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Recent Submissions

Groups of automorphisms with TNIcentralizers
(Elsevier, 201803)A subgroup H of a finite group G is called a TNIsubgroup 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 TNIsubgroup of G. We prove that G is solvable if and only if CG(A) ... 
Finite groups whose character degree graphs coincide with their prime graphs
(Springer, 201809)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 ... 
The spectrum of the Hamiltonian with a PTsymmetric Periodic Optical Potential
(World Scientific, 2017)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 ... 
Finite groups admitting a dihedral group of automorphisms
(Lugansk National Taras Shevchenko University, 2017)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 CG(F)= 1. In the present paper we ... 
On the spectral properties of the Schrodinger operator with a periodic PTsymmetric potential
(World Scientific, 201705)In this paper, we investigate the spectrum and spectrality of the onedimensional Schrodinger operator with a periodic PTsymmetric complexvalued potential. 
Essential spectral singularities and the spectral expansion for the hill operator
(American Institute of Mathematical Sciences, 201711)In this paper we investigate the spectral expansion for the onedimensional Schrodinger operator with a periodic complexvalued potential. For this we consider in detail the spectral singularities and introduce new concepts ... 
On the influence of fixed point free nilpotent automorphism groups
(Springer, 201712)A finite group FH is said to be Frobeniuslike if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that for all nonidentity elements . Let FH be a Frobeniuslike group with complement H ... 
On sharp asymptotic formulas for the SturmLiouville operator with a matrix potential
(Springer, 201607)In this article we obtain the sharp asymptotic formulas for the eigenvalues and eigenfunctions of the nonselfadjoint operators generated by a system of the SturmLiouville equations with Dirichlet and Neumann boundary ... 
Action of a frobeniuslike group with kernel having central derived subgroup
(World Scientific Publishing, 201609)A finite group FH is said to be Frobeniuslike 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 ... 
α metrically chebyshev conformal motions in Riemannian spaces
(Academic Publications, 200802)In this paper we introduced αmetrically Chebyshev nets in a Riemannian manifold with semisymmetric metric connection. We also studied conformal motions with trajectories defined by the components of these nets in Riemannian ... 
Darboux function in a hypersurface of a Riemannian manifold with semisymmetric metric connection
(Hikari, 200810)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 semisymmetric metric connection ... 
Nonselfadjoint sturm–liouville operators with matrix potentials
(Pleiades Publishing, 2007)We obtain asymptotic formulas for nonselfadjoint operators generated by the Sturm–Liouville system and quasiperiodic boundary conditions. Using these asymptotic formulas, we obtain conditions on the potential for which ... 
On quasirecurrent spaces with Ricci quartersymmetric metric connection
(Hikari, 200601)In [3], Mishra and Pandey defined Ricci quartersymmetric metric connection in Riemanian manifold. In [5],Uysal and Doğan defined Drecurrent spaces with semisymmetric metric connection and constructed an example of these ... 
Perturbation theory for the periodic multidimensional Schrödinger Operator and the BetheSommerfeld Conjecture
(Hikari, 2007)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 ... 
On the basis property of the root functions of differential operators with matrix coefficients
(Moscow State University, 2009)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 ... 
Multidimensional periodic Schrödinger operator: Perturbation theory and applications
(Springer, 2015)The book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral ... 
Global attractors for the 3D viscous cahnhillard equations in an unbounded domain
(Taylor & Francis, 200908)In this note the 3D viscous CahnHillard 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 ... 
On the basis property of the root functions of Sturm–Liouville operators with general regular boundary conditions
(Independent University of Moscow, 201507)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 ... 
Formula for the number of eigenvalues of a threeparticle Schrödinger operator on a lattice
(Springer, 201007)We consider a system of three arbitrary quantum particles on a threedimensional lattice that interact via shortrange attractive potentials. We obtain a formula for the number of eigenvalues in an arbitrary interval outside ... 
On the constructive determination of the periodic potentials from the bloch eigenvalues
(IOP Science, 20090825)In this paper, we consider the threedimensional 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 ...