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.     

Prediction of protein structure using a knowledge-based off-lattice united-residue force field and global optimization methods

A united-residue model of polypeptide chains developed in our laboratories with united side-chains and united peptide groups as interaction sites is presented. The model is designed to work in continuous space; hence efficient global-optimization methods can be applied. In this work, we adopted the distance-scaling method that is based on continuous deformation of the original rugged energy hypersurface to obtain a smoothed surface. The method has been applied successfully to predict the structures of simple motifs, such as the three-helix bundle structure of the 10-58 fragment of staphylococcal protein A in de novo folding simulations and more complicated motifs in inverse-folding simulations. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Nonnegative quadratic estimation of the mean squared errors of minimax estimators in the linear regression model

In this paper, the problem of nonnegative quadratic estimation of the mean squared errors of minimax estimators of in the linear regression modelE(y)=X, VAR(y) = ² is discussed. An explicit formula for the admissible nonnegative minimum biased estimator is given. Some applications to one-way classification model are also considered.     

Bayes estimation in linear models: A coordinate-free approach

The unified theory of Bayes estimation in linear models is presented, using a coordinate-free approach. The results are applied to the problem of linear and quadratic estimation in linear regression model.     

6-Nitrohexene-1 Metathesis in the Presence of Rhenium Heterogeneous Catalysts

6-nitrohexene-1 (6-NH-1) undergoes metathesis in the presence of 16 wt.% Re₂O₇/Al₂O₃/R₄M and 3 wt.% Re₂O₇/Al₂O₃-SiO₂/R₄M (where R = methyl, ethyl; M = Sn or Pb) catalysts. The system containing alumina as a support is more active. Tetramethyltin (TMT) and tetraethyllead (TEL) used as co-catalysts, exhibited similar activating effect which was greater than with tetraethyltin (TET). The best results were obtained when the Re:Sn(Pb) and 6-NH-1:Re ratios were equal, respectively, to 1:1 and 10:1. The alumina-silica supported catalysts activity can be enhanced by doping the support with very small amounts of molybdenum ions.     

Nonnegative Minimum Biased Quadratic Estimation in Mixed Linear Models

The problem of nonnegative quadratic estimation of a parametric function γ(β, σ)=β′Fβ+∑^r_i=1 f_iσ²_i in a general mixed linear model {y, Xβ, V(σ)=∑^r_i=1 σ²_iV_i} is discussed. Necessary and sufficient conditions are given for y′A₀y to be a minimum biased estimator for γ. It is shown how to formulate the problem of finding a nonnegative minimium biased estimator of γ as a conic optimization problem, which can be efficiently solved using convex optimization techniques. Models with two variance components are considered in detail. Some applications to one-way classification mixed models are given. For these models minimum biased estimators with minimum norms for square of expectation β² and for σ²₁ are presented in explicit forms.     

EXISTENCE AND CONVERGENCE RESULTS FOR AN ELASTIC FRICTIONAL CONTACT PROBLEM WITH NONMONOTONE SUBDIFFERENTIAL BOUNDARY CONDITIONS

The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions descri...     

Computation of the Folkman number Fe(3, 3; 5)

With the help of computer algorithms, we improve the lower bound on the edge Folkman number F_e(3, 3; 5) and vertex Folkman number F_v(3, 3; 4), and, thus, show that the exact values of these numbers are 15 and 14, respectively. We also present computer enumeration of all critical graphs. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 41–49, 1999