Mathematics Commons^™

A Higher-Order Ensemble/Proper Orthogonal Decomposition Method For The Nonstationary Navier-Stokes Equations, Max Gunzburger, Nan Jiang, Michael Schneier

Mathematics and Statistics Faculty Research & Creative Works

Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and optimization, inference, and several statistical techniques. The solution for even a single case may be quite expensive; whereas parallel computing may be applied, this reduces the total elapsed time but not the total computational effort. In the case of flows governed by the Navier-Stokes equations, a method has been devised for computing an ensemble of solutions. Recently, a reduced-order model derived from a proper orthogonal decomposition (POD) …

Parametrization Of Scale-Invariant Self-Adjoint Extensions Of Scale-Invariant Symmetric Operators, Miron B. Bekker, Martin Bohner, Alexander P. Ugol'nikov, Hristo Voulov

Mathematics and Statistics Faculty Research & Creative Works

On a Hilbert space H, we consider a symmetric scale-invariant operator with equal defect numbers. It is assumed that the operator has at least one scale invariant self-adjoint extension in H. We prove that there is a one-to-one correspondence between (generalized) resolvents of scale-invariant extensions and solutions of some functional equation. Two examples of Dirac-type operators are considered.

On The Chebyshev Coefficients For A General Subclass Of Univalentfunctions, Şahsene Altinkaya, Si̇bel Yalçin Tokgöz

Turkish Journal of Mathematics

In this work, considering a general subclass of univalent functions and using the Chebyshev polynomials, we obtain coefficient expansions for functions in this class.

Linear Methods Of Summing Fourier Series And Approximation In Weighted Orliczspaces, Sadulla Jafarov

Turkish Journal of Mathematics

In the present work, we investigate estimates of the deviations of the periodic functions from the linear operators constructed on the basis of its Fourier series in reflexive weighted Orlicz spaces with Muckenhoupt weights. In particular, the orders of approximation of Zygmund and Abel-Poisson means of Fourier trigonometric series were estimated by the $k-th$~modulus of smoothness in reflexive weighted Orlicz spaces with Muckenhoupt weights.

The Diameter Vulnerability Of The Generalized Petersen Graph ${Gp[Tk,K]}$, Gülnaz Boruzanli Eki̇nci̇, John Baptist Gauci

Turkish Journal of Mathematics

The diameter of a graph gives the length of the longest path among all the shortest paths between any two vertices of the graph, and the diameter vulnerability problem measures the change in the diameter upon the deletion of edges. In this paper we determine the diameter vulnerability of the generalized Petersen graph $GP[tk,k]$, for integers $t\geq 2$ and $k\geq 1$, and show that (except for some small cases) the diameter remains unchanged upon the deletion of one edge. This work contributes towards a solution of the well-known $(\Delta, D, D', s)$-problem, which attempts to find large graphs with maximum …

Construction Of The Second Hankel Determinant For A New Subclass Ofbi-Univalent Functions, Şahsene Altinkaya, Si̇bel Yalçin Tokgöz

Turkish Journal of Mathematics

In this paper, we will discuss a newly constructed subclass of bi-starlike functions. Furthermore, we establish bounds for the coefficients and get the second Hankel determinant for the class $S_{\Sigma }(\alpha ,\beta ).$

Description Of Invariant Subspaces In Terms Of Berezin Symbols, Suna Saltan

Turkish Journal of Mathematics

We consider the stretching operator $\left( T_{w}f\right) \left( z\right) =f(wz)$ and the multiple shift operator $S^{n}f=z^{n}f$ on the Hardy spaces $% H^{p}(\mathbb{D})$ $\left( 1\leq p

Free Modules And Crossed Modules Of $R$-Algebroids, Osman Avcioğlu, İbrahi̇m İlker Akça

Turkish Journal of Mathematics

In this paper, first, we construct the free modules and precrossed modules of $R$-algebroids. Then we introduce the Peiffer ideal of a precrossed module and use it to construct the free crossed module.

