Related papers: The leaky aquifer function revisited
The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor f. To date, the captured flow friction factor f can be extracted from the…
In 1989 H.Karcher rewrote the theory of elliptic functions through an approach that is much more geometrical than analytical. Therewith he obtained an optimal control over the behaviour and image values of these functions, which allowed for…
We present a new algorithm for the computation of the inverse Abel transform, a problem which emerges in many areas of physics and engineering. We prove that the Legendre coefficients of a given function coincide with the Fourier…
We provide an introduction of some basic facts of uniformly almost periodic functions, such as Fourier series representations. A result is then proved about Fourier coefficients which is a generalization of the purely periodic case. We then…
A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results…
Learning about density functional approximations (DFAs), or approximations for the exchange-correlation functional, can be intimidating. Density Functional Theory is now one of the primary simulation tools for the practicing chemist or…
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…
In this paper, some points to the convergence analysis performed in the paper [A new computing approach for power signal modeling using fractional adaptive algorithms, ISA Transactions 68 (2017) 189-202] are presented. It is highlighted…
In this paper, we establish some integral ineuqalities for n- times differentiable quasi-convex functions.
Some problems in the theory and applications of stochastic processes can be reduced to solving integral equations. While explicit solutions for these equations are often elusive, valuable insights can be gained through their asymptotic…
In this paper we compute the Fourier spectrum of the Fractal Interpolation Functions FIFs as introduced by Michael Barnsley. We show that there is an analytical way to compute them. In this paper we attempt to solve the inverse problem of…
We build on a recent paper on Fourier expansions for the Riemann zeta function. We establish Fourier expansions for certain $L$-functions, and offer series representations involving the Whittaker function $W_{\gamma,\mu}(z)$ for the…
In this paper we propose a numerical method to solve the Cauchy problem based on the viscous shallow water equations in an horizontally moving domain. More precisely, we are interested in a flooding and drying model, used to modelize the…
The Wright function arises in the theory of the fractional differential equations. It is a very general mathematical object having diverse connections with other special and elementary functions. The Wright function provides a unified…
This preliminary paper presents initial explorations in rendering Iterated Function System (IFS) fractals using a differentiable rendering pipeline. Differentiable rendering is a recent innovation at the intersection of computer graphics…
Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same…
We consider an abstract functional-differential equation derived from the pressure-less Euler system with variable coefficients that includes several systems of partial differential equations arising in the fluid mechanics. Using the method…
In this paper, we propose a numerical method of Fourier transform based on hyperfunction theory. In the proposed method, we compute analytic functions called the defining functions, which give the desired Fourier transform as a…
In what follows we improve an inequality related to matrix theory. T. Laffey proved (2013) a weaker form of this inequality [2].
In this article we derive Fokker - Planck equation for incompressible fluid and investigate its properties. In version 2 symmetries of linearized equations and some examples of invariant solutions are added.