In this paper, the authors provide several sharp upper and lower bounds for Neuman–Sándor mean in terms of arithmetic contra-harmonic means, present some new inequalities involving hyperbolic sine function cosine function.

Abstract. In this article we study harmonic functions for the Laplace-Beltrami operator on the real hyperbolic space Bn. We obtain necessary and sufficient conditions for this functions and their normal derivatives to have a boundary distribution. In doing so, we put forward different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball Bn. ...

We construct all possible orthogonally intersecting S-brane solutions in 11-dimensions corresponding to standard supersymmetric M-brane intersections. It is found that the solutions can be obtained by multiplying the brane and the transverse directions with appropriate powers of two hyperbolic functions of time. This is the S-brane analog of the " harmonic function rule ". The transverse direct...

We construct all possible orthogonally intersecting S-brane solutions in 11-dimensions corresponding to standard supersymmetric M-brane intersections. It is found that the solutions can be obtained by multiplying the brane and the transverse directions with appropriate powers of two hyperbolic functions of time. This is the S-brane analog of the " harmonic function rule ". The transverse direct...

The purpose of this article is to provide an explicit construction for a family of singular instantons on S 4 \ S 2 with arbitrary real holonomy parameter α. This family includes the original α = 1/4, c2 = 3/2 solution discovered by P. Forgács, Z. Horváth, and L. Palla, and our approach is modeled on that of their 1981 paper. Our primary tool is the ansatz due to Corrigan, Fairlie, Wilczek, and...

In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are presented.

We show that noncompact simply connected harmonic manifolds with volume density Θ p (r) = sinh n−1 r is isometric to the real hyperbolic space and noncompact simply connected Kähler harmonic manifold with volume density Θ p (r) = sinh 2n−1 r cosh r is isometric to the complex hyperbolic space. A similar result is also proved for Quaternionic Kähler manifolds. Using our methods we get an alterna...

We obtain a new result concerning harmonic functions on Cayley graphs X: either every nonconstant harmonic function has large radial variation (in a certain sense), or there is a nontrivial hyperbolic boundary at infinity of X. In the latter case, relying on a theorem of Woess, it follows that the Dirichlet problem is solvable with respect to this boundary. Certain relations to group cohomology...

We obtain a new result concerning harmonic functions on infinite Cayley graphs X : either every nonconstant harmonic function has infinite radial variation in a certain uniform sense, or there is a nontrivial boundary with hyperbolic properties at infinity of X . In the latter case, relying on a theorem of Woess, it follows that the Dirichlet problem is solvable with respect to this boundary. C...