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In 1934, Romanoff proved that there are a positive proportion natural numbers which can be expressed as the sum of a prime and a power of 2. In this paper, a quantitative version of this theorem is given. We show that the proportion is larger than 0.0868 and for a positive proportion of odd integers the number of such representations is between 1 and 16. [Copyright &y& Elsevier]

The numerical simulation of the large scale science and engineering problem in the aerospace area relies on the support of High-Performance Parallel Computing(HPPC)and is the engine of the development of HPPC. The paper gives a survey of recent progress of HPPC in the aerospace area and a brief introducion of the HPPC environment. The relative research areas of HPPC of aerospace, including aerodynamic, aerothermal, chemical non-equilibrium, structure, heat protecion, Monte Carlo method and turbulence et al., are classified and described in detail. The dilemma of high parallel efficiency in scientitic computing and low use in engineering compuing, and the diversity of paralel applications and the lack of scientific paralel methods are concluded. Finally, the prospects of the future HPPC development in aerospace area are presented. [ABSTRACT FROM AUTHOR]