2022-01-29T13:15:54Zhttps://openaccess.dogus.edu.tr/oai/requestoai:openaccess.dogus.edu.tr:11376/12052020-09-22T18:33:16Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2015-03-26T14:43:41Z
2015-03-26T14:43:41Z
2008-09-01
Veliev, O. (2008). On Hill's operator with a matrix potential. Mathematische Nachrichten, 281(9), 1341-1350. https://dx.doi.org/10.1002/mana.200510682
0025-584X
000259379200010 (WOS)
https://dx.doi.org/10.1002/mana.200510682
https://hdl.handle.net/11376/1205
281
9
1341
1350
In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the self-adjoint operator generated by a system of Sturm-Liouville equations with summable coefficients and quasiperiodic boundary conditions. Then using these asymptotic formulas, we find conditions on the potential for which the number of gaps in the spectrum of the Hill's operator with matrix potential is finite.
eng
info:eu-repo/semantics/closedAccess
Hill's Operator
Asymptotic Formulas
On Hill's operator with a matrix potential
article
oai:openaccess.dogus.edu.tr:11376/17862020-09-22T18:33:04Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Yıldız, Güldem
Yılmaz, Bülent
Veliev, Oktay A.
2015-07-09T07:36:00Z
2015-07-09T07:36:00Z
2013
YILDIZ, G., YILMAZ, B., VELIEV, O.A. (2013). Asymptotic and numerical methods in estimating eigenvalues. Mathematical Problems in Engineering, Volume 2013, 8p. https://dx.doi.org/10.1155/2013/415479.
1024-123X
000318709600001 (WOS)
https://dx.doi.org/10.1155/2013/415479
https://hdl.handle.net/11376/1786
2013
1
8
Asymptotic formulas and numerical estimations for eigenvalues of SturmLiouville problems having singular potential functions, with Dirichlet boundary conditions, are obtained. This study gives a comparison between the eigenvalues obtained by the asymptotic and the numerical methods.
eng
info:eu-repo/semantics/openAccess
Boundary-Value-Problems
Sturm-Liouville Problems
Linear-Differential Equations
Approximations
Expansion
Asymptotic and numerical methods in estimating eigenvalues
article
oai:openaccess.dogus.edu.tr:11376/16682020-09-22T18:33:00Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2015-07-06T11:25:15Z
2015-07-06T11:25:15Z
2013-08
VELİEV, O.A. (2013). Isospectral mathieu - hill operators. Letters in Mathematical Physics, 103 (8), pp. 919-925. https://dx.doi.org/10.1007/s11005-013-0627-4.
0377-9017
000320321500007 (WOS)
https://dx.doi.org/10.1007/s11005-013-0627-4
https://hdl.handle.net/11376/1668
103
8
919
925
In this paper we prove that the spectra of the Mathieu-Hill Operators with potentials ae(-i2 pi x) +be (i2 pi x) and ce(-i2 pi x) +de (i2 pi x) , where a, b, c and d are complex numbers, are the same if and only if ab = cd. This immediately results in a generalization of the extension of the Harrell-Avron-Simon formula.
eng
info:eu-repo/semantics/closedAccess
Mathieu - Hill Operator
Spectrum
Isospectral Operators
Isospectral mathieu - hill operators
article
oai:openaccess.dogus.edu.tr:11376/8782020-09-22T18:33:55Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
Yılmaz, Bülent
2015-01-17T16:59:00Z
2015-01-17T16:59:00Z
2005-05
VELIEV, O. A., YILMAZ, B. (2005). Asymptotic formulas for Dirichlet boundary value problems. Studia Scientiarum Mathematicarum Hungarica, 42 (2), pp.153-171. https://dx.doi.org/10.1556/SScMath.42.2005.2.3
0081-6906
1588-2896
000229896200004 (WOS)
https://dx.doi.org/10.1556/SScMath.42.2005.2.3
https://hdl.handle.net/11376/878
42
2
153
171
In this article we obtain asymptotic formulas of arbitrary order for eigenfunctions and eigenvalues of the nonselfadjoint Sturm-Liouville operators with Dirichlet boundary conditions, when the potential is a summable function. Then using these we compute the main part of the eigenvalues in special cases.
eng
info:eu-repo/semantics/closedAccess
Asymptotic Formulas
Sturm - Liouville Operators
Asymptotic formulas for Dirichlet boundary value problems
article
oai:openaccess.dogus.edu.tr:11376/13112020-09-22T18:33:17Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2015-04-13T14:20:16Z
2015-04-13T14:20:16Z
2010-03
VELIEV, O. (2010). On the nonself - adjoint ordinary differential operators with periodic boundary conditions. Israel Journal of Mathematics, 176 (1), pp. 195-207. https://dx.doi.org/10.1007/s11856-010-0025-x.
0021-2172
1565-8511
000278523700008 (WOS)
https://dx.doi.org/10.1007/s11856-010-0025-x
https://hdl.handle.net/11376/1311
176
1
195
207
In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the nonself-adjoint ordinary differential operator with periodic and antiperiodic boundary conditions, when coefficients are arbitrary summable complex-valued functions. Then using these asymptotic formulas, we obtain necessary and sufficient conditions on the coefficient for which the root functions of these operators form a Riesz basis.
eng
info:eu-repo/semantics/closedAccess
Root Functions
Asymptotic Formulas
Nonself - Adjoint Ordinary Differential Operator
On the nonself - adjoint ordinary differential operators with periodic boundary conditions
article
oai:openaccess.dogus.edu.tr:11376/8432020-09-22T18:33:12Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Ercan, Gülin
Güloğlu, İsmail Şuayip
Khukhro, Evgeny
2015-01-05T18:55:30Z
2015-01-05T18:55:30Z
2014-08-15
GÜLOĞLU, İ.Ş., ERCAN, G., KHUKHRO, E. (2014). Derived length of a Frobenius-like kernel. Journal of Algebra 412, pp. 179–188. https://dx.doi.org/10.1016/j.jalgebra.2014.04.025.
0021-8693
https://dx.doi.org/10.1016/j.jalgebra.2014.04.025
https://hdl.handle.net/11376/843
412
179
188
A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F called kernel which has a nontrivial complement H such that FH/[F,F]FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]F/[F,F]. Suppose that a Frobenius-like group FH acts faithfully by linear transformations on a vector space V over a field of characteristic that does not divide |FH||FH|. It is proved that the derived length of the kernel F is bounded solely in terms of the dimension m=dimCV(H) of the fixed-point subspace of H by g(m)=3+[log2(m+1)]g(m)=3+[log2(m+1)]. It follows that if a Frobenius-like group FH acts faithfully by coprime automorphisms on a finite group G , then the derived length of the kernel F is at most g(r)g(r), where r is the sectional rank of CG(H)CG(H). As an application, for a finite solvable group G admitting an automorphism φ of prime order coprime to |G||G|, a bound for the p -length of G is obtained in terms of the rank of a Hall p′p′-subgroup of CG(φ)CG(φ). Earlier results of this kind were known only in the special case when the complement of the acting Frobenius-like group was assumed to have prime order and its fixed-point subspace (or subgroup) was assumed to be one-dimensional (or have all Sylow subgroups cyclic).
eng
info:eu-repo/semantics/closedAccess
Frobenius-Like Group
Derived Length
Fixed Points
Derived length of a Frobenius-like kernel
article
oai:openaccess.dogus.edu.tr:11376/8402020-09-22T18:33:54Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Ercan, Gülin
Güloğlu, İsmail Şuayip
Öğüt, Elif
2015-01-05T18:05:31Z
2015-01-05T18:05:31Z
2014-05-23
ERCAN, G., GÜLOĞLU, İ.Ş., ÖĞÜT, E. (2014). Nilpotent length of a finite solvable group with a frobenius group of automorphisms. Communications in Algebra, 42 (11), pp. 4751-4756. https://dx.doi.org/10.1080/00927872.2013.823776.
00927872
https://dx.doi.org/10.1080/00927872.2013.823776
https://hdl.handle.net/11376/840
42
11
4751
4756
We prove that a finite solvable group G admitting a Frobenius group FH of automorphisms of coprime order with kernel F and complement H such that [G, F] = G and C C G (F)(h) = 1 for all nonidentity elements h ∈ H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H.
eng
info:eu-repo/semantics/openAccess
Automorphisms
Frobenius Group
Nilpotent Length
Solvable Group
Nilpotent length of a finite solvable group with a frobenius group of automorphisms
article
oai:openaccess.dogus.edu.tr:11376/32032020-09-22T18:32:36Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2018-11-28T06:19:10Z
2018-11-28T06:19:10Z
2017-11
Veliev, O. A. (2017). Essential spectral singularities and the spectral expansion for the hill operator. Communications on Pure and Applied Analysis, 16(6), 2227-2251. https://dx.doi.org/10.3934/cpaa.2017110
1534-0392
1553-5258
000411803300016 (WOS)
https://dx.doi.org/10.3934/cpaa.2017110
https://hdl.handle.net/11376/3203
16
6
2227
2251
In this paper we investigate the spectral expansion for the one-dimensional Schrodinger operator with a periodic complex-valued potential. For this we consider in detail the spectral singularities and introduce new concepts as essential spectral singularities and singular quasimomenta.
eng
info:eu-repo/semantics/closedAccess
Schrodinger Operator
Spectral Singularities
Spectral Expansion
Differential-Operators
Translation
Essential spectral singularities and the spectral expansion for the hill operator
article
oai:openaccess.dogus.edu.tr:11376/12792020-09-22T18:33:20Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Shkalikov, A. A.
Veliev, Oktay A.
2015-04-01T12:58:51Z
2015-04-01T12:58:51Z
2009-06
SHKALIKOV, A.A., VELİEV, O.A. (2009). On the riesz basis property of the eigen and associated functions of periodic and antiperiodic Sturm - Liouville problems. Mathematical Notes, 85 (5), pp. 647-660. https://dx.doi.org/10.1134/S0001434609050058.
0001-4346
000267684500005 (WOS)
https://dx.doi.org/10.1134/S0001434609050058
https://hdl.handle.net/11376/1279
85
5-6
647
660
he paper deals with the Sturm-Liouville operator L(y) = -y '' + q(x)y, x is an element of [0,1], generated in the space L(2) = L(2)[0, 1] by periodic or antiperiodic boundary conditions. Several theorems on the Riesz basis property of the root functions of the operator L are proved. One of the main results is the following. Let q belong to the Sobolev space W(1)(P)[0,1] for some integer p >= 0 and satisfy the conditions q((k))(0) = q((k))(1) = 0 for 0 <= k <= s - 1, where s <= p. Let the functions Q and S be defined by the equalities Q(x) = integral(x)(0) q(t) dt, S(x) = Q(2)(x) and let q(n), Q(n), and S(n) be the Fourier coefficients of q, Q, and S with respect to the trigonometric system {e(2 pi inx)}(-infinity)(infinity). Assume that the sequence q(2n) - S(2n) + 2Q(0)Q(2n) decreases not faster than the powers n(-s-2). Then the system of eigenfunctions and associated functions of the operator L generated by periodic boundary conditions forms a Riesz basis in the space L(2)[0, 1] (provided that the eigenfunctions are normalized) if and only if the condition q(2n) - S(2n) + 2Q(0)Q(2n) asymptotic to q(-2n) - S(-2n) + 2Q(0)Q(-2n), n > 1,holds.
eng
info:eu-repo/semantics/closedAccess
Periodic Sturm - Liouville Problem
Hill Operator
Riesz Basis
Sobolev Spaces
Birkhoff Regularity
Fourier Series
Jordan Chain
Root Funtions
On the riesz basis property of the eigen and associated functions of periodic and antiperiodic Sturm - Liouville problems
article
oai:openaccess.dogus.edu.tr:11376/16372020-09-22T18:32:51Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Özsarı, Türker
2015-07-06T08:31:56Z
2015-07-06T08:31:56Z
2013-03
ÖZSARI, T. (2013). Global existence and open loop exponential stabilization of weak solutions for nonlinear schrodinger equations with localized external neumann manipulation. Nonlinear Analysis-Theory Methods & Applications, Volume 80, pp. 179-193. https://dx.doi.org/10.1016/j.na.2012.10.006.
0362-546X
1873-5215
000314873300016 (WOS)
https://dx.doi.org/10.1016/j.na.2012.10.006
https://hdl.handle.net/11376/1637
80
179
193
In this paper, we consider the nonlinear Schrodinger equations (NLS) with (focusing/defocusing) interior source and (possibly nonlinear) damping on a bounded regular domain in the Euclidean space. Moreover, it is assumed that the solutions are subject to external Neumann boundary manipulation on one portion of the boundary. Our aim is to obtain global existence of the weak solutions under various assumptions on the sign of the source and powers of the nonlinearities. In the case of a linear damping, we also prove that solutions decay exponentially under the assumption that the Neumann type control at the boundary decays in a similar manner.
eng
info:eu-repo/semantics/closedAccess
Nonlinear Schrodinger Equations
Inhomogeneous Neumann Boundary Data
Galerkin's Method
Compactness Method
Global Existence
Stabilization
Long Time Behavior
Global existence and open loop exponential stabilization of weak solutions for nonlinear schrodinger equations with localized external neumann manipulation
article
oai:openaccess.dogus.edu.tr:11376/18422020-09-22T18:33:57Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Koç, Ayten
Esin, Songül
Güloğlu, İsmail Şuayip
Kanuni, Müge
2015-07-31T07:27:16Z
2015-07-31T07:27:16Z
2014
KOÇ, A., ESİN, S., GÜLOĞLU, İ.Ş., KANUNİ, M. (2014). A combinatorial discussion on finite dimensional leavitt path algebras. Hacettepe Journal of Mathematics and Statistics, 43 (6), pp. 943-951.
