Expression of theSU(2) rotation matrices D( j ) in terms of normalized irreducible tensorial matrices

TheSU(2) rotation matricesD ^(j), specified in terms of axis and angle of rotation, are expressed as linear combination of normalized irreducible tensorial matricces (NITM) of rankl = 0 to 2j rotated to the polar angles of the axis. The rotated NITM are constructed from spherical harmonics of the same rank. Since this formulation requires no matrix products, it may be computationally more efficient than Euler angle formulas, particularly for largej. Rotated NITM and formulas for theD ^(j) withj = 1/2 andj = 1 are written out explicitly. A formula for the structure constants of the products of conformable NITM is also given in terms of 3-j and 6-j symbols.     

On the existence of <Emphasis Type="Bold">1, 3</Emphasis>P <Emphasis Type="Bold">o</Emphasis> resonances in H<Superscript>-</Superscript> between n = 2 and 3 H thresholds

We examine the influence of relativistic and QED effects on the existence of the ^1,3P ^o H^- resonances between n = 2 and 3 hydrogen thresholds, the relativistic and QED corrections and the coupling effects between the high singlet and triplet states are considered as first-order perturbations. We firstly obtain accurate non-relativistic resonant energies and widths of fifteen ¹P ^o resonances, and fifteen ³P ^o resonances. The fifteen ¹P ^o resonances are classified to be ₃ (2, 0) ^- _n ( 4 ? n ? 12) and ₃ (1, 1) ⁺ _n ( 3 ? n ? 8). The fifteen ³P ^o resonances are classified to be ₃ (2, 0) ⁺ _n ( 3 ? n ? 12) and ₃ (1, 1) ^- _n ( 4 ? n ? 8). We found there exist six Feshbach resonances for ₃ (2, 0) ^- _n (¹P ^o ) series, four Feshbach resonances for ₃ (1, 1) ⁺ _n (¹P ^o ) series, seven Feshbach resonances for ₃ (2, 0) ⁺ _n (³P ^o ) series, and three Feshbach resonances for ₃ (1, 1) ^- _n (¹P ^o ) series. Received 22 February 2002 Published online 24 September 2002     

On finite element approximation and stabilization methods for compressible viscous flows

This work is devoted to the numerical solution of the Navier–Stokes equations for compressible viscous fluids. Finite element approximations and stabilization techniques are addressed. We present methods to implement discontinuous approximations for the pressure and the density. An upwinding methodology is being investigated which combines the ideas behind the stream line Petrov–Galerkin method and the flux limiter methods aiming to introduce numerical diffusion only where it is necessary.     

The amplitude and phase of a transmission holographic grating due to four-wave interaction in a photorefractive medium

Based on a previously developed two-level model of four-wave interaction in photorefractive crystals, expressions for the amplitude and phase of a transmission holographic grating have been obtained. The analysis of these expressions points to the dependence of both the amplitude and the phase of the grating on the intensity of the readout beam.     

Aqueous solution and solid state interactions of lanthanide ions with a methacrylic ester polymer bearing pendant 15‐crown‐5 moieties

The interaction between trivalent lanthanide ions and poly(1,4,7,10,13‐pentaoxacyclopentadecan‐2‐yl‐methyl methacrylate), PCR5, in aqueous solution and in the solid state have been studied. In aqueous solution, evidence of a weak interaction between the lanthanides and PCR5 comes from the small red shift of the Ce(III) emission spectra and the slight broadening of the Gd(III) EPR spectra. From the Tb(III) lifetimes in the presence of H₂O and D₂O the loss of one or two water coordinated molecules is confirmed when Tb(III) is bound to PCR5. An association constant of the order of 200 M^?1 was obtained for a 1:1 (lanthanide:15‐crown‐5) complex from the shift of the polymer NMR signals induced by Tb(III). A similar association constant is obtained from the differences of the molar conductivity of Ce(III) solution at various concentrations in presence and absence of PCR5. When Tb(III) is adsorbed on PCR5 membranes, lifetime experiments in H₂O and D₂O confirm the loss of 5 or 6 water coordinated molecules indicating that in solid state the lanthanide(III)‐PCR5 interaction is stronger than in solution. The adsorption of Ce(III) in PCR5 membranes shows a Langmuir type isotherm, from which an equilibrium constant of 39 M^?1 has been calculated. SEM shows that the membrane morphology is not much affected by lanthanide adsorption. Support for lanthanide ion–crown interactions comes from ab initio calculations on 15‐crown‐5/La(III) complex. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1788–1799, 2007     

Nonlinear optical properties of regioregular main‐chain polyesters

We have prepared new polyesters containing quadratic, nonlinear optical (NLO) active chromophores covalently incorporated into the main chain. In these polymers, the sequence of the chromophore units along the main chain is rigorously head to tail. All the polyesters are processable, both in the melt and in solution. For one polyester, a full second‐order NLO characterization has been performed. An out‐of‐resonance d₃₃ coefficient of 21 pm/V at 1368 nm has been measured. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2719–2725, 2007     

Glass transitions and mixed phases in block SBS

Differential scanning calorimetry (DSC) does not allow for easy determination of the glass‐transition temperature (T_g) of the polystyrene (PS) block in styrene–butadiene–styrene (SBS) block copolymers. Modulated DSC (MDSC), which deconvolutes the standard DSC signal into reversing and nonreversing signals, was used to determine the (T_g) of both the polybutadiene (PB) and PS blocks in SBS. The T_g of the PB block was sharp, at ?92 °C, but that for the PS blocks was extremely broad, from ?60 to 125 °C with a maximum at 68 °C because of blending with PB. PS blocks were found only to exist in a mixed PS–PB phase. This concurred with the results from dynamic mechanical analysis. Annealing did not allow for a segregation of the PS blocks into a pure phase, but allowed for the segregation of the mixed phase into two mixed phases, one that was PB‐rich and the other that was PS‐rich. It is concluded that three phases coexist in SBS: PB, PB‐rich, and PS‐rich phases. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 276–279, 2005