On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm

 We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to J. Galambos, W. Philipp, and H. G. Diamond–J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Perron algorithm. Received September 30, 2001; in revised form January 8, 2002     

Photoinitiated cationic polymerization of cycloaliphatic epoxide with siloxane or alkoxysilane functionalized polyol coatings

Polyols were reacted with tetraethyl orthosilicate (TEOS) or 3-isocyanatopropyltriethoxysilane (IPTES) to form siloxane functionalized polyols. The UV-reactivity of these siloxane functionalized polyols were investigated using real-time FT-IR spectroscopy. The reactivity of TEOS modified polyols was dependent on the relative humidity. However, for the IPTES functionalized polyols the effect of relative humidity was dependent on the degree of IPTES functionalization. When the polyols were only partially functionalized with IPTES, the effect of relative humidity was minimal. However, when polyols were fully functionalized with IPTES, the curing was dependent on relative humidity. The siloxane functionalized polyols were formulated with a cycloaliphatic epoxide and cationic photoinitiator. The photo-induced curing kinetics of these cycloaliphatic epoxide/siloxane functionalized polyol coatings were also investigated. Unlike the TEOS functionalized polyols, the addition of IPTES functionalized polyols into the formulation inhibited the curing speed. This inhibition was attributed to the basicity nitrogen of the urethane linkage. The effect of relative humidity on the UV-curing reaction of cycloaliphatic epoxide coatings was lowered by the incorporation of the TEOS functionalized polyols.     

Cost–benefit modelling for reliability growth

Decisions during the reliability growth development process of engineering equipment involve trade-offs between cost and risk. However slight, there exists a chance an item of equipment will not function as planned during its specified life. Consequently the producer can incur a financial penalty. To date, reliability growth research has focussed on the development of models to estimate the rate of failure from test data. Such models are used to support decisions about the effectiveness of options to improve reliability. The extension of reliability growth models to incorporate financial costs associated with ‘unreliability’ is much neglected. In this paper, we extend a Bayesian reliability growth model to include cost analysis. The rationale of the stochastic process underpinning the growth model and the cost structures are described. The ways in which this model can be used to support cost–benefit analysis during product development are discussed and illustrated through a simple case.     

Atomistic phenomena in dense fluid shock waves

The shock structure problem is one of the classical problems of fluid mechanics and at least for non-reacting dilute gases it has been considered essentially solved. Here we present a few recent findings, to show that this is not the case. There are still new physical effects to be discovered provided that the numerical technique is general enough to not rule them out a priori. While the results have been obtained for dense fluids, some of the effects might also be observable for shocks in dilute gases.     

Approximation of transient temperatures in complex geometries using fractional derivatives

It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.     

The supersymmetric WKB approximation of ring-shaped oscillator potential in r and θ dimensions with spherical polar coordinates

According to calculation of the energy spectrum of ring-shape oscillator potential by using the supersymmetric WKB approximation, it is shown that the energy spectrum of some noncentral separable potentials can be exactly obtained in r and θ dimensions by above method.     

Discrete semi-stable distributions

The purpose of this paper is to introduce and study the concepts of discrete semi-stability and geometric semi-stability for distributions with support inZ ₊. We offer several properties, including characterizations, of discrete semi-stable distributions. We establish that these distributions posses the property of infinite divisibility and that their probability generating functions admit canonical representations that are analogous to those of their continuous counterparts. Properties of discrete geometric semi-stable distributions are deduced from the results obtained for discrete semi-stability. Several limit theorems are established and some examples are constructed.     

卤代对苝醌类光敏剂光敏活性影响的量子化学研究

以一种新型的醌类光敏剂—菌生素 (HMB)为模型化合物 ,利用量子化学从头算HF/ 6 31G和含时密度泛函TD B3LYP/ 6 31G方法计算研究了卤代作用对醌类光敏剂分子性质和光敏活性的影响 .结果发现 ,卤代作用降低了HMB母体的HOMO和LUMO能级 (EHOMO和ELUMO)及其差值△E ,随卤族元素从上到下 ,EHOMO和ELUMO呈增大趋势 ,而△E呈减小趋势 ,使得分子激发光谱有不同程度的红移 ,在增加PQP三重态量子产率的同时降低了分子最低三重激发态的能量 ,两种作用相互抵消 ,使得卤代物的 1O2 量子产率与母体相似 ;增加了分子的绝热电子亲合势 ,使分子产生O2 -的能力下降 ;卤原子的引入 ,降低了HMB母体分子内氢键的强度 ,同时使顺式构型的分子内质子传递势垒增大 ,而使反式构型势垒减小 .     

Fractional Order Disturbance Observer for Robust Vibration Suppression

For the first time, the fractional order disturbance observer (FO-DOB) is proposed for vibration suppression applications such as hard disk drive servo control. It has been discovered in a recently published US patent application (US20010036026) that there is a tradeoff between phase margin loss and strength of the low frequency vibration suppression. Given the required cutoff frequency of the low pass filter, also known as the Q-filter, it turns out that the relative degree of the Q-filter is the major tuning knob for this tradeoff. The solution in US20010036026 was based on an integer order Q-filter with a variable relative degree. This actually motivated the use of a fractional order Q-filter. The fractional order disturbance observer is based on the fractional order Q-filter. The implementation issue is also discussed. The nice point of this paper is that the traditional DOB is extended to the fractional order DOB with the advantage that the FO-DOB design is now no longer conservative nor aggressive, i.e., given the cutoff frequency and the desired phase margin, we can uniquely determine the fractional order of the low pass filter.     

A projection method for solving incompressible viscous flows on domains with moving boundaries

In this paper, a projection method is presented for solving the flow problems in domains with moving boundaries. In order to track the movement of the domain boundaries, arbitrary‐Lagrangian–Eulerian (ALE) co‐ordinates are used. The unsteady incompressible Navier–Stokes equations on the ALE co‐ordinates are solved by using a projection method developed in this paper. This projection method is based on the Bell's Godunov‐projection method. However, substantial changes are made so that this algorithm is capable of solving the ALE form of incompressible Navier–Stokes equations. Multi‐block structured grids are used to discretize the flow domains. The grid velocity is not explicitly computed; instead the volume change is used to account for the effect of grid movement. A new method is also proposed to compute the freestream capturing metrics so that the geometric conservation law (GCL) can be satisfied exactly in this algorithm. This projection method is also parallelized so that the state of the art high performance computers can be used to match the computation cost associated with the moving grid calculations. Several test cases are solved to verify the performance of this moving‐grid projection method. Copyright © 2004 John Wiley Sons, Ltd.