Abstract The problem of minimizing a (nonconvex) quadratic form over the unit simplex, referred to as standard program, admits an exact convex conic formulation computationally intractable cone completely positive matrices. Replacing in this by larger but tractable doubly nonnegative matrices, i.e., semidefinite and componentwise one obtains so-called relaxation, whose optimal value yields lowe...

We assume that each valence quark in a nucleon is in a phenomenological modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where a, b, c and d are constants and ? is one of the Dirac matrices. Then by making use of a suitable ansatz, the Dirac equation has a very simple solution which is exact. We then have calculated the static properties of the nucleon in the ...

Main result of this paper is to derive the exact analytical expressions of information and covariance matrices for multivariate Burr III and logistic distributions. These distributions arise as tractable parametric models in price and income distributions, reliability, economics, Human population, some biological organisms to model agricultural population data and survival data. We showed that ...

For a family of n ∗ n left triangular matrices with binary entries we derive asymptotically exact (as n → ∞) representation for the complete eigenvalues-eigenvectors problem. In particular we show that the dependence of all eigenvalues on n is asymptotically linear for large n. A similar result is obtained for more general (with specially scaled entries) left triangular matrices as well. As an ...

Let B n = (1/N)T 1/2 n is a Hermitian square root of the nonnegative definite Hermitian matrix T n. It is shown in Bai and Silverstein (1998) that, under certain conditions on the eigenvalues of T n , with probability one no eigenvalues lie in any interval which is outside the support of the limiting empirical distribution (known to exist) for all large n. For these n the interval corresponds t...

We show that the Hausdorff dimension of the spectral measure of a class of deterministic, i. e. nonrandom, block–Jacobi matrices may be determined exactly, improving a result of Zlatoš (J. Funct. Anal. 207, 216-252 (2004)).

In several domains of physics like, for instance, in string theory [1] and in quantum chromodynamics [2] we are interested in the spectral properties of random matrices; most results in this domain are included in the correlation functions for the invariants of the matrices like determinants, traces...Although most interesting results are expected from infinitely large matrices, exact results c...

Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact or approximate symmetries, such as matrices with i.i.d. entries, for which precise analytic results and limit theorems are available. Much less well understoo...