Stable Exponents in Discrete Groups

It is known that in a word hyperbolic group the stable exponent of every nontorsion element is an integer. We prove that this is also true in finitely generated nilpotent groups. On the other hand, we show that for any rational number 1 there exists a torsionfree CAT(0) group containing an element whose stable exponent is equal to .     

Blow-up of semilinear pde's at the critical dimension. A probabilistic approach

We present a probabilistic approach which proves blow-up of solutions of the Fujita equation in the critical dimension . By using the Feynman-Kac representation twice, we construct a subsolution which locally grows to infinity as . In this way, we cover results proved earlier by analytic methods. Our method also applies to extend a blow-up result for systems proved for the Laplacian case by Escobedo and Levine (1995) to the case of -Laplacians with possibly different parameters .

     

Stable conformations of 12-crown-O3N and its Li+ complex in aqueous solution

Stable conformations of 12-crown-O3N and its Li complexes in aqueous solution were investigated. To calculate the free energy differences of conformers of 12-crown-O3N and its Li+ complex, our procedure was to make use of two programs, CONFLEX and BOSS. The former generates conformers, and the latter calculates the differences in free energy of solvation between two conformers in aqueous solution. It was confirmed that the present procedure is applicable in solving the question of what is the most stable conformation of 12-crown-O3N in aqueous solution. Results of the calculations suggest that the order of stability for conformers in a vacuum is different from that in aqueous solution. It was also confirmed that the coordination geometry of solvent waters to Li+ changes depending on the distance between the cation and the crown ring.     

Uniform dimension results of multi-parameter stable processes

The problem of uniform dimensions for multi-parameter processes, which may not possess the uniform stochastic Hölder condition, is investigated. The problem of uniform dimension for multi-parameter stable processes is solved. That is, ifZ is a stable (N,d, α)-process and αN ?d, then $\forall E \subseteq \mathbb{R}_ + ^N , \dim Z\left( E \right) = \alpha \cdot \dim E$ holds with probability 1, whereZ(E) = {x : ?t ∈E,Z _t =x} is the image set ofZ onE. The uniform upper bounds for multi-parameter processes with independent increments under general conditions are also given. Most conclusions about uniform dimension can be considered as special cases of our results.     

关于环的稳定度一个注记

我们得到了环的稳定度为2或∞的一个充分条件,并进给出了SBN环的稳定度     

Some remarks on the real rank of non-unital C*-algebras

For a non-unital C-algebra , let be the C-algebra obtained from by adjoining an identity. In this paper we show that

where is a locally compact Hausdorff space with .

     

Certain Probabilistic Aspects of Semistable Laws

We study the extent to which the property of semistability of a random vector in ^d is determined by semistability of its marginals, and the place of semistable laws within the family of type G and sub-stable laws. Similarities and differences between stable and semistable laws are discussed.     

Pre-limit Theorems and Their Applications

There exists a considerable debate in the literature about the applicability of -stable distributions as they appear in Lévy"s central limit theorems. A serious drawback of Lévy"s approach is that, in practice, one can never know whether the underlying distribution is heavy tailed, or just has a long but truncated tail. Limit theorems for stable laws are not robust with respect to truncation of the tail or with respect to any change from 'light" to 'heavy" tail, or conversely. In this talk we provide a new 'pre-limiting" approach that helps overcome this drawback of Lévy-type central limit theorems.     

Derivation of a new class of distributions for the microcanonical ensemble

A new class of distributions for the microcanonical ensemble, which are shown to be stable laws, are derived by applying the central limit theorem to the canonical ensemble. This opens up a whole new host of phenomena that can be treated from a unified thermodynamic point of view. Pressure broadening of line shapes is used as an illustration.1. Work supported, in part, by contributions from the Consiglio Nazionale di Ricerche and the Ministero dell'Università e della Ricerca Scientifica e Tecnologica.2. The interaction parameterC is proportional to the mean square dipole moment. As an order of magnitude of the dipole moment, we can take it as the product of the electric charge and a typical atomic radius for a moderately excited state, which is several times the Bohr radius. Multiplication by the fine structure constant converts the Bohr radius into the Compton wavelength, thereby reducing the magnitude of the interaction by 1/137.     

Two definitions of exponential dichotomy for skew-product semiflow in Banach spaces

In this paper we introduce a concept of exponential dichotomy for linear skew-product semiflows (LSPS) in infinite dimensional Banach spaces, which is an extension of the classical concept of exponential dichotomy for time dependent linear differential equations in Banach spaces. We prove that the concept of exponential dichotomy used by Sacker-Sell and Magalhães in recent years is stronger than this one, but they are equivalent under suitable conditions. Using this concept we where able to find a formula for all the bounded negative continuations. After that, we characterize the stable and unstable subbundles in terms of the boundedness of the corresponding projector along (forward/backward) the LSPS and in terms of the exponential decay of the semiflow. The linear theory presented here provides a foundation for studying the nonlinear theory. Also, this concept can be used to study the existence of exponential dichotomy and the roughness property for LSPS.