Nonstandard second-order arithmetic and Riemannʼs mapping theorem

In this paper, we introduce systems of nonstandard second-order arithmetic which are conservative extensions of systems of second-order arithmetic. Within these systems, we do reverse mathematics for nonstandard analysis, and we can import techniques of nonstandard analysis into analysis in weak systems of second-order arithmetic. Then, we apply nonstandard techniques to a version of Riemannʼs mapping theorem, and show several different versions of Riemannʼs mapping theorem.     

基地化保障模式下飞机四站装备需求确定研究

基地化保障模式对飞机保障资源需求的影响是制约其发展的重要问题.基于离散事件仿真(DES)方法建立了航空兵场站四站保障过程的数学模型,考虑了四站装备自身故障的影响,并在所建模型的基础上提出运用离散系统仿真软件ARENA对四站保障过程进行仿真.仿真结果表明,与现行的航空兵场站单机种保障策略相比,基地化保障模式能够减少各个机种通用的四站装备数量需求,而单个机种特有的四站装备需求不变.     

Optical characterization of polycarbonate: Influence of additives on optical properties

In laser transmission welding of thermoplastics the optical properties of the joining parts determine the quality of the welding result. Especially, the scattering of laser radiation in the transparent welding part has an impact on weld seam properties. This scattering is caused by additives. For polycarbonate (PC) with different additives the transmittance, the reflectance and the collimated transmittance are measured with a UV‐VIS‐NIR spectrometer. From this data, the optical properties, such as scattering coefficient, absorption coefficient, and anisotropy factor are calculated. The calculations are made with the aid of the four‐flux model of radiation transport in the diffusive approximation. The results show that the additives have a significant influence on the scattering coefficient. For most additives under consideration the scattering is forward directed, which means that most of the radiation is transmitted into the absorbing welding part. However, the power density distribution of the transmitted radiation may differ significantly from PC without additives. So, the weld seam may also differ due to different additives. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 451–455, 2010     

A generalization of a conservativity theorem for classical versus intuitionistic arithmetic

A basic result in intuitionism is Π⁰₂‐conservativity. Take any proof p in classical arithmetic of some Π⁰₂‐statement (some arithmetical statement ?x.?y.P(x, y), with P decidable). Then we may effectively turn p in some intuitionistic proof of the same statement. In a previous paper [1], we generalized this result: any classical proof p of an arithmetical statement ?x.?y.P(x, y), with P of degree k, may be effectively turned into some proof of the same statement, using Excluded Middle only over degree k formulas. When k = 0, we get the original conservativity result as particular case. This result was a by‐product of a semantical construction. J. Avigad of Carnegie Mellon University, found a short, direct syntactical derivation of the same result, using H. Friedman's A‐translation. His proof is included here with his permission. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Λ型原子与单模光场的非共振作用制备四光子相干态

根据简并Λ型三能级原子与单模光场的改进型有效哈密顿量 ,通过矩阵形式法推导出原子光场系统的波函数 ,提出利用简并Λ型三能级原子与单模光场的远离共振相互作用制备四光子相干态的有效方案。并且证明按照同样的方法不能制备出四成分以上的相干叠加态 ,即当在腔中注入的第三个原子的速度与第二个原子的速度相等时 ,腔场将保持这种四光子相干叠加态不变     

晶体中三阶有效非线性系数的计算方法

经过对ｘ（３）ｉｊｋｌ的脚标进行简化压缩处理，首次得出了全部晶体点群共１１种不同的Ｘ（３）ｉｍ矩阵表达形式及Ｋｌｅｉｎｍａｎ对称条件成立下的简化形式，给出了各类晶体中四波相互作用过程中Ｘ（３）＾ｅｆｆ的计算方法。     

一个矩阵不等式和Bayes无偏估计（英）

ＡｎＩｎｅｑｕａｌｉｔｙｏｆＭａｔｒｉｘａｎｄＢａｙｅｓＵｎｂｉａｓｅｄＥｓｔｉｍａｔｅｓＺｈａｎｇＹａｏｔｉｎｇ（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙｏｆＦｉｎａｎｃｅａｎｄＥｃｏｎｏｍｉｃｓ，２００４３３）ＡｂｓｔｒａｃｔＴｈｅｉｎｅｑｕａｌｉ...     

Existence test for solution of nonlinear systems applying affine arithmetic

A computational test is proposed for existence of solution in nonlinear systems. In this test, an interval inclusion of Newton mapping is estimated applying affine arithmetic. Numerical examples are presented to show the efficiency of this test.