On two rational difference equations

In this paper, we study the oscillating property of positive solutions and the global asymptotic stability of the unique equilibrium of the two rational difference equations [GRAPHICS] and [GRAPHICS] where a is a nonnegative constant. (c) 2005 Elsevier Inc. All rights reserved.

Global asymptotic stability in a rational recursive sequence

In this paper, we study the global stability of the difference equation x(n) = a + bx(n-1) + cx(n-1)(2)/d - x(n-2), n = 1,2,....., where a, b greater than or equal to 0 and c, d > 0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive Solution of the equation in the basin exponentially converges to the attractor. (C) 2003 Elsevier Inc. All rights reserved.

Fault tolerance of Mobius cubes under two forbidden fault set models

An n-dimensional Mobius cube, 0MQ(n) or 1MQ(n), is a variation of n-dimensional cube Q(n) which possesses many attractive properties such as significantly smaller communication delay and stronger graph-embedding capabilities. In some practical situations, the fault tolerance of a distributed memory multiprocessor system can be measured more precisely by the connectivity of the underlying graph under forbidden fault set models. This article addresses the connectivity of 0MQ(n)/1MQ(n), under two typical forbidden fault set models. We first prove that the connectivity of 0MQ(n)/1MQ(n) is 2n - 2 when the fault set does not contain the neighborhood of any vertex as a subset. We then prove that the connectivity of 0MQ(n)/1MQ(n) is 3n - 5 provided that the neighborhood of any vertex as well as that of any edge cannot fail simultaneously These results demonstrate that 0MQ(n)/1MQ(n) has the same connectivity as Q(n) under either of the previous assumptions.

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.

Modified level set method with Canny operator for image noise removal

The level set method is commonly used to address image noise removal. Existing studies concentrate mainly on determining the speed function of the evolution equation. Based on the idea of a Canny operator, this letter introduces a new method of controlling the level set evolution, in which the edge strength is taken into account in choosing curvature flows for the speed function and the normal to edge direction is used to orient the diffusion of the moving interface. The addition of an energy term to penalize the irregularity allows for better preservation of local edge information. In contrast with previous Canny-based level set methods that usually adopt a two-stage framework, the proposed algorithm can execute all the above operations in one process during noise removal.

A new approach for the solution of the optimal set-point tracking problem for nonlinear systems

In this paper, a discrete time dynamic integrated system optimisation and parameter estimation algorithm is applied to the solution of the nonlinear tracking optimal control problem. A version of the algorithm with a linear-quadratic model-based problem is developed and implemented in software. The algorithm implemented is tested with simulation examples.

Intrinsic chess rating

This paper develops and tests formulas for representing playing strength at chess by the quality of moves played, rather than by the results of games. Intrinsic quality is estimated via evaluations given by computer chess programs run to high depth, ideally so that their playing strength is sufficiently far ahead of the best human players as to be a `relatively omniscient' guide. Several formulas, each having intrinsic skill parameters s for `sensitivity' and c for `consistency', are argued theoretically and tested by regression on large sets of tournament games played by humans of varying strength as measured by the internationally standard Elo rating system. This establishes a correspondence between Elo rating and the parameters. A smooth correspondence is shown between statistical results and the century points on the Elo scale, and ratings are shown to have stayed quite constant over time. That is, there has been little or no `rating inflation'. The theory and empirical results are transferable to other rational-choice settings in which the alternatives have well-defined utilities, but in which complexity and bounded information constrain the perception of the utility values.

Centennial changes in the heliospheric magnetic field and open solar flux: the consensus view from geomagnetic data and cosmogenic isotopes and its implications

Svalgaard and Cliver (2010) recently reported a consensus between the various reconstructions of the heliospheric field over recent centuries. This is a significant development because, individually, each has uncertainties introduced by instrument calibration drifts, limited numbers of observatories, and the strength of the correlations employed. However, taken collectively, a consistent picture is emerging. We here show that this consensus extends to more data sets and methods than reported by Svalgaard and Cliver, including that used by Lockwood et al. (1999), when their algorithm is used to predict the heliospheric field rather than the open solar flux. One area where there is still some debate relates to the existence and meaning of a floor value to the heliospheric field. From cosmogenic isotope abundances, Steinhilber et al. (2010) have recently deduced that the near-Earth IMF at the end of the Maunder minimum was 1.80 ± 0.59 nT which is considerably lower than the revised floor of 4nT proposed by Svalgaard and Cliver. We here combine cosmogenic and geomagnetic reconstructions and modern observations (with allowance for the effect of solar wind speed and structure on the near-Earth data) to derive an estimate for the open solar flux of (0.48 ± 0.29) × 1014 Wb at the end of the Maunder minimum. By way of comparison, the largest and smallest annual means recorded by instruments in space between 1965 and 2010 are 5.75 × 1014 Wb and 1.37 × 1014 Wb, respectively, set in 1982 and 2009, and the maximum of the 11 year running means was 4.38 × 1014 Wb in 1986. Hence the average open solar flux during the Maunder minimum is found to have been 11% of its peak value during the recent grand solar maximum.