A path-space formula for non-abelian gauge theories

A functional integral representation is obtained for a semigroup in an indefinite metric space giving the dynamics of a cutoff Yang-Mills theory in space-time dimensions greater than two. The Fadde'av-Popov formula is shown to arise as a stochastic integral in the Feynman gauge.     

Euclidean field theory

The extension of the Schwinger functions to various positive linear functionals on the Borchers algebra is discussed. In one case, we construct a measure onL and give criteria for uniqueness as well as for the homogeneous chaos to lead to an ?₂-space.     

The Berkeley Center for Structural Biology at the Advanced Light Source

The Berkeley Center for Structural Biology (BCSB) operates and develops a suite of protein crystallography beamlines at the Advanced Light Source (ALS) located at Lawrence Berkeley National Laboratory (LBNL). Although the ALS was conceived as a low-energy (1.9-GeV), third-generation synchrotron source of vacuum ultraviolet (VUV) and soft X-ray radiation, it was realized during the development of the facility in the mid-1990s that a multipole wiggler coupled with brightness-preserving optics would result in a beamline whose performance in the energy range of 5 to 15 keV would be sufficient for most protein crystallographic experiments. Later, the hard X-ray capabilities of the ALS were expanded by the addition of three superconducting bending magnets, resulting in additional protein crystallography facilities at the ALS [1 A.A. MacDowell, J Synchrotron Radiation 11(6), 447–55 (2004).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]].     

Max Dehn and geometry

Max Dehn is famous for his contributions to group theory and topology, but almost half of his publications are on the foundations of geometry. In this article I hope to show that Dehn's interest in geometry was not misplaced, and that his contributions to it are also remarkable. First, let us survey Dehn's main contributions to geometry, in chronological order.     

Arrays of magnetic nanoparticles capped with alkylamines

Magnetic metal and metal oxide nanoparticles capped with alkylamines have been synthesized and characterized by transmission electron microscopy. X-ray diffraction, energy dispersive X-ray analysis and magnetization measurements. Core-shell Pd-Ni particles with composition, Pd₅₆₁Ni₃₀₀₀, (diameter ∼3.3 nm) are superparamagnetic at 5 K and organize themselves into two-dimensional crystalline arrays. Similar arrays are obtained with Pd₅₆₁Ni₃₀₀₀Pd₁₅₀₀ nanoparticles containing an additional Pd shell. Magnetic spinel particles of γ-Fe₂O₃, Fe₃O₄ and CoFe₂O₄ of average diameters in the 4–6 nm range coated with octylamine are all supermagnetic at room temperature and yield close-packed disordered arrays. Relatively regular arrays are formed by dodecylaminecapped Fe₃O₄ nanoparticles (∼8.6 nm diameter) while well-ordered hexagonal arrays were obtained with octylamine-covered Co₃O₄ nanoparticles (∼4.2 nm diameter).     

Semicomplete Permutational Wreath Products

A group is called semicomplete if every automorphism which induces the identity on the factor commutator group is inner. In this paper, we study the connection of the semicompleteness of the permutational wreath product W of two groups with the semicompleteness of these groups. We give necessary conditions under which the group W is semicomplete.2000 Mathematics Subject Classification: 20E22, 20E36     

Large sets of zero analytic capacity

We prove that certain Cantor sets with non-sigma-finite one- dimensional Hausdorff measure have zero analytic capacity.

     

Growth and characteristics of reactive pulsed laser deposited molybdenum trioxide thin films

Molybdenum trioxide thin films were prepared by reactive pulsed laser deposition on Corning 7059 glass substrates. The influence of oxygen partial pressure and deposition temperature on the structure, surface morphology and optical properties of these films was studied to understand the growth mechanism of MoO₃ thin films. The films formed at 473 K in an oxygen partial pressure of 100 mTorr exhibited predominantly a (0k0) orientation, corresponding to an orthorhombic layered structure of α-MoO₃. The evaluated optical band gap of the films was 3.24 eV. The crystallite size increased with increase of deposition temperature. The films formed at an oxygen partial pressure of pO₂=100 mTorr and at a deposition temperature greater than 700 K exhibited both (0k0) and (0kl) orientations, representing α-β mixed phases of MoO₃. The films formed at an oxygen partial pressure less than 100 mTorr were found to be sub-stoichiometric with α-β mixed phases. The investigation revealed the growth of polycrystalline and single-phase orthorhombic-layered-structure α-MoO₃ thin films with composition nearly approaching the nominal stoichiometry at moderate substrate temperatures in an oxygen partial pressure of 100 mTorr. Received: 9 April 2001 / Accepted: 6 August 2001 / Published online: 17 October 2001     

The combinatorics and extreme value statistics of protein threading

In protein threading, one is given a protein sequence, together with a database of protein core structures that may contain the natural structure of the sequence. The object of protein threading is to correctly identify the structure(s) corresponding to the sequence. Since the core structures are already associated with specific biological functions, threading has the potential to provide biologists with useful insights about the function of a newly discovered protein sequence. Statistical tests for threading results based on the theory of extreme values suggest several combinatorial problems. For example, what is the number of waysm′=# _t {L _i >x _i } _i ⁼⁰ⁿ of choosing a sequence {X _i } _i ⁼¹ⁿ from the set {1, 2, ...,t}, subject to the difference constraints {L _i =X _i+1?X _i >x _i } _i ⁼⁰ⁿ , whereX ₀=0,X _n+1=t+1, and {x _i } _i ⁼⁰ⁿ is an arbitrary sequence of integers? The quantitym′ has many attractive combinatorial interpretations and reduces in special continuous limits to a probabilistic formula discovered by the Finetti. Just as many important probabilities can be derived from de Finetti's formula, many interesting combinatorial quantities can be derived fromm′. Empirical results presented here show that the combinatorial approach to threading statistics appears promising, but that structural periodicities in proteins and energetically unimportant structure elements probably introduce statistical correlations that must be better understood.