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On The Spectral Properties Of The Regular Sturm-Liouville Problem With The Lag Argument For Which Its Boundary Conditions Depends On The Spectral Parameter, Mehmet Bayramoğlu, Kevser Özden Köklü, Oya Baykal
On The Spectral Properties Of The Regular Sturm-Liouville Problem With The Lag Argument For Which Its Boundary Conditions Depends On The Spectral Parameter, Mehmet Bayramoğlu, Kevser Özden Köklü, Oya Baykal
Turkish Journal of Mathematics
In this paper, the asymptotic expression of the eigenvalues and eigenfunctions of the Sturm-Liouville equation with the lag argument y''(t) + \lambda^2 y(t) + M(t)y (t - \Delta(t)) = 0 and the spectral parameter in the boundary conditions \lambda y(0) +y'(0) = 0 \lambda^{2}y(\pi) + y'(\pi) = 0 y(t - \Delta(t)) = y(0)\varphi(t - \Delta(t)), t - \Delta(t) < 0 has been founded in a finite interval, where M(t) and \Delta(t) \geq 0 are continuous functions on [0, \pi], \lambda > 0 is a real parameter, \varphi(t) is an initial function which is satisfied with the condition \varphi(0) = 1 and continuous in the initial set.
On The Modular Curve X(6) And Surfaces Admitting Genus 2 Fibrations, Gülay Karadoğan
On The Modular Curve X(6) And Surfaces Admitting Genus 2 Fibrations, Gülay Karadoğan
Turkish Journal of Mathematics
In this paper, we study the moduli spaces of surfaces admitting nonsmooth genus 2 fibrations with slope \lambda = 6 (necessarily) over curves of genus \geq 1. We determine the structure of each connected component of these moduli spaces. Our results fill the gap of earlier work in the literature to complete the picture of the moduli spaces of genus 2 fibrations over curves of genus \geq 2 except for the case of \lambda = 4.
Symplectic Maps To Projective Spaces And Symplectic Invariants, Denis Auroux
Symplectic Maps To Projective Spaces And Symplectic Invariants, Denis Auroux
Turkish Journal of Mathematics
After reviewing recent results on symplectic Lefschetz pencils and symplectic branched covers of \CP^2, we describe a new construction of maps from symplectic manifolds of any dimension to \CP^2 and the associated monodromy invariants. We also show that a dimensional induction process makes it possible to describe any compact symplectic manifold by a series of words in braid groups and a word in a symmetric group.
The Topology Of Symplectic Manifolds, Robert E. Gompf
The Topology Of Symplectic Manifolds, Robert E. Gompf
Turkish Journal of Mathematics
A topological structure is introduced that seems likely to provide a complete topological characterization of compact symplectic manifolds. The article begins with a leisurely introduction to symplectic manifolds from a topological viewpoint. It then focuses on Thurston's construction of a symplectic structure on the total space of a fiber bundle. This is generalized to a technique for putting a symplectic structure on the domain of a J-holomorphic map. A topological structure called a hyperpencil on a compact 2n-manifold is then defined; this is motivated by the special case of a linear system of curves on an algebraic manifold, and it …
Surface Bundles: Some Interesting Examples, Jim Bryan, Ron Donagi, Andras I. Stipsicz
Surface Bundles: Some Interesting Examples, Jim Bryan, Ron Donagi, Andras I. Stipsicz
Turkish Journal of Mathematics
We show two constructions of surface bundles over Riemann surfaces admitting nonvanishing signatures.
Torus Fibrations On Symplectic Four-Manifolds, Ivan Smith
Torus Fibrations On Symplectic Four-Manifolds, Ivan Smith
Turkish Journal of Mathematics
This paper has two essentially unrelated halves. In the first we prove that a closed symplectic four-manifold admitting a fibration by connected, homologically essential Lagrangian tori with "tame" singularities, is fibre-preserving diffeomorphic to a K3 surface or to a torus bundle over a torus with first Betti number at least three. In the second, we prove that these torus bundles over tori admit Lefschetz pencils by genus three curves. It follows that the genus three mapping class group admits infinitely many inequivalent irreducible positive relations. Motivations for the questions are provided from mirror symmetry, integrable systems and Seiberg-Witten theory: in …
Sections Of Lefschetz Fibrations And Stein Fillings, Andras I. Stipsicz
Sections Of Lefschetz Fibrations And Stein Fillings, Andras I. Stipsicz
Turkish Journal of Mathematics
Using Eliashberg's theorem about Stein fillings of S^3 we prove that a section of a Lefschetz fibration over S^2 has nonnegative square. This observation, in particular, implies that the identity element 1\in \Gamma _g ^1 in the mapping class group of a genus-g surface with one boundary component cannot be written as a product of positive Dehn twists.
