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Full-Text Articles in Physical Sciences and Mathematics

On The Extended Hecke Groups \Overline{H}(\Lambda _Q), Ni̇hal Yilmaz Özgür, Recep Şahi̇n Jan 2003

On The Extended Hecke Groups \Overline{H}(\Lambda _Q), Ni̇hal Yilmaz Özgür, Recep Şahi̇n

Turkish Journal of Mathematics

Hecke groups H(\lambda _q) have been studied extensively for many aspects in the literature, [5], [8]. The Hecke group H(\lambda_3), the modular group PSL(2, \Bbb{Z} ) , has especially been of great interest in many fields of mathematics, for example number theory, automorphic function theory and group theory. In this paper we consider the extended Hecke groups \overline{H}(\lambda _q) which are defined analogously with the extended modular group. We find the conjugacy classes of torsion elements in \overline{H}(\lambda _q). Using this we give some results about the normal subgroups and Fuchsian subgroups of \overline{H}(\lambda _q).


On Positive Solutions Of Boundary Value Problems For Nonlinear Second Order Difference Equations, Nüket Aykut, Gusein Sh. Guseinov Jan 2003

On Positive Solutions Of Boundary Value Problems For Nonlinear Second Order Difference Equations, Nüket Aykut, Gusein Sh. Guseinov

Turkish Journal of Mathematics

In this paper we study nonlinear second order difference equations subject to separated linear boundary conditions. Sign properties of the associated Green's functions are investigated and existence results for positive solutions of the nonlinear boundary value problem are established. Upper and lower bounds for these positive solutions also are given.


Shape Operator A_H For Slant Submanifolds In Generalized Complex Space Forms, Adela Mihai Jan 2003

Shape Operator A_H For Slant Submanifolds In Generalized Complex Space Forms, Adela Mihai

Turkish Journal of Mathematics

In this article, we establish an inequality between the sectional curvature function K and the shape operator A_H at the mean curvature vector for slant submanifolds in generalized complex space forms. Also a sharp relationship between the k-Ricci curvature and the shape operator A_H is proved.


Rough Singular Integrals Along Submanifolds Of Finite Type On Product Domains, Hussain Al-Qassem Jan 2003

Rough Singular Integrals Along Submanifolds Of Finite Type On Product Domains, Hussain Al-Qassem

Turkish Journal of Mathematics

We establish the L^p boundedness of singular integrals on product domains with rough kernels in L(log L)^2 and are supported by subvarieties.


Rough Oscillatory Singular Integral Operators-Ii, Ahmad Al-Salman, Ali A. Al-Jarrah Jan 2003

Rough Oscillatory Singular Integral Operators-Ii, Ahmad Al-Salman, Ali A. Al-Jarrah

Turkish Journal of Mathematics

In this paper, we study certain classes of oscillatory singular integral operators with kernels in Llog L(S^{n-1}) which is known to be the most desirable size condition for the L^{p} boundedness to hold. We prove that such operators are bounded on L^{p}. Our results extend and improve previously known results. Variations of our approach in this paper can be applied to handle more general oscillatory singular integral operators. This concludes by indicating a variety of results that can be obtained.


On General Fibonacci Sequences In Groups, Engi̇n Özkan Jan 2003

On General Fibonacci Sequences In Groups, Engi̇n Özkan

Turkish Journal of Mathematics

In this paper, we have constituted 3-step general Fibonacci sequences in a nilpotent group with exponent p (p is a prime number) and nilpotency class 4 and given formulas to find the \alpha term of the sequence.


Affine Manifolds, Log Structures, And Mirror Symmetry, Mark Gross, Bernd Siebert Jan 2003

Affine Manifolds, Log Structures, And Mirror Symmetry, Mark Gross, Bernd Siebert

Turkish Journal of Mathematics

We outline work in progress suggesting an algebro-geometric version of the Strominger-Yau-Zaslow conjecture. We define the notion of a toric degeneration, a special case of a maximally unipotent degeneration of Calabi-Yau manifolds. We then show how in this case the dual intersection complex has a natural structure of an affine manifold with singularities. If the degeneration is polarized, we also obtain an intersection complex, also an affine manifold with singularities, related by a discrete Legendre transform to the dual intersection complex. Finally, we introduce log structures as a way of reversing this construction: given an affine manifold with singularities with …


Duality And Fibrations On G_2 Manifolds, Sergei Gukov, Shing-Tung Yau, Eric Zaslow Jan 2003

Duality And Fibrations On G_2 Manifolds, Sergei Gukov, Shing-Tung Yau, Eric Zaslow

Turkish Journal of Mathematics

We argue that G_2 manifolds for M-theory admitting string theory Calabi-Yau duals are fibered by coassociative submanifolds. Dual theories are constructed using the moduli space of M-five-brane fibers as target space. Mirror symmetry and various string and M-theory dualities involving G_2 manifolds may be incorporated into this framework. To give some examples, we construct two non-compact manifolds with G_2 structures: one with a K3 fibration, and one with a torus fibration and a metric of G_2 holonomy. Kaluza-Klein reduction of the latter solution gives abelian BPS monopoles in 3 + 1 dimensions.


