The Tracy–Widom distributions are among the most famous laws in probability theory, partly due to their connection with Wigner matrices. In particular, for A=1n(aij)1≤i,j≤n∈Rn×n symmetric (aij)1≤i≤j≤n i.i.d. standard normal, fluctuations of its largest eigenvalue λ1(A) asymptotically described by a real-valued distribution TW1:n2/3(λ1(A)−2)⇒TW1. As it often happens, Gaussianity can be relaxed, ...

OBJECTIVES The purpose of the presentin vitro study was to predict to what extent dietary fiber (DF) takes up heterocyclic aromatic amine (HAA) and how DF acts to intercept HAAsin vivo. METHODS The sorption isotherms of 2-amino-3-methyl-3H-imidazo[4,5-f]quinoline (IQ), 2-amino-3,4-dimethyl-3H-imidazo[4,5-f]quinoline (MeIQ), 3-amino-1,4-dimethyl-5H-pyrido[4,3-b]indole acetate (Trp-P-1), and 3-...

Food-safety incidents are costly for everyone in the leafy greens industry. However, it is challenging to estimate size and distribution of these costs today's complex supply chains. Extensive use formal contracts markets such as obscures prices other terms trade from public view. Using proprietary data on sales a major processor operating retail food-service sectors, we able separately short-r...

where Aij = a(i, j) and the domain of the function is just the cross-product of the two index sets. Such a structure is called a matrix. The values Aij are called the elements or entries of the matrix. A sequence of elements with the same first index is called a row of the matrix; similarly, a sequence of elements with the same second index is called a column. The dimension of the matrix specif...

A crucial problem in a decision-making process is the determination of a scale of relative importance for a set X $x1, x2, . . . , xn % of alternatives either with respect to a criterion C or an expert E. A widely used tool in Multicriteria Decision Making is the pairwise comparison matrix A ~aij !, where aij is a positive number expressing how much the alternative xi is preferred to the altern...

The present paper deals with the study of biomass production of manures in the greens such as Amaranthus polygamus and Amaranthus viridis of the family Amaranthaceae and Spinacea oleracea of the family Chenopodiaceae. The medicinal uses and pharmaco - phytochemical analysis were also carried out for the plant species which are widely used as greens.

This work is devoted in the derivation of novel upper and lower bounds for the Rice Ie-function. These bounds are expressed in closed-form and are shown to be quite tight. This is particularly evident by the fact that for a certain range of parameter values, the derived lower bound virtually behaves as a remarkably accurate approximation. As a result, the offered expressions can be considered u...