Stable multi-sets

In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge bounds equal one, stable multi-sets are equivalent to stable sets.  For the stable multi-set problem, we derive reduction rules and study the associated polytope. We state necessary and sufficient conditions for the extreme points of the linear relaxation to be integer. These conditions generalize the conditions for the stable set polytope. Moreover, the classes of odd cycle and clique inequalities for stable sets are generalized to stable multi-sets and conditions for them to be facet defining are determined.  The study of stable multi-sets is initiated by optimization problems in the field of telecommunication networks. Stable multi-sets emerge as an important substructure in the design of optical networks. Received: February 14, 2001/Revised version: September 7, 2001     

Flow and reactive transport in porous media induced by well injection: Similarity solution

The authors study concentration profiles of solutes undergoingequilibrium absorption in the vicinity of a water well. Forthe case of a contamination event, the limit problem of vanishingwell radius, which is of self-similar nature, is analysed indetail. Existence, uniqueness, and qualitative properties ofsolutions of the corresponding ordinary differential equationsare shown. Some numerical examples are also presented.     

A Scanning Electron Microscopy study of water in soil

Cold stage Scanning Electron Microscopy (SEM) with a rapid cooling technique makes it possible to investigate the water phase within unsaturated porous media. It is thought that this technique preserves the main features of the micromorphology of the water menisci as it exists in the liquid phase in soils. Saddle-shaped elements, as well as pendular rings of water, were observed with concave and convex curvatures of the water-air interface. The hydraulic conductivity of an unsaturated soil may be inferred from SEM photographs. Observations of isolated water menisci indicate the existence of an immobile water domain. The surface geometry of the water menisci was analyzed quantitatively and surface tension and capillary pressure were determined.     

BIOLOGICAL ACTIVITIES OF PHTHALOCYANINES-X. SYNTHESES AND ANALYSES OF SULFONATED PHTHALOCYANINES

Abstract— Synthetic methods to obtain selectively sulfonated metallo phthalocyanines are compared. Both condensation and direct sulfonation procedures lead to mixtures of mono- to tetrasulfonated products which are resolved by reverse phase liquid chromatography in buffered aqueous-methanol. The proportion of sulfonated derivatives is examined as a function of the starting reagents in the case of the condensation method, and as a function of the temperature and reaction time in the case of the direct sulfonation procedure. The number of sulfonate groups per phthalocyanine molecule is determined by oxidative degradation of the phthalocyanine ring followed by quantitative chromatographic analysis of the sulfophthalamide and phthalamide fragments.     

Stereo- and regioselectivity in asymmetric synthesis of α-amino substituted benzocyclic compounds

The enantiomerically pure chiral benzocyclic amines 6–8 were obtained by asymmetric transamination of the corresponding prochiral ketones 9a–c. The method involves: (a) formation of chiral imines 10a–c from the prochiral ketones 9a–c and the inexpensive chiral auxiliary (R)- or (S)-phenylethylamine (PEA); (b) asymmetrically induced reduction of these imines to the diastereomeric amines 11a–c and 12a–c; (c) catalytic hydrogenation to remove the benzylic fragment of the chiral PEA auxiliary. The stereoselectivity of the imine reduction, as well as the regioselectivity of the catalytic hydrogenation, are strongly dependent on the size of the saturated ring condensed with the benzene ring. This approach was used to develop a convenient, high yielding, and stereoselective route to several practically important optically active α-amino substituted benzocyclic compounds.     

Thermal expansion properties of organic crystals: a CSD study

The thermal expansion properties of crystalline organic compounds are investigated by data mining of the Cambridge Structural Database (CSD). The mean volumetric thermal expansion coefficient is 168.8 × 10⁻⁶ K⁻¹ and the mean uniaxial thermal expansion coefficient is 71.4 × 10⁻⁶ K⁻¹, based on 745 and 1129 different observations, respectively. Normal and anomalous coefficients can be identified using these values and the associated standard deviations. The anisotropy of the thermal expansion is also evaluated and found to have a very broad distribution. 4719 different structures, comprising 4093 different molecular compounds and 626 additional polymorphs have been analyzed on their thermal expansion properties. Approximately 34% of these structures may have at least one orthogonal axis with negative thermal expansion, much more than generally believed. Moreover 127 structures have been identified which could have negative volumetric thermal expansion. Experimental validation using a robust protocol with data collected at more than 2 different temperatures is required to validate these cases.

