On nearly parallel G2-structures

A nearly parallel G₂-structure on a seven-dimensional Riemannian manifold is equivalent to a spin structure with a Killing spinor. We prove general results about the automorphism group of such structures and we construct new examples. We classify all nearly parallel G₂-manifolds with large symmetry group and in particular all homogeneous nearly parallel G₂-structures.     

Noise reduction method based on weighted manifold decomposition

A noise reduction method based on weighted manifold decomposition is proposed in this paper, which does not need knowledge of the chaotic dynamics and choosing number of eigenvalues.The simulation indicates that the performance of this method can increase the signal-to-noise ratio of noisy chaotic time series.     

The Feynman–Kac formula for Schrödinger operators on vector bundles over complete manifolds

Methods from stochastic analysis are combined with functional analytic methods in order to prove a Feynman–Kac formula för Schrödinger type operators with nonnegative locally square integrable potentials on vector bundles over complete Riemannian manifolds. In particular, we obtain a Feynman–Kac–Itô formula on manifolds for Schrödinger operators with magnetic fields.     

H一射影循环Kaehler流形

本文研究H一射影循环Kaehler流形的性质，导出了该流形曲率张量的代数结构，从而深化了这类流形的已有结果。     

Smooth equivalence of differential equations and linear automorphisms

For systems of ordinary differential equations admitting linear automorphisms, we consider the problems of smooth equivalence and linearization preserving these automorphisms. Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 567–578, October, 1999.     

Iteration-complexity of the subgradient method on Riemannian manifolds with lower bounded curvature

Abstract

The subgradient method for convex optimization problems on complete Riemannian manifolds with lower bounded sectional curvature is analysed in this paper. Iteration-complexity bounds of the subgradient method with exogenous step-size and Polyak's step-size are stablished, completing and improving recent results on the subject.     

The construction and evaluation of a high pressure manifold and vessels for a Calvet type microcalorimeter

A Setaram C-80 calorimeter has been modified in order to measure the heat flow of energetic materials at pressures up to 69 MPa. A manifold and sample cells capable of operating at high pressure were designed, constructed and evaluated. This paper will describe, in detail, the high pressure manifold construction, safety assessment and calibration. As well, the results for initial trials with ammonium nitrate (AN), and pentaerythritol tetranitrate (PETN) at various pressures and heating rates will be discussed.     

An explicit recursive formula for computing the normal forms associated with semisimple cases

This paper presents an explicit, computationally efficient, recursive formula for computing the normal forms, center manifolds and nonlinear transformations for general n-dimensional systems, associated with semisimple singularities. Based on the formula, we develop a Maple program, which is very convenient for an end-user who only needs to prepare an input file and then execute the program to “automatically” generate the result. Several examples are presented to demonstrate the computational efficiency of the algorithm.     

Stability of hyperbolic manifolds with cusps under Ricci flow

We show that every finite volume hyperbolic manifold of dimension greater than or equal to 3 is stable under rescaled Ricci flow, i.e. that every small perturbation of the hyperbolic metric flows back to the hyperbolic metric again. Note that we do not need to make any decay assumptions on this perturbation.