On the transmission problems for the Oseen and Brinkman systems on Lipschitz domains in compact Riemannian manifolds

The purpose of this work is to show the well‐posedness in L²‐Sobolev spaces of the Poisson‐transmission problem for the Oseen and Brinkman systems on complementary Lipschitz domains in a compact Riemannian manifold. The Oseen system appears as a perturbation of order one of the Stokes system, given in terms of the Levi‐Civita connection, while the Brinkman system is a zero order perturbation of the Stokes system. The technical details of this paper rely on the layer potential theory for the Stokes system and the invertibility of some perturbed zero index Fredholm operators by a first order differential operator given in terms of the Levi‐Civita connection. The compactness of this differential operator requires to restrict ourselves to low dimensional compact Riemannian manifolds.     

Substituent Effects on Reduction Potentials of Meta-substituted and Para-substituted Benzylideneanilines

Effects of meta-substituent of 3,4'/4,3'/3,3'-substituted benzylideneanilines (XBAYs) on the electrochemical reduction potentials (E_(Red)) were investigated, in which 49 samples of target compounds were synthesized, and their reduction potentials were measured by cyclic voltammetry. The substituent effects on the E_(Red) of target compounds were analyzed and an optimality equation with four parameters (Hammett constant σ of X, Hammett constant σ of Y, excited-state substituent constant σ_CC^ex of X, and the substituent specific cross-interaction effect Δσ_CC^ex2 between X and Y) was obtained. The results show that the factors affecting the E_(Red) of 3,4'/4,3'/3,3'-substituted XBAYs are different from those of 4,4'-substituted XBAYs. For 3,4'/4,3'/3,3'-substituted XBAYs, σ(X) and σ(Y) must be employed, and the contribution of Δσ_CC^ex2 is important and not negligible. Compared with 4,4'-substituted XBAYs, X group contributes less to 3,4'/4,3'/3,3'-substituted XBAYs, while Y group contributes more to them. Additionally, it was observed that either para-substituted XBAYs or meta-substituted XBAYs, the substituent effects of X are larger than those of Y on the E_(Red) of substituted XBAYs.     

The traces of Bessel potentials on regular subsets of Carnot groups

We prove the direct theorem on the traces of the Bessel potentials L _p ^α defined on a Carnot group, on the regular closed subsets called Ahlfors d-sets. The result is convertible for integer α, i.e., for the Sobolev spaces W _p ^α (the converse trace theorem was proven in [24]). This theorem generalizes A. Johnsson and H. Wallin’s results [13] for Sobolev functions and Bessel potentials on the Euclidean space.     

Lutidyl Radical Photoelectron Spectra Reveal Additive Substituent Effects on Benzyl Derivatives’ Ionization Energy

Understanding how isomerism influences photoelectron spectra helps in the assignment and analysis of reactive mixtures, especially for heterocycles with numerous isomers. Threshold photoelectron spectra of lutidyl radical isomers, i. e., benzyl derivatives with a nitrogen heteroatom and a methyl substituent, are recorded using vacuum ultraviolet synchrotron radiation. The radicals are produced by flash pyrolysis from aminomethyl methylpyridine precursors. Experimental ionization energies are determined to be 7.54, 7.50, and 7.45 eV for 2,4-, 2,6- and 3,5-lutidyl, respectively, in excellent agreement with composite method calculations. Franck–Condon simulations aid the TPES assignment but are also shown to exhibit artifacts if large-amplitude motions, notably the methyl internal rotation are assumed to be active in the double harmonic approximation. Based on calculated adiabatic ionization energies (AIE) of benzyl, picolyl, and xylyl radicals, the N and CH₃ substituent effects are found to be additive, position-dependent and decrease in the para>ortho≳meta order in magnitude with the nitrogen heteroatom increasing and the methyl substituent decreasing the AIE. These effects are discussed in light of the charge distribution upon ionization. The additivity of the substituent effects also helps predict the influence of substituents on the binding energy of the unpaired electron in analogous radicals.     

Specific ion effects: Interaction between nanoparticles in electrolyte solutions

Dependence of colloidal interactions on salt identity, observed frequently in experiments, can be accounted for once ion specific non-electrostatic forces are included in the theory. Ability to predict the effect of added salt on the phase diagram of colloid dispersions is essential for the design of processes involving nanocolloids. The Ornstein–Zernike equation with hypernetted chain closure approximation provides a viable first estimate for the potential of mean force between ionized nanoparticles like alumina aggregates in aqueous electrolytes subject to dispersion interactions with hydrated simple ions. Calculated potentials of mean force enable the prediction of osmotic second virial coefficients and phase diagrams showing a dramatic dependence on ion type. The choice of salt therefore provides an efficient, non-intrusive way to tune the phase behavior of nanoparticle dispersions.     

Structural and electronic properties of stable Aun (n = 2–13) clusters: A density functional study

All-electron scalar relativistic calculations have been performed to investigate the electronic structures of neutral gold clusters (Au_n, n = 2–13) in the gas phase using density functional theory with the generalized gradient approximation. Full geometry optimizations of topologically different clusters and clusters belonging to different symmetry groups have been carried out. Binding energies, ionization potentials, electron affinities, and chemical hardness values are calculated and they are found to be comparable with the available experimental and theoretical results. The most stable structure of each of the cluster has a two-dimensional planar configuration. A three dimensional distorted Y shaped structure (4b) for Au₄, a tri-capped triangle (6b), a chair (6f), and a see-saw structure (6j) for Au₆, an eclipsed sandwich structure (7g) for Au₇, a condensed trigonal bipyramid (9e) and a boat shaped structure (9f) for Au₉, a staggered sandwich (11c) and an eclipsed sandwich structure (11d) for Au₁₁, a ladderane structure (12d) for Au₁₂, and a staggered (13d) and a distorted sandwich structure (13e) for Au₁₃ are characterized for the first time in this work.     

The failure of the Lennard–Jones n,m intermolecular potentials to represent some common gases

It is shown that none of the Lennard–Jones n,m intermolecular potentials can represent any of the gases, neon, argon, krypton, xenon, nitrogen, oxygen, hydrogen, methane, ethane, and propane. In particular, the second and third virial coefficients B^* and C^*, and , computed for these potentials cannot describe the experimental behavior of B, C, and V_T. This is demonstrated by their inability to match the temperature dependence of the dimensionless variable, , thus failing to satisfy a necessary condition for representing the PVT behavior of these gases.     

Ab initio study of the spectroscopy of the XΠ electronic ground states of CNO and NCO

The X²Π electronic ground states of NCO and CNO have been investigated by complete ab initio methods. The dependence of the Renner-Teller parameters, ? and , on the ab initio method and on the basis set have been studied. These parameters have also been compared to experimental data for NCO. The potential energy surfaces of the X²Π state have been determined by the MRCI method and the cc-pVQZ basis set for NCO and CNO. The rovibronic levels of both isomers have been calculated variationally up to approximatively 4000 cm⁻¹ for J ? 5/2 and K ? 2, with the inclusion of the geometry dependence of the spin-orbit coupling. The agreement with experimental data obtained for NCO is remarkable. A similar accuracy for the ab initio rovibronic levels of CNO is expected since no experimental data exists for this isomer.     

Equilibrium points of logarithmic potentials on convex domains

Let be a convex domain in . Let be summable constants and let . If the converge sufficiently rapidly to from within an appropriate Stolz angle, then the function has infinitely many zeros in . An example shows that the hypotheses on the are not redundant and that two recently advanced conjectures are false.