Statistical Inference in a Linear Model for Spatially Located Sensors and Random Input

In the paper we consider a random linear model for observations provided by spatially located sensors measuring signals coming from one source. For this model a set of sufficient and complete statistics are found, and it is shown that the maximum likelihood estimators of unknown parameters (characteristics of the source) are functions of those statistics. The problem of nonnegative estimators of variance components of the model is shortly discussed. Comparisons of the mean squared errors of several estimators are given. Numerical example concerning hunting for defects in solar cells is considered in details.     

Identification of MMP-1 and MMP-9 inhibitors from the roots of Eleutherococcus divaricatus,and the PAMPA test

The purpose of this study was the isolation of metalloproteinases MMP-1 and MMP-9 inhibitors from the chloroform extract of the Eleutherococcus divaricatus roots. Using GC-MS, ¹H and ¹³C NMR, HMQC, HMBC, COSY and DEPT, (+)-sesamin has been identified as a new anti-MMP inhibitor. We report for the first time that (+)-sesamin inhibited MMP-1 and MMP-9 activity in 40% and 17%, respectively. The high inhibitory potential has been shown by ursolic acid (90.9% and 89.8% for MMP-1 and MMP-9). In the PAMPA test, the Pe value for sesamin was established as 17.4 × 10^? 6 cm/s, that for ursolic acid as 30.0 × 10^? 6 cm/s. Verapamil and theophylline were used as a positive and negative control (Pe 42.1 and 2.9 × 10^? 6 cm/s). To our best knowledge, no information was available on this activity of sesamin and other compounds. These studies provide a biochemical basis for the regulation of MMP-1 and MMP-9 by E. divaricatus compounds.     

Optimum experimental design for a regression on a hypercube-generalization of Hoel's result

In the note Hoel's result (1965, Ann. Math. Statist., 36, 1097–1106) is generalized to a large family of experimental design optimality criterions. Sufficient conditions for optimality criterion are given, which ensure existence of the optimum experimental design measure which is a product of design measures on lower dimensional domains.     

Isotropic models for a heat transfer in periodic composites

A macroscopic model for the non – stationary heat transfer processes in a periodic honeycomb – type anisotropic rigid conductor is formulated. The main aim of this contribution is to show that the macroscopic properties of this conductor are isotropic. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)