Partial regularity results up to the boundary for harmonic maps into a Finsler manifold

We study the energy functional for maps from a Riemannian m-manifold M   into a Finsler space N=(Rn,F)$N=({\mathbb{R}}^n,F)$. Under the restriction 2?m?4$2?m?4$, we prove the full Hölder regularity of weakly harmonic maps (i.e., weak solutions of its Euler–Lagrange equation) from M to N   in the case that the Finsler structure F(u,X)$F(u,X)$ depends only on vectors X, and a partial Hölder regularity of energy minimizing maps in general cases.     

Convergence of Riemannian Manifolds and Laplace Operators, II

We study spectral convergence of compact Riemannian manifolds or more generally certain Dirichlet spaces, obtaining some compactness results on harmonic functions and harmonic maps. Mathematics Subject Classifications (2000) 53C21, 58D17, 58J50. Atsushi Kasue: Partly supported by the Grant-in-Aid for Scientific Research (B) No. 15340053 of the Japan Society for the Promotion of Science.     

Vibrational resonance in biological nonlinear maps

We investigate vibrational resonance in two different nonlinear maps driven by a biharmonic force: the Bellows and the Rulkov map. These two maps possess dynamical features of particular interest for the study of these phenomena. In both maps, the resonance occurs at the low-frequency of the biharmonic signal as the amplitude of the high-frequency signal is varied. We also consider an array of unidirectionally coupled maps with the forcing signal applied to the first unit. In this case, a signal propagation with several interesting features above a critical value of the coupling strength is found, while the response amplitude of the ith unit is greater than the first one. This response evolves in a sigmoidal fashion with the system number i, meaning that at some point the amplitudes saturate. The unidirectional coupling acts as a low-pass filter for distant units. Moreover, the analysis of the mean residence time of the trajectory in a given region of the phase space unveils a multiresonance mechanism in the coupled map system. These results point at the relevance of the discrete-time models for the study of resonance phenomena, since analyses and simulations are much easier than for continuous-time models.     

靶流形为球面子流形的调和映射的量子化现象(英文)

本文研究了调和映射和极小子流形的量子化性质.通过运用谱分解方法,获得了靶流形为球面子流形的调和映射的量子化性质,然后将其应用到球面的极小子流形的高斯映射,得到了极小子流形的第二基本形式的量子化性子.     

Hopf bifurcation of the third-order Hénon system based on an explicit criterion

In this paper, Hopf bifurcation of the third-order Hénon system is studied via a simple explicit criterion, which is derived from the Schur–Cohn Criterion. Moreover stability of Hopf bifurcation is also investigated by using the normal form method and center manifold theory for the discrete time system developed by Kuznetsov. Test results containing simulations and circuit measurement are shown to demonstrate that the criterion is correct and feasible.     

Dilation of generalized Toeplitz kernels on ordered groups

We introduce the concept of Toeplitz-Kre?n-Cotlar triplet on ordered groups and we prove a general dilation result and a general representation result for the positive definite case.This general result includes and extends previous generalizations of the Kre?n extension theorem, the Sz.-Nagy and Foias commutant lifting theorem and the generalized Herglotz-Bochner-Weil theorem.     

On Sequential Separability

A new criterion for the sequential separability of the space C(X) of continuous real-valued functions on X in the topology of simple convergence is obtained.     

利普希茨伪紧缩映射下的利普希茨摄动迭代的Bruck公式

在非线性分析中,处理伪紧缩算子及其变形的解(不动点)存在性和近似性,从而使演化方程的求解已经发展成为一个独立的理论.使用近似不动点技术,采用摄动迭代方法,目的是证明利普希茨伪紧缩映射序列的收敛性.该迭代方法适用于比利普希茨伪紧缩算子更一般的非线性算子以及Bruck迭代法无法证明其收敛性的情况.推广了Chidume和Zegeye的结果.     

Class field theory for a product of curves over a local field

We prove that the kernel of the reciprocity map for a product of curves over a p-adic field with split semi-stable reduction is divisible. We also consider the K ₁ of a product of curves over a number field.      

Supercritical biharmonic equations with power-type nonlinearity

We study two different versions of a supercritical biharmonic equation with a power-type nonlinearity. First, we focus on the equation Δ² u = |u| ^p-1 u over the whole space , where n > 4 and p > (n + 4)/(n − 4). Assuming that p < p _c, where p _c is a further critical exponent, we show that all regular radial solutions oscillate around an explicit singular radial solution. As it was already known, on the other hand, no such oscillations occur in the remaining case p ≥ p _c. We also study the Dirichlet problem for the equation Δ² u = λ (1 + u) ^p over the unit ball in , where λ > 0 is an eigenvalue parameter, while n > 4 and p > (n + 4)/(n − 4) as before. When it comes to the extremal solution associated to this eigenvalue problem, we show that it is regular as long as p < p _c. Finally, we show that a singular solution exists for some appropriate λ > 0.