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ON NIL GENERALIZED POWER SERIESWISE ARMENDARIZ RINGS
Ouyang, Lunqun,Liu, Jinwang Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.3
We in this note introduce a concept, so called nil generalized power serieswise Armendariz ring, that is a generalization of both S-Armendariz rings and nil power serieswise Armendariz rings. We first observe the basic properties of nil generalized power serieswise Armendariz rings, constructing typical examples. We next study the relationship between the nilpotent property of R and that of the generalized power series ring [[$R^{S,{\leq}}$]] whenever R is nil generalized power serieswise Armendariz.
OPTIMAL CONTROL OF SYSTEMS OF PARABOLIC PDES IN EXPLOITATION OF OIL
Li, Chunfa,Feng, Enmin,Liu, Jinwang 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.13 No.1
Optimal control problem for the exploitaton of oil is investigated. The optimal control problem under consideration in this paper is governed by weak coupled parabolic PDEs and involves with pointwise state and control constraints. The properties of solution of the state equations and the continuous dependence of state functions on control functions are investigated in a suitable function space; existence of optimal solution of the optimal control problem is also proved.