Construction of best Bregman approximations in reflexive Banach spaces

An iterative method is proposed to construct the Bregman projection of a point onto a countable intersection of closed convex sets in a reflexive Banach space.

     

Minimal operators from a potential-theoretic viewpoint

Minimal positive operators on a Hilbert spaceH are characterized in terms of so-called parallel addition of operators. It is also shown how these operators can be used to reproduce the inverse, respectively generalized inverse, of any positive operator onH.     

Unitary transformation treatment of a single hole in an Ising antiferromagnet

The behavior of a single hole in a two-dimensional Ising antiferromagnet (t-J ^z model), is studied in the generalized Dyson-Maleev representation, where the spins are mapped on boson operators and the hole is described as a spinless fermion. The formal similarity with Fröhlich's polaron Hamiltonian suggests that thet-J ^z model can be approximately diagonalized by means of two successive unitary transformations, analogous to those used by Lee, Low, and Pines in their intermediate-coupling treatment of the polaron. Our approach yields an upper bound to the exact ground state energy, as well as the corresponding ground state eigenvector. Fork=0 our energy bound is remarkably close to the result of the self-consistent Born approximation over a wide range of the coupling parameter, which includes the range typically assumed for the high-T _c materials. The ground state eigenvector is used to calculate the spatial distribution of bosons (spin deviations) surrounding the hole. Here our results are qualitatively very similar to those obtained in previous work, showing that our ground state eigenvector accounts quite well for the small size of the “spin polaron” in thet-J ^z model.     

How can nanobiotechnology oversight advance science and industry: examples from environmental,health, and safety studies of nanoparticles (nano-EHS)

Nanotechnology has great potential to transform science and industry in the fields of energy, material, environment, and medicine. At the same time, more concerns are being raised about the occupational health and safety of nanomaterials in the workplace and the implications of nanotechnology on the environment and living systems. Studies on environmental, health, and safety (EHS) issues of nanomaterials have a strong influence on public acceptance of nanotechnology and, eventually, affect its sustainability. Oversight and regulation by government agencies and non-governmental organizations (NGOs) play significant roles in ensuring responsible and environmentally friendly development of nanotechnology. The EHS studies of nanomaterials can provide data and information to help the development of regulations and guidelines. We present research results on three aspects of EHS studies: physico-chemical characterization and measurement of nanomaterials; emission, exposure, and toxicity of nanomaterials; and control and abatement of nanomaterial releases using filtration technology. Measurement of nanoparticle agglomerates using a newly developed instrument, the Universal NanoParticle Analyzer (UNPA), is discussed. Exposure measurement results for silicon nanoparticles in a pilot scale production plant are presented, as well as exposure measurement and toxicity study of carbon nanotubes (CNTs). Filtration studies of nanoparticle agglomerates are also presented as an example of emission control methods.     

International Symposium on 'Nanoparticles: Technology and Sustainable Development,' Taipei,Taiwan, September 9–10, 2002

Journal of Nanoparticle Research -     

Isomeric states in 214Th and 213Th

Isomeric states in ²¹⁴Th and ²¹³Th were identified by means of γ -rays measured in delayed coincidence with the implanted evaporation residues. These were produced in irradiations of ¹⁶⁴Dy with ⁵⁴Cr projectiles and separated in-flight by the velocity filter SHIP. An isomeric state of I ^π = 8⁺ with a half-life of (1.24±0.12) μs was identified in ²¹⁴Th . The configuration π[1h _9/2 ⊗ 2f _7/2] was assigned to this state. An isomeric state with a half-life of (1.4±0.4) μs was observed in ²¹³Th . Tentatively it was assigned to an I ^π = 13/2⁺ state.     

Horizon-less Spherically Symmetric Vacuum-Solutions in a Higgs Scalar-Tensor Theory of Gravity

The exact static and spherically symmetric solutions of the vacuum field equations for a Higgs Scalar-Tensor theory (HSTT) are derived in Schwarzschild coordinates. It is shown that in general there exists no Schwarzschild horizon and that the fields are only singular (as naked singularity) at the center (i.e. for the case of a point-particle). However, the Schwarzschild solution as in usual general relativity (GR) is obtained for the vanishing limit of Higgs field excitations.     

Slicing the Oppenheimer-Snyder Collapse: Harmonic versus Maximal Slicing

In continuing our studies of temporal slicings of spacetimes, we consider the collapse from rest of an initially homogeneous dust sphere, known as Oppenheimer-Snyder collapse. It is shown that in the case of harmonic slicing the whole spacetime becomes covered by slices extending to spatial infinity in contrast to maximal slicing. The behavior of the lapse function is discussed, especially for various data on the initial slice, and it is demonstrated that not every choice of the initial lapse leads to meaningful slicings.