Variational formulas of higher order mean curvatures

In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total $2p$-th mean curvature functional $\mathcal {M}_{2p}$ of a submanifold $M^n$ in a general Riemannian manifold $N^{n+m}$ for $p=0,1,...,[\frac{n}{2}]$. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional $\mathcal {M}_{2p}$, called relatively $2p$-minimal submanifolds, for all $p$. At last, we discuss the relations between relatively $2p$-minimal submanifolds and austere submanifolds in real space forms, as well as a special variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201

Application of Instantons: Quenching of Macroscopic Quantum Coherence and Macroscopic Fermi-Particle Configurations

Starting from the coherent state representation of the evolution operator with the help of the path-integral, we derive a formula for the low-lying levels $E = \epsilon_0 - 2\triangle\epsilon cos (s+\xi)\pi$ of a quantum spin system. The quenching of macroscopic quantum coherence is understood as the vanishing of $cos (s+\xi)\pi$ in disagreement with the suppression of tunneling (i.e. $\triangle\epsilon = 0$) as claimed in the literature. A new configuration called the macroscopic Fermi-particle is suggested by the character of its wave function. The tunneling rate ($(2\triangle\epsilon)/(\pi)$) does not vanish, not for integer spin s nor for a half-integer value of s, and is calculated explicitly (for the position dependent mass) up to the one-loop approximation.Comment: 13 pages, LaTex, no figure

Graded reflection equation algebras and integrable Kondo impurities in the one-dimensional t-J model

Integrable Kondo impurities in two cases of the one-dimensional $t-J$ model are studied by means of the boundary ${\bf Z}_2$-graded quantum inverse scattering method. The boundary $K$ matrices depending on the local magnetic moments of the impurities are presented as nontrivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, these models are solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.Comment: 14 pages, RevTe

Enhancement of Quantum Tunneling for Excited States in Ferromagnetic Particles

A formula suitable for a quantitative evaluation of the tunneling effect in a ferromagnetic particle is derived with the help of the instanton method. The tunneling between n-th degenerate states of neighboring wells is dominated by a periodic pseudoparticle configuration. The low-lying level-splitting previously obtained with the LSZ method in field theory in which the tunneling is viewed as the transition of n bosons induced by the usual (vacuum) instanton is recovered. The observation made with our new result is that the tunneling effect increases at excited states. The results should be useful in analyzing results of experimental tests of macroscopic quantum coherence in ferromagnetic particles.Comment: 18 pages, LaTex, 1 figur

Field evaluations of Romanomermis yunanensis (Nematoda : Mermithidae) for control of Culicinae mosquitoes in China

L'utilisation de #Romanomermis yunanensis en vue du contrôle de moustiques #Culcinae a été testé au champs dans cinq provinces chinoises de 1986 à 1995. Environ 2 000 à 4 000 larves préparasites de #R. yunanensis$par m2 ont été dispersées dans des rizières inondées, des mares et des ruisseaux. Il en est résulté des taux de parasitisme de 52,2-96,7$ (espèce indigène), 35,5-89,5% pour #C. quinquefasciatus$, 90,1$, 78,3% pour #C. pseudovishnui$et 53,7-92,8$. De plus, des larves préparasites de #R. yunanensis$ont été dispersées dans différents sites aquatiques de surface restreinte dans plusieurs villes. Cela a conduit à des taux de parasitisme de 53,0-100$, 90,1% pour #Ae. pseudalbopictus$et 70,9$, mais de 28,3-32,6% seulement our #Ae. albopictus$dans les sites où l'eau était couverte d'un film huileux et de 6,7-34,2$ dans des ruisseaux où l'eau était turbide ou chargée en matières organiques. Ces résultats suggèrent que, dans des conditions approprées, #R. yunanensis peut se montrer très efficace pour contrôler les moustiques #Culicinae dans les zones tant agricoles qu'urbanisées. Des observations ont été effectuées concernant l'établissement durable de #R. yunanensis$ dans des sites naturels où les moustiques se reproduisent et où des larves préparasites avaient été dispersées 1 à 3 années auparavant. Quelques facteurs affectant l'efficacité des applications au champ sont discutés. (Résumé d'auteur

PROJECTIVE CONVEXITY IN COMPUTATIONAL KINEMATIC GEOMETRY

ABSTRACT In recent years, there is an increasing interest in developing geometric algorithms for kinematic computations. The aim of this paper is to present the notion of projective convexity as a key element for a new framework for kinematic geometry, that allows for the development of more elegant and efficient algorithms for geometric computations with kinematic applications. The resulting framework, called computational kinematic geometry, is developed by combining the oriented projective geometry with the kinematic geometry of rigid body motions