The thermal expansion properties of crystalline organic compounds are investigated by data mining of the Cambridge Structural Database (CSD). Negative uniaxial thermal expansion is much more common than generally believed.     

Wavelength-dependent properties of photodynamic therapy using hypericin in vitro and in an animal model

Wavelength effects in photodynamic therapy (PDT) with hypericin (HY) were examined in a C26 colon carcinoma model both in vitro and in vivo. Irradiation of HY-sensitized cells in vitro with either 550 or 590 nm caused the loss of cell viability in a drug- and light-dose-dependent manner. The calculated ratio of HY-based PDT (HY-PDT) efficiencies at these two wavelengths was found to correlate with the numerical ratio of absorbed photons at each wavelength. In vivo irradiation of C26-derived tumors, 6 h after intraperitoneal administration of HY (5 mg/kg), caused extensive vascular damage and tumor necrosis. The depth of tumor necrosis (d) was more pronounced at 590 than at 550 nm and increased when the light dose was raised from 60 to 120 J/cm2. The maximal depths of tumor necrosis (at 120 J/cm2) were 7.5+/-1.5 mm at 550 nm and 9.9+/-0.8 mm at 590 nm. Both values are rather high in view of the limited penetration of green-yellow light into the tissue. Moreover, the depth ratio, d590/d550 = 1.3 (P < 0.001), is smaller than expected considering the 2.2-fold lower HY absorbance and the 1.7-fold lower tissue penetration of radiation at 550 than at 590 nm. This finding indicates that in vivo the depth at which HY-PDT elicits tumor necrosis is not only determined by photophysical considerations (light penetration, number of absorbed photons) but is also influenced significantly by other mechanisms such as vascular effects. Therefore, despite the relatively short-wavelength peaks of absorption, our observations suggest that HY is an effective photodynamic agent that can be useful in the treatment of tumors with depths in the range of 1 cm.     

RADICAUX LIBRES INDUITS PAR L''ACTION DU RAYONNEMENT ULTRAVIOLET SUR CERTAINS CONSTITUANTS DE L''ACIDE DEOXYRIBONUCLEIQUE

The action of ultra violet rays of 260 nm on aqueous solutions of bases, nucleosides and nucleotides of DNA at 77°K is studied by electron spin resonance. It is shown that the free radicals observed are similar, with a few noteworthy exceptions to those induced by X-rays, under the same conditions of temperature, in the solid state. Contrary to what might be excepted on the basis of the results obtained by X-rays, the variation in the yield in paramagnetic centres in each sequence studied does not seem to be important.     

Analytical pyrolysis of carbohydrates: I. Chemical interpretation of matrix influences on pyrolysis-mass spectra of amylose using pyrolysis-gas chromatography-mass spectrometry

Inorganic additives, viz. Na₂CO₃, NaOH, HCl, ZnC₂, NaH₂PO₄, Na₂HPO₄, NaCl. MgSO₄ and sea salt, to the pyrolysis matrix change the pyrolysis-mass spectrum of amylose significantly. Carbonyl compounds, acids and their lactones, furans, pyranones anhydrosugars and aromatic substances are found in different ratios under the various conditions, as determined by pyrolysis-gas chromatography-mass spectrometry (Py-GC-MS).Carbonyl compounds, acids and lactones are released from alkaline and neutral matrices. Furans and anhydrohexoses are particularly formed under neutral and acidic conditions. Pyranones are specific for phosphate matrices. Unsaturated hydrocarbons and aromatic substances arise from strongly alkaline or dehydrating matrices. Degradation pathways are proposed for various compound categories.The results of pyrolysis-mass spectrometry and Py-GC-MS are highly compatible.