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.

Reply to comment on `Integrable Kondo impurity in one-dimensional q-deformed t - J models

This is a reply to the comment by P Schlottmann and A A Zvyagin.

Integrability and exact solution for coupled BCS systems associated with the su(4) Lie algebra

We introduce an integrable model for two coupled BCS systems through a solution of the Yang-Baxter equation associated with the Lie algebra su(4). By employing the algebraic Bethe ansatz, we determine the exact solution for the energy spectrum. An asymptotic analysis is conducted to determine the leading terms in the ground state energy, the gap and some one point correlation functions at zero temperature. (C) 2002 Published by Elsevier Science B.V.

Accumulation of human heat shock protein 60-reactive T cells in the gingival tissues of periodontitis patients

Heat shock protein 60s (hsp60) are remarkably immunogenic, and both T-cell and antibody responses to hsp60 have been reported in various inflammatory conditions. To clarify the role of hsp60 in T-cell responses in periodontitis, we examined the proliferative response of peripheral blood mononuclear cells (PBMC), as well as the cytokine profile and T-cell clonality, for periodontitis patients and controls following stimulation with recombinant human hsp60 and Porphyromonas gingivalis GroEL. To confirm the infiltration of hsp60-reactive T-cell clones into periodontitis lesions, nucleotide sequences within complementarity-determining region 3 of the T-cell receptor (TCR) beta-chain were compared between hsp60-reactive peripheral blood T cells and periodontitis lesion-infiltrating T cells. Periodontitis patients demonstrated significantly higher proliferative responses of PBMC to human hsp60, but not to P. gingivalis GroEL, than control subjects. The response was inhibited by anti-major histocompatibility complex class 11 antibodies. Analysis of the nucleotide sequences of the TCR demonstrated that human hsp60-reactive T-cell clones and periodontitis lesion-infiltrating T cells have the same receptors, suggesting that hsp60-reactive T cells accumulate in periodontitis lesions. Analysis of the cytokine profile demonstrated that hsp60-reactive PBMC produced significant levels of gamma interferon (IFN-gamma) in periodontitis patients, whereas P. gingivalis GroEL did not induce any, skewing toward a type1 or type2 cytokine profile. In control subjects no significant expression of IFN-gamma or interleukin 4 was induced. These results suggest that periodontitis patients have human hsp60-reactive T cells with a type I cytokine profile in their peripheral blood T-cell pools.

Pulpal heat changes with newly developed resin photopolymerisation systems

Composite resin is a widely-used direct tooth coloured restorative material. Photoactivation of the polymerisation reaction can be achieved by visible blue light from a range of light sources, including halogen lamps, metal halide lamps, plasma arc lamps, and Light Emitting Diode (LED) lights. Concerns have been raised that curing lights may induce a temperature rise that could be detrimental to the vitality of the dental pulp during the act of photoactivation. The present study examined heat changes associated with standardised class V restorations on the buccal surface of extracted premolar teeth, using a curing time of 40 seconds. The independent effects of type of light source, resin shade and remaining tooth thickness were assessed using a matrix experimental design. When a conventional halogen lamp, a metal halide lamp and two different LED lights were compared, it was found that both LED lamps elicited minimal thermal changes at the level of the dental pulp, whereas the halogen lamp induced greater changes and the metal halide lamp caused the greatest thermal insult of all the light sources. These thermal changes were influenced by resin shade, with different patterns for LED versus halogen or halide sources. Thermal stress reduced as the remaining thickness of tooth structure between the pulp and the cavity floor increased. From these results, it is concluded that LED lights produce the least thermal insult during photopolymerisation of composite resins.

