Note on induced subgraphs of the unit distance graphE n

The unit distance graphE ⁿ is the graph whose vertices are the points in Euclideann-space, and two vertices are adjacent if and only if the distance between them is 1. We prove that for anyn there is a finite bipartite graph which cannot be embedded inE ⁿ as an induced subgraph and that every finite graph with maximum degreed can be embedded inE ^N ,N=(d ³ –d)/2, as an induced subgraph.     

On the dimension to represent a graph by a unit distance graph

It is proved that if a graphG has maximum degreed, then its vertices can be represented by distinct unit vectors inR ^2d so that two vectors are orthogonal if and only if the corresponding vertices are adjacent. As a corollary it follows that if a graph has maximum degreed, then it is isomorphic to a unit distance graph inR ^2d.     

A threshold for the size of random caps to cover a sphere

Consider a unit sphere on which are placed N random spherical caps of area 4p(N). We prove that if % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% qGSbGaaeyAaiaab2gaaaWaaeWaaeaacaWGWbWaaeWaaeaacaWGobaa% caGLOaGaayzkaaGaai4Taiaad6eacaGGVaGaaeiBaiaab+gacaqGNb% Gaaeiiaiaad6eaaiaawIcacaGLPaaacqGH8aapcaaIXaaaaa!454E!\[\overline {{\rm{lim}}} \left( {p\left( N \right)\cdotN/{\rm{log }}N} \right) < 1\], then the probability that the sphere is completely covered by N caps tends to 0 as N , and if % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaWaaaeaaca% qGSbGaaeyAaiaab2gaaaWaaeWaaeaacaWGWbWaaeWaaeaacaWGobaa% caGLOaGaayzkaaGaai4Taiaad6eacaGGVaGaaeiBaiaab+gacaqGNb% Gaaeiiaiaad6eaaiaawIcacaGLPaaacqGH+aGpcaaIXaaaaa!4551!\[\underline {{\rm{lim}}} \left( {p\left( N \right)\cdotN/{\rm{log }}N} \right) > 1\], then for any integer n>0 the probability that each point of the sphere is covered more than n times tends to 1 as N .     

On the contact dimensions of graphs

Every simple graphG=(V, E) can be represented by a family of equal nonoverlapping spheres {S _v :v V} in a Euclidean spaceR ⁿ in such a way thatuv E if and only ifS _u andS _v touch each other. The smallest dimensionn needed to representG in such a way is called the contact dimension ofG and it is denoted by cd(G). We prove that (1) cd(T)<(7.3) log |T| for every treeT, and (2)

Transformation of Cinchona alkaloids into 1-N-oxide derivatives by endophytic Xylaria sp isolated from Cinchona pubescens

The microbial transformation of four Cinchona alkaloids (quinine, quinidine, cinchonidine, and cinchonine) by endophytic fungi isolated from Cinchona pubescens was investigated. The endophytic filamentous fungus Xylaria sp. was found to transform the Cinchona alkaloids into their 1-N-oxide derivatives.     

Photoassisted NO reduction with NH3 over TiO2 photocatalyst

Photoassisted selective catalytic reduction of NO with ammonia (photo-SCR) at low temperature over irradiated TiO2 in a flow reactor was confirmed to proceed efficiently and the adsorbed ammonia reacted with NO under irradiation of TiO2.     

Temperature-Responsiveness of A-B-A Block Telomers at Solid-Liquid Interfaces

Macroinitiators were prepared by coupling disuccinimidyl ester of 4,4'-azobis(cyanovaleric acid) with poly(N-isopropylacrylamide) (PIPA), which had an amino group at its end. Styrene was telomerized with the initiators in THF. When the styrene content in the A-B-A block telomer obtained (PIPA-b-PSt-b-PIPA) was high, the telomer formed an irreversible aggregation resulting in microspheres, whereas the telomer with a much shorter styrene block could be dispersed monomolecularly. The telomers dispersed in water were aggregated by raising the temperature above 32 degrees C due to a coil-globule transition of PIPA moieties. The PIPA-b-PSt-b-PIPA could be strongly adsorbed to polystyrene (PSt) solid surfaces to form a layer, and the PSt blocks might lay on the PSt surface and the PIPA blocks might direct to the solution phase. The contact angle of air bubbles on the surface of telomer-coated PSt in the air-in-water system was dependent on temperature; that is, with the increase in temperature the contact angle of air bubbles largely decreased and leveled off above the coil-globule transition temperature (Tc). Correspondingly, the amount of protein Concanavalin A adsorbed to the telomer layer deposited on the PSt surface increased gradually with an increase in temperature and leveled off above the Tc. These phenomena were attributed to the changes in hydrophobicity of the telomer layer below and above the Tc. The usefulness of macroinitiators in preparing various kinds of block telomers which have responsiveness to external stimuli was strongly suggested. Copyright 1999 Academic Press.     

Determination of chemical form of antimony in contaminated soil around a smelter using X-ray absorption fine structure.

Only limited information is available about the behavior of antimony (Sb) in contaminated soils. However, understanding the behavior of Sb in contaminated soils is important, because the toxicity or solubility of this element depends on its chemical state. In this study, we investigated the levels of Sb and the chemical forms of Sb in the soil around a smelter using X-ray absorption fine structure (XAFS) spectra. The highest Sb concentration in the contaminated soil was 2900 mg/kg dry soil. According to Sb-K edge X-ray absorption near edge (XANE) spectra, the Sb in the soil was in the form of Sb(V) compounds. The similarity of extended XAFS (EXAFS) spectra suggests that Sb speciation was independent of the sampling site, which indicates that Sb or Sb2O3 emitted from the smelter was converted into Sb(V) compounds in the soil.