The real interpolation spaces between $$L^{p}({{\mathbb {R}}}^{n})$$ and $${\dot{H}}^{t,p}({{\mathbb (resp. $$H^{t,p}({{\mathbb ), $$t>0,$$ are characterized in terms of fractional moduli smoothness, the underlying seminorms shown to be “the correct” generalization classical Gagliardo seminorms. This is confirmed by fact that, using new combined with extrapolation methods, we able extend Bourga...

In the process of magnifying digitized images, the restoration of high frequency components is essential to recover vivid and useful information contained in the original images. However, many of these high frequency components are lost in the digitizing process due to the prevention of the aliasing problem. We can use conventional interpolation methods to magnify images, but fast algorithms ca...

Since their introduction, mean value coordinates enjoy ever increasing popularity in computer graphics and computational mathematics because they exhibit a variety of good properties. Most importantly, they are defined in the whole plane which allows interpolation and extrapolation without restrictions. Recently, mean value coordinates were generalized to spheres and to ’3. We show that these s...

This paper demonstrates the use of dynamic fuzzy-reasoning-based function estimator (DFFE) to interpolate rainfall data in a case study in Switzerland. The functional parameters are also optimized by genetic algorithms (GA). The procedure operates on a series of overlapping partition surfaces around the study area based on expert knowledge and interpretive judgment. The procedure allows for spa...

This paper describes two eecient algorithms for representing arbitrarily shaped objects. The rst representation, called cosine lling 1], is a DCT-based approach for obtaining a compact description of objects, making it possible to achieve high compression. A wavelet-based approach is also proposed. This representation not only provides compact description, but also facilitates smooth extension,...

Thermochemical and phase diagram data for the Ga–N system were assessed by employing the CALPHADmethod. A consistent model representation of available thermodynamic properties agrees well with the critically evaluated experimental data. Thermodynamic extrapolation/interpolation of these data was applied to estimate the sublimation andmelting characteristics of theGaN compound: at atmospheric pr...

Tadpole improved Wilson quark actions with clover terms on anisotropic lattices are studied numerically. Using asymmetric lattice volumes, the pseudo-scalar meson dispersion relations are measured for 8 lowest lattice momentum modes with quark mass values ranging from the strange to the charm quark with various values of the gauge coupling β and 3 different values of the bare speed of light par...

One problem of image interpolation refers to magnifying a small image without loss in image clarity. We propose a wavelet based method which estimates the higher resolution information needed to sharpen the image. This method extrapolates the wavelet transform of the higher resolution based on the evolution of the wavelet transform extrema across the scales. By identifying three constraints tha...

We present an extrapolation with care set operator to accelerate termination of reachability computation with polyhedra. At the same time, a counterexample guided refinement algorithm is used to iteratively expand the care set to improve the precision of the reachability computation. We also introduce two heuristic algorithms called interpolate and restrict to minimize the polyhedral representa...