Computability relative to a partial function f on the natural numbers can be formalized using notion of an oracle for this f. This generalized arbitrary combinatory algebras, yielding ‘adjoining algebra A’. A similar construction is known second-order functionals, but third-order case more difficult. In paper, we prove several results case. Given functional Φ A, show how construct A[Φ] where ‘c...

Several authors have examined connections among restricted permutations and different combinatorial structures. In this paper we establish a bijection between the set of permutations π which avoid 1322 and the set of odd-dissection convex polygons, where a permutation avoids ab2c if there are no i < j < k − 1 such that πiπjπk is order-isomorphic to abc. We also exhibit bijections between the se...

In this paper, we introduce and investigate two new generalized mixed equilibrium problems and explore the relationship between them and the properties of their solutions in Banach spaces. Based on the generalized f -projection, we construct hybrid algorithms to find common fixed points of a countable family of quasi-φnonexpansive mappings in Banach spaces, a common element of the set of soluti...

Generalized t-tests are constructed under weaker than normal conditions. In the first part of this paper we assume only the symmetry (around zero) of the error distribution (i). In the second part we assume that the error distribution is a Gaussian scale mixture (ii). The optimal (smallest) critical values can be computed from generalizations of Student’s cumulative distribution function (cdf),...

The one-loop effective action corresponding the general model of dilaton gravity given by the Lagrangian L = −√g [ 1 2 Z(Φ)g∂μΦ∂νΦ + C(Φ)R + V (Φ) ] , where Z(Φ), C(Φ) and V (Φ) are arbitrary functions of the dilaton field, is found. The question of the quantum equivalence of classically equivalent dilaton gravities is studied. By specific calculation of explicit examples it is shown that class...

Jachymski [ Proc. Amer. Math. Soc., 136 (2008), 1359-1373] gave modified version of a Banach fixed point theorem on a metric space endowed with a graph. In the present paper, (G, Φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. Also, Hardy-Rogers G-contraction have been introduced and some fixed point theorems have been proved. S...

The Machian cosmological solution satisfying φ = O(ρ/ω) in the generalized scalar-tensor theory of gravitation with the varying cosmological constant is summarized. The scalar field φ with the exponential potential is introduced as dark matter and the barotropic evolution of matter in the universe is discussed. As the universe expands, the coefficient γ of the equation of state approaches to −1...

A subalgebra Mo of a von Neumann algebra M is called weakly sufficient with respect to a pair (φ, ω) of states if the relative entropy of φ and ω coincides with the relative entropy of their restrictions to Mo. The main result says that Mo is weakly sufficient for (φ, ω) if and only if Mo contains the RadonNikodym cocycle [Dφ,Dω]t. Other conditions are formulated in terms of generalized conditi...

In this paper, we firstly consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalized Uhlmann theorem in an infinite dimension Hilbert space. Also, we show that S(Φ(ρ)) = S(ρ) for all quantum states ρ if and only if there exists an isometry operator V such that Φ(ρ) = V ρV , where Φ is a quantum cha...