DOI: http://dx.doi.org/10.1090/noti1454 best explained in the framework of complex symmetric operators, a surprisingly large class of tractable and well-behaved operators. Let H be a complex Hilbert space. Examples include Cn, the Lebesgue spaces L2(X,μ) of square-integrable functions on X with respect to a measure μ, the spaces l2(N) and l2(Z) of square integrable sequences indexed byN andZ, a...

Koike, K., On a conjecture of Stanley on Jack symmetric functions, Discrete Mathematics 115 (1993) 211-216. The Jack symmetric function J,(x; G() is a symmetric function with interesting properties that J,(x; 2) is a spherical function of the symmetric pair (GL(n, FQ O(n, [w)) and that J,(x; 1) is the Schur function S,(x). Many interesting conjectures about the combinatorial properties of J,(x;...

Quasi-symmetric 3-designs with block intersection numbers x, y (0 ≤ x ≤ y < k) are studied. It is proved that the parameter λ of a quasi-symmetric 3-(v, k, λ) design satisfies a quadratic whose coefficients are polynomial functions of k, x and y. We use this quadratic to prove that there exist finitely many quasi-symmetric 3-designs under either of the following two restrictions: 1. The block i...

One of the most basic and most important subfamily of Lévy processes is symmetric stable processes. A symmetric α-stable process X on Rn is a Lévy process whose transition density p(t , x − y) relative to the Lebesgue measure is uniquely determined by its Fourier transform ∫ Rn e ix ·ξp(t , x )dx = e−t|ξ| α . Here α must be in the interval (0, 2]. When α = 2, we get a Brownian motion running wi...

A set (or a collection of sets) contained in the Euclidean space Rm is symmetric if it is invariant under the antipodal map. Given a symmetric unicoherent polyhedron X (like an n dimensional cube or a sphere) and an odd real function f defined on vertices of a certain symmetric triangulation of X, we algorithmically construct a connected symmetric separator of X by choosing a subcollection of t...