Physical Sciences and Mathematics Commons^™

Reliability Studies Of The Skew Normal Distribution, Nicole Dawn Brown

Electronic Theses and Dissertations

It has been observed in various practical applications that data do not conform to the normal distribution, which is symmetric with no skewness. The skew normal distribution proposed by Azzalini(1985) is appropriate for the analysis of data which is unimodal but exhibits some skewness. The skew normal distribution includes the normal distribution as a special case where the skewness parameter is zero. In this thesis, we study the structural properties of the skew normal distribution, with an emphasis on the reliability properties of the model. More specifically, we obtain the failure rate, the mean residual life function, and the reliability …

Symplectic Maps To Projective Spaces And Symplectic Invariants, Denis Auroux

Turkish Journal of Mathematics

After reviewing recent results on symplectic Lefschetz pencils and symplectic branched covers of \CP^2, we describe a new construction of maps from symplectic manifolds of any dimension to \CP^2 and the associated monodromy invariants. We also show that a dimensional induction process makes it possible to describe any compact symplectic manifold by a series of words in braid groups and a word in a symmetric group.

The Topology Of Symplectic Manifolds, Robert E. Gompf

Turkish Journal of Mathematics

A topological structure is introduced that seems likely to provide a complete topological characterization of compact symplectic manifolds. The article begins with a leisurely introduction to symplectic manifolds from a topological viewpoint. It then focuses on Thurston's construction of a symplectic structure on the total space of a fiber bundle. This is generalized to a technique for putting a symplectic structure on the domain of a J-holomorphic map. A topological structure called a hyperpencil on a compact 2n-manifold is then defined; this is motivated by the special case of a linear system of curves on an algebraic manifold, and it …

Surface Bundles: Some Interesting Examples, Jim Bryan, Ron Donagi, Andras I. Stipsicz

Turkish Journal of Mathematics

We show two constructions of surface bundles over Riemann surfaces admitting nonvanishing signatures.

Torus Fibrations On Symplectic Four-Manifolds, Ivan Smith

Turkish Journal of Mathematics

This paper has two essentially unrelated halves. In the first we prove that a closed symplectic four-manifold admitting a fibration by connected, homologically essential Lagrangian tori with "tame" singularities, is fibre-preserving diffeomorphic to a K3 surface or to a torus bundle over a torus with first Betti number at least three. In the second, we prove that these torus bundles over tori admit Lefschetz pencils by genus three curves. It follows that the genus three mapping class group admits infinitely many inequivalent irreducible positive relations. Motivations for the questions are provided from mirror symmetry, integrable systems and Seiberg-Witten theory: in …

Floer Homology And Its Continuity For Non-Compact Lagrangian Submanifolds, Yong-Geum Oh

Turkish Journal of Mathematics

We give a construction of the Floer homology of the pair of vnon-compact Lagrangian submanifolds, which satisfies natural continuity property under the Hamiltonian isotopy that moves the infinity but leaves the intersection set of the pair compact. This construction uses the concept of Lagrangian cobordism and certain singular Lagrangian submanifolds. We apply this construction to conormal bundles (or varieties) in the cotangent bundle, and relate it to a conjecture made by MacPherson on the intersection theory of the characteristic Lagrangian cycles associated to the perverse sheaves constructible to a complex stratification on the complex algebraic manifold.

A Partial Order On The Group Of Contactomorphisms Of $\R^{2n+1}$ Via Generating Functions, Mohan Bhupal

Turkish Journal of Mathematics

In this note we construct a nontrivial partial order on the identity component of the group of compactly supported contactomorphisms of \R^{2n+1} using the method of generating functions. Our construction is in the framework of the theory developed by Viterbo in the paper \cite{V} wherein, among other things, he showed how one could use generating functions to construct a partial order on the group of compactly supported Hamiltonian symplectomorphisms of \R^{2n}.

