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In color spaces where the chromatic term is given in polar coordinates, the shortest distance between colors of the same value is circular. By converting such a space into a complex polar form with a real-valued value axis, a color algebra…
Dimensional regularization is incompatible with the standard covariant projection methods that are used to calculate the short-distance coefficients in inclusive heavy quarkonium production and annihilation rates. A new method is developed…
Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial…
Integer compositions, integer partitions, Fibonacci numbers, and generalizations of these have recently been shown to be interconnected via two-toned tilings of horizontal grids. In this article, we present refinements of two-toned tilings,…
We experimentally implement an optical algorithm for integration of a real-valued bivariate func- tion. A user-defined function is encoded in the position-dependent phase of one of the polarization components of an optical beam. The…
A \emph{fractal} is an object exhibiting complexity at arbitrarily small scales. In order to study and characterise fractals, one is often interested in quantifying how they fill up space on small scales. This gives rise to various notions…
For the interpolation of graph signals with generalized shifts of a graph basis function (GBF), we introduce the concept of positive definite functions on graphs. This concept merges kernel-based interpolation with spectral theory on graphs…
Fractional graph isomorphism is the linear relaxation of an integer programming formulation of graph isomorphism. It preserves some invariants of graphs, like degree sequences and equitable partitions, but it does not preserve others like…
In this paper, we first apply the Fitzpatrick algorithm to osculatory rational interpolation. Then based on Fitzpatrick algorithm, we present a Neville-like algorithm for Cauchy interpolation. With this algorithm, we can determine the value…
A triangulation of a polygon is a subdivision of it into triangles, using diagonals between its vertices. Two different triangulations of a polygon can be related by a sequence of flips: a flip replaces a diagonal by the unique other…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
Interpolation of classes of differentiated functions given on a finite interval by trigonometric splines using the phantom node method is considered. This method consists in supplementing a given sequence of values of an approximate…
We present some work relating to fractal transformations on masked iterated function systems and demonstrate how well known algorithms for generating fractal transformations can be modifed for these systems. We also demonstrate that these…
We present an introduction to fractal interpolation beginning with a global set-up and then extending to a local, a non-stationary, and finally the novel quaternionic setting. Emphasis is placed on the overall perspective with references…
We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebyshev polynomials, which are obtained by composing Chebyshev…
A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…
We introduce the cause of the inefficiency of bivariate glyphs by defining the corresponding error. To recommend efficient and perceptually accurate bivariate-glyph design, we present an empirical study of five bivariate glyphs based on…
We propose an algorithm for the fusion of partial images collected from the visual and infrared cameras such that the visual and infrared images are the real and imaginary parts of a complex function. The proposed image fusion algorithm of…
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…
A good deal of research has been done and published on coloring of the vertices of graphs for several years while studying of the excellent work of those maestros, we get inspire to work on the vertex coloring of graphs in case of a…