We study the the tangent family F = {λ tan z, λ ∈ C − {0}} and give a complete classification of their stable behavior. We also characterize the the hyperbolic components and give a combinatorial description of their deployment in the parameter plane.

In this paper, the hyperbolic tangent function (tanh) method is used in finding soliton solutions of Generalized Fisher Equation (GFE) and Spalding Equation (SE). It is shown that the tanh method provides a straight forward and powerful tool for solving Nonlinear Evolution Equations (NLEEs) in Mathematical Physics.

In this note we construct a family of parametric Soboleva’ modified hyperbolic tangent activation function (PSMHTAF). We prove upper and lower estimates for the Hausdorff approximation of the sign function by means of this family. Numerical examples, illustrating our results are given.

Information about the interval numbers presented in classical form, CENTER-RADIUS system and hyperbolic form is given. Rules for transition from one of forms representation to others are proposed. given on complex numbers, real imaginary parts which form. The rules performing basic arithmetic operations with these calculation values power, exponential, logarithmic functions, direct inverse trig...

We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations...

We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of the dynamics of center disks, is introduced. Some results on shadowing near a non-hyperbolic fixed point of a homeomorphism are obtained.

For complex parameters a, c, we consider the Hénon mapping Ha,c : C → C, given by (x, y) 7→ (x + c−ay, x), and its Julia set, J . In this paper, we describe a rigorous computer program for attempting to construct a cone field in the tangent bundle over J , which is preserved by DH, and a continuous norm in which DH (and DH) uniformly expands the cones (and their complements). We show a conseque...

— We consider a partially hyperbolic set K on a Riemannian manifold M whose tangent space splits as TKM = Ecu⊕Es, for which the centre-unstable direction E expands non-uniformly on some local unstable disk. We show that under these assumptions f induces a Gibbs-Markov hyperbolic structure. Moreover, the decay of the return time function can be controlled in terms of the time typical points need...

New examples of harmonic unit vector fields on hyperbolic 3-space are constructed by exploiting the reduction of symmetry arising from the foliation by horospheres. This is compared and contrasted with the analogous construction in Euclidean 3-space, using a foliation by planes, which produces some new examples of harmonic maps from 3-dimensional Euclidean domains to the 2-sphere. Finally, the ...

The Descartes circle theorem states that if four circles are mutually tangent in the plane, with disjoint interiors, then their curvatures (or “bends”) bi = 1 ri satisfy the relation (b1 + b2 + b3 + b4) 2 = 2(b1 + b 2 2 + b 2 3 + b 2 4). We show that similar relations hold involving the centers of the four circles in such a configuration, coordinatized as complex numbers, yielding a complex Des...