The minimal degree of an inverse semigroup S is the minimal cardinality of a set A such that S is isomorphic to an inverse semigroup of one-to-one partial transformations of A . The main result is a formula that expresses the minimal degree of a finite inverse semigroup S in terms of certain subgroups and the ordered structure of S . In fact, a representation of S by one-to-one partial transfor...

Let G be a finite group. A subset S of G not the identity element 1 of G called C I -subset (C( stands for isomorphism"), if for any isomorphism D(G, S) ~ D(G, T), there is f AutG such that T = f(S). G is called a DCI-group if every subset of G {I} is a CI-subset. G is called a GCl-group or simply a C I -group if every inverse-closed subset of G {I} is a CI-subset. (DCI and GCl stands for "digr...

For a finite group G and a self-inverse subset S of G which does not contain the identity of G, let Cay (G, S) denote the Cayley graph of G with respect to 8. If, for all subsets 8, T ofG of size m, Cay(G, S) ~ Cay(G, T) implies 80. = T for some a E Aut(G), then G is said to have the m-CI property. In this paper we completely determine the positive integers m for which a cyclic group of prime-s...

Data on the location and dimensions of the pivotal surfaces in inverse hexagonal (H(II)) and inverse cubic (Q(II)) phases of phospholipids and glycolipids are reviewed. This includes the H(II) phases of dioleoyl phosphatidylethanolamine, 2:1 mol/mol mixtures of saturated fatty acids with the corresponding diacyl phosphatidylcholine, and glucosyl didodecylglycerol, and also the Q(II)(230/G) gyro...

Cysteinyl leukotrienes (CysLTs) are associated with several inflammatory processes, including asthma. Due to this association, considerable effort has been invested in the development of antagonists to the CysLT receptors (CysLT(1)R). Many of these molecules have been shown to specifically interact with CysLT(1)R, but little is known about their impact on the conformation of the receptor and it...

We consider a system (M, g, ω,X) where (M, g) is a closed Riemannian manifold, ω a closed one form whose all zeros are nondegenerate and X an (−ω, g) gradient like vector field. For t ∈ R+ large enough, the Witten complex (Ω∗, dt = d ∗ + tω∧) decomposes canonically as a direct sum of two one parameter family of cochain complexes (Ωsm(t), dt ) and (Ωla(t), d ∗ t ). We show that under a mild hypo...

Suppose that an algebraic torus G acts algebraically on a projective manifold X with generically trivial stabilizers. Then the Zariski closure of the set of pairs {(x, y) ∈ X × X | y = gx for some g ∈ G} defines a nonzero equivariant cohomology class [∆G] ∈ H G×G(X×X). We give an analogue of this construction in the case where X is a compact symplectic manifold endowed with a hamiltonian action...