Related papers: Bivariate fractal interpolation functions on trian…
The aim of this paper is to characterize a fractal operator associated with multivariate fractal interpolation functions (FIFs) and study the several properties of this fractal operator. Further, with the help of this operator, we…
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting…
Starting with a substitution tiling, we demonstrate a method for constructing infinitely many new substitution tilings. Each of these new tilings is derived from a graph iterated function system and the tiles have fractal boundary. We show…
We provide a general framework to construct fractal interpolation surfaces (FISs) for a prescribed countably infinite data set on a rectangular grid. Using this as a crucial tool, we obtain a parameterized family of bivariate fractal…
Recently, in [Electronic Transaction on Numerical Analysis, 41 (2014), pp. 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional…
We derive an analytic expression for the scalar one-loop pentagon and hexagon functions which is convenient for subsequent numerical integration. These functions are of relevance in the computation of next-to-leading order radiative…
The present work proposes the development of a novel method to provide descriptors for colored texture images. The method consists in two steps. In the first, we apply a linear transform in the color space of the image aiming at…
Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections and mappings. Projective geometry identifies a line with a single point, like the perspective…
A novel method for constructing a nonlinear fractal histopolation function associated with a given histogram is introduced in this paper. In contrast to classical fractal interpolation methods, which produce continuous and interpolatory…
In the process of measuring objects with local self-similarity, such as satellite images or coastlines, we obtain a data set with both local self-similarity and uncertainty. To better interpolate such data sets, an interpolation function…
Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
We compute the distance-dependent two-point function of vertex-bicolored planar maps, i.e., maps whose vertices are colored in black and white so that no adjacent vertices have the same color. By distance-dependent two-point function, we…
In nature, there are many phenomena with both irregularity and uncertainty. Therefore, a fuzzy-valued fractal interpolation is more useful for modeling them than fuzzy interpolation or fractal interpolation. We construct fractal…
This paper introduces the novel concept of fractal interpolation over curves in Banach spaces. The contents are based on the usual methodologies involving the fractal interpolation problem over intervals but the current approach…
This paper describes applications of extrapolation for the computation of coefficients in an expansion of infrared divergent integrals. An extrapolation procedure is performed with respect to a parameter introduced by dimensional…
The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition…
The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued…
In this paper, we introduce fractal interpolation on complete semi-vector spaces. This approach is motivated by the requirements of preservation of positivity or monotonicity of functions for some models in approximation and interpolation…
A fractal surface is a set which is a graph of a bivariate continuous function. In the construction of fractal surfaces using IFS, vertical scaling factors in IFS are important one which characterizes a fractal feature of surfaces…