Numerical integration of the Ostrovsky equation based on its geometric structures

We consider structure preserving numerical schemes for the Ostrovsky equation, which describes gravity waves under the influence of Coriolis force. This equation has two associated invariants: an energy function and the L² norm. It is widely accepted that structure preserving methods such as invariants-preserving and multi-symplectic integrators generally yield qualitatively better numerical results. In this paper we propose five geometric integrators for this equation: energy-preserving and norm-preserving finite difference and Galerkin schemes, and a multi-symplectic integrator based on a newly found multi-symplectic formulation. A numerical comparison of these schemes is provided, which indicates that the energy-preserving finite difference schemes are more advantageous than the other schemes.     

13C-NMR quantification of proton exchange at LewisX hydroxyl groups in water

NMR-based analysis of glycans by directly observing hydroxyl protons has been difficult because of their inherently fast exchange with water. We observed hydroxyl proton exchanges in a LewisX-LewisX interaction by using deuterium isotope shifts on (13)C-NMR. This strategy is suitable for analyzing weak interactions by identifying involved protons.     

Cyclic Acetal-Photosensitized Polymerization. XI. Photoirradiations onto Polycyclic Acetals

Photoirradiations onto polycyclic acetals, i. e., polymers containing cyclic acetal groups in the molecule, were carried out at 30 or 40°C. The terpolymer of vinyl formal/vinyl acetate/vinyl alcohol (PVFAcA) was decomposed by means of irradiation, while poly-2-vinyl-1,3-dioxolane (PVDO) and poly-2-vinyl-4-hydroxy-methyl-1,3-dioxolane (PVHDO) were crosslinked. These results indicate the possibility of control of the decomposition or the crosslinking of polymer.     

Studies of the isotopomer determination method for the hydrogen-deuterium exchange of methane. Introduction of methane by a pulse in a deuterium stream at high temperature

The H/D exchange reactions of methane in a deuterium stream using a fixed bed flow reactor were studied. In order to precisely determine the ratio of the exchanged products by a quadrupole mass spectrometry, a new method of corrections for the fragmentation peaks was developed.     

Asymmetrically modified bimetallic catalyst for the enantio-differentiating hydrogenation of methyl acetoacetate

Summary The effects of addition of a second metal as promoter to (R,R)-tartaric acid-NaBr-modified Ni catalyst were investigated. The addition of Pd increased the enantioselectivity for the hydrogenation of methyl acetoacetate.     

Synthesis of a sialic acid alpha(2-3) galactose building block and its use in a linear synthesis of sialyl Lewis X

[reaction: see text] The ubiquity of the sialic acid alpha(2-3) galactose linkage in oligosaccharides of biological relevance necessitates a building block for the incorporation of this motif into oligosaccharides prepared by modular synthesis. The linear synthesis of the sialyl Lewis X tumor-associated antigen (1) has been accomplished in good yield using a sialic acid alpha(2-3) galactose disaccharide building block. The disaccharide building block was synthesized efficiently from readily available galactal by a high-yielding and selective sialylation reaction.     

Robust Characterization of Multidimensional Scaling Relations between Size Measures for Business Firms

Although the sizes of business firms have been a subject of intensive research, the definition of a “size” of a firm remains unclear. In this study, we empirically characterize in detail the scaling relations between size measures of business firms, analyzing them based on allometric scaling. Using a large dataset of Japanese firms that tracked approximately one million firms annually for two decades (1994–2015), we examined up to the trivariate relations between corporate size measures: annual sales, capital stock, total assets, and numbers of employees and trading partners. The data were examined using a multivariate generalization of a previously proposed method for analyzing bivariate scalings. We found that relations between measures other than the capital stock are marked by allometric scaling relations. Power–law exponents for scalings and distributions of multiple firm size measures were mostly robust throughout the years but had fluctuations that appeared to correlate with national economic conditions. We established theoretical relations between the exponents. We expect these results to allow direct estimation of the effects of using alternative size measures of business firms in regression analyses, to facilitate the modeling of firms, and to enhance the current theoretical understanding of complex systems.     

A Hamiltonian-conserving Galerkin scheme for the Camassa-Holm equation

A new Hamiltonian-conserving Galerkin scheme for the Camassa-Holm equation is presented. The scheme has an additional welcome feature that in exact arithmetic it is unconditionally stable in the sense that the solution is always bounded. Numerical examples that confirm the theory and the effectiveness of the scheme are also given.     

Dissipative/conservative Galerkin method using discrete partial derivatives for nonlinear evolution equations

A new method is proposed for designing Galerkin schemes that retain the energy dissipation or conservation properties of nonlinear evolution equations such as the Cahn–Hilliard equation, the Korteweg–de Vries equation, or the nonlinear Schrödinger equation. In particular, as a special case, dissipative or conservative finite-element schemes can be derived. The key device there is the new concept of discrete partial derivatives. As examples of the application of the present method, dissipative or conservative Galerkin schemes are presented for the three equations with some numerical experiments.