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The purpose of this paper is to find an accurate, efficient and easy-to-implement point estimate method (PEM) for the statistical moments of random systems.

First, by the theoretical and numerical analysis, the approximate reference variables for the frequently used nine types of random variables are obtained; then by combining with the dimension-reduction method (DRM), a new method which consists of four sub-methods is proposed; and finally, several examples are investigated to verify the characteristics of the proposed method.

Two types of reference variables for the frequently used nine types of variables are proposed, and four sub-methods for estimating the moments of responses are presented by combining with the univariate and bivariate DRM.

In this paper, the number of nodes of one-dimensional integrals is determined subjectively and empirically; therefore, determining the number of nodes rationally is still a challenge.

Through the linear transformation, the optimal reference variables of random variables are presented, and a PEM based on the linear transformation is proposed which is efficient and easy to implement. By the numerical method, the quasi-optimal reference variables are given, which is the basis of the proposed PEM based on the quasi-optimal reference variables, together with high efficiency and ease of implementation.

Domain integrals, known as volume potentials in 3D elasticity problems, exist in many boundary-type methods, such as the boundary element method (BEM) for inhomogeneous partial differential equations. The purpose of this paper is to develop an accurate and reliable technique to effectively evaluate the volume potentials in 3D elasticity problems.

An adaptive background cell-based domain integration method is proposed for treatment of volume potentials in 3D elasticity problems. The background cells are constructed from the information of the boundary elements based on an oct-tree structure, and the domain integrals are evaluated over the cells rather than volume elements. The cells that contain the boundary elements can be subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements. The fast multipole method (FMM) is further applied in the proposed method to reduce the time complexity of large-scale computation.

The method is a boundary-only discretization method, and it can be applied in the BEM easily. Much computational time is saved by coupling with the FMM. Numerical examples demonstrate the accuracy and efficiency of the proposed method..

Boundary elements are used to create adaptive background cells, and domain integrals are evaluated over the cells rather than volume elements. Large-scale computation is made possible by coupling with the FMM.

The purpose of this study is to analyze the post-harvest supply chain enablers (PHSCEs) for vertical integration to enhance rural employability, farmer profitability and rural produce marketability (i.e. market prospects) in the post-harvest supply chain (PHSC). The impact of vertical integration is also explored for various commercial produces.

A structural equation modeling (SEM) of PHSCEs for vertical integration was developed to enhance market prospects, rural employability and farmer profitability. The impact of business-to-business (B2B) and business-to-customer market prospects are explored in various dimensions for stakeholders such as farmers, manufacturers (processors), distributors and retailers. The fuzzy technique for order of preference by similarity to ideal solution (F-TOPSIS) was used to prioritize these PHSCEs to improve market prospects and rural employability.

The PHSCEs are clustered into three groups, namely, initiatives at the strategic frontier, initiatives at the tactical frontier and concerns for rural employability via vertical integration using exploratory factor analysis, confirmatory factor analysis and SEM to prove the null hypothesis. With F-TOPSIS results, the availability of warehousing was found to be the most crucial enabler when observing the PHSCEs from the initiatives’ perspective. The technology adaptability and availability, institute for training and research and information infrastructure and information visibility were found to be the key PHSCEs when observed from PHSC stakeholders’ perspectives.

The implementation of this study will improve the rural produce marketability, rural employability, B2B marketing (i.e. effective distribution) and subsequent value chains with the practice of vertical integration for fresh produce at the rural level.

The outcomes of this study have a key role in developing the rural regions and improving rural livelihoods via value addition. The awareness of commercial cultivation and value addition in rural areas needs to be improved. This will help farmers to earn better revenues with improved market prospects in comparison to the revenues obtained from the cultivation of staple/conventional crops.

In an era of cold chains and food processing, this study aims to disseminate awareness about value addition for commercial and fresh produces at the rural level. The implication of this study will improve rural produce marketability, rural employability and farmer profitability at the rural level with the level of vertical integration.