The Perron product integral in Lie groups
The plenary hull of the generalized Jacobian matrix and the inverse function theorem in subdifferential calculus
The point of continuity property, neighbourhood assignments and filter convergences
We show that for some large classes of topological spaces X and any metric space (Z,d), the point of continuity property of any function f: X → (Z,d) is equivalent to the following condition: (*) For every ε > 0, there is a neighbourhood assignment of X such that d(f(x),f(y)) < ε whenever . We also give various descriptions of the filters ℱ on the integers ℕ for which (*) is satisfied by the ℱ-limit of any sequence of continuous functions from a topological space into a metric space.
The power mean and the logarithmic mean.
The projective properties of the extreme path derivatives
The q-gamma function for q > 1.
The q-gamma function for x<0.
The quasi-real extension of the real numbers
The Random Product Homotopy and Deficient Polynomial Systems.
The ratio between the tail of a series and its approximating integral.
The real 3x+1 problem
The regularity properties on the real line
The relationship between the local temperature and the local heat flux within a one-dimensional semi-infinite domain of heat wave propagation.
The role of an integral inequality in the study of certain differential equations.
The role of Onofri type inequalities in the symmetry properties of extremals for Caffarelli-Kohn-Nirenberg inequalities, in two space dimensions
We first discuss a class of inequalities of Onofri type depending on a parameter, in the two-dimensional Euclidean space. The inequality holds for radial functions if the parameter is larger than . Without symmetry assumption, it holds if and only if the parameter is in the interval . The inequality gives us some insight on the symmetry breaking phenomenon for the extremal functions of the Caffarelli-Kohn-Nirenberg inequality, in two space dimensions. In fact, for suitable sets of parameters (asymptotically...
The scalar Oseen operator in
This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in theory.
The Schur-convexity of Stolarsky and Gini means.
The Schur-harmonic-convexity of dual form of the Hamy symmetric function
The second Peano derivative as a composite derivative
The sharp Poincaré inequality for free vector fields: an endpoint result.