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A Lower Bound Of The First Eigenvalue Of Certain Self-Adjoint Elliptic Operators On Manifolds Containing Long Necks, Weimin Chen
A Lower Bound Of The First Eigenvalue Of Certain Self-Adjoint Elliptic Operators On Manifolds Containing Long Necks, Weimin Chen
Turkish Journal of Mathematics
In this note, under certain regularity and transversality conditions we obtain a sharp lower bound of the first eigenvalue for certain self-adjoint elliptic operators on manifolds with long necks. This result is used in the gluing construction of 3-dimensional Seiberg-Witten moduli spaces along T^2. See [C1], [C2].
Algorithms To Disprove The Poincare Conjecture, Colin Rourke
Algorithms To Disprove The Poincare Conjecture, Colin Rourke
Turkish Journal of Mathematics
No abstract provided.
Complex Conjugation Equivariant Topology Of Complex Surfaces, Sergey Finashin
Complex Conjugation Equivariant Topology Of Complex Surfaces, Sergey Finashin
Turkish Journal of Mathematics
Suppose X is a non-singular complex surface defined over \R, which is a complete intersection constructed by the method of a small perturbation, and Y=X/\conj is its quotient by the complex conjugation \conj\: X\to X. Assume that \conj has a fixed point. Then Y is completely decomposable, i.e., splits into a connected sum \#_n \Cp^2\#_m\barCP^2 or \#_n(S^2\!\times\! S^2).
A (--86)-Sphere In The K3 Surface, Sergey Finashin, Grigory Mikhalkin
A (--86)-Sphere In The K3 Surface, Sergey Finashin, Grigory Mikhalkin
Turkish Journal of Mathematics
Consider the self-intersection number [\Sigma].[\Sigma] of a 2-dimensional sphere \Sigma embedded into a K3 surface. Since a K3 surface is spin, [\Sigma].[\Sigma] is even and by Gauge theoretical arguments [\Sigma].[\Sigma]\le 0. No other restriction on [\Sigma].[\Sigma] is known. It is a problem 4.105(D) from the Kirby list \cite{K} to determine the possible values of [\Sigma].[\Sigma]. This paper shows that the even numbers between 0 and -86 do appear as [\Sigma].[\Sigma].
Nc-P-Groups Satisfying The Normalizer Condition, Ali Osman Asar
Nc-P-Groups Satisfying The Normalizer Condition, Ali Osman Asar
Turkish Journal of Mathematics
Let G be a perfect locally nilpotent p-group in which every proper subgroup is nilpotent-by-Chernikov. It is shown that in G/Z(G) every proper subgroup is a Chernikov extension of a nilpotent subgroup Of finite exponent (Theorem 1). This resut is then used to give a characterization of G if, in addition, it satisfies the normalizer condition (Theorem 2).
The Rank And The Crank Modulo 5, A. Bülent Eki̇n
The Rank And The Crank Modulo 5, A. Bülent Eki̇n
Turkish Journal of Mathematics
Let p(n) denote the number of partitions of n . Ramanujan's partition congruences are p(5n + 4) , p(7n + 5) and p(11n + 6) = mod 5, 7, and 11, respectively. These have been proved in number of ways. Atkin and Swinnerton-Dyer proved the congruences and some more relations about partition İn the case of mod5 and 7 in terms of rank, Garvan proved them in three cases in terms of crank. In this study, we give an another proof of their results in the case of mod5 by using the theory of modular forms. Although our method is …
On The Stability Results For Third Order Differential-Operator Equations, Varga Kalantarov, Aydın Ti̇ryaki̇
On The Stability Results For Third Order Differential-Operator Equations, Varga Kalantarov, Aydın Ti̇ryaki̇
Turkish Journal of Mathematics
Sufficient conditions for the stability and the global asymptotic stability of the zero solution of third order linear differential- operator equations are established.
Near Ultrafilters And Compactification Of Topological Groups, Mahmut Koçak, Zekeriya Arvasi̇
Near Ultrafilters And Compactification Of Topological Groups, Mahmut Koçak, Zekeriya Arvasi̇
Turkish Journal of Mathematics
No abstract provided.
Differentiable Functions And The Generators On A Hilbert-Lie Group, Erdal Coşkun
Differentiable Functions And The Generators On A Hilbert-Lie Group, Erdal Coşkun
Turkish Journal of Mathematics
A convolution semigroup plays an important role İn the theory of probability measure on Lie groups. The basic problem is that one wants to express a semigroup as a Lévy-Khinckine formula. If (\mu_t)_{t\epsilonR*_+} is a continuous semigroup of probability + measures on a Hilbert-Lie group G, then we define T{\mu_t}f:=\integral f_a\mu_t(da) (f\epsilonC_u(G),t>0 It is apparent that (\mu_t)_t{t\epsilonR*_+} is a contİnuous operator semigroup on the space + C_u ( G) with the İnfinitesimal generator N. The generatİng functional A of this semigroup is defined by A := Iim_t-->0 1/t(T_{\mu_t}f(e) - f(e). We have the problem of consliuction of a …
The Study Of The Level Zero Crossing Time Of A Semi-Markovian Random Walk With Delaying Screen, Tahir A. Khaniev, İhsan Ünver
The Study Of The Level Zero Crossing Time Of A Semi-Markovian Random Walk With Delaying Screen, Tahir A. Khaniev, İhsan Ünver
Turkish Journal of Mathematics
In this study, a semi-Markovian random walk with delaying screen at (\beta > O and the first crossing time ('\gamma1) of the zero level of this process are constructed. Furthermore, the distribution function with its Laplace transform, expected value and variance of random variable (\gamma1) are calculated. In addition to these, a formula for the higher order moments of ('\gamma1) is given.
