Mathematics Commons^™

Sufficient Conditions For Univalence Obtained By Using Second Order Linear Strong Differential Subordinations, Georgia Irina Oros

Turkish Journal of Mathematics

The concept of differential subordination was introduced in [3] by S.S. Miller and P.T. Mocanu and the concept of strong differential subordination was introduced in [1], [2] by J.A. Antonino and S. Romaguera. In [5] we have studied the strong differential subordinations in the general case and in [6] we have studied the first order linear strong differential subordinations. In this paper we study the second order linear strong differential subordinations. Our results may be applied to deduce sufficient conditions for univalence in the unit disc, such as starlikeness, convexity, alpha-convexity, close-to-convexity respectively.

Nontrivial Periodic Solutions Of Nonlinear Functional Differential Systems With Feedback Control, Yingxin Guo

Turkish Journal of Mathematics

This paper examines the existence of nontrivial periodic solutions for the nonlinear functional differential system with feedback control: \{\aligned x'(t)=x(t)a(t)-\big[\sum_{i=1}^n a_i(t)\int_0^{+\infty} f(t, x(t-\theta)) d}\varphi_i(\theta) +\sum_{j=1}^m b_j(t) \int_0^{+\infty} f(t,x'(t-\theta))\,d}\phi_j(\theta)+\sum_{\mu=1}^p c_\mu(t) \int_0^{\infty} u(t-\theta)\,d}\delta_\mu(\theta)\big], u'(t)=-\rho(t)u(t)+\sum_{\nu=1}^q \beta_\nu(t) \int_0^{\infty} f(t, x(t-\theta))\,d}\psi_\nu(\theta).\endaligned Under certain growth conditions on the nonlinearity f, several sufficient conditions for the existence of nontrivial solution are obtained by using Leray-Schauder nonlinear alternative.

Existence And Uniqueness Of Solutions To Neutral Stochastic Functional Differential Equations With Infinite Delay In L^P(\Omega,C_H), Haibo Bao

Turkish Journal of Mathematics

In this paper, we shall consider the existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay in L^p(\Omega,C_h) space: d[x(t)-G(x_t)]=f(t,x_t)dt+g(t,x_t)dB(t), where we assume f:R^+\times L^p(\Omega,C_h) \to L^p(\Omega,R^n), g:R^+\times L^p(\Omega,C_h) \to L^p(\Omega,L(R^m, R^n)), G: L^p(\Omega,C_h) \to L^p(\Omega,R^n), p>2,\, and B(t) is a given m-dimensional Brownian motion.

On Maximum Principle And Existence Of Positive Weak Solutions For N\Times N Nonlinear Elliptic Systems Involving Degenerated P-Laplacian Operators, H. M. Serag, S. A. Khafagy

Turkish Journal of Mathematics

We study the Maximum Principle and existence of positive weak solutions for the n \times n nonlinear elliptic system -\Delta_{P,p}u_i=\sum_{j=1}^na_{ij}(x) u_j ^{p-2}u_j+f_i(x,u_1,u_2, ... ,u_n) in \Omega, u_i=0,\ i=1,2,. n on \partial \Omega \} where the degenerated p-Laplacian defined as \Delta _{P,p}u=div [P(x) \nabla u ^{p-2}\nabla u] with p>1,p \neq 2 and P(x) is a weight function. We give some conditions for having the Maximum Principle for this system and then we prove the existence of positive weak solutions for the quasilinear system by using ``sub-super solutions method''.

Korovkin Type Approximation Theorem For Functions Of Two Variables In Statistical Sense, Fadi̇me Di̇ri̇k, Kami̇l Demi̇rci̇

Turkish Journal of Mathematics

In this paper, using the concept of A-statistical convergence for double sequences, we investigate a Korovkin-type approximation theorem for sequences of positive linear operator on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical version. We also obtain a Voronovskaya-type theorem \ and some differential properties for sequences of positive linear operators constructed by means of the Bernstein polynomials of two variables.

B.-Y. Chen Inequalities For Slant Submanifolds In Quaternionic Space Forms, Gabriel Eduard Vilcu

Turkish Journal of Mathematics

In this paper some B.-Y. Chen inequalities for slant submanifolds in quaternionic space forms are established.

Extremal Lagrangian Submanifolds In A Complex Space Form N^N(4c), Shichang Shu, Annie Yi Han

Turkish Journal of Mathematics

Let N^n(4c) be the complex space form of constant holomorphic sectional curvature 4c, \varphi: M \to N^n(4c) be an immersion of an n-dimensional Lagrangian manifold M in N^n(4c). Denote by S and H the square of the length of the second fundamental form and the mean curvature of M. Let \rho be the non-negative function on M defined by \rho^2=S-nH^2, Q be the function which assigns to each point of M the infimum of the Ricci curvature at the point. In this paper, we consider the variational problem for non-negative functional U(\varphi)=\int_M\rho^2dv=\int_M(S-nH^2)dv. We call the critical points of U(\varphi) the …

The Riemann Hilbert Problem For Generalized Q-Holomorphic Functions, Sezayi̇ Hizliyel, Mehmet Çağliyan

Turkish Journal of Mathematics

In this work, the classical Riemann Hilbert boundary value problem is extended to generalized Q-holomorphic functions.