U(1)-Invariant Special Lagrangian 3-Folds In {\Mathbb C}^3 And Special Lagrangian Fibrations, Dominic Joyce Jan 2003

U(1)-Invariant Special Lagrangian 3-Folds In {\Mathbb C}^3 And Special Lagrangian Fibrations, Dominic Joyce

Turkish Journal of Mathematics

This is a survey of the author's series of three papers [8, 9, 10] on special Lagrangian 3-folds (SL 3-folds) in {\mathbb C}^3 invariant under the U(1)-action (z_1,z_2,z_3)e^{i\theta}z_1, e^{-i\theta}z_2,z_3), and their sequel {\mathbb C} [11] on special Lagrangian fibrations and the SYZ Conjecture. We briefly present the main results of these four long papers, giving some explanation and motivation, but no proofs. The aim is to make the results and ideas accessible to String Theorists and others who have an interest in special Lagrangian 3-folds and fibrations, but have no desire to read pages of technical analysis. Let N be …


Polyhedral Approximations Of Riemannian Manifolds, Anton Petrunin Jan 2003

Polyhedral Approximations Of Riemannian Manifolds, Anton Petrunin

Turkish Journal of Mathematics

I'm trying to understand which Riemannian manifolds can be Lipschitz approximated by polyhedral spaces of the same dimension with curvature bounded below. The necessary conditions I found consist of some special inequality for curvature at each point (the geometric curvature bound). This inequality is also sufficient condition for local approximation. I conjecture that it is also a sufficient condition for global approximation, and I can prove it if the curvature bound is positive. In general I can prove it only with the additional assumption that tangent bundle of the manifold is stably trivial.


Abelian Fibred Holomorphic Symplectic Manifolds, Justin Sawon Jan 2003

Abelian Fibred Holomorphic Symplectic Manifolds, Justin Sawon

Turkish Journal of Mathematics

We study holomorphic symplectic manifolds which are fibred by abelian varieties. This structure is a higher dimensional analogue of an elliptic fibration on a K3 surface. We investigate when a holomorphic symplectic manifold is fibred in this way, and are led to several natural conjectures. We then study the geometry of these fibrations. The expectation is that this point of view will prove useful in understanding holomorphic symplectic manifolds, and possibly lead to a classification.


Symplectic Surgeries From Singularities, Ivan Smith, Richard Thomas Jan 2003

Symplectic Surgeries From Singularities, Ivan Smith, Richard Thomas

Turkish Journal of Mathematics

We describe a variety of symplectic surgeries (not a priori compatible with Kaehler structures) which are obtained by combining local Kaehler degenerations and resolutions of singularities. The effect of the surgeries is to replace configurations of Lagrangian spheres with symplectic submanifolds. We discuss several examples in detail, relating them to existence questions for symplectic manifolds with c_1 > 0, c_1 = 0, c_1 < 0 in four and six dimensions.


On Locally M-Pseudoconvex A^*-Algebras, A. El Kinani Jan 2003

On Locally M-Pseudoconvex A^*-Algebras, A. El Kinani

Turkish Journal of Mathematics

We consider classical A^*-algebras in the context of locally pseudoconvex algebras. Results concerning the auxiliary topology and A^* -algebras of the first kind are given.


Fuzzy Ideals In Gamma-Rings, Mehmet Ali̇ Öztürk, Mustafa Uçkun, Young Bae Jun Jan 2003

Fuzzy Ideals In Gamma-Rings, Mehmet Ali̇ Öztürk, Mustafa Uçkun, Young Bae Jun

Turkish Journal of Mathematics

The converse of [7, Theorem 3.3] is provided. For an Artinian \Gamma-ring, a few results are investigated.


On The Weak-Integrity Of Trees, Alpay Kirlangiç Jan 2003

On The Weak-Integrity Of Trees, Alpay Kirlangiç

Turkish Journal of Mathematics

In this paper the concept of {\em weak-integrity} is introduced as a new measure of the stability of a graph \( G \) and it is defined as I_{w}(G)={\min_{S\subset V(G)}\{ S +m_{e}(G-S)\}}, where m_{e}(G-S) denotes the number of edges of a largest component of G-S. We investigate the weak-integrity of trees and compute the weak-integrity of a binomial tree and all the trees with at most 7 vertices. We also give some results about the weak-integrity of graphs obtained from binary operations.


