A stability study of Navier-Stokes equations (III)

In this paper, the necessary conditions of the existence of C² solutions in some initial problems of Navier-Stokes equations are given, and examples of instability of initial value (at t=0) problems are also given. The initial value problem of Navier-Stokes equation is one of the most fundamental problem for this equation various authors studies this problem and contributed a number of results. J. Lerav, a French professor, proved the existence of Navier-Stokes equation under certain defined initial and boundary value conditions. In this paper, with certain rigorously defined key concepts, based upon the basic theory of J. Hadamard partial differential equations¹, gives a fundamental theory of instability of Navier-Stokes equations. Finally, many examples are given, proofs referring to Ref. [4].     

REMARK ON STABILITY OF ISHIKAWA ITERATIVE PROCEDURES

1　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＳｕｐｐｏｓｅＥｉｓａｒｅａｌＢａｎａｃｈｓｐａｃｅａｎｄＴｉｓａｓｅｌｆｍａｐｏｆＥ .Ｓｕｐｐｏｓｅｘ0 ∈Ｅａｎｄｘｎ+1=ｆ(Ｔ ,ｘｎ)ｄｅｆｉｎｅｓａｎｉｔｅｒａｔｉｏｎｐｒｏｃｅｄｕｒｅｗｈｉｃｈｙｉｅｌｄｓａｓｅｑｕｅｎｃｅｏｆｐｏｉｎｔｓ ｘｎ ∞ｎ=0 ｉｎＥ .Ｆｏｒａｎｅｘａｍｐｌｅ ,ｔｈｅｆｕｎｃｔｉｏｎｉｔｅｒａｔｉｏｎｘｎ+1=ｆ(Ｔ ,ｘｎ) =Ｔｘ0 .ＳｕｐｐｏｓｅＦ(Ｔ) =ｘ∈Ｅ :Ｔｘ=ｘ ≠ ａｎｄｔｈａｔ ｘｎ ｃｏｎｖｅｒｇｅｓｓ…     

A STATE SPACE BIOECONOMIC MODEL OF PACIFIC HALIBUT

Abstract Evaluation of potential economic consequences of alternative management actions requires an understanding of how the biological stock will be affected by the management action and an understanding of the response of economic systems to changes in the timing, magnitude, and size distribution of harvests and changes in the location and catchability of the biological stock. We use a hybrid structural time series model to represent Pacific halibut (Hippoglossus stenolepis) stock and recruitment dynamics and a system of structural equations to represent supply and demand relationships for Pacific halibut from Alaska and British Columbia. Model simulations explore the economic effects of changes in recruitment success, growth rate, and carrying capacity, and changes in international supplies of halibut.     

A critical look at the definition of multidimensional separations

Multidimensional (MD) separations, especially comprehensive two-dimensional (2D) separations such as comprehensive 2D LC (LC × LC), and comprehensive 2D GC (GC × GC), are potentially powerful separation techniques. It is important to have a clear definition of MD techniques to better understand the scope and boundaries of the subject. Widely accepted definitions of MD Separations have their roots in the definition proposed by Giddings. Giddings also added several comments that clarified the scope of his definition. However, some researchers extend Giddings’ definitions beyond their intended scope. Doing so disqualifies such comprehensive 2D techniques as LC × LC, GC × GC and 2D TLC from being considered as 2D techniques. In other instances, extended treatment of Giddings’ definition is used as a basis to justify design-parameters of comprehensive 2D separations despite the fact that these parameters lead to sub-optimal implementations. We believe that the shortcomings in the definition and its popular interpretations are serious enough to warrant attention, especially by those interested in designing optimal instrumentation for MD separations like comprehensive 2D GC. After discussion of the weaknesses in the currently used definitions, we propose to define n-dimensional analysis as one that generates n-dimensional displacement information. We believe that this definition captures the spirit of Giddings’ definition while avoiding the problems associated with its popular interpretations.     

Convex hull: A new method to determine the separation space used and to optimize operating conditions for comprehensive two-dimensional gas chromatography

It is important to develop methods of optimizing the selection of column sets and operating conditions for comprehensive two-dimensional gas chromatography. A new method for the calculation of the percentage of separation space used was developed using Delaunay's triangulation algorithms (convex hull). This approach was compared with an existing method and showed better precision and accuracy. It was successfully applied to the selection of the most convenient column set and the geometrical parameters of second column for the analysis of 49 target compounds in wastewater.     

计算机辅助装调与传统基准传递技术相结合实现三镜消像散系统的装调

为满足复杂航天光学系统对精度的要求,克服传统基准传递技术与计算机辅助装调技术对多于3片反射镜的复杂光学系统进行装调时存在的局限性,提出了两种技术相结合的装调方法。采用提出的方法对三镜消像散(TMA)空间相机进行了装调,结果显示:三镜在Y向和Z向的失调量分别由18.651和9.879 mm降低到1.036和0.102 mm,系统波前差达到全视场平均值1/14λ(RMS)。结果证明:此方法能有效缩短装调时间并达到系统要求的精度指标,对于多镜复杂光学系统装调具有指导和参考价值。     

碳纤维复合材料在航天领域的应用

综述了碳纤维复合材料的应用现状和发展前景。首先,概述了碳纤维的分类和力学性能以及碳纤维复合材料的特性;重点介绍了碳纤维复合材料在国内外航天领域,特别是在卫星结构、运载火箭、精密支撑构件以及空间镜体等方面的应用情况。指出了目前碳纤维复合材料的主要问题是湿热效应。最后,结合我国国情,对碳纤维复合材料需要解决的问题提出了一些建设性的措施。     

幂集上的线性空间

将线性空间的概念提升到线性空间的幂集上进行讨论,给出了线性空间的幂空间的定义,并研究了一种特殊幂空间的基本性质.