A third order dispersive flow for closed curves into almost Hermitian manifolds

We discuss a short-time existence theorem of solutions to the initial value problem for a third order dispersive flow for closed curves into a compact almost Hermitian manifold. Our equations geometrically generalize a physical model describing the motion of vortex filament. The classical energy method cannot work for this problem since the almost complex structure of the target manifold is not supposed to be parallel with respect to the Levi-Civita connection. In other words, a loss of one derivative arises from the covariant derivative of the almost complex structure. To overcome this difficulty, we introduce a bounded pseudodifferential operator acting on sections of the pullback bundle, and eliminate the loss of one derivative from the partial differential equation of the dispersive flow.     

Quadratic Actions in Dependent Fields and the Action Principle

General field theories are considered, within the functional differential formalism of quantum field theory, with interaction Lagrangian densities L _I (x;λ), with λ a generic coupling constant, such that the following expression ∂ L _I (x;λ)/∂ λ may be expressed as quadratic functions in dependent fields but may, in general, be arbitrary functions of independent fields. These necessarily include, as special cases, present renormalizable gauge theories. It is shown, in a unified manner, that the vacuum-to-vacuum transition amplitude (the generating functional) may be explicitly derived in functional differential form which, in general, leads to modifications to computational rules by including such factors as Faddeev–Popov ones and modifications thereof which are explicitly obtained. The derivation is given in the presence of external sources and does not rely on any symmetry and invariance arguments as is often done in gauge theories and no appeal is made to path integrals.     

A random Euler scheme for Carathéodory differential equations

We study a random Euler scheme for the approximation of Carathéodory differential equations and give a precise error analysis. In particular, we show that under weak assumptions, this approximation scheme obtains the same rate of convergence as the classical Monte–Carlo method for integration problems.     

Rational approximation schemes for bi-continuous semigroups

This paper extends the Hille-Phillips functional calculus and rational approximations results due to R. Hersh, T. Kato, P. Brenner, and V. Thomée to generators of bi-continuous semigroups. The method yields error estimates for rational time-discretization schemes for such semigroups, in particular for dual semigroups, Feller semigroups such as the Ornstein-Uhlenbeck semigroup, the heat semigroup, semigroups induced by nonlinear flows, implemented semigroups, and evolution semigroups. Furthermore, the results provide error estimates for a new class of inversion formulas for the Laplace transform.     

单支方法的收敛性

本文讨论用单支方法数值求解一类多刚性时滞微分代数方程的收敛性。我们获得了A－稳定的且p阶经典相容的单支方法（时滞部分用线性插值）的整体误差估计。     

A ONE-STEP EXPLICIT FORMULA FOR THE NUMERICAL SOLUTION OF STIFF ORDINARY DIFFERENTIAL EQUATION

In this paper, a new one-step explicit method of fourth order is derived. The new method is proved to be A-stable and L-stable, and it gives exact results when applied to the test equation y'=λy with Re(λ)<0, Also several numerical examples are included.     

Photoinitiating monomers based on di‐ and triacryloylated hydroxylamine derivatives

The purpose of our study was to design a new class of acrylate‐based monomers with an UV‐cleavable heteroatom bond, offering the possibility to initiate radical polymerization upon irradiation with UV‐light. A method to derive the double bond conversion from the ATR‐IR spectra of the monomers and the cured polymers was employed, that enabled us to calculate the theoretical polymerization heats of the new monomers. Their photopolymerization properties were determined by Photo Differential Scanning Calorimetry. Surprisingly, some of these new compounds exhibited high photoinitiation activity, comparable to well‐established Type II photoinitiator systems like benzophenone/triethanolamine. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 392–403, 2009     

Dendriform equations

We investigate solutions for a particular class of linear equations in dendriform algebras. Motivations as well as several applications are provided. The latter follow naturally from the intimate link between dendriform algebras and Rota–Baxter operators, e.g. the Riemann integral map or Jackson's q-integral.     

在常微分方程教学中融入数学建模思想的探索与实践

结合常微分方程理论性强和应用性强的特点,探索如何在教材、教学方法等方面融入数学建模思想的方法.     

The spectral method and numerical continuation algorithm for the von Kármán problem with postbuckling behaviour of solutions

In this paper a spectral method and a numerical continuation algorithm for solving eigenvalue problems for the rectangular von Kármán plate with different boundary conditions (simply supported, partially or totally clamped) and physical parameters are introduced. The solution of these problems has a postbuckling behaviour. The spectral method is based on a variational principle (Galerkin’s approach) with a choice of global basis functions which are combinations of trigonometric functions. Convergence results of this method are proved and the rate of convergence is estimated. The discretized nonlinear model is treated by Newton’s iterative scheme and numerical continuation. Branches of eigenfunctions found by the algorithm are traced. Numerical results of solving the problems for polygonal and ferroconcrete plates are presented. Communicated by A. Zhou.