Computational algorithms and their implementations are studied for the treatments of kernel function’s shadow effects, which occurs in the application of the BEM(boundary element method) for radiation heat transfer analysis. In this problem, surfaces are assumed to be diffuse and gray placed in two-dimensional enclosures with transparent medium. Self-blocking or third party blocking is possible when the radiosity from the BEM nodes cannot reach the destination points. Also the third party blocking can be the partial or total blocking case. Algorithms, which can accurately recognize the each blocking cases and reflect the shadow effects to the BEM kernel function, are studied in this paper. Effective implementation methods are presented, and their results are verified by the test problem

Tax is the main revenue of Government, so fighting tax evasion and sustainable growth have been the primary macroeconomic goals being pursued by every developing country, Vietnam included. The existence and development of the shadow economic sector are synonymous with the national budget losing out. In Vietnam, foreign direct investment projects do not promote economic growth and is also a sector that gives way to tax evasion.The purpose of this study is to investigate the impact of foreign direct investment, the quality of the informal institution on the size of the shadow economy in Vietnam, during the period 1991-2015. By applying the Autoregressive Distributed Lag approach and Toda and Yamamoto test, we found evidence to conclude that the quality of the informal institution harms the size of the shadow economy. The results of the causality test show that there is a unidirectional causality running from the shadow economy and the quality of the informal institution to foreign direct investment attraction in Vietnam. Political solutions need to be implemented carefully to counter the harmful effects of the shadow economy. Policymakers should adopt several economic policies to improve the ‘human capital’ and drive the shadow economy into the formal economy.