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,
2010
TÜBİTAK
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.
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.
A Note On Dominant Contractions Of Jordan Algebras,
2010
TÜBİTAK
A Note On Dominant Contractions Of Jordan Algebras, Farrukh Mukhamedov, Seyi̇t Temi̇r, Hasan Akin
Turkish Journal of Mathematics
We consider two positive contractions T,S:L_1(A,\tau) \longrightarrow L_1(A,\tau) such that T\leq S, here (A, \tau) is a semi-finite JBW-algebra. If there is an n_0 \in N such that S^{n_0}-T^{n_0}
The Equivalence Of Centro-Equiaffine Curves,
2010
TÜBİTAK
The Equivalence Of Centro-Equiaffine Curves, Yasemi̇n Sağiroğlu, Ömer Pekşen
Turkish Journal of Mathematics
The motivation of this paper is to find formulation of the SL(n,R)-equivalence of curves. The types for centro-equiaffine curves and for every type all invariant parametrizations for such curves are introduced. The problem of SL(n,R)-equivalence of centro-equiaffine curves is reduced to that of paths. The centro-equiaffine curvatures of path as a generating system of the differential ring of SL(n,R)-invariant differential polinomial functions of path are found. Global conditions of SL(n,R)-equivalence of curves are given in terms of the types and invariants. It is proved that the invariants are independent.
A Gap Theorem For Complete Space-Like Hypersurface With Constant Scalar Curvature In Locally Symmetric Lorentz Spaces,
2010
TÜBİTAK
A Gap Theorem For Complete Space-Like Hypersurface With Constant Scalar Curvature In Locally Symmetric Lorentz Spaces, Jiancheng Liu, Lin Wei
Turkish Journal of Mathematics
Let M^n be a complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz space N^{n+1}_1, S be the squared norm of the second fundamental form of M^n in N^{n+1}_1. In this paper, we obtain a gap property of S: if nP\leq \sup S\leq D(n,P) for some constants P and D(n, P), then either \sup S=nP and M^n is totally umbilical, or \sup S=D(n, P) and M^n has two distinct principal curvatures.
A Note On The Lyapunov Exponent In Continued Fraction Expansions,
2010
TÜBİTAK
A Note On The Lyapunov Exponent In Continued Fraction Expansions, Jianzhong Cheng, Lu-Ming Shen
Turkish Journal of Mathematics
Let T:[0,1) \to [0,1) be the Gauss transformation. For any irrational x \in [0,1), the Lyapunov exponent \alpha(x) of x is defined as \alpha(x)=\lim_{n\to\infty}\frac{1}{n} \log (T^n)'(x) . By Birkoff Average Theorem, one knows that \alpha(x) exists almost surely. However, in this paper, we will see that the non-typical set \{x\in [0,1):\lim_{n\to\infty}\frac{1}{n} \log (T^n)'(x) does not exist\} carries full Hausdorff dimension.
New Inequalities Similar To Hardy-Hilbert's Inequality,
2010
TÜBİTAK
New Inequalities Similar To Hardy-Hilbert's Inequality, Namita Das, Srinibas Sahoo
Turkish Journal of Mathematics
In this paper, we establish a new inequality similar to Hardy-Hilbert's inequality. As applications, some particular results and the equivalent form are derived. The integral analogues of the main results are also given.
The Principal Eigencurves For A Nonselfadjoint Elliptic Operator,
2010
TÜBİTAK
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.
Characterizations Of Slant Helices In Euclidean 3-Space,
2010
TÜBİTAK
Characterizations Of Slant Helices In Euclidean 3-Space, Levent Kula, Nejat Ekmekci̇, Yusuf Yayli, Kazim İlarslan
Turkish Journal of Mathematics
In this paper we investigate the relations between a general helix and a slant helix. Moreover, we obtain some differential equations which they are characterizations for a space curve to be a slant helix. Also, we obtain the slant helix equations and its Frenet aparatus.
Some Sufficient Conditions For Starlikeness And Convexity,
2010
TÜBİTAK
Some Sufficient Conditions For Starlikeness And Convexity, Mamoru Nunokawa, Shigeyoshi Owa, Yaşar Polatoğlu, Mert Çağlar, Emel Yavuz Duman
Turkish Journal of Mathematics
There are many results for sufficient conditions of functions f(z) which are analytic in the open unit disc U to be starlike and convex in U. In view of the results due to S. Ozaki, I. Ono and T. Umezawa (1956), P.T. Mocanu (1988), and M. Nunokawa (1993), some sufficient conditions for starlikeness and convexity of f(z) are discussed.
