Fan-type theorem for path-connectivity

A graphG is said to bek-path-connected if every pair of distinct vertices inG are joined by a path of length at leastk. We prove that if max{deg _G ^x , deg _G ^y }k for every pair of verticesx,y withd _G (x,y)=2 in a 2-connected graphG, whered _G (x,y) is the distance betweenx andy inG, thenG isk-path-connected.     

Generalized Aluthge transformation on -hyponormal operators

We shall introduce a generalized Aluthge transformation on -
hyponormal operators and also, by using the Furuta inequality, we shall give several properties on this generalized Aluthge transformation as further extensions of some results of Aluthge.

     

Nitrosation of Phenolic Substrates under Mildly Basic Conditions: Selective Preparation of p-Quinone Monooximes and Their Antiviral Activities

Nitrosation of 3-methoxyphenol and 1-naphthol were examined under both acidic (NaNO(2)-EtCO(2)H-H(2)O) and basic (i-AmNO(2)-K(2)CO(3)-DMF) conditions. Acidic nitrosations afforded ortho-directed products, whereas para-directed nitrosations were observed under basic conditions to yield p-quinone monooximes. The basic para-directed nitrosation was further examined using 15 phenols, two naphthols, and four phenolic heterocyclics. A one-pot operation of the basic nitrosation followed by methylation with dimethyl sulfate gave the corresponding methyl ethers in high yield. Two p-quinone monooximes derived from 3-methoxyphenol and 8-hydroxyquinoline showed a moderate activity against HSV-1, and the latter oxime was also effective against HSV-2. On the other hand, p-quinone monooximes derived from methyl salicylate, 1-naphthol, 7-hydroxy-2-methylbenzo[b]furan, and 8-hydroxycoumarin showed the comparable activity to that of DDI against HIV-1.     

Information theory of miniaturization advantages of column liquid chromatography for quantitative analysis

Summary The influences of decreasing column diameter and length on two analytical goals, the precision and solvent efficiency, in reversed-phase liquid-chromatography are studied. Low solvent consumption is one of analytical advantages of miniaturized columns and is shown to be quantitatively evaluated by the precision and solvent efficiency which are defined to be the total Shannon mutual information obtained from an assay and the information obtained in a unit solvent volume, respectively. Analysis of paraben food additives on a microbore column is taken as an example. In trace analysis, the relative standard deviation (RSD) of measurements theoretically derived from the precision is shown to approach to the observed ones.