Let x1, · · · ,xn be points randomly chosen from a set G ⊂ R and f(x) be a function. The Euclidean random matrix is given by Mn = (f(∥xi − xj∥))n×n where ∥ · ∥ is the Euclidean distance. When N is fixed and n → ∞ we prove that μ̂(Mn), the empirical distribution of the eigenvalues of Mn, converges to δ0 for a big class of functions of f(x). Assuming both N and n go to infinity proportionally, we ...

The Euclidean distance matrix (EDM) completion problem and the positive semidefinite (PSD) matrix completion problem are considered in this paper. Approaches to determine the location of a point in a linear manifold are studied, which are based on a referential coordinate set and a distance vector whose components indicate the distances from the point to other points in the set. For a given ref...

 This paper present unequal-sized facilities layout solutions generated by a genetic search program named LADEGA (Layout Design using a Genetic Algorithm). The generalized quadratic assignment problem requiring pre-determined distance and material flow matrices as the input data and the continuous plane model employing a dynamic distance measure and a material flow matrix are discussed. Computa...

On page 42, Table 1 should be numbered Table 3, and Table 2 should be numbered Table 4. On page 43, Table 6 should be numbered Table 1 and ordered in first position among the seven tables, Table 7 should be numbered Table 2 and ordered in second position among the seven tables, Table 3 should be numbered Table 5, Table 4 should be numbered Table 6, and Table 5 should be numbered Table 7. The Ta...

Recent work by J. Prades and myself on K ! is described. The rst part describes our method to connect in a systematic fashion the short-distance evolution with long-distance matrix-element calculations taking the scheme dependence of the short-distance evolution into account correctly. In the second part I show the results we obtain for the I = 1=2 rule in the chiral limit.

Let x1, · · · ,xn be points randomly chosen from a set G ⊂ R and f(x) be a function. A special Euclidean random matrix is given by Mn = (f(∥xi − xj∥))n×n. When p is fixed and n → ∞ we prove that μ̂(Mn), the empirical distribution of the eigenvalues of Mn, converges to δ0 for a big class of functions of f(x). Assuming both p and n go to infinity with n/p → y ∈ (0,∞), we obtain the explicit limit ...