This paper concerns the problem of classifying finite-dimensional real solvable Lie algebras whose derived algebras are of codimension 1 or 2. On the one hand, we present an effective method to classify all (n + 1)-dimensional real solvable Lie algebras having 1-codimensional derived algebras provided that a full classification of n-dimensional nilpotent Lie algebras is given. On the other hand, the problem of classifying all (n + 2)-dimensional real solvable Lie algebras having 2-codimensional derived algebras is proved to be wild. In this case, we provide a method to classify a subclass of the considered Lie algebras which are extended from their derived algebras by a pair of derivations containing at least one inner derivation.
In this paper, we discribe some geometric charateristics of the so-called MD(5,3C)-foliations and MD(5,4)- foliations, i.e., the foliations formed by the generic orbits of co-adjoint action of MD(5,3C)-groups and MD(5,4)-groups.
Extending Cooper & Ross’ analysis of competition in markets with informational asymmetry, and Hirth’s researches on non-profit nursing homes in the United States, this paper developed a competitive model for a mixed market of for-profit and non-profit private universities. The model proved the spillover impact of non-profit universities on the overall quality of the market. As a result, the paper sheds some insights on the quality problems faced by private universities in Vietnam, and also offers some policy implications to improve the overall quality of this market.
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