On the Hausdorff dimension of generalized Besicovitch-Eggleston sets of d-tuples of numbers

We give a systematic and detailed account of the Hausdorff dimensions of sets of d-tuples of numbers defined in terms of the asymptotic behaviour of the frequencies of strings of digits in their N-adic expansion.     

Solitary wave interaction

The interaction between solitary wave solutions to a double sine-Gordon equation is examined numerically. Depending on the velocity, formation of breather-like modes or quasi solitonic behaviour are observed when a 2δ-kink interact with a 2π-antikink. As a result of collision between a (2π-2δ)-kink and a (2π-2δ)-antikink two 2δ-kink-antikink pairs always appear.     

Search for direct photons from S-Au collisions at 200 GeV/nucleon

The CERES experiment has measured inclusive photon production in S-Au collisions of 200 GeV/nucleon at the CERN SPS. No evidence for direct emission of photons was found. For the kinematic region 2.1<y<2.65 and 0.4 GeV/c<p??<2.0 GeV/c the yield andp??-dependence of the observed photons are well reproduced by hadron decays. Furthermore, their production rate is found to be proportional to the charged particle density. The systematic errors comparing the measured and expected photon yield result in an upper limit of 14% for the emission of direct photons in central S-Au collisions. For a photon source with a yield depending quadratically on the charged particle density the limit can be reduced to 7%.     

Reflection and transmission of waves near the localization threshold

A theory is presented for propagation of waves in bounded media near the mobility edge, based on the self-consistent theory for localization. It predicts a spatially inhomogeneous diffusion constant that leads to scale dependence in enhanced backscattering and transmission.     

QCD exotics

I review first some theoretical motivations for violation of Lorentz and/or CPT Invariance. Although the latter symmetries may be violated in a quantum gravity setting, nevertheless there are situations in which these violations are due to a given classical background geometry that may characterised early epochs of our Universe, and in fact be responsible for the observed dominance of matter over antimatter in the Universe. In this way I estimate some of the coefficients of the Standard Model Extension (SME), which is a framework for a field theoretic study of such a breakdown of fundamental symmetries. Then I describe briefly some tests of these symmetries, giving emphasis in low-energy antiproton physics and electric dipole moment measurements, of interest to this conference. I also mention the rôle of entangled states of neutral mesons in providing independent measurements of T(ime reversal) and CP Violation, thus providing independent tests of CPT symmetry, as well as novel (“smoking-gun” type) tests of decoherence-induced CPT violation, which may characterise some models of quantum gravity.     

Quantum dynamics of the dissociation of H2 on Cu(100): dependence of the site-reactivity on initial rovibrational state

We perform six-dimensional (6D) quantum wavepacket calculations for H2 dissociatively adsorbing on Cu(100) from a variety of rovibrational initial states. The calculations are performed on a new potential energy surface (PES), the construction of which is also detailed. Reaction probabilities are in good agreement with experimental findings. Using a new flux analysis method, we calculate the reaction probability density as a function of surface site and collision energy, for a variety of initial states. This approach is used to study the effects of rotation and vibration on reaction at specific surface sites. The results are explained in terms of characteristics of the PES and intrinsically dynamic effects. An important observation is that, even at low collision energies, reaction does not necessarily proceed predominantly in the region of the minimum potential barrier, but can occur almost exclusively at a site with a higher barrier. This suggests that experimental control of initial conditions could be used to selectively induce reaction at particular surface sites. Our predictions for site-reactivity could be tested using contemporary experimental methods: The calculations predict that, for reacting molecules, there will be a dependence of the quadrupole alignment of j on the incident vibrational state, v. This is a direct result of PES topography in the vicinity of the preferred reaction sites of v = 0 and v = 1 molecules. Invoking detailed balance, evidence for this difference in preferred reaction site of v = 0 and 1 molecules could be obtained through associative desorption experiments.     

Synthesis of sulfur-bridged piperazinediones by reaction of 3,6-dibromo-1,4-dimethyl-2,5-piperazinedione with geminal dithiols

The reaction of several geminal dithiols with 3,6-dibromo-1,4-dimethyl-2,5-piperazinedione gave in good yields piperazinedione derivatives substituted at the 3,6-position with a geminal dithiol-bridging group. These sulfur-bridged piperazinediones formally represent derivatives of the 2,4-dithia-6,8-diaza-7,9-dioxobicyclo[3.2.2]nonane ring system. Attempts to transform these sulfur-bridged piperazinediones to 3,6-epidithiopiperazinediones by removal of the bridging group common to the sulfur functionality were unsuccessful. Studies also are reported of addition of thioacetic acid to 3,6-dimethylene-2,5-piperazinedione to give 3,6-diacetylthio-3,6-dimethyl-2,5-piperazinedione. Conversion of the 3,6-diacetylthio derivative to the epithiopiperazinedione ring system yielded a mixture of epimono- and epidithiopiperazinediones.     

Nuclear size dependence of inclusive particle production

The inclusive production of π⁺, π^?, K⁺, K^?, p and $\text{p}$ for protons incident on carbon and tungsten targets was studied at the Internal Target Area of the Fermilab. We assume an A^α dependence for the inclusive cross sections and report here on the variation of α with incident momentum, transverse momentum and particle species.     

Synthesis of des-n-tetramethyltriostin a from C-terminal Z-d-serine tetra-and octadepsipeptide intermediates

Des-N-tetramethyltriostin A (1), a known DNA-intercalation agent, has been synthesized from tetra- and octapeptide intermediates that have Z-d-serine at the C-terminal position. The procedure thus allows the fragment coupling and cyclization reactions leading to the synthesis of the title compound to occur without racemization at the C-terminal amino acid. Esterification of Boc-Val-OH with the p-bromophenacyl ester of Z-d-serine provided didepsipeptide Z-d-Ser(Boc-Val)-OBpa (4). Stepwise addition of the requisite amino acids provided tetradepsipeptide Z-d-Ser[Boc-Ala-Cys(Acm)-Val]-OBpa (6). Fragment coupling of the respective C- and N-deprotected tetradepsipeptides 7 and 8, derived from 6, furnished linear octadepsipeptide 9, which upon cyclization and disulfide formation gave the bicyclic octadepsipeptide 11, a known synthetic precursor to 1. The degree of racemization incurred in the alanine and valine residues of selected depsipeptides was measured and the results compared with those obtained in previous studies. It was concluded that alanine, perhaps because of sequence effects, undergoes a degree of racemization (4–10%) during hydrolysis of tetradepsipeptide 6 and octadepsipeptide 9.