We investigate a cone in the symmetric group algebra introduced by Stembridge [2]. It is dual to the cone of monomial-positive immanants of n × n matrices with indeterminate entries. We present a new set of relations between elements of the dual cone, and use these relations to show that the cone is finitely generated for n = 6, generalizing Stembridge’s result for n = 5.

We study the max-plus or tropical analogue of the notion of polar: the polar of a cone represents the set of linear inequalities satisfied by its elements. We establish an analogue of the bipolar theorem, which characterizes all the inequalities satisfied by the elements of a tropical convex cone. We derive this characterization from a new separation theorem. We also establish variants of these...

We discuss the tropical analogues of several basic questions of convex duality. In particular, the polar of a tropical polyhedral cone represents the set of linear inequalities that its elements satisfy. We characterize the extreme rays of the polar in terms of certain minimal set covers which may be thought of as weighted generalizations of minimal transversals in hypergraphs. We also give a t...

Commercial cone penetration testing (CPT) equipment was adapted to allow penetrative testing in hard polar firn to depths of 10m. The apparatus is hydraulically driven, rate-controllable and able to penetrate firn with a resistance of 10MPa. It can be mounted on many types of typical polar vehicles, requiring connection to only hydraulics and 12V electricity. Data recorded include both cone tip...

WD = {z => x + iy\ x Q R , y & D). The distinguished boundary of WD is the set {z = x+iy \ xÇzR, y = 0 } , i.e., just R. In this paper we consider the following problem. Let ƒ be a real function on R satisfying certain regularity conditions. What are the conditions for the existence of a holomorphic function F on WD such that ƒ is the limit of Re -Fas the variable approaches the distinguished b...

Let G be the split solvable Lie group acting simply transitively on a Siegel domain D. We consider irreducible unitary representations of G realized on Hilbert spaces of holomorphic functions on D. We determine all such Hilbert spaces by connecting them with positive Riesz distributions on the dual cone and describe them through the Fourier-Laplace transform. Moreover we classify the representa...

0 Introduction For n 2, Let M n be a nite convex, not necessarily smooth, hypersur-face in Euclidean space R n+1 containing the origin. More precisely, M n is the boundary of some convex domain in R n+1 containing a neighborhood of the origin. We write M n = fR(x) = (x)x j x 2 S n g, where is a function from S n to R +. Let : M n ! S n denote the generalized Gauss map, namely, (Y) is the set of...

New elements of the dual cone of the set of fermion N -representable 2-density operators are proposed. So far, the explicit form of the corresponding necessary conditions for N -representability is obtained for N = 3. In this case the new condition is stronger than the known Band C-conditions for 3-representability. The results provide evidence that in the spectral decomposition of the N -repre...

We consider the system of m linear equations in n integer variables Ax = d and give sufficient conditions for the uniqueness of its integer solution x ∈ {−1,1}n by reformulating the problem as a linear program. Uniqueness characterizations of ordinary linear programming solutions are utilized to obtain sufficient uniqueness conditions such as the intersection of the kernel of A and the dual con...

where b, y ∈ IR; ci, xi, si ∈ IRi , Ai ∈ IRm×ni , i = 1, . . . , r. For each i = 1, . . . , r, xi and si are the primal and dual slack variables associated with the ith cone and K∗ i = { si ∈ IRi : xi si ≥ 0, ∀xi ∈ Ki } (3) is the dual cone to Ki. We assume that Ki,K i , i = 1, . . . , r are pointed closed convex cones with nonempty interiors. Let K = K1 × K2 × . . . × Kr be the overall cone in...