Generalization Of The Cayley Transform In 3d Homogeneous Geometries, Zlatko Erjavec

Turkish Journal of Mathematics

The Cayley transform maps the unit disk onto the upper half-plane, conformally and isometrically. In this paper, we generalize the Cayley transform in three-dimensional homogeneous geometries which are fiber bundles over the hyperbolic plane. Obtained generalizations are isometries between existing models in corresponding homogeneous geometries. Particularly, constructed isometry between two models of { $\widetilde{SL(2,\mathbb{R})}$} geometry is nontrivial and enables comparison and transfer of known and even future results between these two models.

Trigonometric Expressions For Infinite Series Involving Binomial Coefficients, Nadia Li

Turkish Journal of Mathematics

By means of the hypergeometric series approach, we present a new proof of Sun's conjecture on trigonometric series, which is simpler than the original one due to Sun and Meng. Several further infinite series identities are shown as examples.

On The Asymptotic Behavior Of Solution Of Certain Systems Of Volterra Equations, Ewa Schmeidel, Malgorzata Zdanowicz

Turkish Journal of Mathematics

This paper is concerned with the asymptotic property of the solution of a system of the linear Volterra difference equations. The criterion for the existence of a solution of the considered system that is asymptotically equivalent to a given sequence is established. %The results generalize some recent results. The results presented here improve and generalize the results published by Diblik et al. Unlike in those works, here periodicity of the nonhomogeneous term of the equation is not assumed. Examples illustrate the obtained results.

Almost Paracontact Structures Obtained From $G_{2(2)}^*$ Structures, Nüli̇fer Özdemi̇r, Şi̇ri̇n Aktay, Mehmet Solgun

Turkish Journal of Mathematics

In this paper, we construct almost paracontact metric structures by using the fundamental 3-forms of manifolds with $G_{2(2)}^*$ structures. The existence of certain almost paracontact metric structures is investigated due to the properties of the 2-fold vector cross-product. Furthermore, we give some relations between the classes of $G_{2(2)}^*$ structures and almost paracontact metric structures.

On Hochstadt--Lieberman Theorem For Impulsive Sturm-Liouville Problems With Boundary Conditions Polynomially Dependent On The Spectral Parameter, Seyfollah Mosazadeh, Aliasghar Jodayree Akbarfam

Turkish Journal of Mathematics

In the present paper, we consider an inverse problem for the Sturm-Liouville operator with a finite number of discontinuities at interior points and boundary conditions polynomially dependent on the spectral parameter on an arbitrary finite interval, and prove the Hochstadt-Lieberman-type theorem for this problem.

Several Hardy-Type Inequalities With Weights Related To Baouendi--Grushinoperators, Abdullah Yener

Turkish Journal of Mathematics

In this paper we shall prove several weighted $L^{p}$ Hardy-type inequalities associated to the Baouendi-Grushin-type operators $\Delta _{\gamma }=\Delta _{x}+\left\vert x\right\vert ^{2\gamma }\Delta _{y},$ where $\Delta _{x}$ and $\Delta _{y}$ are the classical Laplace operators in the variables $x\in \mathbb{R}^{n}$ and $y\in \mathbb{R}^{k},$ respectively, and $\gamma $ is a positive real number.

Linearized Four-Step Implicit Scheme For Nonlinear Parabolic Interface Problems, Matthew Olayiwola Adewole, Victor Folarin Payne

Turkish Journal of Mathematics

We present the solution of a second-order nonlinear parabolic interface problem on a quasiuniform triangular finite element with a linearized four-step implicit scheme used for the time discretization. The convergence of the scheme in $L^2$-norm is established under certain regularity assumptions using interpolation and elliptic projection operators. A numerical experiment is presented to support the theoretical result. It is assumed that the interface cannot be fitted exactly.

Radii Of Uniform Convexity Of Some Special Functions, İbrahi̇m Aktaş, Evri̇m Toklu, Hali̇t Orhan

Turkish Journal of Mathematics

In this investigation our main aim is to determine the radii of uniform convexity of selected normalized $ q $-Bessel and Wright functions. Here we consider six different normalized forms of $ q $-Bessel functions and we apply three different kinds of the normalization of the Wright function. We also show that the obtained radii are the smallest positive roots of some functional equations.

