Pluriharmonic Clark measures and analogs of model spaces

Let $B_d$ denote the unit ball of ${\mathbb{C}}^d$, $d\ge 1$. Given an inner function $I:B_d\to B_1$, we study the corresponding family ${\sigma }_{\alpha }[I]$, $\alpha \in ?B_1$, of pluriharmonic Clark measures on the complex sphere. We introduce and investigate related unitary operators $U_{\alpha }$ mapping analogs of model spaces onto $L^2({\sigma }_{\alpha })$, $\alpha \in ?B_1$. In particular, we explicitly characterize the set of $U_{\alpha }^{?}f$ such that $f{\sigma }_{\alpha }$ is a pluriharmonic measure.     

The IR spectra of Mg5C(CO) complexes on the (0 0 1) surfaces of polycrystalline and single crystal MgO

The FTIR spectroscopy of carbon monoxide adsorbed on polycrystalline MgO smoke has been investigated as a function of the CO equilibrium pressure at constant temperature (60 K) (optical isotherm) and of the temperature (in the 300–60 K range) at constant CO pressure (optical isobar). In both cases the spectra fully reproduce those of CO adsorbed on the (0 0 1) surface of UHV cleaved single crystals [Heidberg et al., Surf. Sci. 331–333 (1995) 1467]. This result, never attained in previous investigations on dispersed MgO, contribute to bridging the gap which is commonly supposed to exist between surface science and the study of “real” (defective) systems. Depending on the surface coverage θ the main spectral features due to the CO/MgO smoke interaction are a single band shifting from 2157.5 (at θ→0) to 2150.2 cm⁻¹ (at θ=1/4) or a triplet, at 2151.5, 2137.2 and 2132.4 cm⁻¹ (at θ>1/4). These manifestations are due to the ν(CO) modes of Mg_5C²⁺· · · CO adducts formed on the (0 0 1) terminations of the cubic MgO smoke microcrystals. The formation of the CO monolayer is occurring in two different phases: (i) a first phase with CO oscillators perpendicularly oriented to the surface (2157–2150 cm⁻¹) and (ii) a second phase constituted by an array of coexisting perpendicular and tilted species (triplet at 2151.5, 2137.2 and 2132.4 cm⁻¹). A much weaker feature at 2167.5–2164 cm⁻¹ is assigned to Mg_4C²⁺· · · CO adducts at the edges of the microcrystals. The heat of adsorption of the perpendicular Mg_5C²⁺· · · CO complex in the first phase has been estimated from the optical isobar and results to be 11 kJ mol⁻¹.     

Near-infrared fluorophores containing benzo[c]heterocycle subunits

The syntheses and spectroscopic properties of eight new push-pull-type near-infrared fluorophores that contain either isobenzofuran or isothianaphthene subunits are presented. The isobenzofuran dyes demonstrate significantly red-shifted absorption compared with their isothianaphthene counterparts, which is attributed to isobenzofuran's more potent pro-quinoidal character.     

Thermodynamic Parameters of Single‐ or Multi‐Band Superconductors Derived from Self‐Field Critical Currents

Key questions for any superconductor include: what is its maximum dissipation‐free electrical current (its ‘critical current') and can this be used to extract fundamental thermodynamic parameters? Present models focus on depinning of magnetic vortices and implicate materials engineering to maximise pinning performance. But recently we showed that the self‐field critical current for thin films is a universal property, independent of microstructure, controlled only by the penetration depth. Here, using an extended BCS‐like model, we calculate the penetration depth from the temperature dependence of the superconducting energy gap thus allowing us to fit self‐field critical current data. In this way we extract from the T ‐dependent gap a set of key thermodynamic parameters, the ground‐state penetration depth, energy gap and jump in electronic specific heat. Our fits to 79 available data sets, from zinc nanowires to compressed sulphur hydride with critical temperatures of 0.65 to 203 K, respectively, are excellent and the extracted parameters agree well with reported bulk values. Samples include thin films, wires or nanowires of single‐ or multi‐band s ‐wave and d ‐wave superconductors of either type I or type II. For multiband or multiphase samples we accurately recover individual band contributions and phase fractions.     

Discounted cost optimality problem: stability with respect to weak metrics

We find inequalities to estimate the stability (robustness) of a discounted cost optimization problem for discrete-time Markov control processes on a Borel state space. The one stage cost is allowed to be unbounded. Unlike the known results in this area we consider a perturbation of transition probabilities measured by the Kantorovich metric, closely related to the weak convergence. The results obtained make possible to estimate the vanishing rate of the stability index when approximation is made through empirical measures.     

Electronic and infrared absorption spectra of linear and cyclic C6+ in a neon matrix

Electronic and infrared absorption spectra of mass-selected C6+, generated by dissociative electron impact ionization of C6Cl6 and C6Br6, have been recorded in 6 K neon matrices. Linear and cyclic forms of C6+ have been observed. The 2Pig<--Chi2Piu electronic transition of linear C6+ has its origin band at 646 nm whereas for the (2) 2B2<--Chi2A1 system of the cyclic isomer it lies at 570 nm. An infrared active fundamental mode in the ground electronic state of C6+ is observed at 2092 and 1972 cm(-1) for the linear and cyclic isomer, respectively.     

Radial limits of inner functions and Bloch spaces

Let be an inner function in the unit ball , . Assume that

where and is the radial derivative. Then, for all , the set has a non-zero real Hausdorff -content, and it has a non-zero complex Hausdorff -content.

     

Discrete allyl complexes of group 3 metals and lanthanides

Allyl complexes based on group IIIb metals (Sc, Y, La) and lanthanides are reviewed. The diversity, synthesis, and main structural and reactivity features of discrete, well-defined homoleptic and pseudo-homoleptic neutral, anionic and cationic bis-, tris- and tetra(allyl)-lanthanide complexes, as well as heteroleptic allyl-lanthanidocenes and allyl-lanthanide complexes supported by non-Cp ligands are covered. Brief comments on the catalytic performances of some key compounds in polymerization processes are also provided.