Position vector of spacelike biharmonic curves in the Lorentzian Heisenberg group .
In this paper we follow our previous research in the field of positioned agents in the eco-grammar systems and pure grammars. We extend model of the positioned eco-grammar systems by boundary markers and we introduce bordered positioned eco-grammar systems (BPEG systems, for short) and that way we show one of the possible answers to the question stated in [9]. Namely we compare generative power of the BPEG systems with three types of pure regulated grammars with appearance checking.
Gravitational radiation from a small mass particle orbiting a massive black hole can be analytically studied to a very high order in the post-Newtonian expansion. Thus it gives us useful information on the evolution of a coalescing compact binary star. In this talk, I report on recent progress made in the black-hole perturbation approach.
A post-Newtonian approximation scheme for general relativity is defined using the Arnowitt-Deser-Misner formalism. The scheme is applied to perfect fluids and point-mass systems. The two-body point-mass Hamiltonian is given explicitly up to the post-Newtonian order.
The post-Newtonian (PN) hydrodynamic equations are obtained in the (3+1) formalism, which include the 2.5PN order as the reaction due to the quadrupole gravitational radiation. These equations are valid in various slice conditions, while we adopt a kind of transverse gauge condition to determine the shift vector. In particular, we describe methods to solve the 2PN tensor potential which arises from the spatial 3-metric. Our formulaton in the PN approximation using the (3+1) formalism will be useful...