Abstract:
The partition functions of bosonic and fermionic field in Barriola_Vilenkin black hole are directly derived by using the method of quantum statistics. Then the entropy of the Barriola_Vilenkin black hole is calculated by using the improved brick_wall method in the frame of membrane model.

Abstract:
Using the thin film model of black hole, the thermal radiation laws of the Barriola-Vilenkin black hole are studied. We obtained the result that the thermal radiation of the black hole always satisfies the generalized Stenfan-Boltzmann law. The derived generalized Stenfan-Boltzmann coefficient is no longer a constant. When the cut-off distance and the thin film thickness are both fixed, it is a proportional coefficient related to the space-time metric near the event horizon and the average radial effusion velocity of the radiation particles in the thin film. The radiation energy flux of the Dirac field of the Barriola-Vilenkin black hole is proportional to the average radial effusion velocity of the radiation particles in the thin film, and inversely proportional to the square of the black hole mass.

Abstract:
The quantum corrections to the entropy of the Barriola-Vilenkin black hole due to the massless gravitational field are calculated by using the brick-wall model.It is shown that the quantum corrections consist of two parts:One is a quadratic divergent term at the event horizon and is proportional to the surface area of the event horizon.The other is two logarithmically divergent terms which not only depend on the characteristics of the black hole but also on the spin of the field.The whole expression does not take the form of the scalar field.

Abstract:
The quantum tunneling framework is adopted to investigate tunneling radiation of Barriola-Vilenkin black hole with a global monopole. We obtain a conclusion that the emission rate of massive particles is related with the change of Bekenstein-Hawking entropy. The emission rates of massless and massive particles take the same functional form. It is consistent with the underlying unitary theory.

Abstract:
This paper has been withdrawn by the authors in order to replace it with a more correct treatment. The basic results remain the same but the treatment is more rigorously correct.

Abstract:
We consider a class of $(1,M)$-elementary step functions on the $p$-adic Vilenkin group. We prove that $(1,M)$-elementary step function generates a MRA on $p$-adic Vilenkin group iff it is generated by a rooted tree on the set of vertices $\{0,1,\dots p-1\}$ with 0 as a root. Bibliography: 14 titles.

Abstract:
Let G be a locally compact Vilenkin group. In this paper, the authors investigate the boundedness of multilinear commutators of fractional integral operator on Lebesgue spaces on G. Furthermore, the boundedness on Hardy spaces are also obtained in this paper.

Abstract:
In this paper we prove and discuss some new $\left(H_{p},weak-L_{p}\right) $ type inequalities of maximal operators of Vilenkin-N\"orlund means with monotone coefficients. We also apply these results to prove a.e. convergence of such Vilenkin-N\"orlund means. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out.