1303-5010
000348691000006 (WOS)
https://hdl.handle.net/11376/1842
43
6
943
951
Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings. We shall consider the direct sum of finite dimensional full matrix rings over a field K. All such finite dimensional semisimple algebras arise as finite dimensional Leavitt path algebras. For this specific finite dimensional semisimple algebra A over a field K, we define a uniquely determined specific graph - called a truncated tree associated with A - whose Leavitt path algebra is isomorphic to A. We define an algebraic invariant kappa(A) for A and count the number of isomorphism classes of Leavitt path algebras with the same fixed value of kappa(A).Moreover, we find the maximum and the minimum K-dimensions of the Leavitt path algebras. of possible trees with a given number of vertices and we also determine the number of distinct Leavitt path algebras of line graphs with a given number of vertices.
eng
info:eu-repo/semantics/openAccess
Finite Dimensional Semisimple Algebra
Leavitt Path Algebra
Truncated Trees
Line Graphs
A combinatorial discussion on finite dimensional leavitt path algebras
article
oai:openaccess.dogus.edu.tr:11376/32192020-09-22T18:32:35Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2018-12-12T06:54:38Z
2018-12-12T06:54:38Z
2017-05
Veliev, O. A. (2017). On the spectral properties of the Schrodinger operator with a periodic PT-symmetric potential. International Journal of Geometric Methods in Modern Physics, 14(5), 1-16. https://dx.doi.org/10.1142/S0219887817500657
0219-8878
1793-6977
000399397000001 (WOS)
https://dx.doi.org/10.1142/S0219887817500657
https://hdl.handle.net/11376/3219
14
5
1
16
In this paper, we investigate the spectrum and spectrality of the one-dimensional Schrodinger operator with a periodic PT-symmetric complex-valued potential.
eng
info:eu-repo/semantics/closedAccess
Schrodinger Operator
PT-Symmetric Periodic Potential
Real Spectrum
Hill Operators
Differential-Operators
Complex
Translation
On the spectral properties of the Schrodinger operator with a periodic PT-symmetric potential
article
oai:openaccess.dogus.edu.tr:11376/12852020-09-22T18:32:54Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Güngör, Faruk
2015-04-02T18:45:52Z
2015-04-02T18:45:52Z
2010-07
GÜNGÖR, F. (2010). Infinite - dimensional symmetries of two - dimensional generalized Burgers equations. Journal of Mathematical Physics, 51 (7), 12p. https://dx.doi.org/10.1063/1.3456061.
0022-2488
000280854500031 (WOS)
https://dx.doi.org/10.1063/1.3456061
https://hdl.handle.net/11376/1285
51
7
073504-1
073504-12
The conditions for a class of generalized Burgers equations which a priori involve nine arbitrary functions of one or two variables to allow an infinite-dimensional symmetry algebra are determined. Although this algebra can involve up to two arbitrary functions of time, it does not allow a Virasoro subalgebra. This result reconfirms a long-standing fact that variable coefficient generalizations of a nonintegrable equation should be expected to remain as such.
eng
info:eu-repo/semantics/openAccess
Kadomtsev - Petviashvili Equation
Partial - Differential - Equations
Nonlinear Acoustics
Group Classification
Invariant
Algebras
Infinite - dimensional symmetries of two - dimensional generalized Burgers equations
article
oai:openaccess.dogus.edu.tr:11376/23512020-09-22T18:32:39Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391
Koç, Ayten
Esin, Songül
Güloğlu, İsmail Şuayip
Kanuni, Müge
2016-01-25T08:38:00Z
2016-01-25T08:38:00Z
2014
Koç, A., Esin, S., Güloğlu, İ. Ş., & Kanuni, M. (2014). A combinatorial discussion on ﬁnite edimensional Leavitt path algebras. Hacettepe Journal of Mathematics and Statistics, 43(6), 943-951.
1303-5010
https://hdl.handle.net/11376/2351
43
6
943
951
Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings. We shall consider the direct sum of finite dimensional full matrix rings over a field K. All such finite dimensional semisimple algebras arise as finite dimensional Leavitt path algebras. For this specific finite dimensional semisimple algebra A over a field K, we define a uniquely determined specific graph - called a truncated tree associated with A - whose Leavitt path algebra is isomorphic to A. We define an algebraic invariant κ(A) for A and count the number of isomorphism classes of Leavitt path algebras with the same fixed value of κ(A). Moreover, we find the maximum and the minimum K-dimensions of the Leavitt path algebras of possible trees with a given number of vertices and we also determine the number of distinct Leavitt path algebras of line graphs with a given number of vertices.
eng
info:eu-repo/semantics/openAccess
Finite Dimensional Semisimple Algebra
Leavitt Path Algebra
Truncated Trees
Line Graphs
A combinatorial discussion on ﬁnite edimensional Leavitt path algebras
article
oai:openaccess.dogus.edu.tr:11376/8362020-09-22T18:33:52Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Ercan, Gülin
Güloğlu, İsmail Şuayip
2014-12-30T13:19:32Z
2014-12-30T13:19:32Z
2008-07-01
GÜLİN, E., GÜLOĞLU, İ.Ş. (2008). Fixed point free action on groups of odd order. Journal of Algebra, Volume 320, Issue 1, pp. 426-436, https://dx.doi.org/10.1016/j.jalgebra.2008.01.033
0021-8693
https://dx.doi.org/10.1016/j.jalgebra.2008.01.033
https://hdl.handle.net/11376/836
320
1
426
436
Let A be a finite abelian group that acts fixed point freely on a finite (solvable) group G . Assume that |G| is odd and A is of squarefree exponent coprime to 6. We show that the Fitting length of G is bounded by the length of the longest chain of subgroups of A.
eng
info:eu-repo/semantics/closedAccess
Solvable Groups
Fixed Point Free Action
Finite Groups
Representations
Fixed point free action on groups of odd order
article
oai:openaccess.dogus.edu.tr:11376/32242020-09-22T18:33:32Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Ercan, Gülin
Güloğlu, İsmail Şuayip
2018-12-13T12:14:35Z
2018-12-13T12:14:35Z
2017
Ercan, G., Guloglu, I. S. (2017). Finite groups admitting a dihedral group of automorphisms. Algebra and Discrete Mathematics, 23(2), 223-229.
1726-3255
2415-721X
000406416100005 (WOS)
https://hdl.handle.net/11376/3224
23
2
223
229
Let D = alpha, beta be a dihedral group generated by the involutions alpha and beta and let F = alpha beta). Suppose that D acts on a finite group G by automorphisms in such a way that C-G(F)= 1. In the present paper we prove that the nilpotent, length of the group Cr' is equal to the maximum of the nilpotent lengths of the subgroups C-G (alpha) and C-G(beta).
eng
info:eu-repo/semantics/openAccess
Dihedral Group
Fixed Points
Nilpotent Length
Frobenius-Like Group
Fitting Height
Kernel
Finite groups admitting a dihedral group of automorphisms
article
oai:openaccess.dogus.edu.tr:11376/21862020-09-22T18:33:26Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391
Güngör, Faruk
Hasansoy, Mahir
Özemir, Cihangir
2015-11-18T09:32:45Z
2015-11-18T09:32:45Z
2013-06
Güngör, F., Hasanov, M. H., & Özemir, C. (2013). A variable coefficient nonlinear Schrödinger equation with a four-dimensional symmetry group and blow-up. Applicable Analysis, 92(6), 1322-1331. https://dx.doi.org/10.1080/00036811.2012.676165
0003-6811
https://dx.doi.org/10.1080/00036811.2012.676165
https://hdl.handle.net/11376/2186
92
6
1322
1331
A canonical variable coefficient nonlinear Schrödinger equation with a four-dimensional symmetry group containing SL(2, ℝ) group as a subgroup is considered. This typical invariance is then used to transform by a symmetry transformation a known solution that can be derived by truncating its Painlevé expansion and study blow-ups of these solutions in the L p-norm for p > 2, L ∞-norm and in the sense of distributions.
eng
info:eu-repo/semantics/closedAccess
Exact Solutions
SL (2, ℝ) Invariance
Variable Coefficient Nonlinear Schrödinger Equation
Blow-up
A variable coefficient nonlinear Schrödinger equation with a four-dimensional symmetry group and blow-up
article
oai:openaccess.dogus.edu.tr:11376/10162019-09-30T12:42:40Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Duman, Melda
Kıraç, Alp Arslan
Veliev, Oktay A.
2015-02-24T15:21:01Z
2015-02-24T15:21:01Z
2007-09
DUMAN, M., KIRAÇ, A.A., VELİEV, O. (2007). Asymptotic formulas with arbitrary order for nonseleadjoint differential operators. Studia Scientiarum Mathemaicarum Hungarica, 44 (3), pp. 391-409. https://dx.doi.org./10.1556/SScMath.2007.1026.
0081-6906
1588-2896
000249428300008 (WOS)
https://dx.doi.org./10.1556/SScMath.2007.1026
https://hdl.handle.net/11376/1016
44
3
391
409
We obtain asymptotic formulas with arbitrary order of accuracy for the eigenvalues and eigenfunctions of a nonselfadjoint ordinary differential operator of order n whose coefficients are Lebesgue integrable on [0,1] and the boundary conditions are strongly regular. The orders of asymptotic formulas are independent of smoothness of the coefficients.
eng
info:eu-repo/semantics/closedAccess
Nonselfadjoint Differential Operators
Strongly Regular Boundary Conditions
Riesz Basis
Asymptotic formulas with arbitrary order for nonseleadjoint differential operators
article
oai:openaccess.dogus.edu.tr:11376/33072020-09-22T18:33:35Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Ercan, Gülin
Güloğlu, İsmail Şuayip
2019-01-21T06:01:00Z
2019-01-21T06:01:00Z
2018-03
Ercan, G., Güloğlu, İ. Ş. (2018). Groups of automorphisms with TNI-centralizers. Journal of Algebra, 498, 38-46. https://doi.org/10.1016/j.jalgebra.2017.10.021
0021-8693
1090-266X
https://doi.org/10.1016/j.jalgebra.2017.10.021
https://hdl.handle.net/11376/3307
498
38
46
A subgroup H of a finite group G is called a TNI-subgroup if NG(H)∩Hg=1 for any g∈G\NG(H). Let A be a group acting on G by automorphisms where CG(A) is a TNI-subgroup of G. We prove that G is solvable if and only if CG(A) is solvable, and determine some bounds for the nilpotent length of G in terms of the nilpotent length of CG(A) under some additional assumptions. We also study the action of a Frobenius group FH of automorphisms on a group G if the set of fixed points CG(F) of the kernel F forms a TNI-subgroup, and obtain a bound for the nilpotent length of G in terms of the nilpotent lengths of CG(F) and CG(H).
eng
info:eu-repo/semantics/embargoedAccess
TNI-Subgroup
Automorphism
Centralizer
Frobenius Group
Groups of automorphisms with TNI-centralizers
article
oai:openaccess.dogus.edu.tr:11376/11762020-09-22T18:33:16Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2015-03-24T14:06:17Z
2015-03-24T14:06:17Z
2008
VELİEV, O. (2008). Uniform convergence of the spectral expansion for a differential operator with periodic matrix coefficients. Boundary Value Problems, pp. 1-22. https://dx.doi.org/ 10.1155/2008/628973.
1687-2762
000259475000001 (WOS)
https://dx.doi.org/ 10.1155/2008/628973
https://hdl.handle.net/11376/1176
1
22
We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coeffcients and the quasiperiodic boundary conditions. Using these asymptotic formulas, we find conditions on the coeffcients for which the root functions of this operator form a Riesz basis. Then, we obtain the uniformly convergent spectral expansion of the differential operators with the periodic matrix coeffcients.
eng
info:eu-repo/semantics/openAccess
Adjoint Hill Operator
Translation
Eigenfunctions
Differential Equations
Uniform convergence of the spectral expansion for a differential operator with periodic matrix coefficients
article
oai:openaccess.dogus.edu.tr:11376/21752020-09-22T18:33:28Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Koç, Cemal
Esin, Songül
2015-11-18T08:29:10Z
2015-11-18T08:29:10Z
2007
Koç, C., & Esin, S. (2007). Annihilators of principal ideals in the exterior algebra. Taiwanese Journal of Mathematics, 11(4), 1019-1035.
1027-5487
https://hdl.handle.net/11376/2175
11
4
1019
1035
In this paper we describe annihilators of principal ideals of exterior algebras. For odd elements we establish formulae for dimensions of their principal ideals and their annihilators. For even elements we exhibit (multiplicative) generators for annihilator ideals.
eng
info:eu-repo/semantics/openAccess
Annihilator
Exterior Algebra
Frobenius Algebra
Annihilators of principal ideals in the exterior algebra
article
oai:openaccess.dogus.edu.tr:11376/18292020-09-22T18:33:08Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Nur, Cemile
Veliev, Oktay A.
2015-07-30T12:30:02Z
2015-07-30T12:30:02Z
2014-03-15
NUR, C., VELİEV, O.A. (2014). On the basis property of the root functions of some class of non-self-adjoint sturm-liouville operators. Boundary Value Problems, pp. 1-17. https://dx.doi.org/10.1186/1687-2770-2014-57.
1687-2770
000333617500001 (WOS)
https://dx.doi.org/10.1186/1687-2770-2014-57
https://hdl.handle.net/11376/1829
1
17
We obtain the asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators with some regular boundary conditions. Using these formulas, we find sufficient conditions on the potential q such that the root functions of these operators do not form a Riesz basis.
eng
info:eu-repo/semantics/openAccess
Asymptotic Formulas
Regular Boundary Conditions
Riesz Basis
On the basis property of the root functions of some class of non-self-adjoint sturm-liouville operators
article
oai:openaccess.dogus.edu.tr:11376/15722020-09-22T18:33:23Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2015-06-25T06:09:05Z
2015-06-25T06:09:05Z
2013-12
VELİEV, O. (2013). Asymptotic analysis of non - self - adjoint Hill operators. Central European Journal of Mathematics, 11 (12), pp. 2234-2256. https://dx.doi.org/10.2478/s11533-013-0305-x.
