Mathematics Commons^™

Adaptive Wavelet Discretization Of Tensor Products In H-Tucker Format, Mazen Ali

Masters Theses

"In previous work, the solution to a system of coupled parabolic PDEs, modeling the price of a CDO, was approximated numerically. Due to the nature of the problem, the system involved a large number of equations such that the parameters cannot be stored explicitly. The authors combined the data sparse H-Tucker storage format with the Galerkin method to approximate the solution, using wavelets for the space discretization together with time stepping (Method of Lines). The aforementioned approximation is of the linear kind, i.e., using a nonadaptive method. In this work, three methods for solving such systems adaptively are presented, together …

An Iterative Algorithm For Variational Data Assimilation Problems, Xin Shen

Masters Theses

"Data assimilation is a very powerful and efficient tool to use collected raw data for improving model prediction in numerical weather forecasting, hydrology, and many other areas of geosciences. In this thesis, an iterative algorithm [23] of variational data assimilation with finite element method is utilized to study different models. One motivation for this fundamental mathematical study is to provide a potential tool for simulation of CO₂ sequestration by extending it to more realistic and sophisticated models in the future. The basic idea of variational data assimilation is to utilize the framework of optimal control problems. We apply the …

On The Continued Fraction Expansion Of Some Hyperquadratic Functions, Khalil Ayadi, Fatma Taktak

Turkish Journal of Mathematics

In this paper, we consider continued fraction expansions for algebraic power series over a finite field. Especially, we are interested in studying the continued fraction expansion of a particular subset of algebraic power series over a finite field, called hyperquadratic. This subset contains irrational elements \alpha satisfying an equation \alpha = f(\alpha^r), where r is a power of the characteristic of the base field and f is a linear fractional transformation with polynomials coefficients. The continued fraction expansion for these elements can sometimes be given fully explicitly. We will show this expansion for hyperquadratic power series satisfying certain types of …

The New Method Of Determining Koebe Domains For The Class Of Typically Real Functions Under Montel's Normalization, Leopold Koczan, Pawel Zaprawa

Turkish Journal of Mathematics

We consider the class T(r) of typically real functions with the normalization f(0)=0 and f(r)=r for a fixed r \in (0,1). In the limiting case, when r tends to 0, the class T(r) coincides with the class T of typically real functions normalized by f(0)=f'(0)-1=0. In 1980, Lewandowski and Miazga determined the Koebe domain for T(r), i.e. the set of the form \bigcap_{f\in T(r)} f(\Delta). They used the method applied earlier by Goodman. In this paper we present a new, complete method of determining this set. As a corollary, we obtain the Koebe set for T.

An Existence Result For A Quasilinear System With Gradient Term Under The Keller--Osserman Conditions, Dragos Patru Covei

Turkish Journal of Mathematics

We use some new technical tools to obtain the existence of entire solutions for the quasilinear elliptic system of type \Delta _pu_i+h_i(\vert x\vert) \vert \nabla u_i\vert ^{p-1}=a_i(\vert x\vert ) f_i(u_{1},u_2) on R^N (N\geq 3, i=1,2) where N-1\geq p>1, \Delta_p is the p-Laplacian operator, and h_i, a_i, f_i are suitable functions. The results of this paper supplement the existing results in the literature and complete those obtained by Jesse D Peterson and Aihua W Wood (Large solutions to non-monotone semilinear elliptic systems, Journal of Mathematical Analysis and Applications, Volume 384, pages 284--292, 2011).

Osserman Lightlike Hypersurfaces Of Indefinite S-Manifolds, Letizia Brunetti

Turkish Journal of Mathematics

We mainly deal with the problem of admissibility for screen distributions on a lightlike hypersurface of both a semi-Riemannian manifold and an indefinite S-manifold. In the latter case, we first show that a characteristic screen distribution is never admissible, and then we provide a characterization for admissible screen distributions on proper totally umbilical lightlike hypersurfaces. Finally, in studying Osserman conditions, we characterize Osserman totally umbilical hypersurfaces of a semi-Riemannian manifold, obtaining explicit results on the eigenvalues of the pseudo-Jacobi operators in the case of lightlike hypersurfaces with Lorentzian screen leaves.