Knotting Of Algebraic Curves In Complex Surfaces, Sergey Finashin

Turkish Journal of Mathematics

For any d\ge 5, I constructed infinitely many pairwise smoothly non-equivalent surfaces F\subset\Cp{2} homeomorphic to a non-singular algebraic curve of degree d, realizing the same homology class as such a curve and having abelian fundamental group \pi_1(\Cp2\stmin F). It is a special case of a more general theorem, which concerns for instance those algebraic curves, A, in a simply connected algebraic surface, X, which admit irreducible degenerations to a curve A_0, with a unique singularity of the type X_9, and such that A\cite A>16.

Topological Quantum Field Theory And Hyperkähler Geometry, Justin Sawon

Turkish Journal of Mathematics

Rozansky and Witten proposed a 3-dimensional sigma-model whose target space is a hyperkähler manifold. They conjectured that this theory has an associated TQFT, with vector spaces given by certain cohomology groups of the hyperkähler manifold. On the other hand, there is a certain modified TQFT constructed by Murakami and Ohtsuki using the universal quantum invariant. We explain how the Rozansky-Witten TQFT can be obtained from the latter by applying a "hyperkähler weight system".

Induced Cat^1-Groups, Murat Alp

Turkish Journal of Mathematics

In this paper we define the pullback cat^1-group and show that this Pullback has a right adjoint which is the induced cat^1-group. Later we show that this right adjoint is a pushout of category of cat^1-groups. We calculate the Peiffer subgroups to find a finite group of the source of induced cat^1-groups. The generating set of Peiffer subgroups are also given in this paper. All results are corrected by a GAP[13] program package in [4]. This paper also contains the some computational examples which are the calculation-induced cat^1-group and comparative times between the induced crossed modules and induced cat^1-groups.

P -Banach Algebras With Generalized Involution And C^*-Algebra Structure, Abdellah El Kinani, Aziz Ifzarne, Mohamed Oudadess

Turkish Journal of Mathematics

In this paper, we consider p-Banach algebras endowed with a generalized involution. We show that various C^*-like conditions force the algebra to be C^*-algebra under an equivalent norm.

Inequalities For The Vibrating Clamped Plate Problem, Kimberley Mchale, Ünal Ufuktepe

Turkish Journal of Mathematics

We study the eigenvalues of the vibrating clamped plate problem. We have made improvements on the bounds of the ratios of the eigenvalues of the biharmonic operator (clamped plate) using the methods of Payne, Polya, and Weinberger. The difference in our proof lies mainly with the trial functions and the orthogonality arguments. While Payne, Polya, and Weinberger and Hile and Yeh project away components along u_1,u_2,...,u_k to meet the orthogonality conditions,we use a translation/rotation argument to meet these conditions.

A Perturbed Version Of The Ostrowski Inequality For Twice Differentiable Mappings, A. Sofo, S. S. Dragomir

Turkish Journal of Mathematics

A generalisation of a perturbed version of the Ostrowski inequality for twice differentiable mappings is studied. It is shown that the error bounds are better than those obtained previously. Applications for general quadrature formulae are also given.

On The L^P Solutions Of Dilation Equations, İbrahi̇m Kirat

Turkish Journal of Mathematics

In this paper, the concepts concerning the space of constant breadth were extended to E^n-space. An approximate solution of the equation system which belongs to this curve was obtained. Using this solution vectorial expression of the curves of constant breadth was obtained. The relation \int_0^{2\pi}\widetilde{f}(s)\,ds=0 between the curvatures of curves of constant breadth in E^n was obtained. Key Words and Phrases: Curvature, Constant Breadth, Integral Characterization of Curve"> MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']], displayMath: [['\\[','\\]'], ['$$','$$']]}}); Academic Journals Find Manuscript Copyright Release Form Copyright Release Form(Turkey) Copyright Release Form(Other Countries) Manuscript Submission and Evaluation System On the L^p Solutions of Dilation …

Some Characterization Of Curves Of Constant Breadth In E^N Space, Zülfi̇gar Akdoğan, Abdullah Mağden

Turkish Journal of Mathematics

In this paper, the concepts concerning the space of constant breadth were extended to E^n-space. An approximate solution of the equation system which belongs to this curve was obtained. Using this solution vectorial expression of the curves of constant breadth was obtained. The relation \int_0^{2\pi}\widetilde{f}(s)ds=0 between the curvatures of curves of constant breadth in E^n was obtained. Key Words and Phrases: Curvature, Constant Breadth, Integral Characterization of Curve

Fuzzy Maximal Ideals Of Gamma Near-Rings, Young Bae Yun, Kyung Ho Kim, Mehmet Ali̇ Öztürk

Turkish Journal of Mathematics

Fuzzy maximal ideals and complete normal fuzzy ideals in \Gamma-near-rings are considered, and related properties are investigated.

