(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms

Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix elements are sine or cosine functions of one variable each. These functions are eigenfunctions of the Laplace operator, satisfying specific conditions at the boundary of a certain domain F of the n-dimensional Euclidean space. Discrete and continuous orthogonality on F of the functions within each family, allows one to introduce symmetrized and antisymmetrized multivariate Fourier-like transforms, involving the symmetric and antisymmetric multivariate sine and cosine functions.Comment: 25 pages, no figures; LaTaX; corrected typo

Resource-driven Substructural Defeasible Logic

Linear Logic and Defeasible Logic have been adopted to formalise different features relevant to agents: consumption of resources, and reasoning with exceptions. We propose a framework to combine sub-structural features, corresponding to the consumption of resources, with defeasibility aspects, and we discuss the design choices for the framework

Search for optical bursts from the gamma ray burst source GBS 0526-66

Attempts were made to detect optical bursts from the gamma-ray burst source GBS 0526-66 during Dec. 31, 1984 to Jan. 2, 1985 and Feb. 23 to Feb. 24, 1985, using the one meter reflector of the Kavalur Observatory. Jan. 1, 1985 coincided with the zero phase of the predicted 164 day period of burst activity from the source (Rothschild and Lingenfelter, 1984). A new optical burst photon counting system with adjustable trigger threshold was used in parallel with a high speed photometer for the observations. The best time resolution was 1 ms and maximum count rate capability was 255,000 counts s(-1). Details of the instrumentation and observational results are presented

Relativistic Proton Production During the 14 July 2000 Solar Event: The Case for Multiple Source Mechanisms

Protons accelerated to relativistic energies by transient solar and interplanetary phenomena caused a ground-level cosmic ray enhancement on 14 July 2000, Bastille Day. Near-Earth spacecraft measured the proton flux directly and ground-based observatories measured the secondary responses to higher energy protons. We have modelled the arrival of these relativistic protons at Earth using a technique which deduces the spectrum, arrival direction and anisotropy of the high-energy protons that produce increased responses in neutron monitors. To investigate the acceleration processes involved we have employed theoretical shock and stochastic acceleration spectral forms in our fits to spacecraft and neutron monitor data. During the rising phase of the event (10:45 UT and 10:50 UT) we find that the spectrum between 140 MeV and 4 GeV is best fitted by a shock acceleration spectrum. In contrast, the spectrum at the peak (10:55 UT and 11:00 UT) and in the declining phase (11:40 UT) is best fitted with a stochastic acceleration spectrum. We propose that at least two acceleration processes were responsible for the production of relativistic protons during the Bastille Day solar event: (1) protons were accelerated to relativistic energies by a shock, presumably a coronal mass ejection (CME). (2) protons were also accelerated to relativistic energies by stochastic processes initiated by magnetohydrodynamic (MHD) turbulence.Comment: 38 pages, 9 figures, accepted for publication in the Astrophysical Journal, January, 200

Derivation of a dynamic model of the kinetics of nitrogen uptake throughout the growth of lettuce : calibration and validation

A kinetic model of nitrogen (N) uptake throughout growth was developed for lettuce cultivated in nutrient solution under varying natural light conditions. The model couples nitrogen uptake with dry matter accumulation using a two-compartment mechanistic approach, incorporating structural and non-structural pools. Maximum nitrogen uptake rates are assumed to decline with shoot dry weight, to allow for the effects of plant age. The model was parameterized using data from the literature, and calibrated for differences in light intensity using an optimization algorithm utilizing data from three experiments in different growing seasons. The calibrated model was validated against the data from two independent experiments conducted under different light conditions. Results showed that the model made good predictions of nitrogen uptake by plants from seedlings to maturity under fluctuating light levels in a glasshouse. Plants grown at a higher light intensity showed larger maximum nitrogen uptake rates, but the effect of light intensity declined towards plant maturity

