D. Liu and X. Zhu,Erratum to: “Fractional chromatic number and circular chromatic number for distance graphs with large clique size”. Journal of Graph Theory47(2) 2004, 129–146

The original article to which this Erratum refers was published in Journal of Graph Theory 47:129–146,2004 .     

Optimality Conditions for Linear-Convex Optimal Control Problems with Mixed Constraints

Journal of Optimization Theory and Applications - In this paper, we provide sufficient optimality conditions for convex optimal control problems with mixed constraints. On one hand, the data...     

SPECTRAL PROPERTIES,PHOTOTRANSFORMATION KINETICS AND PELLETABILITY OF PHYTOCHROME IN Pharbitis nil Chois*

Abstract— An examination has been made of the involvement of phytochrome in the circadian rhythm of flowering in Pharbitis nil Chois. The peak position of P_fr absorption changes with time after a red light pulse. The shortest absorption wavelength of P_fr occurs at the same time as flowering is inhibited by red light in dark grown, red light pretreated plants. Pelletable and supernatant phytochrome show a similar trend with lowest values found at the time of flower inhibition. Neither phototransformation kinetics nor intermediates of phytochrome which accumulate in white light show such a relationship to the circadian rhythm found in flowering of dark grown P. nil.     

X-ray attenuation coefficients of elements and mixtures

This paper is concerned with X-ray attenuation in samples of pure elements and mixtures of elements. The emphasis is on the energy range 30–150 keV although the energy regions 10–30 and 150–1000 keV are also discussed. The approximations involved in deriving several well known formulae for the photoelectric and scattering cross-sections are described and the accuracy of these formulae is assessed. More accurate formulae are derived by reference to fundamental theory. It is shown that definitions of such quantities as effective atomic number cannot be justified from fundamental theory. The consequences of this result are explored in relation to various experimental conditions and the physical parameters of a complex medium which can be determined by X-ray transmission measurements are identified. Connections with related areas of interest in atomic physics and low energy X-ray scattering are made.     

LambdaO4 upside down: a new molecular structure for supported VO4 catalysts

Vanadium oxide (1 wt %) supported on gamma-Al(2)O(3) was used to investigate the interface between the catalytically active species and the support oxide. Raman, UV-vis-NIR DRS, ESR, XANES, and EXAFS were used to characterize the sample in great detail. All techniques showed that an isolated VO(4) species was present at the catalyst surface, which implies that no V-O-V moiety is present. Surprisingly, a Raman band was present at 900 cm(-1), which is commonly assigned to a V-O-V vibration. This observation contradicts the current literature assignment. To further elucidate on potential other Raman assignments, the exact molecular structure of the VO(4) entity (1 V=O bond of 1.58 A and 3 V-O bonds of 1.72 A) together with its position relative to the support O anions and Al cation of the Al(2)O(3) support has been investigated with EXAFS. In combination with a structural model of the alumina surface, the arrangement of the support atoms in the proximity of the VO(4) entity could be clarified, leading to a new molecular structure of the interface between VO(4) and Al(2)O(3). It was found that VO(4) is anchored to the support oxide surface, with only one V-O support bond instead of three, which is commonly accepted in the literature. The structural model suggested in this paper leaves three possible assignments for the 900 cm(-1) band: a V-O-Al vibration, a V-O-H vibration, and a V-(O-O) vibration. The pros and cons of these different options will be discussed.     

UV–visible spectroscopy for zirconocene activation by MAO in olefin polymerization: activity versus wavenumber

Activation of ansa‐zirconocenes of the type Rac [Zr{1‐Me₂Si(3‐R‐(η⁵‐C₉H₅))(3‐R′‐(η⁵‐C₉H₅))}Cl₂] [R = Et, R′ = H ( 1 ); R = Pr, R′ = H ( 2 ); and R = Et, R′ = Pr ( 3 ), R, R′ = Me ( 4 ) and R, R′ = Bu ( 5 )] by MAO has been studied by UV–visible spectroscopy. Compounds 1–3 have been tested in the polymerization of ethylene at different Al:Zr ratios. UV–vis spectroscopy was used to determine a correlation between the electronic structures of ( 1–5 ) and their polymerization activity. Copyright © 2009 John Wiley & Sons, Ltd.     

Circular consecutive choosability of k‐choosable graphs

Let S(r) denote a circle of circumference r. The circular consecutive choosability ch_cc(G) of a graph G is the least real number t such that for any r≥χ_c(G), if each vertex v is assigned a closed interval L(v) of length t on S(r), then there is a circular r‐coloring f of G such that f(v)∈L(v). We investigate, for a graph, the relations between its circular consecutive choosability and choosability. It is proved that for any positive integer k, if a graph G is k‐choosable, then ch_cc(G)?k + 1 ? 1/k; moreover, the bound is sharp for k≥3. For k = 2, it is proved that if G is 2‐choosable then ch_cc(G)?2, while the equality holds if and only if G contains a cycle. In addition, we prove that there exist circular consecutive 2‐choosable graphs which are not 2‐choosable. In particular, it is shown that ch_cc(G) = 2 holds for all cycles and for K_{2, n} with n≥2. On the other hand, we prove that ch_cc(G)>2 holds for many generalized theta graphs. © 2011 Wiley Periodicals, Inc. J Graph Theory 67: 178‐197, 2011     

Finding mixed strategies with small supports in extensive form games

The complexity of algorithms that compute strategies or operate on them typically depends on the representation length of the strategies involved. One measure for thesize of a mixed strategy is the number of strategies in itssupport — the set of pure strategies to which it gives positive probability. This paper investigates the existence of “small” mixed strategies in extensive form games, and how such strategies can be used to create more efficient algorithms. The basic idea is that, in an extensive form game, a mixed strategy induces a small set ofrealization weights that completely describe its observable behavior. This fact can be used to show that for any mixed strategy μ, there exists a realization-equivalent mixed strategy µ′ whose size is at most the size of the game tree. For a player with imperfect recall, the problem of finding such a strategy µ′ (given the realization weights) is NP-hard. On the other hand, if μ is a behavior strategy, µ′ can be constructed from μ in time polynomial in the size of the game tree. In either case, we can use the fact that mixed strategies need never be too large for constructing efficient algorithms that search for equilibria. In particular, we construct the first exponential-time algorithm for finding all equilibria of an arbitrary two-person game in extensive form.     

Influence of molecular properties on Coulomb capture of negative pions and muons

The meso-molecular model of pion or muon capture involves a parameter which represents the probability of de-excitation from the molecular orbital to an atomic orbital centred on a particular atom. This parameter depends on the fractional ionic character of the bonds in the molecule. An extension to the existing formalism is given so that the influence of molecular structure may be taken into account.