Том 37, № 2 (2016)
- Год: 2016
- Статей: 15
- URL: https://journals.rcsi.science/1995-0802/issue/view/12339
Article
Solution of nonlinear fractional stochastic integro-differential equation
Аннотация
By using admissibility theory and fixed point theorems, we studied the existence and uniqueness of random solution of nonlinear fractional stochastic integro-differential equation of Volterra type. In the end, an example is given to show the application of our results.
On existence of solutions for fractional differential equations with nonlocal multi-point boundary conditions
Аннотация
This paper investigates the existence of solutions for a boundary value problem of nonlinear fractional differential equations with nonlocal boundary conditions. We use Banach fixed point theorem to prove an existence and uniqueness result. Then, by using O’Regan fixed point theorem, we prove an existence result. Finally, illustrative examples of our main results are presented.
An algorithm for counting smooth integers
Аннотация
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.
Para-Sasakian manifolds satisfying certain curvature conditions
Аннотация
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.
On an inequality of Paul Turan concerning polynomials
Аннотация
Let P(z) be a polynomial of degree n and Ps(z) be its sth derivative. In this paper, we shall prove some inequalities for the sth derivative of a polynomial having zeros inside a circle, which as a special case give generalizations and refinements of some results of Turan, Govil, Malik and others.
Normal connections on three-dimensional manifolds with solvable transformation group
Аннотация
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.
Some properties of three dimensional trans-Sasakian manifolds with a semi-symmetric metric connection
Аннотация
In this paper we have studied ξ-projectively flat 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection. Next, we have shown a skew-symmetric property of projective Ricci-tensor with respect to semi-symmetric metric connection in a 3-dimensional trans-Sasakian manifold. Then we have proved quasi-projectively flat, ϕ-projectively flat 3-dimensional trans-Sasakian manifold with semi-symmetric metric connection. In the last section we have shown an example of a three dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection.
Non-existence of harmonic maps on trans-Sasakian manifolds
Аннотация
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.
Stability of Gorenstein X-flat modules
Аннотация
In this paper we introduce the notion of Gorenstein X-flat R-module and study a kind of stability of the class of Gorenstein X-flat R-modules. A ring R is called right GXF-closed if the class of all Gorenstein X-flat right R-modules is closed under extensions. We give an answer for the following natural question in the setting of a right GXF-closed ring R: Given an exact sequence of Gorenstein X-flat right R-modules G = · · ·→G1 → G0 → G0 → G1 →· · · such that the complex G ⊗RH is exact for each Gorenstein X-injective left R-module H, is themodule M:= im(G0 → G0) a Gorenstein X-flat R-module?
Cohomogeneity one anti de Sitter space AdSn+1
Аннотация
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.
Lutz filtration as a Galois module
Аннотация
In the paper, we consider a formal module F(ML) and its Lutz filtration ML ⊃ ML2 ⊃ ML3 ⊃..., where K is a finite extension of the field of p-adic numbers Qp, L/K is a normal extension without higher ramification with Galois group G = Gal(L/K), F(X, Y) is a formal group over a ring of integers OK with finite height. We study its structure as Z[G]-modules. The main result is contained in Theorem 4.
Quantum Hashing. Group approach
Аннотация
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.