Existence results for singular three point boundary value problems on time scales

We prove the existence of a positive solution for the three point boundary value problem on time scale given by

     

Polaroid operators and Weyl's theorem

``Polaroid elements" represent an attempt to abstract part of the condition, ``Weyl's theorem holds" for operators.

     

Self-assembly of chiral DNA nanotubes

A system of DNA "tiles" that is designed to assemble to form two-dimensional arrays is observed to form narrow ribbons several micrometers in length. The uniform width of the ribbons and lack of frayed edges lead us to propose that they are arrays that have curled and closed on themselves to form tubes. This proposal is confirmed by the observation of tubes with helical order.     

Spectral weight contributions of many-particle bound States and continuum

Cluster expansion methods are developed for calculating the spectral weight contributions of multiparticle excitations--continuum and bound states--to high orders. A complete 13th order calculation is carried out for the alternating Heisenberg chain. For lambda=0.27, relevant to the material Cu(NO3)(2).2.5D(2)O, we present detailed spectral weights for the two-triplet continuum and all bound states. We also examine the variation of the relative weights of one- and two-particle states with bond alternation from the dimerized to the uniform chain limit.     

Coulombic energy transfer and triple ionization in clusters

Using neon and its dimer as a specific example, it is shown that excited Auger decay channels that are electronically stable in the isolated monomer can relax in a cluster by electron emission. The decay mechanism, leading to the formation of a tricationic cluster, is based on an efficient energy-transfer process from the excited, dicationic monomer to a neighbor. The decay is ultrafast and expected to be relevant to numerous physical phenomena involving core holes in clusters and other forms of spatially extended atomic and molecular matter.     

Frustrated antiferromagnetism in the Sr<Subscript>2</Subscript>YRuO<Subscript>6</Subscript> double perovskite

The spins of Ru⁵⁺ ions in Sr₂YRuO₆ form a face-centered cubic lattice with antiferromagnetic nearest neighbor interaction J≈25 meV. The antiferromagnetic structure of the first type experimentally observed below the Néel temperature T _N =26 K corresponds to four frustrated spins of 12 nearest neighbors. In the Heisenberg model in the spin-wave approximation, the frustrations already cause instability of the antiferromagnetic state at T=0 K. This state is stabilized by weak anisotropy D or exchange interaction I with the next-nearest neighbors. Low D/J～I/J～10^?3 values correspond to the experimental T _N and sublattice magnetic moment values.     

The DIVAM sequence: selective excitation of signals from both rigid and mobile domains in a fluoropolymer

Simulations have been carried out on z-magnetizations produced by (and hence of the resulting spectra from) the dipolar filter (DF) and the recently suggested "Discrimination Induced by Variable-Amplitude Minipulses" (DIVAM) pulse sequences [S. Ando et al., Polymer 42 (2001) 8137; Magn. Reson. Chem. 40 (2002) 97]. The strengths of dipolar interactions have been modelled by introducing different values for transverse relaxation times. The DF case has been extended by allowing the pulse angles to be smaller than 90 degrees. The pulse intervals have also been used as variables. For the DIVAM case, the variables are similarly the minipulse nutation angles and minipulse intervals. The computations show that DIVAM is superior to DF in terms of selectivity for spectra of heterogeneous materials such as semi-crystalline polymers. The effects of the pulse sequences on 19F spectra of poly(vinylidene fluoride) (PVDF) and of a copolymer of vinylidene fluoride and trifluoroethylene (p(VDF/TrFE)) are presented, together with fits of the experimental results by the simulations.     

Two-dimensional protein map of human vastus lateralis muscle

Protein samples of human vastus lateralis muscle were analyzed by two-dimensional gel electrophoresis, using immobilized pH gradients encompassing several pH regions in the first dimension and sodium dodecyl sulfate-polyacrylamide gel electrophoresis in the second dimension. More than 500 protein spots on each gel were detected by silver staining, of which 150 were excised, digested in-gel with trypsin and characterized by matrix assisted laser desorptioin/ionization-mass spectrometry and tandem electrospray mass spectrometry. Using these techniques, 124 spots including contractile proteins and metabolic enzymes were identified. This database should provide a valuable resource for the definition of the functional properties of muscle fibres and for assessment of the influence of e.g., hypoxia, ischaemia and ageing on protein level.