Mathematics Commons^™

Zero-Dimensional Spaces And Their Inverse Limits, Sahika Sahan

Doctoral Dissertations

"In this dissertation we investigate zero-dimensional compact metric spaces and their inverse limits. We construct an uncountable family of zero-dimensional compact metric spaces homeomorphic to their Cartesian squares. It is known that the inverse limit on [0,1] with an upper semi-continuous function with a connected graph has either one or infinitely many points. We show that this result cannot be generalized to the inverse limits on simple triods or simple closed curves. In addition to that, we introduce a class of zero-dimensional spaces that can be obtained as the inverse limits of arcs. We complete by answering a problem by …

T-Closed Sets, Multivalued Inverse Limits, And Hereditarily Irreducible Maps, Hussam Abobaker

Doctoral Dissertations

"This dissertation consists of three subjects: T-closed sets, inverse limits with multivalued functions, and hereditarily irreducible maps.

For a subset A of a continuum X define T(A) = X \ {x ∈ X : there exists a subcontinuum K of X such that x ∈ int_xX(K) ⊂ K ⊂ X \ A}. This function was defined by F. Burton Jones and extensively investigated in the book [20] by Sergio Macias. A subset A of a continuum X is called T-closed set if T(A) = A. A characterization of T-closed set is given using generalized …

Balanced Truncation Model Reduction Of Nonlinear Cable-Mass Pde System, Madhuka Hareena Lochana Weerasinghe

Doctoral Dissertations

We consider model order reduction of a cable-mass system modeled by a one dimensional wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at the left boundary of the cable. A mass-spring model at the right end of the cable includes a nonlinear stiffening force. The goal of the model reduction is to produce a low order model that produces an accurate approximation to the displacement and velocity of the mass in the nonlinear mass-spring system at the right boundary. We believe the nonlinear cable-mass …

Characterization Of Rectifying And Sphere Curves In R^3, Yun Myung Oh, Julie Logan

Faculty Publications

Studies of curves in 3D-space have been developed by many geometers and it is known that any regular curve in 3D space is completely determined by its curvature and torsion, up to position. Many results have been found to characterize various types of space curves in terms of conditions on the ratio of torsion to curvature. Under an extracondition on the constant curvature, Y.L. Seo and Y. M. Oh found the series solution when the ratio of torsion to curvature is a linear function. Furthermore, this solution is known to be a rectifying curve by B. Y. Chen’s work. This …

A Product Structure On Generating Family Cohomology For Legendrian Submanifolds, Ziva Myer

Bryn Mawr College Dissertations and Theses

One way to obtain invariants of some Legendrian submanifolds in the standard contact manifolds of 1-jet spaces, J1M, is through the Morse theoretic technique of generating families. This dissertation extends the elective but not complete invariant of generating family cohomology by giving it a product μ2. To define the product, moduli spaces of gradient flow trees are constructed and shown to live as the 0-stratum of a compact smooth manifold with corners. These spaces consist of intersecting gradient trajectories of functions whose critical points correspond to Reeb chords of the Legendrian. This dissertation lays the foundation for an A1 algebra …

Occupation Time Problem Of Certain Self-Similar Processes Related To The Fractional Brownian Motion, Aissa Sghir, Mohamed A. Ouahra, Soufiane Moussaten

Communications on Stochastic Analysis

No abstract provided.

Extensions Of The Hitsuda–Skorokhod Integral, Peter Parczewski

Communications on Stochastic Analysis

No abstract provided.

The Double Barrier Problem With Double Exponential Jump Diffusion, Julius Esunge, Kalev Pärna, Dean Teneng

Communications on Stochastic Analysis

No abstract provided.

Complexities Of Bi-Colored Rubik's Cubes, Taylor Pieper

Undergraduate Honors Thesis Collection

Which of two bi-colored cubes is the simpler puzzle? The differences in the coloring of the cubes creates different symmetries that dramatically reduce the number of states each cube can reach. Which of the symmetries is most reductive? The answer to these questions can be achieved by discovering and comparing the “God’s Number” for these cubes.

