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     

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.     

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.     

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.     

Equilibrium of the reaction between dissolved sodium sulfide and biologically produced sulfur

The equilibrium of the heterogeneous reaction between dissolved sodium sulfide and biologically produced sulfur particles has been studied. Biologically produced sulfur was obtained from a bioreactor of a hydrogen sulfide removal process in which the dominating organism is Thiobacillus sp. W5. Detailed knowledge of this reaction is essential to understand its effect on the process. The results were compared with the equilibrium of the reaction of sulfide with ‘inorganic’ elemental sulfur. The equilibrium between dissolved sodium sulfide and biologically produced sulfur particles can be described by an equilibrium constant, K_x, which consists of a weighted sum of constants for polysulfide ions of different chain length, rather than a true single equilibrium constant. For biologically produced sulfur pK_x = 9.10 ± 0.08 (21 °C) and 9.17 ± 0.09 (35 °C) with an average polysulfide chain length x = 4.91 ± 0.32 (21 °C) and 4.59 ± 0.31 (35 °C). The pK_x value for biologically produced sulfur is significantly higher than for reaction of dissolved sodium sulfide with inorganic sulfur (pK_x = 8.82; 21 °C). This difference is probably caused by the negatively charged polymeric organic layer, which is present on biologically produced sulfur but absent with “inorganic” sulfur. Specific binding of polysulfide ions to the organic layer results in a higher polysulfide concentration at the reaction site compared to the bulk concentration. This results in an apparent decrease of the measured equilibrium constant, K_x.     

A multi-technique surface study of the mercury(II) chalcogenide ion-selective electrode in saline media

X-ray photoelectron spectroscopy (XPS), secondary ion mass spectrometry (SIMS), rotating disc electrode-electrochemical impedance spectroscopy (RDE-EIS) and synchrotron radiation-grazing incidence X-ray diffraction (SR-GIXRD) have been used to study the response mechanism of the mercury(II) chalcogenide ion-selective electrode (ISE) in saline media. XPS and SIMS have shown that the chalcogenide surface is poisoned by silver chloride, or a mixture of silver halides, on continuous exposure to synthetic and real seawater. Significantly, the in-situ SR-GIXRD study demonstrated that electrode fouling in synthetic seawater is linked to the formation of poorly crystalline or amorphous silver chloride, and that the low level of free mercury(II) in a calibration buffer (i.e., 10(-14) M) is able to undergo metathesis with silver(II) sulfide in the membrane generating mercury(II) sulfide. Significantly, the results of this detailed surface study have shown that silver chloride fouling of the electrode is ameliorated in real seawater comprising natural organic ligands, and this has been attributed to the peptization of silver chloride by the surfactant-like nature of seawater ligands at pH 8. RDE-EIS aging studies have revealed that the chalcogenide membrane experiences a sluggish charge transfer reaction in seawater, and contrary to a previous report for a static electrode, the seawater matrix does not passivate the RDE. The results of this XPS, SIMS, RDE-EIS and SR-GIXRD study have elucidated the response mechanism of the mercury(II) ISE in saline media.     

The least element property of center location on tree networks with applications to distance and precedence constrained problems

In the classicalp-center location model on a network there is a set of customers, and the primary objective is to selectp service centers that will minimize the maximum distance of a customer to a closest center. Suppose that thep centers receive their supplies from an existing central depot on the network, e.g. a warehouse. Thus, a secondary objective is to locate the centers that optimize the primary objective as close as possible to the central depot. We consider tree networks and twop-center models. We show that the set of optimal solutions to the primary objective has a semilattice structure with respect to some natural ordering. Using this property we prove that there is ap-center solution to the primary objective that simultaneously minimizes every secondary objective function which is monotone nondecreasing in the distances of thep centers from the existing central depot.Restricting the location models to a rooted path network (real line) we prove that the above results hold for the respective classicalp-median problems as well.