Limit theorems in financial market models

Invariance principle states that a scaled simple random walk converges to the standard Brownian motion.In this article, we present a discrete time stochastic process, which reflects a microstructure of market dynamics, and prove a convergence to a scaling limit process with a drift term and a jump term. These terms are derived from a macroscopic condition on volumes traded in some time intervals. The mathematical tools for obtaining our results are Dobrushin-Hryniv theory and the method of cluster expansion developed in mathematical studies of statistical mechanics.     

Influence of intramolecular vibrations in charge redistribution at the pentacene-graphite interface

We have investigated the relation between the intramolecular vibrational modes of pentacene and the charge redistribution at the pentacene-graphite interface by using high-resolution electron-energy-loss-spectroscopy. The three main vibrational peaks shift to lower energies as the pentacene film thickness decreases. In order to discuss this energy shift, we have calculated the vibrational energies of a free pentacene molecule by changing its charge state. We have also calculated the vibrational energies of a pentacene molecule adsorbed on a graphite sheet by changing the pentacene-graphite distance. Taking the experimental and calculation results into account, we conclude that the observed energy shifts result from an intramolecular charge redistribution. The present results indicate that the effect of an intramolecular charge redistribution is essential to discuss the origin of an energy shift observed in a vibrational study of an organic molecule/substrate interface.     

Velocity vector measurement based on correlation process between low coherence interference outputs

Velocity vector measurement by using fiber-optic low coherence interferometers is proposed and demonstrated. The interference outputs between the reference and backscattered light from the probing points in the flow are correlation processed. The probing points can be specified and are set on the x-, y-, and z-axis in the flow by using the fiber-optic low coherence interferometers. The direction (angles from each axis) and absolute value of the flow velocity can be measured from peak positions of correlations.     

OXIDATION OF RIBOSE MOIETY OF ADENOSINE INDUCED BY IRRADIATION OF NEAR-UV LIGHT IN THE PRESENCE OF IRON(III) CHLORIDE

Abstract— Irradiation of near-UV light in the presence of FeCl₃ caused oxidation of adenosine with concomitant reduction of Fe(III) under either aerobic or anaerobic atmosphere. Major photoproducts were adenine and adenosine-5'-aldehyde, showing that oxidation took place mostly at the ribose moiety of adenosine. Detailed study showed that the reaction proceeded by the light absorption due to Fe(III) at 300-350 nm.     

Rattling in the Quadruple Perovskite CuCu3V4O12

Of particular interest is a peculiar motion of guest atoms or ions confined to nanospace in cage compounds, called rattling. While rattling provides unexplored physical properties through the guest–host interactions, it has only been observed in a very limited class of materials. Herein, we introduce an A‐site‐ordered quadruple perovskite, CuCu₃V₄O₁₂, as a new family of cage compounds. This novel AA′₃B₄O₁₂‐type perovskite has been obtained by a high‐pressure synthesis technique and structurally characterized to have cubic Im$\bar 3$ symmetry with an ionic model of Cu²⁺Cu²⁺₃V⁴⁺₄O₁₂. The thermal displacement parameter of the A‐site Cu²⁺ ion is as large as U_iso≈0.045 Ų at 300 K, indicating its large‐amplitude thermal oscillations in the oversized icosahedral cages. Remarkably, the presence of localized phonon modes associated with rattling of the A‐site Cu²⁺ ion manifests itself in the low‐temperature specific heat data. This work sheds new light on the structure–property relations in perovskites.     

Drastic difference in the photo-driven hydrogenation reactions of ruthenium complexes containing NAD model ligands

Successful control of photo-driven NAD(+)/NADH type hydrogenation reactions in ruthenium complexes has been accomplished by using a new NAD(+) model ligand with modulated distortion of the ligand taking advantage of the substituent effect.     

Two-photon absorption properties of two-dimensional π-conjugated chromophores: combined experimental and theoretical study

The two-photon absorption (TPA) properties of four TPEB [tetrakis(phenylethynyl)benzene] derivatives (TD, para, ortho, and meta) with different donor/acceptor substitution patterns have been investigated experimentally by the femtosecond open-aperture Z-scan method and theoretically by the time-dependent density-functional theory (TDDFT) method. The four compounds show relatively large TPA cross sections, and the all-donor substituted species (TD) displays the largest TPA cross-section σ(2) = 520 ± 30 GM. On the basis of the calculated electronic structure, TD shows no TPA band in the lower energy region of the spectrum because the transition density is concentrated on particular transitions due to the high symmetry of the molecular structure. The centrosymmetric donor-acceptor TPEB para shows excitations resulting from transitions centered on D-π-D and A-π-A moieties, as well as transition between the D-π-D and A-π-A moieties; this accounts for the broad nature of the TPA bands for this compound. Calculations for two noncentrosymmetric TPEBs (ortho and meta) reveal that the diminished TPA intensities of higher-energy bands result from destructive interference between the dipolar and three-state terms. The molecular orbitals (MOs) of the TPEBs are derivable with linear combinations of the MOs of the two crossing BPEB [bis(phenylethynyl)benzene] derivatives. Overall, the characteristics of the experimental spectra are well-described based on the theoretical analysis.     

Rhodium-catalyzed allyl transfer from homoallyl alcohols to aldehydes via retro-allylation followed by isomerization into ketones

Retro-allylation of homoallyl alcohol by rhodium catalysis occurs to generate allylrhodium species. This allylrhodium reacts with aldehydes to give the corresponding secondary alcohols in situ. Isomerization of these alcohols proceeds in the same pots to furnish the corresponding saturated ketones in good yields. [reaction: see text]     

Regio-controlled ring-opening polymerization of perfluoroalkyl-substituted epoxides

Highly fluorinated epoxides were polymerized under mild conditions regioregularly, which gave easy access to isotactic polymers by using optically pure epoxides.