Topic
Realizability
About: Realizability is a research topic. Over the lifetime, 1947 publications have been published within this topic receiving 36763 citations.
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01 Jun 1992
TL;DR: In this article, a mathematical notation and review of state equation representation state equation solution transition matrix properties two important cases internal stability Lyapunov stability criteria additional stability criteria controllability and observability realizability minimal realization input-out-put stability controller and observer forms linear feedback state observation polynomial fraction description polynoial fraction applications geometric theory applications of geometric theory.
Abstract: Mathematical notation and review state equation representation state equation solution transition matrix properties two important cases internal stability Lyapunov stability criteria additional stability criteria controllability and observability realizability minimal realization input-out-put stability controller and observer forms linear feedback state observation polynomial fraction description polynoial fraction applications geometric theory applications of geometric theory.
1,575 citations
TL;DR: In this article, the authors considered the problem of matching an arbitrary load impedance to a pure resistance by means of a reactive network and derived necessary and sufficient conditions for the physical realizability of a function of frequency representing the input reflection coefficient of a matching network terminated in a prescribed load impedance.
Abstract: This paper deals with the general problem of matching an arbitrary load impedance to a pure resistance by means of a reactive network. It consists primarily of a systematic study of the origin and nature of the theoretical limitations on the tolerance and bandwidth of match and of their dependence on the characteristics of the given load impedance. Necessary and sufficient conditions are derived for the physical realizability of a function of frequency representing the input reflection coefficient of a matching network terminated in a prescribed load impedance. These conditions of physical realizability are then transformed into a set of integral relations involving the logarithm of the magnitude of the reflection coefficient. Such relations are particularly suitable for the study of the limitations on the bandwidth and tolerance of match. Definite expressions for these quantities are obtained in special cases. The practical problem of approaching the optimum theoretical tolerance by means of a network with a finite number of elements is also considered. Design curves are provided for a particularly simple but very important type of load impedance. In addition, a very convenient method is presented for computing the values of the elements of the resulting matching network.
852 citations
01 Jan 1973
TL;DR: In this paper, Kripke models are used to define inductive definitions, trees and ordinals for intuitionistic formal systems, and normalization theorems for systems of natural deduction.
Abstract: Intuitionistic formal systems.- Models and computability.- Realizability and functional interpretations.- Normalization theorems for systems of natural deduction.- Applications of Kripke models.- Iterated inductive definitions, trees and ordinals.- Erratum.
809 citations
Book•
21 Oct 2010TL;DR: This paper discusses the unwinding of proofs in approximation theory, semi-intuitionistic systems and monotone modified realizability, and the Friedman-Dragalin A-translation.
Abstract: Preface.- Introduction.- Unwinding of proofs ('Proof Mining').- Intuitionistic and classical arithmetic in all finite types.- Representation of Polish metric spaces.- Modified realizability.- Majorizability and the fan rule.- Semi-intuitionistic systems and monotone modified realizability.- Godel's functional ('Dialectica') interpretation.- Semi-intuitionistic systems and monotone functional interpretation.- Systems based on classical logic and functional interpretation.- Functional interpretation of full classical analysis.- A non-standard principle of uniform boundedness.- Elimination of monotone Skolem functions.- The Friedman-Dragalin A-translation.- Applications to analysis: general metatheorems I.- Case study I: Uniqueness proofs in approximation theory.- Applications to analysis: general metatheorems II.- Case study II: Applications to the fixed point theory of nonexpansive mappings.- Final comments.- References.- Index.
456 citations
TL;DR: In this article, it was shown that existing phenomenological models of turbulence in terms of differential equations for the Reynolds stresses do not guarantee realizable solutions, and some means are proposed which can be used to change the existing models into realizable ones.
Abstract: It is shown that certain existing phenomenological models of turbulence in terms of differential equations for the Reynolds stresses Rαβ=〈u′α u′β〉 do not guarantee realizable solutions. The known realizability conditions are Rαβ⩾0 for α=β and Rαβ2⩾Rαα Rββ for α≠β. A stronger requirement is that the matrix Rαβ be positive semi‐definite. This implies three conditions like non‐negative eigenvalues or non‐negative principal invariants. Conditions are given which must be satisfied by the model itself in order to guarantee realizable solutions for any realizable initial and boundary conditions. Some means are proposed which can be used to change the existing models into realizable ones.
443 citations