On the Quasi-regularity of Semi-Dirichlet Forms

We prove that if a right Markov process is associated with a semi-Dirichlet form, then the form is necessarily quasi-regular. As applications, we develop the theory of Revuz measures in the semi-Dirichlet context and we show that quasi-regularity is invariant with respect to time change.     

Nucleon-nucleon interaction with tensor forces in the quark compound bag model

A model forN-N interaction proposed earlier by two of us (VSB and VKG), has been extended to incorporate the tensor component of the nuclear force. Based on the quark compound bag model (QCB), the nucleon-nucleon potential has a short range repulsive core which is non-local and has a characteristic energy dependence and is expressed in terms of the parameters relating to the six-quark compound bag. To account for the low energy properties, this repulsive core interaction is supplemented by a phenomenological non-local potential containing both central (S-wave) and tensor components and operates only outside the QCB. Using this model, we analyse and compare the results with the experimental data for the electromagnetic form factors of the deuteron, theD-state observables, such as the quadrupole moment, theD-state probability, and theD/S ratio along with then-p scattering phase shifts up to about 400 MeV.     

Mixed parallel processors with interdependent blocking

This paper studies a system of parallel service facilities or processors with mixed exponential and non-exponential queues, a non-exponential finite source input and interdependent arrival as well as departure blocking such as due to a common pool or shared resource. A concrete invariance condition upon the blocking protocol is provided. Under this condition the stationary busy source distribution is shown to be of an insensitive product form. The result unifies and extends known product form results as will be illustrated by several examples.     

Formal and analytic linearizability of families of conformal map germs (ℂ, 0) → (ℂ, 0)

We consider a nondegenerate one-parameter family of germs of conformal maps of (?, 0) into (?, 0). We prove that such a family is analytically linearizable whenever it is formally linearizable. In this case, the linearizing coordinate change analytically depends on the parameter.     

The Principal Eigenvalue for Jump Processes

A variational formula for the lower bound of the principal eigenvalue of general Markov jump processes is presented. The result is complete in the sense that the condition is fulfilled and the resulting bound is sharp for Markov chains under some mild assumptions. Received November 15, 1999, Accepted March 9, 2000     

The apolar bilinear form in geometric modeling

Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known in 19th century invariant theory. Using a generalized version of this inner product, we derive in a straightforward way some of the recent results in CAGD, like Marsden's identity, the expression for the de Boor-Fix functionals, and recursion schemes for the computation of B-patches and their derivatives.

     

一类带输入时滞的线性时滞系统的新型自适应控制

针对一类带输入时滞且状态时滞常数未知的线性时滞系统,基于LMI方法,采用一种Lyapunov-Krasovskii函数和新型带记忆的状态反馈控制,突破以往自适应控制对估计值的大小限制,研究了一种新型的对该类系统未知状态时滞常数进行自适应控制的控制器设计问题,并且通过带记忆控制器中的常数的适当选取使得带记忆控制始终能反映未知时滞,仿真例子显示了该种方法的有效性.     

The Lindblad and Redfield forms derived from the Born–Markov master equation without secular approximation and their applications

In this paper, we derive the Lindblad and Redfield forms of the master equation based on the Born–Markov master equation with and without the secular approximation for open multi-level quantum systems. The coefficients of the equations are re-evaluated according to the scheme in[(2019), Phys. Rev. A 99, 022118]. They are complex numbers rather than the real numbers obtained from traditional simplified methods. The dynamics of two models(one is an open threelevel quantum system model, and the other is the model of phycoerythrin 545(PE545) in a photosynthesis system) are studied. It is shown that the secular approximation and the simplified real coefficients may cause a small distortion of the dynamics in some environments, but a large distortion of the dynamics in others. These effects are discussed and characterized by studying the dynamics of nontrivial instances of multi-level systems in the presence of dissipation.     

Residual stress field and reduction of stress intensity factors in cold-worked holes

Closed-form and semi-analytical solutions are obtained for the residual stress distributions in a plate caused by pressure acting on a central circular hole, representing the cold-work process. The material is elastic–perfectly plastic. Both Tresca and von Mises yield criteria are used and the corresponding residual stress distributions are compared. The relation between the dimension of the plastic zone and the value of internal pressure is presented. The relation between the magnitude of the residual stresses and the remote uniform tensile stress required to open symmetrical radial cracks is also presented. The reduction of the stress intensity factors of cracked open and riveted holes as a function of the internal pressure applied (or mandrel radial displacement) is investigated using numerical models for both an elastic–perfectly plastic material and for an Al 2024-T3 Alclad aluminum alloy.