for some positive integer d, then SRLP holds. It is also shown that the inequality (1.2) is always satisfied in a reversible chain. When P = 1, the results given here reduce to those of Orey [7] for recurrent chains, while for P> 1 they imply SRLP for a class of transient chains. (The definition of SRLP given by Orey required that 7=1 and that r< be independent of i since he was dealing with re...

Let K be an algebraically closed field of characteristic zero and let I = (f1, . . . , fn) be a homogeneous R+-primary ideal in R := K[X, Y, Z]. If the corresponding syzygy bundle Syz(f1, . . . , fn) on the projective plane is semistable, we show that the Artinian algebra R/I has the Weak Lefschetz property if and only if the syzygy bundle has a special generic splitting type. As a corollary we...

In previous papers [4; 5; 6] we constructed and studied many classes of operations on groups which have the following properties: (1) Associative; (2) Commutative; (3) The resultant group contains isomorphic images of the original factors and is generated by them; (4) In the resultant group the intersection of a factor with normal subgroup generated by the remaining factors is the unit element....

For 0 ≤ α < 1 we construct examples of even integrable functions Ω on the unit sphere S with mean value zero satisfying

Let G be a locally compact group. Then G is known to be amenable if and only if it has Reiter’s property (P1), i.e., there is a net (mα)α of non-negative norm one functions in L(G) such that limα supx∈K ‖Lx−1mα−mα‖ = 0 for each compact subset K ⊂ G (Lx−1mα stands for the left translate of mα by x). We give a formulation of property (P1) that extends naturally to locally compact quantum groups i...