On the Rotar central limit theorem for sums of a random number of independent random variables

The Rotar central limit theorem is a remarkable theorem in the non-classical version since it does not use the condition of asymptotic infinitesimality for the independent individual summands, unlike the theorems named Lindeberg's and Lindeberg-Feller's in the classical version. The Rotar central limit theorem generalizes the classical Lindeberg-Feller central limit theorem since the Rotar condition is weaker than Lindeberg's. The main aim of this paper is to introduce the Rotar central limit theorem for sums of a random number of independent (not necessarily identically distributed) random variables and the conditions for its validity. The order of approximation in this theorem is also considered in this paper.Comment: 15 page

On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums

summary:Geometric random sums arise in various applied problems like physics, biology, economics, risk processes, stochastic finance, queuing theory, reliability models, regenerative models, etc. Their asymptotic behaviors with convergence rates become a big subject of interest. The main purpose of this paper is to study the asymptotic behaviors of normalized geometric random sums of independent and identically distributed random variables via Gnedenko's Transfer Theorem. Moreover, using the Zolotarev probability metric, the rates of convergence in some weak limit theorems for geometric random sums are estimated

Geometrically nonlinear and dynamic analysis of Euler-Bernoulli beams using isogeometric approach

This paper presents a numerical procedure for geometrically nonlinear and dynamic analysis of Euler-Bernoulli beams based on the framework of isogeometric approach. The method utilizes B-spline as the basis functions for both geometric representation and analysis. Only one deflection variable (without rotational degrees of freedom) is used for each control point. It allows us to use few degrees of freedom while retaining high accuracy of solution. Two numerical examples are provided to illustrate the effectiveness of present method

Static and dynanic analysis of composite plate using the C0-type higher-order shear deformation theory

This paper presents a novel numerical procedure based on edge-based smoothed finite element method (ES–FEM) in combination with the C0-type higher-order shear deformation theory (HSDT) for static and dynamic analysis of laminated composite plate. In the present ES–FEM, only the linear approximation is necessary and the discrete shear gap method (DSG) for triangular plate elements is used to avoid the shear locking and spurious zero energy modes. In addition, the stiffness matrices are computed based on smoothing domains associated with the edges of the triangular elements through a strain smoothing technique. Using the C0-type HSDT, the shear correction factors in the original ES-DSG3 can be removed and replaced by two additional degrees of freedom at each node. Several numerical examples are given to show the performance of the proposed method and results obtained are compared to other available ones

Thermal buckling analysis of laminated composite plates using edge-based smoothed discrete shear gap method

In this paper, we analyze a thermal buckling behavior of laminated composite plates based on first-order shear deformation theory (FSDT) using edge-based smoothed discrete shear gap method (ES–DSG). In the ES-DSG, only the linear approximation is necessary and the discrete shear gap method (DSG) for triangular plate elements is used to avoid the shear locking and spurious zero energy modes. In addition, the stiffness matrices are computed based on smoothing domains created by connecting two end-nodes of the edge to centroids of adjacent triangular elements. The temperature in the plates is assumed to be uniform distribution and rise. Several numerical examples are given to verify the reliability of the obtained results compared to other published solutions