A lower bound for the convexity number of some graphs

Given a connected graphG, we say that a setC ?V(G) is convex inG if, for every pair of verticesx, y ∈ C, the vertex set of everyx-y geodesic inG is contained inC. The convexity number ofG is the cardinality of a maximal proper convex set inG. In this paper, we show that every pairk, n of integers with 2 ≤k ≤ n?1 is realizable as the convexity number and order, respectively, of some connected triangle-free graph, and give a lower bound for the convexity number ofk-regular graphs of ordern withn>k+1.     

A Multisensor Deconvolution Problem

Meisters and Peterson gave an equivalent condition under which the multisensor deconvolution problem has a solution when there are two convolvers, each the characteristic function of an interval. In this article we find additional conditions under which the deconvolution problem for multiple characteristic functions is solvable. We extend the result to the space of Gevrey distributions and prove that every linear operator S, fromthe space of Gevrey functions with compact support onto itself, which commutes with translations can be represented as convolution with a unique Gevrey distribution T of compact support. Finally, we find explicit formula for deconvolvers when the convolvers satisfy weaker conditions than the equivalence conditions using nonperiodic sampling method.     

Determination of carbamazepine by chemiluminescence detection using chemically prepared tris(2,2'-bipyridine)ruthenium(III) as oxidant.

A new chemiluminescence method for the determination of carbamazepine (CBZ) has been developed. The method is based on the chemiluminescence produced in the reaction of tris(2,2'-bipyridine)ruthenium(III) and CBZ in an acidic medium. The chemiluminescence intensity was enhanced by organic solvents in the reaction system. Under the optimum experimental conditions, the calibration curve was linear over the range 4.0 x 10(-3)-8.6 x 10(-7) mol/L for CBZ. The detection limit (S/N = 3) was 2.5 x 10(-7) mol/L and the relative standard deviation of six replicate measurements was 2.6% for 4.0 x 10(-4) mol/L of CBZ. The possible reaction mechanism were also discussed. The chemiluminescence method was successfully applied to assay the CBZ contents in pharmaceutical tablets.     

The vertex-cover polynomial of a graph

In this paper we define the vertex-cover polynomial Ψ(G,τ) for a graph G. The coefficient of τ^r in this polynomial is the number of vertex covers V′ of G with |V′|=r. We develop a method to calculate Ψ(G,τ). Motivated by a problem in biological systematics, we also consider the mappings f from {1, 2,…,m} into the vertex set V(G) of a graph G, subject to f⁻¹(x)f⁻¹(y)≠ for every edge xy in G. Let F(G,m) be the number of such mappings f. We show that F(G,m) can be determined from Ψ(G,τ).     

Application of diaza-18-crown-6-capped beta-cyclodextrin bonded silica particles as chiral stationary phases for ultrahigh pressure capillary liquid chromatography

Two bonded chiral stationary phases (CSPs), 8-aminoquinoline-2-ylmethyl- and 8-aminoquinoline-7-ylmethyl-diaza-18-crown-6-capped [3-(2-O-beta-cyclodextrin)-2-hydroxypropoxy]propylsilyl silica particles (non-porous, 1.5 microm), have been prepared and evaluated using capillary liquid chromatography at high pressures (> or = 8000 p.s.i.). High column efficiency (up to 400 000 plates m(-1)) was achieved for chiral separations. These CSPs with two recognition sites, i.e. substituted-diaza-18-crown-6 and beta-cyclodextrin combined with high chromatographic efficiency provide good resolution of a variety of enantiomers and positional isomers in relatively short times under reversed-phase conditions. After inclusion of a Ni (II) ion from the mobile phase, the positively charged crown ether-capped beta-cyclodextrin facilitates specific static, dipolar, and host-guest complexation interactions with solutes.     

Polymer-coated hollow-fiber microextraction of estrogens in water samples with analysis by gas chromatography-mass spectrometry

A novel sorbent, dihydroxylated polymethylmethacrylate (DHPMM), coated on hollow-fiber membrane, is used for the polymer-coated hollow-fiber microextraction of trace amounts of natural and synthetic estrogens, such as diethylstilbestrol, estrone, 17beta-estradiol and 17alpha-ethynylestradiol, in aqueous samples. In this procedure, estrogens were extracted using the functionalized polar DHPMM polymer with derivatization using N-methyl-N-(trimethylsilyl)trifluoroacetamide followed by gas chromatography-mass spectrometric analysis. The detection limits for estrogens in aqueous sample were between 0.03 and 0.8 ng l(-1) and the calibration curves were linear over the concentration range 0.05-10 microgl(-1) and had correlation coefficients of >0.994. The relative standard deviations (RSDs) were <15% (n = 3). This simple, accurate, sensitive and selective analytical method is applicable to the determination of trace amounts of estrogens in reservoir and potable water samples.     

ToF-SIMS analysis of surface-anchored organometallic clusters

ToF-SIMS analysis of the organometallic cluster Os₃(μ-H)(CO)₁₀(μ-SCH₂CH₂SH) chemically attached onto a silver or gold surface, and of the cluster fragment Os₃(μ-H)(CO)₁₀(μ-OSi) on a silica surface, allows for identification of the surface organometallic species, and also gives information on its reactivity.     

Generalized evaluation subgroups of product spaces relative to a factor

For any -complexes and , we show that . We use this fact to compute generalized evaluation subgroups of generalized tori relative to a sphere.

     

Catalytic enantioselective allylation of aldehydes via a moisture-tolerant chiral BINOL-In(III) complex

A moisture-tolerant chiral indium complex has been developed to effect good enantioselectivities in the addition of allyltributylstannanes to aldehydes. The allylation of a variety of aromatic, α,β-unsaturated and aliphatic aldehydes resulted in both moderate to good yields and high enantioselectivities (up to 86% ee).