Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

A class of compact dwarf galaxies from disruptive processes in galaxy clusters

Dwarf galaxies have attracted increased attention in recent years, because of their susceptibility to galaxy transformation processes within rich galaxy clusters. Direct evidence for these processes, however, has been difficult to obtain, with a small number of diffuse light trails and intra-cluster stars, being the only signs of galaxy disruption. Furthermore, our current knowledge of dwarf galaxy populations may be very incomplete, because traditional galaxy surveys are insensitive to extremely diffuse or compact galaxies. Aware of these concerns, we recently undertook an all-object survey of the Fornax galaxy cluster. This revealed a new population of compact members, overlooked in previous conventional surveys. Here we demonstrate that these 'ultra-compact' dwarf galaxies are structurally and dynamically distinct from both globular star clusters and known types of dwarf galaxy, and thus represent a new class of dwarf galaxy. Our data are consistent with the interpretation that these are the remnant nuclei of disrupted dwarf galaxies, making them an easily observed tracer of galaxy disruption.

Ladder operator for the one-dimensional Hubbard model

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to the separation of spin and charge excitations. The ladder operator is obtained by a very general formalism which is applicable to any model that can be derived from a solution of the Yang-Baxter equation.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

Solution structure of robustoxin, the lethal neurotoxin from the funnel-web spider Atrax robustus

The solution structure of robustoxin, the lethal neurotoxin from the Sydney funnel-web spider Atrax robustus, has been determined from 2D H-1 NMR data, Robustoxin is a polypeptide of 42 residues cross-linked by four disulphide bonds, the connectivities of which were determined from NMR data and trial structure calculations to be 1-15, 8-20, 14-31 and 16-42 (a 1-4/2-6/3-7/5-8 pattern), The structure consists of a small three-stranded, anti-parallel beta-sheet and a series of interlocking gamma-turns at the C-terminus. It also contains a cystine knot, thus placing it in the inhibitor cystine knot motif family of structures, which includes the omega-conotoxins and a number of plant and animal toxins and protease inhibitors. Robustoxin contains three distinct charged patches on its surface, and an extended loop that includes several aromatic and non-polar residues, Both of these structural features may play a role in its binding to the voltage-gated sodium channel. (C) 1997 Federation of European Biochemical Societies.

Solution structure and proposed binding mechanism of a novel potassium channel toxin kappa-conotoxin PVIIA

Background: kappa-PVIIA is a 27-residue polypeptide isolated from the venom of Conus purpurascens and is the first member of a new class of conotoxins that block potassium channels. By comparison to other ion channels of eukaryotic cell membranes, voltage-sensitive potassium channels are relatively simple and methodology has been developed for mapping their interactions with small-peptide toxins, PVIIA, therefore, is a valuable new probe of potassium channel structure. This study of the solution structure and mode of channel binding of PVIIA forms the basis for mapping the interacting residues at the conotoxin-ion channel interface. Results: The three-dimensional structure of PVIIA resembles the triple-stranded beta sheet/cystine-knot motif formed by a number of toxic and inhibitory peptides. Subtle structural differences, predominantly in loops 2 and 4, are observed between PVIIA and other conotoxins with similar structural frameworks, however. Electrophysiological binding data suggest that PVIIA blocks channel currents by binding in a voltage-sensitive manner to the external vestibule and occluding the pore, Comparison of the electrostatic surface of PVIIA with that of the well-characterised potassium channel blocker charybdotoxin suggests a likely binding orientation for PVIIA, Conclusions: Although the structure of PVIIA is considerably different to that of the alpha K scorpion toxins, it has a similar mechanism of channel blockade. On the basis of a comparison of the structures of PVIIA and charybdotoxin, we suggest that Lys19 of PVIIA is the residue which is responsible for physically occluding the pore of the potassium channel.

The structure of quantum Lie algebras for the classical series, B-l, C-l and D-l

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at q = 1. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint --> adjoint We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B-l, C-l and D-l. In the quantum case the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.

Anomalous fluorescence spectra in an extremely weak, broadband squeezed vacuum under monochromatic and bichromatic excitation

We show that a two-level atom interacting with an extremely weak squeezed vacuum can display resonance fluorescence spectra that are qualitatively different to those that can be obtained using fields with a classical analogue. We consider first the free space situation with monochromatic excitation, and then discuss a bichromatically driven two-level atom in a cavity as a practical scenario for experimentally detecting the anomalous features predicted. We show that in the bad cavity limit, the anomalous spectral features appear for a weak squeezed vacuum and large frequency differences of the bichromatic field, conditions which are easily accessible in laboratories. The advantage of bichromatic, as opposed to monochromatic, excitation is that there is no coherent scattering at line centre which could obscure the observations. A scaling law is derived, N similar to Omega(4) which relates the squeezed photon number to the Rabi frequency at which the anomalous features appear. (C) 1998 Elsevier Science B.V.

Data analysis in multiple-frequency bioelectrical impedance analysis

The performance of three analytical methods for multiple-frequency bioelectrical impedance analysis (MFBIA) data was assessed. The methods were the established method of Cole and Cole, the newly proposed method of Siconolfi and co-workers and a modification of this procedure. Method performance was assessed from the adequacy of the curve fitting techniques, as judged by the correlation coefficient and standard error of the estimate, and the accuracy of the different methods in determining the theoretical values of impedance parameters describing a set of model electrical circuits. The experimental data were well fitted by all curve-fitting procedures (r = 0.9 with SEE 0.3 to 3.5% or better for most circuit-procedure combinations). Cole-Cole modelling provided the most accurate estimates of circuit impedance values, generally within 1-2% of the theoretical values, followed by the Siconolfi procedure using a sixth-order polynomial regression (1-6% variation). None of the methods, however, accurately estimated circuit parameters when the measured impedances were low (<20 Omega) reflecting the electronic limits of the impedance meter used. These data suggest that Cole-Cole modelling remains the preferred method for the analysis of MFBIA data.

Resonance fluorescence spectrum in a weak squeezed field with an arbitrary bandwidth

We analyze the linewidth narrowing in the fluorescence spectrum of a two-level atom driven by a squeezed vacuum field of a finite bandwidth. It is found that the fluorescence spectrum in a low-intensity squeezed field can exhibit a (omega - omega(0))(-6) frequency dependence in the wings. We show that this fast fall-off behavior is intimately related to the properties of a narrow-bandwidth squeezed field and does not extend into the region of broadband excitation. We apply the Linear response model and find that the narrowing results from a convolution of the atom response with the spectrum of the incident field. On the experimental side, we emphasize that the linewidth narrowing is not sensitive to the solid angle of the squeezed modes coupled to the atom. We also compare the fluorescence spectrum with the quadrature-noise spectrum and find that the fluorescence spectrum for an off-resonance excitation does not reveal the noise spectrum. We show that this difference arises from the competing three-photon scattering processes. [S1050-2947(98)04308-X].

Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.