Mel 1a melatonin receptors belong to the super-family of guanine nucleotide-binding regulatory protein (G protein)-coupled receptors. So far, interest in Mel 1a receptor signaling has focused mainly on the modulation of the adenylyl cyclase pathway via pertussis toxin (PTX)-sensitive G proteins. To further investigate signaling of the human Mel 1a receptor, we have developed an antibody directe...

Let (G, G) be one of the following complex dual pairs: (O(m,C), Sp(2n,C)), (GL(m,C),GL(2n,C)), (Sp(2m,C),O(4n,C)). We determine the relationship between the space ofG-coinvariants and certain degenerate principal series representations of G. We also show that the space of G-invariant distributions is generated by the Dirac distribution as a G-representation. Introduction and main results Let G ...

Let G be a discrete group which admits an amenable action on a compact space and γ ∈ Aut(G) be an automorphism. We define a notion of entropy for γ and denote the invariant by ha(γ). This notion is dual to classical topological entropy in the sense that if G is abelian then ha(γ) = hTop(γ̂) where hTop(γ̂) denotes the topological entropy of the induced automorphism γ̂ of the (compact, abelian) dual...

In this paper we prove that if G is a connected, simplyconnected, semi-simple algebraic group over an algebraically closed field of sufficiently large characteristic, then all the blocks of the restricted enveloping algebra (Ug)0 of the Lie algebra g of G can be endowed with a Koszul grading (extending results of Andersen, Jantzen, Soergel). We also give information about the Koszul dual rings....

Let M be a manifold, on which a real reductive Lie group G acts transitively. The action of a discrete subgroup Γ on M is not always properly discontinuous. In this paper, we give a criterion for properly discontinuous actions, which generalizes our previous work [6] for an analogous problem in the continuous setting. Furthermore, we introduce the discontinuous dual t(H:G) of a subset H of G , ...

If G is a plane graph and x, y ∈ V (G), then the dual distance of x and y is equal to the minimum number of crossings of G with a closed curve in the plane joining x and y. Riskin [7] proved that if G0 is a 3connected cubic planar graph, and x, y are its vertices at dual distance d, then the crossing number of the graph G0 + xy is equal to d. Riskin asked if his result holds for arbitrary 3-con...

R ring (always commutative and Noetherian) (R,m,k) local ring with maximal ideal m and k = R/m L,M,N, . . . R-modules (always finitely generated) M HomR(M,R), the dual of M D(M) the Auslander dual of M (Definition 2) σM : M wM∗∗ the natural evaluation map; KM = Ker(σM ), CM = Coker(σM ) G-dimR(M),G-dim(M) Gorenstein dimension of M (Definition 16) G-dim(M) <loc ∞ M has locally finite Gorenstein ...

Let G = (V,E) be a plane triangulated graph where each vertex is assigned a positive weight. A rectilinear dual of G is a partition of a rectangle into |V | simple rectilinear regions, one for each vertex, such that two regions are adjacent if and only if the corresponding vertices are connected by an edge in E. A rectilinear dual is called a cartogram if the area of each region is equal to the...

The dual lattice of G is the graph G∗ = (V ∗, E∗) constructed as follows. Imagine to draw G on a plane, using the standard embedding of Z in R. Then, for each edge (i, j) in the original lattice G, draw a perpendicular edge of length 1, centered at the midpoint of (i, j). These are the edges of the G∗. Its vertices are the endpoints of such edges (only whenever two endpoints coincide, the verti...

We continue the study of the Poisson-Sigma model over Poisson-Lie groups. Firstly, we solve the models with targets G and G∗ (the dual group of the Poisson-Lie group G) corresponding to a triangular r-matrix and show that the model over G∗ is always equivalent to BF-theory. Then, given an arbitrary r-matrix, we address the problem of finding D-branes preserving the duality between the models. W...