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Articles 1 - 30 of 34
Full-Text Articles in Physical Sciences and Mathematics
A Quasi-Linear Manifolds And Quasi-Linear Mapping Between Them, Aki̇f Abbasov
A Quasi-Linear Manifolds And Quasi-Linear Mapping Between Them, Aki̇f Abbasov
Turkish Journal of Mathematics
In this article a special class of Banach manifolds (called QL-manifolds) and mapping between them (QL-mappings) are introduced and some examples are given.
On Graded Primary Ideals, Mashhoor Refai, Khaldoun Al-Zoubi
On Graded Primary Ideals, Mashhoor Refai, Khaldoun Al-Zoubi
Turkish Journal of Mathematics
Let G be a group and R be a G-graded commutative ring, i.e., R = \oplus_{g \in G} R_g and R_gR_h \subseteq R_{gh} for all g, h \in G. In this paper, we study the graded primary ideals and graded primary G-decomposition of a graded ideal.
Determination Of A Fractional-Linear Pencil Of Sturm-Liouville Operators By Two Of Its Spectra, R. T. Pashayev
Determination Of A Fractional-Linear Pencil Of Sturm-Liouville Operators By Two Of Its Spectra, R. T. Pashayev
Turkish Journal of Mathematics
In this paper we consider the Sturm-Liouville equations on a finite interval which is fractional-linear in the spectral parameter. The inverse spectral problem consisting of the recovering of the operator from the two spectra is investigated and a uniqueness theorem for solution of the inverse problem is proved.
Perelman's Monotonicity Formula And Applications, Natasa Sesum
Perelman's Monotonicity Formula And Applications, Natasa Sesum
Turkish Journal of Mathematics
This article relies on [15] that the author wrote with Gang Tian and Xiaodong Wang. In view of Hamilton's important work on the Ricci flow and Perelman's paper on the Ricci flow where he developes the techniques that he will later use in completing Hamilton's program for the geometrization conjecture, there may be more interest in the area. We will also discuss the author's theorem which says that the curvature tensor stays uniformly bounded under the unnormalized Ricci flow in a finite time, if the curvatures are uniformly bounded. We will prove that in the case of a Kähler-Ricci flow …
Flops Of Crepant Resolutions, Anda Degeratu
Flops Of Crepant Resolutions, Anda Degeratu
Turkish Journal of Mathematics
Let G be a finite subgroup of SL(3, \mathcal{C}) acting with an isolated singularity on \mathcal{C}^3. A crepant resolution of \mathcal{C}^3/G comes together with a set of tautological line bundles associated to each irreducible representation of G. In this note we give a formula for the triple product of the first Chern class of the tautological bundles in terms of both the geometry of the crepant resolution and the representation theory of G. From here we derive the way these triple products change when we perform a flop.
The Cross Curvature Flow Of 3-Manifolds With Negative Sectional Curvature, Bennett Chow, Richard S. Hamilton
The Cross Curvature Flow Of 3-Manifolds With Negative Sectional Curvature, Bennett Chow, Richard S. Hamilton
Turkish Journal of Mathematics
We consider the cross curvature flow, an evolution equation of metrics on 3-manifolds. We establish short time existence when the sectional curvature has a sign. In the case of negative sectional curvature, we obtain some monotonicity formulas which support the conjecture that after normalization, for initial metrics on closed 3-manifolds with negative sectional curvature, the solution exists for all time and converges to a hyperbolic metric. This conjecture is still open at the present time.
