Transitions to chaos in squeeze-film dampers

This work reports on a numerical study undertaken to investigate the imbalance response of a rigid rotor supported by squeeze-film dampers. Two types of damper configurations were considered, namely, dampers without centering springs, and eccentrically operated dampers with centering springs. For a rotor fitted with squeeze-film dampers without centering springs, the study revealed the existence of three regimes of chaotic motion. The route to chaos in the first regime was attributed to a sequence of period-doubling bifurcations of the period-1 (synchronous) rotor response. A period-3 (one-third subharmonic) rotor whirl orbit, which was born from a saddle-node bifurcation, was found to co-exist with the chaotic attractor. The period-3 orbit was also observed to undergo a sequence of period-doubling bifurcations resulting in chaotic vibrations of the rotor. The route to chaos in the third regime of chaotic rotor response, which occurred immediately after the disappearance of the period-3 orbit due to a saddle-node bifurcation, was attributed to a possible boundary crisis. The transitions to chaotic vibrations in the rotor supported by eccentric squeeze-film dampers with centering springs were via the period-doubling cascade and type 3 intermittency routes. The type 3 intermittency transition to chaos was due to an inverse period-doubling bifurcation of the period-2 (one-half subharmonic) rotor response. The unbalance response of the squeeze-film-damper supported rotor presented in this work leads to unique non-synchronous and chaotic vibration signatures. The latter provide some useful insights into the design and development of fault diagnostic tools for rotating machinery that operate in highly nonlinear regimes.     

On Polynomial Representations of Lie Algebras

We study polynomial representations of finite dimensional (R or C) Lie algebras. As a total classification, we show that there are altogether three types of such nontrivial representations and give their subtle structures.     

量子代数wsl_q(2)上的伴随作用

本文证明了量子代数wslq(2)在左伴随作用下是其自身上的拟模代数,并研究了wslq(2)的局部有限子模(?)(wslq(2))的子模结构．     

A proof of Selberg's orthogonality for automorphic L-functions

Let π and π′ be automorphic irreducible cuspidal representations of GL_m(Q_A) and GL_m′(Q_A), respectively. Assume that π and π′ are unitary and at least one of them is self-contragredient. In this article we will give an unconditional proof of an orthogonality for π and π′, weighted by the von Mangoldt function Λ(n) and 1−n/x. We then remove the weighting factor 1−n/x and prove the Selberg orthogonality conjecture for automorphic L-functions L(s,π) and L(s,π′), unconditionally for m≤4 and m′≤4, and under the Hypothesis H of Rudnick and Sarnak [20] in other cases. This proof of Selberg's orthogonality removes such an assumption in the computation of superposition distribution of normalized nontrivial zeros of distinct automorphic L-functions by Liu and Ye [12].     

The Star Chromatic Numbers of Some Planar Graphs Derived from Wheels

The notion of the star chromatic number of a graph is a generalization of the chromatic number. In this paper, we calculate the star chromatic numbers of three infinite families of planar graphs. The first two families are derived from a 3-or 5-wheel by subdivisions, their star chromatic numbers being 2+2/(2n + 1), 2+3/(3n + 1), and 2+3(3n−1), respectively. The third family of planar graphs are derived from n odd wheels by Hajos construction with star chromatic numbers 3 + 1/n, which is a generalization of one result of Gao et al. Received September 21, 1998, Accepted April 9, 2001.     

On General Volume-Preserving Mechanical Systems via Cohomology

We present the general form of equations that generate a volume-preserving flow on a symplectic manifold(Μ,ω) via the highest Euler-Lagrange cohomology. It is shown that for every volume-preserving fiow there are some 2-forms that play a similar role to the Hamiltonian in the Hamilton mechanics and the ordinary canonical equations with Hamiltonian H are included as a special case with a 2-form Hω/(n - 1).     

The Global Existence of Solutions for a Cross-diffusion System

This paper is concerned with the global existence of solutions for a class of quasilinear cross-diffusion system describing two species competition under self and cross population pressure. By establishing and using more detailed interpolation results between several different Banach spaces, the global existence of solutions are proved when the self and cross diffusion rates for the first species are positive and there is no self or cross-diffusion for the second species.     

Love waves in layered anisotropic media

A modified transfer-matrix method is proposed to describe Love waves in multilayered anisotropic (monoclinic) media. Dispersion relations for media consisting of one and two anisotropic elastic layers in contact with an anisotropic half-space are obtained in closed form. The conditions for Love waves to exist are analysed. Waves with horizontal transverse polarization of the non-canonical type are investigated.     

多元Kantorovich算子L_p范数下的渐近展开

本文给出了高维单纯形上Kantorovich算子在Lp（1＜P＜∞）范数下的高阶渐近展开公式．