Parity Proofs of the Bell-Kochen-Specker Theorem Based on the 600-cell

The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical proof is one that fails if even a single basis is deleted from it). The proofs vary considerably in size, with the smallest having 26 rays and 13 bases and the largest 60 rays and 41 bases. There are at least 90 basic types of proofs, with each coming in a number of geometrically distinct varieties. The replicas of all the proofs under the symmetries of the 600-cell yield a total of almost a hundred million parity proofs of the BKS theorem. The proofs are all very transparent and take no more than simple counting to verify. A few of the proofs are exhibited, both in tabular form as well as in the form of MMP hypergraphs that assist in their visualization. A survey of the proofs is given, simple procedures for generating some of them are described and their applications are discussed. It is shown that all four-dimensional parity proofs of the BKS theorem can be turned into experimental disproofs of noncontextuality.     

A gaussian upper bound for gaussian multi-stage stochastic linear programs

This paper deals with two-stage and multi-stage stochastic programs in which the right-hand sides of the constraints are Gaussian random variables. Such problems are of interest since the use of Gaussian estimators of random variables is widespread. We introduce algorithms to find upper bounds on the optimal value of two-stage and multi-stage stochastic (minimization) programs with Gaussian right-hand sides. The upper bounds are obtained by solving deterministic mathematical programming problems with dimensions that do not depend on the sample space size. The algorithm for the two-stage problem involves the solution of a deterministic linear program and a simple semidefinite program. The algorithm for the multi-stage problem invovles the solution of a quadratically constrained convex programming problem.     

Meeting the Welch and Karystinos-Pados Bounds on DS-CDMA Binary Signature Sets

The Welch lower bound on the total-squared-correlation (TSC) of binary signature sets is loose for binary signature sets whose length L is not a multiple of 4. Recently Karystinos and Pados [6,7] developed new bounds that are better than the Welch bound in those cases, and showed how to achieve the bounds with modified Hadamard matrices except in a couple of cases. In this paper, we study the open cases.     

Self-assembled, helically stacked anionic aggregates of 2,5,8,11-tetra-tert-butylcycloocta[1,2,3,4-def;5,6,7,8-d'e'f']bisbiphenylene, stabilized by electrostatic interactions

Tetraanions of alkyl-substituted derivatives of cycloocta[1,2,3,4-def;5,6,7,8-d'e'f']bisbiphenylene (BPD) and their counter lithium cations self-assemble to form helically stacked assemblies, including a dimer, a trimer, and a tetramer. NMR self-diffusion measurements and unprecedented magnetic shielding effects for the sandwiched lithium cations support their aggregated nature. The D(2)-tetramer assembly is fully characterized by NMR spectroscopy, providing unequivocal evidence for a helix of four tetraanionic BPD layers with an estimated relative twist angle of about 45 degrees and interlayer spacing of ca. 4 A. The barrier for racemization through the in-plane inter-deck rotation is DeltaG(200)= 9.5 +/- 0.2 kcal mol(-1) in the dimer compared to >15 kcal mol(-1) in the tetramer.     

Hydroxide ion initiated reactions under phase transfer catalysis conditions—IV : Effect of catalyst structure

The nature of the quat-anion interactions in a PTC/OH^? system was probed by examining the reactivity and selectivity of a CA/O-ambident anion towards an alkylating agent in the presence of various quats. It is suggested that the accessibility of the positive N center of the qual for association with the anion is the major factor in determining the behavior of PTC/OH^? reactions proceeding through the Makosza mechanism.