We provide a description of the interpolating and sampling sequences on a space of holomorphic functions with a uniform growth restriction defined on finite Riemann surfaces.

In this paper, we extend the study of superconvergence properties of ChebyshevGauss-type spectral interpolation in [24, SINUM,Vol. 50, 2012] to general Jacobi-Gauss-type interpolation. We follow the same principle as in [24] to identify superconvergence points from interpolating analytic functions, but rigorous error analysis turns out much more involved even for the Legendre case. We address t...

The accuracy and efficiency of the elements proposed by finite element method (FEM) considerably depend on the interpolating functions namely shape functions used to formulate the displacement field within the element. In the present study, novel functions, namely basic displacements functions (BDFs), are introduced and exploited for structural analysis of nanobeams using finite element method ...

Discontinuities between distinct regions, described by different equation sets, cause difficulties for PDE/ODE solvers. We present a new algorithm that eliminates integrator discontinuities through regularizing discontinuities. First, the algorithm determines the optimum switch point between two functions spanning adjacent or overlapping domains. The optimum switch point is determined by search...

In the ofice. it is often ecessary to scan a picture at a certain resolution and then reproduce it at a different (usually higher) resolution. This conversion can be achieved by interpolating the scanned signal between the sample intervals. This paper discusses a class of linear interpolating methods based on resampling polynomial functions. In addition, we introduce new methods to compare the ...

Fractional diffusion and Fokker-Planck equations are widely used tools to describe anomalous in a large variety of complex systems. The equivalent formulations terms Caputo or Riemann-Liouville fractional derivatives can be derived as continuum limits continuous-time random walks associated with the Mittag-Leffler relaxation Fourier modes, interpolating between short-time stretched exponential ...

We give a full description for the shape of the classical (2+1)d Solid-On-Solid model above a wall, introduced by Temperley (1952). On an L× L box at a large inverse-temperature β the height of most sites concentrates on a single level h = ⌊ 1 4β logL⌋ for most values of L. For a sequence of diverging boxes the ensemble of level lines of heights (h, h − 1, . . .) has a scaling limit in Hausdorf...

Introduction ........................................................................................................................... 1 Caveat ............................................................................................................................... 2 Linear weight size scaling .................................................................................................

In this paper, a second-order Hermite basis of the space of C2quartic splines on the six-directional mesh is constructed and the refinable mask of the basis functions is derived. In addition, the extra parameters of this basis are modified to extend the Hermite interpolating property at the integer lattices by including Lagrange interpolation at the half integers as well. We also formulate a co...

In this paper, a second-order Hermite basis of the space of C2quartic splines on the six-directional mesh is constructed and the refinable mask of the basis functions is derived. In addition, the extra parameters of this basis are modified to extend the Hermite interpolating property at the integer lattices by including Lagrange interpolation at the half integers as well. We also formulate a co...