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RECTANGULAR DOMAIN DECOMPOSITION METHOD FOR PARABOLIC PROBLEMS

  • Jun, Youn-Bae;Mai, Tsun-Zee
    • The Pure and Applied Mathematics
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    • v.13 no.4 s.34
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    • pp.281-294
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    • 2006
  • Many partial differential equations defined on a rectangular domain can be solved numerically by using a domain decomposition method. The most commonly used decompositions are the domain being decomposed in stripwise and rectangular way. Theories for non-overlapping domain decomposition(in which two adjacent subdomains share an interface) were often focused on the stripwise decomposition and claimed that extensions could be made to the rectangular decomposition without further discussions. In this paper we focus on the comparisons of the two ways of decompositions. We consider the unconditionally stable scheme, the MIP algorithm, for solving parabolic partial differential equations. The SOR iterative method is used in the MIP algorithm. Even though the theories are the same but the performances are different. We found out that the stripwise decomposition has better performance.

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THE EFFECTS OF EGR AND SPLIT FUEL INJECTION ON DIESEL ENGINE EMISSION

  • Gao, Z.;Schreiber, W.
    • International Journal of Automotive Technology
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    • v.2 no.4
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    • pp.123-133
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    • 2001
  • An important goal in diesel engine research is the development of a means to reduce the emission of oxides of nitrogen ($NO_x$) and soot particulate. A phenomenological model based on the multizone concept is used in the current paper to analyze and compare the effects of exhaust gas recirculation (EGR) and split fuel injection on emission from a compression-ignited, direct-injection engine. The present results show that $NO_x$ can be reduced with a minimum penalty of soot particle emission with cooled EGR. Compared with EGR, split fuel injection has a higher soot penalty at a given level of $NO_x$ reduction.

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DEFORMATIONS OF d/BCK-ALGEBRAS

  • Allen, Paul J.;Kim, Hee-Sik;Neggers, Joseph
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.2
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    • pp.315-324
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    • 2011
  • In this paper, we study the effects of a deformation mapping on the resulting deformation d/BCK-algebra obtained via such a deformation mapping. Besides providing a method of constructing d-algebras from BCK-algebras, it also highlights the special properties of the standard BCK-algebras of posets as opposed to the properties of the class of divisible d/BCK-algebras which appear to be of interest and which form a new class of d/BCK-algebras insofar as its not having been identified before.