζ(s) is one of the most fundamental functions in number theory. Euler demonstrated that ζ(s) is closely connected to the prime numbers and Riemann gave proofs of the basic analytic properties of the zeta function. Values of the zeta function and its derivatives have been studied by several mathematicians. Apostol in particular gave a computable formula for the values of the derivatives of ζ(s) at s = 0. The Hurwitz zeta function ζ(s,q) is a generalization of ζ(s). We modify Apostolʼs methods to find values of the derivatives of ζ(s,q) with respect to s at s …

Completeness Of The Leibniz Field And Rigorousness Of Infinitesimal Calculus, James F. Hall, Todor D. Todorov

Mathematics

We present a characterization of the completeness of the field of real numbers in the form of a collection of ten equivalent statements borrowed from algebra, real analysis, general topology and non-standard analysis. We also discuss the completeness of non-Archimedean fields and present several examples of such fields. As an application we exploit one of our results to argue that the Leibniz infinitesimal calculus in the 18^th century was already a rigorous branch of mathematics – at least much more rigorous than most contemporary mathematicians prefer to believe. By advocating our particular historical point of view, we hope to …

The Monodromy Conjecture For Hyperplane Arrangements, Nero Budur, Mircea Mustaţă, Zach Teitler

Mathematics Faculty Publications and Presentations

The Monodromy Conjecture asserts that if c is a pole of the local topological zeta function of a hypersurface, then exp(2πic) is an eigenvalue of the monodromy on the cohomology of the Milnor fiber. A stronger version of the conjecture asserts that every such c is a root of the Bernstein-Sato polynomial of the hypersurface. In this note we prove the weak version of the conjecture for hyperplane arrangements. Furthermore, we reduce the strong version to the following conjecture: −n/d is always a root of the Bernstein-Sato polynomial of an indecomposable essential central hyperplane arrangement …

Randic And Sum Connectivity Indices Of Certain Trees, Jennifer L. Feiner

Theses, Dissertations and Culminating Projects

The focus of this thesis is on new development of the Randic and Sum Connec­tivity Indices of certain molecular and symmetric trees representing acyclic alkanes, or aliphatic hydrocarbons. The Randic Connectivity Index is one of the most used molecular descriptors in Quantitative Structure-Property and Structure-Activity Relationship modeling because of the relation that the isomers have between their properties and their structure. The structure-boiling point relationship models of aliphatic alcohols have been studied using the Sum Connectivity Index and compared to the Randic Connectivity Index. A specific type of tree T_n,a, well-known in graph theory as a double star, …

An Examination Of The Yang-Baxter Equation, Alexandru Cibotarica

Master's Theses

The Yang-Baxter equation has been extensively studied due to its application in numerous fields of mathematics and physics. This thesis sets out to analyze the equation from the viewpoint of the algebraic product of matrices, i.e., the composition of linear maps, with the intent of characterizing the solutions of the Yang-Baxter equation.

We begin by examining the simple case of 22 matrices where it is possible to fully characterize the solutions. We connect the Yang-Baxter equation to the Cecioni-Frobenius Theorem and focus on obtaining solutions to the Yang-Baxter equation for special matrices where solutions are more easily found. Finally, …

A Comparison Of Two Different Methods For Solving Biharmonic Boundary Valve Problems, Megan Lashea Richardson

Master's Theses

We use the methods of compactly supported radial basis functions (CS-RBFs) and Delta-shaped basis functions (DBFs) to obtain the numerical solution of a two-dimensional biharmonic boundary value problem. The biharmonic equation is difficult to solve due to its existing fourth order derivatives, besides it requires more than one boundary conditions on the same part of the boundary. In this thesis, we use either a one-level or a two-level technique for constructing the approximate solution in the context of Kansa’s collocation method. This thesis will compare the accuracy of the methods of CS-RBFs and DBFs when applied to the biharmonic boundary …

Qualitative Analysis To A Nonlinear System, Pengcheng Xiao

Theses and Dissertations - UTB/UTPA

In this thesis, we first present a qualitative analysis to a nonlinear system under certain parametric conditions. Then for a special case, we make a series of variable transformation and apply the Prelle-Singer Method to find the first integrals of the simplified equations without complicated calculations. Through the inverse transformations we get the first integrals of the original equation. Finally, we use the same Prelle-Singer method to get the first integral for an extended nonlinear system.

Inverse Synthetic Aperture Radar Imaging Theory And Application, Jaime Xavier Lopez

Theses and Dissertations - UTB/UTPA

Inverse Synthetic Aperture Radar (ISAR) is an electromagnetic sensing system that is capable of producing high resolution microwave images of moving targets. Despite being developed within the engineering community, the theory of radar imaging is a subject of tremendous mathematical richness. The theory of ISAR imaging alone is filled with many applications and open problems that the mathematician and physicist may find interesting. In this thesis, the basis for a filtered back projection imaging algorithm is derived from a popular scalar wave model. This imaging algorithm is based on a filtered-adjoint method for inverting ISAR data, and allows for the …

The First-Integral Method For Duffing-Van Der Pol-Type Oscillator System, Xiaochuan Hu

Theses and Dissertations - UTB/UTPA

In this thesis, we restrict our attention to nonlinear Duffing–van der Pol–type oscillator system by means of the First-integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. Firstly we apply the Division Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to explore a quasi-polynomial first integral to an equivalent autonomous system. Then through a certain parametric condition, we derive a more general first integral of the Duffing–van …

Mathematical Methods For Biosensor Models, Qi Wang

Doctoral

A biosensor is defined as a compact analytical device incorporating a biological sensing element integrated within a physico-chemical transducer whose aim is to produce optical or electronic signals proportional to the concentration of an analyte in a sample. Biosensors offer enormous potential to detect a wide range of analytes in health care, the food industry, environmental monitoring, security and defence. The beneficial impact on society as a result of the availability of such systems is immense, therefore investigating any strategy that could reduce development times and costs and reveal alternative designs is of utmost importance. In particular, mathematical modelling and …

Modeling Instabilities Of Electrically Driven Jets Under Constant Or Variable Applied Field And Non-Zero Basic State Velocity, Sayantan Das

Theses and Dissertations - UTB/UTPA

We investigate the problem of instability of electrically forced axisymmetric jets with respect to temporally and spatially growing disturbances, within parameter regimes that affects the process of electrospinnning. Deriving a dispersion relation based on the relevant approximated versions of the equations of the electro-hydrodynamics for an electrically forced jet flow. For temporal instability, we find in the non-zero basic state velocity, the growth rate of the unstable mode is unaffected by the value of the basic state velocity. But, the basic state velocity affects the period of the unstable mode in the sense that it decreases the period, and the …

On The Acceleration Of Explicit Finite Difference Methods For Option Pricing, Stephen O'Sullivan, Conall O'Sullivan

Articles

Implicit finite difference methods are conventionally preferred over their explicit counterparts for the numerical valuation of options. In large part the reason for this is a severe stability constraint known as the Courant–Friedrichs–Lewy (CFL) condition which limits the latter class’s efficiency. Implicit methods, however, are difficult to implement for all but the most simple of pricing models, whereas explicit techniques are easily adapted to complex problems. For the first time in a financial context, we present an acceleration technique, applicable to explicit finite difference schemes describing diffusive processes with symmetric evolution operators, called Super-Time-Stepping. We show that this method can …