Complexity of Monte Carlo algorithms for a class of integral equations

In this work we study the computational complexity of a class of grid Monte Carlo algorithms for integral equations. The idea of the algorithms consists in an approximation of the integral equation by a system of algebraic equations. Then the Markov chain iterative Monte Carlo is used to solve the system. The assumption here is that the corresponding Neumann series for the iterative matrix does not necessarily converge or converges slowly. We use a special technique to accelerate the convergence. An estimate of the computational complexity of Monte Carlo algorithm using the considered approach is obtained. The estimate of the complexity is compared with the corresponding quantity for the complexity of the grid-free Monte Carlo algorithm. The conditions under which the class of grid Monte Carlo algorithms is more efficient are given.

On the system of rational difference equations x(n) = A+(1)over-bar y(n-p), y(n) = A+(gamma(n-1))over-bar x(n-r)y(n-5)

In this paper, we study the behavior of the positive solutions of the system of two difference equations [GRAPHICS] where p >= 1, r >= 1, s >= 1, A >= 0, and x(1-r), x(2-r),..., x(0), y(1-max) {p.s},..., y(0) are positive real numbers. (c) 2005 Elsevier Inc. All rights reserved.

Phosphorus dynamics in the ditch system of a restored peat wetland

The restoration of wetlands as bird habitats often involves the maintenance of a fluctuating water regime by careful, localised ditch water management using pumps and sluices. However, there is evidence in the literature to Suggest that alternate flood/drainage cycles can accelerate nutrient cycling and transport within the soil and, therefore, pose a threat to water quality through the process of eutrophication. This study focused on the dynamics and losses of soil P in a recently re-wetted, eutrophic fen peat developed on alluvium ill South west England. During the 2-year Study (2001 and 2002), soil water tensiometry revealed that the field water table (fluctuating annually between +20 and 60 cm relative to ground level) was extensively influenced across most of the 8.4 ha field site by the management of the adjacent ditch water levels. This conservation-led, prescribed water balance was facilitated by the high hydraulic conductivity (1.1 x 10(-s) ms(-1)) of the lower (70-140 cm), degraded layer of peat. However, only during a 7-day period of water table drawdown by intermittent pump drainage, approximately 45 g ha(-1) of dissolved reactive P (DRP) entered the pumped ditch from the field via this degraded layer. Summer rainfall events >35 mm d(-1) also coincided with significant peaks ill ditch water P concentration (up to 200 mu g L-1 DRP). Even larger peaks (Up to 700 mu g L-1 DRP) Occurred With the annual onset of autumn reflooding. These episodic P loss events pose a serious potential threat to biological water quality. (C) 2009 Elsevier B.V. All rights reserved.

A concise summary of the International System of Units, the SI

The Bureau International des Poids et Mesures, the BIPM, was established by Article 1 of the Convention du Mètre, on 20 May 1875, and is charged with providing the basis for a single, coherent system of measurements to be used throughout the world. The decimal metric system, dating from the time of the French Revolution, was based on the metre and the kilogram. Under the terms of the 1875 Convention, new international prototypes of the metre and kilogram were made and formally adopted by the first Conférence Générale des Poids et Mesures (CGPM) in 1889. Over time this system developed, so that it now includes seven base units. In 1960 it was decided at the 11th CGPM that it should be called the Système International d’Unités, the SI (in English: the International System of Units). The SI is not static but evolves to match the world’s increasingly demanding requirements for measurements at all levels of precision and in all areas of science, technology, and human endeavour. This document is a summary of the SI Brochure, a publication of the BIPM which is a statement of the current status of the SI. The seven base units of the SI, listed in Table 1, provide the reference used to define all the measurement units of the International System. As science advances, and methods of measurement are refined, their definitions have to be revised. The more accurate the measurements, the greater the care required in the realization of the units of measurement.

The v2, v5 Raman band system of 13CH3F

The anisotropic and isotropic components of the ν2, ν5 rotation-vibrational Raman bands of 13CH3F were obtained separately. The two upper states are coupled by a strong second-order Coriolis resonance. The anisotropic spectrum was analyzed by means of a program system due to R. Escribano. A contour simulation and a least-squares fit of 233 assigned transitions yielded values for ν5, ΔA5, ΔA2, and Aζ5a, 5b(z). The 13C shifts of ν2 and ν5 were obtained from the isotropic spectrum.