G 󸀠 /G-expansion method which is employed to investigate the solitary and periodic traveling waves of this equation. As a result, some new traveling wave solutions involving hyperbolic functions, the trigonometric functions, are obtained.When the parameters are taken as special values, the solitary wave solutions are derived from the hyperbolic function solutions, and the periodic wave solution...

There is a quadratic-time algorithm that determines conjugacy between finite subsets in any torsion-free hyperbolic group. Moreover, in any k-generator, δ-hyperbolic group Γ, if two finite subsets A and B are conjugate, then x−1Ax = B for some x ∈ Γ with ‖x‖ less than a linear function of max{‖γ‖ : γ ∈ A∪B}. (The coefficients of this linear function depend only on k and δ.) These results have i...

We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to “Hyperbolic phase space” (η, pη). We show that this new unitary change of basis from the position x on the half line to the Hyperbolic momentum pη, transforms the wavefunction via a Mellin transform on to the critial line s = 1/2 − ipη. We utilise this new transform to find quantum...

The infeasibility problem in traditional super efficiency models has been well established. A generalization of traditional inputor output-oriented super efficiency models, the directional distance function also suffers from infeasibility and related problems. The hyperbolic-oriented efficiency measure provides an alternative to the input-oriented, output-oriented, and directional efficiency me...

We calculate the Chern-Simons invariants of hyperbolic double twist knot orbifolds using Schl\"{a}fli formula for generalized function on family cone-manifold structures knots.

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.

It is proved that the volume of spherical or hyperbolic simplices, when considered as a function of the dihedral angles, can be extended continuously to degenerated simplices. §1. Introduction 1.1. It is well known that the area of a spherical or a hyperbolic triangle can be expressed as an affine function of the inner angles by the Gauss-Bonnet formula. In particular, the area considered as a ...

Let f : D → C be an analytic function on the unit disc which is in the Dirichlet class, so the Euclidean area of the image, counting multiplicity, is finite. The Euclidean length of a radial arc of hyperbolic length ρ is then o(ρ). In this note we consider the corresponding results when f maps into the unit disc with the hyperbolic metric or the Riemann sphere with the spherical metric. Similar...

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...