Angle theorems for the Lagrangian mean curvature flow

We prove that symplectic maps between Riemann surfaces L, M of constant, nonpositive and equal curvature converge to minimal symplectic maps, if the Lagrangian angle for the corresponding Lagrangian submanifold in the cross product space satisfies . If one considers a 4-dimensional K?hler-Einstein manifold of nonpositive scalar curvature that admits two complex structures J, K which commute and assumes that is a compact oriented Lagrangian submanifold w.r.t. J such that the K?hler form w.r.t.K restricted to L is positive and , then L converges under the mean curvature flow to a minimal Lagrangian submanifold which is calibrated w.r.t. . Received: 11 April 2001 / Published online: 29 April 2002     

Global stability of the Armstrong-Frederick model with periodic biaxial inputs

The paper is concerned with the study of plasticity models described by differential equations with stop and play operators. We suggest sufficient conditions for the global stability of a unique periodic solution for the scalar models and for the vector models with biaxial inputs of a particular form, namely the sum of a uniaxial function and a constant term. For another class of simple biaxial inputs, we present an example of the existence of unstable periodic solutions. The paper was written during the research stay of D. Rachinskii at the Technical University Munich supported by the research fellowship from the Alexander von Humboldt Foundation. His work was partially supported by the Russian Science Support Foundation, Russian Foundation for Basic Research (Grant No. 01-01-00146, 03-01-00258), and the Grants of the President of Russia (Grant No. MD-87.2003.01, NS-1532.2003.1). The support is gratefully acknowledged.     

Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example.     

On the realization of Riemannian symmetric spaces in Lie groups

In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK∩P are also discussed, where gK is a coset space in G.     

Conditional independence models for seemingly unrelated regressions with incomplete data

We consider normal ≡ Gaussian seemingly unrelated regressions (SUR) with incomplete data (ID). Imposing a natural minimal set of conditional independence constraints, we find a restricted SUR/ID model whose likelihood function and parameter space factor into the product of the likelihood functions and the parameter spaces of standard complete data multivariate analysis of variance models. Hence, the restricted model has a unimodal likelihood and permits explicit likelihood inference. In the development of our methodology, we review and extend existing results for complete data SUR models and the multivariate ID problem.     

Fundamental groups of the complements of certain plane non-tame torus sextics

The moduli space of torus sextics with the configuration of singularities {A₂+A₅+2E₆} has two connected components. We compute the fundamental groups π₁(CP²−C) for sextics C in both components and study their differences.     

New examples of Osserman metrics with nondiagonalizable Jacobi operators

Explicit examples of Osserman 4-manifolds with exactly two distinct eigenvalues of the Jacobi operators, α and β=4α≠0, are given. The former has multiplicity two and is a double root of the minimal polynomial of the Jacobi operators.     

Inclusion of carbon nanotubes in a TiO2 sol-gel matrix

We report here the successful inclusion of carbon nanotubes (CNs) into a TiO₂ matrix prepared by a sol-gel method. The presence of CNs in the sol-gel matrix and the structure of the film were analyzed principally by transmission electron microscopy. Complementary information about the behavior of embedded carbon nanotubes versus heat treatment and ion irradiation were obtained by X-ray photoelectron spectroscopy. The elaboration of an inorganic matrix containing embedded carbon nanotubes leads to a new nanocomposite. The possible applications of this nanocomposite are discussed.     

On a conjecture of Cox and Katz

This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces. Received: 8 February 2001; in final form: 17 September 2001 / Published online: 1 February 2002