The Wright-Fisher family of diffusion processes is a class of evolutionary models widely used in population genetics, with applications also in finance and Bayesian statistics. Simulation and inference from these diffusions is therefore of widespread interest. However, simulating a Wright-Fisher diffusion is difficult because there is no known closed-form formula for its transition function. In...

A classical result of Toponogov [12] states that if a complete Riemannian manifold M with nonnegative sectional curvature contains a straight line, thenM is isometric to the metric product of a nonnegatively curved manifold and a line. We then know that the Busemann function associated with the straight line is an affine function, namely, a function which is affine on each unit speed geodesic i...

In the present paper we consider an elliptic divergence form operator in Rn∖Rd with d<n−1 and prove that its Green function is almost affine, sense normalized difference between a sufficiently far away pole suitable affine at every scale satisfies Carleson measure estimate. The coefficients of can be very oscillatory, only need to satisfy some condition similar traditional quadratic condition.

In this paper, the authors define a new generic class of functions involving certain modified Fox–Wright function. A useful identity using fractional integrals and function with two parameters is also found. Applying as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by above-mentioned functions. Some special cases are derived relevant details. Moreover, in or...

We study the decidability of some properties of self-affine sets specified by a graph-directed iterated function system (GIFS) with rational coefficients. We focus on topological properties and we prove that having empty interior is undecidable in dimension two. These results are obtained by studying a particular class of self-affine sets associated with multitape automata. We first establish t...

Several extensions of the classical Mittag-Leffler function, including multi-parameter and multivariate versions, have been used to define fractional integral derivative operators. In this paper, we consider a function one variable with five parameters, special case Fox–Wright function. It turns out that most natural way based on requires considering it as two variables. This gives rise model b...

Affine Differential Geometry provides a set of measures invariant under a larger set of transformations compared to rigid motions. This leads to several applications using robust shape descriptors. Although affine invariant operations are already used for surfaces, they do not intend to approximate the definitions of Affine Differential Geometry, which are the basis for further differential inv...

A procedure to improve the convergence rate for affine registration methods of medical brain images when the images differ greatly from the template is presented. The methodology is based on a histogram matching of the source images with respect to the reference brain template before proceeding with the affine registration. The preprocessed source brain images are spatially normalized to a temp...

In this paper, we define a generalized class of starlike functions with negative coefficients and obtain coefficient estimates, distortion bounds, closure theorems and extreme points. Further we obtain modified Hadamard product, radii of close-to-convex, starlikeness and convexity for functions belonging to this class. Furthermore neighborhood results are discussed.