Scalarization and lagrange duality in multiobjective optimization

In this paper, we are concerned with scalarization and the Lagrange duality in multiobjective optimization. After exposing a property of a cone-subconvexlike function, we prove two theorems on scalarization and three theorems of the Lagrange duality.     

The enumeration of cyclic mutually nearly orthogonal Latin squares

In this paper, we study collections of mutually nearly orthogonal Latin squares (MNOLS), which come from a modification of the orthogonality condition for mutually orthogonal Latin squares. In particular, we find the maximum such that there exists a set of cyclic MNOLS of order for , as well as providing a full enumeration of sets and lists of cyclic MNOLS of order under a variety of equivalences with . This resolves in the negative a conjecture that proposed that the maximum for which a set of cyclic MNOLS of order exists is .     

A NEW SEMI-ANALYTIC ALGORITHM OF NEARLY SINGULAR INTEGRALS IN HIGH ORDER BOUNDARY ELEMENT ANALYSIS OF 3D POTENTIAL

分析了三维边界元法高阶曲面单元几何特征,定义接近度来表征源点与积分单元的接近程度.利用源点在积分单元上的垂足点建立局部极坐标系,构造与几乎奇异积分核函数具有相同奇异性的近似函数.从奇异积分核函数中扣除其近似函数,分离出积分核中主导的奇异函数部分,将奇异积分分解为规则核函数和奇异核函数两项积分.规则核函数积分应用常规Gauss数值积分计算,奇异核函数积分在局部极坐标系ρθ下分离积分变量ρ和θ,对ρ积分建立解析计算列式,对θ积分应用常规Gauss数值积分计算,从而对三维位势问题高阶边界单元几乎强奇异和几乎超奇异积分建立一种新的半解析算法.给出了若干温度场算例,采用边界元法高阶单元几乎奇异积分半解析法计算了近边界内点位势和位势梯度,并与线性单元正则化算法计算结果对比,结果证明提出的半解析法计算几乎奇异面积分和薄壁结构更加高效.     

Analytic intermediate dimensional elliptic tori for the planetary many-body problem

In our context,the planetary many-body problem consists of studying the motion of(n+1)-bodies under the mutual attraction of gravitation,where n planets move around a massive central body,the Sun.We establish the existence of real analytic lower dimensional elliptic invariant tori with intermediate dimension N lies between n and 3n-1 for the spatial planetary many-body problem.Based on a degenerate KolmogorovArnold-Moser(abbr.KAM)theorem proved by Bambusi et al.(2011),Berti and Biasco(2011),we manage to handle the difficulties caused by the degeneracy of this real analytic system.     

LF拟仿紧空间

本文定义了ＬＦ拟仿紧空间的概念，用半内部等概念给出ＬＦ拟仿紧空间的刻划，作者讨论了ＬＦ拟仿紧空间的半正则化，Ｌ－好的推广等问题，得到一系列结果，还在几乎Ｈｕｔｔｏｎ正则ＬＦ拓扑空间中讨论了ＬＦ拟仿紧空间的进一步的性质。     

集值优化问题的强有效解与Kuhn—Tucker鞍点

首先在局部凸Hausdorff拓扑向量空间中定义了集值优化问题的Kuhn—Tucker鞍点，在近似锥一次类凸集值映射下，讨论了集值优化问题的强有效解与Kuhn—Tucker鞍点之间的关系．     

Characterizations of the Benson Proper Efficiency for Nonconvex Vector Optimization

Under generalized cone-subconvexlikeness for vector-valued mappings in locally-convex Hausdorff topological vector spaces, a Gordan-form alternative theorem is derived. Some characterizations of the Benson proper efficiency under this generalized convexity are established in terms of scalarization, Lagrangian multipliers, saddle-point criterion, and duality.     

EFFECTIVE STABILITY FOR NEARLY INTEGRABLE MAPPINGS WITH INTERSECTION PROPERTY

We consider a nearly integrable mapping with a fixed twist frequency. Under the intersection property and Diophantine condition we prove that the mapping possesses effective stability. In particular, the mapping considered may have different dimensions of action-angle variables in our case.     

Derivation and Consideration of Governing Equations of the Envelope Surface Created by Directional,Nearly Monochromatic Waves

In this paper we expand frequency-based nearly monochromatic waves to propagation-direction-based nearly monochromatic waves, and givesthe new concept of directional, nearly monochromaticwaves, whose energy is almost concentrated in a singlepropagation direction. We show directional,nearly monochromatic waves also create the envelopesurface, which is featured by time-invariant in alinear system. The fact that a non-linear systemmakes the envelope surface time-variant is shown.