The geometry of Ingarden spaces

The Randers spaces RFⁿ were introduced by R. S. Ingarden. They are considered as Finsler spaces Fⁿ = (M, α + β) equipped with the Cartan nonlinear connection. In the present paper we define and study what we call the Ingarden spaces, I Fⁿ, as Finsler spaces I Fⁿ = (M, α + β) equipped with the Lorentz nonlinear connection. The spaces R Fⁿ and I Fⁿ are completely different. For I Fⁿ we discuss: the variational problem, Lorentz nonlinear connection, canonical N-metrical connection and its structure equations, the Cartan 1-form ω, the electromagnetic 2-form tF and the almost symplectic 2-form 0. The formula dω = F+θ is established. It has as a consequence the generalized Maxwell equations. Finally, the almost Hermitian model of I Fⁿ is constructed.     

Simplified analytic solutions and a novel fast algorithm for Yb-doped double-clad fiber lasers

In this paper, continuous wave Yb³⁺-doped double-clad fiber lasers (DCFLs) with linear-cavity are investigated theoretically and numerically using the rate equations. Under the steady state conditions, the simplified analytic solutions of Yb³⁺-doped DCFLs under considering the scattering loss are deduced in the strongly pump condition. Compared with the known analytic solutions in published literatures, our analytic solutions are more accurate, especially, at higher reflectivity of output mirror. In addition, a fast and stable algorithm based on the Newton-Raphson method is proposed to simulate numerically Yb³⁺-doped DCFLs. The results by simplified analytic solutions are in good agreement with those by the numerical simulation. Moreover, we have performed the optimization of an Yb³⁺-doped DCFL using the simplified analytic solutions and the numerical simulations, respectively.     

Nonlinear Cauchy problems with small analytic data

We study the lifespan of solutions to fully nonlinear Cauchy problems with small real- or complex-analytic data. Our proofs are based on the method of majorants and the fixed point theorem for a contraction mapping.

     

Autour du théorème de Ferrand–Obata (Concerning the Theorem of Ferrand–Obata)

The aim of this article is to give a new dynamical proof of the Ferrand–Obata theorem when the manifold is compact. This will give us a generalisation of this theorem to transversally conformal foliations ofcodimension greater than three and constant basic functions.     

几类B值小指标鞅空间的原子分解

本文对几类B值小指标鞅空间建立了原子分解定理,利用原子分解讨论了它们之间的相互嵌入关系,其原子分解的存在性和它们之间的关系均与Banach空间的凸性和光滑性有密切联系.     

Analytic Independence of an Ideal Relative to Certain Injective Module Over a Commutative Noetherian Ring

In this paper we will introduce the concepts of analytic independence and analytic spread for ideals relative to certain injective module over a commutative Noetherian ring.     

倒置结构锥形束计算机层析的精确成像与Grangeat算法实现

研究了一种新的圆加垂直单弧段的锥顶轨迹的锥形束计算机层析（CT）的完全性条件和精确重建的Grangeat方法，提出了倒置结构锥形束计算机层析的便于实现的圆加垂直多弧段的成像结构及进行精确重建的完全性条件。利用倒置成像结构与现有成像结构之间的等价关系，给出了倒置结构锥形束计算机层析的重建算法。最后，对上述几方面进行了计算机模拟。     

刚性方程组M~.(t)+C~.X(t)+KX(t)=F(t)解的探讨

讨论了刚性常微分方程组(1)的解析解和数值解,给出了解的一般形式和应用该算法的数值例子.     

描述光伏效应的新解析模型

 对陆启生等人提出的描述光伏效应的解析模型涉及的边界条件进行了讨论，提出了一个适用性更宽的解析模型。通过对新模型、陆的模型以及另一个解析模型的比较，对前两个模型能够描述光伏型光电探测器在强光辐照时的信号饱和效应的原因进行了解释。