An Incompressible Fluid in a Weakly Deformable Shell. Part I: Analysis of the Model

We consider the flow of a viscous incompressible fluid in a pipe when the boundary is a deformable shell of Naghdi type. We prove that the corresponding system of partial differential equations has a solution when the deformation of the shell is smooth and small enough. We propose an algorithm that uncouples the unknowns and prove its convergence.     

Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.     

光泵分子气体远红外光谱的AC Stark效应

本文应用图论法研究光泵激光气体分子的波谱特性。假定了:1.分子与外来信号场相互作用输运过程中只涉及到六个能级;2.泵场强远大于探测场强。在这些假定下求解密度矩阵方程,获得一套反映受激分子波谱特性的解析表达式。应用这些表达式,可求得不同频率的泵场作用下分子气体的远红外波谱特性。本文特别叙述分子振动基态远红外光谱的AC aStark效应。结果表明:在谐振点AC aStark分裂的值与C.H.Townes所得结果基本相同,在受激发射和吸收共存的情况下,特性曲线的总趋向与他的结果基本一致。调谐曲线有些部份反映发射特性,有些部份反映吸收特性,在发射和吸收的过渡部份,吸收和发射都很小,而且具有特殊的过渡特性。     

Scheduling Parts in a Combined Production-transportation Work Cell

This paper is concerned with a combined production-transportation scheduling problem. The problem comprises a simple, two-machine, automated manufacturing cell, which either stands alone or is a subunit of a complete flexible manufacturing system. The cell consists of two machines in series with a dedicated part-handling device such as a crane or robotic arm for transferring parts from the first machine to the second. The loading of a new piece on the first machine and the ejection of a finished piece from the second machine are performed by dedicated automated mechanisms. The introduction of parts into the system is done n at a time, whereby the parts are reshuffled into a sequence that minimizes completion time. All processing and transfer times are considered deterministic—a reasonable assumption for a cell comprising a robotic transfer device and two CNC machining units. What complicates the problem is the assumption of a non-negligible time for the transfer device to return (empty) from the second machine to the first. The operation is a generalization of a two-machine flowshop problem, and is formulated as a specially structured, asymmetric travelling salesman problem. An approximate polynomial time 0(n log n) algorithm is proffered. The procedure incorporates a lower bound using the Gilmore–Gomory algorithm for the no-wait, two-machine flowshop problem.     

Lower Bounds for the Height and Size of the Ideal Class Group in CM-Fields

 We prove that, under the assumption of the Generalized Riemann Hypothesis, the exponent of the ideal class group of a CM-field goes to infinity with its absolute discriminant. This gives a positive answer to a question raised by Louboutin and Okazaki [4]. Received September 10, 2001; in revised form April 5, 2002     

OSCILLATORY SINGULAR INTEGRALS WITH VARIABLE ROUGH KERNEL,Ⅱ

Let n≥2. In this paper, the author establishes the L^2 (R^n)-boundedness of some oscillatory singular integrals with variable rough kernels by means of some estimates on hypergeometric functions and congqucnt hypergeometric funtions.     

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     

The Dual Properties of Lk-UR and k-SS Space

In this paper, we get some properties in the dual space of Lk-UR and k-SS Banach space.AMS Subject Classification: 46B09