Fuzzy quasi-interpolations help to reduce the complexity of solving a linear system of equations compared with fuzzy interpolations. Almost all fuzzy quasi-interpolations are focused on the form of $widetilde{f}^{*}:mathbb{R}rightarrow F(mathbb{R})$ or $widetilde{f}^{*}:F(mathbb{R})rightarrow mathbb{R}$.  In this paper, we intend to offer a novel fuzzy radial basis function by the concept of so...

By means of the Ehrhart theory of inside-out polytopes we establish a general counting theory for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen, on a polygonal convex board. The number of ways to place q identical nonattacking pieces on a board of variable size n but fixed shape is (up to a normalization) given by a quasipolynomial function of n, ...

| This paper presents a quasi-interpolation method for DIV-CURL vector splines in two dimensions on both innnite and nite domains. The quasi-interpolant is a linear combination of translates of dilates of a basis function. In particular, our discussion focuses on the approximation of a vector-valued function deened on a nite domain for practical application purposes. In such a case, edge functi...

The aim of this course is to introduce the reader to the general techniques appearing in the spectral theory of the semiclassical magnetic Laplacian. We explain how we can construct quasi-eigenpairs and how the investigation of the magnetic Laplacian can be reduced to the one of model operators. In particular, the localization estimates of Agmon and the Born-Oppenheimer approximation are discus...

In this paper, we show how by a very simple modification of bivariate spline discrete quasi-interpolants, we can construct a new class of quasi-interpolants, which have remarkable properties such as high order of regularity and polynomial reproduction. More precisely, given a spline discrete quasi-interpolation operator Qd, which is exact on the space Pm of polynomials of total degree at most m...

Quasi-interpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations. Based on the good performance, Chen and Wu presented a kind of multiquadric (MQ) quasi-interpolation, which is generalized from the LD operator, and used it to solve hyperbolic conservation laws and Burgers’...