Confidence regions in a multivariate regression model with constraints II

The multivariate model, where not only parameters of the mean value of the observation matrix, but also some other parameters occur in constraints, is considered in the paper. Some basic inference is presented under the condition that the covariance matrix is either unknown, or partially unknown, or known. Supported by the grant of the Council of Czech Republic MSM 6 198 959 214.     

Compact coaxial driver for small-size Z-pinch

The presented one-capacitor pinch driver, designed as a compact coaxial structure (including spark-gap and discharge section) consistent with the capacitor output, generates a current of 200 kA with 700 ns quarter-period, suitable for studying the optimization of Z-pinch radiative characteristics. The driver is described, measurements of its parameters summarized, and relations to our previous and future activities briefly reviewed.This work was supported in part by the Grant Agency of the Czech Republic under contract No. 202/93/1023.     

1H and13C nuclear magnetic relaxation and local dynamics of lysozyme and synthetic polypeptides

The combined analysis of¹H and¹³C NMR relaxation data in solid lysozyme and some typical homopolypeptides was carried out by using “model-free” approach. Three types of relaxation transitions (γ’, γ and β) were revealed in the temperature range investigated. The microdynamical parameters of these motions were determined. From the comparison of these parameters with those of selected synthetic polymers it follows that the molecular motions in proteins and synthetic polymers are of the same nature. All these motions show pronounced anisotropic character. In the investigated temperature range no molecular motions corresponding to α-relaxation (liquid-like) transition were revealed. The hydration effects on parameters of the motions in proteins were considered. The most pronounced effect takes place for β-transition. The effect of Brownian rotation of protein molecule in solution on measured correlation function of local motions was also discussed.     

Projectivep-algebras

Presented by R. Freese.     

Multiple-scattering-theory analysis of XANES spectra of SO2 adsorbed on Cu(100)

The sulphur K-edge x-ray absorption spectra of SO₂ multilayer and of SO₂ submonolayer adsorbed on Cu(100) are analysed. It is found that the dominant spectral features are of a molecular origin. The results support earlier findings that the SO₂ molecule stands perpendicular to the surface. Use of non-selfconsistent potentials does not lead to a good quantitative agreement between theory and experiment.     

On Nash Equilibria for Noncooperative Games Governed by the Burgers Equation

Existence of a Nash equilibrium in a noncooperative game governed by the one-dimensional Burgers equation, proposed in the case of pointwise controls in Ref. 1, is proved under data qualifications that guarantee the diffusion term in the Burgers’ equation to be dominant enough with respect to the uniform convexity of the payoffs. This work was partly supported by Grants 201/03/0934 (GA čR) and MSM 0021620839 (MšMT čR). Inspiring discussions with Angel M. Ramos are acknowledged.     

External influence on magnetic properties of Fe-based nanocrystalline alloys

Amorphous and nanocrystalline ribbons of NANOPERM, FINEMET and HITPERM were studied by Mössbauer spectroscopy (MS) after the influence of external factors: different annealing atmospheres, tensile stress and several kinds of corrosion. MS is a suitable tool for such studies because the spectral parameters are very sensitive to changes in the vicinity of the probe — ⁵⁷Fe nuclei. The most sensitive parameters were hyperfine magnetic field in crystalline component, average hyperfine field in amorphous component and direction of net magnetic moments. Influence of external factors modified also the structure of the alloys, i.e. new or modified phases were identified by MS phase analysis.     

On matrices with operator entries

In this paper we consider certain matrix equations in the field of Mikusiński operators, and construct a method for obtaining an approximate solution which allows working with numerical constants instead of operators. The theory of diagonally dominant matrices is applied for the analysis, existence and character of the obtained solutions. We introduce a method for determining approximate solutions of a discrete analogue for operational differential equations and give conditions for their existence. The error of the approximation is estimated.     

Thee + e −→¯nn cross section predicted remarkably larger than thee + e −→¯pp one

It is shown that all global analyses of nucleon electromagnetic form factor data predict the electron-positron annihilation into neutron-antineutron cross section (for which there are no data till now) to be in a finite energy region substantially larger than the electron-positron annihilation into the proton-antiproton one.Dedicated to the memory of M. Gmitro.     

IR finite one-loop box scalar integral with massless internal lines

The IR finite one-loop box scalar integral with massless internal lines has been recalculated. The result is very compact, simple and valid for arbitrary values of the relevant kinematic variables. It is given in terms of only two dilogarithms and a few logarithms, all of very simple arguments. Received: 31 January 2002 / Published online: 26 April 2002