Most matching models of the marriage market assume increasing returns to scale, that is, they postulate that a larger pool of eligibles will lead to a higher marriage rate. Empirically, the difficulty in studying the cross-section relationship between the size of the marriage market and marriage behavior is that, in general, market size is endogenous. We address this issue in two ways. First, w...

In this paper, we introduce the concept of interval valued fuzzy weak bi-ideals of $Gamma$-near-rings, which is a generalized concept of fuzzy weak bi-ideals of $Gamma$- near-rings. We also characterize some properties and examples of interval valued fuzzy weak bi-ideals of $Gamma$-near-rings.

In this paper, we introduce the class of ideals with $(d_1,ldots,d_m)$-linear quotients generalizing the class of ideals with linear quotients. Under suitable conditions we control the numerical invariants of a minimal free resolution of ideals with $(d_1,ldots,d_m)$-linear quotients. In particular we show that their first module of syzygies is a componentwise linear module.

We study the degree of nonhomogeneous lattice ideals over arbitrary fields, and give formulas to compute the degree in terms of the torsion of certain factor groups of Zs and in terms of relative volumes of lattice polytopes. We also study primary decompositions of lattice ideals over an arbitrary field using the Eisenbud–Sturmfels theory of binomial ideals over algebraically closed fields. We ...

Multiplier ideals are very important in higher dimensional geometry to study the singularities of ideal sheaves. It reflects the singularities of the ideal sheaves and provides strong vanishing theorem called the Kawamata-Viehweg-Nadel vanishing theorem (see [3]). However, the multiplier ideals are defined via a log resolution of the ideal sheaf and divisors on the resolved space, and it is dif...

The marriage market is a dynamic bilateral matching market with finitely lived participants. The growth rate of the number of marriages between two types of individuals estimates the systematic benefit to them delaying marriage for a period versus marrying immediately. Identification of the semi-parametric model is transparent. The model is estimated with 1990 US marriage data. The estimated mo...

We provide a new combinatorial approach to study the minimal free resolutions of edge ideals, that is, quadratic square-free monomial ideals. With this method we can recover most of the known results on resolutions of edge ideals with fuller generality, and at the same time, obtain new results. Past investigations on the resolutions of edge ideals usually reduced the problem to computing the di...