Finite states in 4 quantized dimensional gravity. The anisotropic minisuperspace Ashtekar–Klein–Gordon model (Part I). Abstract In this paper we construct the generalized Kodama state for gravity in the homogeneous anisotropic case coupled to a Klein–Gordon scalar field with constant scalar potential. The basic method is to generate an asymptotic expansion about the pure Kodama state, viewed as...

We present an example of a separable metrizable topological group G having the property that no remainder of it is (topologically) homogeneous. 1. Introduction. All topological spaces under discussion are Tychonoff. A space X is homogeneous if for any two points x, y ∈ X there is a homeomorphism h from X onto itself such that h(x) = y. If bX is a com-pactification of a space X, then bX \ X is c...

This article is concerned with strong propagations of chaos properties in Moran’s type particle interpretations of continuous time Feynman-Kac formulae. These particle schemes can also be seen as approximating models of simple generalized spatially homogeneous Boltzmann equations. We provide a simple, and original semigroup analysis based on empirical tensor measures combinatorics properties, m...

By considering the most general metric which can occur on a contractable two dimensional symplectic manifold, we find the most general Hamiltonians on a two dimensional phase space to which equivariant localization formulas for the associated path integrals can be applied. We show that in the case of a maximally symmetric phase space the only applicable Hamiltonians are essentially harmonic osc...

It turns out that if a reductive complement m of a homogeneous reductive space G/H possesses a number of properties (including its decomposability into an orthogonal sum of three Ad(H)-invariant irreducible subspaces) then there exists a simple way of determining whether an f -structure F on this space belongs to the classes G1f , NKf and Kill f of generalized Hermitian geometry with respect to...

Let V be a finite dimensional Hermitian vector space and K be a compact Lie subgroup of U(V ) for which the representation of K on C[V ] is multiplicity free. One obtains a canonical basis {pα} for the space C[VR] ofK-invariant polynomials on VR and also a basis {qα} via orthogonalization of the pα’s. The polynomial pα yields the homogeneous component of highest degree in qα. The coefficients t...

Finite states in 4 quantized dimensional gravity. The anisotropic minisuperspace Ashtekar–Klein–Gordon model (Part I). Abstract In this paper we construct the generalized Kodama state for gravity in the homogeneous anisotropic case coupled to a Klein–Gordon scalar field with constant scalar potential. The basic method is to generate an asymptotic expansion about the pure Kodama state, viewed as...

We introduce various new type of recurrent sets for finitely generated semigroups on non-compact metric spaces that are conjugacy invariant, and obtain some basic properties chain via these definitions. Moreover, we define the notion weak shadowing property group actions compact spaces, which is weaker than property, prove equivalence a generalized homogeneous space without isolated points.

Let  $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $zeta$ for $varpi$  and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.