Surgery Diagrams For Contact 3-Manifolds, Fan Ding, Hansjörg Geiges, Andras I. Stipsicz
Surgery Diagrams For Contact 3-Manifolds, Fan Ding, Hansjörg Geiges, Andras I. Stipsicz
Turkish Journal of Mathematics
In two previous papers, the two first-named authors introduced a notion of contact r-surgery along Legendrian knots in contact 3-manifolds. They also showed how (at least in principle) to convert any contact r-surgery into a sequence of contact (\pm 1)-surgeries, and used this to prove that any (closed) contact 3-manifold can be obtained from the standard contact structure on S^3 by a sequence of such contact (\pm 1)-surgeries. In the present paper, we give a shorter proof of that result and a more explicit algorithm for turning a contact r-surgery into (\pm 1)-surgeries. We use this to give explicit surgery …
Quasipositivity Problem For 3-Braids, Stepan Yu. Orevkov
Quasipositivity Problem For 3-Braids, Stepan Yu. Orevkov
Turkish Journal of Mathematics
A braid is called quasipositive if it is a product of conjugates of standard generators of the braid group. We present an algorithm deciding if a given braid with three strings is quasipositive or not. The complexity (the time of work) of our algorithm is O(n^{k+1}) where n is the length of the word in standard generators representing the braid and k is the algebraic length of the braid. The algorithm is based on the Garside normal form. The problem of quasipositivity in braid groups is motivated by the topology of plane real algebraic curves (16th Hilbert's problem). In particular, …
Solution Of The Word Problem In The Singular Braid Group, Stepan Yu. Orevkov
Solution Of The Word Problem In The Singular Braid Group, Stepan Yu. Orevkov
Turkish Journal of Mathematics
Singular braids are isotopy classes of smooth strings which are allowed to cross each other pairwise with distinct tangents. Under the usual multiplication of braids, they form a monoid. The singular braid group was introduced by Fenn-Keyman-Rourke as the quotient group of the singular braid monoid. We give a solution of the word problem for this group. It is obtained as a combination of the results by Fenn-Keyman-Rourke and some simple geometric considerations based on the mapping class interpretation of braids. Combined with Corran's normal form for the singular braid monoid, our algorithm provides a computable normal form for the …
The Theory Of Jacobi Systems And Their Abelian Representations, M. Shahryari, Y. Zamani
The Theory Of Jacobi Systems And Their Abelian Representations, M. Shahryari, Y. Zamani
Turkish Journal of Mathematics
In this article we introduce a new generalization of the concept of Lie ring which we call Jacobi system and we investigate some elementary properties of these systems and their Abelian representations.
New Special Curves And Developable Surfaces, Shyuichi Izumiya, Nobuko Takeuchi
New Special Curves And Developable Surfaces, Shyuichi Izumiya, Nobuko Takeuchi
Turkish Journal of Mathematics
We define new special curves in Euclidean 3-space which we call slant helices and conical geodesic curves. Those notions are generalizations of the notion of cylindrical helices. One of the results in this paper gives a classification of special developable surfaces under the condition of the existence of such a special curve as a geodesic. As a result, we consider geometric invariants of space curves. By using these invariants, we can estimate the order of contact with those special curves for general space curves. All arguments in this paper are straight forward and classical. However, there have been no papers …
Groups With Rank Restrictions On Non-Subnormal Subgroups, Leonid Andreevich Kurdachenko, Howard Smith
Groups With Rank Restrictions On Non-Subnormal Subgroups, Leonid Andreevich Kurdachenko, Howard Smith
Turkish Journal of Mathematics
Let G be a group in which every non-subnormal subgroup has finite rank. This paper considers the question as to which extra conditions on such a group G ensure that G has all subgroups subnormal. For example, if G is torsion-free and locally soluble-by-finite then either G has finite 0-rank or G is nilpotent. Several results are obtained on soluble (respectively, locally soluble-by-finite) groups satisfying the stated hypothesis on subgroups.
On Orthogonal Generalized Derivations Of Semiprime Rings, Nurcan Argaç, Atsushi Nakajima, Emi̇ne Albaş
On Orthogonal Generalized Derivations Of Semiprime Rings, Nurcan Argaç, Atsushi Nakajima, Emi̇ne Albaş
Turkish Journal of Mathematics
In this paper, we present some results concerning two generalized derivations on a semiprime ring. These results are a generalization of results of M. Bre\u{s}ar and J. Vukman in [2], which are related to a theorem of E. Posner for the product of derivations on a prime ring.
Ideal Theory In Topological Algebras, A. Najmi
Ideal Theory In Topological Algebras, A. Najmi
Turkish Journal of Mathematics
Given a simplicial topologically non radical algebra A, we characterize its topological radical, radA. If furthermore A is advertive, then radA coincides with the Jacobson radical RadA. On the other hand, it is shown that every two-sided invertive simplicial topological Gelfand-Mazur algebra has a functional spectrum and for every topologically nonradical simplicial Gelfand-Mazur amits the set \mathcal{X}(A), of all continuous multiplicative linear functionals, is not empty.
Moments Equalities For Nonnegative Integer-Valued Random Variables, Mohamed I. Riffi
Moments Equalities For Nonnegative Integer-Valued Random Variables, Mohamed I. Riffi
Turkish Journal of Mathematics
We present and prove two theorems about equalities for the nth moment of nonnegative integer-valued random variables. These equalities generalize the well known equality for the first moment of a nonnegative integer-valued random variable X in terms of its cumulative distribution function, or in terms of its tail distribution.
