in an earlier work we showed that for ordered fields f not isomorphic to the reals r, there are continuous 1-1 unctions on [0, 1]f which map some interior point to a boundary point of the image (and so are not open). here we show that over closed bounded intervals in the rationals q as well as in all non-archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 func...

Using only basic topological properties of real algebraic sets and regular morphisms we show that any injective regular self-mapping of a real algebraic set is surjective. Then we show that injective morphisms between germs of real algebraic sets define a partial order on the equivalence classes of these germs divided by continuous semi-algebraic homeomorphisms. We use this observation to deduc...

Recently, quantile regression (QR) models are often applied for longitudinal data analysis. When the distribution of responses seems to be skew and asymmetric due to outliers and heavy-tails, QR models may work suitably. In this paper, a semi-parametric quantile regression model is developed for analysing continuous longitudinal responses. The error term's distribution is assumed to be Asymmetr...

In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we...

This paper studies a Laplace operator on semi-discrete surfaces. A semidiscrete surface is represented by a mapping into three-dimensional Euclidean space possessing one discrete and one continuous variable. It can be seen as a limit case of a quadrilateral mesh, or as a semi-discretization of a smooth surface. Laplace operators on both smooth and discrete surfaces have been an object of intere...

We study the convex hull of the feasible set of the semi-continuous knapsack problem, in which the variables belong to the union of two intervals. Besides being important in its own right, the semi-continuous knapsack problem arises in a number of other contexts, e.g. it is a relaxation of general mixed-integer programming. We show how strong inequalities valid for the semi-continuous knapsack ...