Let L be a sparse context-free language over a finite alphabet A = {a1, . . . , at} and let fL : N t → N be its Parikh (counting) function. We prove that the map fL is a box spline, that is there exists a finite set Π of hyperplanes of R, through the origin, such that fL is a quasi-polynomial on every polyhedral cone determined by Π. Moreover we prove that the Parikh function of such a language...

Numerical Solution of hyperbolic conservation laws is important in computational fluid dynamics. In this paper, we present a new numerical method to solve the hyperbolic conservation laws, which is constructed by using the derivative of the cubic B-spline quasi-interpolation to approximate the spatial derivative of the dependent variable and first order forward difference to approximate the tim...

We show that a nested sequence of C macro-element spline spaces on quasi-uniform triangulations gives rise to hierarchical Riesz bases of Sobolev spaces H(Ω), 1 < s < r+ 3 2 , and H 0(Ω), 1 < s < σ+ 3 2 , s / ∈ Z+ 1 2 , as soon as there is a nested sequence of Lagrange interpolation sets with uniformly local and bounded basis functions, and, in case of H 0(Ω), the nodal interpolation operators ...

We propose a general framework for computing invariant features from images. The proposed approach is based on a simple concept of basis expansion. It is widely applicable to many popular basis representations, such as wavelets 4, 5, 24, 25], short-time Fourier analysis 15, 30], and splines 2, 6, 33]. Exploiting formulations that use both global and local information about shape and color, the ...

We introduce an adaptive scattered data fitting scheme as extension of local least squares approximations to hierarchical spline spaces. To efficiently deal with non-trivial data configurations, the local solutions are described in terms of (variable degree) polynomial approximations according not only to the number of data points locally available, but also to the smallest singular value of th...

A fully relativistic approach to calculating photoionization and photon-atom scattering cross sections for quasi one-electron atoms is presented. An extensive set of have been calculated alkali atoms: lithium, sodium, potassium, rubidium cesium. The importance effects core polarization on the depth position Cooper minimum in section investigated. Good agreement was found with previous Dirac-bas...

We introduce curvature continuous regular free form surfaces with triangular control nets These surfaces are composed of quartic box spline surfaces and are piecewise polynomial multisided patches of total degree which minimize some energy integral The B ezier nets can be computed e ciently form the spline control net by some xed masks i e matrix multiplications x Introduction Most methods know...

The giant single-celled slime mould Physarum polycephalum is known to approximate a number of network problems via growth and adaptation of its protoplasmic transport network and can serve as an inspiration towards unconventional, material-based computation. In Physarum, predictable morphological adaptation is prevented by its adhesion to the underlying substrate. We investigate what possible c...

Unlike the visual trimming of B-spline surfaces, which hides unwanted portions in rendering, the geometric trimming approach provides a mathematically clean representation without redundancy. However, the process may lead to significant deviation from the corresponding portion on the original surface. Optimization is required to minimize approximation errors and obtain higher accuracy. In this ...