Abstract. We study some properties of the randomized series and their applications to the geometric structure of Banach spaces. For n ≥ 2 and 1 < p < ∞, it is shown that l ∞ is representable in a Banach space X if and only if it is representable in the Lebesgue-Bochner Lp(X). New criteria for various convexity properties in Banach spaces are also studied. It is proved that a Banach lattice E is...

Recently, Gregório and Oliveira developed a proximal point scalarization method (applied to multiobjective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of Auslender et al. as regularization. In this work we propose a variation of this method, taking into account the regularization with logarithm and quasi-distance, wher...

Abstract Intracranial chondromas are benign, slow-growing, cartilaginous tumors, which comprise only about 0.2% of all intracranial tumors. The majority of these lesions occur at the base of the skull, where they are thought to arise from residual embryonic chondrogenic cells along the basal synchondrosis. Very rarely, they may also originate from the convexity dura, falx cerebri, or the brain ...

Abstract— A smooth curve interpolation is very significant in computer graphics or in data visualization. In the present paper -piecewise rational cubic spline function with tension parameter is considered which produces a monotonic interplant to a given monotonic data set. The parameters in the description of the spline curve can be used to modify the shape of the curve, locally and globally. ...

Abstract. We are interested in the Logarithmic Sobolev Inequality for the infinite volume Gibbs measure with no quadratic interactions. We consider unbounded spin systems on the one dimensional Lattice with interactions that go beyond the usual strict convexity and without uniform bound on the second derivative. We assume that the one dimensional single-site measure with boundaries satisfies th...

We introduce a notion of fractional convexity that extends naturally the usual in Euclidean space to setting. With this convexity, we study convex envelope inside domain an exterior datum (the largest possible function is below outside) and show characterized as viscosity solution non-local equation given by infimum among all directions 1-dimensional laplacian. For prove existence, uniqueness c...

Polyhedral analysis [9] is an abstract interpretation used for automatic discovery of invariant linear inequalities among numerical variables of a program. Convexity of this abstract domain allows efficient analysis but also loses precision via convex-hull and widening operators. To selectively recover the loss of precision, sets of polyhedra (disjunctive elements) may be used to capture more p...

Constructive properties of uniform convexity, strict convexity, near convexity, and metric convexity in real normed linear spaces are considered. Examples show that certain classical theorems, such as the existence of points of osculation, are constructively invalid. The methods used are in accord with principles introduced by Errett Bishop.

We study how convergence of an observer whose state lives in a copy of the given system’s space can be established using a Riemannian metric. We show that the existence of an observer guaranteeing the property that a Riemannian distance between system and observer solutions is nonincreasing implies that the Lie derivative of the Riemannian metric along the system vector field is conditionally n...