On The Lebesgue Measure Of Self-Affine Sets, İbrahi̇m Kirat

Turkish Journal of Mathematics

Flaherty and Wang studied Haar-type multiwavelets and multi-tiles. The information on what digit sets give multi-attractors with positive Lebesgue measure is very limited. In this note, we give a few classes of digit sets leading to multi-attractors with positive measure. The attractors we obtain include the Haar-type multi-tiles of Flaherty and Wang.

On An Application Of The Hardy Classes To The Riemann Zeta-Function, K. Ilgar Eroglu, Iossif V. Ostrovskii

Turkish Journal of Mathematics

We show that the function f(z) : = \frac{z}{1-z} \zeta (\frac{1}{1-z}), z < 1, belongs to the Hardy class H_{p} if and only if 0 < p < 1.

Tangent Lines Of Generalized Regular Curves Parametrized By Time Scales, Gusei̇n Gusei̇nov, Emi̇n Özyilmaz

Turkish Journal of Mathematics

In this paper a generalization of the notion of regular curve is introduced. For such curves the concept of tangent line is investigated.

The Renner Monoids And Cell Decompositions Of The Classical Algebraic Monoids, Zhenheng Li

Digitized Theses

The Renner monoids, cross section lattices and cell decompositions of the classical algebraic monoids are studied.

The Renner monoid is extremely important in the theory of reductive algebraic monoids. It is well know that the Renner monoid [Special characters omitted.] of M_n (K ) is the monoid of all zero-one matrices which have at most one entry equal to one in each row and column, i.e., [Special characters omitted.] consists of injective partial maps on a set of n elements. We obtain that the Renner monoids of the symplectic algebraic monoids and special orthogonal algebraic monoids turn out …

Ranked Set Sampling From Location-Scale Families Of Symmetric Distributions, Ram C. Tiwari, Paul H. Kvam

Department of Math & Statistics Faculty Publications

Statistical inference based on ranked set sampling has primarily been motivated by nonparametric problems. However, the sampling procedure can provide an improved estimator of the population mean when the population is partially known. In this article, we consider estimation of the population mean and variance for the location-scale families of distributions. We derive and compare different unbiased estimators of these parameters based on independent replications of a ranked set sample of size n. Large sample properties, along with asymptotic relative efficiencies, help identify which estimators are best suited for different location-scale distributions.

A Multigrid Method For Elliptic Grid Generation Using Compact Schemes, Balaji S. Iyangar

Doctoral Dissertations

Traditional iterative methods are stalling numerical processes, in which the error has relatively small changes from one iteration to the next. Multigrid methods overcome the limitations of iterative methods and are computationally efficient. Convergence of iterative methods for elliptic partial differential equations is extremely slow. In particular, the convergence of the non-linear elliptic Poisson grid generation equations used for elliptic grid generation is very slow. Multigrid methods are fast converging methods when applied to elliptic partial differential equations. In this dissertation, a non-linear multigrid algorithm is used to accelerate the convergence of the non-linear elliptic Poisson grid generation method. The …

The Problem Of A Viscoelastic Cylinder Rolling On A Rigid Half-Space, John Murrough Golden, G.A.C. Graham

Articles

The problem of a viscoelastic cylinder rolling on a rigid base, propelled by a line force acting at its centre, is solved in the noninertial approximation. The method used is based on a decomposition of hereditary integrals developed by the authors in previous work, and on the viscoelastic Kolosov-Muskhelishvili equations which are used to generate a Hilbert problem. In this formulation, the problem reduces to a nonsingular integral equation in space and time, which simplifies under steady-state conditions and for exponential decay materials, to algebraic form. There are also two subsidiary conditions.