On L_{P}-Approximation By A Linear Combination Of A New Sequence Of Linear Positive Operators, P. N. Agrawal, Ali Jassim Mohammad Jan 2003

On L_{P}-Approximation By A Linear Combination Of A New Sequence Of Linear Positive Operators, P. N. Agrawal, Ali Jassim Mohammad

Turkish Journal of Mathematics

In the present paper, we study some direct results in L_{p} -approximation by a linear combination of a new sequence of linear positive operators. The error in the approximation is estimated in terms of the higher order integral modulus of smoothness using some properties of the Steklov means.


Left Adjoint Of Pullback Cat^1- Profinite Groups, Murat Alp Jan 2002

Left Adjoint Of Pullback Cat^1- Profinite Groups, Murat Alp

Turkish Journal of Mathematics

In this paper, we present a brief review crossed modules \cite{whitehead}, cat^1-groups \cite{loday}, profinite crossed modules \cite{kortim}, cat^1-profinite groups \cite{kortim}, pullback profinite crossed modules \cite{kortim} and also the pullback cat^1- profinite groups \cite{hind}. We prove that the pulback cat^1-profinite group has a left adjoint which is the induced cat^1-group.


New Tensor Norms And Operator Ideals Associated To Interpolation Spaces Between Sequence Spaces, G. Castaneda, J. A. Lopez Molina, M. J. Rivera Jan 2002

New Tensor Norms And Operator Ideals Associated To Interpolation Spaces Between Sequence Spaces, G. Castaneda, J. A. Lopez Molina, M. J. Rivera

Turkish Journal of Mathematics

We introduce a wide class of tensor norms g_{\lambda,\rho} which are defined with the help of interpolation spaces between perfect sequence spaces defined by a general parameter real interpolation method. We also characterize the associated \lambda_{\rho}-nuclear and \lambda_{\rho}-integral operators.


Characterizations Of Artinian And Noetherian Gamma-Rings In Terms Of Fuzzy Ideals, Mehmet Ali̇ Öztürk, Mustafa Uçkun, Young Bae Jun Jan 2002

Characterizations Of Artinian And Noetherian Gamma-Rings In Terms Of Fuzzy Ideals, Mehmet Ali̇ Öztürk, Mustafa Uçkun, Young Bae Jun

Turkish Journal of Mathematics

Using fuzzy ideals, characterizations of Noetherian \Gamma-rings are given, and a condition for a \Gamma-ring to be Artinian is also given.


On Non-Existence Of Korovkin's Theorem In The Space Of L_{P}-Locally Integrable Functions, A. D. Gadjiev, Ertan İbi̇kli̇ Jan 2002

On Non-Existence Of Korovkin's Theorem In The Space Of L_{P}-Locally Integrable Functions, A. D. Gadjiev, Ertan İbi̇kli̇

Turkish Journal of Mathematics

It is shown that a Korovkin-type theorem does not hold in the weighted space of L_{p}-locally integrable functions on the whole real axis.


Deformation Inequivalent Complex Conjugated Complex Structures And Applications, Viatcheslav Kharlamov, Viktor Kulikov Jan 2002

Deformation Inequivalent Complex Conjugated Complex Structures And Applications, Viatcheslav Kharlamov, Viktor Kulikov

Turkish Journal of Mathematics

We start from a short summary of our principal result from [KK]: an example of a complex algebraic surface which is not deformation equivalent to its complex conjugate and which, moreover, has no homeomorphisms reversing the canonical class. Then, we generalize this result to higher dimensions and construct several series of higher dimensional compact complex manifolds having no homeomorphisms reversing the canonical class. After that, we resume and broaden the applications given in [KK] and [KK2], in particular, as a new application, we propose examples of (deformation) non equivalent symplectic structures with opposite canonical classes.


Combinatorial Patchworking Of Real Pseudo-Holomorphic Curves, Ilia Itenberg, Eugenii Shustin Jan 2002

Combinatorial Patchworking Of Real Pseudo-Holomorphic Curves, Ilia Itenberg, Eugenii Shustin

Turkish Journal of Mathematics

The Viro method of construction of real algebraic varieties with prescribed topology uses convex subdivisions of Newton polyhedra. We show that in the case of arbitrary (not necessarily convex) subdivisions of polygons corresponding to C P^2 and rational ruled surfaces \Sigma_a, a \geq 0 the Viro method produces pseudo-holomorphic curves. The version of the Viro method discussed in the paper also gives a possibility to construct singular pseudo-holomorphic curves by gluing singular algebraic curves whose collections of singularities do not permit to glue these curves in the framework of the standard Viro method. As an application, we construct a series …


On 1-Point Gromov-Witten Invariants Of The Hilbert Schemes Of Points On Surfaces, Wei-Ping Li, Zhenbo Qin Jan 2002

On 1-Point Gromov-Witten Invariants Of The Hilbert Schemes Of Points On Surfaces, Wei-Ping Li, Zhenbo Qin

Turkish Journal of Mathematics

We compute certain 1-point genus-0 Gromov-Witten invariants of the Hilbert scheme of points on a simply-connected smooth projective surface.