Injective Simplicial Maps Of The Arc Complex,
2010
TÜBİTAK
Injective Simplicial Maps Of The Arc Complex, Elmas Irmak, John D. Mccarthy
Turkish Journal of Mathematics
In this paper, we prove that each injective simplicial map of the arc complex of a compact, connected, orientable surface with nonempty boundary is induced by a homeomorphism of the surface. We deduce, from this result, that the group of automorphisms of the arc complex is naturally isomorphic to the extended mapping class group of the surface, provided the surface is not a disc, an annulus, a pair of pants, or a torus with one hole. We also show, for each of these special exceptions, that the group of automorphisms of the arc complex is naturally isomorphic to the quotient …
Some Properties Of C-Fusion Frames,
2010
TÜBİTAK
Some Properties Of C-Fusion Frames, Mohammad Hasan Faroughi, Reza Ahmadi
Turkish Journal of Mathematics
In [10], we generalized the concept of fusion frames, namely, c-fusion frames, which is a continuous version of the fusion frames. In this article we give some important properties about the generalization, namely erasures of subspaces, the bound of c-erasure reconstruction error for Parseval c-fusion frames, perturbation of c-fusion frames and the frame operator for fusion pair.
Notes On Null Curves In Minkowski Spaces,
2010
TÜBİTAK
Notes On Null Curves In Minkowski Spaces, Makoto Sakaki
Turkish Journal of Mathematics
We show a correspondence between the evolute of a null curve and the involute of a certain spacelike curve in the 4-dimensional Minkowski space. Also we characterize pseudo-spherical null curves in the n-dimensional Minkowski space in terms of the curvature functions.
Warped Product Semi-Slant Submanifolds In Kenmotsu Manifolds,
2010
TÜBİTAK
Warped Product Semi-Slant Submanifolds In Kenmotsu Manifolds, Mehmet Atçeken
Turkish Journal of Mathematics
In this paper, we research the existence or non-existence of warped product semi-slant submanifolds in Kenmotsu manifolds. Consequently, we see that there are no proper warped product semi-slant submanifolds in Kenmotsu manifolds such that totally geodesic and totally umbilical submanifolds of warped product are proper semi-slant and invariant (or anti-invariant), respectively.
Generalized Catalan Numbers, Sequences And Polynomials,
2010
TÜBİTAK
Generalized Catalan Numbers, Sequences And Polynomials, Cemal Koç, İsmai̇l Güloğlu, Songül Esi̇n
Turkish Journal of Mathematics
In this paper we present an algebraic interpretation for generalized Catalan numbers. We describe them as dimensions of certain subspaces of multilinear polynomials. This description is of utmost importance in the investigation of annihilators in exterior algebras.
Swan Conductors And Torsion In The Logarithmic De Rham Complex,
2010
TÜBİTAK
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].
On Abelian Rings,
2010
TÜBİTAK
On Abelian Rings, Nazim Agayev, Abdullah Harmanci, Sai̇t Halicioğlu
Turkish Journal of Mathematics
Let \alpha be an endomorphism of an arbitrary ring R with identity. In this note, we introduce the notion of \alpha-abelian rings which generalizes abelian rings. We prove that \alpha-reduced rings, \alpha-symmetric rings, \alpha-semicommutative rings and \alpha-Armendariz rings are \alpha-abelian. For a right principally projective ring R, we also prove that R is \alpha-reduced if and only if R is \alpha-symmetric if and only if R is \alpha-semicommutative if and only if R is \alpha-Armendariz if and only if R is \alpha-Armendariz of power series type if and only if R is \alpha-abelian.
Pseudo Simplicial Groups And Crossed Modules,
2010
TÜBİTAK
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.
On Construction Of Coherent States Associated With Homogeneous Spaces,
2010
TÜBİTAK
On Construction Of Coherent States Associated With Homogeneous Spaces, Ali Akbar Arefijamaal
Turkish Journal of Mathematics
In this article, assume that G=H\times_{\tau} K is the semidirect product of two locally compact groups H and K, respectively and consider the quasi regular representation on G. Then for some closed subgroups of G we investigate an admissible condition to generate the Gilmore-Perelomov coherent states. The construction yields a wide variety of coherent states, labelled by a homogeneous space of G.
