On Unentangled Gleason Theorems for Quantum Information Theory

It is shown here that a strengthening of Wallach's Unentangled Gleason Theorem can be obtained by applying results of the present authors on generalised Gleason theorems for quantum multi-measures arising from investigations of quantum decoherence functionals.     

Analytical study of the Middle Kingdom group of gold jewellery from tomb 124 at Riqqa,Egypt

The jewellery from tomb 124 at Riqqa, consisting of one pectoral and one winged beetle in gold and cloisonné work, one gold shell pendant decorated with wires and granulation, and one hollow gold amulet in the form of god Min, was analysed by handheld X-ray fluorescence and scanning electron microscopy with energy-dispersive X-ray spectroscopy. This group of jewellery, dated to the second half of the 12th Dynasty (c. 1900–1840 B.C.), was excavated inside the coffin of an adult male, which had been crushed after burial by the collapse of the chamber roof during an episode of looting. Both the male and the looter's body were found inside the chamber, evidencing that the group of jewellery was intact. Despite having been highly restored in the past, as referenced in the correspondence between the excavator Flinders Petrie and the curators of the Manchester Museum, it could be shown that the jewellery was produced using Ag-rich electrum alloys containing platinum group element inclusions that indicate the use of alluvial gold. The analysis of some joins has confirmed the use of hard-soldering, with solders obtained by addition of Cu to the base-alloy. Data obtained for the jewellery of tomb 124 were compared with data previously obtained for tomb 296, also excavated at Riqqa, but dated to the 18th Dynasty. The comparison demonstrates the continuity of the workshop traditions in one location between the Middle Kingdom and the New Kingdom but also reveals discrepancies in the alloys employed in those two periods.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

A microwave-excited strontium-ion (λ430.5 nm) recombination laser

Laser oscillation on the 430.5 nm transition of Sr⁺, which replies on three-body electron-ion recombination for its excitation, has been achieved in a pulsed, selfheated, microwave-pumped discharge.     

The phenylcarbene rearrangement revisited

The evolution of mechanistic ideas about the phenylcarbene rearrangement has been reviewed, and three closely linked problems have been identified toward whose solution this research has been aimed: 1. Why do the ratios of the stable end products from the rearrangements of o-, m- and p-tolylmethylene differ when all three reactions have been throught to pass through a common intermediate? 2. Why does the rearrangement of 2-methylcycloheptatrienylidene lead to exclusive formation of styrene? 3. What is the mechanism of styrene formation from o-tolylmethylene? New mechanisms have been proposed in which m- and p-tolylmethylene can rearrange to styrene without necessarily being converted to o-tolylmethylene. The formation of a small amount of 2,6-dimethylstyrene from the rearrangement of 3,4,5-trimethylphenylmethylene is viewed as evidence for such a mechanism, and a set of interconverting norcaradienylidenes are believed to be the crucial intermediates. Other alternatives are considered and rejected on the basis of the rearrangement products of 3,5-dimethyl- and 3,4,5-trimethylphenylmethylene.     

Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Correlation Analysis of the Alternating Step Generator

The alternating step generator is a well-known keystream generator consisting of two stop/go clocked LFSRs, LFSR₁ and LFSR₂, whose clocks are controlled by another LFSR, LFSR₃, which is clocked regularly. A probabilistic analysis of this generator is conducted which shows that the posterior probabilites of individual bits of the first derivatives of the regularly clocked LFSR₁ and LFSR₂ sequences, when conditioned on a given segment of the first derivative of the keystream sequence, can be computed efficiently in a number of probabilistic models of interest. The expected values of these probabilities, for a random keystream sequence, are derived by an approximate theoretical analysis and are also verified by systematic computer experiments. It is pointed out that these posterior probabilities can be enhanced in a resynchronization scenario and thus used for a low-complexity fast correlation attack on the two LFSRs. More generally, it is argued that even without resynchronization these probabilities may be significantly different from one half for fast correlation attacks based on iterative decoding algorithms to be successful, although with incresead complexity. A related method for computing the posterior probabilities of individual bits of the LFSR₃ sequence, when conditioned on both the keystream sequence and the LFSR₁ and LFSR₂ sequences, is also developed. As these posterior probabilities are much more different from one half, they can be used for a low-complexity fast correlation attack on LFSR₃, provided that the initial states of LFSR₁ and LFSR₂ are previously reconstructed.