A sign pattern is a matrix with entries in {+, −, 0}. A full sign pattern has no zero entries. The refined inertia of a matrix pattern is defined and techniques are developed for constructing potentially nilpotent full sign patterns. Such patterns are spectrally arbitrary. These techniques can also be used to construct potentially nilpotent sign patterns that are not full, as well as potentiall...

In 1937, Stone [6] introduced and investigated the regular open sets. These sets are contained in the family of open sets since a set is regular open if it is equal to the interior of its closure. In 1978, Cameron [2] also introduced and investigated the concept of a regular semiopen set. A set A is regular semiopen if there is a regular open set U such that U ⊆ A ⊆ U . In 2007, a new class of ...

For each n, let $$A_n=(\sigma _{ij})$$ be an $$n\times n$$ deterministic matrix and $$X_n=(X_{ij})$$ random with i.i.d. centered entries of unit variance. In the companion article (Cook et al. in Electron J Probab 23:Paper No. 110, 61, 2018), we considered empirical spectral distribution $$\mu _n^Y$$ rescaled entry-wise product $$\begin{aligned} Y_n = \frac{1}{\sqrt{n}} A_n\odot X_n \left( \sig...

a cartan manifold is a smooth manifold m whose slit cotangent bundle 0t *m is endowed with a regularhamiltonian k which is positively homogeneous of degree 2 in momenta. the hamiltonian k defines a (pseudo)-riemannian metric ij g in the vertical bundle over 0 t *m and using it, a sasaki type metric on 0 t *m is constructed. a natural almost complex structure is also defined by k on 0 t *m in su...

— A characterization oj decreasing rational transductions is given, We show that x is a decreasing rational transduction jrom X* into Y* if and only ij there exist an alphabet Z, two alphabetic morphisms h:Z* -> X*,g:Z* -» Y*t with h e-jree and a regular language R o Z* such that x = go(nR)oh~. Résumé. — Nous proposons une caracterisation des transductions rationnelles décroissantes. Nous montr...

in this paper we demonstrate the existence of a set of polynomials pi , 1 i  n , which arepositive semi-definite on an interval [a , b] and satisfy, partially, the conditions of polynomials found in thelagrange interpolation process. in other words, if a  a1  an  b is a given finite sequence of realnumbers, then pi (a j )  ij (ij is the kronecker delta symbol ) ; moreover, the sum of ...

we shall also denote by P [∂ x ] the differential operator P (∂ x) = P The transposition that interchanges x i and x j will be denoted s ij. It is easily shown that for any P ∈ R and 1 ≤ i < j ≤ n we have the factorization (1 − s ij)P (x) = (x i − x j) 1+2r P ij (x) I .1 with r ≥ 0, P ij (x) prime with (x i − x j) and symmetric in x i , x j. This given, a polynomial P (x) ∈ Q[X n ] is said to b...

It is interesting to ask how the invariants of the maps i, such as the ideal Ij(bi) generated by the j x j minors of q, reflect the properties of M. For example, it is not hard to show (see Buchsbaum-Eisenbud [4]) that if the grade of M is g (that is, g is the length of a maximal regular sequence contained in J) and r is the rank of the map b (that is, the size of the largest nonvanishing minor...