Numerical Solution of Mixed Volterra – Fredholm Integral Equation Using the Collocation Method

Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained from the numerical experiments in order to investigate the accuracy and the efficiency of scheme.

Common Fixed Point Theorems on Generalized Ratio Contraction Mapping in Extended Rectangular b-Metric Spaces

In this paper, we propose and prove the common fixed point theorems on generalized contraction mappings in extended rectangular b-metric spaces by utilizing the weakly compatible function property.

The Characteristic Function Property of Mixture Negative Binomial-Exponential Distribution

This paper introduces a new distribution by mixing the negative binomial distribution and exponential distribution namely negative binomial-exponential (NB-E) distribution. In is given the probability distribution function of NB-E distribution and its characteristic function by using Fourier-Stieltjes transform. In addition we present the some properties of characteristic function from NB-E distribution.

Can brief marking campaigns provide reliable dispersal estimates? A Nickerl’s Fritillary (Melitaea aurelia, Lepidoptera: Nymphalidae) case study

Functions expressing dispersal probability decays with increasing distance are widely used in studies of animal movements. The inverse power function (IPF) exhibits the property of self-similarity, and hence should perform robustly against variation in marking efforts, allowing comparisons across studies. We investigated this function property using dispersal data of Nickerl’s fritillary (Melitaea aurelia), a little studied checkerspot butterfly which is currently expanding in Central Europe. During mark-recapture in South Moravia, Czech Republic, a single researcher worked for the entire flight period in 2005, while in 2006 five researchers worked for just 5 days. Slopes of the fitted functions did not differ between the two seasons, illustrating the robustness of the function and suggesting the possibility to obtain reliable dispersal estimates even from brief marking campaigns. For both years, it was predicted that approximately one individual per one thousand would cross 10 km distance, the maximum distance separating the most isolated colonies in the region.

A Hybrid Radial Boundary Node Method for Biharmonic Problems

The hybrid radial boundary node method is applied to solve the biharmonic problems. Based on modified variational principle, the variational formula of the biharmonic problems is established. The radial basis point interpolation is employed to approximate the boundary variables, while the domain variables are interpolated by a combination of the fundamental solution of the laplace equation and the biharmonic equation. Compared to the regular hybrid boundary node method, as the shape function has the delta function property, the boundary conditions of the original problem can be easily implemented, and the fictitious source points are not involved. Numerical examples show that this method is efficient for solving the biharmonic equation.