Unbounded derivations tangential to compact groups of automorphisms,II

Let G be a compact abelian group, and τ an action of G on a C¹-algebra $\text{U}$, such that $\text{U}$^τ(γ)$\text{U}$^τ(γ)¹ = $\text{U}$^τ(0) $\text{U}$^τ for all $\text{γ ?}\text{G}\text{?}$, where $\text{U}$^τ(γ) is the spectral subspace of $\text{U}$ corresponding to the character γ on G. Derivations δ which are defined on the algebra $\text{U}$_F of G-finite elements are considered. In the special case δ¦_{$\text{U}$^τ} = 0 these derivations are characterized by a cocycle on $\text{G}\text{?}$ with values in the relative commutant of $\text{U}$^τ in the multiplier algebra of $\text{U}$, and these derivations are inner if and only if the cocycles are coboundaries and bounded if and only if the cocycles are bounded. Under various restrictions on G and τ properties of the cocycle are deduced which again give characterizations of δ in terms of decompositions into generators of one-parameter subgroups of τ(G) and approximately inner derivations. Finally, a perturbation technique is devised to reduce the case δ($\text{U}$_F) ? $\text{U}$_F to the case δ($\text{U}$_F) ? $\text{U}$_F and δ¦_{$\text{U}$^τ} = 0. This is used to show that any derivation δ with D(δ) = $\text{U}$_F is wellbehaved and, if furthermore G = T¹ and δ($\text{U}$_F) ? $\text{U}$_F the closure of δ generates a one-parameter group of ¹-automorphisms of $\text{U}$. In the case G = T^d, d = 2, 3,… (finite), and δ($\text{U}$_F) ? $\text{U}$_F it is shown that δ extends to a generator of a group of ¹-automorphisms of the σ-weak closure of $\text{U}$ in any G-covariant representation.     

Steady-state fully noninductive current driven by electron cyclotron waves in a magnetically confined plasma

A steady-state, fully noninductive plasma current has been sustained for the first time in a tokamak using electron cyclotron current drive only. In this discharge, 123 kA of current have been sustained for the entire gyrotron pulse duration of 2 s. Careful distribution across the plasma minor radius of the power deposited from three 0. 5-MW gyrotrons was essential for reaching steady-state conditions. With central current drive, up to 153 kA of current have been fully replaced transiently for 100 ms. The noninductive scenario is confirmed by the ability to recharge the Ohmic transformer. The dependence of the current drive efficiency on the minor radius is also demonstrated.     

Refined fixture design for effective essential work of fracture toughness characterization of m-LLDPE thin films

Characterization of Mode-I fracture toughness of ductile polymeric thin films is nontrivial. Proper specimen preparation and experimental procedures are required to ensure in-plane tensile loading. In this study, a custom-built double-edge notched tensile test fixture was employed to characterize the Mode-I essential work of fracture (EWF) toughness of metallocene linear low-density polyethylene (m-LLDPE) films. Effects of specimen geometry, strain rate and film orientation on the specific essential work of fracture, w_e, and the specific non-essential work of fracture, w_p, were investigated. Results indicate both EWF parameters are independent of the crosshead speed, gauge length (distance between upper and lower clamps) and specimen width within the ranges tested. w_e is significantly higher for thinner films and for crack propagation perpendicular to the blown film machine direction (MD). The usefulness of EWF for evaluating m-LLDPE fracture toughness is discussed.     

An analytical approach for computing Franck‐Condon integrals of harmonic oscillators with arbitrary dimensions

We have developed an analytical approach for computing Franck‐Condon integrals (FCIs) of harmonic oscillators (HOs) with arbitrary dimensions in which the mode‐mixing Duschinsky effect is taken into account. A general formula of FCIs of HOs was obtained and was applied to study the photoelectron spectroscopy of vinyl alcohol and ovalene (C₃₂H₁₄). The equilibrium geometries, harmonic vibrational frequencies and normal modes of vinyl alcohol, ovalene, and their cations were computed at the B3LYP/aug‐cc‐pVTZ or the B3LYP/6‐31G(d) level, from which Franck‐Condon factors were calculated and photoelectron spectra were simulated. The adiabatic ionization energies of vinyl alcohol were also computed by extrapolating the CCSD(T) energies to the complete basis set limit with aug‐cc‐pVXZ (X = D, T, Q, 5). The simulated photoelectron spectra of both vinyl alcohol and ovalene are in agreement with the experiments. The computed adiabatic ionization energies of syn‐ and anti‐vinyl alcohol are in consistent with the experiment within 0.008 eV and 0.014 eV, respectively. We show, for the first time, that the analytical approach of computing FCIs is also efficient and promising for the studies of vibronic spectra of macrosystems. © 2012 Wiley Periodicals, Inc.     

Synthesis of Unsymmetrical 1,4-Diketones Via the Michael-Stetter Reaction

The cyanide catalyzed 1,4-Michael addition of aldehydes to α, β-unsaturated ketones has been examined with regard to substituent effects. Adjustment of the donor/acceptor relationship allows for the synthesis of multisubstituted diaryl 1,4-diketones.