Narrow Results

The solution to many problems in applied probability requires the evaluation of Riemann-Stieltjes integrals involving the convolution of cumulative distribution functions. Closed form expressions for the solution are very rare indeed. In this paper we examine the evaluation of the Stieltjes integral, which plays a fundamental role in the numerical solution of Volterra-Stieltjes integral equations that appear frequently in renewal theoretic problems. The evaluation of Stieltjes integrals on which this paper concentrates is thus, it is argued, germane to the solution of such problems. A generalised trapezoidal rule is utilised and a priori error bounds are determined in the current development.

With the transformation of people’s concerns from physical space to study of urban public space, this study put forward ideas and strategies for the renewal of public space in the old district from the perspective of the user environmental behavior pattern. This article researched Luosibang district in Soochow Old Town as a case study. In investigating the composition of user-group and using status of public space, found that the elderly and children were the main users in the public space of the old district. It proposed the principle of the renewal of public space in the old district based on the elderly and children’s environmental behavior characteristics, and finally put forward concrete strategies by a conceptual design. This study is a meaningful exploration in the field of urban transformation.