1895-1074
1644-3616
000325421100015 (WOS)
https://dx.doi.org/10.2478/s11533-013-0305-x
https://hdl.handle.net/11376/1572
11
12
2234
2256
We obtain uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L (t) (q) with a potential q a L (1)[0,1] and t-periodic boundary conditions, t a (-pi, pi]. Using these formulas, we find sufficient conditions on the potential q such that the number of spectral singularities in the spectrum of the Hill operator L(q) in L (2)(-a,a) is finite. Then we prove that the operator L(q) has no spectral singularities at infinity and it is an asymptotically spectral operator provided that the potential q satisfies sufficient conditions.
eng
info:eu-repo/semantics/openAccess
Asymptotic Formulas
Hill Operator
Spectral Singularities
Spectral Operator
Boundary - Value - Problems
Riesz Basis Property
Differential - Operators
Root Functions
Spectral Expansion
Scalar Type
Coefficients
Convergence
Translation
Schrodinger
Asymptotic analysis of non - self - adjoint Hill operators
article
oai:openaccess.dogus.edu.tr:11376/1532020-09-22T18:33:41Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3392col_11376_3390
Koç, Cemal
Güloğlu, İsmail Şuayip
Esin, Songül
2014-06-27T18:33:46Z
2014-06-27T18:33:46Z
2010
Koç, C., Güloğlu, İ., Esin, S. (2010). Generalized catalan numbers, sequences and polynomials. Turkish Journal of Mathematics, 34 (4), 441-449.ss.
1300-0098
1303-6149
000284435200002 (WOS)
https://dx.doi.org/10.3906/mat-0811-25
https://hdl.handle.net/11376/153
In this paper we present an algebraic interpretation for generalized Catalan numbers. We describe them as dimensions of certain subspaces of multilinear polynomials. This description is of utmost importance in the investigation of annihilators in exterior algebras.
eng
info:eu-repo/semantics/openAccess
Number
Polynomial
Sequence
Catalan Numbers
Subspace
Sayı
Polinom
Dizi
Katalan Sayılar
Alt Uzay
Generalized catalan numbers, sequences and polynomials
article
oai:openaccess.dogus.edu.tr:11376/2732020-09-22T18:33:44Zcom_11376_129com_11376_101com_11376_3388col_11376_130
Özen, Mehmet
Şiap, İrfan
Çallıalp, Fethi
2014-07-13T14:58:31Z
2014-07-13T14:58:31Z
2004
ÖZEN, M., ŞİAP, İ., ÇALLIALP F. (2004). Non-hamming (rosenbloom-tsfasman) metriğine göre kodların yapısı. Anadolu University Journal of Science and Technology, 5 (2), pp. 253-258.
2146-0205
https://hdl.handle.net/11376/273
5
2
253
258
Bu çalışmada ρ metriğine göre lineer kodların yapıları incelendi. Kodların yapılarından faydalanılarak, bu met-riğe göre lineer ve devirli kodların minimum uzaklığının kolaylıkla tespit edilebildiği gösterildi. Bu metriğe bağlı olarak lineer kodların dualleri incelendi ve MDS kodların ağarlık sayaçları bulundu.
We explore the structure of linear codes with respect to the ρ metric. Taking advantage of this structure, we show that the minimum distance of linear and cyclic codes can be determined easily. We investigate the dual of linear codes and the weight enumerator of MDS codes with respect to this metric.
tur
info:eu-repo/semantics/openAccess
Lineer Kodlar
Non-Hamming Metriği
MDS Kodlar
Linear Codes
Non-Hamming Metric
MDS Codes
Non-hamming (rosenbloom-tsfasman) metriğine göre kodların yapısı
article
oai:openaccess.dogus.edu.tr:11376/18572020-09-22T18:33:25Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Şeref, Fulya
Veliev, Oktay A.
2015-08-03T11:51:37Z
2015-08-03T11:51:37Z
2014
ŞEREF, F., VELİEV, O.A. (2014). On non-self-adjoint sturm-liouville operators in the space of vector functions. Mathematical Notes, 95 (1-2). pp.180-190. https://dx.doi.org/10.1134/S0001434614010192.
0001-4346
1573-8876
000335457200019 (WOS)
https://dx.doi.org/10.1134/S0001434614010192
https://hdl.handle.net/11376/1857
95
1-2
180
190
In this article we obtain asymptotic formulas for the eigenvalues and eigenfunctions of the non-self-adjoint operator generated in L-2(m) [0, 1] by the Sturm-Liouville equation with m x m matrix potential and the boundary conditions which, in the scalar case (m = 1), are strongly regular. Using these asymptotic formulas, we find a condition on the potential for which the root functions of this operator form a Riesz basis.
eng
info:eu-repo/semantics/closedAccess
Differential Operators
Matrix Potential
Riesz Basis
On non-self-adjoint sturm-liouville operators in the space of vector functions
article
oai:openaccess.dogus.edu.tr:11376/14012019-09-24T07:30:13Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Özen Zengin, Füsun
Uysal, Samiye Aynur
Altay Demirbağ, Sezgin
2015-04-24T09:22:07Z
2015-04-24T09:22:07Z
2011
Özen Zengin, F., Uysal, S. A., Altay Demirbağ, S.(2011). On sectional curvature of a Riemannian manifold with semi - symmetric metric connection. Annales Polonici Mathematici, 101 (2), pp. 131-138. https://dx.doi.org/10.4064/ap101-2-3.
0066-2216
1730-6272
000289576100003 (WOS)
https://dx.doi.org/10.4064/ap101-2-3
https://hdl.handle.net/11376/1401
101
2
131
138
We prove that if the sectional curvature of an n-dimensional pseudosymmetric manifold with semi-symmetric metric connection is independent of the orientation chosen then the generator of such a manifold is gradient and also such a manifold is subprojective in the sense of Kagan.
eng
info:eu-repo/semantics/closedAccess
Semi - Symmetric Metric Connection
Sectional Curvature
Conformally Flat Manifold
Pseudo - Symmetric Manifold
Concircular Vector Field
On sectional curvature of a Riemannian manifold with semi - symmetric metric connection
article
oai:openaccess.dogus.edu.tr:11376/18602020-09-22T18:33:02Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2015-08-03T13:06:16Z
2015-08-03T13:06:16Z
2014
VELİEV, O.A. (2014). On the simplicity of the eigenvalues of non-self-adjoint mathieu-hill operators. Applied and Computational Mathematics, 13 (1), pp. 122-134.
1683-3511
000332593000011 (WOS)
https://hdl.handle.net/11376/1860
13
1
122
134
Firstly, we analyze some spectral properties of the non-self-adjoint Hill operator with piecewise continuous even potential. Then using this we find conditions on the potential of the non-self-adjoint Mathieu operator, such that all eigenvalues of the periodic, antiperiodic, Dirichlet, and Neumann boundary value problems are simple.
eng
info:eu-repo/semantics/openAccess
Mathieu-Hill Operator
Simple Eigenvalues
Boundary Value Problems
On the simplicity of the eigenvalues of non-self-adjoint mathieu-hill operators
article
oai:openaccess.dogus.edu.tr:11376/8442020-09-22T18:33:50Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3392col_11376_3390
Ercan, Gülin
Güloğlu, İsmail Şuayip
Khukhro, Evgeny
2015-01-06T09:15:21Z
2015-01-06T09:15:21Z
2014-11-21
ERCAN, G., GÜLOĞLU, İ.Ş., KHUKHRO, E. (2014). Frobenius-Like groups as groups of automorphisms. Turkish Journal of Mathematics, 38, pp. 965-976. https://dx.doi.org/10.3906/mat-1403-62.
1300-0098
1303-6149
https://dx.doi.org/10.3906/mat-1403-62
https://hdl.handle.net/11376/844
38
6
965
976
A finite group F H is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a
nontrivial complement H such that F H/[F, F] is a Frobenius group with Frobenius kernel F/[F, F]. Such subgroups
and sections are abundant in any nonnilpotent finite group. We discuss several recent results about the properties of a
finite group G admitting a Frobenius-like group of automorphisms F H aiming at restrictions on G in terms of CG(H)
and focusing mainly on bounds for the Fitting height and related parameters. Earlier such results were obtained for
Frobenius groups of automorphisms; new theorems for Frobenius-like groups are based on new representation-theoretic
results. Apart from a brief survey, the paper contains the new theorem on almost nilpotency of a finite group admitting
a Frobenius-like group of automorphisms with fixed-point-free almost extraspecial kernel.
eng
info:eu-repo/semantics/openAccess
Frobenius Group
Frobenius-Like Group
Fixed Points
Fitting Height
Nilpotency Class
Derived Length
Rank
Order
Frobenius-like groups as groups of automorphisms
article
oai:openaccess.dogus.edu.tr:11376/28212020-09-22T18:32:34Zcom_11376_129com_11376_101com_11376_3388col_11376_130
Uysal, Samiye Aynur
Laleoğlu, Özlem R.
2016-12-20T16:22:18Z
2016-12-20T16:22:18Z
2008-02
Uysal, S. A., and Laleoğlu, Ö. R. (2008). α -metrically chebyshev conformal motions in riemannian spaces. International Journal of Pure and Applied Mathematics, 44(2), 249-257.
1311-8080
https://hdl.handle.net/11376/2821
44
2
249
257
In this paper we introduced α-metrically Chebyshev nets in a Riemannian manifold with semi-symmetric metric connection. We also studied conformal motions with trajectories defined by the components of these nets in Riemannian spaces with Riemannian connection and with semi-symmetric metric connection.
eng
info:eu-repo/semantics/openAccess
Riemannian Space
Chebyshev Net
Conformal Motion
Connection
α -metrically chebyshev conformal motions in Riemannian spaces
article
oai:openaccess.dogus.edu.tr:11376/14842020-09-22T18:32:58Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Hasansoy, Mahir
2015-05-06T08:48:05Z
2015-05-06T08:48:05Z
2012
HASANSOY, M. (2012). A variational approach to the problem of oscillations of an elastic half cylinder. Bulletin of the Iranian Mathematical Society, 38 (1), pp. 223-240.
1735-8515
1018-6301
000312720300016 (WOS)
https://hdl.handle.net/11376/1484
38
1
223
240
This paper is devoted to the spectral theory (more precisely, to the variational theory of the spectrum) of guided waves in an elastic half cylinder. We use variational methods to investigate several aspects of propagating waves, including localization (see Figure 1), existence criteria and the formulas to find them. We approach the problem using two complementary methods: The variational methods for non-overdamped operator pencils to describe eigenvalues in definite spectral zones, and Ljusternik-Schnirelman critical point theory to investigate eigenvalues in the mixed spectral zone where the classical variational theory of operator pencils is not applicable.
eng
info:eu-repo/semantics/openAccess
Propagating Waves
Eigenvalue
Variational Principle
Critical Point
A variational approach to the problem of oscillations of an elastic half cylinder
article
oai:openaccess.dogus.edu.tr:11376/35482020-01-09T15:48:41Zcom_11376_129com_11376_101com_11376_3388col_11376_130
Veliev, Oktay
2020-01-09T15:48:40Z
2020-01-09T15:48:40Z
2019
Veliev, O. (2019). On a class of nonself-adjoint multidimensional periodic Schrodinger operators. Turkish Journal of Mathematics, 43(5), 2415-2432. https://doi.org/10.3906/mat-1906-69
1300-0098
1303-6149
000488222100030 (WOS)
https://doi.org/10.3906/mat-1906-69
https://hdl.handle.net/11376/3548
43
5
2415
2432
We investigate the Schrodinger operator L(q) in L-2 (R-d) (d >= 1) with the complex-valued potential q that is periodic with respect to a lattice Q. Besides, it is assumed that the Fourier coefficients q(gamma) of q with respect to the orthogonal system {e(i <gamma x >) : gamma is an element of Gamma} vanish if gamma belongs to a half-space, where F is the lattice dual to Omega. We prove that the Bloch eigenvalues are vertical bar gamma + t vertical bar(2) for gamma is an element of Gamma, where t is a quasimomentum and find explicit formulas for the Bloch functions. Moreover, we investigate the multiplicity of the Bloch eigenvalue and consider necessary and sufficient conditions on the potential which provide some root functions to be eigenfunctions. Besides, in case d =1 we investigate in detail the root functions of the periodic and antiperiodic boundary value problems.
eng
http://creativecommons.org/licenses/by/3.0/us/
info:eu-repo/semantics/openAccess
Attribution 3.0 United States
Periodic Schrodinger Operator
Bloch Eigenvalues
Bloch Function
On a class of nonself-adjoint multidimensional periodic Schrodinger operators
article
oai:openaccess.dogus.edu.tr:11376/13042020-09-22T18:32:54Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Koç, Cemal
2015-04-13T10:09:26Z
2015-04-13T10:09:26Z
2010-05
KOÇ, C. (2010). C-lattices and decompositions of generalized clifford algebras. Advances in Applied Clifford Algebras, 20 (2), pp. 313-320. https://dx.doi.org/10.1007/s00006-009-0178-z.
0188-7009
1661-4909
000277335100009 (WOS)
https://dx.doi.org/10.1007/s00006-009-0178-z
https://hdl.handle.net/11376/1304
20
2
313
320
In this note we introduce C-lattices to make use of them to provide a short and self-contained proof to the decomposition theorems of generalized Clifford algebras established by T. Y. Lam and T. L. Smith.
eng
info:eu-repo/semantics/closedAccess
Generalized Clifford Algebra
Graded Tensor Product
CLE - Groups
C - Lattice
C-lattices and decompositions of generalized clifford algebras
article
oai:openaccess.dogus.edu.tr:11376/28152020-09-22T18:32:30Zcom_11376_129com_11376_101com_11376_3388col_11376_130
Uysal, Samiye Aynur
Özkara Canfes, Elif
Dinç, Cemile Elvan
2016-12-20T14:41:38Z
2016-12-20T14:41:38Z
2006-01
Uysal, S. A., Canfes, E.Ö., & Dinç, C. E. (2006). On quasi-recurrent spaces with Ricci quarter-symmetric metric connection. International Mathematical Forum, 1(40), 1961-1968. https://dx.doi.org/10.12988/imf.2006.06173
1312-7594
1314-7536
https://dx.doi.org/10.12988/imf.2006.06173
https://hdl.handle.net/11376/2815
1
40
1961
1968
In [3], Mishra and Pandey defined Ricci quarter-symmetric metric connection in Riemanian manifold. In [5],Uysal and Doğan defined D-recurrent spaces with semi-symmetric metric connection and constructed an example of these spaces. In these paper we define quasirecurrent spaces with Ricci quarter- symmetric metric connection and establish an example of such spaces.
eng
info:eu-repo/semantics/openAccess
Ricci Quarter-Symmetric Metric Connection
Recurrent Space
Quasi-Recurrent Spaces
On quasi-recurrent spaces with Ricci quarter-symmetric metric connection
article
oai:openaccess.dogus.edu.tr:11376/8372020-09-22T18:32:49Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Ercan, Gülin
Güloğlu, İsmail Şuayip
Sağdıçoğlu, Öznur Mut
2014-12-30T15:10:35Z
2014-12-30T15:10:35Z
2011-02
ERCAN, G., GÜLOĞLU, İ.Ş., SAĞDIÇOĞLU, Ö.M. (2011). Fixed-point free action of an abelian group of odd non-squarefree exponent. Proceedings of the Edinburgh Mathematical Society (Series 2), 54 (1), pp 77-89. https://dx.doi.org/10.1017/S0013091509000583.
