Real-time onboard wind and windshear determination,part 2: Detection

This paper is concerned with windshear detection in connection with real-time wind identification (Ref. 1). It presents a comparative evaluation of two techniques, one based on the shear/downdraft factor and one based on the wind difference index. The comparison is done with reference to a particular microburst, that which caused the 1985 crash of Flight Delta 191 at Dallas-Fort Worth International Airport.The shear/downdraft factor has the merit of combining the effects of the shear and the downdraft into a single entity. However, its effectiveness is hampered by the fact that, in a real situation, the windshear is accompanied by free-stream turbulence, which tends to blur the resulting signal. In turn, this results in undesirable nuisance warnings if the magnitude of the shear factor due to free-stream turbulence is temporarily larger than that due to true windshear. Therefore, proper filtering is necessary prior to using the shear/downdraft factor in detection and guidance. One effective way for achieving this goal is to average the shear/downdraft factor over a specified time interval . The effect of on the average shear/downdraft factor is studied.     

Randomized algorithms for the separation of point sets and for solving quadratic programs

A randomized algorithm for finding a hyperplane separating two finite point sets in the Euclidean space ^d and a randomized algorithm for solving linearly constrained general convex quadratic problems are proposed. The expected running time of the separating algorithm isO(dd! (m + n)), wherem andn are cardinalities of sets to be separated. The expected running time of the algorithm for solving quadratic problems isO(dd! s) wheres is the number of inequality constraints. These algorithms are based on the ideas of Seidel's linear programming algorithm [6]. They are closely related to algorithms of [8], [2], and [9] and belong to an abstract class of algorithms investigated in [1]. The algorithm for solving quadratic problems has some features of the one proposed in [7].This research was done when the author was supported by the Alexander von Humboldt Foundation, Germany.On leave from the Institute of Mathematics and Mechanics, Ural Department of the Russian Academy of Sciences, 620219 Ekaterinburg, S. Kovalevskaya str. 16, Russia.     

On the classification of geometric codes by polynomial functions

It is shown how to represent algebraically all functions that have a zero sum on all -dimensional subspaces ofPG(n,q) or ofAG(n,q). In this way one can calculate the dimensions of related codes, or one can represent interesting sets of points by functions.     

A universal constant for the convergence of Newton's method and an application to the classical homotopy method

We give a new theorem concerning the convergence of Newton's method to compute an approximate zero of a system of equations. In this result, the constanth ₀=0.162434... appears, which plays a fundamental role in the localization of good initial points for the Newton iteration. We apply it to the determination of an appropriate discretization of the time interval in the classical homotopy method.     

Multistep methods for differential algebraic equations

Multistep methods for the differential/algebraic equations (DAEs) in the form of

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.     

Exponential distributions on semigroups

Three fundamental characterizations of the standard exponential distribution on [0, ) are the remaining life, memoryless and constant failure properties. Analogs of these properties are studied for distributions on a class of semigroups in which the semigroup operation replaces addition, a compatible partial order replaces the ordinary order, and a left-invariant measure replaces Lebesgue measure. Partial characterizations of exponential distributions on such semigroups are obtained and the semigroup formulation provides new characterizations of certain aging properties studied in reliability-increasing failure rate, new better than used, and increasing failure rate average.