On Coincidence Points Of Densifying Mappings, M. S. Khan, Z. Q. Liu
On Coincidence Points Of Densifying Mappings, M. S. Khan, Z. Q. Liu
Turkish Journal of Mathematics
A coincidence point theorem for anew class of densifying mappings is obtained. Our result generalizes many previously known theorems and can be regarded as an extension of Jungck's fixed point theorem for densifying mappings. Key words and phases: complete metric space, common fixed points, densifying mappings, commuting mappings.
On The Curves Of Constant Breadth In E^4 Space, Abdullah Mağden, Ömer Köse
On The Curves Of Constant Breadth In E^4 Space, Abdullah Mağden, Ömer Köse
Turkish Journal of Mathematics
In this paper, the concepts concerning the space curves of constant breadth were extended to E^4 -space. The integral of third curvature of the curve was obtained as (bak) \sigmads = 2k7\pi(k E Z) . In addition, the relation (bak) g(\kappa, \tau, \sigma)ds = O was obtained between the curvatures of curves of constant breadth in E^4 . Key words and phrases: Curvature, Constant Breadth, Integral characterization of Curve, Spherical Curves.
On A Generalisation Of Lie Ideals In Prime Rings, Arif Kaya
On A Generalisation Of Lie Ideals In Prime Rings, Arif Kaya
Turkish Journal of Mathematics
Let R be a prime ring of characteristic 3, \sigma and \tau automorphisms of R, U a non zero ( \sigma, \tau) - Lie ideal of R, d a nonzero derivation of R such that \sigmad = d\sigma , \taud = d\tau,d(U) (bak) U, and d^2(U) (bak) Z, the center of R. Then we prove that U (bak) Z. This provides a proof of the Theorem in [4], when char R = 3.
On One Sided (\Sigma, \Tau)-Lie Ideals In Prime Rings, Neşet Aydin
On One Sided (\Sigma, \Tau)-Lie Ideals In Prime Rings, Neşet Aydin
Turkish Journal of Mathematics
In this paper, we proved some results for one-sided (\sigma, \tau)-Lie ideals in prime rings.
Certain Meromorphically Starlike Functions With Positive And Fixed Second Coefficients, M. K. Aouf, H. E. Darwish
Certain Meromorphically Starlike Functions With Positive And Fixed Second Coefficients, M. K. Aouf, H. E. Darwish
Turkish Journal of Mathematics
In this paper we consider the class \SigmaS*{_o,c} ( \alpha ) consisting of meromorphically starlike univalent functions with positive coefficients and fixed second coefficients. The object of the present paper is to show coefficient estimates and closure theorems for this class. Also, we obtain the radius of convexity for functions belonging to the class \SigmaS*{_o,c} ( \alpha ).
Characterization Of Some Rings By Functor Z*(.), Ayşe Çiğdem Özcan, Abdullah Harmanci
Characterization Of Some Rings By Functor Z*(.), Ayşe Çiğdem Özcan, Abdullah Harmanci
Turkish Journal of Mathematics
Let X = {M : Z*(M) = 0} and X* = {M : Q ]]] Keywords:
An Application Of Linear Topological Invariants, Bora Arslan, Mefharet Kocatepe
An Application Of Linear Topological Invariants, Bora Arslan, Mefharet Kocatepe
Turkish Journal of Mathematics
We consider a possible isomorphism of cartesian product of two Dragilev spaces of infinite type, and by making use of Zahariuta invariants and some structural properties, we show that if there is such an isomorphism, then any factor on the left is nearly isomorphic to the corresponding factor on the right. Key Words and Phrases: Linear topological invariants, Dragilev space, Dragilev function, rapidly increasing function.
Arithmetic Of A Semigroup Of Series In Legendre Functions Of The Second Kind, I. P. Il'inskaja
Arithmetic Of A Semigroup Of Series In Legendre Functions Of The Second Kind, I. P. Il'inskaja
Turkish Journal of Mathematics
In the framework of D. Kendall's theory of Delphic semigroups, a semigroup of series in Legendre functions of the second kind is studied. The basic factorization theorems are prowed, the classes of infinitely divisible elements and of elements without indecomposable factors are completely described, the density of the class of indecomposable elements is established.