Inequalities For Submanifolds Of Sasaki-Like Statistical Manifolds, Hülya Bostan Ayti̇mur, Ci̇han Özgür

Turkish Journal of Mathematics

We consider statistical submanifolds in Sasaki-like statistical manifolds. We give some examples of invariant and antiinvariant submanifolds of Sasaki-like statistical manifolds. We prove Chen-like inequality involving scalar curvature and Chen-Ricci inequality for these kinds of submanifolds.

Spectrum And Scattering Function Of The Impulsive Discrete Dirac Systems, Elgiz Bairamov, Şeyda Solmaz

Turkish Journal of Mathematics

In this paper, we investigate analytical and asymptotic properties of the Jost solution and Jost function of the impulsive discrete Dirac equations. We also study eigenvalues and spectral singularities of these equations. Then we obtain characteristic properties of the scattering function of the impulsive discrete Dirac systems. Therefore, we find the Jost function, point spectrum, and scattering function of the unperturbed impulsive equations.

Inclusions And The Approximate Identities Of The Generalized Grand Lebesgue Spaces, Ahmet Turan Gürkanli

Turkish Journal of Mathematics

Let $\left( \Omega ,\sum ,\mu \right) $ and $\left( \Omega ,\sum ,v\right) $ be two finite measure spaces and let $L^{p),\theta }\left( \mu \right) $ and $L^{q),\theta }\left( v\right) $ be two generalized grand Lebesgue spaces $\left[ 9,10\right] ,$ where $1

Digital Topological Complexity Numbers, İsmet Karaca, Meli̇h İs

Turkish Journal of Mathematics

The intersection of topological robotics and digital topology leads to us a new workspace. In this paper we introduce the new digital homotopy invariant digital topological complexity number $TC(X,\kappa)$ for digital images and give some examples and results about it. Moreover, we examine adjacency relations in the digital spaces and observe how $TC(X,\kappa)$ changes when we take a different adjacency relation in the digital spaces.

Existence And Nonexistence Of Global Solutions For Nonlinear Transmission Acoustic Problem, Akbar Aliyev, Sevda Isayeva

Turkish Journal of Mathematics

In this paper we consider a mixed problem for the nonlinear wave equations with transmission acoustic conditions, that is, the wave propagation over bodies consisting of two physically different types of materials, one of which is clamped. We prove the existence of a global solution. Under the condition of positive initial energy we show that the solution for this problem blows up in finite time.

Frequently Hypercyclic Weighted Backward Shifts On Spaces Of Real Analytic Functions, Berkay Anahtarci, Can Deha Kariksiz

Turkish Journal of Mathematics

We study frequent hypercyclicity in the case of weighted backward shift operators acting on locally convex spaces of real analytic functions. We obtain certain conditions on frequent hypercyclicity and linear chaoticity of these operators using dynamical transference principles and the frequent hypercyclicity criterion.

Ellipses And Similarity Transformations With Norm Functions, Ni̇hal Yilmaz Özgür

Turkish Journal of Mathematics

In this paper, we deal with a conjecture related to the images of ellipses (resp. circles) under similarities that are the special Möbius transformations. We consider ellipses (resp. circles) corresponding to any norm function (except in the Euclidean case) on the complex plane and examine some conditions to confirm this conjecture. Some illustrative examples are also given.

The Cohomological Structure Of Fixed Point Set For Pro-Torus Actions On Compact Spaces, Mehmet Onat

Turkish Journal of Mathematics

In this paper, we study the relationships between the cohomological structure of a space and that of the fixed point set of a finite dimensional pro-torus action on the space.

An Extension Of The Jeu De Taquin, Joanna Mckinney

Theses, Dissertations and Capstones

The Knuth transformations on words, the jeu de taquin moves on tableaux, and the Robinson–Schensted–Knuth algorithm produce the same equivalence classes for words. By observing the connections between these three methods we find and prove there exists connections between the Assaf–Knuth transformations, our extension of the jeu de taquin, and p-RSK. We know there exists an algebraic way to expand Macdonald polynomials in terms of the Schur functions. The form of the expansion implies there should be a combinatorial way to find the expansion. Loehr found a Robinson–Schensted–Knuth like algorithm that works in some cases. By finding an extension of …

A Note On A Generalized Shishkin-Type Mesh, Thái Ahn Nhan, Relja Vulanović

Mathematics and Computer Science

The one-dimensional linear singularly perturbed convection-diffusion problem is discretized using the upwind scheme on a mesh which is a mild generalization of Shishkin-type meshes. The generalized mesh uses the transition point of the Shishkin mesh, but it does not require any structure of its fine and course parts. Convergence uniform in the perturbation parameter is proved by the barrier-function technique, which, because of the unstructured mesh, does not rely on any mesh-generating function. In this way, the technical requirements needed in the existing barrier-function approaches are simplified.

