开端同轴线应用于无损检测的理论分析

基于测量待测物质在开端波导处的反射以确定其介电特性，由于无需制作样品而成为一种简便的无损检测方法，其关键是要确定反向系数与待测物质介电常数之间的对应关系。在本文中，应用并矢格林函数和特征模理论研究了同轴线开端处的电磁场。利用矩量法进行数值计算，得出介电常数与反射系数的数值对应关系。数值结果与有关文献的比较分析证实了理论分析的可靠性。     

Finite element solution of an enclosed turbulent diffusion flame

A finite element formulation of enclosed turbulent diffusion flames is presented. A primitive variables approach is preferred in the analysis. A mixed interpolation is employed for the velocity and pressure. In the solution of the Navier-Stokes equations, a segregated formulation is adopted, where the pressure discretization equation is obtained directly from the discretized continuity equation, considering the velocity-pressure relationships in the discretized momentum equations. The state of turbulence is defined by a κ–? model. Near solid boundaries, a wall function approach is employed. The combustion rates are estimated using the eddy dissipation concept. The expensive direct treatment of the integrodifferential equations of radiation is avoided by employing the moment method, which allows the derivation of an approximate local field equation for the radiation intensity. The proposed finite element model is verified by investigating a technical turbulent diffusion flame of semi-industrial size, and comparing the results with experiments and finite difference predictions.     

Stability of neutral stochastic functional differential equations with Markovian switching driven by G-Brownian motion

Little seems to be known about stability results on the neutral stochastic function differential equations with Markovian switching driven by G-Brownian (G-NSFDEwMSs). This paper aims at investigating the pth moment exponential stability for G-NSFDEwMSs to fill this gap. Some sufficient conditions on the pth moment exponential stability of the trivial solution are derived by employing the Razumikhin-type method, stochastic analysis, and algebraic inequality technique. Moreover, an example is provided to illustrate the effectiveness of the obtained results.     

A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit

We revisit a result by Coron and Guerrero stating that the one-dimensional transport-diffusion equation

     

Improved moment estimates for invariant measures of semilinear diffusions in Hilbert spaces and applications

We study regularity properties for invariant measures of semilinear diffusions in a separable Hilbert space. Based on a pathwise estimate for the underlying stochastic convolution, we prove a priori estimates on such invariant measures. As an application, we combine such estimates with a new technique to prove the L¹-uniqueness of the induced Kolmogorov operator, defined on a space of cylindrical functions. Finally, examples of stochastic Burgers equations and thin-film growth models are given to illustrate our abstract result.     

图像修复中BSCB模型的粘性分析

考虑图像修复中BSCB方程和变形的BSCB方程组的粘性问题.运用半群理论,得到粘性BSCB方程光滑解的存在唯一性.此外,利用粘性消失方法还得到:当粘性系数v→0时,粘性变形的BSCB方程组的解在经典意义下收敛到变形的BSCB方程组的解.     

The Index theorem for quasi-tori

The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the signature of the associated hermitian form. In this article, this theorem is generalized to quasi-tori, i.e. connected complex abelian Lie groups which are not necessarily compact. In view of the Remmert–Morimoto decomposition of quasi-tori as well as the Künneth formula, it suffices to consider only Cousin-quasi-tori, i.e. quasi-tori which have no non-constant holomorphic functions. The Index theorem is generalized to holomorphic line bundles, both linearizable and non-linearizable, on Cousin-quasi-tori using L²$L^2$-methods coupled with the Kazama–Dolbeault isomorphism and Bochner–Kodaira formulas.     

Parabolic Schemes for Quasi-Linear Parabolic and Hyperbolic PDEs via Stochastic Calculus

We consider two quasi-linear initial-value Cauchy problems on ? ^d : a parabolic system and an hyperbolic one. They both have a first order non-linearity of the form φ(t, x, u)·?u, a forcing term h(t, x, u) and an initial condition u ₀ ∈ L ^∞(? ^d ) ∩ C ^∞(? ^d ), where φ (resp. h) is smooth and locally (resp. globally) Lipschitz in u uniformly in (t, x). We prove the existence of a unique global strong solution for the parabolic system. We show the existence of a unique local strong solution for the hyperbolic one and we give a lower bound regarding its blow up time. In both cases, we do not use weak solution theory but a direct construction based on parabolic schemes studied via a stochastic approach and a regularity result for sequences of parabolic operators. The result on the hyperbolic problem is performed by means of a non-classical vanishing viscosity method.