On The Size Of The Third Homotopy Group Of The Suspension Of An Eilenberg--Maclane Space, Peyman Niroomand, Francesco Russo

Turkish Journal of Mathematics

The nonabelian tensor square G \otimes G of a group G of G = p^n and G' = p^m (p prime and n,m \ge 1) satisfies a classic bound of the form G \otimes G \le p^{n(n-m)}. This allows us to give an upper bound for the order of the third homotopy group \pi_3(SK(G,1)) of the suspension of an Eilenberg--MacLane space K(G,1), because \pi_3(K(G,1)) is isomorphic to the kernel of \kappa : x \otimes y \in G \otimes G \mapsto [x,y] \in G'. We prove that G \otimes G \le p^{(n-1)(n-m)+2}, sharpening not only G \otimes G \le p^{n(n-m)} but …

Degenerate Hopf Bifurcations, Hidden Attractors, And Control In The Extended Sprott E System With Only One Stable Equilibrium, Zhouchao Wei, Irene Moroz, Anping Liu

Turkish Journal of Mathematics

In this paper, we introduce an extended Sprott E system by a general quadratic control scheme with 3 arbitrary parameters for the new system. The resulting system can exhibit codimension-one Hopf bifurcations as parameters vary. The control strategy used can be applied to create degenerate Hopf bifurcations at desired locations with preferred stability. A complex chaotic attractor with only one stable equilibrium is derived in the sense of having a positive largest Lyapunov exponent. The chaotic attractor with only one stable equilibrium can be generated via a period-doubling bifurcation. To further suppress chaos in the extended Sprott E system coexisting …

Continuity Of Wigner-Type Operators On Lorentz Spaces And Lorentz Mixed Normed Modulation Spaces, Ayşe Sandikçi

Turkish Journal of Mathematics

We study various continuity properties for \tau-Wigner transform on Lorentz spaces and \tau-Weyl operators W_{\tau}^{a} with symbols belonging to appropriate Lorentz spaces. We also study the action of \tau-Wigner transform on Lorentz mixed normed modulation spaces.

On Semiparallel Anti-Invariant Submanifolds Of Generalized Sasakian Space Forms, Ci̇han Özgür, Fatma Gürler, Cengi̇zhan Murathan

Turkish Journal of Mathematics

We consider minimal anti-invariant semiparallel submanifolds of generalized Sasakian space forms. We show that the submanifolds are totally geodesic under certain conditions.

Seiberg--Witten-Like Equations On 5-Dimensional Contact Metric Manifolds, Nedi̇m Deği̇rmenci̇, Şenay Bulut

Turkish Journal of Mathematics

In this paper, we write Seiberg--Witten-like equations on contact metric manifolds of dimension 5. Since any contact metric manifold has a Spin^c-structure, we use the generalized Tanaka--Webster connection on a Spin^c spinor bundle of a contact metric manifold to define the Dirac-type operators and write the Dirac equation. The self-duality of 2-forms needed for the curvature equation is defined by using the contact structure. These equations admit a nontrivial solution on 5-dimensional strictly pseudoconvex CR manifolds whose contact distribution has a negative constant scalar curvature.

Adjoints Of Rationally Induced Composition Operators On Bergman And Dirichlet Spaces, Aliakbar Goshabulaghi, Hamid Vaezi

Turkish Journal of Mathematics

We will state a connection between the adjoints of a vast variety of bounded operators on 2 different weighted Hardy spaces. We will apply it to determine the adjoints of rationally induced composition operators on Dirichlet and Bergman spaces.

Essential Norms Of Weighted Composition Operators Between Zygmund-Type Spaces And Bloch-Type Spaces, Amir Hossein Sanatpour, Mostafa Hassanlou

Turkish Journal of Mathematics

We investigate the boundedness of weighted composition operator u C_{\varphi} mapping the Zygmund-type space Z^{\alpha} into the Bloch-type space B^{\beta}. Then we give essential norm estimates of such an operator in terms of u and \varphi.

General Rotational Surfaces In The 4-Dimensional Minkowski Space, Georgi Ganchev, Velichka Milousheva

Turkish Journal of Mathematics

General rotational surfaces as a source of examples of surfaces in the 4-dimensional Euclidean space were introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the basis of our invariant theory of spacelike surfaces we study general rotational surfaces with special invariants. We describe analytically the flat general rotational surfaces and the general rotational surfaces with flat normal connection. We classify completely the minimal general rotational surfaces and the general rotational surfaces consisting of parabolic points.

