This paper investigates analogs of the Kreisel-Lacombe-Shoenfield Theorem in the context of the type-2 basic feasible functionals. We develop a direct, polynomial-time analog of effective operation in which the time boundingon computations is modeled after Kapron and Cook’s scheme for their basic polynomial-time functionals. We show that if P = NP, these polynomial-time effective operations are...

We consider two applications of recursive functionals. The first application concerns Gödel’s theory T , which provides a rudimentary foundation for the formalization of mathematics. T can be understood as a theory of the simply-typed lambda calculus that is extended to include the constant 0N, the successor function S, and the operator Rτ for primitive recursion on objects of type τ . It is kn...

This paper investigates analogs of the Kreisel-Lacombe-Shoenfield Theorem in the context of the type-2 basic feasible functionals. We develop a direct, polynomial-time analog of effective operation in which the time boundingon computations is modeled after Kapron and Cook’s scheme for their basic polynomial-time functionals. We show that if P = NP, these polynomial-time effective operations are...

In this paper we give a geometric condition which ensures that (q, p)-Poincaré-Sobolev inequalities are implied from generalized (1, 1)-Poincaré related to L1 norms in the context of product spaces. The concept eccentricity plays central role paper. We provide several type adapted different geometries and then show our self-improving method can be applied obtain special interesting Poincaré-Sob...

Many science and engineering problems can be formulated as optimization problems that are governed by m-flow type PDEs (multitime evolution systems) and by cost functionals expressed as multiple integrals or curvilinear integrals. Our paper discuss the m-flow type PDEconstrained optimization problems, focussing on a simplified multitime maximum principle. This extends the simplified single-time...

We consider estimation of linear functionals of the error distribution for two regression models: parametric and nonparametric, and for two types of errors: independent of the covariate and centered (type I), and conditionally centered given the covariate (type II). We show that the residual-based empirical estimators for the nonparametric type I model remain efficient in the type II model. For...

We study the asymptotic behaviour of convolution-type functionals defined on general periodic domains by proving an extension theorem.