A general method for solving the Cosmological Einstein’s Field Equations (EFE) in vacuum is presented, and is applied to the Bianchi Type III vacuum cosmology. As a result, the entire space of solutions for this model is found. This space is composed of two distinct, disconnected ,three-parameter families. Both of them admit four Killing vector Fields and no homothetic vector. One family repres...

We review the similarity solutions proposed by Waylen for a regular time-dependent axisymmetric vacuum space-time, and show that the key equation introduced to solve the invariant surface conditions is related by a Bäcklund transform to a restriction on the similarity variables. We further show that the vacuum space-times produced via this path automatically possess a (possibly homothetic) Kill...

We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the matter field is provided by a YangMills field, with or without mass term, if the spatial geometry of the underlying spacetime is homothetic to R. The energy levels of the resulting quantum model, i.e., the eigenvalues of the corresponding self-adjoint Hamiltonian with a pure point spectrum, are strictly posi...

We consider n-body problems given by potentials of the form α r + β r with a, b, α, β constants, 0 ≤ a < b. To analyze the dynamics of the problem, we first prove some properties related to central configurations, including a generalization of Moulton’s theorem. Then we obtain several qualitative properties for collision and near-collision orbits in the Manev-type case a = 1. At the end we poin...

A large class of Type II fluid solutions to Einstein field equations in Ndimensional spherical spacetimes is found, wich includes most of the known solutions. A family of the generalized collapsing Vaidya solutions with homothetic self-similarity, parametrized by a constant λ, is studied, and found that when λ > λc(N), the collapse always forms black holes, and when λ < λc(N), it always forms n...

the main objective of this article is to optimize the walking pattern of a 2d humanoid robot with heel-off and toe-off motions in order to minimize the energy consumption and maximize the stability margin. to this end, at first, a gait planning method is introduced based on the ankle and hip joint position trajectories. then, using these trajectories and the inverse kinematics, the position tra...

The traditional economic approach to index number theory is based on a ratio concept. The Konüs true cost of living index is a ratio of cost functions evaluated at the same utility level but with the prices of the current period in the cost function that appears in the numerator and the prices of the base period in the denominator cost function. The Allen quantity index is also a ratio of cost ...

Wide field interferometry has become a subject of increasing interest in the recent years. New methods have been suggested in order to avoid the drawbacks of the standard wide field method (homothetic mapping) which is not applicable when the aperture is highly diluted; for this reason imaging with non-homothetic arrays is being extensively studied1,2. The field of view of a pupil plane interfe...