k-convexn-person games and their cores

For any natural numbersk andn, the subclass ofk-convexn-person games is introduced. In casek=n, the subclass consists of the convexn-person games. Ak-convexn-person game is characterized in several ways in terms of the core and certain marginal worth vectors. The marginal worth vectors of a game are described in terms of an upper bound for the core and the corresponding gap function. It is shown that thek-convexity of ann-person gamev is equivalent to

1. all marginal worth vectors ofv belong to the core ofv; or
2. the core ofv is the convex hull of the set consisting of all marginal worth vectors ofv; or
3. the extreme points of the core ofv are exactly the marginal worth vectors ofv.

Examples ofk-convexn-person games are also treated.     

Ethers as ligands. Part VI. Transition metal(II) complexes with 18-crown-6

Summary Seven new coordination compounds are reported with the cyclicpolyether 18-crown-6 as the ligand,viz. [Mg(18-crown-6) (H₂O)₂](SbCl₆)₂, [M(18-crown-6)(MeNO₆)₂](SbCl₆)₂ with M is Ca²⁺ and Sr²⁺, [M(18-crown-6)(MeNO₂)](SbCl₆)₂ with M is Mn²⁺ and Co²⁺, and [M(18-crown-6)](SbCl₆)₂ with M is Ni²⁺ and Zn²⁺.     

A solvent-controlled switch of manganese complex assemblies with a beta-diketonate-based ligand

The coordination properties of the new polynucleating ligand H(3)L1 (1,3-bis(3-oxo-3-phenylpropionyl)-2-hydroxy-5-methylbenzene) with Mn(II/III) are described. Depending on the solvent used, the reaction of H(3)L1 with Mn(OAc)(2) yields either of the two new multinuclear assemblies [Mn(2)(HL1)(2)(py)(4)] (1) and [Mn(3)(HL1)(3)] (2), as revealed by X-ray crystallography. The structure of 2 is remarkable in that it shows a unique asymmetric triple-stranded helicate. Complexes 1 and 2 can be interconverted by controlling the solvent of the reaction system, and therefore, this ensemble constitutes an interesting externally addressable switch. In the presence of Mn(III)/pyridine, partial degradation of H(3)L1 occurs via oxidative cleavage, and the new complex [Mn(2)(L2)(2)(py)(4)] (3) is formed. The crystal structure of this complex has shown the fully deprotonated form of the new donor H(3)L2 (3-(3-oxo-3-phenylpropionyl)-5-methylsalicylic acid). From the same reaction, the Mn(II) complex 1 is also obtained. A rational synthesis of H(3)L2 is reported, and this has been used to prepare 3 in high yields, directly from its components. Variable-temperature magnetic susceptibility (chi(m)) measurements were performed on complexes 1-3 under a magnetic field of 1 kG. The data for each complex were fit to the appropriate chi(m) vs T theoretical equation, respectively. In 1, the Mn(II) ions are uncoupled, with g = 2.01. The data from 2 were fit by assuming the presence of an exchange coupled Mn(II)...Mn(II) pair next to a magnetically isolated Mn(II) center. The fit gave J = -2.75 cm(-1), g(12) = 1.97, and g(3) = 1.92, respectively. In 3, two models fit the experimental data. In the most satisfactory, the Mn(III) ions are coupled antiferromagnetically with J = -1.48 cm(-1) and g = 1.98 and a term for weak ferromagnetic intermolecular exchange is included with zJ' = 0.39 cm(-1). The other model contemplates the presence of two uncoupled zero field split Mn(III) ions.     

Assessing calves as carriers of Cryptosporidium and Giardia with zoonotic potential on dairy and beef farms within a water catchment area by mutation scanning

In the present study, we undertook a molecular epidemiological survey of Cryptosporidium and Giardia in calves on three dairy and two beef farms within an open drinking water catchment area (Melbourne, Australia). Faecal samples (n = 474) were collected from calves at two time points (5 months apart) and tested using a PCR‐based mutation scanning‐targeted sequencing phylogenetic approach, employing regions within the genes of small subunit (SSU) of ribosomal RNA (designated partial SSU), 60 kDa glycoprotein (pgp60) and triose phosphate isomerase (ptpi) as genetic markers. Using partial SSU, the C. bovis, C. parvum, C. ryanae and a new genotype of Cryptosporidium were characterised from totals of 74 (15.6%), 35 (7.3%), 37 (7.8%) and 9 (1.9%) samples, respectively. Using pgp60, C. parvum genotype IIa subgenotype A18G3R1 was detected in 29 samples. Using ptpi, G. duodenalis assemblages A and E were detected in totals of 10 (2.1%) and 130 (27.4%) samples, respectively. The present study showed that a considerable proportion of dairy and beef calves in this open water catchment region excreted Cryptosporidium (i.e. subgenotype IIaA18G3R1) and Giardia (e.g. assemblage A) that are consistent with those infecting humans, inferring that they are of zoonotic importance. Future work should focus on exploring, in a temporal and spatial way, whether these parasites occur in the environment and water of the catchment reservoir.     

Asymmetry reversal in the reflection from a two-dimensional photonic crystal

The measured, angle-dependent, reflection spectra of a two-dimensional GaAs photonic crystal consist of an asymmetric peak on top of an oscillating background. At large angles of incidence (>70 degrees), the asymmetry of the peak is observed to flip for p-polarized light. We explain the observed spectra with a Fano model that includes loss and interference between a resonant waveguide component and direct Fresnel reflection of the layered structure. We show that the reversal of the asymmetry of the line is due to a change in sign of the direct reflection at Brewster's angle.     

Integrated optical microcavities for enhanced evanescent-wave spectroscopy

The use of integrated optical microcavities (MCs) for enhanced optical spectroscopy and sensing is investigated. The MC sustains high- Q whispering-gallery modes, in which the energy of the optical field can be efficiently stored. The resulting enhanced field can be used to probe fluorescent molecules in the cladding of the MC. Enhanced fluorescence excitation with an integrated optical MC is demonstrated experimentally for what is believed to be the first time. A comparison between a MC and a straight waveguide shows that the MC may give an increase of 40 times in fluorescence excitation. Because of the ultrasmall size of the MC (15 microm in radius), the fluorescence signal may be observed from only 20 molecules in the cladding.     

The equation of state of solid molecular hydrogen and deuterium

Isochores of solid H₂ and D₂ have been measured to 2 kbar. Our results lead to reevaluation of the 4.2 K isotherm of Anderson and Swenson to 25 kbar. The equation of state has been determined, including ortho-para dependence. The pre-melting phase transition cited in recent russian literature has not been detected.