Quasimode theory of quantum optical processes in photonic band gap materials

This paper deals with atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in photonic band gap materials. The case of high Q cavities has been treated elsewhere using Fano diagonalization based on a quasimode approach, showing that the cavity quasimodes are responsible for pseudomodes introduced to treat non-Markovian behaviour. The paper considers a simple model of a photonic band gap case, where the spatially dependent permittivity consists of a constant term plus a small spatially periodic term that leads to a narrow band gap in the spectrum of mode frequencies. Most treatments of photonic band gap materials are based on the true modes, obtained numerically by solving the Helmholtz equation for the actual spatially periodic permittivity. Here the field modes are first treated in terms of a simpler quasimode approach, in which the quasimodes are plane waves associated with the constant permittivity term. Couplings between the quasimodes occur owing to the small periodic term in the permittivity, with selection rules for the coupled modes being related to the reciprocal lattice vectors. This produces a field Hamiltonian in quasimode form. A matrix diagonalization method may be applied to relate true mode annihilation operators to those for quasimodes. The atomic transitions are coupled to all the quasimodes, and the true mode atom-EM field coupling constants (one-photon Rabi frequencies) are related to those for the quasimodes and also expressions are obtained for the true mode density. The results for the one-photon Rabi frequencies differ from those assumed in other work. Expressions for atomic decay rates are obtained using the Fermi Golden rule, although these are valid only well away from the band gaps.

Limits to squeezing in the degenerate optical parametric oscillator

We develop a systematic theory of quantum fluctuations in the driven optical parametric oscillator, including the region near threshold. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction in this nonequilibrium quantum phase transition. In particular, we compute the squeezing spectrum near threshold and calculate the optimum value. We find that the optimal noise reduction occurs at different driving fields, depending on the ratio of damping rates. The largest spectral noise reductions are predicted to occur with a very high-Q second-harmonic cavity. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory.

Turning up the heat on subzero fish: thermal dependence of sustained swimming in an Antarctic notothenioid

We determined the maximum sustained swimming speed (U-crit), and resting and maximum ventilation rates of the Antarctic fish Pagothenia borchgrevinki at five temperatures between -1degreesC and 8degreesC. We also determined resting metabolic rate (VO2) at -1degreesC, 2degreesC, and 4degreesC. U-crit of P. borchgrevinki was highest at -1degreesC (2.7+/-0.1 BL s(-1)) and rapidly decreased with temperature, representing a thermal performance breadth of only 5degreesC. This narrow thermal performance supports our prediction that specialisation to the subzero Antarctic marine environment is associated with a physiological trade-off in performance at high temperatures. Resting oxygen consumption and ventilation rate increased by more than 200% across the temperature range, which most likely contribute to the decrease in aerobic swimming capabilities at higher temperatures. (C) 2002 Published by Elsevier Science Ltd.

Simulations of thermal Bose fields in the classical limit

We demonstrate that the time-dependent projected Gross-Pitaevskii equation (GPE) derived earlier [M. J. Davis, R. J. Ballagh, and K. Burnett, J. Phys. B 34, 4487 (2001)] can represent the highly occupied modes of a homogeneous, partially-condensed Bose gas. Contrary to the often held belief that the GPE is valid only at zero temperature, we find that this equation will evolve randomized initial wave functions to a state describing thermal equilibrium. In the case of small interaction strengths or low temperatures, our numerical results can be compared to the predictions of Bogoliubov theory and its perturbative extensions. This demonstrates the validity of the GPE in these limits and allows us to assign a temperature to the simulations unambiguously. However, the GPE method is nonperturbative, and we believe it can be used to describe the thermal properties of a Bose gas even when Bogoliubov theory fails. We suggest a different technique to measure the temperature of our simulations in these circumstances. Using this approach we determine the dependence of the condensate fraction and specific heat on temperature for several interaction strengths, and observe the appearance of vortex networks. Interesting behavior near the critical point is observed and discussed.

Techniques for detailed heat transfer measurements in cold supersonic blowdown tunnels using thermochromic liquid crystals

The paper presents methods for measurement of convective heat transfer distributions in a cold flow, supersonic blowdown wind tunnel. The techniques involve use of the difference between model surface temperature and adiabatic wall temperature as the driving temperature difference for heat transfer and no active heating or cooling of the test gas or model is required. Thermochromic liquid crystals are used for surface temperature indication and results presented from experiments in a Mach 3 flow indicate that measurements of the surface heat transfer distribution under swept shock wave boundary layer interactions can be made. (C) 2002 Elsevier Science Ltd. All rights reserved.

