On Ergodic Operator Means in Banach Spaces

We consider a large class of operator means and prove that a number of ergodic theorems, as well as growth estimates known for particular cases, continue to hold in the general context under fairly mild regularity conditions. The methods developed in the paper not only yield a new approach based on a general point of view, but also lead to results that are new, even in the context of the classical Cesàro means.     

Representation Results for Equivariant Rigid Analytic Functions

Given a prime number p and the Galois orbit O(x) of an element x of ℂ _p , the topological completion of the algebraic closure of the field of p-adic numbers, we are interested in the representation results for equivariant rigid analytic functions defined on ℙ¹(ℂ _p ) O(x) with values in ℂ _p that vanishes at ∞.     

On the singularities of multiple L-functions

We investigate the singularities of a class of multiple L-functions considered by Akiyama and Ishikawa [2].     

Hindered rotation around the N(sp2)-C(sp3) single bond in 2,4,6-trimethyl-N-alkylpyridinium cations:H DNMR analysist

Pairwise chemical shift nonequivalence of the 2,6-methyl and 3,5-protons in ¹H NMR spectra, as well as of the 2,6-methyl, 2,6-ring and 3,5-ring carbons in ¹³C NMR spectra, was observed for N-alkyl-2,4,6-trimethylpyridinium salts 2. Dynamic NMR spectroscopy demonstrates appreciably higher activation free energies ΔG^# for rotation around the N(sp²)-C(sp³ bond than ΔG# for the analogously substituted mesityl derivatives, in agreement with the shorter N-C bond distance than for the C-C bond.     

On a multivariate Pareto distribution

A multivariate distribution possessing arbitrarily parameterized Pareto margins is formulated and studied. The distribution is believed to allow for an adequate modeling of dependent heavy tailed risks with a non-zero probability of simultaneous loss. Numerous links to certain existing probabilistic models, as well as seemingly useful characteristic results are proved. Expressions for, e.g., decumulative distribution functions, densities, (joint) moments and regressions are developed. An application to the classical pricing problem is considered, and some formulas are derived using the recently introduced economic weighted premium calculation principles.     

Search for nondegenerate real vertex invariants and derived topological indexes

Two new types of real (i.e., noninteger) local vertex invariants (LOVIs), denoted by c_i and c′_i and called distance-enhanced exponential connectivities, are defined via eqs. (1)–(3) and (1′)–(3′), respectively. Only the case when the exponent z equals 1 in eqs. (3) and (3′) is discussed in detail. Both these LOVIs span the range from 0–1, but their dependence upon topology is fairly different, as seen from Table II, where c_i and c′_i values for all heptane and octane isomers are displayed. From these LOVIs, by simple summation over all graph vertices two new topological indexes (TIs), denoted by XC and XC′, respectively, are obtained. Their intermolecular ordering of all alkanes with four to nine carbon atoms is discussed. On their basis, correlations with boiling points and critical pressures of alkanes are presented. © 1993 John Wiley & Sons, Inc.     

Dual action of Impurities in Crystal Growth from Solutions

A dual action of impurities becomes evidently in growth kinetic of prismatic faces of KDP. At higher supersaturation two-dimensional nucleation mechanism due to impurities prevails. At smaller supersaturation the blocking effect of the steps created by the dislocation mechanism of growth become efficient. The limit of the “dead” growth zone depending on the impurity's concentration and the solution pH is a result of this last effect and agrees with the Cabrera-Vermilyea mechanism.