We study Stanley decompositions and show that Stanley’s conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay simplicial complexes. We also prove these conjectures for all Cohen-Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3.

We study Stanley decompositions and show that Stanley’s conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay simplicial complexes. We also prove these conjectures for all Cohen-Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3.

To every directed graph G one can associate a complex (G) consisting of directed subforests. This construction, suggested to us by R. Stanley, is especially important in the case of a complete double directed graph Gn, where it leads to studying some interesting representations of the symmetric group and corresponds (via Stanley-Reisner correspondence) to an interesting quotient ring. Our main ...

The Weinbaum-Jiji equation can be applied to situations where: 1) the vascular anatomy is know; 2) the blood velocities are known; 3) the effective modeling volume includes many vessels; and 4) the vessel equilibration length is small compared to the actual length of the vessel. These criteria are satisfied in the situation where steady-state heated thermistors are placed in the kidney cortex. ...

mustafa lutfi el-manfaluti is one of the literary men whose writing method was effective on literary change of the previous generation. he was born in egypt. he was interested in reading literary books; that’s why he had completed the science by mohammad abdoh. he had translated many stories and articles and had applied some french stories in his writings. his books are the most eloquent arabic...