\Xi^{\Perp}-Submanifolds Of Para-Sasakian Manifolds, Selcen Yüksel Perktaş, Mukut Mani Tripathi, Erol Kiliç, Sadik Keleş

Turkish Journal of Mathematics

Almost semiinvariant \xi^{\perp}-submanifolds of an almost paracontact metric manifold are defined and studied. Some characterizations of almost semiinvariant \xi^{\perp}-submanifolds and semiinvariant \xi^{\perp}-submanifolds are presented. A para-CR-structure is defined and it is proven that an almost semiinvariant \xi^{\perp}-submanifold of a normal almost paracontact metric (and hence para-Sasakian) manifold with the proper invariant distribution always possesses a para-\textit{CR}-structure. A counter example is also given. Integrability conditions for certain natural distributions arising on almost semiinvariant \xi^{\perp} -submanifolds are obtained. Finally, certain parallel operators on submanifolds are investigated.

A Characterization Of The Projective Transformation In Minkowski 3-Space, Yasemi̇n Alagöz

Turkish Journal of Mathematics

We consider transformations preserving asymptotic directions of surfaces in Minkowski 3-space and show that a transformation preserves the asymptotic directions of a surface if only if it is the projective one. Therefore, we obtain a characterization of the projective transformation.

A Cohen Type Inequality For Laguerre--Sobolev Expansions With A Mass Point Outside Their Oscillatory Regime, Edmundo José Huertas Cejudo, Francisco Marcellán Espanol, María Francisca Pérez Valero, Yamilet Quintana

Turkish Journal of Mathematics

Let consider the Sobolev type inner product \langle f, g\rangle_S = \int_0^{\infty} f(x)g(x)d \mu (x) + Mf(c)g(c) + Nf^{\prime}(c) g^{\prime}(c), where d\mu (x) = x^{\alpha} e^{-x}dx, \alpha > -1, is the Laguerre measure, c < 0, and M, N \geq 0. In this paper we get a Cohen-type inequality for Fourier expansions in terms of the orthonormal polynomials associated with the above Sobolev inner product. Then, as an immediate consequence, we deduce the divergence of Fourier expansions and Cesàro means of order \delta in terms of this kind of Laguerre--Sobolev polynomials.

Highly Nonconcurrent Longest Paths And Cycles In Lattices, Yasir Bashir

Turkish Journal of Mathematics

We investigate here the connected graphs with the property that any pair of vertices are missed by some longest paths (or cycles), embeddable in n-dimensional lattices L^n where L denotes the set of integers.

On Transformations Of Index 1, Leyla Bugay, Osman Kelekci̇

Turkish Journal of Mathematics

The index and the period of an element a of a finite semigroup are defined as the smallest values of m \geq 1 and r \geq 1 such that a^{m+r}=a^m, respectively. If m=1 then a is called an element of index 1. The aim of this paper is to find some properties of the elements of index 1 in T_n, which we call transformations of index 1.

On Biharmonic Legendre Curves In S-Space Forms, Ci̇han Özgür, Şaban Güvenç

Turkish Journal of Mathematics

We study biharmonic Legendre curves in S-space forms. We find curvature characterizations of these special curves in 4 cases.

Electrical Conductivity Imaging Via Boundary Value Problems For The 1-Laplacian, Johann Veras

Electronic Theses and Dissertations

We study an inverse problem which seeks to image the internal conductivity map of a body by one measurement of boundary and interior data. In our study the interior data is the magnitude of the current density induced by electrodes. Access to interior measurements has been made possible since the work of M. Joy et al. in early 1990s and couples two physical principles: electromagnetics and magnetic resonance. In 2007 Nachman et al. has shown that it is possible to recover the conductivity from the magnitude of one current density field inside. The method now known as Current Density Impedance …

The Tutte Polynomial Formula For The Class Of Twisted Wheel Graphs, Amanda Hall

Honors Theses

The 20th century work of William T. Tutte developed a graph polynomial that is modernly known as the Tutte polynomial. Graph polynomials, such as the Tutte polynomial, the chromatic polynomial, and the Jones polynomial, are at the heart of combinatorical and algebraic graph theory and can be used as tools with which to study graph invariants. Graph invariants, such as order, degree, size, and connectivity which are defined in Section 2, are graph properties preserved under all isomorphisms of a graph. Thus any graph polynomial is not dependent upon a particular labeling or drawing but presents relevant information about the …

Independence Polynomials And Extended Vertex Reduction, Jonathan Broom

Honors Theses

The independence polynomial of a graph is a polynomial whose coefficients number the independent sets of each size in that graph. This paper looks into methods of obtaining these polynomials for certain classes of graphs which prove too large to easily find the polynomial by traditional methods.

