Time-scale and excitation energy partition in sequential binary decays induced by heavy-ion collisions at ≃6 MeV·A

We studied the sequential binary decay of the systems ³²S+⁴⁵Sc, ⁷⁶Ge, ⁸⁹Y, ⁵⁹Co, ⁶³Cu and ¹⁹F+⁶³Cu induced by collisions at ≃6 MeV·A. The two stages of the process have reaction-times compatible with the dynamics of different mechanisms. The study of the excitation energy partition shows that the reaction mechanism of the first step has influence on the de-excitation of the primary fragments producing two decay components which have different time scale. Received: 25 March 1997 / Revised version: 2 December 1997     

Successions in Words and Compositions

We consider words over the alphabet [k] = {1, 2, . . . , k}, k ?? 2. For a fixed nonnegative integer p, a p-succession in a word w ₁ w ₂ . . . w _n consists of two consecutive letters of the form (w _i , w _i ?+ p), i = 1, 2, . . . , n ? 1. We analyze words with respect to a given number of contained p-successions. First we find the mean and variance of the number of p-successions. We then determine the distribution of the number of p-successions in words of length n as n (and possibly k) tends to infinity; a simple instance of a phase transition (Gaussian-Poisson-degenerate) is encountered. Finally, we also investigate successions in compositions of integers.     

Order series of labelled posets

Order series of labelled posets are multi-analogues of the more familiar order polynomials; the corresponding multi-analogues of the related representation polynomials are calledE-series. These series can be used to describe the effect of composition of labelled posets on their order polynomials, whence their interest for us. We give a reciprocity theorem forE-series, and show that for an unlabelled poset the form of theE-series depends only upon the comparability graph of the poset. We also prove that theE-series of any labelled poset is a rational power series (in many indeterminates) and give an algorithm for computing it which runs in polynomial time when the poset is strictly labelled and of bounded width. Finally, we give an explicit product formula for theE-series of strictly labelled interval posets.This research was supported by the Natural Sciences and Engineering Research Council of Canada under operating grant #0105392.     

Crowns,cutsets, and valuable partial orders

We consider the problem of recognizing those partial orders which admit a valuation: this is a linear-algebraic condition which arises naturally in an algebraic/geometric context. We show that a partial order has at most one valuation (which is integer-valued) and present various structural conditions which are either necessary or sufficient for a partial order to be valuable. The first main result is a reduction theorem which allows us to restrict attention to those partial orders which do not have a bounded cutset. We use this and a theorem of Kelly and Rival to prove the second main result: that every contraction of a bounded partial order is fibre-valuable if and only if the partial order is a dismantlable lattice. This result has a geometric interpretation.This research was supported by the Natural Sciences and Engineering Research Council of Canada under operating grant OGP0105392.     

Examples of Twisted Cyclic Cocycles from Covariant Differential Calculi

For two covariant differential *-calculi, the twisted cyclic cocycle associated with the volume form is represented in terms of commutators for some self-adjoint operator and some *-representation of the underlying *-algebra.     

Formation of gold nanoparticles in gold ruby glass: The influence of tin

A ¹¹⁹Sn Mössbauer study was carried out of tin(IV) complexes with 2-benzoylpyridine thiosemicarbazone (H2Bz4DH) and its N(4)-methyl (H2Bz4M) and N(4)-phenyl (H2Bz4Ph) derivatives: [Sn(2Bz4DH)Cl₃] (1), [Sn(2Bz4DH)PhCl₂] (2), [Sn(2Bz4M)Cl₃] (3), [H₂2Bz4M]₂[Ph₂SnCl₄] (4), [Sn(2Bz4Ph)PhCl₂] (5), [Sn(2Bz4Ph)Ph₂Cl] (6), in which H2Bz4R stands for the neutral ligand and 2Bz4R stands for the anionic thiosemicarbazone. In addition, ¹¹⁹Sn Mössbauer studies of the tin(IV) complexes [Sn(H4Bz4DH)₂Cl₄H₂O] (7), [Sn(H4BzPS)₂Cl₄H₂O] (8) with 4-benzoylpyridine thiosemicarbazone (H4Bz4DH) and the correspondent semicarbazone (H4BzPS) were performed. The isomer shifts decrease upon coordination due to the variation in the percentage of s character as tin changes from approximately sp³ hybridization in the tin salts to sp³d² in the octahedral or sp³d³ in the heptahedral complexes. The Mössbauer parameters of compound (4) showed the existence of two tin(IV) sites, which have been attributed to the presence of the cis and trans isomers.     

Proton acceleration from high-intensity laser interactions with thin foil targets

Measurements of energetic proton production resulting from the interaction of high-intensity laser pulses with foil targets are described. Through the use of layered foil targets and heating of the target material we are able to distinguish three distinct populations of protons. One high energy population is associated with a proton source near the front surface of the target and is observed to be emitted with a characteristic ring structure. A source of typically lower energy, lower divergence protons originates from the rear surface of the target. Finally, a qualitatively separate source of even lower energy protons and ions is observed with a large divergence. Acceleration mechanisms for these separate sources are discussed.