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Groups Whose Proper Subgroups Are Hypercentral Of Length At Most \Leq \Omega, Selami̇ Ercan
Groups Whose Proper Subgroups Are Hypercentral Of Length At Most \Leq \Omega, Selami̇ Ercan
Turkish Journal of Mathematics
Groups, all proper subgroups of which are hypercentral of length at most \omega and every proper subgroup of which is a B_{n}-group for a natural number n depending on the subgroup, are studied in this article.
On Pseudohyperbolical Curves In Minkowski Space-Time, Çeti̇n Camci, Kazim İlarslan, Emilija Sucurovic
On Pseudohyperbolical Curves In Minkowski Space-Time, Çeti̇n Camci, Kazim İlarslan, Emilija Sucurovic
Turkish Journal of Mathematics
In this paper, we characterize all spacelike, timelike and null curves lying on the pseudohyperbolic space H_0^3 in the Minkowski space--time E_1^4. Moreover, we prove that there are no timelike and no null curves lying on the pseudohyperbolic space H_0^3 in Minkowski space--time E_1^4.
On Prime Submodules Of Finitely Generated Free Modules, Di̇lek Pusat Yilmaz
On Prime Submodules Of Finitely Generated Free Modules, Di̇lek Pusat Yilmaz
Turkish Journal of Mathematics
The aim of this work is to investigate prime submodules of finitely generated free modules over commutative domains in some special cases.
On Locally M-Pseudoconvex A^*-Algebras, A. El Kinani
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.
On The Weak-Integrity Of Trees, Alpay Kirlangiç
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
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.
On Invariant Submanifolds Of Riemannian Warped Product Manifold, Mehmet Atçeken, Bayram Şahi̇n, Erol Kiliç
On Invariant Submanifolds Of Riemannian Warped Product Manifold, Mehmet Atçeken, Bayram Şahi̇n, Erol Kiliç
Turkish Journal of Mathematics
In this paper, we generalize the geometry of the invariant submanifolds of Riemannian product manifold to the geometry of the invariant submanifolds of Riemannian warped product manifold. We investigate some properties of an invariant submanifolds of a Riemannian warped product manifold. We show that every invariant submanifold of the Riemannian warped product manifold is a Riemannian warped product manifold. Also, we give a theorem on the pseudo-umbilical invariant submanifold. Further, we obtain that integral manifolds on an invariant submanifold are curvature-invariant submanifolds. Finally, we give a necessary condititon on a totally umbilical invariant submanifold to be totally geodesic.
Automorphism Groups Of (M-1)-Surfaces With The M-Property, Adnan Melekoğlu
Automorphism Groups Of (M-1)-Surfaces With The M-Property, Adnan Melekoğlu
Turkish Journal of Mathematics
A compact Riemann surface X of genus g is called an (M-1)-surface if it admits an anticonformal involution that fixes g simple closed curves, the second maximum number by Harnack's theorem. If X also admits an automorphism of order g which cyclically permutes these g curves, then we shall call X an (M-1)-surface with the M-property. In this paper we investigate the automorphism groups of (M-1)-surfaces with the M-property.
On Some Properties Of Szasz-Mirakyan Operators In Hölder Spaces, Zbigniew Walczak, Lucyna Rempulska
On Some Properties Of Szasz-Mirakyan Operators In Hölder Spaces, Zbigniew Walczak, Lucyna Rempulska
Turkish Journal of Mathematics
We study some properties of modified Szasz-Mirakyan operators in Hölder exponential weighted spaces. We give theorems on the degree of approximation of functions by these operators.
On Intuitionistic Fuzzy Subhypernear-Rings Of Hypernear-Rings, Kyung Ho Kim
On Intuitionistic Fuzzy Subhypernear-Rings Of Hypernear-Rings, Kyung Ho Kim
Turkish Journal of Mathematics
In this paper, we introduce the concept of an intuitionistic fuzzy subhypernear-ring of a hypernear-ring and obtain some results in this connection.
