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1.
AbstractRealistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries. 相似文献
2.
3.
The paper proves the existence of solutions to the magneto-hydrodynamics equations driven by random exterior forcing terms
both in the velocity and in the magnetic field. The existence and uniqueness of an invariant measure is also obtained via
coupling methods. 相似文献
4.
The generation of acetoxyphenylketene (4) in the cold in the presence of biacetyl yields the single β-lactone , which undergoes a novel rearrangement to the tricyclic orthoester lactone above 130°. 相似文献
5.
Similarity measures between pairs of molecular wave functions are described. They are based on the geometrical structure of the LCAO–MO framework and upon multivariate analysis ideas. The theoretical framework is presented, and formulae for some integrals needed are given. Two main measures, distance and correlation coefficients, are used. Distance and correlation matrices induce relationships in the whole MO set, which can be depicted through minimal spanning tree techniques. Furthermore, principal component analysis allows a two-dimensional visualization of the Mo manifold geometrical relationships. Various examples are given in order to obtain information on how basis set, environment, excitation, bending, stretching, and electronegativity affect the induced order. For this purpose “ab initio” SCF–LCAO–MO calculations with double- and single-zeta quality basis sets have been used for various simple molecular structures: H2O, NH3, CH4, N2, O2, C2, NO, CN, and CO. The results obtained can open the way to LCAO–MO taxonomy. Using this information, other areas of interest are connected with similarity measures (SCF and CI , localization procedures, etc.), proving in this manner their potential utility. 相似文献
6.
Transition structures associated with the C-C bond-formation step of the proline-catalyzed intermolecular aldol reaction
between acetone and isobutyraldehyde have been studies using density functional theory methods at the B3LYP/6-31G** computational
level. A continuum model has been selected to represent solvent effects. For this step, which is the stereocontrolling and
rate-determining step, four reactive channels corresponding to the syn and anti arrangement of the active methylene of the
enamine relative to the carboxylic acid group of l-proline and the re and si attack modes to both faces of the aldehyde carbonyl group have been analyzed. The B3LYP/6-31G**
energies are in good agreement with experiment, allowing us to explain the origin of the catalysis and stereoselectivity for
these proline-catalyzed aldol reactions.
Received: 2 April 2002 / Accepted: 18 July 2002 / Published online: 11 October 2002
Acknowledgements. This work was supported by research funds provided by the Ministerio de Educación y Cultura of the Spanish Government by
DGICYT (project PB98–1429). All the calculations were performed on a Cray–Silicon Graphics Origin 2000 of the Servicio de
Informática de la Universidad de Valencia. We are most indebted to this center for providing us with computer capabilities.
Correspondence to: L. R. Domingo e-mail: domingo@utopia.uv.es 相似文献
7.
Guldi DM Hirsch A Scheloske M Dietel E Troisi A Zerbetto F Prato M 《Chemistry (Weinheim an der Bergstrasse, Germany)》2003,9(20):4968-4979
Control over the interchromophore separation, their angular relationship, and the spatial overlap of their electronic clouds in several ZnP-C(60) dyads (ZnP=zinc porphyrin) is used to modulate the rates of intramolecular electron transfer. For the first time, a detailed analysis of the charge transfer absorption and emission spectra, time-dependent spectroscopic measurements, and molecular dynamics simulations prove quantitatively that the same two moieties can produce widely different electron-transfer regimes. This investigation also shows that the combination of ZnP and C(60) consistently produces charge recombination in the inverted Marcus region, with reorganization energies that are remarkably low, regardless of the solvent polarity. The time constants of electron transfer range from the mus to the ps regime, the electronic couplings from a few tens to several hundreds of cm(-1), and the reorganization energies remain below 0.54 eV and can be as low as 0.16 eV. 相似文献
8.
Philippe Gerbier Daniel Ruiz-Molina Neus Domingo David B. Amabilino José Vidal-Gancedo Javier Tejada David N. Hendrickson Jaume Veciana 《Monatshefte für Chemie / Chemical Monthly》2003,134(2):265-276
Summary. A new modified approach for the synthesis of Mn12 clusters, based on the use of complex [Mn12O12(O2C
t
Bu)16(H2O)4] (2) as starting material to promote the acidic ligand replacement, is presented here. This new synthetic approach allowed us
to obtain complex [Mn12O12(O2CC6H4N(O•)
t
Bu)16(H2O)4] (3), whose preparation remained elusive by direct replacement of the acetate groups of Mn12Ac (1). Complex 3 bearing open-shell radical units, was prepared to increase the total spin number of its ground state, and consequently, to
increase T
B
, with the expectation that the radical ligands may couple ferromagnetically with the Mn12 core. Unfortunately, magnetic measurements of complex 3 revealed that the sixteen radical carboxylate ligands interact antiferromagnetically with the Mn12 core to yield a S = 2 magnetic ground state.
Corresponding author. E-mail: vecianaj@icmab.es
Received March 27, 2002; accepted May 2, 2002 相似文献
9.
Organic functionalization of carbon nanotubes 总被引:11,自引:0,他引:11
Georgakilas V Kordatos K Prato M Guldi DM Holzinger M Hirsch A 《Journal of the American Chemical Society》2002,124(5):760-761
A very general and versatile method for functionalizing different types of carbon nanotubes is described, using the 1,3-dipolar cycloaddition of azomethine ylides. Approximately one organic group per 100 carbon atoms of the nanotube is introduced, to yield remakably soluble bundles of nanotubes, as seen in transmission electron micrographs. The solubilization of the nanotubes generates a novel, interesting class of materials, which combines the properties of the nanotubes and the organic moiety, thus offering new opportunities for applications in materials science, including the preparation of nanocomposites. 相似文献
10.
Thehomotopical rank of a mapf:M →N is, by definition, min{dimg(M) ¦g homotopic tof}. We give upper bounds for this invariant whenM is compact Kähler andN is a compact discrete quotient of a classical symmetric space, e.g., the space of positive definite matrices. In many cases the upper bound is sharp and is attained by geodesic immersions of locally hermitian symmetric spaces. An example is constructed (Section 9) to show that there do, in addition, exist harmonic maps of quite a different character. A byproduct is construction of an algebraic surface with large and interesting fundamental group. Finally, a criterion for lifting harmonic maps to holomorphic ones is given, as is a factorization theorem for representations of the fundamental group of a compact Kähler manifold. The technique for the main result is a combination of harmonic map theory, algebra, and combinatorics; it follows the path pioneered by Siu in his ridigity theorem and later extended by Sampson. 相似文献