Conditions For Determinacy Research Articles

Germes de d\'etermination infinie dans des classes lisses

We give sufficient conditions of infinite determinacy (in the sense of Mather) with respect to right equivalence, in subrings of C ∞ (ℝ n ,0) defined by estimates on successive derivatives, such as rings of Gevrey germs. In this quantitative setting, a defect (hidden in the classical C ∞ case) appears between the regularity of equivalent germs and the regularity of local diffeomorphisms of (ℝn,0) giving the equivalence. Our conditions yield precise estimates of this defect, related to some suitable Łojasiewicz exponents of critical loci. We also show that the result is sharp in general.

Execution termination and computation determinacy of data-flow program nets

This paper deals with execution termination and computation determinacy of data-flow program nets, which are extended from conventional data-flow program graphs by allowing edge thresholds α and β to be any positive integer number, while a conventional data-flow graph has α = β = 1. First detailed description of program nets is presented and then the problems of execution termination and computation determinacy of a given data-flow program net are analysed. Through structural analysis of net activities, the following results are obtained in this paper: (1) necessary and sufficient conditions for any execution of a switchless net to terminate; (2) sufficient conditions for any execution of a program net, including SWITCH-nodes, to terminate; and (3) sufficient conditions of computation determinacy.

A note on the Carleman condition for determinacy of moment problems

A note on the Carleman condition for determinacy of moment problems

On a criterion for determinate moment sequences

Attributed to Perron [2], it is obtainable only by transforming a criterion for Stieltjes determinacy due to Perron. In doing so, I find (1) not to follow from Perron's result. In this note, I shall make the proper correction to eliminate confusion caused by the error (e.g., (1) if valid would be more general than Carleman's well known criterion [l]). I also give an example to show that (1) is invalid. Symmetrization of all mass distributions with the moments pn shows that {p„} is determinate provided that there is no more than one symmetric distribution with the moments po, 0, ju2, 0, • • ■ . But the latter condition is easily shown to be equivalent to Stieltjes determinacy of the moment sequence {m2»J (not the same as Hamburger determinacy of {p2n} [4]). Perron [2] gives as a sufficient condition for Stieltjes determinacy Of {p2n}