Mathematics Commons^™

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, …

When Is A Permutation Of The Set $\Z^N$ (Resp. $\Z_P^N$, $P$ Prime) An Automorphism Of The Group $\Z^N$ (Resp. $\Z_P^N$)?, Ben-Eben De Klerk, Johan H. Meyer

Turkish Journal of Mathematics

For a given positive integer $n$, the structure, i.e. the number of cycles of various lengths, as well as possible chains, of the automorphisms of the groups $(\Z^n, +)$ and $(\Z_p^n,+)$, \ $p$ prime, is studied. In other words, necessary and sufficient conditions on a bijection $f : A \ra A$, where $ A $ is countably infinite (alternatively, of order $p^n$), are determined so that $A$ can be endowed with a binary operation $*$ such that $(A,*)$ is a group isomorphic to $(\Z^n,+)$ (alternatively, $(\Z_p^n,+)$) and such that $f\in \Aut(A)$.

Some Characterizations Of Right $C$-Regularity And $(B,C)$-Inverse, Ruju Zhao, Hua Yao, Long Wang, Junchao Wei

Turkish Journal of Mathematics

Let $R$ be a ring and $a,b,c\in R$. We give a novel characterization of group inverses (resp. EP elements) by the properties of right (resp. left ) $c$-regular inverses of $a$ and discuss the relation among the strongly left $(b,c)$-invertibility of $a$, the right $ca$-regularity of $b$, and the $(b,c)$-invertibility of $a$. Finally, we investigate the sufficient and necessary condition for a ring to be a strongly left min-Abel ring by means of the $(b,c)$-inverse of $a$.

On The Solution Of An Inverse Sturm-Liouville Problem With A Delay And Eigenparameter-Dependent Boundary Conditions, Seyfollah Mosazadeh

Turkish Journal of Mathematics

In this paper, a boundary value problem consisting of a delay differential equation of the Sturm-Liouville type with eigenparameter-dependent boundary conditions is investigated. The asymptotic behavior of eigenvalues is studied and the parameter of delay is determined by eigenvalues. Then we obtain the connection between the potential function and the canonical form of the characteristic function.

Closed Range Properties Of Li-Steviç Integral-Type Operators Between Bloch-Type Spaces And Their Essential Norms, Maryam Mohammadi Pirasteh, Nasrin Eghbali, Amir Hossein Sanatpour

Turkish Journal of Mathematics

We investigate closed range properties of certain integral-type operators introduced by Li and Steviç. The operators are considered between Bloch-type spaces. We also give the essential norm of such operators. Our results are given in a general setting and we also give the essential norm of Li-Steviç integral-type operators between other well-known spaces of analytic functions.

Conditional Expectation Type Operators And Modular Inequalities, Dah-Chin Luor

Turkish Journal of Mathematics

In this paper we discuss the connection between conditional expectation type operators and integral operators. A variant of Schur's lemma is established and we obtain modular inequalities for a class of conditional expectation type operators.

Curves Whose Pseudo Spherical Indicatrices Are Elastic, Ahmet Yücesan, Gözde Özkan Tükel, Tunahan Turhan

Turkish Journal of Mathematics

The pseudo spherical indicatrix of a curve in Minkowski $3$-space emerges as three types: the pseudo spherical tangent indicatrix, principal normal indicatrix, and binormal indicatrix of the curve. The pseudo spherical tangent, principal normal, and binormal indicatrix of a regular curve may be positioned on De Sitter $2$-space (pseudo sphere), pseudo hyperbolic 2-space, and two-dimensional null cone in terms of causal character of the curve. In this paper, we separately derive Euler-Lagrange equations of all pseudo spherical indicatrix elastic curves in terms of the causal character of a curve in Minkowski $3$-space. Then we give some results of solutions of …

Jackson And\ Stechkin Type Inequalities Of Trigonometricapproximation In $A_{W,\Vartheta }^{P,Q(\Cdot )}$, Ahmet Hamdi̇ Avşar, Hüseyi̇n Koç

Turkish Journal of Mathematics

In this paper, we study Jackson and Stechkin type theorems of trigonometric polynomial approximation in the space $A_{w,\vartheta }^{p,q(\cdot )}$ by considering a modulus of smoothness defined by virtue of the Steklov operator.