This paper deals with multi- objective nonlinear programming problem having rough intervals in the constraints. The problem is approached by taking maximum value range and minimum value range inequalities as constraints conditions, reduces it into two classical multi-objective nonlinear programming problems, called lower and upper approximation problems.  All of the lower and upper approximatio...

in this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. we introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some of their important properties.

Brucella abortus rough lipopolysaccharide (LPS) mutants were obtained by transposon insertion into two wbk genes (wbkA [putative glycosyltransferase; formerly rfbU] and per [perosamine synthetase]), into manB (pmm [phosphomannomutase; formerly rfbK]), and into an unassigned gene. Consistent with gene-predicted roles, electrophoretic analysis, 2-keto-3-manno-D-octulosonate measurements, and immu...

The random process theory (RPT) has been widely applied to predict the joint probability distribution functions (PDFs) of asperity heights and curvatures of rough surfaces. A check of the predictions of RPT against the actual statistics of numerically generated random fractal surfaces and of real rough surfaces has been only partially undertaken. The present experimental and numerical study pro...

The RER retains a specific subset of ER proteins, many of which have been shown to participate in the translocation of nascent secretory and membrane proteins. The mechanism of retention of RER specific membrane proteins is unknown. To study this phenomenon in yeast, where no RER-specific membrane proteins have yet been identified, we expressed the human RER-specific protein, ribophorin I. In a...

Let (U, R) be an approximation space with U being non-empty set and R equivalence relation on U, let $${\overline{G}}$$ $${\underline{G}}$$ the upper lower of subset G U. A topological rough group is a $$G=({\underline{G}}, {\overline{G}})$$ endowed topology, which induced from , such that product mapping $$f: G\times G\rightarrow {\overline{G}}$$ inverse are continuous. In class groups, relati...