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     

Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

Determination of the Lipophilicity of Xanthines by Reversed-Phase Liquid Chromatography

JPC – Journal of Planar Chromatography – Modern TLC -     

n-Butyllithium/α-methylstyrene/benzene/diethyl ether: A suitable initiation system for anionic syntheses of model co- and homopolymers of styrene and isoprene

An initiation system of the anionic polymerization, intended for the syntheses of homopolymers and block copolymers with narrow molar mass distribution, was tested with styrene and isoprene. The actual initiating species, viz., the oligomeric α-methylstyryl anion, originates by the reaction of n-butyllithium with α-methylstyrene in a benzene/diethyl ether 1:1 (v:v) solvent mixture at room temperature. The homopolymers and two-block copolymers of styrene and isoprene, prepared by using this system, were characterized by light scattering, membrance osmometry, GPC, and ¹H NMR spectroscopy. By using the suggested initiation system, it is possible to synthesize well-defined homopolymers and block copolymers with low polydispersity (as judged by the shape of the GPC peaks and by the values of the polydispersity index), especially in a molar mass region between 4 × 10⁴ and 1.5 × 10⁵ g/mol. Above the upper limit of this interval, an appropriate decrease of the diethyl ether/benzene volume ratio is recommended, though the polymerization time must then be prolonged.     

31P and 1h NMR as probes of domain alignment in a rigid crystalline surfactant mesophase

A viscous reverse hexagonal surfactant mesophase containing bis(2-ethylhexyl) sodium sulfosuccinate (AOT) and alpha-phosphatidylcholine (lecithin), with comparable volume fractions of isooctane and water, was characterized by Fourier transform (31)P and (1)H NMR spectroscopy. Shear alignment was reflected through both (31)P NMR and (1)H NMR spectra. A complicated (31)P spectrum was observed as a result of superposition of chemical shifts according to the distribution of crystalline domains prior to shear. The initially disordered samples with polydomain structures become macroscopically aligned after Couette shear. (31)P NMR chemical shift anisotropy characteristics are used to elucidate orientation of the hexagonal phase. Interestingly, (1)H NMR spectra exhibit spectral changes upon shear alignment closely corresponding with that of (31)P NMR spectra. These observations complement the findings of mesophase alignment obtained using SANS and imply that (31)P and (1)H NMR spectroscopy can be used as probes to define microstructure and monitor orientation changes in this binary surfactant system. This is especially beneficial if these mesophases are used as templates for materials synthesis.     

Dynamic mechanical and thermal behavior of thermotropic polyesters based on 4,4-alkane-1-ω-diylbis(4-hydroxybenzoic acid) and 4,4-(pentane-1,5-diyloxy)dibenzoic acid

Thermotropic polyesters based on 4,4^′-alkane-1-ω-diylbis(4-hydroxybenzoic acid) and 4,4^′-(pentane-1,5-diyloxy)dibenzoic acid were studied by dynamic mechanical spectroscopy, X-ray scattering, differential scanning calorimetry and polarizing microscopy. The effect of structure changes in the mesogenic group as well as in the flexible spacer, in particular the incorporation of Cl atoms into the mesogen, introduction of ether oxygen into spacer and the number of CH₂ groups in spacer was investigated. More complex mechanical and thermal behaviour was found on second heating scan than on first cooling of the isotropic melt; higher values of mechanical functions were observed in the isotropic state than in the nematic state of melts. While an even number of CH₂ groups and the presence of ether oxygen in spacer shifts the transition temperatures to higher values, the incorporation of Cl atoms into the mesogen leads to disappearance of ordered structure and the polymers behave as amorphous materials.     

Ca(2.5)Sr(0.5)GaMn2O8: diamagnetic Ga in control of the structural and electronic properties of a bilayered manganate

The temperature dependence of the crystal structure and electronic properties of brownmillerite-like Ca(2.5)Sr(0.5)GaMn(2)O(8) has been studied by neutron powder diffraction and muSR spectroscopy. The results show that short-range 2D magnetic order begins to develop within the perovskite-like bilayers of MnO(6) octahedra approximately 50 K above the 3D Néel temperature of approximately 150 K. The bilayers show a structural response to the onset of magnetism throughout this temperature range whereas the GaO(4) layers that separate the bilayers only respond below the 3D ordering temperature. XANES spectroscopy shows that the sample contains Mn(3+) and Mn(4+) cations in a 1:1 ratio, and the behavior in the region of the Néel transition is interpreted as a local charge ordering. Electron diffraction and high-resolution electron microscopy have been used to show that the local microstructure is more complex than the average structure revealed by neutron diffraction, and that microdomains exist in which the GaO(4) tetrahedra show different orientations. It is argued that the bonding requirements of diamagnetic gallium control the electronic behavior within the perovskite-like bilayers.     

On relatively short and long sides of convex pentagons

By the relative distance of pointsa andb of a convex bodyC we mean the ratio of the Euclidean distance ofa andb to the half of the Euclidean distance ofa, b C such thatab is a longest chord ofC parallel to the segmentab. We say that a sideab of a convexn-gon is relatively short (respectively: relatively long) if the relative distance ofa andb is at most (respectively: at least) the relative distance of two consecutive vertices of the regularn-gon. We show that every convexn-gon, wheren 5, has a relatively short side and a relatively long side, and that it is affine-regular if and only if all its sides are of equal relative lengths.Research supported in part by Komitet Bada Naukowych (Committee of Scientific Research), grant number 2 2005 92 03.     

On functions having Cauchy differences in some prescribed sets

Summary AssumeE is a real topological vector space,F is a real Banach space,K is a discrete subgroup ofF andC is a symmetric, convex and compact subset ofF such thatK (6C) = {0}. If a functionh:E F is continuous at at least one point andh(x + y) – h(x) – h(y) K + C for allx, y E, then there exists a continuous linear functiona:E F such thath(x) – a(x) K + C for everyx E.     

Electron impact mass spectra of some tertiary aliphatic nitro compounds. Nitrocarbonyl compounds and some analogues

The mass spectra of some tertiary aliphatic nitroaldehydes, nitroketones, nitroesters, nitronitriles and related nitrocarbonyl compounds are discussed and compared with those of some analogous nitro compounds lacking the carbonyl function. The M⁺˙ ? NO₂˙ and in several cases M⁺˙ ? HNO₂ fragmentation seem to be the most characteristic features of all tertiary aliphatic nitro compounds. In the presence of the primary nitro group, the loss of NHO₂ is always observed.