Fiber Sums Of Genus 2 Lefschetz Fibrations, Denis Auroux
Fiber Sums Of Genus 2 Lefschetz Fibrations, Denis Auroux
Turkish Journal of Mathematics
Using the recent results of Siebert and Tian about the holomorphicity of genus 2 Lefschetz fibrations with irreducible singular fibers, we show that any genus 2 Lefschetz fibration becomes holomorphic after fiber sum with a holomorphic fibration.
Galois Symmetry On Floer Cohomology, Kenji Fukaya
Galois Symmetry On Floer Cohomology, Kenji Fukaya
Turkish Journal of Mathematics
In this article, we define an action of \hat{\Bbb Z} on the A_{\infty} category whose objects are rational Lagrangian submanifolds together with some other data. The group \hat{\Bbb Z} is a Galois group of the (universal) Novikov ring (field) over Laurent polynomial field. By mirror symmetry it will corresponds to the algebraic fundamental group of a punctured disk which parametrize the maximal degenerate family of the mirror complex manifold.
On Cofinite Subgroups Of Mapping Class Groups, Mustafa Korkmaz
On Cofinite Subgroups Of Mapping Class Groups, Mustafa Korkmaz
Turkish Journal of Mathematics
For every positive integer n, we exhibit a cofinite subgroup \Gamma_n of the mapping class group of a surface of genus at most two such that \Gamma_n admits an epimorphism onto a free group of rank n. We conclude that H^1 (\Gamma_n; {\mathbb Z}) has rank at least n and the dimension of the second bounded cohomology of each of these mapping class groups is the cardinality of the continuum. In the case of genus two, the groups \Gamma_n can be chosen not to contain the Torelli group. Similarly for hyperelliptic mapping class groups. We also exhibit an automorphism of …
A Monopole Homology For Integral Homology 3-Spheres, Weiping Li
A Monopole Homology For Integral Homology 3-Spheres, Weiping Li
Turkish Journal of Mathematics
To an integral homology 3-sphere Y, we assign a well-defined {\mathbb Z}-graded (monopole) homology MH_*(Y, I_{\eta}(\Theta; \eta_0)) whose construction in principle follows from the instanton Floer theory with the dependence of the spectral flow I_{\eta}(\Theta; \eta_0), where \Theta is the unique U(1)-reducible monopole of the Seiberg-Witten equation on Y and \eta_0 is a reference perturbation datum. The definition uses the moduli space of monopoles on Y \times {\mathbb R} introduced by Seiberg-Witten in studying smooth 4-manifolds. We show that the monopole homology MH_*(Y, I_{\eta}(\Theta; \eta_0)) is invariant among Riemannian metrics with same I_{\eta}(\Theta; \eta_0). This provides a chamber-like structure for …
Adjunction Inequality And Coverings Of Stein Surfaces, Stefan Nemirovski
Adjunction Inequality And Coverings Of Stein Surfaces, Stefan Nemirovski
Turkish Journal of Mathematics
A stronger form of the adjunction inequality is proved for immersed real surfaces in non simply-connected Stein surfaces. The result is applied to the geometry of Stein domains and analytic continuation on complex surfaces.
Comparing Open Book And Heegaard Decompositions Of 3-Manifolds, J. Hyam Rubinstein
Comparing Open Book And Heegaard Decompositions Of 3-Manifolds, J. Hyam Rubinstein
Turkish Journal of Mathematics
We study the maximal value of the Euler characteristic of the pages of all open book decompositions of closed orientable 3-manifolds. In particular, we describe some examples where the minimal genus Heegaard splittings of such 3-manifolds give rise to open book decompositions and other examples where the simplest open book decomposition has larger maximal Euler characteristic of pages than the smallest genus Heegaard splittings. Also, special properties of the Heegaard splitting associated to an open book decomposition are given. Techniques of minimal surface theory and hyperbolic geometry are shown to be useful for such problems.
Abelian Fibred Holomorphic Symplectic Manifolds, Justin Sawon
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
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.
Affine Manifolds, Log Structures, And Mirror Symmetry, Mark Gross, Bernd Siebert
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
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
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
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.
Fuzzy Ideals In Gamma-Rings, Mehmet Ali̇ Öztürk, Mustafa Uçkun, Young Bae Jun
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.
Left Adjoint Of Pullback Cat^1- Profinite Groups, Murat Alp
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
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
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
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.