In the case of a standard linear model, …

On Powers Of 2 Dividing The Values Of Certain Plane Partition Functions, Darrin D. Frey, James A. Sellers

Science and Mathematics Faculty Publications

We consider two families of plane partitions: totally symmetric self-complementary plane partitions (TSSCPPs) and cyclically symmetric transpose complement plane partitions (CSTCPPs). If T(n) and C(n) are the numbers of such plane partitions in a 2n × 2n × 2nbox, then

ord₂(T(n)) = ord₂(C(n))

for all n >= 1. We also discuss various consequences, along with other results on ord₂(T(n)).

Identities For The Multiple Polylogarithm Using The Shuffle Operation, Ji Hoon Ryoo

Electronic Theses and Dissertations

At the beginning of my research, I understood the shuffle operation and iterated integrals to make a new proof-method (called a combinatorial method). As a first work, I proved an combinatorial identity 2 using a combinatorial method. While proving it, I got four identities and showed that one of them is equal to an analytic identity 1 which is found at the paper [2] written by David M. Bradley and Doug Bowman. Furthermore, I derived an formula involving nested harmonic sums. Using Maple (a mathematical software), I found a new combinatorial identity 3 and derived two formulas: One is related …

On The Semi-Markovian Random Walk Process With Reflecting And Delaying Barrriers, Selahatti̇n Maden

Turkish Journal of Mathematics

In this paper, a semi-Markovian random walk process X(t) with reflecting barrier on the zero-level and delaying barrier on the \beta(\beta>0 )-level and the first falling moment of the process into the delaying barrier, (\gamma), are considered. Some probability characteristics of \gamma , such as its distribution function, moment generating function and expected value are calculated.

The Multiplicities Of A Dual-Thin Q-Polynomial Association Scheme, Bruce E. Sagen, John S. Caughman Iv

Mathematics and Statistics Faculty Publications and Presentations

Let Y=(X,{Ri}1≤i≤D) denote a symmetric association scheme, and assume that Y is Q-polynomial with respect to an ordering E₀,...,E_D of the primitive idempotents. Bannai and Ito conjectured that the associated sequence of multiplicities mi (0≤i≤D) of Yis unimodal. Talking to Terwilliger, Stanton made the related conjecture that mi≤mi+1 and mi≤mD−i for i<D/2. We prove that if Y is dual-thin in the sense of Terwilliger, then the …

On Qr-Submanifolds Of A Quaternionic Space Form, Bayram Şahi̇n

Turkish Journal of Mathematics

In this paper, we investigate mixed QR-submanifolds in a quaternionic space form and pseudo umbilical QR-submanifold of a quaternionic space form under some additional condition. Finally we give a necessary condition for QR-submanifold of a quaternion Kaehler manifold such that \dim \upsilon ^{\perp }=1 to be a 3-quasi Sasakian Manifold.

On The Existence Of Finite Type Link Homotopy Invariants, Blake Mellor, Dylan Thurston

Mathematics, Statistics and Data Science Faculty Works

We show that for links with at most 5 components, the only finite type homotopy invariants are products of the linking numbers. In contrast, we show that for links with at least 9 components, there must exist finite type homotopy invariants which are not products of the linking numbers. This corrects previous errors of the first author.

What To Do On Your Summer Vacation, Alissa Crans

Mathematics, Statistics and Data Science Faculty Works

Summer vacation brings back fond memories: playing frisbee in the park, bike-riding till dusk, sipping lemonade on the porch with Grandpa, collecting shells at the beach, solving that difficult math problem you've been working on for the past several weeks. Wait a minute, you say? Many mathematics majors don't realize that numerous summer opportunities exist (many of them paid, so you don't need to get that job bagging groceries, too). A math program provides intellectual stimulation during those hot summer months, bringing your level of concentration up from swatting flies and applying sunscreen. The following descriptions are from actual participants …