Floer Homology And Its Continuity For Non-Compact Lagrangian Submanifolds, Yong-Geum Oh
Floer Homology And Its Continuity For Non-Compact Lagrangian Submanifolds, Yong-Geum Oh
Turkish Journal of Mathematics
We give a construction of the Floer homology of the pair of vnon-compact Lagrangian submanifolds, which satisfies natural continuity property under the Hamiltonian isotopy that moves the infinity but leaves the intersection set of the pair compact. This construction uses the concept of Lagrangian cobordism and certain singular Lagrangian submanifolds. We apply this construction to conormal bundles (or varieties) in the cotangent bundle, and relate it to a conjecture made by MacPherson on the intersection theory of the characteristic Lagrangian cycles associated to the perverse sheaves constructible to a complex stratification on the complex algebraic manifold.
The Canonical Class Of A Symplectic Four Manifold, Ronald Fintushel, Ronald Stern
The Canonical Class Of A Symplectic Four Manifold, Ronald Fintushel, Ronald Stern
Turkish Journal of Mathematics
In this article we present examples of simply connected symplectic 4-manifolds X whose canonical classes are represented by complicated disjoint unions of symplectic submanifolds of X: Theorem. Given finite collections {g_i}, {m_i}, i=1,...,n, of positive integers, there is a minimal symplectic simply connected 4-manifold X whose canonical class is represented by a disjoint union of embedded symplectic surfaces K ~ S_{g_1,1} « ... « S_{g_1,m_1} « ... « S_{g_n,1} «... « S{g_n,m_n} where S_{g_i,j} is a surface of genus g_i. Furthermore, c_1^2(X) = c_h(X) - (2+ b) where b= S{i=1}^n m_i is the total number of connected components of the …
A Partial Order On The Group Of Contactomorphisms Of $\R^{2n+1}$ Via Generating Functions, Mohan Bhupal
A Partial Order On The Group Of Contactomorphisms Of $\R^{2n+1}$ Via Generating Functions, Mohan Bhupal
Turkish Journal of Mathematics
In this note we construct a nontrivial partial order on the identity component of the group of compactly supported contactomorphisms of \R^{2n+1} using the method of generating functions. Our construction is in the framework of the theory developed by Viterbo in the paper \cite{V} wherein, among other things, he showed how one could use generating functions to construct a partial order on the group of compactly supported Hamiltonian symplectomorphisms of \R^{2n}.
Knotting Of Algebraic Curves In Complex Surfaces, Sergey Finashin
Knotting Of Algebraic Curves In Complex Surfaces, Sergey Finashin
Turkish Journal of Mathematics
For any d\ge 5, I constructed infinitely many pairwise smoothly non-equivalent surfaces F\subset\Cp{2} homeomorphic to a non-singular algebraic curve of degree d, realizing the same homology class as such a curve and having abelian fundamental group \pi_1(\Cp2\stmin F). It is a special case of a more general theorem, which concerns for instance those algebraic curves, A, in a simply connected algebraic surface, X, which admit irreducible degenerations to a curve A_0, with a unique singularity of the type X_9, and such that A\cite A>16.
The Verlinde Algebra Is Twisted Equivariant K-Theory, Daniel S. Freed
The Verlinde Algebra Is Twisted Equivariant K-Theory, Daniel S. Freed
Turkish Journal of Mathematics
The Verlinde algebra, which mathematically appears in the theory of loop groups and is related to moduli spaces of bundles over curves, turns out to be describable in terms of K-theory. This is a joint discovery with M. Hopkins and C. Teleman. Here we explain in heuristic terms how this fits naturally into ideas about the Chern-Simons topological field theory.
