An abstract Pick interpolation theorem for a family of positive semi-definite kernels on a set X is formulated. The result complements those in [Ag] and [AM02] and will subsequently be applied to Pick interpolation on distinguished varieties [JKM].

In air pollution models, semi-Lagrangian methods are often used to solve the ad-vective part of the corresponding model equation. Interpolation is an essential part of these methods. In this note, ve diierent interpolation methods will be discussed and results of numerical experiments will be presented. To keep the concentration eld nonnegative, ltering techniques are used. Also a monotone inte...

This article gives an algorithm to recover the absolute factorization of a bivariate polynomial, taking into account the geometry of its monomials. It is based on algebraic criterions inherited from algebraic interpolation and toric geometry.

We introduce partial dcpo’s and show their some applications. A partial dcpo is a poset associated with a designated collection of directed subsets. We prove that (i) the dcpo-completion of every partial dcpo exists; (ii) for certain spaces X, the corresponding partial dcpo’s of continuous real valued functions on X are continuous partial dcpos; (iii) if a space X is Hausdorff compact, the latt...

In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to stor...

soil alkalinity and salinity are serious problems in arid and semi-arid regions, and therefore monitoring of soil ph and electrical conductivity (ec) is necessary in any region. the present study aimed to properly interpolate soil ph and ec as soil quality indices in a semi-arid mountainous area with annual precipitation of 342.4 mm. the study area is the karimabad rangelands in hamadan provinc...

Continual Learning (CL) investigates how to train Deep Networks on a stream of tasks without incurring forgetting. CL settings proposed in literature assume that every incoming example is paired with ground-truth annotations. However, this clashes many real-world applications: gathering labeled data, which itself tedious and expensive, becomes infeasible when data flow as stream. This work expl...