Thue's theorem and the diophantine equation x2 - Dy2 = ±N

A constructive version of a theorem of Thue is used to provide representations of certain integers as x(2) - Dy-2, where D = 2, 3, 5, 6, 7.

Steiner trades that give rise to completely decomposable latin interchanges

In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into six disjoint latin interchanges.

On the Hamilton-Waterloo problem

The Hamilton-Waterloo problem asks for a 2-factorisation of K-v in which r of the 2-factors consist of cycles of lengths a(1), a(2),..., a(1) and the remaining s 2-factors consist of cycles of lengths b(1), b(2),..., b(u) (where necessarily Sigma(i)(=1)(t) a(i) = Sigma(j)(=1)(u) b(j) = v). In thus paper we consider the Hamilton-Waterloo problem in the case a(i) = m, 1 less than or equal to i less than or equal to t and b(j) = n, 1 less than or equal to j less than or equal to u. We obtain some general constructions, and apply these to obtain results for (m, n) is an element of {(4, 6)1(4, 8), (4, 16), (8, 16), (3, 5), (3, 15), (5, 15)}.

The three-way intersection problem for latin squares

The set of integers k for which there exist three latin squares of order n having precisely k cells identical, with their remaining n(2) - k cells different in all three latin squares, denoted by I-3[n], is determined here for all orders n. In particular, it is shown that I-3[n] = {0,...,n(2) - 15} {n(2) - 12,n(2) - 9,n(2)} for n greater than or equal to 8. (C) 2002 Elsevier Science B.V. All rights reserved.

Pathways to Melanoma Development: Lessons from the Mouse

Because of subtle differences between mouse and human skin, mice have traditionally not been an ideal model to study melanoma development. Understanding of the molecular mechanisms of melanoma predisposition, however, has been greatly improved by modeling various pathway defects in the mouse. This review analyzes the latest developments in mouse models of melanoma, and summarizes what these may indicate about the development of this neoplasm in humans. Mutations of genes involved in human melanoma have been recapitulated with some unexpected results, particularly with respect to the role of the two transcripts (Ink4a and Arf) encoded by the Cdkn2a locus. Both the Ink4a/pRb and Arf/p53 pathways are involved in melanoma development in mice, and possible mechanisms of cross-talk between the two pathways are discussed. We also know from mouse models that Ras/mitogen-activated protein kinase pathway activation is very important in melanoma development, either through direct activation of Ras (e.g., Hras G12V), or via activation of Ras-effector pathways by other oncogenes (e.g., Ret, Hgf/Sf). Ras can cooperate with the Arf/p53 pathway, and probably the Ink4a/Rb pathway, to induce melanoma. These three growth regulation pathways (Ink4a/pRb, Arf/p53, and Ras/mitogen-activated protein kinase) seem to represent three major axes of melanoma development in mice. Finally, we summarize experiments using genetically modified mice that have given indications of the intensity and timing of ultraviolet radiation exposure that may be most responsible for melanoma development.

Atom lasers, coherent states, and coherence II. Maximally robust ensembles of pure states

As discussed in the preceding paper [Wiseman and Vaccaro, preceding paper, Phys. Rev. A 65, 043605 (2002)], the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of rho(ss) as a stationary ensemble of pure states, is more natural. In the preceding paper we concentrated upon the question of whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy chi of the bosons in the laser mode, and the excess phase noise nu. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit (nu=chi=0), the most robust states are coherent states. As the phase noise or phase dispersion is increased through nu or the self-interaction of the bosons chi, respectively, the most robust states become more and more amplitude squeezed. We find scaling laws for these states, and give analytical derivations for them. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR ensemble being an ensemble of states with a well-defined coherent amplitude. This lends support to our approach of regarding robust PR ensembles as the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large.

An inverse design of an open, head/neck RF coil for MRI

Radio-frequency (RF) coils are a necessary component of magnetic resonance imaging (MRI) systems. When used in transmit operation, they act to generate a homogeneous RF magnetic field within a volume of interest and when in receive operation, they act to receive the nuclear magnetic resonance signal from the RF-excited specimen. This paper outlines a procedure for the design of open RF coils using the time-harmonic inverse method. This method entails the calculation of an ideal current density on a multipaned planar surface that would generate a specified magnetic field within the volume of interest. Because of the averaging effect of the regularization technique in the matrix solution, the specified magnetic field is shaped within an iterative procedure until the generated magnetic field matches the desired magnetic field. The stream-function technique is used to ascertain conductor positions and a method of moments package is then used to finalize the design. An open head/neck coil was designed to operate in a clinical 2T MRI system and the presented results prove the efficacy of this design methodology.

