In this paper we investigate some existence questions of positive semi-definite solutions for certain classes of matrix equations known as the generalized Lyapunov equations. We present sufficient and necessary conditions for certain equations and only sufficient for others.
We establish the existence of mild solutions for a class of abstract second-order partial neutral functional integro-differential equations with finite delay in a Banach space using the theory of cosine families of bounded linear operators and Schaefer's fixed-point theorem.
Lü and Wang (1985) published a counterexample showing that the approach of Rutovitz (1966) for parallel thinning of digital pictures (see also Hilditch 1969, Stefanelli and Rosenfeld Cheap Babyliss Pro Perfect Curl
1971) is not universally valid. In this paper it is shown that the example given by Lü and Wang is the only possible counterexample. A reformulation of Rutovitz' approach is suggested which does not exhibit further defects.
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died at 7 weeks of age from respiratory failure.