In this article, we prove that the commensurability class of a closed, orientable, hyperbolic 3–manifold is determined by the surface subgroups of its fundamental group. Moreover, we prove that there can be only finitely many closed, orientable, hyperbolic 3–manifolds that have the same set of surfaces.

In this study, we define the hyperbolic Jacobsthal-Lucas numbers and obtain recurrence relations, Binet’s formula, generating function summation formulas for these numbers.

The contrast of an image is a feature which determines how image looks better visually. In this paper, we are analysing the capability of activation functions for contrast enhancement. Activation functions are classically used in neural network. In this paper, Activation function creates a mask which is operated on the image on pixel by pixel basis. On the basis of activation function the pixel...

Despite recent interest in hyperbolic discounting, there has been little discussion of exactly what property of time preferences is instantiated by hyperbolic or quasi-hyperbolic functional forms. The paper revives an earlier proposal in Prelec (1989) that the key property is Pratt– Arrow convexity of the log of the discount function, which corresponds to decreasing impatience (DI) at the level...

We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, the determinant can be related to the Selberg zeta function and thus shown to be an entire function of order two with zeros at the eigenvalues and resonances of the Laplacian. In the hyperbolic near infinity case the d...

A definition and justify a method for constructing the Green’s function of second Darboux problem two-dimensional linear hyperbolic equation order in characteristic triangle is given. In contrast to (well-developed) theory self-adjoint elliptic problems, this has not yet been developed. And case asymmetric boundary value problems such studies have carried out. It shown that general form can be ...

By gluing together copies of an all-right angled Coxeter polytope a number of open hyperbolic 6-manifolds with Euler characteristic −1 are constructed. They are the first known examples of hyperbolic 6-manifolds having the smallest possible volume.