On the symmetry-breaking bifurcation of chaotic attractors

A new type of crisis is shown to exist in a broad class of systems (including the Lorenz model) which leads to an anomalous band splitting or to a symmetry-breaking bifurcation of the strange attractor, depending on the actual values of the control parameters. A piecewise linear model is used to understand the mechanism of this crisis and to obtain exact results.     

Some BMO estimates for vector-valued multilinear singular integral operators

In this paper, we prove some BMO end-point estimates for some vector-valued multilinear operators related to certain singular integral operators.     

A partial differential equation connected to option pricing with stochastic volatility: Regularity results and discretization

This paper completes a previous work on a Black and Scholes equation with stochastic volatility. This is a degenerate parabolic equation, which gives the price of a European option as a function of the time, of the price of the underlying asset, and of the volatility, when the volatility is a function of a mean reverting Orstein-Uhlenbeck process, possibly correlated with the underlying asset. The analysis involves weighted Sobolev spaces. We give a characterization of the domain of the operator, which permits us to use results from the theory of semigroups. We then study a related model elliptic problem and propose a finite element method with a regular mesh with respect to the intrinsic metric associated with the degenerate operator. For the error estimate, we need to prove an approximation result.

     

Banach空间中增生算子方程的Ishikawa迭代解

在没有∑∞n=0αnβn<∞的更弱条件下,使用与完全不同的方法,证明了Ishikawa迭代序列强收敛Lipschitz连续的增生算子T的方程x+Tx=f的唯一解,并提供了更为全面和一般的收敛率的估计.本文结果是引文[3-4]中相应结果的统一和发展.     

Spectral theory of left definite difference operators

This paper is concerned with the spectral theory for the second-order left definite difference boundary value problems. Existence of eigenvalues of boundary value problems is proved, numbers of their eigenvalues are calculated and fundamental spectral results are obtained.     

Fixed point theorems of ? convex −ψ concave mixed monotone operators and applications

In this paper, ? convex −ψ concave mixed monotone operators are introduced and some new existence and uniqueness theorems of fixed points for mixed monotone operators with such convexity concavity are obtained. As an application, we give one example to illustrate our results.     

一类切换线性系统的动态输出反馈H_∞控制:LMIs方法

研究一类由任意有限多个线性子系统组成的切换系统的动态输出反馈H∞控制问题.利用共同Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的控制器存在的充分条件,并设计了相应的子控制器和切换规则.采用消元法,将该矩阵不等式转化为一组线性矩阵不等式(LMIs).最后给出一个数值仿真实例证明结论的有效性.     

Solvable infinite-dimensional linear groups with restrictions on the nonabelian subgroups of infinite rank

Under study are the solvable nonabelian linear groups of infinite central dimension and sectional p-rank, p ≥ 0, in which all proper nonabelian subgroups of infinite sectional p-rank have finite central dimension. We describe the structure of the groups of this class.     

Compact operators which factor through subspaces of lp

Let 1 ≤ p ≤ ∞. A subset K of a Banach space X is said to be relatively p ‐compact if there is an 〈x_n 〉 ∈ l^s _p (X) such that for every k ∈ K there is an 〈α_n 〉 ∈ l_{p ′} such that k = σ^∞_n=1 α_n x_n . A linear operator T: X → Y is said to be p ‐compact if T (Ball (X)) is relatively p ‐compact in Y. The set of all p ‐compact operators K_p (X, Y) from X to Y is a Banach space with a suitable factorization norm κ_p and (K_p , κ_p ) is a Banach operator ideal. In this paper we investigate the dual operator ideal (K^d _p , κ^d _p ). It is shown that κ^d _p (T) = π_p (T) for all T ∈ B (X, Y) if either X or Y is finite‐dimensional. As a consequence it is proved that the adjoint ideal of K^d _p is I_{p ′}, the ideal of p ′‐integral operators. Further, a composition/decomposition theorem K^d _p = Π_p K is proved which also yields that (Π^min _p )^inj = K^d _p . Finally, we discuss the density of finite rank operators in K^d _p and give some examples for different values of p in this respect. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Polyhedral functions and multiparametric linear programming

In a linear programming problem with a vector parameter appearing on the right-hand side, the minimum value of the objective is a polyhedral function of this parameter. We show how different characterizations of a polyhedral function correspond to different ways of solving the right-hand side multiparameteric linear programming problem.