On Clique-Transversals and Clique-Independent Sets

A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. A clique-independent set is a subset of pairwise disjoint cliques of G. Denote by _C (G) and _C (G) the cardinalities of the minimum clique-transversal and maximum clique-independent set of G, respectively. Say that G is clique-perfect when _C (H)= _C (H), for every induced subgraph H of G. In this paper, we prove that every graph not containing a 4-wheel nor a 3-fan as induced subgraphs and such that every odd cycle of length greater than 3 has a short chord is clique-perfect. The proof leads to polynomial time algorithms for finding the parameters _C (G) and _C (G), for graphs belonging to this class. In addition, we prove that to decide whether or not a given subset of vertices of a graph is a clique-transversal is Co-NP-Complete. The complexity of this problem has been mentioned as unknown in the literature. Finally, we describe a family of highly clique-imperfect graphs, that is, a family of graphs G whose difference _C (G)– _C (G) is arbitrarily large.     

-Weyl's theorem for operator matrices

If is a upper triangular matrix on the Hilbert space , then -Weyl's theorem for and need not imply -Weyl's theorem for , even when . In this note we explore how -Weyl's theorem and -Browder's theorem survive for operator matrices on the Hilbert space.

     

Determination of phosphorus in fertilizers by inductively coupled plasma atomic emission spectrometry

An inductively coupled plasma atomic emission spectrometry (ICP-AES) method was developed for the determination of phosphorus in fertilizers. Total phosphorus, direct extraction available phosphorus (EDTA), and water-soluble phosphorus, reported as phosphorus pentoxide (P205), in 15 Magruder check fertilizers were measured by ICP-AES, and the results were compared with those obtained by the AOAC official method. Five analytical wavelengths of phosphorus, 177.499, 178.287, 213.618, 214.914, and 253.565 nm, were tested for the determination of phosphorus in fertilizers, and their detection limits were obtained. Acid effects of perchloric acid and possible matrix effects of aluminum, calcium, magnesium, potassium, and sodium were negligible for phosphorus determination. Wavelength 213.618 nm was the best analytical wavelength for phosphorus determination by all 3 sample preparation methods for the selected Magruder fertilizers. The results demonstrated that the accuracy and precision of the ICP-AES method were comparable with those of the official methods.     

An improved western blotting technique effectively reduces background

We have developed a simple method to dramatically improve Western blotting by use of water washing as well as altered buffer conditions. Our improved protocol reduces the cost and labor of Western blotting by shortening the washing time and uses less buffer and other reagents. This procedure does not significantly change existing protocols of Western blotting analysis; it simply contains a few modifications to the washing step and buffer conditions. Our improved technique may therefore have broad applications in various experimental conditions.     

Alkaline-Earth Metal Complexes with Pivaloylacetone

Pivaloylacetonates of alkaline-earth elements with composition M(Pa)₂ · nH₂O (n = 1, M = Sr, Ca; n = 0, 2, M = Ba) were synthesized and studied by IR and thermal analysis; their solubilities and volatility were estimated. It was found that the volatility changes regularly in the series M(Acac)₂–M(Pa)₂–M(Thd)₂ (HAcac is acetylacetone, HThd is dipivaloylmethane). The replacement of one methyl radical by the tert-butyl radical when going from acetylacetonates to pivaloylacetonates was shown to noticeably increase the volatility only for Sr(Pa)₂ · H₂O. Complexes of barium pivaloylacetonate with tetraglyme and -phenanthroline were synthesized and characterized.     

Electrophilic aromatic nitration using perfluorinated rare earth metal salts in fluorous phase

In this paper, we describe a practical, useful electrophilic aromatic nitration process in fluorous phase by using perfluorodecalin (C10F18, cis- and trans-mixture) as a fluorous solvent and perfluorinated rare earth metal salt [Yb(OSO2C8F17)3] as a catalyst for the electrophilic aromatic nitration.     

Efficient soluble polymer-supported sharpless alkene epoxidation catalysts

High chemical yields and good enantiomeric excesses are obtained by using soluble polymer-supported tartrate ester in the epoxidation of trans-hex-2-en-1-ol using Ti(OPri)4/tert-butyl hydroperoxide.     

Can the minimal supersymmetric standard model with light bottom squark and light gluino survive Z-peak constraints?

In the framework of the minimal supersymmetric model we examine the Z-peak constraints on the scenario of one light bottom squark (sbottom) ( approximately 2-5.5 GeV) and light gluino (approximately 12-16 GeV), which has been successfully used to explain the excess of bottom quark production in hadron collisions. Such a scenario is found to be severely constrained by the CERN LEP Z-peak observables, especially by R(b), due to the large effect of gluino-sbottom loops. To account for the R(b) data in this scenario, the other mass eigenstate of sbottom, i.e., the heavier one, must be lighter than 125 (195) GeV at 2sigma(3sigma) level, which, however, is disfavored by CERN LEP II experiments.     

Dependence of enhanced Kerr nonlinearity on coupling power in a three-level atomic system

We study the enhanced Kerr-nonlinear coefficient in a three-level A-type atomic system for various coupling-beam powers. The Kerr-nonlinear coefficient behaves very differently in the strong and the weak coupling power regions and changes sign when the coupling or probe frequency detuning changes sign. Comparisons of Kerr-nonlinear coefficients as functions of probe frequency detuning, coupling power, and coupling frequency detuning are presented.