Topological Quantum Field Theory And Hyperkähler Geometry, Justin Sawon
Topological Quantum Field Theory And Hyperkähler Geometry, Justin Sawon
Turkish Journal of Mathematics
Rozansky and Witten proposed a 3-dimensional sigma-model whose target space is a hyperkähler manifold. They conjectured that this theory has an associated TQFT, with vector spaces given by certain cohomology groups of the hyperkähler manifold. On the other hand, there is a certain modified TQFT constructed by Murakami and Ohtsuki using the universal quantum invariant. We explain how the Rozansky-Witten TQFT can be obtained from the latter by applying a "hyperkähler weight system".
G-Bundles On Abelian Surfaces, Hyperk\"Aler Manifolds, And Stringy Hodge Numbers, Jim Bryan, Ron Donagi, Naichung Conan Leung
G-Bundles On Abelian Surfaces, Hyperk\"Aler Manifolds, And Stringy Hodge Numbers, Jim Bryan, Ron Donagi, Naichung Conan Leung
Turkish Journal of Mathematics
We study the moduli space M_{G} (A) of flat G-bundles on an Abelian surface A, where G is a compact, simple, simply connected, connected Lie group. Equivalently, M_{G} (A) is the (coarse) moduli space of s-equivalence classes of holomorphic semi-stable G^{\cnums }-bundles with trivial Chern classes. M_{G} (A) has the structure of a hyperk\"ahler orbifold. We show that when G is Sp(n) or SU (n), M_{G} (A) has a natural hyperk\"ahler desingularization which we exhibit as a moduli space of G^{\cnums }-bundles with an altered stability condition. In this way, we obtain the two known families of hyperk\"ahler manifolds, the …
On The Tautological Ring Of \Bar{\Mathcal{M}}_{G,N}, Tom Graber, Ravi Vakil
On The Tautological Ring Of \Bar{\Mathcal{M}}_{G,N}, Tom Graber, Ravi Vakil
Turkish Journal of Mathematics
We prove that the dimension 0 part of the tautological ring of the moduli space of stable pointed curves is one-dimensional. This provides the first genus-free evidence for a conjecture of Faber and Pandharipande that the tautological ring of the moduli space is Gorenstein, answering in the affirmative a question of Hain and Looijenga.
Induced Cat^1-Groups, Murat Alp
Induced Cat^1-Groups, Murat Alp
Turkish Journal of Mathematics
In this paper we define the pullback cat^1-group and show that this Pullback has a right adjoint which is the induced cat^1-group. Later we show that this right adjoint is a pushout of category of cat^1-groups. We calculate the Peiffer subgroups to find a finite group of the source of induced cat^1-groups. The generating set of Peiffer subgroups are also given in this paper. All results are corrected by a GAP[13] program package in [4]. This paper also contains the some computational examples which are the calculation-induced cat^1-group and comparative times between the induced crossed modules and induced cat^1-groups.
A Class Of Monoids Embeddable In A Group, Ebru Keyman
A Class Of Monoids Embeddable In A Group, Ebru Keyman
Turkish Journal of Mathematics
In this paper, we develop a new method to show that a monoid, given by a certain kind of presentation, embeds in a group. A mathematical device called the diamond condition was used in [5] to prove that the singular braid monoid SB_n embeds. Motivated by this, we consider monoid presentations which have the basic properties of the presentation of the singular braid monoid. In the same way as in [5], we prove that the monoid embeds. The proof of the diamond condition is completely geometric in [5], but here we prove it by using elementary algebraic properties.
On The Semi-Markovian Random Walk Process With Reflecting And Delaying Barrriers, Selahatti̇n Maden
On The Semi-Markovian Random Walk Process With Reflecting And Delaying Barrriers, Selahatti̇n Maden
Turkish Journal of Mathematics
In this paper, a semi-Markovian random walk process X(t) with reflecting barrier on the zero-level and delaying barrier on the \beta(\beta>0 )-level and the first falling moment of the process into the delaying barrier, (\gamma), are considered. Some probability characteristics of \gamma , such as its distribution function, moment generating function and expected value are calculated.
