Sampling designs for regression coefficient estimation with correlated errors

The problem of estimating regression coefficients from observations at a finite number of properly designed sampling points is considered when the error process has correlated values and no quadratic mean derivative. Sacks and Ylvisaker (1966,Ann. Math. Statist.,39, 66–89) found an asymptotically optimal design for the best linear unbiased estimator (BLUE). Here, the goal is to find an asymptotically optimal design for a simpler estimator. This is achieved by properly adjusting the median sampling design and the simpler estimator introduced by Schoenfelder (1978, Institute of Statistics Mimeo Series No. 1201, University of North Carolina, Chapel Hill). Examples with stationary (Gauss-Markov) and nonstationary (Wiener) error processes and with linear and nonlinear regression functions are considered both analytically and numerically.Research supported by the Air Force Office of Scientific Research Contract No. 91-0030.     

Routing to reduce the cost of wavelength conversion

We consider all-optical networks that use wavelength-division multiplexing and employ wavelength conversion at specific nodes in order to maximize their capacity usage. We investigate the effect of allowing reroutings on the number of necessary wavelength converters. We disprove a claim of Wilfong and Winkler [G. Wilfong, P. Winkler, Ring routing and wavelength translation, in: Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’98, 1998, pp. 333-341] according to which reroutings do not have any effect on the number of necessary wavelength converters on bidirected networks. We show that there exist (bidirected) networks on n nodes that require Θ(n) converters without reroutings, but only O(1) converters if reroutings are allowed. We also address the cases of undirected networks and networks with shortest-path routings. In each case, we resolve the complexity of computing optimal placements of converters.     

Epoxidation of olefins with H2O2 catalyzed by new symmetrical acetylacetone-based Schiff bases/Mn(II) homogeneous systems: A catalytic and EPR study

Two new symmetrical acetylacetone-based Schiff bases, herein called L_A and L_B, have been synthesized. The complexes formed by their association with Mn(II) have been evaluated for catalytic alkene epoxidation with H₂O₂. The catalytic efficiency of Mn(II)/L_A and Mn(II)/L_B systems were shown to be switched on by ammonium acetate with remarkable effectiveness and selectivity towards epoxides. EPR spectroscopy for Mn(II)/L_A shows that the catalytic centre is a mononuclear Mn complex. Additives that allow easier oxidation of Mn(II) to higher oxidation states, i.e. such as acetate and bicarbonate, can promote decisively the catalytic function. Additives that do not allow oxidation of Mn(II) to higher oxidation states, i.e. such as formate and oxalate, inhibit severely the catalytic function. Monocarboxylate ions, i.e. acetate, bicarbonate and formate do not disturb considerably the first coordination sphere of Mn(II). Dicarboxylate additives, i.e. such as oxalate, form strong complex with the Mn(II).Based on the catalytic and EPR data, a double role is suggested for ammonium acetate. This is to promote Mn(II) oxidation, and to function as a dual acid-base system, participating into the catalytic cycle.     

Stable mixed moving averages

Summary The class of (non-Gaussian) stable moving average processes is extended by introducing an appropriate joint randomization of the filter function and of the stable noise, leading to stable mixed moving averages. Their distribution determines a certain combination of the filter function and the mixing measure, leading to a generalization of a theorem of Kanter (1973) for usual moving averages. Stable mixed moving averages contain sums of independent stable moving averages, are ergodic and are not harmonizable. Also a class of stable mixed moving averages is constructed with the reflection positivity property.Research supported by AFSOR Contract 91-0030Research also supported by ARO DAAL-91-G-0176Research also supported by AFOSR 90-0168Research also supported by ONR N00014-91-J-0277     

Innovations and Wold decompositions of stable sequences

Summary For symmetric stable sequences, notions of innovation and Wold decomposition are introduced, characterized, and their ramifications in prediction theory are discussed. As the usual covariance orthogonality is inapplicable, the non-symmetric James orthogonality is used. This leads to right and left innovations and Wold decompositions, which are related to regression prediction and least p ^th moment prediction, respectively. Independent innovations and Wold decompositions are also characterized; and several examples illustrating the various decompositions are presented.Research supported by the Air Force Office of Scientific Research Contract F49620 82 C 0009     

On a conjectured inequality of Gautschi and Leopardi for Jacobi polynomials

Motivated by work on positive cubature formulae over the spherical surface, Gautschi and Leopardi conjectured that the inequality holds for α,β > − 1 and n ≥ 1, θ ∈ (0, π), where are the Jacobi polynomials of degree n and parameters (α, β). We settle this conjecture in the special cases where .