Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

The multifacility minimax location problem with rectilinear distances is considered. It is reduced to a parametric shortest path problem in a network with no negative length arcs. The reduction scheme contributes to this location problem and yields an efficient algorithm with time complexity 0 (n max(m log m, n3 )) where n and m denote the numbers of the new and existing facilitie,s in the plan...

The purpose of this paper is to give two different constructions of irregular surfaces of degree 12 in P4. These surfaces are new and of interest in the classification of smooth non-general type surfaces in P4. This classification problem is motivated by the theorem of Ellingsrud and Peskine [9] which says that the degree of smooth non-general type surfaces in P4 is bounded. Moreover the new fa...

I. Bar-On, B. Codenotti, and M. Leoncini presented a linear time algorithm for checking the nonsingularity of general tridiagonal matrices [BIT, 36:206, 1996]. A detailed implementation of their algorithm, with some extensions to possibly reducible matrices, is further described in the present paper.

A double 2-(v,k,2λ) design is a design which is reducible into two 2-(v,k,λ) designs. It is called uniquely reducible if it has, up to equivalence, only one reduction. We present properties of uniquely reducible double designs which show that their total number can be determined if only the designs with non-trivial automorphisms are classified with respect to their automorphism group. As an app...

The contribution of reducible connections to the U(N) Chern-Simons invariant of a Seifert manifold M can be expressed in some cases in terms of matrix integrals. We show that the U(N) evaluation of the LMO invariant of any rational homology sphere admits a matrix model representation which agrees with the Chern-Simons matrix integral for Seifert spheres and the trivial connection.

I. BarOn , B. Codenotti, and M. Leoncini presented a linear time algorithm for checking the nonsingularity of general tridiagonal matrices BIT, 36:206, 19966. A detailed implementation of their algorithm, with some extensions to possibly reducible matrices, is further described in the present paper.