Formula For The Highly Regularized Trace Of The Sturm-Liouville Operator With Unbounded Operator Coefficients Having Singularity, İnci̇ Albayrak, Oya Baykal, Erdal Gül
Formula For The Highly Regularized Trace Of The Sturm-Liouville Operator With Unbounded Operator Coefficients Having Singularity, İnci̇ Albayrak, Oya Baykal, Erdal Gül
Turkish Journal of Mathematics
In this work, a formula for the n^{th} regularized trace of the Sturm-Liouville operator with unbounded operator coefficients having singularity is obtained
Inequalities For The Vibrating Clamped Plate Problem, Kimberley Mchale, Ünal Ufuktepe
Inequalities For The Vibrating Clamped Plate Problem, Kimberley Mchale, Ünal Ufuktepe
Turkish Journal of Mathematics
We study the eigenvalues of the vibrating clamped plate problem. We have made improvements on the bounds of the ratios of the eigenvalues of the biharmonic operator (clamped plate) using the methods of Payne, Polya, and Weinberger. The difference in our proof lies mainly with the trial functions and the orthogonality arguments. While Payne, Polya, and Weinberger and Hile and Yeh project away components along u_1,u_2,...,u_k to meet the orthogonality conditions,we use a translation/rotation argument to meet these conditions.
On The Expansions In Eigenfunctions Of Hill's Operator, Fi̇li̇z Aras, Gusei̇n Sh Gusei̇nov
On The Expansions In Eigenfunctions Of Hill's Operator, Fi̇li̇z Aras, Gusei̇n Sh Gusei̇nov
Turkish Journal of Mathematics
In this paper we show how one can deduce the Titchmarsh expansion formula in eigenfunctions of Hill's operator from the Gel'fand expansion formula.
Global Convergence For Discrete Dynamical Systems And Forward Neural Networks, Asuman G. Aksoy, Mario Martelli
Global Convergence For Discrete Dynamical Systems And Forward Neural Networks, Asuman G. Aksoy, Mario Martelli
Turkish Journal of Mathematics
Using a theoretical result regarding the global stability of discrete dynamical systems of lower triangular form, we establish convergence properties of forward neural networks when the neuron response functions fail to be continuous.
On Modified Baskakov Operators On Weighted Spaces, Nurhayat İspi̇r
On Modified Baskakov Operators On Weighted Spaces, Nurhayat İspi̇r
Turkish Journal of Mathematics
The author presents a modification of the Baskakov operator for the intervals [0,b_{n}], where b_{n} is an increasing sequence of positive numbers with either finite or infinite limit. Convergence properties of such an operator for continuous and differentiable functions in weighted space are established.
On The Centroid Of The Prime Gamma Rings Ii, Mehmet Ali̇ Öztürk, Young Bae Jun
On The Centroid Of The Prime Gamma Rings Ii, Mehmet Ali̇ Öztürk, Young Bae Jun
Turkish Journal of Mathematics
The aim of this paper is to study the properities of the extended centroid of the prime \Gamma-rings. Main results are the following theorems: (1) Let M be a simple \Gamma-ring with unity. Suppose that for some a\neq 0 in M we have a\gamma_{1} x\gamma_{2} a\beta_{1} y\beta_{2}a = a\beta_{1} y\beta_{2} a\gamma_{1} x\gamma_{2}a for all x, y\in M and \gamma_{1} ,\gamma_{2} ,\beta_{1} ,\beta_{2} \in \Gamma. Then M is isomorphic onto the \Gamma-ring D_{n,m}, where D_{n,m} is the additive abelian group of all rectangular matrices of type n\times m over a division ring D and \Gamma is a nonzero subgroup of the …
A Perturbed Version Of The Ostrowski Inequality For Twice Differentiable Mappings, A. Sofo, S. S. Dragomir
A Perturbed Version Of The Ostrowski Inequality For Twice Differentiable Mappings, A. Sofo, S. S. Dragomir
Turkish Journal of Mathematics
A generalisation of a perturbed version of the Ostrowski inequality for twice differentiable mappings is studied. It is shown that the error bounds are better than those obtained previously. Applications for general quadrature formulae are also given.
On Qr-Submanifolds Of A Quaternionic Space Form, Bayram Şahi̇n
On Qr-Submanifolds Of A Quaternionic Space Form, Bayram Şahi̇n
Turkish Journal of Mathematics
In this paper, we investigate mixed QR-submanifolds in a quaternionic space form and pseudo umbilical QR-submanifold of a quaternionic space form under some additional condition. Finally we give a necessary condition for QR-submanifold of a quaternion Kaehler manifold such that \dim \upsilon ^{\perp }=1 to be a 3-quasi Sasakian Manifold.