Pi-bonded quinonoid transition-metal complexes

Coordination of the carbocyclic ring of hydroquinones to electrophilic transition-metal fragments such as Mn(CO)3+ and Rh(COD)+ produces stable pi-bonded eta6-complexes that are activated to facile reversible deprotonation of the -OH groups. The deprotonations are accompanied by electron transfer to the transition metal, which acts as an internal oxidizing agent or electron sink. With manganese as the metal, the resulting eta5-semiquinone and eta4-quinone complexes have been used to synthesize one- two- and three-dimensional polymeric metal-organometallic coordination networks. With rhodium as the metal, the pi-quinonoid complexes have been demonstrated to play a unique role in multifunctional C-C coupling catalysis and in the synthesis of new organolithium reagents. Both classes of pi-quinonoid complexes appear to have significant applications in nanochemistry by providing an excellent vehicle for templating the directed self-assembly of nanoparticles into functional materials.     

Generic Bell inequalities for multipartite arbitrary dimensional systems

We present generic Bell inequalities for multipartite arbitrary dimensional systems. The inequalities that any local realistic theory must obey are violated by quantum mechanics for even dimensional systems. A large set of variants are shown to naturally emerge from the generic Bell inequalities. We discuss particular variants of Bell inequalities that are violated for all the systems including odd dimensional systems.     

Organometallic crystal engineering of [(1,4- and 1,3-hydroquinone)Rh(P(OPh)3)2]BF4 by charge assisted hydrogen bonding

The ionic complexes [(1,4- and 1,3-hydroquinone)Rh(P(OPh)3)2]BF4 form porous organometallic structures dictated by charge assisted hydrogen bonding.     

Observation of multiferroic properties in a CdTe:Mn thin film grown by pulsed laser deposition techniques

We report multiferroic properties in a 3% Mn-doped CdTe (CdTe:Mn or CTM) thin film grown in a co-deposition system constituting pulsed laser deposition and radio frequency (RF) sputtering, in which the Mn concentration was tuned by the sputtering rate of Mn. We observed a clear ferroelectric hysteresis loop in the CTM thin film with remanent polarization of 3.5 μC/cm² and ferromagnetism in the film at a temperature lower than the Curie temperature of 15 K. Both features show direct evidence of multiferroics in the CTM thin film.     

The Webster Scalar Curvature and Sharp Upper and Lower Bounds for the First Positive Eigenvalue of the Kohn-Laplacian on Real Hypersurfaces

Let(M, θ) be a compact strictly pseudoconvex pseudohermitian manifold which is CR embedded into a complex space. In an earlier paper, Lin and the authors gave several sharp upper bounds for the first positive eigenvalue λ_1 of the Kohn-Laplacian □_b on(M, θ). In the present paper, we give a sharp upper bound for λ_1, generalizing and extending some previous results. As a corollary, we obtain a Reilly-type estimate when M is embedded into the standard sphere. In another direction, using a Lichnerowicz-type estimate by Chanillo, Chiu, and Yang and an explicit formula for the Webster scalar curvature, we give a lower bound for λ_1 when the pseudohermitian structure θ is volume-normalized.     

E expansion for a Fermi gas at infinite scattering length

We show that there exists a systematic expansion around four spatial dimensions for Fermi gas in the unitarity regime. We perform the calculations to leading and next-to-leading orders in the expansion over E = 4-d, where d is the dimensionality of space. We find the ratio of chemical potential and Fermi energy to be mu/epsilon(F) =1/2 (E 3/2) + 1/16 (E 5/2) lnE -0.0246E (5/2) + ... and the ratio of the gap in the fermion quasiparticle spectrum and the chemical potential to be Delta/mu =2E(-1) - 0.691 + ... . The minimum of the fermion dispersion curve is located at |p|=(2mepsilon(0))(1/2), where epsilon_(0)/mu=2+O(E). Extrapolation to d=3 gives results consistent with Monte Carlo simulations.     

No-gap optimality conditions for an optimal control problem with pointwise control-state constraints

An optimal control problem with pointwise mixed constraints of the instationary three-dimensional Navier–Stokes–Voigt equations is considered. We derive second-order optimality conditions and show that there is no gap between second-order necessary optimality conditions and second-order sufficient optimality conditions. In addition, the second-order sufficient optimality conditions for the problem where the objective functional does not contain a Tikhonov regularization term are also discussed.