Conjugacy Classes Of Finite Subgroups Of Certain Mapping Class Groups, Michal Stukow
Conjugacy Classes Of Finite Subgroups Of Certain Mapping Class Groups, Michal Stukow
Turkish Journal of Mathematics
We give a complete description of conjugacy classes of finite subgroups of the mapping class group of the sphere with r marked points. As a corollary we obtain a description of conjugacy classes of maximal finite subgroups of the hyperelliptic mapping class group. In particular, we prove that, for a fixed genus g, there are at most five such classes.
Coisotropic Submanifolds Of A Semi-Riemannian Manifold, Erol Kiliç, Bayram Şahi̇n, H. B. Karadağ, R. Güneş
Coisotropic Submanifolds Of A Semi-Riemannian Manifold, Erol Kiliç, Bayram Şahi̇n, H. B. Karadağ, R. Güneş
Turkish Journal of Mathematics
In this paper, we study coisotropic submanifolds of a semi-Riemannian manifold. We investigate the integrability condition of the screen distribution and give a necessary and sufficient condition on Ricci tensor of a coisotropic submanifold to be symmetric. Finally, we present some new theorems and results about totally umbilical coisotropic submanifolds of a semi-Riemannian manifold
On Simultaneous Approximation By A Linear Combination Of A New Sequence Of Linear Positive Operators, P. N. Agrawal, Ali J. Mohammad
On Simultaneous Approximation By A Linear Combination Of A New Sequence Of Linear Positive Operators, P. N. Agrawal, Ali J. Mohammad
Turkish Journal of Mathematics
In [1] we introduced a new sequence of linear positive operators M_{n} to approximate unbounded continuous functions of exponential growth on [0,\infty). As this sequence is saturated with O(n^{-1}), to accelerate the rate of convergence we applied the technique of linear combination introduced by May [3] and Rathore et al. [4] to these operators. The object of the present paper is to study the phenomena of simultaneous approximation (approximation of derivatives of functions by the corresponding order derivatives of operators) by the linear combination M_{n} ( . , k, x) of M_{n}. First, we establish a Voronovskaja-type asymptotic formula and …
A Generalization Of A Result On Torsion-Free Groups With All Subgroups Subnormal, Tahi̇re Özen
A Generalization Of A Result On Torsion-Free Groups With All Subgroups Subnormal, Tahi̇re Özen
Turkish Journal of Mathematics
The main result in this paper is the following: Let G be a torsion-free locally nilpotent group and let F be a finitely generated subgroup of G. If every subgroup of G containing F is subnormal in G, then G is nilpotent.
A Note On Groups With All Subgroups Subnormal, Ahmet Arikan, Tahi̇re Özen
A Note On Groups With All Subgroups Subnormal, Ahmet Arikan, Tahi̇re Özen
Turkish Journal of Mathematics
We prove that if G is a periodic group with all subgroups subnormal, and if for every x, y \in G, ^{G} is an FC-group, then G is nilpotent.
An Algorithm To Recognise Small Seifert Fiber Spaces, J. Hyam Rubinstein
An Algorithm To Recognise Small Seifert Fiber Spaces, J. Hyam Rubinstein
Turkish Journal of Mathematics
The homeomorphism problem is, given two compact n-manifolds, is there an algorithm to decide if the manifolds are homeomorphic or not. The homeomorphism problem has been solved for many important classes of 3-manifolds - especially those with embedded 2-sided incompressible surfaces (cf [12], [15], [16]), which are called Haken manifolds. It is also well-known that the homeomorphism problem is easily solvable for two 3-manifolds which admit geometries in the sense of Thurston [36], [31]. Hence the recognition problem, to decide if a 3-manifold has a geometric structure, is a significant problem. The recognition problem has been solved for all geometric …
On The Power Subgroups Of The Extended Modular Group \Gamma, Recep Şahi̇n, Sebahatti̇n İki̇kardeş, Özden Koruoğlu
On The Power Subgroups Of The Extended Modular Group \Gamma, Recep Şahi̇n, Sebahatti̇n İki̇kardeş, Özden Koruoğlu
Turkish Journal of Mathematics
In this paper we describe the group structure of power subgroups \Gamma^m of the extended modular group \Gamma and the quotients to them. Then we give some relations between the power subgroups \Gamma^m, the commutator subgroups \Gamma^{\prime} and \Gamma^{\prime \prime} and also the information of interest about free normal subgroups of the extended modular group \Gamma.
