Parseval frames for ICC groups

We analyze Parseval frames generated by the action of an ICC group on a Hilbert space. We parametrize the set of all such Parseval frames by operators in the commutant of the corresponding representation. We characterize when two such frames are strongly disjoint. We prove an undersampling result showing that if the representation has a Parseval frame of equal norm vectors of norm , the Hilbert space is spanned by an orthonormal basis generated by a subgroup. As applications we obtain some sufficient conditions under which a unitary representation admits a Parseval frame which is spanned by a Riesz sequences generated by a subgroup. In particular, every subrepresentation of the left-regular representation of a free group has this property.     

Regularity of Rees Algebras

Let B = k[x₁, ..., x_n] be a polynomial ring over a field k,and let A be a quotient ring of B by a homogeneous ideal J.Let m denote the maximal graded ideal of A. Then the Rees algebraR = A[m t] also has a presentation as a quotient ring of thepolynomial ring k[x₁, ..., x_n, y₁, ..., y_n] by a homogeneousideal J^*. For instance, if A = k[x₁, ..., x_n], then Rk[x₁,...,x_n,y₁,...,y_n]/(x_iy_j–x_jy_i|i, j=1,...,n). In this paper we want to compare the homological propertiesof the homogeneous ideals J and J^*.     

On the regularity of -Borel ideals

In this paper we prove Pardue's conjecture on the regularity of principal -Borel ideals. As a consequence we obtain an upper bound for the regularity of general -Borel ideals.

     

Imaging the evolution of lateral composition modulation in strained alloy superlattices

Scanning tunneling microscopy is used to investigate the morphological evolution of GaAs/InAs short period superlattice structures. The layers of the superlattice, either grown in compression or tension, exhibit an island or trench morphology. With increasing film thickness, the islands or trenches grow in size and develop a characteristic spacing along [110] of approximately 150 A. This is the first experimental evidence to suggest that lateral composition modulation arises from both thickness variations of the layers and compositional nonuniformities within the atomic plane.     

Analytical relationship for the cranking inertia

The wave functions of a spheroidal harmonic oscillator without spin-orbit interaction are expressed in terms of associated Laguerre and Hermite polynomials. The pairing gap and Fermi energy are found by solving the BCS system of two equations. Analytical relationships for the matrix elements of inertia are obtained as a function of the main quantum numbers and potential derivative. They may be used to test complex computer codes developed in a realistic approach of the fission dynamics. Results given for the ²⁴⁰Pu nucleus are compared with a hydrodynamical model. The importance of taking into account the correction term due to the variation of the occupation number is stressed.