Galewski, Marek
Published in
Proceedings Mathematical Sciences

We provide existence and stability results for semilinear Dirichlet problems with nonlinearity satisfying general growth conditions. We consider the case when both the coefficients of the differential operator and the nonlinear term depend on the numerical parameter. We show applications for the fourth order semilinear Dirichlet problem.

Wen, Jiajin Yuan, Jun Yuan, Shufeng
Published in
Proceedings Mathematical Sciences

Let (GA)n[k](a), An(a), Gn(a) be the third symmetric mean of k degree, the arithmetic and geometric means of a1, …, an (ai > 0, i = 1, …, n), respectively. By means of descending dimension method, we prove that the maximum of p is k−1/n−1 and the minimum of q is n/n−1(k−1/k)k/n so that the inequalities {fx505-1} hold.

Gupta, Ved Prakash
Published in
Proceedings Mathematical Sciences

We give an identification between the planar algebra of the subgroupsubfactor R ⋊ H ⊂ R ⋊ G and the G-invariant planar subalgebra of the planar algebra of the bipartite graph ★n, where n = [G: H]. The crucial step in this identification is an exhibition of a model for the basic construction tower, and thereafter of the standard invariant of R ⋊ H ⊂...

Santhanam, G.
Published in
Proceedings Mathematical Sciences

Let M be a hypersurface in a simply connected space form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{M}\left( \kappa \right) $$\end{document}. We prove som...

Draouil, Belgacem
Published in
Proceedings Mathematical Sciences

We prove a local duality for some schemes associated to a 2-dimensional complete local ring whose residue field is an n-dimensional local field in the sense of Kato-Parshin. Our results generalize the Saito works in the case n = 0 and are applied to study the Bloch-Ogus complex for such rings in various cases.

Gumber, Deepak Kumar Karan, Ram Pal, Indu
Published in
Proceedings Mathematical Sciences

Let G be a group and H be a subgroup of G. A complete description of Δ(G)Δn(H)/Δn + 1(H) is given, and as a consequence the structures of Δ(G)/Δ(H) and Δ2(G)/Δ2(H) are determined. Also, the structure of Δn(G)/Δn(H) for all n ≥ 1 is determined when G is a free group.

Sahin, Bayram
Published in
Proceedings Mathematical Sciences

We study harmonic Riemannian maps on locally conformal Kaehler manifolds (lcK manifolds). We show that if a Riemannian holomorphic map between lcK manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we prove that a Riemannian holomorphic map is har...

Mao, Li-Xin
Published in
Proceedings Mathematical Sciences

A ring is called right P-coherent if every principal right ideal is finitely presented. Let MR be a right R-module. We study the P-coherence of the endomorphism ring S of MR. It is shown that S is a right P-coherent ring if and only if every endomorphism of MR has a pseudokernel in add MR; S is a left P-coherent ring if and only if every endomorphi...

Kulkarni, S. H. Nair, M. T. Ramesh, G.
Published in
Proceedings Mathematical Sciences

Let H1, H2 be Hilbert spaces and T be a closed linear operator defined on a dense subspace D(T) in H1 and taking values in H2. In this article we prove the following results: Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T*T) of T*T, In addition, if H1 = H2 and T is self-adjoint, then inf {‖T x‖: x ∈ D(T) ∩ N(...

Batir, Necdet
Published in
Proceedings Mathematical Sciences

We establish various new inequalities for the Hurwitz zeta function. Our results generalize some known results for the polygamma functions to the Hurwitz zeta function.