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 -     

Solid-phase synthesis of dihydrovirginiamycin S1, a streptogramin B antibiotic

We describe the first solid-phase synthesis of dihydrovirginiamycin S(1), a member of the streptogramin B family of antibiotics, which are nonribosomal-peptide natural products produced by Streptomyces. These compounds, along with the synergistic group A components, are "last line of defense" antimicrobial agents for the treatment of life-threatening infections such as vancomycin-resistant enterococci. The synthesis features an on-resin cyclization and is designed to allow production of streptogramin B analogues with diversification at positions 1', 1, 2, 3, 4, and 6. Several synthetic challenges known to hinder the synthesis of this class of compounds were solved, including sensitivity to acids and bases, and epimerization and rearrangements, through the judicious choice of deprotection conditions, coupling conditions, and synthetic strategy. This work should enable a better understanding of structure-activity relationships in the streptogramin B compounds, possible identification of analogues that bypass known resistance mechanisms, and perhaps the identification of analogues with novel biological activities.     

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.     

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.     

Untersuchung der Absorption der bei der Verbrennung phosphororganischer Verbindungen entstehenden P-Oxide mittels32P-markierter Verbindungen

Zusammenfassung Bei der Pyrolyse phosphor-organischer Verbindungen in Sauerstoffatmosphäre bilden sich P-Oxide, die die C,H-Bestimmung stören. Deren Verhalten im Verbrennungsrohr und ihre Absorption an geeigneten Kontakten wurden untersucht. Durch den Einsatz³²P- markierter Ausgangsverbindungen und Aktivitätsmessung des³²P sowohl durch die Wandung des Verbrennungsrohres als auch im zerkleinerten Füllungsmaterial war die laufende Bestimmung der durch die Kontaktschicht absorbierten Phosphormenge möglich. 30 verschiedene Absorptionsmittel wurden geprüft. Der Einfluß der Strömungsgeschwindigkeit des Trägergases, der Temperatur der Kontaktschicht, der Art der Verbrennung sowie der Anordnung des Verbrennungsrohres wurde untersucht. Die Absorptionsleistung der Kontakte ist stark von der Gasgeschwindigkeit abhängig.

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Investigation of absorption of the phosphorus oxides arising in the combustion of organophosphorus compounds by means of³²P-labelled substances

Summary In the pyrolysis of organophosphorus compounds in an oxygen atmosphere P oxides are formed which interfere with determination of carbon and hydrogen. Their behaviour in the combustion tube and their absorption on suitable contacts were investigated. By the use of³²P-labelled starting compounds and measuring the activity of³²P both through the wall of the combustion tube and in the comminuted filling material, continuous determination of the amount of phosphorus absorbed through the contact layer was possible. Thirty different absorption media were tested. The influence of the flow rate of the carrier gas, the temperature of the contact layer, the nature of combustion as well as the arrangement of the combustion tube was examined. The absorption efficiency of the contacts is highly dependent on the speed of the gas.

     

An investigation of the reliability of the Galerkin-Petrov method

It is shown that the Galerkin-Petrov method if applied in a controlled way yields reliable results for excited states of the same symmetry classifications as the ground state. Computations are performed for the 2¹ S and 3¹ S states of He. The problem of optimizing nonlinear parameters of the basis functions by means of the GP method is discussed. A special optimization scheme is suggested and numerically illustrated for someS states of He.