1464-3839
https://dx.doi.org/10.1017/S0013091509000583
https://hdl.handle.net/11376/837
54
1
77
89
Let A be a finite group acting fixed-point freely on a finite (solvable) group G. A longstanding conjecture is that if (|G|, |A|) = 1, then the Fitting length of G is bounded by the length of the longest chain of subgroups of A. It is expected that the conjecture is true when the coprimeness condition is replaced by the assumption that A is nilpotent. We establish the conjecture without the coprimeness condition in the case where A is an abelian group whose order is a product of three odd primes and where the Sylow 2-subgroups of G are abelian.
eng
info:eu-repo/semantics/closedAccess
Automorphisms of Solvable Groups
Non-Coprime Action
Fixed-Point Free Action
Carter Subgroup
Fixed-point free action of an abelian group of odd non-squarefree exponent
article
oai:openaccess.dogus.edu.tr:11376/11842020-09-22T18:32:53Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3390
Veliev, Oktay A.
2015-03-25T10:11:37Z
2015-03-25T10:11:37Z
2009
VELIEV, O. (2009). On the differential operators with periodic matrix coefficients. Abstract and Applied Analysis, pp. 1-21. https://dx.doi.org/10.1155/2009/934905.
1085-3375
1687-0409
000271591200001 (WOS)
https://dx.doi.org/10.1155/2009/934905
https://hdl.handle.net/11376/1184
1
21
We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then by using these asymptotic formulas, we find conditions on the coefficients for which the number of gaps in the spectrumof the self-adjoint differential operator with the periodic matrix coefficients is finite.
eng
info:eu-repo/semantics/openAccess
Differential Operators
Periodic Matrix Coefficients
Quasiperiodic Boundary Conditions
Summable Coefficients
On the differential operators with periodic matrix coefficients
article
oai:openaccess.dogus.edu.tr:11376/8832020-09-22T18:33:13Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2015-01-20T08:27:45Z
2015-01-20T08:27:45Z
2006-12
VELİEV, O. (2006). Asymptotic formulae for the Bloch eigenvalues near planes of diffraction. Reports on Mathematical Physics, 58 (3), pp. 445-469. https://dx.doi.org./10.1016/S0034-4877(06)80964-X.
0034-4877
000243144200010 (WOS)
https://dx.doi.org./10.1016/S0034-4877(06)80964-X
https://hdl.handle.net/11376/883
58
3
445
469
In this paper we obtain asymptotic formulae of arbitrary order for the Bloch eigenvalue of the periodic Schrödinger operator -△ + q(x), of arbitrary dimension, when the corresponding quasi-momentum lies near planes of diffraction.
eng
info:eu-repo/semantics/closedAccess
Bloch Eigenvalue
Schrodinger Operator
Perturbation
Peiodic Schrodinger Operator
Asymptotic formulae for the Bloch eigenvalues near planes of diffraction
article
oai:openaccess.dogus.edu.tr:11376/8712019-09-25T13:15:05Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
Dernek, Neşe
2015-01-16T09:26:44Z
2015-01-16T09:26:44Z
2005
VELIEV, O. A., DERNEK, N. (2005). On the Riesz basisness of the root functions of the nonself-adjoint Sturm-Liouville operator. Israel Journal of Mathematics, 145 (1), pp. 113-123. https://dx.doi.org/10.1007/BF02786687.
0021-2172
1565-8511
000229325900004 (WOS)
https://dx.doi.org/10.1007/BF02786687
https://hdl.handle.net/11376/871
145
1
113
123
In this article we obtain the asymptotic formulas for eigenfunctions and eigenvalues of the nonself-adjoint Sturm-Liouville operators with periodic and antiperiodic boundary conditions, when the potential is an arbitrary summable complex-valued function. Then using these asymptotic formulas, we find the conditions on Fourier coefficients of the potential for which the eigenfunctions and associated functions of these operators form a Riesz basis in L-2(0, 1).
eng
info:eu-repo/semantics/closedAccess
Mathematics, General
Algebra
Group Theory and Generalizations
Analysis
Applications of Mathematics
Mathematical and Computational Physics
On the Riesz basisness of the root functions of the nonself-adjoint Sturm-Liouville operator
article
oai:openaccess.dogus.edu.tr:11376/28142020-09-22T18:32:32Zcom_11376_129com_11376_101com_11376_3388col_11376_130
Veliev, Oktay A.
2016-12-20T14:17:52Z
2016-12-20T14:17:52Z
2007
Veliev, O. A. (2007). Perturbation Theory for the Periodic Multidimensional Schrödinger Operator and the Bethe-Sommerfeld Conjecture. International Journal Of Contemporary Mathematical Sciences, 2(2), 19-87.
1312-7586
1314-7544
https://hdl.handle.net/11376/2814
2
2
19
87
In this paper we obtain asymptotic formulas of arbitrary order for the Bloch eigenvalue and the Bloch function of the periodic Schr¨odinger operatör −Δ + q(x), of arbitrary dimension, when corresponding quasimomentum lies near a diffraction hyperplane. Besides, writing the asymptotic formulas for the Bloch eigenvalue and the Bloch function, when corresponding quasimomentum lies far from the diffraction hyperplanes, obtained in my previous papers in improved and enlarged form, we obtain the complete perturbation theory for the multidimensional Schr¨odinger operator with a periodic potential. Moreover, we estimate the measure of the isoenergetic surfaces in the high energy region which implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimension and arbitrary lattice.
eng
info:eu-repo/semantics/openAccess
Periodic Schrödinger Operator
Perturbation Theory
Perturbation theory for the periodic multidimensional Schrödinger Operator and the Bethe-Sommerfeld Conjecture
article
oai:openaccess.dogus.edu.tr:11376/8462020-09-22T18:33:51Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Yılmaztürk, Utku
Erkoç, Temha
Güloğlu, İsmail Şuayip
2015-01-06T09:25:21Z
2015-01-06T09:25:21Z
2013-10-15
YILMAZTÜRK, U., ERKOÇ, T., and GÜLOĞLU, İ. Ş. (2013). Some sufficient conditions for the Taketa inequality. Proceedings of the Japan Academy Series A Mathematical Sciences, 89 (9), pp. 103-106. 1https://dx.doi.org/10.3792/pjaa.89.103.
0386-2194
https://dx.doi.org/10.3792/pjaa.89.103
https://hdl.handle.net/11376/846
89
9
103
106
In this study we have obtained some sufficient conditions for the Taketa inequality namely dl(G)≤|cd(G)| for finite solvable groups G.
eng
info:eu-repo/semantics/openAccess
Taketa Inequality
Character Degrees
Supersolvable Groups
Some sufficient conditions for the Taketa inequality
article
oai:openaccess.dogus.edu.tr:11376/13712020-09-22T18:32:33Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Hasansoy, Mahir
2015-04-20T10:52:13Z
2015-04-20T10:52:13Z
2011-07
HASANOV, M. (2011). The spectra of two-parameter quadratic operator pencils. Mathematical and Computer Modelling, 54 (1), pp. 742-755. https://dx.doi.org/10.1016/j.mcm.2011.03.018.
0895-7177
000290014600069 (WOS)
https://dx.doi.org/10.1016/j.mcm.2011.03.018
https://hdl.handle.net/11376/1371
54
1-2
742
755
This paper is devoted to a variational theory of the eigenvalue spectra of two-parameter, unbounded operator pencils, of the so-called waveguide type, which have important physical applications. It is known that the classical, nonlinear variational theory of these spectra is only applicable to eigenvalues with a definite type (positive or negative), provided +/- type eigenvalues are separated. However, the classical theory has recently been extended to mixed-type eigenvalues: first for linear matrix and operator pencils of the form L(lambda) = lambda A - B, and later for self-adjoint operators in a Krein space (see Binding et al. (2005) [17] and references therein). The real eigenvalues of the operator pencils studied in this paper can be split into five intervals according to type, the central range containing mixed-type eigenvalues (see Fig. 3). The main goal of this paper is to investigate the variational principles for real eigenvalues in this zone. In addition, this paper studies neutral (resonance) pairs and their existence criteria. We provide a complete analysis of the spectra of two-parameter, waveguide-type operator pencils. We use a variational approach for the spectrum of non-overdamped pencils, relying on Krein space techniques and the Ljusternik-Schnirelman theory of critical points of nonlinear functionals. By using the Ljusternik-Schnirelman theory we investigate neutral eigenvalues in a mixed spectral zone.
eng
info:eu-repo/semantics/closedAccess
Eigenvalues
Operator Pencils
Variational Principles
Waveguides
Critical Points
The spectra of two - parameter quadratic operator pencils
article
oai:openaccess.dogus.edu.tr:11376/25452020-09-22T18:33:28Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Polat, Mustafa
Çelebi, Ahmet Okay
Çalışkan, Nurettin
2016-05-03T07:22:42Z
2016-05-03T07:22:42Z
2009-08
Polat, M., Çelebi, A. O., & Çalışkan, N. (2009). Global attractors for the 3D viscous cahn-hillard equations in an unbounded domain. Applicable Analysis, 88(8), 1157-1171.
0003-6811
https://dx.doi.org/10.1080/00036810903156172
https://hdl.handle.net/11376/2545
88
8
1157
1171
In this note the 3D viscous Cahn-Hillard equation is considered in an unbounded domain. It is shown that the semigroup generated by this equation has a global attractor. The asymptotic compactness of the solution operator is obtained by the uniform estimates on the tail of solutions.
eng
info:eu-repo/semantics/closedAccess
Absorbing Ball
Dissipative Systems
Global Attractor
Unbounded Domain
Viscous Cahn-Hillard Equation
Global attractors for the 3D viscous cahn-hillard equations in an unbounded domain
article
oai:openaccess.dogus.edu.tr:11376/8452020-09-22T18:33:49Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Ercan, Gülin
Güloğlu, İsmail Şuayip
Khukhro, Evgeny
2015-01-06T09:20:09Z
2015-01-06T09:20:09Z
2014-07-20
ERCAN, G., GÜLOĞLU, İ.Ş, KHUKHRO, E. (2014). Rank and order of a finite group admitting a Frobenius-like group of automorphisms. Algebra and Logic, 53 (3), pp. 258-265. https://dx.doi.org/10.1007/s10469-014-9287-4
0002-5232
1573-8302
https://dx.doi.org/10.1007/s10469-014-9287-4
https://hdl.handle.net/11376/845
53
3
258
265
A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Suppose that a finite group G admits a Frobenius-like group of automorphisms FH of coprime order with certain additional restrictions (which are satisfied, in particular, if either |FH| is odd or |H| = 2). In the case where G is a finite p-group such that G = [G, F] it is proved that the rank of G is bounded above in terms of |H| and the rank of the fixed-point subgroup C G (H), and that |G| is bounded above in terms of |H| and |C G (H)|. As a corollary, in the case where G is an arbitrary finite group estimates are obtained of the form |G| ≤|C G (F)| · f(|H|, |C G (H)|) for the order, and r(G) ≤ r(C G (F)) + g(|H|, r(C G (H))) for the rank, where f and g are some functions of two variables.
eng
info:eu-repo/semantics/closedAccess
Algebra
Mathematical Logic and Foundations
Frobenius-Like
Rank and order of a finite group admitting a Frobenius-like group of automorphisms
article
oai:openaccess.dogus.edu.tr:11376/18082020-09-22T18:33:57Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3392col_11376_3390
Çallıalp, Fethi
Tekir, Ünsal
Aslan Karayiğit, Emel
2015-07-28T11:55:28Z
2015-07-28T11:55:28Z
2014-08
CALLIALP, F., TEKİR, Ü., ASLAN KARAYİĞİT, E. (2014). On multiplication lattice modules. Hacettepe Journal of Mathematics and Statistics, 43 (4), pp: 571-578.
1303-5010
000346137700003 (WOS)
https://hdl.handle.net/11376/1808
43
4
571
578
In this paper we study multiplication lattice modules. Next we characterize hollow lattices modules. We also establish maximal elements in multiplication lattices modules. In [16], we introduced the concept of a multiplication lattice L-module and we characterized it by principal elements. In this paper, we continue study on multiplication lattice L-module.
eng
info:eu-repo/semantics/openAccess
Multiplicative Lattices
Lattices Modules
Prime Elements
On multiplication lattice modules
article
oai:openaccess.dogus.edu.tr:11376/30392020-09-22T18:33:30Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Şeref, Fulya
Veliev, Oktay A.