The metamorphosis of lambda-fold K-3,K-3-designs into lambda-fold 6-cycle systems

In this paper necessary and sufficient conditions are given for the metamorphosis of a lambda-fold K-3,K-3-design of order n into a lambda-fold 6-cycle system of order n, by retaining one 6-cycle subgraph from each copy of K-3,K-3, and then rearranging the set of all the remaining edges, three from each K-3,K-3, into further 6-cycles so that the result is a lambda-fold 6-cycle system.

Comparative analysis of genetic diversity in the mangrove species Avicennia marina (Forsk.) Vierh. (Avicenniaceae) detected by AFLPs and SSRs

Avicennia marina is an important mangrove species with a wide geographical and climatic distribution which suggests that large amounts of genetic diversity are available for conservation and breeding programs. In this study we compare the informativeness of AFLPs and SSRs for assessing genetic diversity within and among individuals, populations and subspecies of A. marina in Australia. Our comparison utilized three SSR loci and three AFLP primer sets that were known to be polymorphic, and could be run in a single analysis on a capillary electrophoresis system, using different-colored fluorescent dyes. A total of 120 individuals representing six populations and three subspecies were samplcd. At the locus level, SSRs were considerably more variable than AFLPs, with a total of 52 alleles and an average heterozygosity of 0.78. Average heterozygosity for AFLPs was 0.193, but all of the 918 bands scored were polymorphic. Thus, AFLPs were considerably more efficient at revealing polymorphic loci than SSRs despite lower average heterozygosities. SSRs detected more genetic differentiation between populations (19 vs 9%) and subspecies (35 vs 11%) than AFLPs. Principal co-ordinate analysis revealed congruent patterns of genetic relationships at the individual, population and subspecific levels for both data sets. Mantel testing confirmed congruence between AFLP and SSR genetic distances among, but not within, population comparisons, indicating that the markers were segregating inde- pendently but that evolutionary groups (populations and subspecies) were similar. Three genetic criteria of importance for defining priorities for ex situ collections or in situ conservation programs (number of alleles, number of locally common alleles and number of private alleles) were correlated between the AFLP and SSR data sets. The congruence between AFLP and SSR data sets suggest that either method, or a combination, is applicable to expanded genetic studies of mangroves. The codominant nature of SSRs makes them ideal for further population-based investigations, such as mating-system analyses, for which the dominant AFLP markers are less well suited. AFLPs may be particularly useful for monitoring propagation programs and identifying duplicates within collections, since a single PCR assay can reveal many loci at once.

Trade spectra of complete partite graphs

The trade spectrum of a graph G is essentially the set of all integers t for which there is a graph H whose edges can be partitioned into t copies of G in two entirely different ways. In this paper we determine the trade spectrum of complete partite graphs, in all but a few cases.

Dynamic Behavior of the Jahn-Teller distorted Cu(H2O)(6)(2+) ion in Cu2+ doped Cs-2[Zn(H2O)(6)](ZrF6)(2) and the crystal structure of the host lattice

The temperature dependence of the X- and Q-band EPR spectra of Cs-2[Zn(H2O)(6)](ZrF6)(2) containing similar to1% Cu2+ is reported. All three molecular g-values vary with temperature, and their behavior is interpreted using a model in which the potential surface of the Jahn-Teller distorted Cu(H2O)(6)(2+) ion is perturbed by an orthorhombic strain induced by interactions with the surrounding lattice. The strain parameters are significantly smaller than those reported previously for the Cu(H2O)(6)(2+) ion in similar lattices. The temperature dependence of the two higher g-values suggests that in the present compound the lattice interactions change slightly with temperature. The crystal structure of the Cs-2[Zn(H2O)(6)](ZrF6)(2) host is reported, and the geometry of the Zn(H2O)(6)(2+) ion is correlated with lattice strain parameters derived from the EPR spectrum of the guest Cu2+ complex.