Asymptotic Behavior of the Density in a Parabolic SPDE

Consider the density of the solution X(t, x) of a stochastic heat equation with small noise at a fixed t[0, T], x[0, 1]. In this paper we study the asymptotics of this density as the noise vanishes. A kind of Taylor expansion in powers of the noise parameter is obtained. The coefficients and the residue of the expansion are explicitly calculated. In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximating process and the limit one is proved. Also a suitable iterative local integration by parts formula is developed.     

Remarks on Herz-Type Hardy Spaces

Basic properties of the Herz-type Hardy spaces , such as the boundedness of singular integral operators and the fractional integration operators, atomic decomposition, dense subspaces, etc., are established in the full range 0 < q < ∞. Partly supported by the Grants-in-Aid for Scientific Research (A)(1)11304009, (B)(1)10440046, Japan Society for the Promotion of Science.     

Effect of the stagnation temperature on supersonic flow parameters: Application for air in nozzles

When the stagnation temperature of a perfect gas increases, the specific heats and their ratio do not remain constant any more and start to vary with this temperature. The gas remains perfect and its state equation always remains valid, except it will be called a calorically imperfect gas. The aim of this research is to develop the relations of the necessary thermodynamics and geometrical ratios and to study the supersonic flow at high temperature (lower than the threshold of dissociation). The results are found by the resolution of nonlinear algebraic equations and integration of complex analytical functions where the exact calculation is impossible. The dichotomy method is used to solve the nonlinear equation, and the Simpson algorithm is used for the numerical integration of the found integrals. A condensation of the nodes is used, since the functions to be integrated have a high gradient at the extremity of the interval of integration. A comparison is made with a calorifcally perfect gas to determine the error of this. An application is made for air in a supersonic nozzle. The text was submitted by the authors in English.     

On the integrated behaviour of non-stationary volatility in stock markets

This paper analyses the behaviour of volatility for several international stock market indexes, namely the SP 500 (USA), the Nikkei (Japan), the PSI 20 (Portugal), the CAC 40 (France), the DAX 30 (Germany), the FTSE 100 (UK), the IBEX 35 (Spain) and the MIB 30 (Italy), in the context of non-stationarity. Our empirical results point to the evidence of the existence of integrated behaviour among several of those stock market indexes of different dimensions. It seems, therefore, that the behaviour of these markets tends to some uniformity, which can be interpreted as the existence of a similar behaviour facing to shocks that may affect the worldwide economy. Whether this is a cause or a consequence of market globalization is an issue that may be stressed in future work.     

Extending the applicability of the discrete dipole approximation for multi-scale features on surface

Many problems in science and engineering involve significant physical entities and processes that span a substantial range of dimensions. In the case of characterization of bacteria on growth media using light scattering the length scales of interest can be classified as micro-scale (single bacterium), macro-scale (bacterial colonies of more than 10¹² bacterium that have passed through the exponential growth phase and reached mm size), and the intermediate or meso-scale of several tens of hundreds of bacteria. Light scattering approaches, to be effective in determining physical properties such as morphology and material composition, must comprehend this spectrum of length scales. The discrete dipole approximation (DDA), a powerful modeling tool for rigorous 3-D vector scattering, has shown its capability to predict the light scattering from micro-scale objects. To be able to accommodate meso-scale objects, we need to extend the computational limits of the DDA method such that it could compute object sizes of 10λ-30λ characteristic dimension (i.e. volumes of 10³-10⁴ cubic wavelengths). To accomplish this, an analysis of the DDA method was performed for meso-scale cases of interest especially in biological applications. Based on this study, we propose new Sommerfeld integration paths and a revised iterative algorithm that combine to provide substantial improvements in the size of the computational domain that can be modeled for a given convergence criterion.     

Adaptive selection of parameters for precise computation of matrix exponential based on padé approximation

讨论了基于Pad\'{e}逼近的矩阵指数精细积分方法中加权系数N 和展开项数q的自适应选择问题. 参数(N,q)的选择直接影响到矩阵指数计算的精度和效 率. 采用矩阵函数逼近理论，研究了参数N和q的增加对精度的影响程度，据此，提出了 参数(N,q)优化组合的递推自适应选择方法. 该方法可以根据矩阵本身的性态选择合适的参 数(N,q),而参数选择的计算量与矩阵指数的计算量相比几乎可以忽略，这对于增强矩阵指 数精细积分方法的适应性和提高计算效率是很有益处的. 算例验证了该方法的正确性和有效性.     

Exponential time integration using Krylov subspaces

The application of exponential integrators based on Krylov techniques to large‐scale simulations of complex fluid flows with multiple time‐scales demonstrates the efficiency of these schemes in reducing the associated time‐step restrictions due to numerical stiffness. Savings of approximately 50% can be achieved for simulations of the three‐dimensional compressible Navier–Stokes equations while still maintaining a truncation error typical of explicit time‐stepping schemes. Exponential time integration techniques of this type are particularly advantageous for fluid flows with a wide range of temporal scales such as low‐Mach number, reactive or acoustically dominated flows. Copyright © 2008 John Wiley & Sons, Ltd.     

A combined Filon/asymptotic quadrature method for highly oscillatory problems

A crossing between the asymptotic expansion of an oscillatory integral and Filon-type methods is obtained by applying a Filon-type method to the error term in the asymptotic expansion, which is in itself an oscillatory integral. The efficiency of the approach is investigated through analysis and numerical experiments, revealing a method which in many cases performs better than the Filon-type method. It is shown that considerable savings in terms of the required number of potentially expensive moments can be expected. The case of multivariate oscillatory integrals is discussed briefly. AMS subject classification (2000)  65D30     

A random approach to the Lebesgue integral

We construct an integral of a measurable real function using randomly chosen Riemann sums and show that it converges in probability to the Lebesgue integral where this exists. We then prove some conditions for the almost sure convergence of this integral.     

On the Sociobiology of Hawks and Doves. A phase diagram for integration and segregation

Competing groups in a population will be integrated or segregated depending on their contest strategies. In this work a population of a fixed proportion of hawks and doves is supposed to be able to employ two different contest strategies, one more competitive than the other one. Energies are derived for populations employing these strategies and these energies depend on the availability of the resource for which hawks and doves compete. The energy for the less competitive strategy is lower than the other one when the resource is abundant. In that case hawks and doves can be in cohabitation in all proportions. If, however, the resource is scarce, the energy of the more competitive strategy is lower than the other one. In that case complete segregation of hawks and doves into colonies will result. The situation is akin to the phase pressure diagram of a binary solution with eutectic point, miscibility gap in the liquid phase and complete miscibility in the vapour phase. This revised version was published online in August 2006 with corrections to the Cover Date.