2018-02-22T20:12:36Z
2018-02-22T20:12:36Z
2016-07
Şeref, F., and Veliev, O. A. (2016). On sharp asymptotic formulas for the Sturm-Liouville operator with a matrix potential. Mathematical Notes, 100(1-2), 291-297, https://dx.doi.org/10.1134/S0001434616070245
0001-4346
1573-8876
000382193300024 (WOS)
https://dx.doi.org/10.1134/S0001434616070245
https://hdl.handle.net/11376/3039
100
1-2
291
297
In this article we obtain the sharp asymptotic formulas for the eigenvalues and eigenfunctions of the non-self-adjoint operators generated by a system of the Sturm-Liouville equations with Dirichlet and Neumann boundary conditions. Using these asymptotic formulas, we find a condition on the potential for which the root functions of these operators form a Riesz basis.
eng
info:eu-repo/semantics/openAccess
Differential Operator
Matrix Potential
Asymptotic Formulas
Riesz Basis
On sharp asymptotic formulas for the Sturm-Liouville operator with a matrix potential
article
oai:openaccess.dogus.edu.tr:11376/23912019-09-03T15:00:45Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2016-02-15T14:57:59Z
2016-02-15T14:57:59Z
2009-08-25
Veliev, O.A. (2009). On the constructive determination of the periodic potentials from the bloch eigenvalues. Journal of Physics A: Mathematical and Theoretical, 42(37) 19p. https://dx.doi.org/10.1088/1751-8113/42/37/375201
1751-8113
https://dx.doi.org/10.1088/1751-8113/42/37/375201
https://hdl.handle.net/11376/2391
42
37
1
19
In this paper, we consider the three-dimensional Schrödinger operator with a periodic, relative to a lattice Ω of , potential q. We construct a set D of trigonometric polynomials such that D is dense in , where s > 3, in the -topology, any element q of the set D can be determined constructively and uniquely, modulo inversion and translation q(x) → q(-x), q(x) → q(x + τ), where , from the given Bloch eigenvalues of the Schrödinger operator with the potential q.
eng
info:eu-repo/semantics/closedAccess
Schrödinger Operator
Periodic Potentials
Bloch Eigenvalues
On the constructive determination of the periodic potentials from the bloch eigenvalues
article
oai:openaccess.dogus.edu.tr:11376/20342020-09-22T18:33:56Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Ercan, Gülin
Güloğlu, İsmail Şuayip
2015-08-19T12:00:49Z
2015-08-19T12:00:49Z
2015
Ercan, G., & Güloğlu, İ. Ş. (2015). The influence of Hughes type action. Communications in Algebra, 43(5), 1898-1902. https://dx.doi.org/10.1016/10.1080/00927872.2013.879432
0092-7872
1532-4125
000350570100013 (WOS)
https://dx.doi.org/10.1080/00927872.2013.879432
https://hdl.handle.net/11376/2034
43
5
1898
1902
We call the action of an automorphism of a finite group G a Hughes type action if it is described by conditions on the orders of elements of G-G. In the present paper we study the structure of finite group G admitting an automorphism of prime order p so that the orders of elements in G-G are not divisible by p(2).
eng
info:eu-repo/semantics/closedAccess
Automorphisms
Exceptional Action
Nilpotent Length
P-Length
Splitting
20D10
20D15
20D45
The influence of Hughes type action
article
oai:openaccess.dogus.edu.tr:11376/29912019-09-03T15:00:58Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Ercan, Gülin
Güloğlu, İsmail Şuayip
2017-04-13T23:24:15Z
2017-04-13T23:24:15Z
2016-09
Ercan, G., & Güloğlu, İ. Ş. (2016). Action of a frobenius-like group with kernel having central derived subgroup. International Journal of Algebra and Computation, 26(6), 1257-1265. https://dx.doi.org/10.1142/S0218196716500533
0218-1967
1793-6500
000383987200007 (WOS)
https://dx.doi.org/10.1142/S0218196716500533
https://hdl.handle.net/11376/2991
26
6
1257
1265
A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that [F, h] = F for all nonidentity elements h is an element of H. Suppose that a finite group G admits a Frobenius-like group of auto-morphisms FH of coprime order with [F', H] = 1. In case where C-G( F) = 1 we prove that the groups G and C-G( H) have the same nilpotent length under certain additional assumptions.
eng
info:eu-repo/semantics/closedAccess
Frobenius-Like Group
Fixed Points
Nilpotent Length
Action of a frobenius-like group with kernel having central derived subgroup
article
oai:openaccess.dogus.edu.tr:11376/8382020-09-22T18:33:53Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Ercan, Gülin
Güloğlu, İsmail Şuayip
2014-12-31T08:25:33Z
2014-12-31T08:25:33Z
2012-06
ERCAN, G., GÜLOĞLU, İ.Ş. (2012). A generalized fixed point free automorphism of prime power order. International Journal of Algebra and Computation, 22 (4), pp. 1250029-1-1250029-5. https://dx.doi.org/10.1142/S0218196712500294
0218-1967
1793-6500
https://dx.doi.org/10.1142/S0218196712500294
https://hdl.handle.net/11376/838
22
4
1250029-1
1250029-5
Let G be a finite group and α be an automorphism of G of order pn for an odd prime p. Suppose that α acts fixed point freely on every α-invariant p′-section of G, and acts trivially or exceptionally on every elementary abelian α-invariant p-section of G. It is proved that G is a solvable p-nilpotent group of nilpotent length at most n + 1, and this bound is best possible.
eng
info:eu-repo/semantics/closedAccess
Noncoprime Automorphism
Nilpotent Length
P-Length
Exceptional Action
A generalized fixed point free automorphism of prime power order
article
oai:openaccess.dogus.edu.tr:11376/8002020-09-22T18:33:11Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Özdemir, Mehmet Emin
Kırmacı, Uğur Selamet
Ocak, Rahim
Dönmez, Ali
2014-12-22T11:20:49Z
2014-12-22T11:20:49Z
2004-05-13
ÖZDEMİR, M. E., KIRMACI, U. S., OCAK, R., DÖNMEZ, A. (2004). On automorphic and modular forms in the space of the homogeneous polynomials with degree 2l and applications to the special matrix. Applied Mathematics and Computation, Volume 152, Issue 3, pp. 897-904. https://dx.doi.org/10.1016/S0096-3003(03)00618-0
0096-3003
000222064900023 (WOS)
https://dx.doi.org/10.1016/S0096-3003(03)00618-0
https://hdl.handle.net/11376/800
152
3
897
904
An interesting connection exists between the space of homogeneous polynomials and the representations of the homogeneous modular group F(l). This linkage leads to become automorphic and modular forms for the representations of the modular group. In this paper we also obtain new special functions, a study of which leads to new relations for usual functions.
eng
info:eu-repo/semantics/closedAccess
Homogeneous Polynomials
Automorphic Form
Modular Form
Modular Group
Poincare Series
On automorphic and modular forms in the space of the homogeneous polynomials with degree 2l and applications to the special matrix
article
oai:openaccess.dogus.edu.tr:11376/2742020-09-22T18:32:41Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3392
Koç, Cemal
2014-07-13T15:14:58Z
2014-07-13T15:14:58Z
2003
KOÇ. C. (2003). Professor Masatoshi Gündüz Ikeda: a life devoted to mathematics. Turkish Journal of Mathematics, 27 (4), pp. 461-471.
1300-0098
1303-6149
https://hdl.handle.net/11376/274
27
4
461
471
In the summer of 1963 as a new graduate I paid a visit to the newly established Mathematics Department of Ege University, in _Izmir, to apply for a post. In the very moments of my arrival, they introduced to me a young faculty member: Doctor Ikeda. Apparently he was Japanese, polite yet authoritative, and there was an air of general admiration about him; however the rest was a complete mystery for me. I complied with his suggestions and brought a few more documents to support my application, and thus completed the application process and joined the department. My rst duty there was to assist his lectures. However, this was not as easy as I had expected. One of his two courses was totally unfamiliar to me; the other one in turn was a course of which I covered much less as an undergraduate than had been taught by Dr. Ikeda. My ability to keep up with the subject was slowed by the fact that the books in Turkish or French I had access to were too few, causing me to consult desperately all the existing books thoroughly. The professor gave no credit for the clich e \az olsun ama tam olsun" (let it be little but complete) which is commonly used by lecturers as an excuse for covering limited teaching material...
eng
info:eu-repo/semantics/openAccess
Mathematics
Masatoshi Gunduz Ikeda
TUBITAK
Matematik
Masatoshi Gündüz Ikeda
TÜBİTAK
Professor Masatoshi Gündüz Ikeda: a life devoted to mathematics
article
oai:openaccess.dogus.edu.tr:11376/9522020-09-22T18:32:50Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2015-02-12T16:11:30Z
2015-02-12T16:11:30Z
2006-03
VELİEV, O.A. (2006). Spectral expansion for a nonselfadjoint periodic differential operator. Russian Journal of Mathematical Physics, 13 (1), pp. 101-110. DOI:https://dx.doi.org./10.1134/S1061920806010109.
1061-9208
000245617000010 (WOS)
https://dx.doi.org./10.1134/S1061920806010109
https://hdl.handle.net/11376/952
13
1
101
110
In the paper, we construct the spectral expansion for the differential operator generated in L-2(-infinity,infinity) by an ordinary differential expression of arbitrary order with periodic complex-valued coefficients Lebesgue integrable on bounded intervals.
eng
info:eu-repo/semantics/closedAccess
Translation
Mathematical and Computational Physics
Spectral expansion for a nonselfadjoint periodic differential operator
article
oai:openaccess.dogus.edu.tr:11376/14652020-09-22T18:33:24Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Güngör, Faruk
Hasansoy, Mahir
2015-04-29T08:45:04Z
2015-04-29T08:45:04Z
2012-05-15
GÜNGÖR, F., HASANSOY, M. (2012). A class of multi - parameter eigenvalue problems for perturbed p-Laplacians. Journal of Mathematical Analysis and Applications, 389 (2), pp. 821-832. https://dx.doi.org/10.1016/j.jmaa.2011.12.027.
0022-247X
000300206700010 (WOS)
https://dx.doi.org/10.1016/j.jmaa.2011.12.027
https://hdl.handle.net/11376/1465
389
2
821
832
This paper is devoted to multi-parameter eigenvalue problems for one-dimensional perturbed p-Laplacians, modelling travelling waves for a class of nonlinear evolution PDE. Dispersion relations between the eigen-parameters, the existence of eigenfunctions and positive eigenfunctions, variational principles for eigenvalues and constructing solutions in the analytical and implicit forms are the main subject of this paper. We use both variational and analytical methods.
eng
info:eu-repo/semantics/closedAccess
Travelling Wave
Perturbed P - Laplacian
Eigenvalue
Eigenfunction
Variational Principle
Critical Point
Analytical and Implicit Solutions
Elliptic - Equations
Regularity
Existence
A class of multi - parameter eigenvalue problems for perturbed p-Laplacians
article
oai:openaccess.dogus.edu.tr:11376/20462020-09-22T18:33:08Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Çallıalp, Fethi
Tekir, Ünsal
2015-08-26T12:44:22Z
2015-08-26T12:44:22Z
2004-06
ÇALLIALP, F., TEKİR, Ü. (2004). On the prime radical of a module over a noncommutative ring. Taiwanese Journal of Mathematics, 8 (2), pp. 337-341.
1027-5487
2224-6851
https://hdl.handle.net/11376/2046
8
2
337
341
Let R be a ring and M a left R - module. The radical of M is the intersection of all prime submodules of M. It is proved that if R is a hereditary, noetherian, prime and non right artinian and M a finitely generated R-module then the radical of M has a certain form.
eng
info:eu-repo/semantics/openAccess
Hereditary Rings
Noetherian Rings
Prime Submodule
On the prime radical of a module over a noncommutative ring
article
oai:openaccess.dogus.edu.tr:11376/1402020-09-22T18:33:37Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3392
Bağdatlı Yılmaz, Hülya
Özen Zengin, Füsun
Uysal, Samiye Aynur
2014-06-26T20:19:48Z
2014-06-26T20:19:48Z
2011
BAĞDATLI YILMAZ, H., ÖZEN ZENGİN, F., UYSAL, S. A. (2011). On a semi symmetric metric connection with a special condition on a Riemannian manifold. European Journal of Pure and Applied Mathematics, 4 (2), 152-161.ss.
1307-5543
https://hdl.handle.net/11376/140
In this study, we consider a manifold equipped with semi symmetric metric connection whose the torsion tensor satisfies a special condition. We investigate some properties of the Ricci tensor and the curvature tensor of this manifold . We obtain a necessary and sufficient condition for the mixed generalized quasi-constant curvature of this manifold. Finally, we prove that if the manifold mentioned above is conformally flat, then it is a mixed generalized quasi- Einstein manifold and we prove that if the sectional curvature of a Riemannian manifold with a semi symmetric metric connection whose the special torsion tensor is independent from orientation chosen, then this manifold is of a mixed generalized quasi constant curvature.
eng
info:eu-repo/semantics/openAccess
Semi Symmetric Metric Connection
Generalized Quasi - Einstein Manifold
Mixed Generalized Quasi Constant Curvature Manifold
Mixed Generalized Quasi - Einstein Manifold
On a semi symmetric metric connection with a special condition on a Riemannian manifold
article
oai:openaccess.dogus.edu.tr:11376/1672020-09-22T18:33:38Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3392col_11376_3390
Güloğlu, İsmail Şuayip
Koç, Cemal
2014-06-28T16:52:14Z
2014-06-28T16:52:14Z
2009
GÜLOĞLU, İ. Ş., KOÇ, C. (2009). Stack-sortable permutations and polynomials. Turkish Journal of Mathematics, 33 (1), 1-8.ss.
1300-0098
1303-6149
https://dx.doi.org/10.3906/mat-0705-6/
https://hdl.handle.net/11376/167
The Catalan numbers show up in a diverse variety of counting problems. In this note we give yet another characterization of the Catalan number C(n). It is characterized as the dimension of a certain space of multilinear polynomials by exhibiting a basis.
tur
info:eu-repo/semantics/openAccess
Mathematics
Number
Permutation
Polynomial
Matematik
Sayı
Permütasyon
Polinom
Stack-sortable permutations and polynomials
article
oai:openaccess.dogus.edu.tr:11376/2572020-09-22T18:33:42Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3392
Karakılıç, Sedef
Veliev, Oktay A.
Atılgan, Şirin
2014-07-10T10:38:17Z
2014-07-10T10:38:17Z
2005
KARAKILIÇ, S., VELİEV, O. A., ATILGAN, Ş. (2005). Asymptotic formulas for the resonance eigenvalues of the Schrödinger operator. Turkish Journal of Mathematics, 29 (4), 323-347. ss.
