Abstract:
We have prepared supramolecular systems of chiral Schiff base Ni(II), Cu(II), Zn(II) complexes and colloidal gold nanoparticles (AuNP) of 10 nm diameters. They demonstrated that direct adsorption of chiral Schiff base metal complex on the surface of AuNP owing to observation of clear induced CD spectra for the first time. We observed and discussed induced CD bands on AuNP from chiral Schiff base Ni(II), Cu(II), Zn(II) complexes.

Abstract:
Statistical thermodynamics allows us to estimate atomistic interactions in interstitial non-stoichiometric compounds MX_{x} through analysis of experimentally determined pressure-temperature-composition (PTC) relationships for MX_{x} being in equilibrium with X_{2} in gaseous state？(X=H,N,P or S)？or for non-stoichiometric carbide MCx being in equilibrium with excess C. In case of analysis for MC_{x}, chemical activity a(C) of C in place of partial pressure p(X_{2}) of X_{2} gas must be known. On statistical modelling of crystal lattice structure for MX_{x}, an a priori assumption of constant nearest-neighbour X-X interaction energy E(X-X) within a homogeneity composition range at arbitrary temperature T was accepted to determine number θ of available interstitial sites for occupation by X atoms per M atom. Values of interaction parame-ters estimated as such appear rational and realistic noting consistency of the values for M’s in the same group in the Periodic Table of the Elements and compatibility with enthalpy values evaluated by conventional thermodynamic approach. Engineering insights gained for MX_{x} through analysis of atomistic interaction parameter values evaluated by the statistical thermodynamics are reviewed comprehensively in this paper. M might be substitutional alloy A_{1-y}B_{y} composed of constituents, A and B, or MZ_{z} containing another interstitial constituent Z besides X. Insights acquired from this line of statistical thermodynamic analysis appear to be of pragmatic use for advanced alloy design as shall be demonstrated hereafter.

Abstract:
functions on Riemannian manifolds. As a corollary, there is no non-constant $infty$-harmonic function on positively (or negatively) curved manifolds.

Abstract:
It has been recognized that the turbulent cross helicity (correlation between the velocity and magnetic-field fluctuations) can play an important role in several magnetohydrodynamic (MHD) plasma phenomena such as the global magnetic-field generation, turbulence suppression, etc. Despite its relevance to the cross-helicity evolution, little attention has been paid to the dissipation rate of the turbulent cross helicity, $\epsilon_W$. In this paper, we consider the model expression for the dissipation rate of the turbulent cross helicity. In addition to the algebraic model, an evolution equation of $\epsilon_W$ is proposed on the basis of the statistical analytical theory of inhomogeneous turbulence. A turbulence model with the modeling of $\epsilon_W$ is applied to the solar-wind turbulence. Numerical results on the large-scale evolution of the cross helicity is compared with the satellite observations. It is shown that, as far as the solar-wind application is concerned, the simplest possible algebraic model for $\epsilon_W$ is sufficient for elucidating the large-scale spatial evolution of the solar-wind turbulence. Dependence of the cross-helicity evolution on the large-scale velocity structures such as velocity shear and flow expansion is also discussed.

Abstract:
The turbulent cross helicity is directly related to the coupling coefficients for the mean vorticity in the electromotive force and for the mean magnetic-field strain in the Reynolds stress tensor. This suggests that the cross-helicity effects are important in the cases where global inhomogeneous flow and magnetic-field structures are present. Since such large-scale structures are ubiquitous in geo/astrophysical phenomena, the cross-helicity effect is expected to play an important role in geo/astrophysical flows. In the presence of turbulent cross helicity, the mean vortical motion contributes to the turbulent electromotive force. Magnetic-field generation due to this effect is called the cross-helicity dynamo. Several features of the cross-helicity dynamo are introduced. Unlike the case in the helicity or $\alpha$ effect, where ${\bf{J}}$ is aligned with ${\bf{B}}$ in the turbulent electromotive force, we in general have a finite mean-field Lorentz force ${\bf{J}} \times {\bf{B}}$ in the cross-helicity dynamo. This gives a distinguished feature of the cross-helicity effect. By considering the effects of cross helicity in the momentum equation, we see several interesting consequences of the effect. Turbulent cross helicity coupled with the mean magnetic shear reduces the effect of turbulent or eddy viscosity. Flow induction is an important consequence of this effect. One key issue in the cross-helicity dynamo is to examine how and how much cross helicity can be present in turbulence. On the basis of the cross-helicity transport equation, its production mechanisms are discussed. Some recent developments in numerical validation of the basic notion of the cross-helicity dynamo are also presented.