Modules Supplemented Relative To A Torsion Theory, M. Tamer Koşan, Abdullah Harmanci
Modules Supplemented Relative To A Torsion Theory, M. Tamer Koşan, Abdullah Harmanci
Turkish Journal of Mathematics
This article introduces the concept of a \tau-supplemented module as follows: Given a hereditary torsion theory in Mod R with associated torsion functor \tau, we say that a module M is \tau-supplemented when for every submodule N of M there exists a direct summand K of M such that K\leq N and N/K is \tau-torsion module. We present here some fundamental properties of this class of modules and study the decompositions of \tau-supplemented modules under certain conditions on modules. The question of which direct sum of \tau-supplemented R-modules are \tau-supplemented is treated here.
On Near-Rings With Two-Sided \Alpha-Derivations, Nurcan Argaç
On Near-Rings With Two-Sided \Alpha-Derivations, Nurcan Argaç
Turkish Journal of Mathematics
In this paper, we introduce the notion of two-sided \alpha-derivation of a near-ring and give some generalizations of [1]. Let N be a near ring. An additive mapping f: N\rightarrow N is called an { \it (\alpha, \beta)-derivation } if there exist functions \alpha,\beta : N\rightarrow N such that f(xy)=f(x)\alpha(y)+\beta (x)f(y) for all x,y\in N. An additive mapping d:N\rightarrow N is called a two-sided \alpha-derivation if d is an (\alpha,1)-derivation as well as a (1,\alpha)-derivation. The purpose of this paper is to prove the following two assertions: (i) Let N be a semiprime near-ring, I be a subset of N …
Radical Submodules And Uniform Dimension Of Modules, Patrick F. Smith
Radical Submodules And Uniform Dimension Of Modules, Patrick F. Smith
Turkish Journal of Mathematics
We investigate the relations between a radical submodule N of a module M being a finite intersection of prime submodules of M and the factor module M/N having finite uniform dimension. It is proved that if N is a radical submodule of a module M over a ring R such that M/N has finite uniform dimension, then N is a finite intersection of prime submodules. The converse is false in general but is true if the ring R is fully left bounded left Goldie and the module M is finitely generated. It is further proved that, in general, if a …
Fuzzy \Beta-Compactness And Fuzzy \Beta-Closed Spaces, I. M. Hanafy
Fuzzy \Beta-Compactness And Fuzzy \Beta-Closed Spaces, I. M. Hanafy
Turkish Journal of Mathematics
The concepts of \beta-compactness and \beta-closed spaces in the fuzzy setting are defined and investigated. Fuzzy filterbases are used to characterize these concepts. A comparison between these types and some different forms of compactness in fuzzy topology is established.
The Trace Formula For A Differential Operator Of Fourth Order With Bounded Operator Coefficients And Two Terms, Erdal Gül
Turkish Journal of Mathematics
L Yıldız Teknik Üniversitesi Fen-Edebiyat Fakültesi Matematik Bölümü Davutpaşa Kampüsü İstanbul-TURKEY e-mail: gul@yildiz.edu.tr We investigate the spectrum of a differential operator of fourth order with bounded operator coefficients and find a formula for the trace of this operator.
Splitting Of Sharply 2-Transitive Groups Of Characteristic 3, Seyfi̇ Türkelli̇
Splitting Of Sharply 2-Transitive Groups Of Characteristic 3, Seyfi̇ Türkelli̇
Turkish Journal of Mathematics
We give a group theoretic proof of the splitting of sharply 2-transitive groups of characteristic 3.
A New Characteristic Of Möbius Transformations By Use Of Apollonius Points Of Pentagons, Serap Bulut, Ni̇hal Yilmaz Özgür
A New Characteristic Of Möbius Transformations By Use Of Apollonius Points Of Pentagons, Serap Bulut, Ni̇hal Yilmaz Özgür
Turkish Journal of Mathematics
In this paper, we give a new characterization of Möbius transformations. To this end, a new concept of ''Apollonius points of pentagons'' is used.
Rate Of Convergence Of Durrmeyer Type Baskakov-Bezier Operators For Locally Bounded Functions, Vijay Gupta
Rate Of Convergence Of Durrmeyer Type Baskakov-Bezier Operators For Locally Bounded Functions, Vijay Gupta
Turkish Journal of Mathematics
In the present paper, we introduce the Durrmeyer variant of Baskakov-Bezier operators B_{n,\alpha} (f,x), which is the modified form of Baskakov-Beta operators. Here we obtain an estimate on the rate of convergence of B_{n,\alpha} (f,x) for functions of bounded variation in terms of Chanturiya's modulus of variation. In the end we also propose an open problem for the readers.