1300-0098
1303-6149
https://hdl.handle.net/11376/257
29
4
323
347
In this paper, we consider the Schrödinger operators defined by the differential expression ... in d-dimensional paralellepiped F, with the Dirichlet and the Neumann boundary conditions, where q(x) is a real valued function of L2(F). We obtain the asymptotic formulas for the resonance eigenvalues of these operators.
eng
info:eu-repo/semantics/openAccess
Mathematics
Eigenvalue
Schroedinger Operator
Asymptotic Formula
Matematik
Asimptotik Formül
Kontrollü Kelimeler
Özdeğer
Schroedinger Operatörü
Asymptotic formulas for the resonance eigenvalues of the Schrödinger operator
article
oai:openaccess.dogus.edu.tr:11376/35522020-01-09T15:49:37Zcom_11376_129com_11376_101com_11376_3388col_11376_130
Ercan, Gülin
Güloğlu, İsmail Şuayip
2020-01-09T15:49:36Z
2020-01-09T15:49:36Z
2019
Ercan, G., & Güloğlu, İ. Ş. (2019). On abelian group actions with TNI-centralizers. Communications in Algebra, 47(7), 3003-3006. https://doi.org/10.1080/00927872.2018.1549662
0092-7872
1532-4125
000478072000032 (WOS)
https://doi.org/10.1080/00927872.2018.1549662
https://hdl.handle.net/11376/3552
47
7
3003
3006
A subgroup H of a group G is said to be a TNI-subgroup if for any Let A be an abelian group acting coprimely on the finite group G by automorphisms in such a way that for all is a solvable TNI-subgroup of G. We prove that G is a solvable group with Fitting length h(G) is at most . In particular whenever is nonnormal. Here, h(G) is the Fitting length of G and is the number of primes dividing A counted with multiplicities.
eng
info:eu-repo/semantics/embargoedAccess
Automorphism
Centralizer
TNI-subgroup
Fitting Length
On abelian group actions with TNI-centralizers
article
oai:openaccess.dogus.edu.tr:11376/17112020-09-22T18:33:05Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Özemir, Cihangir
Güngör, Faruk
2015-07-07T09:46:50Z
2015-07-07T09:46:50Z
2013-02
ÖZDEMİR, C., GÜNGÖR, F. (2013). Symmetry classification of variable coefficient cubic-quintic nonlinear schrodinger equations. Journal of Mathematical Physics, 54 (2), 13p. https://dx.doi.org/10.1063/1.4789543.
0022-2488
000315596100029 (WOS)
https://dx.doi.org/10.1063/1.4789543
https://hdl.handle.net/11376/1711
54
2
1
13
A Lie-algebraic classification of the variable coefficient cubic-quintic nonlinear Schrodinger equations involving 5 arbitrary functions of space and time is performed under the action of equivalence transformations. It is shown that the symmetry group can be at most four-dimensional in the case of genuine cubic-quintic nonlinearity. It may be five-dimensional (isomorphic to the Galilei similitude algebra gs(1)) when the equation is of cubic type, and six-dimensional (isomorphic to the Schrodinger algebra sch(1)) when it is of quintic type.
eng
info:eu-repo/semantics/openAccess
Lie Symmetries
Differential-Equations
Wave-Guides
Models
Symmetry classification of variable coefficient cubic-quintic nonlinear schrodinger equations
article
oai:openaccess.dogus.edu.tr:11376/35512020-01-09T15:49:28Zcom_11376_129com_11376_101com_11376_3388col_11376_130
Ercan, Gülin
Güloğlu, İsmail Şuayip
2020-01-09T15:49:26Z
2020-01-09T15:49:26Z
2019
Ercan, G., & Güloğlu, İ. Ş. (2019). Frobenius groups of automorphisms with almost fixed point free kernel. Journal of Algebra, 521, 384-389. https://doi.org/10.1016/j.jalgebra.2018.12.004
0021-8693
1090-266X
000457070000018 (WOS)
https://doi.org/10.1016/j.jalgebra.2018.12.004
https://hdl.handle.net/11376/3551
521
384
389
Let FH be a Frobenius group with kernel F and complement H, acting coprimely on the finite solvable group G by automorphisms. We prove that if C-G(H) is of Fitting length n then the index of the n-th Fitting subgroup F-n(G) in G is bounded in terms of vertical bar C-G(F)vertical bar and vertical bar F vertical bar. This generalizes a result of Khukhro and Makarenko [6] which handles the case n = 1.
eng
info:eu-repo/semantics/embargoedAccess
Solvable Group
Automorphism
Fitting Length
Frobenius Group
Frobenius groups of automorphisms with almost fixed point free kernel
article
oai:openaccess.dogus.edu.tr:11376/12572020-09-22T18:33:19Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3390
Güngör, Faruk
2015-04-01T06:59:37Z
2015-04-01T06:59:37Z
2010-12-15
GÜNGÖR, F. (2010). Comment on "group analysis of KdV equation with time dependent coefficients". Applied Mathematics and Computation, 217 (8). 4293-4294. https://dx.doi.org/10.1016/j.amc.2010.10.001.
0096-3003
000284600700067 (WOS)
https://dx.doi.org/10.1016/j.amc.2010.10.001
https://hdl.handle.net/11376/1257
217
8
4293
4294
We show that the group classification results of the article entitled "Group analysis of KdV equation with time dependent coefficients" which appeared in (A.G. Johnpillai, M.C. Khalique, Group analysis of KdV equation with time dependent coefficients, Appl. Math. Comput. 216 (2010) 3761-3771) can be obtained from those of a more general class by a change of variables.
eng
info:eu-repo/semantics/closedAccess
Variable Coefficient KDV Equations
Group Classification
Point Symmetries
Comment on "group analysis of KdV equation with time dependent coefficients"
article
oai:openaccess.dogus.edu.tr:11376/32322020-09-22T18:33:31Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2018-12-17T07:16:44Z
2018-12-17T07:16:44Z
2017
Veliev, O. A. (2017). The Spectrum of the Hamiltonian with a PT-symmetric Periodic Optical Potential. International Journal of Geometric Methods in Modern Physics, 15(1), 1-25. https://dx.doi.org/10.1142/S0219887818500081
0219-8878
1793-6977
https://dx.doi.org/10.1142/S0219887818500081
https://hdl.handle.net/11376/3232
15
1
1
25
We give a complete description, provided with a mathematical proof, of the shape of the spectrum of the Hill operator with potential 4 cos2 x+4iV sin 2x, where V ∈ (0, ∞). We prove that the second critical point V2, after which the real parts of the first and second band disappear, is a number between 0.8884370025 and 0.8884370117. Moreover we prove that V2 is the degeneration point for the first periodic eigenvalue. Besides, we give a scheme by which one can find arbitrary precise value of the second critical point as well as the k-th critical points after which the real parts of the (2k −3)-th and (2k − 2)-th bands disappear, where k = 3, 4, ...
eng
info:eu-repo/semantics/closedAccess
PT-Symmetric Operators
Optical Potentials
Band Structure
The spectrum of the Hamiltonian with a PT-symmetric Periodic Optical Potential
article
oai:openaccess.dogus.edu.tr:11376/25192020-09-22T18:33:27Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391
Nur, Cemile
Veliev, Oktay A.
2016-04-11T08:29:19Z
2016-04-11T08:29:19Z
2015-07
Nur, C., & Veliev, O. A. (2015). On the basis property of the root functions of Sturm–Liouville operators with general regular boundary conditions. Moscow Mathematical Journal, 15(3), 511-526.
1609-3321
https://hdl.handle.net/11376/2519
15
3
511
526
We obtain the asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm–Liouville operators with general regular boundary conditions. Using these formulas, we find sufficient condi- tions on the potential q such that the root functions of these operators do not form a Riesz basis.
eng
info:eu-repo/semantics/openAccess
Asymptotic Formulas
Regular Boundary Conditions
Riesz Basis
On the basis property of the root functions of Sturm–Liouville operators with general regular boundary conditions
article
oai:openaccess.dogus.edu.tr:11376/13262020-09-22T18:33:24Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Özemir, Cihangir
Güngör, Faruk
2015-04-15T06:16:55Z
2015-04-15T06:16:55Z
2011-09
ÖZEMİR, C., GÜNGÖR, F. (2011). Variable coefficient nonlinear Schrödinger equations with four - dimensional symmetry groups and analysis of their solutions. Journal of Mathematical Physics, 52 (9), 19p. https://dx.doi.org/10.1063/1.3634005.
0022-2488
1089-7658
000295622100030 (WOS)
https://dx.doi.org/10.1063/1.3634005
https://hdl.handle.net/11376/1326
52
9
1
19
Analytical solutions of variable coefficient nonlinear Schroumldinger equations having four-dimensional symmetry groups, which are in fact the next closest to the integrable ones occurring only when the Lie symmetry group is five-dimensional, are obtained using two different tools. The first tool is to use one-dimensional subgroups of the full symmetry group to generate solutions from those of the reduced ordinary differential equations, namely, group invariant solutions. The other is by truncation in their Painleveacute expansions.
eng
info:eu-repo/semantics/openAccess
Differential Equations
Nonlinear Equations
Schrodinger Equation
Variable coefficient nonlinear Schrödinger equations with four - dimensional symmetry groups and analysis of their solutions
article
oai:openaccess.dogus.edu.tr:11376/17832020-09-22T18:33:07Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Dinibütün, Seza
Veliev, Oktay A.
2015-07-09T07:27:26Z
2015-07-09T07:27:26Z
2013
DİNİBÜTÜN, S., VELİEV, O. A. (2013). On the estimations of the small periodic eigenvalues. Abstract and Applied Analysis, Volume 2013, 12p. https://dx.doi.org/10.1155/2013/145967.
1085-3375
000322484700001 (WOS)
https://dx.doi.org/10.1155/2013/145967
https://hdl.handle.net/11376/1783
2013
1
12
We estimate the small periodic and semiperiodic eigenvalues of Hill's operator with sufficiently differentiable potential by two different methods. Then using it we give the high precision approximations for the length of nth gap in the spectrum of Hill-Sehrodinger operator and for the length of nth instability interval of Hill's equation for small values of n. Finally we illustrate and compare the results obtained by two different ways for some examples.
eng
info:eu-repo/semantics/openAccess
Sturm-Liouville Problems
Finite-Difference Eigenvalues
Boundary-Conditions
Shooting Algorithm
On the estimations of the small periodic eigenvalues
article
oai:openaccess.dogus.edu.tr:11376/8412020-09-22T18:32:38Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Ercan, Gülin
Güloğlu, İsmail Şuayip
2015-01-05T18:43:53Z
2015-01-05T18:43:53Z
2014-02
ERCAN, G., GÜLOĞLU, İ.Ş. (2014). Action of a frobenius-like group with fixed-point free kernel. Journal of Group Theory, 17 (5) pp. 863-873. https://dx.doi.org/10.1515/jgt-2014-0002.
1435-4446
1433-5883
https://dx.doi.org/10.1515/jgt-2014-0002
https://hdl.handle.net/11376/841
https://dx.doi.org/10.1515/jgt-2014-0016
17
5
863
873
We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [F,h]=F for all nonidentity elements h ∈ H. We prove that any irreducible nontrivial FH-module for a Frobenius-like group FH of odd order over an algebraically-closed field has an H-regular direct summand if either F is fixed-point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of this result are also derived.
eng
info:eu-repo/semantics/closedAccess
Frobenius Groups
Automorphisms
Kernel (Mathematics)
Feit-Thompson Theorem
Irreducible Polynomials
Finite Groups
Action of a Frobenius-like group with fixed-point free kernel
article
oai:openaccess.dogus.edu.tr:11376/28162020-09-22T18:32:30Zcom_11376_129com_11376_101com_11376_3388col_11376_130
Veliev, Oktay A.
2016-12-20T15:16:39Z
2016-12-20T15:16:39Z
2007
Veliev, O. A. (2007). Non-self-adjoint sturm–liouville operators with matrix potentials. Mathematical Notes, 81(4), 496-506. https://dx.doi.org/10.1134/S0001434607030200
0001-4346
1573-8876
https://dx.doi.org/10.1134/S0001434607030200
https://hdl.handle.net/11376/2816
81
4
496
506
We obtain asymptotic formulas for non-self-adjoint operators generated by the Sturm–Liouville system and quasiperiodic boundary conditions. Using these asymptotic formulas, we obtain conditions on the potential for which the system of root vectors of the operator under consideration forms a Riesz basis.
eng
info:eu-repo/semantics/openAccess
Sturm–Liouville Operator
Non-Self-Adjoint Operator
Quasiperiodic Boundary Condition
Riesz Basis
Root Function
Jordan Chain
Bessel Operator
Non-self-adjoint sturm–liouville operators with matrix potentials
article
oai:openaccess.dogus.edu.tr:11376/13852020-09-22T18:33:21Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Hasansoy, Mahir
2015-04-22T12:58:29Z
2015-04-22T12:58:29Z
2011
HASANSOY, M. (2011). On the travelling waves for the generalized nonlinear schrodinger equation. Abstract and Applied Analysis, 12p. https://dx.doi.org/10.1155/2011/181369
1687-0409
1085-3375
000294624500001 (WOS)
https://dx.doi.org/10.1155/2011/181369
https://hdl.handle.net/11376/1385
2011
1
12
This paper is devoted to the analysis of the travelling waves for a class of generalized nonlinear Schrodinger equations in a cylindric domain. Searching for travelling waves reduces the problem to the multiparameter eigenvalue problems for a class of perturbed p-Laplacians. We study dispersion relations between the eigenparameters, quantitative analysis of eigenfunctions and discuss some variational principles for eigenvalues of perturbed p-Laplacians. In this paper we analyze the Dirichlet, Neumann, No-flux, Robin and Steklov boundary value problems. Particularly, a "duality principle" between the Robin and the Steklov problems is presented.
eng
info:eu-repo/semantics/openAccess
P - Laplacian
Eienvalue Problems
Schrodinger Equations
Cylindric Domain
On the travelling waves for the generalized nonlinear schrodinger equation
article
oai:openaccess.dogus.edu.tr:11376/1312020-09-22T18:33:36Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Koç, Cemal
Kurtulmaz, Yosum
2014-06-26T14:22:25Z
2014-06-26T14:22:25Z
2012
KOÇ, C., KURTULMAZ, Y. (2012). Structure theory of central simple Zd-graded algebras. Turkish Journal of Mathematics, 36 (4), 560-577.ss.
1300-0098
1303-6149
https://hdl.handle.net/11376/131
https://dx.doi.org/10.3906/mat-1011-535
This paper investigates the structure theory of Zd- central simple graded algebras and gives the complete decomposition into building block algebras. The results are also applied to generalized Clifford algebras, which are motivating examples of Zd-central simple graded algebras.
tur
info:eu-repo/semantics/openAccess
Clifford Algebra
Graded Algebra
Unity
Clifford Cebiri
Aşmaçlı Cebir
Teklik
Structure theory of central simple Zd-graded algebras
article
oai:openaccess.dogus.edu.tr:11376/28202020-09-22T18:32:47Zcom_11376_129com_11376_101com_11376_3388col_11376_130
Özen Zengin, Füsun
Altay Demirbağ, Sezgin
Uysal, Samiye Aynur
2016-12-20T16:14:00Z
2016-12-20T16:14:00Z
2008-10
Özen Zengin, F., Altay Demirbağ, S., and Uysal, S. A. (2008). Darboux function in a hypersurface of a Riemannian manifold with semi-symmetric metric connection. International Mathematical Forum, 3(15), 739-749.
