On variational inequalities over polyhedral sets

Mathematical Programming - The results on regularity behavior of solutions to variational inequalities over polyhedral sets proved in a series of papers by Robinson, Ralph and Dontchev-Rockafellar...     

Facile Separation,Spectroscopic Identification,and Electrochemical Properties of Higher Trifluoromethylated Derivatives of [70]Fullerene

We survey the structure and electronic properties of the family of higher trifluoromethylated C₇₀(CF₃)_n molecules with n=14, 16, 18, and 20. Twenty‐two available compounds, of which thirteen are newly obtained and characterized, demonstrate the broad diversity of π‐system topologies, which enabled us to study the interplay between the CF₃ addition pattern and the electronic properties. UV/Vis spectroscopic and cyclic voltammetric studies demonstrate the importance of the exact addition pattern rather than the plain number of addends. Of particular interest is the skew pentagonal pyramid (SPP) addition pattern, which enables formation of closed‐shell cyclopentadienyl anions C₇₀(CF₃)_{n? 1} ^? through CF₃ detachment upon electron transfer. A detailed study of the process is presented for a SPP‐C₇₀(CF₃)₁₆ where potentiostatic electrolysis at the second reduction potential gives C₇₀(CF₃)₁₅^? oxidizable to a persistent C₇₀(CF₃)₁₅^· radical. Together with the literature data for the lower C₇₀(CF₃)_n compounds with n=2–12, the present results show good correlation between the experimental boundary level positions and the DFT predictions. The compounds turn out to be electron acceptor molecular semiconductors with experimental LUMO energies and HOMO–LUMO gaps within the ranges of ?4.3 to ?3.7 eV and 1.6 to 3.3 eV, respectively, depending on the shape of the conjugated fragments. The HOMO levels fall within the range of ?5.6 to ?6.9 eV and show linear correlation with the number of addends.     

Limiting subhessians, limiting subjets and their calculus

We study calculus rules for limiting subjets of order two. These subjets are obtained as limits of sequences of subjets, a subjet of a function at some point being the Taylor expansion of a twice differentiable function which minorizes and coincides with at . These calculus rules are deduced from approximate (or fuzzy) calculus rules for subjets of order two. In turn, these rules are consequences of delicate results of Crandall-Ishii-Lions. We point out the similarities and the differences with the case of first order limiting subdifferentials.

     

Synthesis, structure and theoretical study of mixed fluoro-trifluoromethyl derivatives of C60. Molecular structures of C60F18(CF3)6 and C60F16(CF3)6

A series of novel mixed C60Fn(CF3)m compounds has been produced by trifluoromethylation of C60F18 with CF3I in ampoules at 380-420 degrees C. Two of these compounds, C60F18(CF3)6 and C60F16(CF3)6, have been characterized by X-ray crystallography, which has revealed addition of six CF3 groups to the C3v-C60F18 for the former and replacement/elimination of two outermost F atoms in the latter. Quantum chemical calculations have been employed to predict the most stable possible isomers of C60F16/18(CF3)6 in order to rationalize the experimental results.     

New isomers of trifluoromethylated fullerene: C60(CF3)12 and C60(CF3)14

HPLC separation of the products of high-temperature reaction of a sublimed mixture of C₆₀–C₇₀ (10: 1) with CF₃I in a sealed ampoule allowed isolation and determination of molecular structures (X-ray crystallography and ¹⁹F NMR) of two new isomers of C₆₀(CF₃)₁₂ and one isomer of C₆₀(CF₃)₁₄. These isomers are characterized by low relative formation energies, which suggests that the trifluoromethylation process is basically under the thermodynamic control.     

Synthesis of 1,4,6,10-tetraazaadamantane quaternary derivatives

Methods for the preparation of stable 1,4,6,10-tetraazaadamantane quaternary derivatives were developed based on quaternization of a tertiary nitrogen atom in tris(β-oximinoalkyl)amines or isomeric 4,6,10-trihydroxy-1,4,6,10-tetraazaadamantanes. This process constitutes a convenient approach to the introduction of a hydrophilic 1,4,6,10-tetraazaadamantane moiety into lipophilic molecules in order to increase their solubility in water. 4,6,10-Trihydroxy-1,4,6,10-tetraazaadamantane N-oxide was synthesized by the oxidation of the tertiary nitrogen atom in the tris-oxime and subsequent intramolecular cyclotrimerization of the oximino groups. Quantum chemical calculations showed that the quaternization of the annular nitrogen atom led to a considerable stabilization of tetraazaadamantane framework as compared to the open-chain form of tris-oxime.     

The former "C60F16" is actually a double-caged adduct: (C60F16)(C60)

X-ray diffraction study of the substance originally believed to be C(60)F(16) reveals a double-caged structure, (C(60)F(16))(C(60)); MALDI mass spectra, 19F NMR spectral data and reasons for stability are discussed.     

A parallel spectral Fourier–Nonlinear Galerkin algorithm for simulation of turbulence

We present a high-order parallel algorithm, which requires only the minimum interprocessor communication dictated by the physical nature of the problem at hand. The parallelization is achieved by domain decomposition. The discretization in space is performed using the Local Fourier Basis method. The continuity conditions on the interfaces are enforced by adding homogeneous solutions. Such solutions often have fast decay properties, which can be utilized to minimize interprocessor communication. In effect, the predominant part of the computation is performed independently in the subdomains (processors) or using only local communication. A novel element of the present parallel algorithm is the incorporation of a Nonlinear Galerkin strategy to accelerate the computation and stabilize the time integration process. The basic idea of this approach consists of decomposition of the variables into large scale and small scale components with different treatment of these large and small scales. The combination of the Multidomain Fourier techniques with the Nonlinear Galerkin (NLG) algorithm is applied here to solve incompressible Navier–Stokes equations. Results are presented on direct numerical simulation of two-dimensional homogeneous turbulence using the NLG method. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 699–715, 1997