On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces

This paper is concerned with the stationary problem of the Stokes equation in an infinite layer and provides a condition on the external force sufficient for the existence of the solution. Since the Poiseuille flow is a solution to the homogeneous equation, the solution is not unique when p = ∞. It is also proved that, under some suitable conditions, solutions to the homogeneous equation are limited only to the Poiseuille flow.     

Restricted generalized Nash equilibria and controlled penalty algorithm

The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem, in which each player’s strategy set may depend on the rival players’ strategies. The GNEP has recently drawn much attention because of its capability of modeling a number of interesting conflict situations in, for example, an electricity market and an international pollution control. However, a GNEP usually has multiple or even infinitely many solutions, and it is not a trivial matter to choose a meaningful solution from those equilibria. The purpose of this paper is two-fold. First we present an incremental penalty method for the broad class of GNEPs and show that it can find a GNE under suitable conditions. Next, we formally define the restricted GNE for the GNEPs with shared constraints and propose a controlled penalty method, which includes the incremental penalty method as a subprocedure, to compute a restricted GNE. Numerical examples are provided to illustrate the proposed approach.     

Oxygen‐sensing properties of 5,10,15,20‐tetraphenylporphinato platinum(II) and palladium(II) covalently bound on poly(isobutyl‐co‐2,2,2‐trifluoroethyl methacrylate)

A novel methacrylate monomer bearing 5,10,15,20‐tetraphenylporphyrinato palladium(II) (PdTPP) (monomer 1a ) was synthesized and copolymerized with isobutyl methacrylate (IBM) and 2,2,2‐trifluoroethyl methacrylate (TFEM) to give poly (IBM‐co‐TFEM) bearing PdTPP (copolymer 2a ) as a dye‐conjugated oxygen‐permeable polymer for pressure‐sensitive paint applications. The introduction of PdTPP into copolymer 2a was confirmed by UV–vis spectroscopy and extended X‐ray absorption fine structure analysis. The Stern–Volmer plots of the copolymer 2a and a mixture of PdTPP and poly(IBM‐co‐TFEM) both showed downward curvature, unlike that of the platinum complex analogue (copolymer 2b ) previously reported. The plots were successfully fitted with a two‐site model to give two distinct Stern–Volmer constants (K_SV1 and K_SV2) and the partition ratio f₁. Interestingly, the f₁ values for the copolymer 2a were almost constant at about 0.98, whereas those of the mixture of PdTPP and poly(IBM‐co‐TFEM) increased from 0.889 to 0.967 as the temperature was increased. This finding suggests that there are two distinct microheterogeneities, one temperature‐dependent and the other temperature‐independent, in the mixture of PdTPP and poly(IBM‐co‐TFEM). The dye‐conjugation approach effectively eliminates the temperature‐dependent, but not the temperature‐independent microheterogeneity. The luminescence decays of copolymers 2a and 2b and the corresponding mixtures in the absence of oxygen indicated that the temperature‐dependent microheterogeneity involves an oxygen diffusion process, whereas the temperature‐independent one appears to be inherent nature in PdTPP. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 663–670, 2010     

A characteristic ribbon-like supramolecular structure and intermolecular D–A interactions in the crystals of triptycenequinones, triptycene-TCNQs and their clathrates as studied by X-ray investigations

A common ribbon-like structure was found in the crystals of triptycenequinones (TPQs), triptycene-TCNQs (TP-TCNQs) and their clathrates. The characteristic structure can be regarded as a supramolecular unit the formation of which is aided by weak intermolecular D–A interactions. This view is supported by the host–guest D–A interactions appeared in the crystals of the clathrates of 5,8-dimethyl-TPQ and 5,8-dimethoxy-TP-TCNQ. Intermolecular C–HO hydrogen bonds seem to be present in TPQ derivatives.     

First-principles energy band calculation for undoped and N-doped InTaO4 with layered wolframite-type structure

The electronic structures of undoped and N-doped InTaO₄ with optimized structures are calculated within the framework of the density functional theory. Calculated lattice constants are in excellent agreement with experimental values, within a difference of 2%. The valence band maximum (VBM) is located near the middle point on the ZD line and the conduction band minimum (CBM) near the middle point on the DX line. This means that InTaO₄ is an indirect-gap material and a minimum theoretical gap between VBM and CBM is ca. 3.7 eV. The valence band in the range from −6.0 to 0 eV mainly consists of O 2p orbitals, where In 4d5s5p and Ta 5d orbitals are slightly hybridized with O 2p orbitals. On the other hand, the conduction band below 5.5 eV is mainly composed of the Ta 5d orbitals and the contributions of In and O orbitals are small. The band gap of N-doped InTaO₄ decreases by 0.3 eV than that of undoped InTaO₄, because new gap states originating from N 2p orbitals appear near the top of the valence band. This result indicates that doping of N atoms into metal oxides is a useful method to develop photocatalysts sensitive to visible light.     

Ground state for point particles interacting through a massless scalar Bose field

We consider a massless scalar Bose field interacting with two particles, one of them infinitely heavy. Neither an infrared nor an ultraviolet cutoff is imposed. In case the charge of the particles is of the same sign and sufficiently small, we prove the existence of a ground state.     

Applications of minor summation formula III, Plücker relations, lattice paths and Pfaffian identities

The initial purpose of the present paper is to provide a combinatorial proof of the minor summation formula of Pfaffians in [Ishikawa, Wakayama, Minor summation formula of Pfaffians, Linear and Multilinear Algebra 39 (1995) 285-305] based on the lattice path method. The second aim is to study applications of the minor summation formula for obtaining several identities. Especially, a simple proof of Kawanaka's formula concerning a q-series identity involving the Schur functions [Kawanaka, A q-series identity involving Schur functions and related topics, Osaka J. Math. 36 (1999) 157-176] and of the identity in [Kawanaka, A q-Cauchy identity involving Schur functions and imprimitive complex reflection groups, Osaka J. Math. 38 (2001) 775-810] which is regarded as a determinant version of the previous one are given.     

Frequency-dependent changes in absolute hearing threshold caused by perception of a previous sound

This study investigated effects of a previous sound presentation at the absolute threshold of hearing. Changes in threshold were measured when a pure tone at 60 dB SPL preceded a test tone in the contra- or ipsilateral ear. When the previous and test sounds both had the same frequency of 500 Hz, threshold decreased approximately 2 dB in the contralateral ear, and increased slightly in the ipsilateral ear. On the other hand, when the frequency of the previous sound differed from that of the test sound, the threshold was decreased slightly in the ipsilateral ear.     

Fermi-surface reconstruction without breakdown of Kondo screening at the quantum critical point

Motivated by recent Hall-effect experiment in YbRh(2)Si(2), we study ground state properties of a Kondo lattice model in a two-dimensional square lattice using variational Monte Carlo method. We show that there are two types of phase transition, an antiferromagnetic transition and a topological one (Fermi-surface reconstruction). In a wide region of parameters, these two transitions occur simultaneously without the breakdown of Kondo screening, accompanied by a discontinuous change of the Hall coefficient. This result is consistent with the experiment and gives a novel theoretical picture for the quantum critical point in heavy-fermion systems.