Volume 68 , issue 4 ( 2016 ) | back |

Locally contractive maps on perfect Polish ultrametric spaces | 233$-$240 |

**Abstract**

In this paper, we present a result concerning locally contractive maps defined on subsets of perfect Polish ultrametric spaces (i.e. separable complete ultrametric spaces). Specifically, we show that a perfect compact ultrametric space cannot be contained in its locally contractive image, a corollary relating this result to minimal dynamical systems, and pose a conjecture for the general Polish ultrametric case.

**Keywords:** contractive map; Polish space; ultrametric space, R-tree; dynamical system.

**MSC:** 37B05; 54H20, 54E40

Almost para-Hermitian submersions | 241$-$253 |

**Abstract**

In this paper, we introduce the concept of almost para-Hermitian submersions between almost para-Hermitian manifolds. We investigate the influence of a given structure defined on the total manifold on the determination of the corresponding structure on the base manifold. Moreover, we provide an example, investigate various properties of the O'Neill's tensors for such submersions, find the integrability of the horizontal distribution and obtain necessary and sufficient conditions for the fibres of an almost para-Hermitian submersion to be totally geodesic. We also obtain curvature relations between the base manifold and the total manifold.

**Keywords:** almost para-Hermitian manifold; semi-Riemannian submersion; almost para-Hermitian submersion.

**MSC:** 53C15; 53C20, 53C50

Some homological properties of amalgamation | 254$-$258 |

**Abstract**

Let $R$ and $S$ be commutative rings, let $J$ be an ideal of $S$ and let $f \: R\to S$ be a ring homomorphism. In this paper, we investigate some homological properties of the amalgamation of $R$ with $S$ along $J$ with respect to $f$ (denoted by $R\bowtie^{f} J$), introduced by D'Anna and Fontana in $2007$. In addition, we deal with the strongly cotorsion properties of local cohomology module of $R\bowtie^{f} J$, when $R\bowtie^{f} J$ is a local Noetherian ring.

**Keywords:** amalgamation; strongly cotorsion; local cohomology.

**MSC:** 13H10

Antinormal composition operators on $l^{2}(\lambda)$ | 259$-$266 |

**Abstract**

In this paper, we characterize self-adjoint and normal composition operators on Poisson weighted sequence spaces $l^{2}(\lambda)$. However, the main purpose of this paper is to determine explicit conditions on inducing map under which a composition operator admits a best normal approximation. We extend results of Tripathi and Lal [Antinormal composition operators on $l^2$, Tamkang J. Math. 39 (2008), 347-352] to characterize antinormal composition operators on $l^{2}(\lambda)$.

**Keywords:** composition operator; normal operator; antinormal operator; Fredholm operator;
self-adjoint operator; Poisson weighted sequence spaces.

**MSC:** 47B33; 47A05, 47A58, 47B37

Characterization of $(\eta,\gamma,k,2)$-Dini-Lipschitz functions in terms of their Helgason Fourier transform | 267$-$276 |

**Abstract**

In this paper, using a generalized translation operator, we obtain an analog of Younis Theorem 5.2 in [M. S. Younis, Fourier transforms of Dini-Lipschitz functions, Int. J. Math. Math. Sci. 9 (2),(1986), 301--312.] for the Helgason Fourier transform of a set of functions satisfying the $(\eta,\gamma,k,2)$-Dini-Lipschitz condition in the space $L^{2}$ for functions on noncompact rank one Riemannian symmetric spaces.

**Keywords:** symmetric space; Helgason Fourier transform; Lipschitz condition; generalized translation operator.

**MSC:** 42B37

Topological properties of tripled fixed points set of multifunctions | 277$-$286 |

**Abstract**

In 1970, Schirmer provided some results about topological properties of the fixed points set of multifunctions. Later, some authors continued this review by providing different conditions. In 2008, 2009 Sintamarian proved some results on absolute retractivity of the common fixed points set of two multivalued operators. In this paper we shall present some new results on absolute retractivity of tripled fixed points set for multifunctions of the form $F:X\times X\times X\rightarrow P_{b,cl}(X)$.

**Keywords:** absolute retract; tripled fixed points set; multifunction.

**MSC:** 47H10; 54H25

Addition formula for complementary error function with associated integral representations | 287$-$297 |

**Abstract**

In this paper, using the Mellin transform of parabolic cylinder functions we present an addition formula for the complementary error function in terms of the Gaussian functions. Also, some inverse Laplace transforms of the complementary error functions are shown and new integral representations for the exponential integral and Bessel functions are given. Moreover, the solution of diffusion equation in finite domain is presented in terms of the theta functions.

**Keywords:** addition formula; Mellin transform; Laplace transform; complementary error function; Theta function.

**MSC:** 33B20; 44A10

Difference scheme for an interface problem for subdiffusion equation | 298$-$314 |

**Abstract**

An implicit finite-difference scheme for numerical approximation of an initial-boundary value problem with an interface for a two-dimensional subdiffusion equation with variable coefficients is proposed. Its stability is investigated and the corresponding convergence rate estimate is obtained. In a special case an efficient factorized scheme is proposed and investigated.

**Keywords:** fractional derivatives; interface problem; finite differences; factorized scheme; stability;
convergence rate.

**MSC:** 35R11; 65M12, 65M15