We apply certain recent results pertaining to the rank minimization problem under LMI constraints to determine non-trivial lower and upper bounds for the minimal order dynamic output feedback which stabilizes a given linear time invariant plant, via Semi-Definite Programs.

We demonstrate that the analytic solution for the set of energy eigenvalues of the semi-relativistic Coulomb problem reported by B. and L. Durand is in clear conflict with an upper bound on the ground-state energy level derived by some straightforward variational procedure.

If T and S are quasisimilar bounded operators on Banach spaces, we prove that each closed-and-open subset of the lower semiBrowder essential spectrum of T intersects one special part of the upper semi-Browder essential spectra of T and S. AMS Mathematics Subject Classification (1991): 47A53, 47A10

In this paper we present a sequence f2, f3, f4, . . . of upper semi-continuous set-valued functions with the property that the graph of fn n is not connected but the graph of fk n is connected for 1 ≤ k < n. Thus, for each positive integer n, lim ←−n is not connected but the difficulty of detecting this fact increases with n.

In this paper we prove the semi-circular law for the eigenvalues of regular random graph Gn,d in the case d→∞, complementing a previous result of McKay for fixed d. We also obtain a upper bound on the infinity norm of eigenvectors of Erdős-Rényi random graph G(n, p), answering a question raised by Dekel-Lee-Linial.

Toward establishing the decidability of the two quantifier theory of the ∆ 2 Turing degrees with join, we study extensions of embeddings of upper-semi-lattices into the initial segments of Turing degrees determined by computably enumerable sets, in particular the degree of the halting set 0. We obtain a good deal of sufficient and necessary conditions.

We show that a nite graph that is the inverse limit with a single surjective upper semi-continuous set valued function f : [0, 1] → 2[0,1] is either an arc or a simple triod. It is not known if there is such a simple triod.

This paper is devoted to the concepts of fuzzy upper and fuzzy lower contra-continuous, contra-irresolute and contra semi-continuous multifunctions. Several characterizations and properties of these multifunctions along with their mutual relationships are established in L-fuzzy topological spaces. Later, composition and union between these multifunctions have been studied. AMS (MOS) Subject Cla...

We present a Borsuk’s theorem published first in [3] (compare also [4, pages 119–120]). It is slightly generalized, the assumption of metrizability is omitted. We introduce concepts needed for the formulation and the proof of theorems on upper semi-continuous decompositions, retracts, strong deformation retract. However, only those facts that are necessary in the proof have been proved.

In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of left (right) semi-uninorms and implications satisfying the order property by means of some examples. Then we give out the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation.