This paper addresses the problem of obtaining a consistent estimate (or upper bound) of the covariance matrix when combining two quantities with unknown correlation. The combination is defined linearly with two gains. When the gains are chosen a priori, a family of consistent estimates is presented in the paper. The member in this family having minimal trace is said to be “family-optimal”. When...

Let X be a Hausdorff space and A EX a continuum. A is said to be a Universal Subcontinuum (USC) if AH\B is connected for every continuum B EX. Let a be a collection of USC's of a Hausdorff space. Then a is said to have the finite partition property if a has a decomposition into a finite number of subcollections each having the finite intersection property. A result due to W. J. Gray [l] can be ...

In this paper, at first we define the concepts of response function and accessible states of a complete residuated lattice-valued (for simplicity we write $mathcal{L}$-valued) tree automaton with a threshold $c.$ Then, related to these concepts, we prove some lemmas and theorems that are applied in considering some decision problems such as finiteness-value and emptiness-value of recognizable t...

Abstract We show that the cohomology intersection number of a twisted Gauss–Manin connection with regularization condition is rational function. As an application, we obtain new quadratic relation associated to period integrals certain family K3 surfaces.