Pandres has developed a theory in which the geometrical structure of a real four-dimensional space-time is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group called the conservation group. This paper extends the geometrical foundation for Pandres’ theory by developing an appropriate covariant derivative which is covariant under all local Loren...

We suggest two grand unified models where the fifth dimensional coordinate is compactified on an S1/(Z2 × Z ′ 2) orbifold. Before showing the models, let us see the compactification of the fifth dimension. We denote the five dimensional coordinate as y, which is compactified on an S1/(Z2 × Z ′ 2) orbifold. Under the parity transformation of Z2 and Z ′ 2, which transform y → −y and y ′ → −y (y =...

The brain processes sensory and motor information in a wide range of coordinate systems, ranging from retinal coordinates in vision to body-centered coordinates in areas that control musculature. Here we focus on the coordinate system used in the motor cortex to guide actions and examine physiological and psychophysical evidence for an allocentric reference frame based on spatial coordinates. W...

The unified hybrid censoring is a mixture of generalized Type-I and Type-II hybrid censoring schemes. This article presents the statistical inferences on Generalized Exponential Distribution parameters when the data are obtained from the unified hybrid censoring scheme. It is observed that the maximum likelihood estimators can not be derived in closed form. The EM algorithm for computing the ma...

We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the Minkowskian spacetimes by an extra “dilatonic” coordinate, whose rotation, Lorentz and conformal groups are SO(d−1), SO(d−1, 1)×SO(1, 1) and SO(d, 2)×SO(2, 1), respective...

Evolution characteristics of a Kerr black hole (BH) are investigated by considering coexistence of disc accretion with the Blandford-Znajek process (the BZ process) and magnetic coupling of the BH with the surrounding disc (MC process). (i) The rate of extracting energy from the rotating BH in the BZ process and that in MC process are expressed by a unified formula, which is derived by using an...

We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the Minkowskian spacetimes by an extra “dilatonic” coordinate, whose rotation, Lorentz and conformal groups are SO(d−1), SO(d−1, 1)×SO(1, 1) and SO(d, 2)×SO(2, 1), respective...

Multiresolution motion analysis has gained great research interest as a unified framework to facilitate a variety of motion editing tasks. In this framework, motion data are represented as a collection of coefficients that form a coarse-to-fine hierarchy. The coefficients at the coarsest level describe the global pattern of a motion signal, while those at fine levels provide different details a...

In this paper, I show that multimodal categorial type logic provides us with a system of linguistic inference which is fine-grained enough to give an adequate account of the forms of ellipsis that show up in coordinate constructions and comparatives. I present a unified account of Gapping in coordinate constructions and Subdeletion in clausal comparatives, improving on earlier work of Morrill (...

This paper aims to introduce readers with backgrounds in classical molecular dynamics to some ideas in geometric mechanics that may be useful. This is done through some simple but specific examples: (i) the separation of the rotational and internal energies in an arbitrarily floppy N-body system and (ii) the reduction of the phase space accompanying the change from the laboratory coordinate sys...