In this paper, we will address a problem raised by Bauer, Escardó and Simpson. We define two hierarchies of total, continuous functionals over the reals based on domain theory, one based on an “extensional” representation of the reals and the other on an “intensional” representation. The problem is if these two hierarchies coincide. We will show that this coincidence problem is equivalent to th...

We construct the time evolution for states of Glauber dynamics for a spatial infinite particle system in terms of generating functionals. This is carried out by an Ovsjannikov-type result in a scale of Banach spaces, leading to a local (in time) solution which, under certain initial conditions, might be extended to a global one. An application of this approach to Vlasov-type scaling in terms of...

Abstract We introduce the coupled Ricci–Calabi functional and H-functional which measure how far a Kähler metric is from Kähler–Einstein in sense of Hultgren–Witt Nyström. first give corresponding moment weight type inequalities estimate each terms algebraic invariants. Secondly, we Hessian formulas for these functionals at critical point, have an application to Matsushima obstruction theorem e...

The system of Gegenbauer polynomials fC n (x); n = 0; 1; : : :g is a classical family of polynomials orthogonal with respect to the weight function ! (x) = (1?x 2) ? 1 2 on the support interval ?1; +1]. Integral functionals of Gegenbauer polynomials with kernel f(x))C n (x)] 2 ! (x), where f(x) is an arbitrary function which does not depend on n or , are considered in this paper. Firstly, a gen...

We show that the extensional ordering of the sequential functionals of pure type 3, e.g. as defined via game semantics [2, 4], is not cpo-enriched. This shows that this model does not equal Milner’s [9] fully abstract model for PCF .

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Some inequalities of Ostrowski type for isotonic linear functionals defined on a linear class of function L := {f : [a, b] → R} are established. Applications for integral and discrete inequalities are also given.