On Edgeworth expansions for dependency-neighborhoods chain structures and Stein's method

Let W be the sum of dependent random variables, and h(x) be a function. This paper provides an Edgeworth expansion of an arbitrary ``length' for %E{h(W)} in terms of certain characteristics of dependency, and of the smoothness of h and/or the distribution of W. The core of the class of dependency structures for which these characteristics are meaningful is the local dependency, but in fact, the class is essentially wider. The remainder is estimated in terms of Lyapunov's ratios. The proof is based on a Stein's method.Supported in part by NSF grant DMS-98-03623Supported in part by the Russian Foundation of Basic Research, grant # 00-01-00194, and by NSF grant DMS-98-03623Mathematics Subject Classification (2000):Primary 62E20; Secondary 60E05     

Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions

A function f(x) defined on $\text{X}$ = $\text{X}$₁ × $\text{X}$₂ × … × $\text{X}$_n where each $\text{X}$_i is totally ordered satisfying f(x ∨ y) f(x ∧ y) ≥ f(x) f(y), where the lattice operations ∨ and ∧ refer to the usual ordering on $\text{X}$, is said to be multivariate totally positive of order 2 (MTP₂). A random vector Z = (Z₁, Z₂,…, Z_n) of n-real components is MTP₂ if its density is MTP₂. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix Σ satisfies ?DΣ^?1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP₂ properties. The MTP₂ property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP₂ kernels are presented and amplified by a wide variety of applications.     

Boxlike filter response based on complementary photonic bandgaps in two-dimensional microresonator arrays

We propose that a boxlike filter response can be obtained by utilizing complementary photonic bandgap properties of the column and row configurations in two-dimensional microresonator arrays. The filters are fabricated using deep-UV lithography in silicon-on-insulator technology. The observed sidelobes reduction is approximately 10 dB, and the usable bandwidth can be as high as 500-750 GHz.     

Reactions along the astrophysical s-process path and prospects for neutron radiotherapy with the Liquid-Lithium Target (LiLiT) at the Soreq Applied Research Accelerator Facility (SARAF)

The European Physical Journal A - An empirical formula is proposed for the two-proton decay half-lives. This study is an extension of the empirical formula reported recently by us for calculating...     

Set-indexed Brownian Motion on Increasing Paths

We prove that a square-integrable set-indexed stochastic process is a set-indexed Brownian motion if and only if its projections on all the strict increasing continuous paths are one-parameter time-change Brownian motions. We present some applications.     

Nanoscale zinc antimonides: synthesis and phase stability

Highly crystalline single-phase nanoparticles of the important thermoelectric materials Zn4Sb3 and ZnSb were prepared from solvochemically activated powders of elemental zinc and elemental antimony. Low-temperature reactions with reaction temperatures of 275-300 degrees C were applied using an excess of elemental zinc. The nanoscale thermoelectrics obtained were characterized by X-ray powder diffraction, transmission electron microscopy, and thermal analysis. nc-Zn4Sb3 showed particle sizes of 50-70 nm, whereas particle sizes of 15-20 nm were observed for nc-ZnSb. Calorimetric investigations showed an increased heat capacity, Cp, for nc-Zn4Sb3 with respect to the bulk material which could be reduced to the bulk value by annealing nc-Zn4Sb3 at 190 degrees C. Interestingly, nc-Zn4Sb3 showed exothermic decomposition into zinc-poorer ZnSn at 196 degrees C in an open system, indicating that Zn4Sb3 is metastable in nanocrystalline form at room temperature.     

ON THE RELATIONSHIPS BETWEEN NATURAL AND HARVEST MORTALITIES OF THE MALLARD

A discrete optimal control approach is used to show that the intensity of harvest of mallard populations in North America, at steady state, is sensitive to the strength of compensation between natural mortality and harvest mortality. Optimal harvest is less sensitive to changes in the natural mortality rate than to the interaction between natural and harvest mortalities. The management implications are: (1) if compensatory mortality operates, then more animals may be harvested without endangering the population, and (2) managers should pay particular attention to this mechanism in studying population dynamics.