Uniqueness and nondegeneracy for some nonlinear elliptic problems in a ball

In this paper we study the uniqueness and nondegeneracy of positive solutions of nonlinear problems of the type Δ_pu+f(r,u)=0 in the unit ball B, u=0 on ∂B. Here Δ_p denotes the p Laplace operator Δ_p=div(|∇u|^p−2∇u), p>1. The main ideas rely on the Maximum Principle and an implicit function theorem that we derive in a suitable weighted space. This space is essential to deal with the case p≠2.     

Some aspects of the high resolution mass spectra of toluene-p-sulphonamides

The cracking patterns of twenty five toluene-p-sulphonamides have been studied. In certain cases an abundant [M ? SO₂] ion is detected: the structural features associated with this phenomenon are discussed.     

Non-existence of vortices in the small density region of a condensate

In this paper, we answer a question raised by Lev Pitaevskii and prove that the ground state of the Gross-Pitaevskii energy describing a Bose-Einstein condensate in a rotationally symmetric trap at low rotation does not have vortices in the low density region. Therefore, the first ground state with vortices has its vortices in the bulk. In fact we prove something stronger, which is that the ground state for the model at low and moderate rotations is equal to the ground state in a condensate with no rotation. This is obtained by proving that for small rotational velocities, the ground state is multiple of the ground state with zero rotation. We rely on sharp bounds of the decay of the wave function combined with weighted Jacobian estimates.     

Highly Stereoselective Synthesis of Primary, Secondary, and Tertiary α-S-Sialosides under Lewis Acidic Conditions

N-Acetyl 4-O,5-N-oxazolidinone protected sialyl phosphates of either anomeric configuration are excellent donors for the formation of α-S-sialosides at -78 °C in dichloromethane with primary, secondary, and tertiary thiols including galactose 3-, 4-, and 6-thiols. The reactions, which proceed under typical Lewis acid promoted glycosylation conditions, are highly α-selective and do not suffer from competing elimination of the phosphate.     

Excited State Properties of Lanthanide(III) Complexes with a Nonadentate Bispidine Ligand

Eu^III, Tb^III, Gd^III and Yb^III complexes of the nonadentate bispidine derivative L² (bispidine=3,7-diazabicyclo[3.3.1]nonane) were successfully synthesized and their emission properties studied. The X-ray crystallography reveals full encapsulation by the nonadentate ligand L² that enforces to all Ln^III cations a common highly symmetrical capped square antiprismatic (CSAPR) coordination geometry (pseudo C_4v symmetry). The well-resolved identical emission spectra in solid state and in solution confirm equal structures in both media. As therefore expected, this results in long-lived excited states and high emission quantum yields ([Eu^IIIL²]⁺, H₂O, 298 K, τ=1.51 ms, ϕ=0.35; [Tb^IIIL²]⁺, H₂O, 298 K, τ=1.95 ms, ϕ=0.68). Together with the very high kinetic and thermodynamic stabilities, these complexes are a possible basis for interesting biological probes.     

On the minimizers of the Ginzburg-Landau energy for high kappa: the axially symmetric case

The Ginzburg-Landau theory of superconductivity is examined in the case of a special geometry of the sample, the infinite cylinder. We restrict to axially symmetric solutions and consider models with and without vortices. First putting the Ginzburg-Landau parameter κ formally equal to infinity, the existence of a minimizer of this reduced Ginzburg-Landau energy is proved. Then asymptotic behaviour for large κ of minimizers of the full Ginzburg-Landau energy is analyzed and different convergence results are obtained. Our main result states that, when κ is large, the minimum of the energy is reached when there are about κ vortices at the center of the cylinder. Numerical computations illustrate the various behaviours.     

Compositional elucidation of heavy petroleum base oil by GC × GC‐EI/PI/CI/FI‐TOFMS

Comprehensive two‐dimensional gas chromatography (GC × GC) coupled to time‐of‐flight mass spectrometry is a powerful separation tool for complex petroleum product analysis. However, the most commonly used electron ionization (EI) technique often makes the identification of the majority of hydrocarbons impossible due to the exhaustive fragmentation and lack of molecular ion preservation, prompting the need of soft‐ionization energies. In this study, three different soft‐ionization techniques including photo ionization (PI), chemical ionization (CI), and field ionization (FI) were compared against EI to elucidate their relative capabilities to reveal different base oil hydrocarbon classes. Compared with EI (70 eV), PI (10.8 eV) retained significant molecular ion (M^+·) information for a large number of isomeric species including branched‐alkanes and saturated monocyclic hydrocarbons along with unique fragmentation patterns. However, for bicyclic/polycyclic naphthenic and aromatic compounds, EI played upper hand by retaining molecular as well as fragment ions to identify the species, whereas PI exhibited mainly molecular ion signals. On the other hand, CI revealed selectivity towards different base oil groups, particularly for steranes, sulfur‐containing thiophenes, and esters, yielding protonated molecular ions (M + H)⁺ for unsaturated and hydride abstracted ions (M‐H⁺) for saturated hydrocarbons. FI, as expected, generated intact molecular ions (M^+·) irrespective to the base oil chemical classes. It allowed elemental composition by TOFMS with a mass resolving power up to 8000 (FWHM) and a mass accuracy of 1 mDa, leading to the calculation of heteroatomic content, double bond equivalency, and carbon number of the compounds. The qualitative and quantitative results presented herein offer a unique perspective into the detailed comparison of different ionization techniques corresponding to several hydrocarbon classes.     

Non-Heme FeII Diastereomeric Complexes Bearing a Hexadentate Ligand: Unexpected Consequences for the Spin State and Catalytic Oxidation Properties

The reactivity and selectivity of non-heme Fe^II complexes as oxidation catalysts can be substantially modified by alteration of the ligand backbone or introduction of various substituents. In comparison with the hexadentate ligand N,N,N′,N′-tetrakis(pyridin-2-ylmethyl)ethane-1,2-diamine (TPEN), N,N′-bis[1-(pyridin-2-yl)ethyl]-N,N′-bis(pyridin-2-ylmethyl)ethane-1,2-diamine (_2MeL₆²) has a methyl group on two of the four picolyl positions. Fe^II complexation by _2MeL₆² yields two diastereomeric complexes with very similar structures, which only differ in the axial/equatorial positions occupied by the methylated pyridyl groups. In solution, these two isomers exhibit different magnetic behaviors. Whereas one isomer exhibits temperature-dependent spin-state conversion between the S=0 and S=2 states, the other is more reluctant towards this spin-state equilibrium and is essentially diamagnetic at room temperature. Their catalytic properties for the oxidation of anisole by H₂O₂ are very different and correlate with their magnetic properties, which reflect their lability/inertness. These different properties most likely depend on the different steric constraints of the methylated pyridyl groups in the two complexes.     

Radial Symmetry of Overdetermined Boundary-Value Problems in Exterior Domains

In this paper, we extend a classical result by J. Serrin [15] to exterior domains , where Ω is a bounded domain. We prove, under some hypotheses on f, that if there exists a solution of satisfying the overdetermined boundary conditions that and u are constant on , and such that , then the domain Ω is a ball. Under different assumptions on f, this result has been obtained by W. Reichel in [13]. The main result here covers new cases like with . When Ω is a ball, almost the same proof allows us to derive the symmetry of positive bounded solutions satisfying only the Dirichlet condition that u is constant on . Our method relies on Kelvin transforms, various forms of the maximum principle and the device of moving planes up to a critical position. (Accepted May 30, 1997)