Nonlinear Young integrals via fractional calculus

For H\"older continuous functions $W(t,x)$ and $\varphi_t$, we define nonlinear integral $\int_a^b W(dt, \varphi_t)$ via fractional calculus. This nonlinear integral arises naturally in the Feynman-Kac formula for stochastic heat equations with random coefficients. We also define iterated nonlinear integrals.Comment: arXiv admin note: substantial text overlap with arXiv:1404.758

Relationship between ferroelectricity and Dzyaloshinskii-Moriya interaction in multiferroics and the effect of bond-bending

We studied the microscopic mechanism of multiferroics, in particular with the "spin current" model (Hosho Katsura, Naoto Nagaosa and Aleander V. Balatsky, Phys. Rev. Lett. 95, 057205 (2005)). Starting from a system with helical spin configuration, we solved for the forms of the electron wave functions and analyzed their characteristics. The relation between ferroelectricity and Dzyaloshinskii-Moriya interaction (I. Dzyaloshinskii, J. Phys. Chem. Solids 4, 241 (1958) and T. Moriya, Phys. Rev. 120, 91 (1960)) is clearly established. There is also a simple relation between the electric polarization and the wave vector of magnetic orders. Finally, we show that the bond-bending exists in transition metal oxides can enhance ferroelectricity.Comment: 14 pages, 3 figures. acceptby Physical Review

The rise of new farmer cooperatives in China; evidence from Hubei Province

Since the late 1990s, the number of farmer cooperatives in China has rapidly grown. The adoption of the national law on farmer professional cooperatives in 2007 has led to significant governmental support for the establishment and management of farmer professional cooperatives. This paper explores the organizational features of the newly established cooperatives as well as the services they provide to their members. Particular attention is given to the role of local entrepreneurs in grouping farmers and in acquiring support from local and regional state agencies. The paper is based on data about a group of 200 agriculture and aquaculture cooperatives in Hubei Province, central China

Heisenberg equation for a nonrelativistic particle on a hypersurface: from the centripetal force to a curvature induced force

In classical mechanics, a nonrelativistic particle constrained on an $N-1$ curved hypersurface embedded in $N$ flat space experiences the centripetal force only. In quantum mechanics, the situation is totally different for the presence of the geometric potential. We demonstrate that the motion of the quantum particle is "driven" by not only the the centripetal force, but also a curvature induced force proportional to the Laplacian of the mean curvature, which is fundamental in the interface physics, causing curvature driven interface evolution.Comment: 4 page

Periodic subvarieties of a projective variety under the action of a maximal rank abelian group of positive entropy

We determine positive-dimensional G-periodic proper subvarieties of an n-dimensional normal projective variety X under the action of an abelian group G of maximal rank n-1 and of positive entropy. The motivation of the paper is to understand the obstruction for X to be G-equivariant birational to the quotient variety of an abelian variety modulo the action of a finite group.Comment: Asian Journal of Mathematics (to appear), Special issue on the occasion of Prof N. Mok's 60th birthda

The centripetal force law and the equation of motion for a particle on a curved hypersurface

It is pointed out that the current form of extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once the fact be taken into consideration, the equation takes that same form as that for centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is favorable.Comment: 5 pages, major revisio