We discuss from a bi-Hamiltonian point of view the Hamilton–Jacobi separability of a few dynamical systems. They are shown to admit, in their natural phase space, a quasi–bi– Hamiltonian formulation of Pfaffian type. This property allows us to straightforwardly recover a set of separation variables for the corresponding Hamilton–Jacobi equation.

This paper is concerned with embeddings of homogeneous spaces into Euclidean spaces. We show that any homogeneous metric space can be embedded into a Hilbert space using an almost bi-Lipschitz mapping (biLipschitz to within logarithmic corrections). The image of this set is no longer homogeneous, but ‘almost homogeneous’. We therefore study the problem of embedding an almost homogeneous subset ...

We prove a few basic facts about the space of bi-invariant (or left-invariant) total order relations on a torsion-free, nonabelian, nilpotent group G. For instance, we show that the space of bi-invariant orders has no isolated points (so it is a Cantor set if G is countable), and give examples to show that the outer automorphism group of G does not always act faithfully on this space. Also, it ...

In this study, we consider bi-f -harmonic Legendre curves in Sasakian space forms. We investigate necessary and sufficient conditions for a curve to be various cases.

We give a sufficient condition for a projective metric on a subset of a Euclidean space to admit a bi-Lipschitz embedding into Euclidean space of the same dimension.

Bi-Objective Modelling for Hazardous Materials Road-Rail Multimodal Routing Problem with Railway Schedule-Based Space-Time Constraints.[...].

We show how to combine, into one unified spline complex, C2 tensorproduct bi-cubic NURBS and G2 bi-cubic rational splines. The G2 splines are capable of exactly representing basic shapes such as (pieces of) quadrics and surfaces of revolution, including tori and cyclides. The main challenge is to bridge the differing continuity. We transform the G2 splines to splines that are C2 in homogeneous ...

The genesis of this paper is the construction of a new operator that, when combined with a theorem of Herrero, settles a question of Herrero. Herrero proved that a strictly cyclic operator on an infinite dimensional Hilbert space is never triangular. He later asks whether the adjoint of a strictly cyclic operator is necessarily triangular. We settle the question by constructing an operator T fo...