Dynamics of Magnetized Bulk Viscous Strings in Brans-Dicke Gravity

We explore locally rotationally symmetric Bianchi I universe in Brans-Dicke gravity with self-interacting potential by using charged viscous cosmological string fluid. We use a relationship between the shear and expansion scalars and also take the power law for scalar field as well as self-interacting potential. It is found that the resulting universe model maintains its anisotropic nature at all times due to the proportionality relationship between expansion and shear scalars. The physical implications of this model are discussed by using different parameters and their graphs. We conclude that this model corresponds to an accelerated expanding universe for particular values of the parameters.Comment: 17 pages, 6 figure

Vanishing largest Lyapunov exponent and Tsallis entropy

We present a geometric argument that explains why some systems having vanishing largest Lyapunov exponent have underlying dynamics aspects of which can be effectively described by the Tsallis entropy. We rely on a comparison of the generalised additivity of the Tsallis entropy versus the ordinary additivity of the BGS entropy. We translate this comparison in metric terms by using an effective hyperbolic metric on the configuration/phase space for the Tsallis entropy versus the Euclidean one in the case of the BGS entropy. Solving the Jacobi equation for such hyperbolic metrics effectively sets the largest Lyapunov exponent computed with respect to the corresponding Euclidean metric to zero. This conclusion is in agreement with all currently known results about systems that have a simple asymptotic behaviour and are described by the Tsallis entropy.Comment: 15 pages, No figures. LaTex2e. Some overlap with arXiv:1104.4869 Additional references and clarifications in this version. To be published in QScience Connec

Glassy transition and metastability in four-spin Ising model

Using Monte Carlo simulations we show that the three-dimensional Ising model with four-spin (plaquette) interactions has some characteristic glassy features. The model dynamically generates diverging energy barriers, which give rise to slow dynamics at low temperature. Moreover, in a certain temperature range the model possesses a metastable (supercooled liquid) phase, which is presumably supported by certain entropy barriers. Although extremely strong, metastability in our model is only a finite-size effect and sufficiently large droplets of stable phase divert evolution of the system toward the stable phase. Thus, the glassy transitions in this model is a dynamic transition, preceded by a pronounced peak in the specific heat.Comment: extensively revised, with further simulations of metastability properties, response to referees tactfully remove

Discriminating cool-water from warm-water carbonates and their diagenetic environments using element geochemistry: the Oligocene Tikorangi Formation (Taranaki Basin) and the dolomite effect

Fields portrayed within bivariate element plots have been used to distinguish between carbonates formed in warm- (tropical) water and cool- (temperate) water depositional settings. Here, element concentrations (Ca, Mg, Sr, Na, Fe, and Mn) have been determined for the carbonate fraction of bulk samples from the late Oligocene Tikorangi Formation, a subsurface, mixed dolomite-calcite, cool-water limestone sequence in Taranaki Basin, New Zealand. While the occurrence of dolomite is rare in New Zealand Cenozoic carbonates, and in cool-water carbonates more generally, the dolomite in the Tikorangi carbonates is shown to have a dramatic effect on the "traditional" positioning of cool-water limestone fields within bivariate element plots. Rare undolomitised, wholly calcitic carbonate samples in the Tikorangi Formation have the following average composition: Mg 2800 ppm; Ca 319 100 ppm; Na 800 ppm; Fe 6300 ppm; Sr 2400 ppm; and Mn 300 ppm. Tikorangi Formation dolomite-rich samples (>15% dolomite) have average values of: Mg 53 400 ppm; Ca 290 400 ppm; Na 4700 ppm; Fe 28 100 ppm; Sr 5400 ppm; and Mn 500 ppm. Element-element plots for dolomite-bearing samples show elevated Mg, Na, and Sr values compared with most other low-Mg calcite New Zealand Cenozoic limestones. The increased trace element contents are directly attributable to the trace element-enriched nature of the burial-derived dolomites, termed here the "dolomite effect". Fe levels in the Tikorangi Formation carbonates far exceed both modern and ancient cool-water and warm-water analogues, while Sr values are also higher than those in modern Tasmanian cool-water carbonates, and approach modern Bahaman warm-water carbonate values. Trace element data used in conjunction with more traditional petrographic data have aided in the diagenetic interpretation of the carbonate-dominated Tikorangi sequence. The geochemical results have been particularly useful for providing more definitive evidence for deep burial dolomitisation of the deposits under the influence of marine-modified pore fluids