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A new algebraic criterion is given for a polynomial phi with complex coefficients to have all its zeros in a certain type of algebraic region T of the complex plane. In particular, T may be any circle or half plane. The criterion is effectively computable from the coefficients of the polynomial phi. The classical results of Hermite, Hurwitz, Lyapunov,… (More)
The need to assess subtle, potentially exploitable changes in serial structure is paramount in the analysis of financial data. Herein, we demonstrate the utility of approximate entropy (ApEn), a model-independent measure of sequential irregularity, toward this goal, by several distinct applications. We consider both empirical data and models, including… (More)
The need to assess the randomness of a single sequence, especially a finite sequence, is ubiquitous, yet is unaddressed by axiomatic probability theory. Here, we assess randomness via approximate entropy (ApEn), a computable measure of sequential irregularity, applicable to single sequences of both (even very short) finite and infinite length. We indicate… (More)
The realization theory linear dynamical systems, previously developed over a field, are extended to a large class of commutative rings. The principal result is that the existence criterion for a finite realization extends without modification from a field to a Noetherian integral domain.
Along with the increasing availability of high-speed, large-storage digital computers, there has been growing interest in their utilization for real-time control purposes. A typical problem in this connection and one of long-standing interest is the optimal static and dynamic operation of chemical reactors. To our knowledge, no digital computer is being… (More)