Periodicity In Iterated Algebraic K-Theory Of Finite Fields, Gabriel Angelini-Knoll

Wayne State University Dissertations

In this dissertation, we study the interactions between periodic phenomena in the homotopy groups of spheres and algebraic K-theory of ring spectra. C. Ausoni and J. Rognes initiated a program to study the arithmetic of ring spectra using algebraic K-theory and gave a higher chromatic version of the Lichtenbaum-Quillen conjecture, called the red-shift conjecture, that is expected to govern this arithmetic. This dissertation provides a proof of a special case of a variation on the red-shift conjecture. Specifically, we show that, under conditions on the order of the fields, iterated algebraic K-theory of finite fields detects a periodic family chromatic …

Paraboline Variation Of P-Adic Families Of (Φ; Γ)-Modules, John Bergdall

Mathematics Faculty Research and Scholarship

We study the p-adic variation of triangulations over p-adic families of 𝜑 𝛤 -modules. In particular, we study certain canonical sub-filtrations of the pointwise triangulations and show that they extend to affinoid neighborhoods of crystalline points. This generalizes results of Kedlaya, Pottharst and Xiao and (independently) Liu in the case where one expects the entire triangulation to extend. We also study the ramification of weight parameters over natural -adic families.

Dialectric Materials With Memory 1: Minimum And General Free Energies., Scott Glascow, John Murrough Golden

Articles

A general tensor isothermal theory of free energies and free enthalpies for dielectrics is presented, corresponding to linear constitutive relations with memory. Starting from the general equations of continuum thermodynamics, various properties of and constraints on free energy/enthalpy functionals in dielectric media are noted. It is well-known that free enthalpies are particularly convenient in that their properties are closely analogous with those of free energies in mechanics, though different in crucial ways. General constitutive equations with memory are determined from a given free enthalpy. The form of the relaxation function, which occurs in these constitutive equations, is discussed from a …

Dressing Method For The Degasperis-Procesi Equation, Adrian Constantin, Rossen Ivanov

Articles

The soliton solutions of the Degasperis–Procesi equations are constructed by the implementation of the dressing method. The form of the one and two soliton solutions coincides with the form obtained by Hirota's method.

Dielectric Materials With Memory Ii: Free Energies In Non- Magnetic Materials, Scott Glascow, John Murrough Golden

Articles

An isothermal theory of free energies and free enthalpies, corresponding to linear constitutive relations with memory, is presented for isotropic non-magnetic materials. This is a second paper, following recent work on a general tensor theory of isothermal dielectrics and on the form of the minimum free energy. Both papers are based on continuum thermodynamics. For a standard choice of relaxation function, the minimum and maximum free energies are given explicitly, using a method previously developed in a mechanics context. Also, a new family of intermediate free energy functionals is derived for dielectrics. All these are solutions of a constrained optimization …

Cutaneous Malignant Melanoma Incidences Analyzed Worldwide By Skin Type Over Advancing Age Of Males And Females: Evidence Estrogen And Androgenic Hair Are Risk Factors, Dianne E. Godar, Madhan Subramanian, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

We previously analyzed cutaneous malignant melanoma (CMM) incidences worldwide by sex, age, and Fitzpatrick skin type over time (1955-2007) and found only European-ancestry populations have exponential increasing incidences and about a 2-log increase in the risk between the youngest age groups (0-14 and 15-29 yr). We proposed the increasing incidence over time may be from the spread of Human Papilloma Virus (HPV) found in CMM biopsies, and that the 2-log incidence increase between the youngest age groups might be from developing androgenic hair. The increasing incidence with age may be from white hairs transmitting UV radiation to follicular melanocytes. Here …

Accuracy And Precision In Force-Distance Curves, Stephen Morgan

Summer Community of Scholars Posters (RCEU and HCR Combined Programs)

No abstract provided.

Suborbital Graphs For The Atkin-Lehner Group, Tuncay Köroğlu, Bahadir Özgür Güler, Zeynep Şanli

Turkish Journal of Mathematics

We investigate suborbital graphs for an imprimitive action of the Atkin-Lehner group on a maximal subset of extended rational numbers on which a transitive action is also satisfied. Obtaining edge and some circuit conditions, we examine some combinatorial properties of these graphs.

