Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution

Summary. We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian ([26], \[30]) is also included in the study. We prove and estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear systems. We present computational results related to image processing and plane curve evolution. Received April 25, 2000 / Revised version received June 11, 2001 / Published online November 15, 2001     

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.     

[VS_4Cu_6(Py)_8I_3]的合成和晶体结构

在(NH4)3VS4/CuI/Py反应体系中合成了新化合物 [VS4Cu6(Py)8I3]并测定其晶体结构。该化合物(C40H40N8Cu6I3S4V)属正交晶系, 空间群为Fdd2, 晶胞参数为: a = 29.924(6), b = 13.475(3), c = 25.853(5) , V = 10425(4) ?, Dc = 2.006 g/cm3, Mr = 1573.92, Z = 8, (MoK) = 4.546 mm-1, F(000) = 6048。结构由直接法解出, 用全矩阵最小二乘法修正, 最终偏离因子R = 0.023, wR = 0.069。簇合物分子是由6个带端基配体的Cu沿着四面体单元VS4的6条SS边配位而成, 6个Cu排列成了1个八面体, V基本位于八面体的中心, 整个分子具有C2对称性。     

Arithmetic functions with linear recurrence sequences

We obtain asymptotic formulas for all the moments of certain arithmetic functions with linear recurrence sequences. We also apply our results to obtain asymptotic formulas for some mean values related to average orders of elements in finite fields.     

Shape preservation regions for six-dimensional spaces

We analyze the critical length for design purposes of six-dimensional spaces invariant under translations and reflections containing the functions 1, cos t and sin t. These spaces also contain the first degree polynomials as well as trigonometric and/or hyperbolic functions. We identify the spaces whose critical length for design purposes is greater than 2π and find its maximum 4π. By a change of variables, two biparametric families of spaces arise. We call shape preservation region to the set of admissible parameters in order that the space has shape preserving representations for curves. We describe the shape preserving regions for both families. To our friend Mariano Gasca on occasion of his 60th birthday Research partially supported by the Spanish Research Grant MTM2006-03388, by Gobierno de Aragón and Fondo Social Europeo.