The gauge transformations of the Schwinger model

We determine the group of implementable local gauge transformations of massless quantum electrodynamics in two space-time dimensions in the covariant Landau gauge. It splits into an infinite discrete set of disjoint classes. The unitary operators representing the implementable gauge transformations are constructed explicitly. A subset of these operators does not reduce to multiples of the identity in the physical Hilbert space constructed according to the usual rules. The disappearance of the fermionic degrees of freedom is related to this fact. Combined with the properties of the global chiral transformations, it provides a better understanding of the model's vacuum structure.     

Error bound for an osculatory quadrature formula

Sharper estimates have been found for Donaldson's osculatory quadrature formula.     

A Laurent series expansion formula and its applications

This paper gives a certain Laurent series expansion for a generalized Rodrigues type formula. The main result finds many applications which are enumerated briefly.     

Two-neutrino positron double-beta decay of <Superscript>106</Superscript>Cd for the 0<Superscript>+</Superscript> → 0<Superscript>+</Superscript> transition

The two-neutrino positron double-beta decay of ¹⁰⁶Cd for the 0 ⁺ 0⁺ transition has been studied in the Hartree-Fock-Bogoliubov model in conjunction with the summation method. In the first step, the reliability of the intrinsic wave functions of ¹⁰⁶Cd and ¹⁰⁶Pd nuclei has been tested by comparing the theoretically calculated results for yrast spectra, reduced B(E2: 0⁺ 2⁺) transition probabilities, quadrupole moments Q(2⁺) and gyromagnetic factors g(2⁺) with the available experimental data. In the second step, the nuclear transition matrix element M₂ and the half-life T_1/2² for the 0 ⁺ 0⁺ transition have been calculated with these wave functions. Moreover, we have studied the effect of deformation on the nuclear transition matrix element M₂.     

An algebraic geometry study of theb−c system with arbitrary twist fields and arbitrary statistics

We present an analysis of the generalb–c system (including the – system) on a compact Riemann surface of arbitrary genusg0 by postulating that its correlation functions should only have the singularities imposed by the operator product expansion (OPE) of the system. Studying a very (in fact optimally) general form of theb–c system, we prove rigorously that the standard practice of eliminating zero modes, and even the standard lagrangian, follow from the analyticity structure dictated by the OPE alone. We extend the analysis to consider the most general case of the presence of twist (e.g. spin) fields. We then determine all the possible correlation functions of theb–c system, with statistics unspecified, compatible with the OPE. On imposing Fermi and Bose statistics, we obtain the correlation functions of the fermionicb–c and – systems, respectively.     

Template synthesis,characterization and electrochemical studies of copper(II) macrocyclic complexes derived from 4-methyl-2,6-di(formyl/benzoyl) phenol and diamines

Copper(II) macrocyclic complexes [Cu(L)Cl2]·2H2O (1,2) have been synthesized from the copper(II)-directed condensation of 4-methyl-2,6-diformylphenol (1) or 4-methyl-2,6-dibenzoylphenol (2) with diamines [1,2-diaminopropane (a), 1,3-diaminopropane (b) and o-phenylenediamine (c)] in EtOH in high yields. These complexes are monomeric, non-electrolytes and paramagnetic, indicating a distorted octahedral geometry around copper, which is supported by i.r., electronic, e.s.r. and magnetic susceptibility measurements. Electrochemical studies of (1) and (2) using c.v. indicate an irreversible cathodic peak (ca. –0.65 to –0.76 V) corresponding to reduction of copper(II) to copper(I) and the diffusion-controlled nature of the electrode process.     

Aminoaryltellurium(IV) trihalides

The preparation and properties of some aminoaryltellurium(IV) trihalides are reported. Conductivity measurements show the compounds to behave as 1:1 electrolytes when in dilute solution. Cryoscopic measurements reflect the molecular, and sometimes polymeric, nature of the materials in more concentrated solutions. The ¹H nmr and infrared spectra are discussed.     

Heterogeneous nucleation of nitric acid trihydrate on clay minerals: relevance to type ia polar stratospheric clouds

Although critical to atmospheric modeling of stratospheric ozone depletion, selective heterogeneous nuclei that promote the formation of Type Ia polar stratospheric clouds (PSCs) are largely unknown. While mineral particles are known to be good ice nuclei, it is currently not clear whether they are also good nuclei for PSCs. In the present study, a high-vacuum chamber equipped with transmission Fourier transform infrared spectroscopy and a quadrupole mass spectrometer was used to study heterogeneous nucleation of nitric acid trihydrate (NAT) on two clay minerals-Na-montmorillonite and kaolinite-as analogs of atmospheric terrestrial and extraterrestrial minerals. The minerals are first coated with a 3:1 supercooled H2O/HNO3 solution prior to the observed nucleation of crystalline NAT. At 220 K, NAT formation was observed at low SNAT values of 12 and 7 on kaolinite and montmorillonite clays, respectively. These are the lowest SNAT values reported in the literature on any substrate. However, NAT nucleation exhibited significant temperature dependence. At lower temperatures, representative of typical polar stratospheric conditions, much higher supersaturations were required before nucleation was observed. Our results suggest that NAT nucleation on mineral particles, not previously treated with sulfuric acid, may not be an important nucleation platform for Type Ia PSCs under normal polar stratospheric conditions.     

A strong discontinuity based adaptive refinement approach for the modeling of crack branching

In the current work, the physical phenomena of dynamic fracture of brittle materials involving crack growth, acceleration and consequent branching is simulated. The numerical modeling is based on the approach where the failure in the form of cracks or shear bands is modeled by a jump in the displacement field, the so called ‘strong discontinuity’. The finite element method is employed with this strong discontinuity approach where each finite element is capable of developing a strong discontinuity locally embedded into it. The focus in this work is on branching phenomena which is modeled by an adaptive refinement method by solving a new sub-boundary value problem represented by a finite element at the growing crack tip. The sub-boundary value problem is subjected to a certain kinematic constraint on the boundary in the form of a linear deformation constraint. An accurate resolution of the state of material at the branching crack tip is achieved which results in realistic dynamic fracture simulations. A comparison of resulting numerical simulations is provided with the experiment of dynamic fracture from the literature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)