Time- and space-summation studies of the diffusion equation: experimental test of the ergodic hypothesis

One-atom detection techniques have been used to test the equality between time and ensemble averages, following a gedanken experiment on the diffusion of atoms suggested by Einstein and Fürth. Experimental results confirmed that a system of freely diffusing atoms was ergodic.     

Scaling of the energy gap withT c in Bi2Sr2CaCu2O8+δ

The results of a high-resolution photoemission study using synchrotron radiation of two single crystals of Bi₂Sr₂CaCu₂O₈₊, with different critical temperaturesT _c due to a variation in oxygen stoichiometry are reported. Within experimental accuracy, the energy gap 2 is found to scale withT _c , amounting to a reduced gap parameter of 2/k _BT_c7.4. Employing resonant photoemission at the O–2s and Cu–3p thresholds, two spectral peaks at binding energies of 180 meV and 320 meV were identified as predominantly O–2p-and Cu–3d 4s-derived states, respectively.     

X-ray diffraction studies on cis- and trans-4'-cyanobiphenyl-4-yl 3-n-propylcyclobutane-1-carboxylate

X-ray diffraction has been used to study the nematic phases of the cis and trans isomers of an elongated molecule containing the cyclobutane group. It has been shown that these nematic phases consist of a mixture of single molecules and overlapping core dimers. It has been found that increasing the temperature of the cis isomer rapidly reduces the dimer population, whereas increasing the temperature of the trans isomer enhances the dimer population. This provides an explanation of the relatively high clearing temperature of the trans isomer. The different temperature dependences of the dimer population in the cis and trans isomers has been explained by a model involving inversion of the cylobutane group.     

Chemical and chemoenzymatic synthesis of glycosyl-amino acids and glycopeptides related to Trypanosoma cruzi mucins

This study describes the synthesis of the alpha- and beta-linked N-acetyllactosamine (Galp-beta-1,4-GlcNAc; LacNAc) glycosides of threonine (LacNAc-Thr). LacNAc-a-Thr was prepared by direct chemical coupling of a 2-azido-2-deoxy-lactose disaccharide donor to a suitable partially protected threonine unit. In contrast, stepwise chemical generation of beta-linked N-acetylglucosamine followed by enzymatic galactosylation to give LacNAc-beta-Thr proved effective, whereas use of a 2-azido-2-deoxy-lactose donor in acetonitrile failed to give the desired beta-linked disaccharyl glycoside. This study illustrates that it is possible to overcome the inherent stereoselection for 1,2-trans chemical glycosylation with a GlcNAc donor, and that the well-established preference of bovine beta-1,4-galactosyltransferase for beta-linked acceptor substrates can also be overcome. Using this knowledge, short glycopeptide fragments based on T. cruzi mucin sequences, Thr-Thr-[LacNAcThr]-Thr-Thr-Gly, were synthesised. All LacNAc-based compounds outlined were shown to serve as acceptor substrates for sialylation by T. cruzi trans-sialidase.     

REPLY TO “COMMENT ON QUANTUM PHASE SHIFT CAUSED BY SPATIAL CONFINEMENT” BY M. PESHKIN

We describe a force-free phase shift due only to temporal geometric boundary conditions placed on a neutron de Broglie wave packet.     

Breaking the chain

We consider the motion of a Brownian particle in R$\mathbb{R}$, moving between a particle fixed at the origin and another moving deterministically away at slow speed ε>0$\epsilon >0$. The middle particle interacts with its neighbours via a potential of finite range b>0$b>0$, with a unique minimum at a>0$a>0$, where b<2a$b<2a$. We say that the chain of particles breaks on the left- or right-hand side when the middle particle is at a distance greater than b$b$ from its left or right neighbour, respectively. We study the asymptotic location of the first break of the chain in the limit of small noise, in the case where ε=ε(σ)$\epsilon =\epsilon \left(\sigma \right)$ and σ>0$\sigma >0$ is the noise intensity.     

Abelian Subgroups of Finitely Generated Kleinian Groups are Separable

By a Kleinian group we mean a discrete subgroup of PSL(2, C).We prove that abelian subgroups of finitely generated Kleiniangroups are separable. In other words, if M = H³/ is a hyperbolic3-orbifold, with finitely generated, then abelian subgroupsof are separable in . 1991 Mathematics Subject Classification20E26, 51M10, 57M05.