For a canonical formulation of quantum gravity, the superspace of all possible 3-geometries on a Cauchy hypersurface of a 3 + 1-dimensional Lorentzian manifold plays a key role. While in the analogous 2 + 1-dimensional case the superspace of all Riemannian 2-geometries is well known, the structure of the superspace of all Riemannian 3-geometries has not yet been resolved at present. In this pap...

A construction of W-symmetries is given only in terms of the nonlocal fields (parafermions ψ α), which take values on the homogeneous space G/U (1) r , where G is a simply connected compact Lie group manifold (its accompanying Lie algebra G is a simple one of rank r). Only certain restriction of the root set of Lie algebra on which the parafermionic fields take values are satisfied, then a cons...

Abstract. We review the current state of the homogeneous Banach space problem. We then formulate several questions which arise naturally from this problem, some of which seem to be fundamental but new. We give many examples defining the bounds on the problem. We end with a simple construction showing that every infinite dimensional Banach space contains a subspace on which weak properties have ...

In 1972, Bennett studied the countable dense homogeneous CDH spaces and in 1992, Fitzpatrick, White, and Zhou proved that every CDH space is a T1 space. Afterward Bsoul, Fora, and Tallafha gave another proof for the same result, also they defined the almost CDH spaces and almost T1, T0 spaces, indeed they prove that every ACDH space is an almost T1 space. In this paper we introduce a new type o...

This note explores the method of A. Néron [5] for constructing elliptic curves of (fairly) high rank over Q . Néron’s basic idea is very simple: although the moduli space of elliptic curves is only 1-dimensional, the vector space of homogeneous cubic polynomials in three variables is 10-dimensional. Therefore, one can construct elliptic curves which pass through any given 9 rational points. Wit...

We consider the mass-subcritical Hartree equation with a homogeneous kernel, in the space of square integrable functions whose Fourier transform is integrable. We prove a global well-posedness result in this space. On the other hand, we show that the Cauchy problem is not even locally wellposed if we simply work in the space of functions whose Fourier transform is integrable. Similar results ar...

We consider two operator space versions of type and cotype, namely Sp-type, Sq-cotype and type (p, H), cotype (q, H) for a homogeneous Hilbertian operator space H and 1 ≤ p ≤ 2 ≤ q ≤ ∞, generalizing “OH-cotype 2” of G. Pisier. We compute type and cotype of some Hilbertian operator spaces and Lp spaces, and we investigate the relationship between a homogeneous Hilbertian space H and operator spa...

We investigate the distribution of eigenvalues of completely nuclear maps on an operator space. We prove that eigenvalues of completely nuclear maps are square-summable in general and summable if the underlying operator space is Hilbertian and homogeneous. Conversely, if eigenvalues are summable for all completely nuclear maps, then every finite dimensional subspace of the underlying operator s...

In absence of explicit solutions of the perturbation equation of a static symmetrical homogeneous space-time, the best we can do is to construct a quasi-transformation. In this framework, we solve the perturbation equation with initial data and a number of results are derived. Far from the horizon of a black hole of even space dimension N , a mass-less field decays as r(−r + t) 1−N 2 −l in spac...