Generalized SYZ mirror transformation

Strominger-Yau-Zaslow proposed that mirror symmetry can be understood by torus duality. In this article we explain how it fits into a bigger framework, where tori are replaced by general Lagrangian immersions. The generalized construction is applicable to a wider class of geometries. We also give a brief introduction to our ongoing work on gluing local mirrors into global geometries

Minimum Equivalent Precedence Relation Systems

In this paper two related simplification problems for systems of linear inequalities describing precedence relation systems are considered. Given a precedence relation system, the first problem seeks a minimum subset of the precedence relations (i.e., inequalities) which has the same solution set as that of the original system. The second problem is the same as the first one except that the ``subset restriction'' in the first problem is removed. This paper establishes that the first problem is NP-hard. However, a sufficient condition is provided under which the first problem is solvable in polynomial-time. In addition, a decomposition of the first problem into independent tractable and intractable subproblems is derived. The second problem is shown to be solvable in polynomial-time, with a full parameterization of all solutions described. The results in this paper generalize those in [Moyles and Thompson 1969, Aho, Garey, and Ullman 1972] for the minimum equivalent graph problem and transitive reduction problem, which are applicable to unweighted directed graphs

Testing the relationship between government expenditure and national income in Malaysia

The present study aims to investigate the relationship between national income and Government expenditure in Malaysia. The annual data over the period 1960 to 1998 were used. The result of Johansen multivariate cointegration revealed that no long run relationship among the non-stationary variables existed. Further, a unidirectional causality was observed, that is, from national income growth to Government expenditure growth. Thus, Wagner's law is supported by the data, in the short run. Some relevant policy issues and implications are discussed