in the present paper, a numerical method is considered for solving one-dimensionalheat equation subject to both neumann and dirichlet initial boundaryconditions. this method is a combination of collocation method and radial basis functions (rbfs). the operational matrix of derivative for laguerre-gaussians (lg) radial basis functions is used to reduce the problem to a set of algebraic equations...

The oblique effect is a ubiquitous visual psychological effect. To explore its underlying neural basis, we quantitatively analyzed the proportion and response amplitude of the cardinal preferred areas and the oblique preferred areas in a fairly large region of the primary visual cortex of cats, using optical imaging based on intrinsic signals. The results show that cardinal preferred areas were...

In this paper, some meshless methods based on the local Newton basis functions are used to solve some time dependent partial differential equations. For stability reasons, used variably scaled radial kernels for constructing Newton basis functions. In continuation, with considering presented basis functions as trial functions, approximated solution functions in the event of spatial variable wit...

A cardinal related to compositions of Sierpiński-Zygmund functions will be considered. A combinatorial characterization of the cardinal is given and is used to answer some questions of K. Ciesielski and T. Natkaniec. It is shown that the bounding number of the continuum may be strictly smaller than continuum.

Some properties of sinc-approximations of continuous functions on a segment are studied. For the first time, the sinc-approximations arose in the work of Pleynet. Later, in connection with developments in signals coding theory, E. Borel and E. T. Whittaker introduced the notions of a cardinal function and a truncated cardinal function, the restriction of which to [0, π] looks like this:

This paper discusses application of the piecewise sinusoidal (PWS) basis function (BF) over a chain of several wire segments, i.e. as a multiple domain basis functions. The usage of PWS BF is compared to results based on the piecewise linear (PWL) basis functions. An example of meander monopole demonstrates the advantages associated with the PWS BF.

Abstract. R-limited functions are multivariate generalization of band-limited functions whose Fourier transforms are supported within a compact region R ⊂ Rn. In this work, we generalize sampling and interpolation theorems for band-limited functions to R-limited functions. More precisely, we investigated the following question: “For a function compactly supported within a region similar to R, d...