The continuous wavelet derived by smoothing function and its application in cosmology

The wavelet analysis technique is a powerful tool and is widely used in broad disciplines of engineering, technology, and sciences. In this work, we present a novel scheme of constructing continuous wavelet functions, in which the wavelet functions are obtained by taking the first derivative of smoothing functions with respect to the scale parameter. Due to this wavelet constructing scheme, the inverse transforms are only one-dimensional integrations with respect to the scale parameter, and hence the continuous wavelet transforms(CWTs) constructed in this way are more ready to use than the usual scheme. We then apply the Gaussian-derived wavelet constructed by our scheme to computations of the density power spectrum for dark matter, the velocity power spectrum and the kinetic energy spectrum for baryonic fluid. These computations exhibit the convenience and strength of the CWTs. The transforms are very easy to perform, and we believe that the simplicity of our wavelet scheme will make CWTs very useful in practice.     

非平整运动海底上n层流动中波浪传播的Hamilton逼近

在海洋水域，界面波对大尺度变化流的作用是一种典型的分层流动现象．考虑一不可压缩、无黏的分层势流运动，建立了一个在非平整运动海底上的n层流体演化系统，并对其进行了Hamilton描述．每层流体具有各自的常密度、均匀流水平速度，其厚度由未扰动和扰动部分构成．相对于顶层流体的自由表面，刚性、运动的海底具有一般地形变化特征．在明确指出n层流体运动的控制方程和各层交界面上的运动学、动力学边界条件(包含各层交界面上张力效应)后，对该分层流动力系统进行了Hamilton构造，即给出其正则方程和其下述的正则变量：各交界面位移和各交界面上的动量势密度差。     

Three-dimensional unsaturated flow in heterogeneous systems and implications on groundwater contamination: A stochastic approach

A stochastic approach for modeling transient unsaturated flow in large-scale spatially variable soils is developed in order to overcome the problem of limited information about the local details of spatial soil variability. It is assumed that local soil properties are realizations of three-dimensional stationary random fields, and a large-scale model representation is derived by averaging the local governing flow equation over the ensemble of realizations of the underlying soil property random fields. The three-dimensionality of the local flow equations and the nonlinear dependence of the local flow output on the local soil properties are considered. The resulting mean representation (structure) is in the form of a partial differential equation in which averaged or effective model parameters occur. These effective model parameters are evalutated using a quasi-linearized fluctuation equation and a spectral representation of stationary processes. The large-scale model structure considers the large-scale effects of soil variability and have relatively few parameters which should be identifiable from a realistic data set. The general stochastic theory is then applied to the case of flow in stratified soil formations, which is of practical importance in applications such as waste disposal control. An important finding of this study is that spatial variability of the hydraulic soil properties produces significant large-scale effects, such as large-scale hysteresis and anisotropy of the effective parameters. These large-scale effects should be considered in field applications such as for predicting the movement of liquid wastes in the unsaturated zone.     

Monotone projected gradient methods for large-scale box-constrained quadratic programming

Inspired by the success of the projected Barzilai-Borwein (PBB) method for large-scale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods, it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.     

Robust stabilization of large-scale time-delay systems with estimated state feedback

This paper proposes a class of observers and uses the estimated state feedback to stabilize a perturbed large-scale time-delay system in which the state is unmeasurable. An inequality representing the relationship among the perturbation bounds, interconnection magnitudes, and gains of observers and controllers is derived to ensure that the system is stabilized and the state is estimated. Moreover, this inequality does not need the solution of a Lyapunov equation or Riccati equation and is independent of time delays.This work was supported in part by the National Science Council, Taiwan, ROC, under Grant NSC-83-0404-E-008-040.     

Flexural fatigue behavior of threaded connections for large diameter pipes

Full-scale flexural fatigue tests were conducted to investigate the fatigue behavior of a patented threaded connection for large diameter (0.61 m (24 in) outside diameter, 25.4 mm (1 in) wall thickness) offshore pipes. Fifteen fatigue tests were performed by subjecting the threaded connection to constant amplitude stress ranges (between 69 MPa (10 ksi) and 151.8 MPa (22 ksi) on gross cross section) with zero mean stress. The corresponding measured fatigue lives varied from 45000 to 4852200 cycles. Fatigue failures were in the form of cracks through the thickness of the wall and located at the root of the first full contact thread. The failure surfaces were ‘typical’ with identifiable zones of crack initiation, propagation and fracture. Linear regression analysis of the experimental results, namely the applied stress range (S _r ) and the measured number of cycles to failure (N) data, in the log-log domain gave anR ² value of 0.88 and the least-squares best fit equation asS _r (MPa)=1573.2N ^−0.212. The 90% probable fatigue strength prediction equation was estimated asS _r =1393.8N ^−0.212. This equation is recommended for design purposes.     

Revised dantzig-wolfe decomposition for staircase-structured linear programs

Staircase structured linear programs arise naturally in the study of engineering economic systems. One general approach to solving such LP's is the technique of nested decomposition of the primal or dual problem. The research described in this paper proposes a revised decomposition algorithm that incorporates knowledge of the structure of the staircase basis in forming the decomposed linear programs. Column proposals from the revised subproblems are shown to achieve maximum penetration against the master problem basis. The proposed algorithm resorts to the regular Dantzig-Wolfe subproblem to test for optimality. The algorithm is shown to be finite and is compared to the Abrahamson-Wittrock algorithm. Computational results indicate substantial improvement over the Dantzig-Wolfe algorithm in most cases. A numerical example of the algorithm is provide in the appendix. This research was supported by National Science Foundation grant ECS-8106455 to Cornell University.     

Multimodel design of a Nash strategy

For interconnected systems with slow and fast modes, we analyze a multimodel design of a Nash equilibrium strategy. Decision makers use different models of the same system to obtain a composite strategy that approximates the exact Nash strategy. It is discussed in what sense this approximation holds.This work was supported by the Department of Energy, Electrical Energy Systems Division, under Contract No. EX-76-C-01-2088. The author wishes to thank Professor P. V. Kokotovic for his helpful suggestions in the course of this work.     

NORTHERN HEMISPHERIC SUMMER CLIMATIC JUMP IN THE 1960s (Ⅰ)——RAINFALL AND TEMPERATURE

With the conception of the climatic jump, the authors revealed the large-scale characteristics of the abrupt summer climatic change in the Northern Hemisphere in the 1960s. This paper concerns the change of the summer rainfall, air temperature and sea surface temperature in 1951—1980. There was a wide zone including North Africa, northwest India, central China and Japan where the rainfall decreased abruptly in the 1960s while two zones, respectively south and north of the drying zone, experienced increasing rainfall. The temperature decreased abruptly in most of the northern mid-high latitudinal regions and increased significantly in some of the lower-latitudinal regions, leading to a sudden enlarging of the equator-polar thermal difference. It was noted that the climatic jump seemed to occur asynchronously from one region to another.     

Numerical Experience with a Reduced Hessian Method for Large Scale Constrained Optimization

The reduced Hessian SQP algorithm presented in Biegler et al. [SIAM J. Optimization, Vol. 5, no. 2, pp. 314–347, 1995.] is developed in this paper into a practical method for large-scale optimization. The novelty of the algorithm lies in the incorporation of a correction vector that approximates the cross term Z^TWYp_Y. This improves the stability and robustness of the algorithm without increasing its computational cost. The paper studies how to implement the algorithm efficiently, and presents a set of tests illustrating its numerical performance. An analytic example, showing the benefits of the correction term, is also presented.