In order to gain insight into the possible Ground State of Quantized Einstein’s Gravity, we have derived a variational calculation of the energy of the quantum gravitational field in an open space, as measured by an asymptotic observer living in an asymptotically flat space-time. We find that for Quantum Gravity (QG) it is energetically favourable to perform its quantum fluctuations not upon fl...

Let X be a rank one Riemannian symmetric space of noncompact type. We recall that such a space can be realized as G/K, where G is a connected noncompact semisimple Lie group of real rank one with finite center and K is a maximal compact subgroup of G. Anker [2], in his paper gave a remarkably short and elegant proof of the Lp-Schwartz space isomorphism theorem for K bi-invariant functions on G ...

Die Verwendung von ID/LP-Grammatiken und komplexen Symbolen ist bei Flektionsreichen und in der Wortstellung flexiblen Sprachen wie dem Deutschen erfolgversprechender als der Rückgriff auf kontextfreie Grammatiken (cfg). Dieser Artikel beschreibt in einem ersten Schritt die dafür notwendigen Veränderungen des TomitaAlgorithmus und dessen Tabellengenerators. In einem zweiten Schritt werden wir a...

1. Notation and introduction. By LP (1 ^ p < oo ) will be understood the class of real valued measurable functions c/>(P), O^P^l, for which f \iP) \pdP< oo, by SPiX) the class of measurablef functions/(P) on (0,1) to the space X of type B [seej 1, p. 53] for which /J|/(P)||pdP< oo. With ||/||= {/J|/(P)||pdP}1/",5P(Ar) is a Banach space. In case p > 1, Lp. is defined by the equality p,=1p/ip—...

The pulvinar is the largest extrageniculate thalamic visual nucleus in mammals. It establishes reciprocal connections with virtually all visual cortexes and likely plays a role in transthalamic cortico-cortical communication. In cats, the lateral posterior nucleus (LP) of the LP-pulvinar complex can be subdivided in two subregions, the lateral (LPl) and medial (LPm) parts, which receive a predo...

In the last few years a large number of papers have appeared in the literature dealing with the weak convergence of iterates of contractions and strong convergence of their averages. The trend started with the Blum-Hanson Theorem [3]. The latest result in this direction is due to Akcoglu and Sucheston [ 1 ], [2]. The purpose of this paper is to give a simple, straightforward proof of the Adcogl...

This paper presents novel techniques that allow the solution to several open problems regarding embedding of finite metric spaces into Lp. We focus on proving near optimal bounds on the dimension with which arbitrary metric spaces embed into Lp. The dimension of the embedding is of very high importance in particular in applications and much effort has been invested in analyzing it. However, no ...

We develop a detailed regularity theory of −∆+ b · ∇ in L(R), for a wide class of vector fields. The L-theory allows us to construct associated strong Feller process in C∞(R ). 1. Let Ld be the Lebesgue measure on Rd, Lp = Lp(Rd,Ld) and W 1,p = W 1,p(Rd,Ld) the standard Lebesgue and Sobolev spaces, C0,γ = C0,γ(Rd) the space of Hölder continuous functions (0 < γ < 1), Cb = Cb(R d) the space of b...

In this paper, we present an analysis expression of p∗(A, b) such that the unique solution to l0-minimization also can be the unique solution to lp-minimization for any 0 < p < p ∗(A, b). Furthermore, the main contribution of this paper isn’t only the analysis expressed of such p∗(A, b) but also its proof. Finally, we display the results of two examples to confirm the validity of our conclusion...

We analyse the well-posedness of the initial value problem for the dissipative quasigeostrophic equations in the subcritical case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions. We prove that the only small self-similar solution in the strong Lp space is the null solution while infinitely many self-similar solutions do ...