A Reverse Theorem on the·-w*Continuity of the Dual Map

Given a Banach spaceX,x∈𝖲X, and𝖩Xx=x*∈𝖲X*:x*x=1, we define the set𝖩X*xof allx*∈𝖲X*for which there exist two sequencesxnn∈N⊆𝖲X∖{x}andxn*n∈N⊆𝖲X*such thatxnn∈Nconverges tox,xn*n∈Nhas a subnetw*-convergent tox*, andxn*xn=1for alln∈N. We prove that ifXis separable and reflexive andX*enjoys the Radon-Riesz property, then𝖩X*xis contained in the boundary of𝖩Xxrelative to𝖲X*. We also show that ifXis infinite dimensional and separable, then there exists an equivalent norm onXsuch that the interior of𝖩Xxrelative to𝖲X*is contained in𝖩X*x.

TEMPERED SPECTRAL TRANSFER IN THE TWISTED ENDOSCOPY OF REAL GROUPS

Suppose that $G$ is a connected reductive algebraic group defined over $\mathbf{R}$, $G(\mathbf{R})$ is its group of real points, ${\it\theta}$ is an automorphism of $G$, and ${\it\omega}$ is a quasicharacter of $G(\mathbf{R})$. Kottwitz and Shelstad defined endoscopic data associated to $(G,{\it\theta},{\it\omega})$, and conjectured a matching of orbital integrals between functions on $G(\mathbf{R})$ and its endoscopic groups. This matching has been proved by Shelstad, and it yields a dual map on stable distributions. We express the values of this dual map on stable tempered characters as a linear combination of twisted characters, under some additional hypotheses on $G$ and ${\it\theta}$.

The extreme points of SU(2)-irreducibly covariant channels

In this paper, we introduce EPOSIC channels, a class of SU(2)-covariant quantum channels. For each of them, we give a Kraus representation, its Choi matrix, a complementary channel, and its dual map. We show that they are the extreme points of all SU(2)-irreducibly covariant channels. As an application of these channels, we get an example of a positive map that is not completely positive.

Implementation of the Two-Point Angular Correlation Function on a High-Performance Reconfigurable Computer

We present a parallel implementation of an algorithm for calculating the two-point angular correlation function as applied in the field of computational cosmology. The algorithm has been specifically developed for a reconfigurable computer. Our implementation utilizes a microprocessor and two reconfigurable processors on a dual-MAP SRC-6 system. The two reconfigurable processors are used as two application-specific co-processors. Two independent computational kernels are simultaneously executed on the reconfigurable processors while data pre-fetching from disk and initial data pre-processing are executed on the microprocessor. The overall end-to-end algorithm execution speedup achieved by this implementation is over 90× as compared to a sequential implementation of the algorithm executed on a single 2.8 GHz Intel Xeon microprocessor.