Some Recent Progress and Applications in Graph Minor Theory

In the core of the seminal Graph Minor Theory of Robertson and Seymour lies a powerful theorem capturing the ``rough' structure of graphs excluding a fixed minor. This result was used to prove Wagner's Conjecture that finite graphs are well-quasi-ordered under the graph minor relation. Recently, a number of beautiful results that use this structural result have appeared. Some of these along with some other recent advances on graph minors are surveyed. Research partly supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research, Grant number 16740044, by Sumitomo Foundation, by C & C Foundation and by Inoue Research Award for Young Scientists Supported in part by the Research Grant P1–0297 and by the CRC program On leave from: IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia     

Ten years3H survey at the Krško Nuclear Power Plant

As part of the general off-site radioactivity monitoring at the Krško Nuclear Power Plant, tritium is measured in the water of the river Sava at two locations (one upstream reference point and downstream point of total dispersion), the inlet and discharge of the essential plant service supply water, in four borehole waters, in tap water in Krško and Bre zice, and in precipitations at four points. Since 1992 tritium has also been analysed in gaseous effluents in the exhaust stack. Tritium is electrolytically enriched and determined by a liquid scintillation technique. For liquid effluents an average normalized release of 17.6 TBq per GW_e·y was obtained, while this value for gaseous effluents is 2.3 TBq per GW_e·y.     

Chemical composition and antimicrobial activity of Satureja kitaibelii essential oil against pathogenic microbial strains

Plant species Satureja kitaibelii Wierzb. ex Heuff. is used as a spice and as a natural preservative for food and herbal tea, owing to its characteristic scent and flavor as well as high antimicrobial activity. In the present study, the antimicrobial activity of isolated essential oil of S. kitaibelii was tested against a panel of 30 pathogenic microorganisms (foodborne microbes, selected multiresistant bacterial isolates from the patient wounds and dermatophyte isolates). Limonene (15.54%), p-cymene (9.99%), and borneol (8.91%) appeared as the main components in 44 identified compounds representing 98.44% of the oil. Essential oil of S. kitaibelii showed significant activity against a wide spectrum of foodborne microbes (MIC=0.18-25.5 microg mL(-1)) and multiresistant bacterial isolates (MIC=6.25-50.0 microg mL(-1)), as well as against dermatophyte strains (MIC=12.5-50.0 microg mL(-1)). These results demonstrate that S. kitaibelii essential oil could be used as a natural potential antimicrobial agent against pathogenic strains in the treatment of foodborne disease, wound and skin infections.     

Vibrational Studies of Palladium(II) Acetate Compounds I. Infrared Spectra of Hexa-μ-acetato-triangulo-tripalladium-water (2/1)

The infrared spectra of palladium(II) acetate crystals obtained from a benzene-acetic acid solution show that hexa-μ-acetato-triangulo-tripalladium(II)-water (2/1) i.e. the hemihydrate of hexa-μ-acetato-triangulo-tripalladium(II) was obtained. An empirical assignment of the observed bands is proposed.     

Phenethyl Ester of Gallic Acid Ameliorates Experimental Autoimmune Encephalomyelitis

Gallic acid is a phenolic acid present in various plants, nuts, and fruits. It is well known for its anti-oxidative and anti-inflammatory properties. The phenethyl ester of gallic acid (PEGA) was synthesized with the aim of increasing the bioavailability of gallic acid, and thus its pharmacological potential. Here, the effects of PEGA on encephalitogenic cells were examined, and PEGA was found to modulate the inflammatory activities of T cells and macrophages/microglia. Specifically, PEGA reduced the release of interleukin (IL)-17 and interferon (IFN)-γ from T cells, as well as NO, and IL-6 from macrophages/microglia. Importantly, PEGA ameliorated experimental autoimmune encephalomyelitis, an animal model of chronic inflammatory disease of the central nervous system (CNS)—multiple sclerosis. Thus, PEGA is a potent anti-inflammatory compound with a perspective to be further explored in the context of CNS autoimmunity and other chronic inflammatory disorders.     

A spectral approach to bandwidth and separator problems in graphs

Lower bounds on the bandwidth, the size of a vertex separator of general undirected graphs, and the largest common subgraph of two undirected (weighted) graphs are obtained. The bounds are based on a projection technique developed for the quadratic assignment problem, and once more demonstrate the importance of the extreme eigenvalues of the Laplacian. They will be shown to be strict for certain classes of graphs and compare favourably to bounds already known in literature. further improvement is gained by applying nonlinear optimization methods.     

Tessellation and Visibility Representations of Maps on the Torus

The model of the torus as a parallelogram in the plane with opposite sides identified enables us to define two families of parallel lines and to tessellate the torus, then to associate to each tessellation a toroidal map with an upward drawing. It is proved that a toroidal map has a tessellation representation if and only if its universal cover is 2-connected. Those graphs that admit such an embedding in the torus are characterized. Received November 22, 1995, and in revised form May 1, 1997.     

Über alkylierte Amide bicyclischer Dicarbonsäuren, 2. Mitt.

Zusammenfassung Zur Untersuchung auf pharmakologische Eigenschaften wurden verschiedene N-Alkyl- und N-Arylderivate des 1,4-Endoäthylen-⁵-cyclohexen-2,3-trans-dicarbonsäurediamids sowie ihre Hydrierungsprodukte dargestellt.1. Mitt:H. Koch undH. Mohar, Mh. Chem.94, 178 (1963).