Recently, folk questions on the smoothability of Cauchy hypersurfaces and time functions of a globally hyperbolic spacetime M , have been solved. Here we give further results, applicable to several problems: (1) Any compact spacelike acausal submanifold H with boundary can be extended to a spacelike Cauchy hypersurface S. If H were only achronal, counterexamples to the smooth extension exist, b...

The duality between “regular” and “topological” as convergence space properties extends in a natural way to the more general properties “p-regular” and “p-topological.” Since earlier papers have investigated regular,p-regular, and topological Cauchy completions, we hereby initiate a study of p-topological Cauchy completions. A p-topological Cauchy space has a p-topological completion if and onl...

The usual domains for Cauchy distributions have been straight lines and unit circles. These domains are closed under arbitrary changes in location and scale, whether done sequentially or simultaneously. Such closure properties have been extended to spherical Cauchy distributions. Higher dimensional Cauchy based domains are created herein for unit hyperspheres and sets of straight lines of arbit...

We study asymptotic expansions in free probability. In a class of classical limit theorems Edgeworth expansion can be obtained via a general approach using sequences of “influence” functions of individual random elements described by vectors of real parameters (ε1, . . . , εn), that is by a sequence of functions hn(ε1, . . . , εn; t), |εj | ≤ 1 n , j = 1, . . . , n, t ∈ A ⊂ R (or C) which are s...

The standard choice for mutating an individual of an evolutionary algorithm with con tinuous variables is the normal distribution however other distributions especially some versions of the multivariate Cauchy distribution have recently gained increased popularity in practical applications Here the extent to which Cauchy mutation distributions may a ect the local convergence behavior of evoluti...

In this contribution we deal with the development, theoretical examination and numerical examples of a method of lines approximation for the Cauchy problem for elliptic partial differential equations. We restrict ourselves to the Laplace equation. A more general elliptic equation containing a diffusion coefficient will be considered in a forthcoming paper. Our main results are the regularizatio...

The space l^p with 1≤p∞ is the set of real numbers that satisfy _(n=1)^∞▒〖|x_n |^p∞〗.The function in vector X which has value fulfills norm-2 properties denoted by ,⋅‖ and pair (X,‖⋅,⋅‖) called space.A said to be complete or a Banach-2 if every Cauchy sequence converges an element space.This research was conducted prove norm-2.The first step completeness norm contained satisfies norm-2.Next, de...

In this paper, we investigate the convergence of Faedo-Galerkin approximations, in a strong sense, to T-periodic solution torso-coupled bidomain model where T is period activation inner wall heart. First, define operator and prove some its more important properties for our work. After, abstract evolution system equations that are associated with give definition solution. We Faedo-Galerkin’s app...

An MV-convergence is a convergence on an MV-algebra which renders the operations continuous. We show that such convergences on a given MV-algebra A are exactly the restrictions of the bounded `-convergences on the abelian `-group in which A appears as the unit interval. Thus the theory of `-convergence and Cauchy structures transfers to MV-algebras. We outline the general theory, and then apply...

Motivated by the Novikov equation and its peakon problem, we propose a new mixed type Hermite–Padé approximation whose unique solution is sequence of polynomials constructed with help Pfaffians. These belong to family recently proposed partial-skew-orthogonal polynomials. The relevance especially visible in problem germane so that obtain explicit inverse formulae terms Pfaffians reformulating s...