Edge-Transitive Bipartite Direct Products, Cameron M. Crenshaw

Theses and Dissertations

In their recent paper ``Edge-transitive products," Hammack, Imrich, and Klavzar showed that the direct product of connected, non-bipartite graphs is edge-transitive if and only if both factors are edge-transitive, and at least one is arc-transitive. However, little is known when the product is bipartite. This thesis extends this result (in part) for the case of bipartite graphs using a new technique called "stacking." For R-thin, connected, bipartite graphs A and B, we show that A x B is arc-transitive if and only if A and B are both arc-transitive. Further, we show A x B is edge-transitive only …

Adult Learners, Learning Disabilities, And Mathematics : A Case Study, Marguerite Sheehan Flood

Theses, Dissertations and Culminating Projects

The purpose of this research was to understand how mathematics is taught at a small, liberal arts college that self-advertised as accommodating diverse learners. A qualitative case study was conducted on the mathematics program at Waterview College. Waterview College is unique in that almost half of their students self-identify with a disability, including learning disabilities (LD). The number of students with learning disabilities that attend college is increasing; therefore it is important for mathematics instructors to understand and accommodate diverse learners. The data for this research were collected using one-on-one instructor interviews, classroom observations, and student focus group interviews. The …

Torsion Freeness Of Symmetric Powers, Exterior Powers, And Schur Functors, Muberra Allahverdi

Legacy Theses & Dissertations (2009 - 2024)

Let $R$ be a local Noetherian commutative ring and $I$ an ideal with projective dimension less than or equal to 1. Necessary and sufficient conditions were provided in \cite{T2007} for a symmetric power $S_kI$ of an ideal of projective dimension 1 to be torsion free, where $k \geq 2$. We extend this result to symmetric powers and a broad class of Schur functors of finitely generated $R$-modules with projective dimension 1. While doing so, we also study the structure of Schur complexes from \cite{ABW1982}, and provide necessary and sufficient conditions for the acyclicity of the Schur complex by computing the …

Complexity Theoretic Parallels Among Automata, Formal Languages And Real Variables : Including Multi-Patterns, L-Systems And Cellular Automata, Jingnan Xie

Legacy Theses & Dissertations (2009 - 2024)

In this dissertation, we emphasize productiveness not just undecidability since pro- ductiveness implies constructive incompleteness. Analogues of Rice’s Theorem for different classes of languages are investigated, refined and generalized. In particular, several sufficient but general conditions are presented for predicates to be as hard as some widely discussed predicates such as “= ∅” and “= {0,1}∗”. These conditions provide several general methods for proving complexity/productiveness results and apply to a large number of simple and natural predicates. As the first step in apply- ing these general methods, we investigate the complexity/productiveness of the pred- icates “= ∅”, “= {0,1}∗” and …

The Alexander Polynominal For Virtual Twist Knots, Isaac Benioff, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

We define a family of virtual knots generalizing the classical twist knots. We develop a recursive formula for the Alexander polynomial Δ0 (as defined by Silver and Williams [Polynomial invariants of virtual links, J. Knot Theory Ramifications12 (2003) 987–1000]) of these virtual twist knots. These results are applied to provide evidence for a conjecture that the odd writhe of a virtual knot can be obtained from Δ0 .

On The Volume Of The Indicatrix Of A Complex Finsler Space, Elena Popovici

Turkish Journal of Mathematics

Following the study on volume of indicatrices in a real Finsler space, in this paper we are investigating some volume properties of the indicatrix considered in an arbitrary fixed point of a complex Finsler manifold. Since for each point of a complex Finsler space the indicatrix is an embedded CR-hypersurface of the punctured holomorphic tangent bundle, by means of its normal vector, the volume element of the indicatrix is determined. Thus, the volume function is pointed out and its variation is studied. Conditions under which the volume is constant are also determined and some classes of complex Finsler spaces with …

Nonpolynomial Spline Technique For The Solution Of Ninth Order Boundary Value Problems, Ghazala Akram, Zara Nadeem

Turkish Journal of Mathematics

In this paper, a nonpolynomial spline technique is applied to solve the ninth order linear special case boundary value problems. The end conditions are derived to complete the definition of a spline. Three examples are numerically illustrated to check the efficiency of the method. The comparative analysis shows that the proposed technique gives better results than the homotopy perturbation method and the modified variational iteration method.

