Recently, certain higher dimensional complex manifolds were obtained in [1] by associating a higher dimensional uniformisation to the generalised Teichmüller spaces of Hitchin. The extra dimensions are provided by the “times” of the generalised KdV hierarchy. In this paper, we complete the proof that these manifolds provide the analog of superspace for W-gravity and that Wsymmetry linearises on...

A scale–dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies modified BRS Ward–Identities. The evolution equation is solved for a simple truncation of the space of actions. In 2+ε dimensions, nonperturbative corrections t...

An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after reconstructing an algebraic canonical formulation on analytical dynamics. The remarkable fact is that the constraint equation of the gravitational system is algebraical...

AUSTRACT: T o reduce the roinplex walking dynamics of a biped, we note a particular class of trajectories that is derived by application of gravity compensation to an ideal biped model. The trajectories have following properties: (a) the center of gravity of the body moves horizontally, and (b) the horizontal motion of the center of gravity can be expressed by a simple linear differential equat...

The gravity model of international trade is often applied by economists to explain bilateral between countries. Nevertheless, some estimation practices have been subject criticism, namely how zero values and the heteroskedasticity are handled. This paper proposes new nonlinear techniques address these issues. In particular, we propose standard generalized versions Heckman two-step approach that...

We address the issue of recovering the time-dependent Schrödinger equation from quantum gravity in a natural way. To reach this aim it is necessary to understand the nonoccurrence of certain superpositions in quantum gravity. We explore various possible explanations and their relation. These are the delocalisation of interference terms through interaction with irrelevant degrees of freedom (dec...

This article reports on a student summer project performed in 2006 at the University of Frankfurt. It is addressed to undergraduate students familiar with the basic principles of relativistic quantum mechanics and general relativity. The aim of the project was to study the Dirac equation in curved space time. To obtain the general relativistic Dirac equation we use the formulation of gravity as...