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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.
Characterizations Of Matroid Via Ofr-Sets, Talal Ali̇ Al-Hawary
Characterizations Of Matroid Via Ofr-Sets, Talal Ali̇ Al-Hawary
Turkish Journal of Mathematics
The aim of this paper is to introduce the class of OFR-sets as the sets that are the intersection of an open set and a feeble-regular set. Several classes of matroids are studied via the new concept. New decompositions of strong maps are provided.
Fuzzy Maximal Ideals Of Gamma Near-Rings, Young Bae Yun, Kyung Ho Kim, Mehmet Ali̇ Öztürk
Fuzzy Maximal Ideals Of Gamma Near-Rings, Young Bae Yun, Kyung Ho Kim, Mehmet Ali̇ Öztürk
Turkish Journal of Mathematics
Fuzzy maximal ideals and complete normal fuzzy ideals in \Gamma-near-rings are considered, and related properties are investigated.
A General Fixed Point Theorem For Weakly Compatible Mappings In Compact Metric Spaces, Valeriu Popa
A General Fixed Point Theorem For Weakly Compatible Mappings In Compact Metric Spaces, Valeriu Popa
Turkish Journal of Mathematics
A general fixed point theorem for weakly compatible mappings satisfying an implicit relation in compact metric spaces is proved generalizing the results by [1],[3],[13],[14] and others.
Some Applications Of The Lattice Finite Representability In Spaces Of Measurable Functions, P. Gomez Palaci̇o, J. A. Lopez Molina, M. J. Rivera
Some Applications Of The Lattice Finite Representability In Spaces Of Measurable Functions, P. Gomez Palaci̇o, J. A. Lopez Molina, M. J. Rivera
Turkish Journal of Mathematics
We study the lattice finite representability of the Bochner space L_p(\mu_1,L_q(\mu_2)) in \ell_p{\ell_q}, 1 \le p,q < \infty, and then we characterize the ideal of the operators which factor through a lattice homomorphism between L_{\infty}(\mu) and L_p(\mu_1,L_q(\mu_2)).
Diagonal Lift In The Cotangent Bundle And Its Applications, Sezgi̇n Akbulut, Murat Özdemi̇r, Ari̇f A. Salimov
Diagonal Lift In The Cotangent Bundle And Its Applications, Sezgi̇n Akbulut, Murat Özdemi̇r, Ari̇f A. Salimov
Turkish Journal of Mathematics
The purpose of this paper is to define a diagonal lift ^{\mathcal{D }}g of a Riemannian metric g of a manifold M_{n} to the cotangent bundle T^{*}(M_{n}) of M_{n}, to associate with ^{\mathcal{D}}g an Levi-Civita connection of T^{*}(M_{n}) in a natural way and to investigate applications of the diagonal lifts.
Absolutely Representing Systems Of Exponentials In The Spaces Of Infinitely-Differentiable Functions And Extendability In The Sense Of Whitney, Yu. F. Korobeinik
Absolutely Representing Systems Of Exponentials In The Spaces Of Infinitely-Differentiable Functions And Extendability In The Sense Of Whitney, Yu. F. Korobeinik
Turkish Journal of Mathematics
Let Q be a compactum in~\mathbb{R}^p, p\geqslant1, such that int Q\neq\varnothing and Q=\overline{ int Q}. Denote by C^{\infty}[Q] the space of functions from C^{\infty}( int Q) uniformly continuous in int Q together with all their partial derivatives. The conditions of the existence of absolutely representing systems of exponentials with purely imaginary exponents in the space C^{\infty}[Q] and some of its subspaces of Denjoy--Carleman type are investigated. It is also proved under rather general assumptions that there is no such absolutely representing systems in the space E(G)=\operatornamewithlimits{proj}\limits_ {\overleftarrow {Q\in \mathcal{F}_G}}E[Q] where G is an arbitrary open set in~\mathbb{R}^p, E[Q] is C^{\infty}[Q] …
L^P Boundedness Of A Class Of Singular Integral Operators With Rough Kernels, Ahmad Al-Salman, Hussain Al-Quassem
L^P Boundedness Of A Class Of Singular Integral Operators With Rough Kernels, Ahmad Al-Salman, Hussain Al-Quassem
Turkish Journal of Mathematics
In this paper, we study the L^p mapping properties of singular integral operators with kernels belonging to certain block spaces. These operators have singularities along sets of the form {x=\Phi ( y )y^'} where \Phi satisfies certain growth conditions. Our results improve as well as extend previously known results on singular integrals.