Abstract:
With today's advances in Peer-to-Peer (P2P) searching technology, a lot of non-document content has become searchable and usable. In the near future, since a huge amount of content is distributed over the networks, not only index server searching but also P2P searching will become important because of its scalability and robustness. Typical P2P contents sharing services have some problems, such as low search precision ratio, significant increase in traffic and inundations of malicious content such as virus. In this paper, with ideas of the CAN (Content Addressable Network) topology and a vector space method where vectors have a variable length, we propose a new P2P content searching method in which a query is effectively forwarded only to peers that have indices of content semantically similar to the desired one but not forwarded to the same peer repeatedly. The main part of our proposal is to map non-document content to a vector space based on users' evaluation and to manage vector space or to route queries using the CAN topology control. The effectiveness of the proposal is shown both by analytical estimations and simulation experiments. Our simulation experiments clarify that the proposed method is effective in improving the precision and recall ratios while reducing the amount of traffic compared with the Gnutella flooding and the vector space method in which vector lengths are fixed (close to pSearch method). In particular, when there is a lot of malicious content, the proposed method exhibited a higher precision ratio than other methods.

Abstract:
In the presence of large-scale vortical motions and/or magnetic-field strains, the turbulent cross helicity (velocity--magnetic-field correlation in fluctuations) may contribute to the turbulent electromotive force and the Reynolds stress. These effects of cross helicity are considered to balance the primary effects of turbulence such as the turbulent magnetic diffusivity in magnetic-field evolution and the eddy viscosity in the momentum transport. The cross-helicity effects may suppress the enhanced transports due to turbulence. Physical interpretation of the effects is presented with special emphasis on the difference between the cross-helicity effect and the usual $\alpha$ or helicity effect in the dynamo action. The relative importance of the cross-helicity effect in dynamo action is validated with the aid of a direct numerical simulation (DNS) of the Kolmogorov flow with an imposed magnetic field. Several mechanisms that provide turbulence with the cross helicity are also discussed.

Abstract:
Roles of turbulence in the context of magnetic reconnection are investigated with special emphasis on the mutual interaction between flow (large-scale inhomogeneous structure) and turbulence. In order to evaluate the effective transport due to turbulence, in addition to the {\it intensity} information of turbulence represented by the turbulent energy, the {\it structure} information represented by pseudoscalar statistical quantities (helicities) is important. On the basis of the evolution equation, mechanisms that provide turbulence with cross helicity are presented. Magnetic-flux freezing in highly turbulent media is considered with special emphasis on the spatial distribution of the turbulent cross helicity. The cross-helicity effects in the context of magnetic reconnection are also investigated. It is shown that the large-scale flow and magnetic-field configurations favorable for the cross-helicity generation is compatible with the fast reconnection. In this sense, turbulence and large-scale structures promote magnetic reconnection mediated by the turbulent cross helicity.

Abstract:
The effect of kinetic helicity (velocity--vorticity correlation) on turbulent momentum transport is investigated. The turbulent kinetic helicity (pseudoscalar) enters into the Reynolds stress (mirrorsymmetric tensor) expression in the form of a helicity gradient as the coupling coefficient for the mean vorticity and/or the angular velocity (axial vector), which suggests the possibility of mean-flow generation in the presence of inhomogeneous helicity. This inhomogeneous helicity effect, which was previously confirmed at the level of a turbulence- or closure-model simulation, is examined with the aid of direct numerical simulations of rotating turbulence with non-uniform helicity sustained by an external forcing. The numerical simulations show that the spatial distribution of the Reynolds stress is in agreement with the helicity-related term coupled with the angular velocity, and that a large-scale flow is generated in the direction of angular velocity. Such a large-scale flow is not induced in the case of homogeneous turbulent helicity. This result confirms the validity of the inhomogeneous helicity effect in large-scale flow generation and suggests that a vortex dynamo is possible even in incompressible turbulence where there is no baroclinicity effect.

Abstract:
In this paper, we show that, for a biharmonic hypersurface $(M,g)$ of a Riemannian manifold $(N,h)$ of non-positive Ricci curvature, if $\int_M|H|^2 v_g<\infty$, where $H$ is the mean curvature of $(M,g)$ in $(N,h)$, then $(M,g)$ is minimal in $(N,h)$. Thus, for a counter example $(M,g)$ in the case of hypersurfaces to the generalized Chen's conjecture (cf. Sect.1), it holds that $\int_M|H|^2 v_g=\infty$.