关于局部对称空间中2-调和子流形

本文研究局部对称完备黎曼流形中的紧致2－调和子流形，得到了这类流形第二基本模式长平方的Pinching定理及推广的J．Simons型积分不等式。     

Ultrasonic evaluation of anisotropic damage in multiaxially textile-reinforced thermoplastic composites made from hybrid yarns

The basic damage and failure models of multiaxially reinforced composites with a thermoplastic matrix are presented and verified. Within the framework of continuum damage mechanics, a phenomenological model is introduced, where the damage is defined as a change in the elasticity tensor. For damage identification, a specific ultrasonic device was developed. A combination of an immersion set-up and a contact coupling device formed a system for an efficient determination of stiffness-tensor components from convenient sets of velocity measurements. Linked to a tensile machine, it allowed us to measure the anisotropic damage of the new materials group caused by tensile loading. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 221–234, March–April, 2006.     

Detecting and Diagnostic Checking Multivariate Conditional Heteroscedastic Time Series Models

Two tests for multivariate conditional heteroscedastic models are proposed. One is based on the cross-correlations of standardized squared residuals and the other is a score (Lagrange multiplier) test. The cross-correlations test can be used to detect the presence of multivariate conditional heteroscedasticity whereas the other test can be used for diagnostic checking. Simulation studies on the size and power of the test statistics are reported. The application of the tests is illustrated by an example using the S & P 500 and Sydney All Ordinary Indexes.     

Estimating Invariant Probability Densities for Dynamical Systems

Knowing a probability density (ideally, an invariant density) for the trajectories of a dynamical system allows many significant estimates to be made, from the well-known dynamical invariants such as Lyapunov exponents and mutual information to conditional probabilities which are potentially more suitable for prediction than the single number produced by most predictors. Densities on typical attractors have properties, such as singularity with respect to Lebesgue measure, which make standard density estimators less useful than one would hope. In this paper we present a new method of estimating densities which can smooth in a way that tends to preserve fractal structure down to some level, and that also maintains invariance. We demonstrate with applications to real and artificial data.     

RICE CONDITION NUMBERS OF CERTAIN CHARACTERISTIC SUBSPACES

This paper proposes the Rice condition numbers for invariant subspace, singular sub-spaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are derived by applying perturbation expansions of orthogonal projection operators.     

~2样本深度的基本性质

本文讨论由L2深度修正得到的L2深度相应的样本深度的性质,得到了样本深度的相合性和渐近正态性,并证明了它在任意紧集上的一致相合性．最后,基于上述性质简要讨论了样本深度等高的一些性质．     

On the invariant measure for the quasi‐linear Lasota equation

The problem of the existence of the invariant measure is important considering its connections with chaotic behaviour. In the papers (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123; Ann. Pol. Math. 1983; XLI :129–137; J. Differential Equations 2004; 196 :448–465) the existence of invariant and ergodic measures according to the dynamical system generated by the Lasota equation was proved, i.e. the equation describing the dynamics and becoming different of the population of cells. In this paper, the existence of such measure for the quasi‐linear Lasota equation is proved. This measure is the carriage of the measure described by Dawidowicz (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123). Copyright © 2006 John Wiley & Sons, Ltd.     

Vassiliev invariants for braids on surfaces

We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit a universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the surface.

     

A geometric formula for Haefliger knots

Haefliger has shown that a smooth embedding of the (4k−1)-sphere in the 6k-sphere can be knotted in the smooth sense. In this paper, we give a formula with which we can detect the isotopy class of such a Haefliger knot. The formula is expressed in terms of the geometric characteristics of an extension, analogous to a Seifert surface, of the given embedding. In particular, the Hopf invariant associated to the extension plays a crucial role. This leads us to a new characterisation of Haefliger knots.     

Choquet-type Integral Representation of Invariant Functions for some Product Semigroups

We show that functions which are invariant for suitable product semigroups (one of which is a quasi-Poisson semigroup on a general state space) decompose into a singular eigen-function and a mixture of products of minimal eigen-functions.