1312-7594
1314-7536
https://hdl.handle.net/11376/2820
3
15
739
749
In 1970, Yano, [1], studied Riemannian manifolds which admit semisymmetric metric connections whose curvature tensors vanish (see also [2]). The properties of a Riemannian manifold admitting a semi-symmetric metric connection were studied by many authors ([1], [3]). In [3], an expression of the curvature tensor of a manifold was obtained under assumption that the manifold admits a semi-symmetric metric connection with vanishing curvature tensor and recurrent torsion tensor. In this paper, we study a Darboux function in hypersurface of a Riemannian manifold with semi-symmetric metric connection. The purpose of this paper is that the relations between the Darboux function with respect to the linear connection and the Darboux function with respect to the Levi-Civita connection of a Riemannian manifold are obtained. In this paper, some theorems about this function are proved.
eng
info:eu-repo/semantics/openAccess
Semi-symmetric Metric Connection
Levi-Civita Connection Darboux Function
Totally Umbilical Hypersurface
Darboux function in a hypersurface of a Riemannian manifold with semi-symmetric metric connection
article
oai:openaccess.dogus.edu.tr:11376/14782020-09-22T18:32:59Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Haji, Ahmedov
Aliev, Alikram N.
2015-04-30T19:46:36Z
2015-04-30T19:46:36Z
2012-05-01
HAJI, A., ALIEV, A.N. (2012). Type N spacetimes as solutions of extended new massive gravity. Physic Letters B, 711 (1), pp. 117-121. https://dx.doi.org/10.1016/j.physletb.2012.03.061.
0370-2693
000303306700019 (WOS)
https://dx.doi.org/10.1016/j.physletb.2012.03.061
https://hdl.handle.net/11376/1478
711
1
117
121
We study algebraic type N spacetimes in the extended new massive gravity (NMG), considering both the Born-Infeld model (BI-NMG) and the model of NMG with any finite order curvature corrections. We show that for these spacetimes, the field equations of BI-NMG take the form of the massive (tensorial) Klein-Gordon type equation, just as it happens for ordinary NMG. This fact enables us to obtain the type N solution to BI-NMG, utilizing the general type N solution of NMG, earlier found in our work. We also obtain type N solutions to NMG with all finite order curvature corrections and show that, in contrast to BI-NMG, this model admits the critical point solutions, which are counterparts of "logarithmic" AdS pp-waves solutions of NMG.
eng
info:eu-repo/semantics/closedAccess
Gauge - Theories
Type N Spacetimes
Massive Gravity
Born - Infeld Model
Type N spacetimes as solutions of extended new massive gravity
article
oai:openaccess.dogus.edu.tr:11376/32942020-09-22T18:32:48Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Erkoç, Temha
Yılmaztürk, Utku
Güloğlu, İsmil Şuayip
2019-01-16T11:49:18Z
2019-01-16T11:49:18Z
2018-09
Erkoç, T., Yılmaztürk, U., Güloğlu, İ. Ş. (2018). Finite groups whose character degree graphs coincide with their prime graphs. Czechoslovak Mathematical Journal, 68(3), 647-656. https://dx.doi.org/10.21136/CMJ.2018.0553-16
0011-4642
1572-9141
https://dx.doi.org/10.21136/CMJ.2018.0553-16
https://hdl.handle.net/11376/3294
68
3
647
656
In the literature, there are several graphs related to a finite group G. Two of them are the character degree graph, denoted by ΔG), and the prime graph ΓG), In this paper we classify all finite groups whose character degree graphs are disconnected and coincide with their prime graphs. As a corollary, we find all finite groups whose character degree graphs are square and coincide with their prime graphs.
eng
info:eu-repo/semantics/openAccess
Finite Groups
Character Degree Graph
Prime Graph
Finite groups whose character degree graphs coincide with their prime graphs
article
oai:openaccess.dogus.edu.tr:11376/14812020-09-22T18:33:22Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Özsarı, Türker
2015-05-01T14:16:25Z
2015-05-01T14:16:25Z
2012-05-01
ÖZSARI, T. (2012). Weakly - damped focusing nonlinear Schrodinger equations with Dirichlet control. Journal of Mathematical Analysis and Applications, 389 (1), pp. 84-97. https://dx.doi.org/10.1016/j.jmaa.2011.11.053.
0022-247X
000302391400008 (WOS)
https://dx.doi.org/10.1016/j.jmaa.2011.11.053
https://hdl.handle.net/11376/1481
389
1
84
97
In this article we consider the weakly damped focusing nonlinear Schrodinger equations on bounded domains at the natural H-1-energy level with Dirichlet control acting on a portion of the boundary. We introduce the dynamic extension method for homogenizing the inhomogeneous boundary input. Then, we construct approximate solutions using monotone operator theory. A hidden trace regularity is proved to control the norm of the solutions in a global sense. This allows the use of compactness techniques by which we prove the existence of weak solutions. Finally, using multiplier techniques, we prove the exponential decay of solutions under the assumption that the boundary control also decays in a similar fashion.
eng
info:eu-repo/semantics/closedAccess
Nonlinear Schrodinger Equations
Inhomogeneous Dirichlet Boundary Value
Dynamic Extension
Hidden Regularity
Monotone Operator Theory
Compactness Method
Global Existence
Exponential Stabilization
Boundary - Value - Problem
Controllability
Weakly - damped focusing nonlinear Schrodinger equations with Dirichlet control
article
oai:openaccess.dogus.edu.tr:11376/14522020-09-22T18:33:56Zcom_11376_129com_11376_101com_11376_3388col_11376_130
Özen Zengin, Füsun
Altay Demirbağ, Sezgin
Uysal, Samiye Aynur
Bağdatlı Yılmaz, Hülya
2015-04-28T09:17:25Z
2015-04-28T09:17:25Z
2012-07
ÖZEN ZENGİN, F., ALTAY DEMİRBAĞ, S., UYSAL, S. A., BAĞDATLI YILMAZ, H. (2012). Some vector fields on a riemannian manifold with semi - symmetric metric connection. Bulletin of the Iranian Mathematical Society, 38 (2), pp. 479-490.
1735-8515
000313174400016 (WOS)
https://hdl.handle.net/11376/1452
38
2
479
490
In the first part of our work, some results are given for a Riemannian manifold with semi-symmetric metric connection. In the second part, some special vector fields, such as torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. We obtain some properties of this manifold having the vectors mentioned above.
eng
info:eu-repo/semantics/openAccess
Semi - Symmetric Metric Connection
Torse - Forming Vector Field
Recurrent Vector Field
Concurrent Vector Field
Spaces
Some vector fields on a riemannian manifold with semi - symmetric metric connection
article
oai:openaccess.dogus.edu.tr:11376/15322020-09-22T18:33:03Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Çallıalp, Fethi
Jayaram, C.
Tekir, Ünsal
2015-06-01T11:13:38Z
2015-06-01T11:13:38Z
2012
ÇALLIALP, F., JAYARAM, C., TEKİR, Ü. (2012). Weakly prime elements in multiplicative lattices. Communications in Algebra, 40(8), pp. 2825-2840. https://dx.doi.org/10.1080/00927872.2011.587212.
0092-7872
000308019400012 (WOS)
https://dx.doi.org/10.1080/00927872.2011.587212
https://hdl.handle.net/11376/1532
40
8
2825
2840
In this article, we study weakly prime elements and almost prime elements in multiplicative lattices. Next we characterize weak pi-lattices and weak principal element lattices. We also establish new characterizations for pi-domains and principal element lattices in terms of almost prime elements. Finally, we show that in a Noether lattice L, every proper element of L is a finite product of almost prime elements if and only if L is a finite direct product of principal element domains, special principal element lattices, and special product of almost prime elements lattices.
eng
info:eu-repo/semantics/closedAccess
Almost Prime Element
Invertible Element
Pi - Lattice
Principal Element
Principal Element Lattice
Regular Lattice
Weak Pi - Lattice
Weakly Prime Element
Weak Principal Element Lattice
Weakly prime elements in multiplicative lattices
article
oai:openaccess.dogus.edu.tr:11376/35502020-01-09T15:49:07Zcom_11376_129com_11376_101com_11376_3388col_11376_130
Foruzanfar, Zeinab
Güloğlu, İsmail Şuayip
Rezaei, Mehdi
2020-01-09T15:49:05Z
2020-01-09T15:49:05Z
2019
Foruzanfar, Z., Güloğlu, İ. Ş., & Rezaei, M. (2019). Classification of finite groups according to their conjugacy class lengths. Journal of Group Theory, 22(1), 137-156. https://doi.org/10.1515/jgth-2018-0025
1435-4446
1433-5883
000454602000010 (WOS)
https://doi.org/10.1515/jgth-2018-0025
https://hdl.handle.net/11376/3550
22
1
137
156
In this paper, we classify all finite groups satisfying the following property: their conjugacy class lengths are set-wise relatively prime for any six distinct classes.
eng
info:eu-repo/semantics/embargoedAccess
Graphs
Classification of finite groups according to their conjugacy class lengths
article
oai:openaccess.dogus.edu.tr:11376/8422020-09-22T18:33:12Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Güloğlu, İsmail Şuayip
Ercan, Gülin
2015-01-05T18:49:54Z
2015-01-05T18:49:54Z
2014-03-15
GÜLOĞLU, İ.Ş., ERCAN, G. (2014). Action of a Frobenius-likegroup. Journal of Algebra, Volume 402, pp. 533-543. https://dx.doi.org/10.1016/j.jalgebra.2014.01.005.
0021-8693
https://dx.doi.org/10.1016/j.jalgebra.2014.01.005
https://hdl.handle.net/11376/842
402
533
543
We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [F,h]=F[F,h]=F for all nonidentity elements h∈Hh∈H. We prove that any irreducible nontrivial FH-module for a Frobenius-like group FH of odd order over an algebraically closed field has an H-regular direct summand if either F is fixed point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of this result are also derived.
eng
info:eu-repo/semantics/closedAccess
Frobenius Action
Automorphisms
Fixed Points
Action of a Frobenius-likegroup
article
oai:openaccess.dogus.edu.tr:11376/13842020-09-22T18:32:56Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Esin, Songül
Kanuni, Müge
Koç, Ayten
2015-04-22T12:49:09Z
2015-04-22T12:49:09Z
2011
ESİN, S., KOÇ, M., KOÇ, A. (2011). Characterization of some ring properties in incidence algebras. Communications in Algebra, 39 (10), pp. 3836-3848. https://dx.doi.org/10.1080/00927872.2010.512589.
0092-7872
000297049800024 (WOS)
https://dx.doi.org/10.1080/00927872.2010.512589
https://hdl.handle.net/11376/1384
39
10
3836
3848
Let R be a ring with identity and I(X, R) be the incidence algebra of a locally finite partially ordered set X over R. In this article, we investigate the necessary and sufficient conditions for the incidence ring to be Ikeda-Nakayama, nil injective, NI, reduced, nonsingular and Kasch ring.
eng
info:eu-repo/semantics/closedAccess
Ikeda - Nakayama Ring
Incidence Algebra
Kasch Ring
Nil - Injective Ring
Singular Ideal
Characterization of some ring properties in incidence algebras
article
oai:openaccess.dogus.edu.tr:11376/8542020-09-22T18:33:46Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Karakılıç, Sedef
Atılgan, Şirin
Veliev, Oktay A.
2015-01-09T21:34:48Z
2015-01-09T21:34:48Z
2005-04
KARAKILIÇ, S., ATILGAN, S., VELİEV, O.A. (2005). Asymptotic formulae for the Schrodinger operator with Dirichlet and Neumann boundary conditions. Reports on Mathematical Physics, Volume 55, Issue 2, pp. 221-239. https://dx.doi.org/10.1016/S0034-4877(05)80029-1.
0034-4877
000228441300006 (WOS)
https://dx.doi.org/10.1016/S0034-4877(05)80029-1
https://hdl.handle.net/11376/854
55
2
221
239
In this paper, we consider the Schrodinger operators defined by the differential expression Lu = -Delta u+q(x)u in d-dimensional parallelepiped F, with the Dirichlet and Neumann boundary conditions, and obtain the asymptotic formulae for the eigenvalues of these operators.
eng
info:eu-repo/semantics/closedAccess
Perturbation
Dirichlet and Neumann Boundary Conditions
Schrodinger Operator
Spectrum
Asymptotic formulae for the Schrodinger operator with Dirichlet and Neumann boundary conditions
article
oai:openaccess.dogus.edu.tr:11376/32022020-09-22T18:33:33Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Ercan, Gülin
Güloğlu, İsmail Şuayip
2018-11-28T06:13:53Z
2018-11-28T06:13:53Z
2017-12
Ercan, G., Guloglu, İ. S. (2017). On the influence of fixed point free nilpotent automorphism groups. Monatshefte Fur Mathematik, 184(4), 531-538. https://dx.doi.org/10.1007/s00605-016-0970-5
0026-9255
1436-5081
000414159400003 (WOS)
https://dx.doi.org/10.1007/s00605-016-0970-5
https://hdl.handle.net/11376/3202
184
4
531
538
A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that for all nonidentity elements . Let FH be a Frobenius-like group with complement H of prime order such that is of prime order. Suppose that FH acts on a finite group G by automorphisms where in such a way that In the present paper we prove that the Fitting series of coincides with the intersections of with the Fitting series of G, and the nilpotent length of G exceeds the nilpotent length of by at most one. As a corollary, we also prove that for any set of primes , the upper -series of coincides with the intersections of with the upper -series of G, and the - length of G exceeds the -length of by at most one.
eng
info:eu-repo/semantics/closedAccess
Frobenius-Like Group
Fixed Points
Nilpotent Length
Pi-Length
Frobenius-Like Group
Kernel
Length
On the influence of fixed point free nilpotent automorphism groups
article
oai:openaccess.dogus.edu.tr:11376/8392020-09-22T18:33:52Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Güloğlu, İsmail Şuayip
Ercan, Gülin
2015-01-05T11:29:28Z
2015-01-05T11:29:28Z
2013-05
GÜLOĞLU, İ.Ş., ERCAN, G. (2012). A generalized fixed-point-free action. Journal of Algebra and Its Applications, 12 (3), pp 1250172-1-1250172-4. https://dx.doi.org/10.1142/S0219498812501721.
