Some properties of complete congruence lattices

For a complete lattice C, we consider the problem of establishing when the complete lattice of complete congruence relations on C is a complete sublattice of the complete lattices of join- or meet-complete congruence relations on C. We first argue that this problem is not trivial, and then we show that it admits an affirmative answer whenever C is continuous for the join case and, dually, co-continuous for the meet case. As a consequence, we prove that if C is continuous then each principal filter generated by a continuous complete congruence on C is pseudocomplemented. Received January 6, 1998; accepted in final form July 2, 1998.     

A Finite Hilbert-Style Axiomatization of the Implication-Less Fragment of the Intuitionistic Propositional Calculus

In this paper we obtain a finite Hilbert-style axiomatization of the implicationless fragment of the intuitionistic propositional calculus. As a consequence we obtain finite axiomatizations of all structural closure operators on the algebra of {–}-formulas containing this fragment. Mathematics Subject Classification: 03B20, 03B22, 06D15.     

ON NECESSARY AND SUFFICIENT CONDITIONS FOR DUALS OF WAVELET FRAMES

（张泽银）（王建忠）ＯＮＮＥＣＥＳＳＡＲＹＡＮＤＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＳＦＯＲＤＵＡＬＳＯＦＷＡＶＥＬＥＴＦＲＡＭＥＳ￥ＺｈａｎｇＺｅｙｉｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＨｕｂａｉＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈａｎ４３００６２，Ｃｈｉｎａ...     

化学反应流中分子扩散的二点封闭MCA模型

在化学反应流的概率密度函数(PDF)方法中,对流项和化学反应项都是封闭的,但分子扩散项必须模拟。现有的分子扩散模型都是唯象的,需要引入外加参数,并难以通过一些基本物理过程的检验。本文发展了随机映射逼近(mapping closure approximation,MCA)方法,解析地从控制方程导出一个封闭的分子扩散模型。该方法考虑两点联合概率密度函数方程,引入空间特征尺度,因此解决了以往映射封闭方法中分子扩散速率无法确定的问题。数值模拟表明该方法能用于预测标量扩散的速度,以及概率密度函数和条件平均扩散等统计量。     

Homogeneous turbulence subjected to rotation-dominated plane distortion

A new configuration of distorted homogeneous turbulence is investigated in the domain of rotation-dominated elliptical flows. The experimental results are compared with exact numerical solutions obtained in Fourier space for the linear part of the problem. The inherently periodic character of the flow results in typical oscillatory variations of the anisotropy and the pressure-strain correlations. A new two-point closure approach of the EDQNM type is proposed for the nonlinear problem; it is based on a representation of the spectral tensor by scalar functions expanded in terms of spherical harmonics.     

A two-scale second-moment turbulence closure based on weighted spectrum integration

A two-scale second-moment turbulence closure has been derived based on the weighted integration of the dynamic equation for the covariance spectrum. The goal is to close the Reynolds stress equations with two additional scalar equations that provide separately the scales of the spectral energy transfer and of the turbulence energy dissipation rate. Such a model should provide better prediction of nonequilibrium turbulent flows. The derivation consists of analytical integration of the wave-number-weighted covariance spectrum using a model of the spectral equations with an assumed simple representation of the shape of the energy spectrum. The resulting closure consists of a set of three tensorial equations, one for the Reynolds stress and two for length scale tensors, the latter representing the energy containing- and dissipative eddies respectively. The trace of the two tensor-scale equations leads to a set of two scalar scale parameters. In the equilibrium limit, the model reduces to the standard second-moment single-scale closure. The approach makes it also possible to derive the scale equations in a more systematic manner as compared with the common single-scale and other multi-scale models. The performance of the model in capturing the scale dynamics is illustrated by predictions of several generic homogeneous and inhomogeneous unsteady flows, demonstrating the expected response of the two scale equations. PACS 03.50.De, 04.20-q, 42.65-k     

A new photoelastic model for studying fatigue crack closure

The photoelastic analysis of crack tip stress intensity factors has been historically developed for use on sharp notches in brittle materials that idealize the cracked structure. This approach, while useful, is not applicable to cases where residual effects of fatigue crack development (e.g., plasticity, surface roughness) affect the applied stress intensity range. A photoelastic model of these fatigue processes has been developed using polycarbonate, which is sufficiently ductile to allow the growth of a fatigue crack. The resultant stress field has been modeled mathematically using the stress potential function approach of Muskhelishvili to predict the stresses near a loaded but closed crack in an elastic body. The model was fitted to full-field photoelastic data using a combination of a generic algorithm and the downhill simplex method. The technique offers a significant advance in the ability to characterize the behavior of fatigue cracks with plasticity-induced closure, and hence to gain new insights into the associated mechanisms.     

Nonlinear random coupled motions of structural elements with quadratic nonlinearities

The second-order closure method is used to analyze the nonlinear response of two-degree-of-freedom systems with quadratic nonlinearities. The excitation is assumed to be the sum of a deterministic harmonic component and a random component. The case of primary resonance of the second mode in the presence of a two-to-one internal (autoparametric) resonance is investigated. The method of multiple scales is used to obtain four first-order ordinary-differential equations that describe the modulation of the amplitudes and phases of the two modes. Applying the second-order closure method to the modulation equations, we determine the stationary mean and mean-square responses. For the case of a narrow-band random excitation, the results show that the presence of the nonlinearity causes multi-valued mean-square responses. The multi-valuedness is responsible for a jump phenomenon. Contrary to the results of the linear analysis, the nonlinear analysis reveals that the directly excited second mode takes a small amount of the input energy (saturates) and spills over the rest of the input energy into the first mode, which is indirectly excited through the autoparametric resonance.     

Structure dependent sampling in compressed sensing: Theoretical guarantees for tight frames

Many of the applications of compressed sensing have been based on variable density sampling, where certain sections of the sampling coefficients are sampled more densely. Furthermore, it has been observed that these sampling schemes are dependent not only on sparsity but also on the sparsity structure of the underlying signal. This paper extends the result of Adcock, Hansen, Poon and Roman (arXiv:1302.0561, 2013) [2] to the case where the sparsifying system forms a tight frame. By dividing the sampling coefficients into levels, our main result will describe how the amount of subsampling in each level is determined by the local coherences between the sampling and sparsifying operators and the localized level sparsities – the sparsity in each level under the sparsifying operator.