Global existence and time decay of the non-cutoff Boltzmann equation with hard potential

This paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces $H^N\left({\mathbb{R}}_{x,v}^6\right)$ with $N\ge 2$. But if we want to obtain the optimal temporal decay estimates, we need to add the velocity weight function, in this case the global existence and the optimal temporal decay estimate of the Boltzmann equation are all established. Meanwhile, we further gain a more accurate energy estimate, which can guarantee the validity of the assumption in Chen et al. (0000).     

An inequality connecting entropy distance,Fisher Information and large deviations

In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large deviation rate functional. In addition to possessing various favourable properties, we show that this generalised Fisher Information converges to the classical Fisher Information in an appropriate limit. We then use this generalised Fisher Information and the aforementioned inequality to qualitatively study coarse-graining problems for jump processes on discrete spaces.     

Capturing the experimental behaviour of a point-absorber WEC by simplified numerical models

The paper presents a wave basin experiment of a direct-driven point-absorber wave energy converter moving in six degrees of freedom. The goal of the work is to study the dynamics and energy absorption of the wave energy converter, and to verify under which conditions numerical models restricted to heave can capture the behaviour of a point-absorber moving in six degrees of freedom. Several regular and irregular long-crested waves and different damping values of the power take-off system have been tested. We collected data in terms of power output, device motion in six degrees of freedom and wave elevation at different points of the wave basin. A single-body numerical model in the frequency domain and a two-body model in the time domain are used in the study. Motion instabilities due to parametric resonance observed during the experiments are discussed and analysis of the buoy motion in terms of the Mathieu instability is also presented. Our results show that the simplified models can reproduce the body dynamics of the studied converter as long as the transverse non-linear instabilities are not excited, which typically is the case in irregular waves. The performance of the more complex time domain model is able to reproduce both the buoy and PTO dynamics, while the simpler frequency domain model can only reproduce the PTO dynamics for specific cases. Finally, we show that the two-body dynamics of the studied wave energy converter affects the power absorption significantly, and that common assumptions in the numerical models, such as stiff mooring line or that the float moves only in heave, may lead to incorrect predictions for certain sea states.     

Kalman filtering of a space-time Markov random field

In this paper, finite-dimensional recursive filters for space-time Markov random fields are derived. These filters can be used with the expectation maximization (EM) algorithm to yield maximum likelihood estimates of the parameters of the model.     

Simulated annealing with noisy or imprecise energy measurements

The annealing algorithm (Ref. 1) is modified to allow for noisy or imprecise measurements of the energy cost function. This is important when the energy cannot be measured exactly or when it is computationally expensive to do so. Under suitable conditions on the noise/imprecision, it is shown that the modified algorithm exhibits the same convergence in probability to the globally minimum energy states as the annealing algorithm (Ref. 2). Since the annealing algorithm will typically enter and exit the minimum energy states infinitely often with probability one, the minimum energy state visited by the annealing algorithm is usually tracked. The effect of using noisy or imprecise energy measurements on tracking the minimum energy state visited by the modified algorithms is examined.The research reported here has been supported under Contracts AFOSR-85-0227, DAAG-29-84-K-0005, and DAAL-03-86-K-0171 and a Purdue Research Initiation Grant.     

小波变换在金融数据分析中的应用

市场上的数据,从本质上讲都是一种时间序列。它和小波分析中的信号具有相同的特性。因此,完全可以将这些经济时间序列看成信号,应用小波变换进行分析和预测。     

Weak convergence of the U-statistic and weak invariance of the one-sample rank order statistic for Markov processes and ARMA models

Harel and Puri (1989, J. Multivariate Anal. 29) studied the asymptotic behavior of the U-statistic and the one-sample rank order statistic for nonstationary absolutely regular processes. In this note, we present some applications of these results for Markov processes as well as ARMA processes.     

Modelling recruitment training in mathematical human resource planning

This paper deals with mathematical human resource planning; more specifically, it suggests a new model for a manpower‐planning system. In general, we study a k‐classed hierarchical system where the workforce demand at each time period is satisfied through internal mobility and recruitment. The motivation for this work is based on various European Union incentives, which promote regional or local government assistance programs that could be exploited by firms not only for hiring and training newcomers, but also to improve the skills and knowledge of their existing personnel. In this respect, in our augmented mobility model we establish a new ‘training/standby’ class, which serves as a manpower inventory position for potential recruits. This class, which may very well be internal or external to the system, is incorporated into the framework of a non‐homogeneous Markov chain model. Furthermore, cost objectives are employed using the goal‐programming approach, under different operating assumptions, in order to minimize the operational cost in the presence of system's constraints and regulations. Copyright © 2002 John Wiley & Sons, Ltd.