ar X iv : 0 70 6 . 01 03 v 2 [ cs . L O ] 3 J un 2 00 7 Four concepts and two logics of algorithmic reduction

ar X iv : 0 70 7 . 33 03 v 1 [ m at h . O A ] 2 3 Ju l 2 00 7 OPERATOR - VALUED FRAMES

ar X iv : 0 80 6 . 01 70 v 1 [ m at h . Q A ] 2 J un 2 00 8 WEIGHT MULTIPLICITY POLYNOMIALS OF MULTI - VARIABLE WEYL MODULES

This paper is based on the observation that dimension of weight spaces of multi-variable Weyl modules depends polynomially on the highest weight (Conjecture 1). We support this conjecture by various explicit answers for up to three variable cases and discuss the underlying combinatorics.

ar X iv : 0 70 7 . 10 59 v 1 [ cs . P L ] 6 J ul 2 00 7 Projection semantics for rigid loops ∗

A rigid loop is a for-loop with a counter not accessible to the loop body or any other part of a program. Special instructions for rigid loops are introduced on top of the syntax of the program algebra PGA. Two different semantic projections are provided and proven equivalent. One of these is taken to have definitional status on the basis of two criteria: ‘normative semantic adequacy’ and ‘indi...

ar X iv : 0 70 6 . 09 93 v 1 [ m at h . A T ] 7 J un 2 00 7 v 1 - PERIODIC HOMOTOPY GROUPS OF THE DWYER - WILKERSON SPACE

The Dwyer-Wilkerson space DI(4) is the only exotic 2-compact group. We compute its v1-periodic homotopy groups v 1 π∗(DI(4)).

ar X iv : h ep - e x / 03 12 01 4 v 1 3 D ec 2 00 3 Single - Spin Asymmetry in Inclusive π 0 Production Measured at the Protvino 70 GeV Accelerator

Single Spin Asymmetries (SSA) AN measured in the two reactions at the Protvino 70 GeV accelerator are presented. AN in the reaction p + p↑ → π 0 + X in the central region is close to zero within the error bars. SSA in the reaction π + p↑ → π 0 + X in the polarized target fragmentation region is equal to (−15 ± 4)% at |xF | > 0.4. There is an indication that the asymmetry arises at the same pion...