Related papers: Computation and applications of Mathieu functions:…
The main purpose of this paper is to revisit the well known potentials, called stress functions, needed in order to study the parametrizations of the stress equations, respectively provided by G.B. Airy (1863) for 2-dimensional elasticity,…
Starting from the vortex filament flow introduced in 1906 by Da Rios, there is a hierarchy of commuting geometric flows on space curves. The traditional approach relates those flows to the nonlinear Schr\"odinger hierarchy satisfied by the…
Application of computation in many fields are growing fast in last two decades. Increasing on computation performance helps researchers to understand natural phenomena in many fields of science and technology including in life sciences.…
Peculiarities of the turbulent two phase and multiphase flows of the mutually immiscible liquids and averaged differential equations for their modeling are considered based on the approach, which was first developed and proposed by Prof.…
We presented background information about various entropies in the literature. The pathway idea of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure and established connections to…
We introduce an entropy analysis of time series, repeated measurements of statistical observables, based on an Eulerian homogeneous degree-one entropy function $\Phi(t,n)$ of time $t$ and number of events $n$. The duality of $\Phi$, in…
Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic…
Inequalities, asymptotics and, for some specific cases, asymptotical expansions were obtained for generalized Mathieu's series. A connection between inequalities for Mathieu's series and positive definite and completely monotonic functions.
The Bayesian statistical paradigm uses the language of probability to express uncertainty about the phenomena that generate observed data. Probability distributions thus characterize Bayesian analysis, with the rules of probability used to…
In the absence of CMB precision measurements, a Taylor expansion has often been invoked to parametrize the Hubble flow function during inflation. The standard "horizon flow" procedure implicitly relies on this assumption. However, the…
We find continuous families of supersymmetric flux vacua in IIB Calabi-Yau compactifications for multiparameter manifolds with an appropriate $\mathbb{Z}_2$ symmetry. We argue, supported by extensive computational evidence, that the…
Several asymptotic expansions of parabolic cylinder functions are discussed and error bounds for remainders in the expansions are presented. In particular Poincar{\'e}-type expansions for large values of the argument $z$ and uniform…
In \cite{mccarthy2}, McCarthy defined a function $_{n}G_{n}[\cdots]$ using Teichm\"{u}ller character of finite fields and quotients of $p$-adic gamma function, and expressed the trace of Frobenius of elliptic curves in terms of special…
Let $M$ be an $n$-dimensional closed Riemannian manifold with metric $g$, $d\mu=e^{-\phi(x)}d\nu$ be the weighted measure and $\Delta_{p,\phi}$ be the weighted $p$-Laplacian. In this article we will investigate monotonicity for the first…
It is well known that phase function methods allow for the numerical solution of a large class of oscillatory second order linear ordinary differential equations in time independent of frequency. Unfortunately, these methods break down in…
In this paper we study the Cauchy problem for diffusion equations associated to a class of strongly hypoelliptic pseudo-differential operators on graded Lie groups. To do so, we develop a global complex functional calculus on graded Lie…
Renaud Parentani has given a vast contribution to the development of gravitational analogue models as tools to explore various important aspects of general relativity and of quantum field theory in curved space-time. In these systems,…
Mixed-dimensional elliptic equations exhibiting a hierarchical structure are commonly used to model problems with high aspect ratio inclusions, such as flow in fractured porous media. We derive general abstract estimates based on the theory…
The functional Ito formula, firstly introduced by Bruno Dupire for continuous semimartingales, might be extended in two directions: different dynamics for the underlying process and/or weaker assumptions on the regularity of the functional.…
In this paper we describe an algorithm and a Fortran 90 module ({\bf Conical}) for the computation of the conical function $P^m_{-\tfrac12+i\tau}(x)$ for $x>-1$, $m \ge 0$, $\tau >0$. These functions appear in the solution of Dirichlet…