In the literature, little attention is paid to devising and analyzing novel one dimensional chaotic mappings. our previous efforts, we have tried fold, translation & scale on arctangent function sigmoid respectively, which brings good results. this paper, do same obtain a variant of Hyperbolic Cosine Function. Both Bifurcation Diagram Lyapunov Exponent Spectrum manifest that new mapping pos...

In this paper, we show that the number of hyperbolic gravitational instantons grows superexponentially with respect to volume. As an application, we show that the Hartle-Hawking wave function for the universe is infinitely peaked at a certain closed hyperbolic 3-manifold. PACS numbers: 0460M, 9880H

Inequalities connecting inverse circular and inverse hyperbolic functions are obtained. Also, bounds for the inverse hyperbolic sine function are established. Some of the results presented in this paper are derived from the inequalities satisfied by particular bivariate means which belong to the family of the Schwab-Borchardt means. Mathematics subject classification (2010): Primary: 26D07; Sec...

This paper is devoted to the study of the compact hyperbolic 3-manifolds uniformized by the Fibonacci groups. It is shown that their volumes are equal to volumes of non-compact hyperbolic 3-manifolds arising as complements of some well-known knots. All these volumes are described in terms of the Lobachevsky function.

We deal with a perturbation of a hyperbolic integrable Hamiltonian system with n+ 1 degrees of freedom. The integrable system is assumed to have n-dimensional hyperbolic invariant tori with coincident whiskers (separatrices). Following Eliasson, we use a geometric approach closely related to the Lagrangian properties of the whiskers, to show that the splitting distance between the perturbed sta...

A large class of explicit hyperbolic monopole solutions can be obtained from JNR instanton data, if the curvature of hyperbolic space is suitably tuned. Here we provide explicit formulae for both the monopole spectral curve and its rational map in terms of JNR data. Examples with platonic symmetry are presented, together with some one-parameter families with cyclic and dihedral symmetries. Thes...

In Analytic SSA, an approximate upper bound to the logdet term in Eq. 4 is computed (Hara et al., 2012). Without re-deriving this bound entirely, we present its final steps, which we use to obtain the bounds for KSSA and NLSSA.

This work presents a control strategy using a network with radial basis function (RBF network) with adaptation in dual mode. The objective of the strategy is to use the approximate capacity of the RBF network to control nonlinear systems with unknown parameters or with uncertainties. The proposed control uses the structure of Model Reference Adaptive Control (MRAC) and a RBF network whose param...