A Bitangential Interpolation Problem on the Closed Unit Ball for Multipliers of the Arveson Space

We solve a bitangential interpolation problem for contractive multipliers on the Arveson space with an arbitrary interpolating set in the closed unit ball . The solvability criterion is established in terms of positive kernels. The set of all solutions is parametrized by a Redheffer transform. Submitted: February 2, 2002.     

Information processing,memories, and synchronization in chaotic neural network with the time delay

Information processing and two types of memory in an analog neural network model with time delay that produces chaos similar to the human and animal EEGs are considered. There are two levels of information processing in this neural network: the level of individual neurons and the level of the neural network. Similar to the state of brain, the state of chaotic neural network is defined. It is characterized by two types of memories (memory I and memory II) and correlation structure between the neurons. In normal (unperturbed) state, the neural network generates chaotic patterns of averaged neuronal activities (memory I) and patterns of oscillation amplitudes (memory II). In the presence of external stimulation, the activity patterns change, showing changes in both types of memory. As in experiments on stimulation of the brain, the neural network model shows synchronization of neuronal activities due to stimulus measured by Pearson's correlation coefficient. An increase in neural network asymmetry (increase of the neural network excitability) leads to the phenomenon similar to the epilepsy. Modeling of brain injury, Parkinson's disease, and dementia is performed by removing and weakening interneuron connections. In all cases, the chaotic neural network shows a decrease of the degree of chaos and changes in both types of memory similar to those observed in experiments with healthy human subjects and patients with Parkinson's disease and dementia. © 2005 Wiley Periodicals, Inc. Complexity 11:39–52, 2005     

Crystallographic report: Crystal structure of 1‐bromo‐1′‐[(2S)‐N‐(1‐hydroxy‐3‐methylbutane‐2‐yl)]‐ferroceneamide

For the unsymmetrical title compound, 1‐bromo‐1′‐[(2S)‐N‐(1‐hydroxy‐3‐methylbutane‐2‐yl)]‐ferroceneamide, two independent molecules were found in the asymmetric unit. Copyright © 2003 John Wiley & Sons, Ltd.     

The quantum Weyl group and the universal quantumR-matrix for affine lie algebraA1(1)

The universal quantumR-matrix is obtained in the case of the affine Kac-Moody Lie algebra sl(2).     

Estimates for the Rapid Decay of Concentration Functions of n-Fold Convolutions

We estimate the concentration functions of n-fold convolutions of one-dimensional probability measures. The Kolmogorov–Rogozin inequality implies that for nondegenerate distributions these functions decrease at least as O(n ^–1/2). On the other hand, Esseen⁽³⁾ has shown that this rate is o(n ^–1/2) iff the distribution has an infinite second moment. This statement was sharpened by Morozova.⁽⁹⁾ Theorem 1 of this paper provides an improvement of Morozova's result. Moreover, we present more general estimates which imply the rates o(n ^–1/2).     

ContributionsTriangular embeddings of Kn−Km with unboundedly large m

The author has proposed methods of constructing index 2 and 3 current graphs generating triangular embeddings of graphs K_n−K_m with unboundedly large m (as n increases). As a result, triangular embeddings of graphs of many families of graphs K_n−K_m with unboundedly large m were constructed. The paper gives a survey of these results and a short explanation of the methods.