Quadratic Relations Between Feynman Integrals, David Broadhurst, David P. Roberts

Mathematics Publications

Feynman integrals come in two varieties: polylogarithmic, or not. They are used in two ways: as contributions to an amplitude that is squared, or as contributions to an observable matrix element. In the former case, products of integrals occur, in the latter they do not. We report on products of non-polylogarithmic Feynman integrals related to the magnetic moment of the electron, giving details of an infinite set of quadratic relations between these integrals at all loops L > 2.

Ssaw: A New Sequence Similarity Analysis Method Based On The Stationary Discrete Wavelet Transform, Jie Lin, Donald Adjeroh, Bing-Hua Jiang, Yue Jiang

Faculty & Staff Scholarship

Background: Alignment-free sequence similarity analysis methods often lead to significant savings in computational time over alignment-based counterparts.

Results: Anewalignment-freesequencesimilarityanalysismethod,calledSSAWisproposed.SSAWstandsfor Sequence Similarity Analysis using the Stationary Discrete Wavelet Transform (SDWT). It extracts k-mers from a sequence, then maps each k-mer to a complex number field. Then, the series of complex numbers formed are transformed into feature vectors using the stationary discrete wavelet transform. After these steps, the original sequence is turned into a feature vector with numeric values, which can then be used for clustering and/or classification.

Conclusions: Usingtwodifferenttypesofapplications,namely,clusteringandclassification,wecomparedSSAW against the the-state-of-the-art alignment free sequence analysis methods. SSAW demonstrates competitive or …

Graphene Nanoplatelets-Sericin Surface-Modified Gum Alloy For Improved Biological Response, Valentina Mitran, Valentina Dinca, Raluca Ion, Vasile D. Cojocaru, Patricia Neacsu, Cerasela Zoica Dinu, Laurentiu Rusen, Simona Brajnicov, Anca Bonciu, Maria Dinescu, Doina Raducanu, Ioan Dan

Faculty & Staff Scholarship

In this study a “Gum Metal” titanium-based alloy, Ti-31.7Nb-6.21Zr-1.4Fe-0.16O, was synthesized by melting and characterized in order to evaluate its potential for biomedical applications. The results showed that the newly developed alloy presents a very high strength, high plasticity and a low Young's modulus relative to titanium alloys currently used in medicine. For further bone implant applications, the newly synthesized alloy was surface modified with graphene nanoplatelets (GNP), sericin (SS) and graphene nanoplatelets/sericine (GNP–SS) composite films via Matrix Assisted Pulsed Laser Evaporation (MAPLE) technique. The characterization of each specimen was monitored by scanning electron microscopy (SEM), atomic force microscopy (AFM), …

Mechanism Of Byproducts Formation In The Isobutane/Butene Alkylation On Hy Zeolites, Zhiwei Chen, Feng Gao, Kun Ren, Quangui Wu, Yan Luo, Hongjun Zhou, Meng Zhang, Quan Xu

Faculty & Staff Scholarship

Submicron-size HY zeolites with a particles size of 200–700 nm were synthesized employing a crystal precipitation method in this study. The catalytic activity for the isobutane/butene alkylation was evaluated. The results indicated that butene conversion was above 90% and the selectivity of expected products (C8) was nearly at 90% within 72 h. The micropores-blocking and coverage of acid sites resulting from high hydrocarbons increased the difficulty for the diffusion of products to the bulk and inhibited the adsorption of reactant on activity sites, which caused deactivation of catalyst. The ultimate C12 content in alkylate oil, stemmed from trimerization of butene, …