Rocky coast processes: with special reference to the recession of soft rock cliffs

Substantial progress in research on the recession of coastal cliffs composed of soft materials has been made in recent years and data with higher accuracy have been accumulated. This paper provides the state of the art review in the recession studies and highlights two new findings obtained from the reanalysis of existing data. The review topics are: episodic and localized nature of cliff recession; the development of cliffline; the relationship between cliff height and recession rate; mechanisms of cliff toe erosion by waves; a fundamental equation for wave-induced toe erosion; factors controlling toe erosion; and slope instabilities and mass movements. The findings are presented on (1) the temporal change in cliffline recession mode and (2) the effect of beach sediment at the cliff base on the cliff erosion.     

Analysis of G/D/1 Queueing Systems with Inputs Satisfying Large Deviation Principle under Weak* Topology

The large deviation principle (LDP) which has been effectively used in queueing analysis is the sample path LDP, the LDP in a function space endowed with the uniform topology. Chang [5] has shown that in the discrete-time G/D/1 queueing system under the FIFO discipline, the departure process satisfies the sample path LDP if so does the arrival process. In this paper, we consider arrival processes satisfying the LDP in a space of measures endowed with the weak^* topology (Lynch and Sethuraman [12]) which holds under a weaker condition. It is shown that in the queueing system mentioned above, the departure processes still satisfies the sample path LDP. Our result thus covers arrival processes which can be ruled out in the work of Chang [5]. The result is then applied to obtain the exponential decay rate of the queue length probability in an intree network as was obtained by Chang [5], who considered the arrival process satisfying the sample path LDP.     

关于NA情况下重对数律收敛速度的一般形式

研究了NA序列重对数律收敛速度的一般形式，把Davis和Gut的结果推广到了NA的情形，并使梁汉营等人关于对数律一个结果成为特例；作为推论，得到了关于NA序列重对数律收敛速度的充分条件．     

修饰态布居的选择性激发对无反转激光的作用

以三能级V型系统为例研究修饰态布居的选择性激发对无反转激光增益的作用. 当非 相干驱动场的频谱宽度远小于驱动场产生的修饰态能级的间距时，非相干驱动场只将一个修 饰态的布居抽运至激发态. 借助原子的衰减通道，系统中形成单向布居转移通道，从而建立 修饰态布居的选择性激发. 利用修饰态布居的选择性激发，可以摆脱裸态共振无反转激光的 三个限制: (1) 不再要求辅助的低频驱动跃迁比高频激光跃迁具有更高的衰减速率；(2) 显 著降低非相干激发速率的阈值；(3) 无反转激光的线性增益不再反比于相干驱动场的强 关键词： 修饰态布居的选择性激发 无反转激光增益 原子衰减速率 非相干激发阈值速率     

BMAP/G/1 queue with correlated arrivals of customers and disasters

We consider a single server queue with disasters where the arrivals of customers and disasters are correlated. When a disaster occurs, it removes all the customers in the system and there requires repair time for the system to be operated normally. The stationary queue length distribution at the embedded points and at an arbitrary time are presented.     

A note on conservation laws for a multiclass service queueing system with setup times

This paper derives a conservation law for mean waiting times in a single-server multi-class service queueing system (M ^X/G/1 type queue) with setup times which may be dependent on multiple customer classes and its arrival batch size by using the work decomposition property in the queueing system with vacations.     

On the convergence rate and optimization of a numerical method with splitting of boundary conditions for the stokes system in a spherical layer in the axisymmetric case: Modification for thick layers

The convergence rate of a fast-converging second-order accurate iterative method with splitting of boundary conditions constructed by the authors for solving an axisymmetric Dirichlet boundary value problem for the Stokes system in a spherical gap is studied numerically. For R/r exceeding about 30, where r and R are the radii of the inner and outer boundary spheres, it is established that the convergence rate of the method is lower (and considerably lower for large R/r) than the convergence rate of its differential version. For this reason, a really simpler, more slowly converging modification of the original method is constructed on the differential level and a finite-element implementation of this modification is built. Numerical experiments have revealed that this modification has the same convergence rate as its differential counterpart for R/r of up to 5 × 10³. When the multigrid method is used to solve the split and auxiliary boundary value problems arising at iterations, the modification is more efficient than the original method starting from R/r ～ 30 and is considerably more efficient for large values of R/r. It is also established that the convergence rates of both methods depend little on the stretching coefficient η of circularly rectangular mesh cells in a range of η that is well sufficient for effective use of the multigrid method for arbitrary values of R/r smaller than ～ 5 × 10³.     

On bulk-service MAP/PH L,N /1/N G-Queues with repeated attempts

We consider a retrial queue with a finite buffer of size N, with arrivals of ordinary units and of negative units (which cancel one ordinary unit), both assumed to be Markovian arrival processes. The service requirements are of phase type. In addition, a PH^L,N bulk service discipline is assumed. This means that the units are served in groups of size at least L, where 1≤ L≤ N. If at the completion of a service fewer than L units are present at the buffer, the server switches off and waits until the buffer length reaches the threshold L. Then it switches on and initiates service for such a group of units. On the contrary, if at the completion of a service L or more units are present at the buffer, all units enter service as a group. Units arriving when the buffer is full are not lost, but they join a group of unsatisfied units called “orbit”. Our interest is in the continuous-time Markov chain describing the state of the queue at arbitrary times, which constitutes a level dependent quasi-birth-and-death process. We start by analyzing a simplified version of our queueing model, which is amenable to numerical calculation and is based on spatially homogeneous quasi-birth-and-death processes. This leads to modified matrix-geometric formulas that reveal the basic qualitative properties of our algorithmic approach for computing performance measures. AMS Subject Classification: Primary 60K25 Secondary 68M20 90B22.