0219-4988
1793-6829
https://dx.doi.org/10.1142/S0219498812501721
https://hdl.handle.net/11376/839
12
3
1250172-1
1250172-4
In this paper we study the structure of a finite group G admitting a solvable group A of automorphisms of coprime order so that for any x ∈ CG(A) of prime order or of order 4, every conjugate of x in G is also contained in CG(A). Under this hypothesis it is proven that the subgroup [G, A] is solvable. Also an upper bound for the nilpotent height of [G, A] in terms of the number of primes dividing the order of A is obtained in the case where A is abelian.
eng
info:eu-repo/semantics/closedAccess
Solvable
Nilpotent Height
Automorphism
Fixed Point Free Action
A generalized fixed-point-free action
article
oai:openaccess.dogus.edu.tr:11376/13232020-09-22T18:33:18Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Özsarı, Türker
Kalantarov, Varga K.
Lasiecka, Irena
2015-04-14T17:34:00Z
2015-04-14T17:34:00Z
2011-10-01
ÖZSARI, T., KALANTAROV, V. K., LASIECKA, I. (2011). Uniform decay rates for the energy of weakly damped defocusing semilinear Schrodinger equations with inhomogeneous Dirichlet boundary control. Journal of Differential Equations, 251 (7), pp. 1841-1863. https://dx.doi.org/10.1016/j.jde.2011.04.003.
0022-0396
000293673700006 (WOS)
https://dx.doi.org/10.1016/j.jde.2011.04.003
https://hdl.handle.net/11376/1323
251
7
1841
1863
In this paper, we study the open loop stabilization as well as the existence and regularity of solutions of the weakly damped de-focusing semilinear Schrodinger equation with an inhomogeneous Dirichlet boundary control. First of all, we prove the global existence of weak solutions at the H(1)-energy level together with the stabilization in the same sense. It is then deduced that the decay rate of the boundary data controls the decay rate of the solutions up to an exponential rate. Secondly, we prove some regularity and stabilization results for the strong solutions in H(2)-sense. The proof uses the direct multiplier method combined with monotonicity and compactness techniques. The result for weak solutions is strong in the sense that it is independent of the dimension of the domain, the power of the nonlinearity, and the smallness of the initial data. However, the regularity and stabilization of strong solutions are obtained only in low dimensions with small initial and boundary data.
eng
info:eu-repo/semantics/closedAccess
Nonlinear Schrodinger Equation
Inhomogeneous Dirichlet Boundary Condition
Existence
Stabilization
Boundary Control
Direct Multiplier Method
Monotone Operator Theory
Compactness
Uniform decay rates for the energy of weakly damped defocusing semilinear Schrodinger equations with inhomogeneous Dirichlet boundary control
article
oai:openaccess.dogus.edu.tr:11376/13312020-09-22T18:33:18Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Güloğlu, İsmail Şuayip
2015-04-15T11:26:34Z
2015-04-15T11:26:34Z
2010
GÜLOĞLU, İ.Ş. (2010). A short survey on mathematical work of Cemal Koc. Turkish Journal of Mathematics, 34 (4), pp. 433-440. https://dx.doi.org/10.3906/mat-1009-43.
1300-0098
000284435200001 (WOS)
https://dx.doi.org/10.3906/mat-1009-43
https://hdl.handle.net/11376/1331
34
4
433
440
first met Cemal Koç during Spring semester of 1977. He was then a young associate professor at the Middle East Technical University, Ankara, and I was a Ph.D. student attending his graduate course on noncommutative rings. I had previously attended lectures in Germany given by leading experts on several topics in algebra, yet the course I took that year from Cemal Ko¸c was the one that has left a strong impression on me as a live example of how one should lecture and teach. Later, on many other occasions, I had the chance to observe his enthusiasm for and dedication to teaching. Being a first grade researcher as well, he possessed a combination of talents that one does not find very often. Unfortunately, I won’t be able to give you a taste of what his teaching was like but instead I shall try to summarize his mathematical research.
eng
info:eu-repo/semantics/openAccess
Cemal Koç
Commutativity of Rings
Theorem Jacobson
Theorem Herstein
Clifford Algebras
A short survey on mathematical work of Cemal Koc
article
oai:openaccess.dogus.edu.tr:11376/35172020-01-02T05:45:37Zcom_11376_129com_11376_101com_11376_3388col_11376_130
Veliev, Oktay
2020-01-02T05:45:35Z
2020-01-02T05:45:35Z
2020
Veliev, O. (2020). On the spectrality and spectral expansion of the non-self-adjoint mathieu-hill operator in L2(−∞,∞). Communications on Pure and Applied Analysis, 19(3), 1537-1562. http://dx.doi.org/10.3934/cpaa.2020077
1534-0392
1553-5258
http://dx.doi.org/10.3934/cpaa.2020077
https://hdl.handle.net/11376/3517
19
3
1537
1562
In this paper we investigate the non-self-adjoint operator H generated in L-2(-infinity, infinity) by the Mathieu-Hill equation with a complex-valued potential. We find a necessary and sufficient conditions on the potential for which H has no spectral singularity at infinity and it is an asymptotically spectral operator. Moreover, we give a detailed classification, stated in term of the potential, for the form of the spectral decomposition of the operator H by investigating the essential spectral singularities.
eng
info:eu-repo/semantics/closedAccess
Mathieu-Hill Operator
Spectral Operator
Spectral Expansion
On the spectrality and spectral expansion of the non-self-adjoint mathieu-hill operator in L2(−∞,∞)
article
oai:openaccess.dogus.edu.tr:11376/14492020-09-22T18:33:00Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3390
Çallıalp, Fethi
Tekir, Ünsal
2015-04-28T07:31:23Z
2015-04-28T07:31:23Z
2011
ÇALLIALP, F., TEKİR, Ü. (2011). Multiplication lattice modules. Iranian Journal of Science and Technology Transaction A: Science, 35 (A4), pp. 309-313.
1028-6276
000307919300007 (WOS)
https://hdl.handle.net/11376/1449
35
A4
309
313
Let M be a lattice module over the multiplicative lattice L. An L-module M is called a multiplication lattice module if for every element N is an element of M there exists an element a is an element of L such that N = a1(M). Our objective is to investigate properties of prime elements of multiplication lattice modules.
eng
info:eu-repo/semantics/openAccess
Multiplicative Lattice
Lattice Modules
Maximal Element
Prime Element
Multiplication lattice modules
article
oai:openaccess.dogus.edu.tr:11376/8482020-09-22T18:33:15Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2015-01-06T15:10:19Z
2015-01-06T15:10:19Z
2015-02-15
Veliev, O. A. (2015). Spectral problems of a class of non-self-adjoint one-dimensional Schrodinger operators. Journal of Mathematical Analysis and Applications, 442(2), 1390-1401. https://dx.doi.org/10.1016/j.jmaa.2014.09.074
0022-247X
1096-0813
000344911800037 (WOS)
https://dx.doi.org/10.1016/j.jmaa.2014.09.074
https://hdl.handle.net/11376/848
442
2
1390
1401
In this paper we investigate the one-dimensional Schrodinger operator L(q) with complex-valued periodic potential q when q is an element of L-1[0,1] and q(n) = 0 for n = 0, -1, -2, ..., where qn are the Fourier coefficients of q with respect to the system{e(iota 2 pi nx)}. We prove that the Bloch eigenvalues are (2 pi n + t)(2) for n is an element of Z, t is an element of C and find explicit formulas for the Bloch functions. Then we consider the inverse problem for this operator.
eng
info:eu-repo/semantics/closedAccess
Hill Qperator
Spectrum
Inverse Problems
Spectral problems of a class of non-self-adjoint one-dimensional Schrodinger operators
article
oai:openaccess.dogus.edu.tr:11376/16382020-09-22T18:33:02Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Basarab - Horwath, P.
Güngör, Faruk
Lahno, V.
2015-07-06T08:38:32Z
2015-07-06T08:38:32Z
2013-04
BASARAB - HORWATH, P., GÜNGÖR, F., LAHNO, V. (2013). Symmetry classification of third - order nonlinear evolution equations. Part I: semi - simple algebras. Acta Applicandae Mathematicae, 124 (1), pp. 123-170. https://dx.doi.org/10.1007/s10440-012-9773-4.
0167-8019
000316009000007 (WOS)
https://dx.doi.org/10.1007/s10440-012-9773-4
https://hdl.handle.net/11376/1638
124
1
123
170
We give a complete point-symmetry classification of all third-order evolution equations of the form u (t) =F(t,x,u,u (x) ,u (xx) )u (xxx) +G(t,x,u,u (x) ,u (xx) ) which admit semi-simple symmetry algebras and extensions of these semi-simple Lie algebras by solvable Lie algebras. The methods we employ are extensions and refinements of previous techniques which have been used in such classifications.
eng
info:eu-repo/semantics/closedAccess
Symmetries
Lie Algebras
Equivalence Group
Semi - Simple Lie Algebras
Solvable Lie Algebras
Partial - Differential - Equations
Lie- Algebras
Symmetry classification of third - order nonlinear evolution equations. Part I: semi - simple algebras
article
oai:openaccess.dogus.edu.tr:11376/442020-09-22T20:58:58Zcom_11376_14com_11376_13com_11376_12com_11376_342com_11376_604com_11376_129com_11376_101com_11376_3388col_11376_15col_11376_130
Dönmez, Ali
2014-05-16T19:01:08Z
2014-05-16T19:01:08Z
2000-01-15
DÖNMEZ, A. (2000). Some paradoxes in mathematics. Doğuş Üniversitesi Dergisi, 1 (1), pp. 79-87.
1302-6739
1308-6979
http://journal.dogus.edu.tr/index.php/duj/article/view/255
https://hdl.handle.net/11376/44
1
1
79
87
We have explained some paradoxes in the set theory of mathematics.
Matematiğin kümeler kuramındaki bazı paradoksları inceledik.
eng
info:eu-repo/semantics/openAccess
Küme
Çeldirmeler
Seriler
Set
Paradox
Series
Some paradoxes in mathematics
article
oai:openaccess.dogus.edu.tr:11376/24142020-09-22T18:32:37Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Muminov, Mukhiddin E.
2016-03-21T08:19:27Z
2016-03-21T08:19:27Z
2010-07
Muminov, M. E. (2010). Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice. Theoretical and Mathematical Physics, 164(1), 869-882. https://dx.doi.org/10.1007/s11232-010-0069-4
0040-5779
https://dx.doi.org/10.1007/s11232-010-0069-4
https://hdl.handle.net/11376/2414
164
1
869
882
We consider a system of three arbitrary quantum particles on a three-dimensional lattice that interact via short-range attractive potentials. We obtain a formula for the number of eigenvalues in an arbitrary interval outside the essential spectrum of the three-particle discrete Schrödinger operator and find a sufficient condition for the discrete spectrum to be finite. We give an example of an application of our results.
eng
info:eu-repo/semantics/closedAccess
Compact Operator
Discrete Spectrum
Essential Spectrum
Positive Operator
Schrödinger Operator
Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice
article
oai:openaccess.dogus.edu.tr:11376/13742020-09-22T18:32:55Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3392col_11376_3390
Veliev, Oktay A.
2015-04-20T11:05:52Z
2015-04-20T11:05:52Z
2011-06
VELİEV, O.A. (2011). On the basis property of the root functions of differential operators with matrix coefficients. Central European Journal of Mathematics, 9 (3), pp. 657-672. https://dx.doi.org/10.2478/s11533-011-0015-1.
1895-1074
1644-3616
000289114900012 (WOS)
https://dx.doi.org/10.2478/s11533-011-0015-1
https://hdl.handle.net/11376/1374
9
3
657
672
We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and periodic or antiperiodic boundary conditions. Then using these asymptotic formulas, we find necessary and sufficient conditions on the coefficients for which the system of eigenfunctions and associated functions of the operator under consideration forms a Riesz basis.
eng
info:eu-repo/semantics/closedAccess
Differential Operators
Eigenfunction Expansion
Ordinary Differential Equations
On the basis property of the root functions of differential operators with matrix coefficients
article
oai:openaccess.dogus.edu.tr:11376/13782020-09-22T18:32:57Zcom_11376_129com_11376_101com_11376_3388com_11376_3389col_11376_130col_11376_3391col_11376_3390
Veliev, Oktay A.
2015-04-22T10:21:45Z
2015-04-22T10:21:45Z
2011-04-15
VELİEV, O.A. (2011). An algorithm for finding the periodic potential of the three-dimensional Schrodinger operator from spectral invariants. Journal of Physics A: Mathematical and Theoretical, 44 (15), 23p. https://dx.doi.org/10.1088/1751-8113/44/15/155202.
1751-8113
000288752500008 (WOS)
https://dx.doi.org/10.1088/1751-8113/44/15/155202
https://hdl.handle.net/11376/1378
44
15
1
23
In this paper, we investigate the three-dimensional Schrodinger operator with a periodic, relative to a lattice Omega of R(3), potential q. A special class V of the periodic potentials is constructed, which is easily and constructively determined from the spectral invariants. First, we give an algorithm for the unique determination of the potential q is an element of V of the three-dimensional Schrodinger operator from the spectral invariants that were determined constructively from the given Bloch eigenvalues. Then, we consider the stability of the algorithm with respect to the spectral invariants and Bloch eigenvalues. Finally, we prove that there are no other periodic potentials in the set of large class of functions whose Bloch eigenvalues coincides with the Bloch eigenvalues of q is an element of V.
eng
info:eu-repo/semantics/openAccess
Equations
Periodic Potential
Three - Dimensional Schrodinger Operator
Spectral Invariants
An algorithm for finding the periodic potential of the three-dimensional Schrodinger operator from spectral invariants
article