The Matrix Method Of Linear Dichroism, Kenna Collums

Honors Theses

This thesis discusses linear dichroism, and in particular the matrix method behind the spectroscopic technique. Linear dichroism uses the difference in the absorption of light that is parallel to the orientation axis and the absorption of light that is perpendicular to the orientation axis. From this process, the structure and function of molecules can be studied. The matrix method diagonalizes a Hamiltonian matrix with a unitary matrix. This Hamiltonian matrix is constructed from the transition energies, which are the diagonal elements, and coupling energies, which are off-diagonal elements.

L∞-Extremal Mappings In Amle And Teichmüller Theory, Luca Capogna

Mathematics Sciences: Faculty Publications

These lecture focus on two vector-valued extremal problems which have a common feature in that the corresponding energy functionals involve L ∞ norm of an energy density rather than the more familiar L p norms. Specifically, we will address (a) the problem of extremal quasiconformal mappings and (b) the problem of absolutely minimizing Lipschitz extensions.

The Classification Of V -Transverse Knots And Loose Legendrians, Patricia Cahn, Vladimir Chernov

Mathematics Sciences: Faculty Publications

We classify knots in a 3-manifold M that are transverse to a nowhere zero vector field V up to the corresponding isotopy relation. When V is the coorienting vector field of a contact structure, these knots are the same as pseudo-Legendrian knots, which were introduced by Benedetti and Petronio. We show that two loose Legendrian knots with the same overtwisted disk in their complement are Legendrian isotopic if and only if they are pseudoLegendrian isotopic.

V -transverse knots are naturally framed. We show that each framed isotopy class corresponds to infinitely many V -transverse isotopy classes whose elements are pairwise …

The T-Tone Chromatic Number Of Random Graphs, Deepak Bal, Patrick Bennett, Andrzej Dudek, Alan Frieze

Department of Mathematics Faculty Scholarship and Creative Works

A proper 2-tone k-coloring of a graph is a labeling of the vertices with elements from (formula presented.) such that adjacent vertices receive disjoint labels and vertices distance 2 apart receive distinct labels. The 2-tone chromatic number of a graph G, denoted τ 2(G) is the smallest k such that G admits a proper 2-tone k coloring. In this paper, we prove that w.h.p. for (formula presented.) where X represents the ordinary chromatic number. For sparse random graphs with p = c/n, c constant, we prove that (formula presented.) where Δ represents the maximum degree. For the more general concept …

Interlace Polynomials Of N-Claw Graphs, Sarita Nemani, Aihua Li

Department of Mathematics Faculty Scholarship and Creative Works

In this paper, we present the study of the interlace polynomials for n-claw graphs. For a positive integer n > 1, an n-claw graph Wn is a tree that has one center vertex and n claws. The center vertex is connected to one vertex of each of the n claws using one edge of the claw. We present iterative formulas and explicit formulas for the interlace polynomial of W n. Furthermore, some interesting properties of the polynomial are discussed.

Fast Algorithm For Finding Lattice Subspaces In Rn And Its Implementation, Andrew Martin Pownuk

Open Access Theses & Dissertations

There are known necessary and sufficient conditions for a subspace of Rm to be lattice-ordered. Let Y = {y1,…,ym} and yi are rows of the matrix X. A subspace ⟨X⟩, of linear space generated by the set X of n linearly independent positive vectors is lattice-ordered if and only the set X admits a fundamental set of indices I, which means that the subset YI ⊆ Y of vectors indexed by I is linearly independent, and every vector from Y\YI is a nonnegative linear combination of vectors form YI.

In economics it is possible to prove that the minimum-cost insured …

Homeomorphisms Between Pairs Of Genus Two Handlebodies And Separating Circles In Their Boundaries, Daniel Orlando Vazquez

Open Access Theses & Dissertations

A known result in low-dimensional topology is that every incompressible surface properly embedded in a genus two handlebody is boundary compressible. This result produces a pair consisting of a genus two handlebody and a separating curve in its boundary.

We study particular examples of genus two handlebodies and essential simple closed curves which separate their boundaries. The aim of this paper is to give our own construction of separating curves on the boundary of genus two handlebodies and compare them with previously studied pairs. These constructions involve taking 2n arcs on either side of a waist disk of a genus …