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11.
Lionel Thibault 《Annali di Matematica Pura ed Applicata》1980,125(1):157-192
Summary We introduce the concept of compactly lipschitzian functions taking values in a topological vector space F. We show that if F is finite dimensional the Lipschitz functions are compactly lipschitizian. We define the notions of generalized directional derivatives and subdifferentials for such functionsf taking values in an ordered topological vector space. It is shown that this notion of subdifferential coincides with the one of F. H. Clarke whenf is Lispchits and F=. Some formulas for this subdifferential concerning the cases of finite sum, composition, pointwise supremum and continuous sum are studied. 相似文献
12.
Mark S. Mashuta Lionel Cheruzel Robert M. Buchanan 《Acta Crystallographica. Section C, Structural Chemistry》2002,58(10):o629-o631
Cocrystallization of a polyimidazole compound with boric acid results in the formation of the title compound, C15H21N7·B(OH)3, which has an extensive hydrogen‐bonding network. The O?N(im) separations (im is imidazole) range from 2.6991 (15) to 2.7914 (14) Å, with O—H?N angles ranging from 170.6 (18) to 175 (2)°. In addition, symmetry‐related boric acid molecules form intermolecular hydrogen bonds, with an O?O distance of 2.7582 (14) Å, and symmetry‐related imidazole groups form π–π stacks, with a centroid‐to‐centroid separation of 3.533 Å. 相似文献
13.
Ali G. Ozkabak Surya N. Thakur Lionel Goodman 《International journal of quantum chemistry》1991,39(3):411-422
C6H6 Raman scattering activities calculated from harmonic model ab initio Hartree–Fock 6–311 ++ G(d, p) polarizability derivatives (and harmonic force fields calculated at the same level) accurately simulate experiment (to within 1% for the a1g modes). Accurate predictions are also made for the e2g modes (to within 5% for ν7 and ν9, and more poorly for ν6 and ν8 [in Fermi resonance with ν6 + ν1]) and for the e1g out-of-plane mode, ν10. Only the ν6 in-plane CCC bending mode scattering activity is found to be anomalous. Systematic variation of the basis set indicates that the benzene scattering activities and depolarization ratios are strongly dependent on inclusion of both carbon and hydrogen atom diffuse functions in the basis set. Predictions are also made for 12C6D6 and for unmeasured intensities in 13C6H6. Measurements of a1g mode scattering activities in the latter molecule are predicted to be useful in testing the harmonic Hartree–Fock Raman intensity model. 相似文献
14.
Treatment of the uranium(IV) complexes [{ML1(py)}2UIV] (M = Cu, Zn; L1 = N,N′-bis(3-hydroxysalicylidene)-1,3-propanediamine) with silver nitrate in pyridine led to the formation of the corresponding cationic uranium(V) species which were found to be thermally unstable and were converted back into the parent UIV complexes; no electron transfer was observed in solution between the UIV and UV compounds. In the crystals of [{ML1(py)}2UIV][{ML1(py)}2UV][NO3], the neutral UIV and cationic UV species are clearly identified by the distinct U–O distances. Similar reaction of [{ZnL2(py)}2UIV] [L2 = N,N′-bis(3-hydroxysalicylidene)-1,4-butanediamine] with AgNO3 gave crystals of [{ZnL2(py)}UV{ZnL2(py)2}][NO3] but the copper counterpart was not isolated. Crystals of [{ZnL1(py)}2UV][OTf] · THF (OTf = OSO2CF3) were obtained fortuitously from the reaction of [Zn(H2L1)] and U(OTf)3. 相似文献
15.
Pierre Beaujean Lionel Sanguinet Vincent Rodriguez Frdric Castet Benoît Champagne 《Molecules (Basel, Switzerland)》2022,27(9)
This contribution employs quantum chemistry methods to describe the variations of the second nonlinear optical responses of molecular switches based on benzazolo-oxazolidine (BOX) units, connected by π-linkers, along their successive opening/closing. Under the fully closed forms, all of them display negligible first hyperpolarizability (β) values. When one BOX is opened, which is sketched as C→O, a push–pull π-conjugated segment is formed, having the potential to enhance β and to set the depolarization ratio (DR) to its one-dimensional-like value (DR = 5). This is observed when only one BOX is open, either for the monoBOX species (C→O) or for the diBOX (CC→CO) and triBOX (CCC→CCO) compounds, i.e., when the remaining BOXs stay closed. The next BOX openings have much different effects. For the diBOXs, the second opening (CO→OO) is associated with a decrease of β, and this decrease is tuned by controlling the conformation of the π-linker, i.e., the centrosymmetry of the whole compound because β vanishes in centrosymmetric compounds. For the triBOXs, the second opening gives rise to a Λ-shape compound, with a negligible change of β, but a decrease of the DR whereas, along the third opening, β remains similar and the DR decreases to the typical value of octupolar systems (DR = 1.5). 相似文献
16.
17.
Lionel Mathelin Olivier P. Le Ma?tre 《Theoretical and Computational Fluid Dynamics》2012,26(5):415-434
This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization frameworks. It requires the resolution of two additional (dual) problems to yield the local error estimate. The stochastic error estimate can then be used to adapt the stochastic discretization. Different anisotropic refinement strategies are proposed, leading to a cost-efficient tool suitable for multi-dimensional problems of moderate stochastic dimension. The adaptive strategies allow both for refinement and coarsening of the stochastic discretization, as needed to satisfy a prescribed error tolerance. The adaptive strategies were successfully tested on a model for the hydrogen oxidation in supercritical conditions having 8 random parameters. The proposed methodologies are however general enough to be also applicable for a wide class of models such as uncertain fluid flows. 相似文献
18.
Hong-Peng Jia John C. Forgie Shi-Xia Liu Lionel Sanguinet Eric Levillain Franck Le Derf Marc Sallé Antonia Neels Peter J. Skabara Silvio Decurtins 《Tetrahedron》2012,68(5):1590-1594
A tetrathiafulvalene donor has been annulated to 2,3-di(1H-2-pyrrolyl)quinoxaline affording a new chemosensor 1, which shows a unique optical selectivity and reactivity for the fluoride ion over other anions in CH2Cl2 leading to a colorimetric response. Electrochemical polymerization of 1 occurred in the presence of fluoride. 相似文献
19.
We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in ? d . Any site with at least 2d particles then topples by sending one particle to each neighbor. We find that with constant background height h≤2d?2, the diameter of the set of sites that topple has order n 1/d . This was previously known only for h<d. Our proof uses a strong form of the least action principle for sandpiles, and a novel method of background modification. We can extend this diameter bound to certain backgrounds in which an arbitrarily high fraction of sites have height 2d?1. On the other hand, we show that if the background height 2d?2 is augmented by 1 at an arbitrarily small fraction of sites chosen independently at random, then adding finitely many particles creates an explosion (a sandpile that never stabilizes). 相似文献
20.
Dr. Tran Quang Hung Dr. Ferial Terki Dr. Souleymane Kamara Mourad Dehbaoui Prof. Salam Charar Brajalal Sinha Prof. CheolGi Kim Dr. Philippe Gandit Il'ya A. Gural'skiy Dr. Gabor Molnar Dr. Lionel Salmon Dr. Helena J. Shepherd Dr. Azzedine Bousseksou 《Angewandte Chemie (International ed. in English)》2013,52(4):1058-1058