Vol 37, No 2 (2016)

For analytic functions, we study poly-element linear functional equation generated by a pentagon. Such equations are connected with the moment problem for entire functions of exponential type.

Using a generalized translation operator, we obtain an analog of Titchmarsh’s theorem for the generalized Fourier–Bessel transform for functions satisfying the 2n-Bessel–Lipschitz condition in the space L_α,n².

An integer number n > 0 is called y-smooth for y > 0 if any prime factor p of n satisfies p ≤ y. Let ψ(x, y) be the number of all y-smooth integers less or equal to x. In this paper we elaborate a new algorithm for approximate calculation of ψ(x, y) at large x and relatively small y < log x.

In this paper, we investigate P-Sasakian manifolds satisfying the conditions R(X, ξ) · C = 0 and \(C \cdot \widetilde Z = 0\), where C and \(\widetilde Z\) are the Weyl conformal curvature tensor and the concircular curvature tensor respectively. Next, we study 3-dimensional P-Sasakianmanifolds. Finally, we give an example of a 3-dimensional P-Sasakian manifold.

The purpose of the work is the classification of three-dimensional homogeneous spaces, allowing a normal connection, description of invariant affine connections on those spaces together with their curvature and torsion tensors, holonomy algebras. We consider only the case, when Lie group is solvable. The local classification of homogeneous spaces is equivalent to the description of the effective pairs of Lie algebras. We study the holonomy algebras of homogeneous spaces and find when the invariant connection is normal. Studies are based on the use of properties of the Lie algebras, Lie groups and homogeneous spaces and they mainly have local character.

In this paper, we have studied harmonic maps on trans-Sasakian manifolds. First it is proved that if F: M₁ → M₂ is a Riemannian ϕ-holomorphic map between two trans-Sasakian manifolds such that ξ₂ ∈ (Im dF)^⊥, then F can not be harmonic provided that β₂ ≠ 0. We have also found the necessary and sufficient condition for the harmonic map to be constant map from Kaehler to trans-Sasakian manifold. Finally, we prove the non-existence of harmonic map from locally conformal Kaehler manifold to trans-Sasakian manifold.

In this paper we study the anti de Sitter space AdSⁿ⁺¹ under a cohomogeneity one action of a connected closed Lie subgroup G of the isometry group. Among various results, for compact groups we determine the possible acting groups, the orbit space and principal and singular orbits. For noncompact groups it is shown that if there is a principal orbit which is either simply connected or totally umbilic, then there is only one orbit type. Furthermore, in the totally umbilic case, all orbits are congruent to AdSⁿ.

In this paper we consider a generalization of quantum hash functions for arbitrary groups. We show that quantum hash function exists for arbitrary abelian group. We construct a set of “good” automorphisms—a key component of quantum hash funciton. We prove some restrictions on Hilbert space dimension and group used in quantum hash function.