Enriched behavioral prediction equation and its impact on structured learning and the dynamic calculus

This theoretical note describes an expansion of the behavioral prediction equation, in line with the greater complexity encountered in models of structured learning theory (R. B. Cattell, 1996a). This presents learning theory with a vector substitute for the simpler scalar quantities by which traditional Pavlovian-Skinnerian models have hitherto been represented. Structured learning can be demonstrated by vector changes across a range of intrapersonal psychological variables (ability, personality, motivation, and state constructs). Its use with motivational dynamic trait measures (R. B. Cattell, 1985) should reveal new theoretical possibilities for scientifically monitoring change processes (dynamic calculus model; R. B. Cattell, 1996b), such as encountered within psycho therapeutic settings (R. B. Cattell, 1987). The enhanced behavioral prediction equation suggests that static conceptualizations of personality structure such as the Big Five model are less than optimal.

Physiological responses to the menstrual cycle - Implications for the development of heat illness in female athletes

Fluctuations in estrogen and progesterone during the menstrual cycle can cause changes in body systems other than the reproductive system. For example, progesterone is involved in the regulation of fluid balance in the renal tubules and innervation of the diaphragm via the phrenic nerve. However, few significant changes in the responses of the cardiovascular and respiratory systems, blood lactate, bodyweight, performance and ratings of perceived exertion are evident across the cycle. Nevertheless, substantial evidence exists to suggest that increased progesterone levels during the luteal phase cause increases in both core and skin temperatures and alter the temperature at which sweating begins during exposure to both ambient and hot environments. As heat illness is characterised by a significant increase in body temperature, it is feasible that an additional increase in core temperature during the luteal phase could place females at an increased risk of developing heat illness during this time. In addition, it is often argued that physiological gender differences such as oxygen consumption, percentage body fat and surface area-to-mass ratio place females at a higher risk of heat illness than males. This review examines various physiological responses to heat exposure during the menstrual cycle at rest and during exercise, and considers whether such changes increase the risk of heat illness in female athletes during a particular phase of the menstrual cycle.

Analysis of the wind field and heat budget in an alpine lake basin during summertime fair weather conditions

Observational data collected in the Lake Tekapo hydro catchment of the Southern Alps in New Zealand are used to analyse the wind and temperature fields in the alpine lake basin during summertime fair weather conditions. Measurements from surface stations, pilot balloon and tethersonde soundings, Doppler sodar and an instrumented light aircraft provide evidence of multi-scale interacting wind systems, ranging from microscale slope winds to mesoscale coast-to-basin flows. Thermal forcing of the winds occurred due to differential heating as a consequence of orography and heterogeneous surface features, which is quantified by heat budget and pressure field analysis. The daytime vertical temperature structure was characterised by distinct layering. Features of particular interest are the formation of thermal internal boundary layers due to the lake-land discontinuity and the development of elevated mixed layers. The latter were generated by advective heating from the basin and valley sidewalls by slope winds and by a superimposed valley wind blowing from the basin over Lake Tekapo and up the tributary Godley Valley. Daytime heating in the basin and its tributary valleys caused the development of a strong horizontal temperature gradient between the basin atmosphere and that over the surrounding landscape, and hence the development of a mesoscale heat low over the basin. After noon, air from outside the basin started flowing over mountain saddles into the basin causing cooling in the lowest layers, whereas at ridge top height the horizontal air temperature gradient between inside and outside the basin continued to increase. In the early evening, a more massive intrusion of cold air caused rapid cooling and a transition to a rather uniform slightly stable stratification up to about 2000 m agl. The onset time of this rapid cooling varied about 1-2 h between observation sites and was probably triggered by the decay of up-slope winds inside the basin, which previously countered the intrusion of air over the surrounding ridges. The intrusion of air from outside the basin continued until about mid-night, when a northerly mountain wind from the Godley Valley became dominant. The results illustrate the extreme complexity that can be caused by the operation of thermal forcing processes at a wide range of spatial scales.