The ability of several density-functional theory methods to describe the kinetics and energetics of a series of ring-opening reactions of cyclopropyl and cyclobutyl-type radicals was explored. PBE, B971 and B3LYP perform quite well in their ability to replicate experiment, based upon the ring opening of cyclopropylcarbinyl, two α-trialkylsilyloxycyclopropylmethyl radicals, pentamethylcyclopropy...

The continuous functionals were independently introduced by Kleene [6] and Kreisel [7]. Kleenes motivation was to isolate a subclass of the total functionals of pure, finite type closed under S1-S9-computations (Kleene [5]) which could be described using countable information. He defined his functionals via the associates and the idea is that an associate for a functional Ψ contains sufficient ...

A general approach to Bayesian learning revisits some classical results, which study which functionals on a prior distribution are expected to increase, in a preposterior sense. The results are applied to information functionals of the Shannon type and to a class of functionals based on expected distance. A close connection is made between the latter and a metric embedding theory due to Schoenb...

In one of his recent papers, Molnár showed that if $\mathcal{A}$ is a von Neumann algebra without $I_1, I_2$-type direct summands, then any function from the positive definite cone to real numbers preserving Kubo-Ando power mean, for some $0 \neq p \in (-1,1),$ necessarily constant. It was shown in paper $I_1$-type algebras admit nontrivial $p$-power mean functionals, and it conjectured $I_2$-t...

The contribution focuses on the stability analysis of linear time-delay systems within the framework of the Lyapunov – Krasovskii functionals. The method used is based on the idea to check positive definiteness of the functionals exclusively on the specific Razumikhin-type set of functions. For the systems with incommensurate delays, it is proposed to use the modified functionals depend on the ...

Abstract. In this note, we construct families of functionals of the type of F-functional and W-functional of Perelman. We prove that these new functionals are nondecreasing under the Ricci flow. As applications, we give a proof of the theorem that compact steady Ricci breathers must be Ricci-flat. Using these new functionals, we also give a new proof of Perelman’s no non-trivial expanding breat...

In his paper on machine characterizations of feasible functionals at all simple types, Seth [Set95] introduced the higher-type complexity class D and conjectured that this class is strictly larger than BFF, the basic feasible functionals of Cook and Urquhart [CU93]. In this paper we clarify the nature of D by characterizing D−, a subclass of D, through a typed programming formalism and show D− ...

Higher order variational functionals, emerging in the study of problems from materials science and engineering, have attracted a great deal of attention in last few years (e.g. [4], see [5]). In particular, the regularity of minimizers of such functionals has been studied very recently. In [15] and [16] the partial Ck,α regularity has been established for quasiconvex integrals with a p-power gr...

In this paper we consider positively 1-homogeneous supremal functionals of the type F (u) := supΩ f(x,∇u(x)). We prove that the relaxation F̄ is a difference quotient, that is F̄ (u) = RF (u) := sup x,y∈Ω, x6=y u(x)− u(y) dF (x, y) for every u ∈ W (Ω), where dF is a geodesic distance associated to F . Moreover we prove that the closure of the class of 1-homogeneous supremal functionals with respe...

We consider homogenization of sequences of integral functionals of the type