Pricing American options with uncertain volatility through stochastic linear complementarity models

We consider the problem of pricing American options with uncertain volatility and propose two deterministic formulations based on the expected value method and the expected residual minimization method for a stochastic complementarity problem. We give sufficient conditions that ensure the existence of a solution of those deterministic formulations. Furthermore we show numerical results and discuss the usefulness of the proposed approach.     

Non-Gaussian fluctuations resulting from power-law trapping in a lipid bilayer

Anomalous diffusion in lipid bilayers is usually attributed to viscoelastic behavior. We compute the scaling exponent of relative fluctuations of the time-averaged mean square displacement in a lipid bilayer, by using a molecular dynamics simulation. According to the continuous time random walk theory, this exponent indicates non-Gaussian behavior caused by a power-law trapping time. Our results provide the first evidence that a lipid bilayer has not only viscoelastic properties but also trapping times distributed according to a power law.     

An M2L4 molecular capsule with an anthracene shell: encapsulation of large guests up to 1 nm

A new M(2)L(4) molecular capsule with an aromatic shell was prepared using two Pd(II) ions and four bisanthracene ligands. The self-assembled capsule possesses a cavity with a diameter of ~1 nm that can encapsulate medium-sized spherical and planar molecules as well as a very large molecule (C(60)) in quantitative yields. The encapsulated guests are fully segregated and shielded from the external environment by the large anthracene panels.     

Direct arylation of polycyclic aromatic hydrocarbons through palladium catalysis

We have discovered that the combination of Pd(OAc)(2)/o-chloranil can catalyze the direct C-H bond arylation of polycyclic aromatic hydrocarbons (PAHs) with arylboroxins that occurs selectively at the K-region. The sequential integration of Pd-catalyzed direct arylation of PAHs and FeCl(3)-mediated cyclodehydrogenation is effective in rapidly extending a parent PAH π-system with high directionality.     

Catalytic asymmetric oxidation of cyclic dithioacetals: highly diastereo- and enantioselective synthesis of the S-oxides by a chiral aluminum(salalen) complex

Aluminum(salalen) complex 1 [salalen = half-reduced salen, salen = N,N'-ethylenebis(salicylideneiminato)] was found to be a highly efficient catalyst for asymmetric oxidation of cyclic dithioacetals in the presence of 30% hydrogen peroxide as an oxidant. In the reaction of a series of 2-substituted 1,3-dithianes bearing alkyl, alkenyl, alkynyl, and aryl groups as the substituent, the trans-monoxides were obtained in high yields with 19:1 → >20:1 dr (diastereomeric ratio) and 98-99% ee (enamtiomeric excess). The reaction of nonsubstituted 1,3-dithiane also proceeded in a highly enantioselective manner to give the monoxide with a small formation of the trans-1,3-dioxide, an overoxidation product. Five-membered 1,3-dithiolanes and seven-membered 1,3-dithiepanes also underwent oxidation to give monoxides with high diastereo- and enantioselectivity. It was found that the equilibrium between the two chairlike conformers of dithianes has relevance to the observed diastereoselectivity in the first oxidation process, and the dioxide formation in the oxidation of 1,3-dithiane and its stereochemistry also can be explained by the conformational equilibrium of the product monoxide.     

Global aspects of turbulence induced by heteroclinic cycles in competitive diffusion Lotka-Volterra equation

This paper presents detailed numerical results of the competitive diffusion Lotka-Volterra equation (May-Leonard type). First, we derive the global phase diagrams of attractors in the parameter space including the system size, where transition lines between simple attractors are clearly obtained in accordance with the results of linear stability analysis, but the transition borders become complex when multi-basin structures appear. The complex aspects of the transition borders are studied in the case when the system size decreases. Next, we show the statistical aspects of the turbulence with special attention to the onset of the supercritical Hopf bifurcation. Several characteristic quantities, such as correlation length, correlation time, Lyapunov spectra and Lyapunov dimension, are investigated in detail near the onset of turbulence. Our data show the critical scaling law near the onset only in the restricted parameter domain. However even when the critical indices are not determined accurately, it is shown that the empirical scaling relations are obtained in a wide parameter domain far from the onset point and those scaling indices satisfy several relations. These scaling relations are discussed in comparison with the result derived by the phase reduction method. Lastly, we make a conjecture about the stability of an ecosystem based on the bifurcation diagram: the ecosystem obeying the Lotka-Volterra equation in the case of May-Leonard type is stabilized more as the system size increases.     

Surface morphology and crystalline structure of high-stable polycrystalline transparent conductive zinc oxide films

Surface morphology and crystalline structure of high-stable zinc oxide films were evaluated by atomic force microscopy, scanning electron microscopy and X-ray diffraction (XRD) measurements. AFM measurement revealed that the higher stable samples have smaller roughness (average roughness and root mean square) parameters than the lower stable samples. Furthermore, in-plane XRD measurement showed that the crystallite size of high stable samples is smaller than that of the low stable samples. These results indicate that the larger surface area and lower film density deteriorates the stability of zinc oxide films through the adsorption and reaction of water or oxygen molecules. They also suggest that we can prepare the high stable zinc oxide transparent electrode films by controlling the surface morphology.     

Optical emission spectroscopy by Ar ion sputtering of Ti surface under O2 environment

Visible light emission from atoms and ions sputtered on a polycrystalline Ti surface was observed under irradiation of 30 keV Ar³⁺ ions. A number of atomic lines of Ti I and II were observed in the wavelength of 250-850 nm. The intensity of Ti II emission increased 1.3-5.6 times by introducing oxygen molecules at a pressure of 5.8 × 10⁻⁵ Pa, whereas that of Ti I decreased 0.5-0.8 times. Factors enhancing or reducing photon intensities were plotted as a function of energy of the corresponding electrons in the excited states for Ti atoms and Ti⁺ ions.     

Two‐Dimensional Perovskite Oxynitride K2LaTa2O6N with an H+/K+ Exchangeability in Aqueous Solution Forming a Stable Photocatalyst for Visible‐Light H2 Evolution

Undoped layered oxynitrides have not been considered as promising H₂‐evolution photocatalysts because of the low chemical stability of oxynitrides in aqueous solution. Here, we demonstrate the synthesis of a new layered perovskite oxynitride, K₂LaTa₂O₆N, as an exceptional example of a water‐tolerant photocatalyst for H₂ evolution under visible light. The material underwent in‐situ H⁺/K⁺ exchange in aqueous solution while keeping its visible‐light‐absorption capability. Protonated K₂LaTa₂O₆N, modified with an Ir cocatalyst, exhibited excellent catalytic activity toward H₂ evolution in the presence of I^? as an electron donor and under visible light; the activity was six times higher than Pt/ZrO₂/TaON, one of the best‐performing oxynitride photocatalysts for H₂ evolution. Overall water splitting was also achieved using the Ir‐loaded, protonated K₂LaTa₂O₆N in combination with Cs‐modified Pt/WO₃ as an O₂ evolution photocatalyst in the presence of an I₃^?/I^? shuttle redox couple.