Characterization of the organization in shear layers via the Proper Orthogonal Decomposition

Experiments are performed in an incompressible plane turbulent mixing layer, using various hot wire rake configurations. From these experiments, the Proper Orthogonal Decomposition is applied for kernels where the space-time correlation tensor is evaluated over different spatial meshes and velocity components configurations. The resulting decompositions are then discussed in terms of characterization of the organization of the flow for various scalar or vectorial approaches of the POD. An incrtial range law is evidenced. The instantaneous contribution of the first modes of the POD to the organization of the flow is analyzed. A dynamical behavior for the organization of the flow is observed from the correlation between the first two modes contribution.     

Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates

Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution belongs to the range of the operator (T ^* T) ^v , o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India.     

Kinetic-catalytic determination of osmium by fluorescence quenching with salicylfluorone and hydrogen peroxide

A highly sensitive and selective fluorescence-quenching kinetic method is proposed for the determination of trace osmium(IV), based on the catalytic effect of osmium(IV) on the salicylfluorone (_ex = 510 nm, _em = 535 nm)-H₂O₂ system at pH 9.3–9.6. Using the fixed time method, osmium(IV) in the range 0.008–0.6 ng/ml can be determined. The detection limit is 0.006 ng/ml. Over thirty anions and cations, including other platinum metal ions, do not interfere, even when present in large excess. The method has been applied successfully for the determination of osmium in a series of synthetic mixtures and refined ore with relative standard deviations of 2–6%.     

On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds

We consider a new algorithm, an interior-reflective Newton approach, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach generatesstrictly feasible iterates by using a new affine scaling transformation and following piecewise linear paths (reflection paths). The interior-reflective approach does not require identification of an activity set. In this paper we establish that the interior-reflective Newton approach is globally and quadratically convergent. Moreover, we develop a specific example of interior-reflective Newton methods which can be used for large-scale and sparse problems.Research partially supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under grant DE-FG02-86ER25013.A000, and in part by NSF, AFOSR, and ONR through grant DMS-8920550, and by the Advanced Computing Research Institute, a unit of the Cornell Theory Center which receives major funding from the National Science Foundation and IBM Corporation, with additional support from New York State and members of its Corporate Research Institute.Corresponding author.     

Fastiterative methods for least squares estimations

Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037.     

Migration of seismic data

Prospecting for oil and gas resources poses the problem of determining the geological structure of the earth's crust from indirect measurements. Seismic migration is an acoustic image reconstruction technique based on the inversion of the scalar wave equation. Extensive computation is necessary before reliable information can be extracted from large sets of recorded data. In this paper a collection of industrial migration techniques, each giving rise to a data parallel algorithm, is outlined. Computer simulations on synthetic seismic data illustrate the problem and the approach.     

The studies of the effect of photostimulated changes in thin carbon films

Photostimulated changes in thin carbon films deposited onto fused silica substrates by reactive magnetron sputtering and irradiated by the light of the first (1060nm) and the second (530nm) harmonics of a QW-switched Nd³⁺ AVG laser were investigated. The changes are supposed to be connected with the reordering of chemical bounds.     

用“参数多项式方法”确定风力透平叶片的失速振荡流

用“参数多项式方法”确定风力透平叶片的失速振荡流陈佐一,孙永忠,杨玲（清华大学热能工程系北京１０００８４）关键词：参数多项式方法,风力透平,颤振在现代各类流动诱导振动问题的研究中,流体激振的安全性分析与诊断,要求在较短的时间内,对大量的复杂流动工况进...     

关于模拟法描会聚点电场的讨论

本文论证了“ＱＥ－２”型静电场描迹中模拟聚焦电场的电极在设计上有误的观点。     

Turán's Pure Power Sum Problem

Let be complex numbers, and consider the power sums , . Put , where the minimum is over all possible complex numbers satisfying the above. Turán conjectured that , for some positive absolute constant. Atkinson proved this conjecture by showing . It is now known that , for . Determining whether or approaches some other limiting value as is still an open problem. Our calculations show that an upper bound for decreases for , suggesting that decreases to a limiting value less than as .