We give an overview of statistical models and likelihood, together with two of its variants: penalized and hierarchical likelihood. The Kullback-Leibler divergence is referred to repeatedly, for defining the misspecification risk of a model, for grounding the likelihood and the likelihood crossvalidation which can be used for choosing weights in penalized likelihood. Families of penalized likel...

Sieve Residue Sieve residue refers to non-dispersable contaminants (such as coke, refractory particles, water soluble salts and metal oxides) and is expressed as a percentage of the carbon black by weight. Sixty and 325 Mesh sieves are used for this test. The resulting grit can cause blemishes and may affect the appearance and performance of some rubber and plastic products. The 325 Mesh grit i...

This paper reviews various types of heterogeneous acid-base catalysts for fragrances preparation. Catalytic activities of the various types of heterogeneous acid and base catalysts in fragrances preparation, i.e. nonzeolitic, zeolitic, and mesoporous molecular sieves, have been reported. Generally, heterogeneous acid catalysts are more commonly used in fragrance synthesis as compared to heterog...

Recently, several algorithms using number field sieves have been given to factor a number n in heuristic expected time Ln[1/3; c], where Ln[v; c] = exp{(c + o(1))(log n) (log log n)}, for n → ∞. In this paper we present an algorithm to solve the discrete logarithm problem for GF (p) with heuristic expected running time Lp[1/3; 3 ]. For numbers of a special form, there is an asymptotically slowe...

A~trac t -A recursive, nonparametric method is developed for performing density estimation derived from mixture models, kernel estimation and stochastic approximation. The asymptotic performance of the method, dubbed "adaptive mixtures" (Priebe and Marchette, Pattern Recognition 24, 1197-1209 (1991)) for its data-driven development of a mixture model approximation to the true density, is invest...