Positive Solutions Of First Order Boundary Value Problems With Nonlinear Nonlocal Boundary Conditions, Smita Pati, Seshadev Padhi

Turkish Journal of Mathematics

We consider the existence of positive solutions of the nonlinear first order problem with a nonlinear nonlocal boundary condition given by $x^{\prime}(t) = r(t)x(t) + \sum_{i=1}^{m} f_i(t,x(t)), t \in [0,1]$ $\lambda x(0) = x(1) + \sum_{j=1}^{n} \Lambda_j(\tau_j, x(\tau_j)),\tau_j \in [0,1],$ where $r:[0,1] \rightarrow [0,\infty)$ is continuous, the nonlocal points satisfy $0 \leq \tau_1 < \tau_2 < ... < \tau_n \leq 1$, the nonlinear functions $f_i$ and $\Lambda_j$ are continuous mappings from $[0,1] \times [0,\infty) \rightarrow [0,\infty)$ for $i = 1,2,...,m$ and $j = 1,2,...,n$ respectively, and $\lambda >1$ is a positive parameter. The Leray-Schauder theorem and Leggett--Williams fixed point theorem were used to prove our results.

Some Results On The $\Mathcal{P}_{V,2n}$, $\Mathcal{K}_{V,N}$, And $\Mathcal{H}_{V,N}$-Integral Transforms, Ayşe Neşe Dernek, Fati̇h Aylikci

Turkish Journal of Mathematics

In this paper, the authors consider the $\mathcal{P}_{v,2n}$-transform, the $\mathcal{G}_n$-transform, and the $\mathcal{K}_{v,n}$-transform as generalizations of the Widder potential transform, the Glasser transform, and the $\mathcal{K}_v$-transform, respectively. Many identities involving these transforms are given. A number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. Some useful corollaries for evaluating infinite integrals of special functions are presented. Illustrative examples are given for the results.

Sufficient Conditions On Nonunitary Operators That Imply The Unitary Operators, Pabitra Kumar Jena

Turkish Journal of Mathematics

In this paper, we give sufficient conditions on nonunitary operators on the Bergman space that imply the unitary operators.

On Certain Gbs-Durrmeyer Operators Based On $Q$-Integers, Dan Barbosu, Ana Maria Acu, Carmen Violeta Muraru

Turkish Journal of Mathematics

In the present paper we introduce the $GBS$ (Generalized Boolean Sum) operators of Durrmeyer type based on $q$-integers and the approximation of B-continuous functions using the above operators is studied. In addition, a uniform convergence theorem is established and the degree of approximation in terms of mixed modulus of continuity is evaluated. The study contains in the last section numerical considerations regarding the constructed operators based on MATLAB algorithms.

A Bivariate Sampling Series Involving Mixed Partial Derivatives, Rashad Mudhish Asharabi, Hamoud Al-Haddad

Turkish Journal of Mathematics

Recently Fang and Li established a sampling formula that involves only samples from the function and its first partial derivatives for functions from Bernstein space, $B^{p}_{\sigma}(\mathbb{R}^{2})$. In this paper, we derive a general bivariate sampling series for the entire function of two variables that satisfy certain growth conditions. This general bivariate sampling formula involves samples from the function and its mixed and nonmixed partial derivatives. Some known sampling series will be special cases of our formula, like the sampling series of Parzen, Peterson and Middleton, and Gosselin. The truncated series of this formula are used to approximate functions from the …

An Age-Structured Model For The Transmission Dynamics Of Hepatitis B: Asymptotic Analysis, Rodrigue Yves M'Pika Makoussou, Aboubakari Traore

Turkish Journal of Mathematics

In this paper, we consider the age-structured model for the transmission dynamics of Hepatitis B virus (HBV) proposed earlier in the article by Zou et al.: An age-structured model for transmission dynamics of hepatitis B. SIAM J Appl Math 2010; 70: 3121-3139, where a slight modification is made. We consider that the HBV infection processes act on a time scale different from that of the vital processes. Such a model becomes a multiple time scale model and thus it often can be significantly simplified by various asymptotic methods. We apply, as in the paper of Banasiak and M'pika Massoukou: A …