The Hessian Tensor On A Hypersurface In Euclidean Space And Otsuki's Lemma, Erdal Gül
The Hessian Tensor On A Hypersurface In Euclidean Space And Otsuki's Lemma, Erdal Gül
Turkish Journal of Mathematics
The purpose of this paper is to obtain a condition for a hypersurface in Euclidean space with belongs to Hessian Tensor and is to give an alternative proof of Otsuki's lemma by applying this condition.
Integral Closure Of An Ideal Relative To A Module And \Delta-Closure, Yücel Tiraş
Integral Closure Of An Ideal Relative To A Module And \Delta-Closure, Yücel Tiraş
Turkish Journal of Mathematics
The aim in this paper is to give the relation between the \Delta-closure of an ideal I in a commutative Noetherian ring R, (see [3]), and the integral closure of the ideal i relative to a Noetherian R-module (see (1.1). Definition) and to give the closure cancellation law
On A Certain Family Of Linear Positive Operators, Ogün Doğru
On A Certain Family Of Linear Positive Operators, Ogün Doğru
Turkish Journal of Mathematics
In this study, a family of linear positive operators, which includes the sequence of linear positive operators built in a paper of A. D. Gadjiev and I. I. Ibragimov and later investigated by B. Wood and P. Radatz, is defined and using the some inequalities proved by P. J. Davis, results related to approximation properties of this family are obtained.
Unique Factorisation For Commutative Rings Without Identity, A. G. Ağargün, C.R. Fletcher
Unique Factorisation For Commutative Rings Without Identity, A. G. Ağargün, C.R. Fletcher
Turkish Journal of Mathematics
This paper concerns the unique factorisation property in commutative rings not necessarily with identity. We give a new definition of irreducibility and associates in a commutative ring with 1 (crwl), and define a UFR R in terms of a monomorphism from R into a crwl. This becomes equivalent to the definition in [3] when R has an identity. We generalize results on direct sums and direct summands. By our definition we have new members of the family of UFR's.
Extension And Separation Of Vector Valued Functions, Zafer Ercan
Extension And Separation Of Vector Valued Functions, Zafer Ercan
Turkish Journal of Mathematics
It is proved that: If X is a paracompact Hausdorff space and E is a Frechet lattice then (X, E) has the separation property. This is employed to extend some varies of functions that are known for spaces of Banach lattice valued functions.
Some Commutativity Properties For Rings With Unity, Hamza A.S. Abujabal
Some Commutativity Properties For Rings With Unity, Hamza A.S. Abujabal
Turkish Journal of Mathematics
In this paper, we prove the commutativity of a ring R with unity satisfying one of the following ring properties: (P_1) For each x, y in R, {1- h(yx^r)}[x,yx^r - f(yx^r)]{1-g(yx^r)}=0 for some (P_2) Given x, y in R, {1- h(yx^r)} [x,yx^r - f(x^ry)] {1-g(yx^r)}=0 and {1-~h(xy^r)}[y,y^rx-~f(xy^r)]{1-~g(xy^r)}=0 for some f(X),~f(X)\epsilonX^2Z[X] and g(X), ~g(X), h(X), ~h(X)\epsilonXZ[X]. (P_3) For each x, y \epsilon R, [x, yx^r - x^sf(y)x^t]=0 for some f(X)\epsilon X^2Z[X].
On Existence Of A Meromorphic Function With Infinitely Many Of Deficient Functions, Halil Ardahan
On Existence Of A Meromorphic Function With Infinitely Many Of Deficient Functions, Halil Ardahan
Turkish Journal of Mathematics
Let {a_n(z) : {a_n(z)}_n^w, 0 do not depend on r,0
The Linear Mean Value Of The Remainder Term In The Problem Of Asymptotic Behavior Of Eigenfunctions Of The Automorphic Laplacian, Zernişan Emi̇rleroğlu
The Linear Mean Value Of The Remainder Term In The Problem Of Asymptotic Behavior Of Eigenfunctions Of The Automorphic Laplacian, Zernişan Emi̇rleroğlu
Turkish Journal of Mathematics
The purpose of this paper is to obtain the estimate for the average mean value of the remainder term of the asymptotic formula for the quadratic mean value of the Fourier coefficients of the eigenfunctions over the discrete spectrum of the automorphic Laplacian.
On Hill's Equation With Piecewise Constant Coefficient, I. Yaslan, G.Sh. Guseinov
On Hill's Equation With Piecewise Constant Coefficient, I. Yaslan, G.Sh. Guseinov
Turkish Journal of Mathematics
In this paper the eigenvalues of the periodic and the semi-periodic boundary value problems associated with Hill's equation are investigated in the case of piecewise constant coefficient. As a corollary the asymptotic formula for the lengths of the instability intervals of Hill's equation is derived and it is shown that they increase beyond all bounds. Also, the conditions for coexistence of periodic and semi-periodic solutions are indicated.
A Characterization Of ^-Nc P-Groups, Ali Osman Asar
A Characterization Of ^-Nc P-Groups, Ali Osman Asar
Turkish Journal of Mathematics
In this work, presented is a partial characterization of a perfect locally nilpotent p-group in which every proper subgroup is nilpotent-by-Chernikov.