Evidence For A Conjecture Of Pandharipande, Jim Bryan Jan 2002

Evidence For A Conjecture Of Pandharipande, Jim Bryan

Turkish Journal of Mathematics

In his paper ``Hodge integrals and degenerate contributions'', Pandharipande studied the relationship between the enumerative geometry of certain 3-folds and the Gromov-Witten invariants. In some good cases, enumerative invariants (which are manifestly integers) can be expressed as a rational combination of Gromov-Witten invariants. Pandharipande speculated that the same combination of invariants should yield integers even when they do not have any enumerative significance on the 3-fold. In the case when the 3-fold is the product of a complex surface and an elliptic curve, Pandharipande has computed this combination of invariants on the 3-fold in terms of the Gromov-Witten invariants of …


Variations On Fintushel-Stern Knot Surgery On 4-Manifolds, Selman Akbulut Jan 2002

Variations On Fintushel-Stern Knot Surgery On 4-Manifolds, Selman Akbulut

Turkish Journal of Mathematics

We discuss some consequences Fintushel-Stern `knot surgery' operation coming from its handlebody description. We give some generalizations of this operation and give a counterexample to their conjecture.


Braids And Symplectic Four-Manifolds With Abelian Fundamental Group, Paul Seidel Jan 2002

Braids And Symplectic Four-Manifolds With Abelian Fundamental Group, Paul Seidel

Turkish Journal of Mathematics

We explain how a version of Floer homology can be used as an invariant of symplectic manifolds with b_1>0. As a concrete example, we look at four-manifolds produced from braids by a surgery construction. The outcome shows that the invariant is nontrivial; however, it is an open question whether it is stronger than the known ones.


Low-Dimensional Homology Groups Of Mapping Class Groups: A Survey, Mustafa Korkmaz Jan 2002

Low-Dimensional Homology Groups Of Mapping Class Groups: A Survey, Mustafa Korkmaz

Turkish Journal of Mathematics

In this survey paper, we give a complete list of known results on the first and the second homology groups of surface mapping class groups. Some known results on higher (co) homology are also mentioned.


Gauge Theory And Stein Fillings Of Certain 3-Manifolds, Andras I. Stipsicz Jan 2002

Gauge Theory And Stein Fillings Of Certain 3-Manifolds, Andras I. Stipsicz

Turkish Journal of Mathematics

In the following we show that a Stein filling S of the 3-torus T^3 is homeomorphic to D^2 \times T^2. In the proof we also show that if S is Stein and \partial S is diffeomorphic to the Seifert fibered 3-manifold -\Sigma (2,3,11) then b_1(S)=0 and Q_S=H. Similar results are obtained for the Poincaré homology sphere \pm \Sigma (2,3,5); in studying these fillings we apply recent gauge theoretic results, and prove our theorems by determining certain Seiberg-Witten invariants.


On Summand Sum And Summand Intersection Property Of Modules, Mustafa Alkan, Abdullah Harmanci Jan 2002

On Summand Sum And Summand Intersection Property Of Modules, Mustafa Alkan, Abdullah Harmanci

Turkish Journal of Mathematics

R will be an associative ring with identity and modules M will be unital left R- modules. In this work, extending modules and lifting modules with the SSP (or SIP) are studied. A necessary and sufficient condition for a module M to have the SSP is that for every decomposition M = A\oplus B and f\in Hom(A,B), Im(f) is a direct summand of B. Among others it is shown also that a (C_3) module with the SIP has the SSP, and a (D_3) module with SSP has the SIP.


Asymptotic Formulas For The Eigenvalues Of The Schrodinger Operator, Şi̇ri̇n Atilgan, Sedef Karakiliç, Oktay A. Veliev Jan 2002

Asymptotic Formulas For The Eigenvalues Of The Schrodinger Operator, Şi̇ri̇n Atilgan, Sedef Karakiliç, Oktay A. Veliev

Turkish Journal of Mathematics

In this paper, we obtain asymptotic formulas for the eigenvalues of the d-dimensional Schrodinger operator L=-\Delta +q(x) in d-dimensional parallelepiped F with Dirichlet and Neumann boundary conditions.