The Principal Eigencurves For A Nonselfadjoint Elliptic Operator, Aomar Anane, Omar Chakrone, Abdellah Zerouali

Turkish Journal of Mathematics

In this paper we study the existence of the principal eigencurves for a nonselfadjoint elliptic operator. We obtain their variational formulation. We establish also the continuity and the differentiability of the principal eigencurves.

Weak Hardy Space And Endpoint Estimates For Singular Integrals On Space Of Homogeneous Type, Yong Ding, Xinfeng Wu

Turkish Journal of Mathematics

We develop the theory of weak Hardy spaces H^{1,\infty} on space of homogeneous type. As some applications, we show that certain singular integral operators and fractional integral operators are bounded from H^{1,\infty} to L^{1,\infty} and L^{\frac{1}{1-\alpha},\infty}, respectively. We give also the endpoint estimates for Nagel and Stein's singular integrals studied in [10].

On Harmonicity In Some Moufang-Klingenberg Planes, Basri̇ Çeli̇k, Ati̇lla Akpinar, Süleyman Çi̇ftçi̇

Turkish Journal of Mathematics

In this paper we study Moufang-Klingenberg planes M (A) defined over a local alternative ring A of dual numbers. We show that some collineations of M (A) preserve cross-ratio and thus establish a relation between harmonicity and harmonic position.

On Purely Real Surfaces In Kaehler Surfaces, Bang-Yen Chen

Turkish Journal of Mathematics

An immersion \phi colon M to \tilde M^2 of a surface M into a Kaehler surface is called purely real if the complex structure J on \tilde M^2 carries the tangent bundle of M into a transversal bundle. In the first part of this article, we prove that the equation of Ricci is a consequence of the equations of Gauss and Codazzi for purely real surfaces in any Kaehler surface. In the second part, we obtain a necessary condition for a purely real surface in a complex space form to be minimal. Several applications of this condition are provided. In …

An Expansion Result For A Sturm-Liouville Eigenvalue Problem With Impulse, Şeri̇fe Faydaoğlu, Gusein Sh. Guseinov

Turkish Journal of Mathematics

The paper is concerned with an eigenvalue problem for second order differential equations with impulse. Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite. The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.

A Short Survey On Mathematical Work Of Cemal Koç, İsmai̇l Şuayi̇p Güloğlu

Turkish Journal of Mathematics

No abstract provided.

Swan Conductors And Torsion In The Logarithmic De Rham Complex, Si̇nan Ünver

Turkish Journal of Mathematics

We prove, for an arithmetic scheme X/S over a discrete valuation ring whose special fiber is a strict normal crossings divisor in X, that the Swan conductor of X/S is equal to the Euler characteristic of the torsion in the logarithmic de Rham complex of X/S. This is a precise logarithmic analog of a theorem by Bloch [1].

Pseudo Simplicial Groups And Crossed Modules, İlker Akça, Sedat Pak

Turkish Journal of Mathematics

In this paper, we define the notion of pseudo 2-crossed module and give a relation between the pseudo 2-crossed modules and pseudo simplicial groups with Moore complex of length 2.

The Essential Norm Of A Composition Operator On Orlicz Spaces, M. R. Jabbarzadeh

Turkish Journal of Mathematics

In this note we determine the lower and upper estimates for the essential norm of a composition operator on the Orlicz spaces under certain conditions.

Number Of Pseudo--Anosov Elements In The Mapping Class Group Of A Four--Holed Sphere, Feri̇he Atalan, Mustafa Korkmaz

Turkish Journal of Mathematics

We compute the growth series and the growth functions of reducible and pseudo-Anosov elements of the pure mapping class group of the sphere with four holes with respect to a certain generating set. We prove that the ratio of the number of pseudo-Anosov elements to that of all elements in a ball with center at the identity tends to one as the radius of the ball tends to infinity.

Edge Coloring Bibds And Constructing Moelrs , John S. Asplund

Dissertations, Master's Theses and Master's Reports - Open

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Some historical uses and background are touched upon as well. The majority of the definitions are contained within this chapter as well.

In Chapter 2 we consider the question whether one can decompose λ copies of monochromatic K_v into copies of K_k such that each copy of the K_k contains at most one edge from each K_v. This is called a proper edge coloring (Hurd, Sarvate, [29]). The majority of the content in this section is a wide variety of …

Mastery Of Sixth-Grade Mathematics Expectations As Measured By The Seventh-Grade Michigan Education Assessment Program From 2005 To 2007, Marian Prince

Dissertations

Purpose

The purpose of this study is to document sixth-grade mathematics mastery as measured by the seventh-grade Michigan Education Assessment Program (MEAP) over a period of 3 years: 2005, 2006, and 2007. This study investigated whether mathematics performance in Michigan is related to ethnicity by analyzing student responses on the seventh-grade MEAP which evaluates students’ mastery of the Michigan sixth-grade mathematics expectations.

Method

Data from the Michigan Department of Education (MDE) containing the student scores of individual test items on the mathematics Michigan Education Assessment Program (MEAP) for seventh-grade students in Michigan for 2005 to 2007 formed the basis for …