A level set approach for computing discontinuous solutions of Hamilton-Jacobi equations

We introduce two types of finite difference methods to compute the L-solution and the proper viscosity solution recently proposed by the second author for semi-discontinuous solutions to a class of Hamilton-Jacobi equations. By regarding the graph of the solution as the zero level curve of a continuous function in one dimension higher, we can treat the corresponding level set equation using the viscosity theory introduced by Crandall and Lions. However, we need to pay special attention both analytically and numerically to prevent the zero level curve from overturning so that it can be interpreted as the graph of a function. We demonstrate our Lax-Friedrichs type numerical methods for computing the L-solution using its original level set formulation. In addition, we couple our numerical methods with a singular diffusive term which is essential to computing solutions to a more general class of HJ equations that includes conservation laws. With this singular viscosity, our numerical methods do not require the divergence structure of equations and do apply to more general equations developing shocks other than conservation laws. These numerical methods are generalized to higher order accuracy using weighted ENO local Lax-Friedrichs methods as developed recently by Jiang and Peng. We verify that our numerical solutions approximate the proper viscosity solutions obtained by the second author in a recent Hokkaido University preprint. Finally, since the solution of scalar conservation law equations can be constructed using existing numerical techniques, we use it to verify that our numerical solution approximates the entropy solution.

     

Spectrophotometric determination of uric acid based on fading of o-hydroxyhydroquinonephthalein-palladium(II)-hexadecyltrimethyl-ammonium complex.

A simple and highly sensitive spectrophotometric method for the determination of uric acid (UA) was established based on fading of the o-hydroxyhydroquinonephthalein-palladium(II)-hexadecyltrimethylammonium complex. In the determination of UA, Beer's law is obeyed in the range of 0.01-0.20 microg ml(-1), with an effective molar absorptivity at 635 nm, the relative standard deviation being 6.5 x 10(5) dm(3) mol(-1) cm(-1) and 1.5% (n = 5). This method is about 20-times more sensitive than the conventional methods. The method was successfully applied to the assay of UA in human urine.     

Von den vielen Verfahren zum Nachweis von kleinsten Mengen Formaldehyd

Ohne Zusammenfassung     

High Catalytic Activity of Nitrogen and Sulfur Co‐Doped Nanoporous Graphene in the Hydrogen Evolution Reaction

Chemical doping has been demonstrated to be an effective way to realize new functions of graphene as metal‐free catalyst in energy‐related electrochemical reactions. Although efficient catalysis for the oxygen reduction reaction (ORR) has been achieved with doped graphene, its performance in the hydrogen evolution reaction (HER) is rather poor. In this study we report that nitrogen and sulfur co‐doping leads to high catalytic activity of nanoporous graphene in HER at low operating potential, comparable to the best Pt‐free HER catalyst, 2D MoS₂. The interplay between the chemical dopants and geometric lattice defects of the nanoporous graphene plays the fundamental role in the superior HER catalysis.     

Revisiting the extrapolation of correlation energies to complete basis set limit

The extrapolation scheme of correlation energy is revisited to evaluate the complete basis set limit from double‐zeta (DZ) and triple‐zeta levels of calculations. The DZ level results are adjusted to the standard asymptotic behavior with respect to the cardinal number, observed at the higher levels of basis sets. Two types of adjusting schemes with effective scaling factors, which recover errors in extrapolations with the DZ level basis set, are examined. The first scheme scales the cardinal number for the DZ level energy, while the second scheme scales the prefactor of the extrapolation function. Systematic assessments on the Gaussian‐3X and Gaussian‐2 test sets reveal that these calibration schemes successfully and drastically reduce errors without additional computational efforts. © 2015 Wiley Periodicals, Inc.     

Rotating Navier-Stokes Equations in $${\mathbb R}^{3}_{+}$$ with Initial Data Nondecreasing at Infinity: The Ekman Boundary Layer Problem

We prove time local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary solution called the Ekman spiral. We choose initial data in the vector-valued homogeneous Besov space for 2 <  p <  ∞. Here the L ^p -integrability is imposed in the normal direction, while we may have no decay in tangential components, since the Besov space contains nondecaying functions such as almost periodic functions. A crucial ingredient is theory for vector-valued homogeneous Besov spaces. For instance we provide and apply an operator-valued bounded H ^∞-calculus for the Laplacian in for a general Banach space .     

Spectrophotometric determination of titanium with o-carboxyphenylfluorone in cationic micellar media, and its equilibrium and kinetic studies

Spectrophotometric determination of titanium(IV) was accomplished with o-carboxyphenylfluorone (OCPF) in the presence of hexadecyltrimethyl ammonium chloride (HTAC) under strongly acidic media. In the determination of titanium(IV), Beer's law was obeyed in the range of 24-340 ng mL⁻¹ with an effective molar absorption coefficient (at 530 nm) and relative standard deviation of 2.24 × 10⁵ dm³ mol⁻¹ cm⁻¹ and 0.64% (n = 8), respectively. The severe interference of iron ions was easily eliminated by the addition of ethylenediaminetetraacetic acid (EDTA); the effects of other foreign substances were low. Equilibrium and kinetic studies under analytical conditions were investigated to quantitatively evaluate the reaction mechanism. The obtained orange complex is considered to be Ti(OCPF)₄. Its stability log K_f and rate constant K_obs are 16.88 and 1.65 × 10⁻² s⁻¹, respectively. It is suggested that the color of the complex is related to the species of OCPF in the solution.     

Linearity condition for orbital energies in density functional theory: construction of orbital-specific hybrid functional

This study proposes a novel approach to construct the orbital-specific (OS) hybrid exchange-correlation functional by imposing the linearity condition: ?(2)E/?f(i)(2)|(0≤f(i)≤1) = ??(i)/?f(i)|(0≤f(i)≤1) = 0, where E, ε(i), and f(i) represent the total energy, orbital energy, and occupation number of the ith orbital. The OS hybrid exchange-correlation functional, of which the OS Hartree-Fock exchange (HFx) portion is determined by the linearity condition, reasonably reproduces the ionization potentials not only from valence orbitals but also from core ones in a sense of Koopmans' theorem. The obtained short-range HFx portions are consistent with the parameters empirically determined in core-valence-Rydberg-Becke-3-parameter-Lee-Yang-Parr hybrid functional [Nakata et al., J. Chem. Phys., 124, 094105 (2006); ibid, 125, 064109 (2006)].