光滑曲线与可求长曲线的注记

文献[1]指出光滑性不是建立弧长计算公式的必要条件,并在导数x’（t）,y’（t）可积的条件下建立了弧长计算公式．本文对可求长曲线弧长的计算问题进一步探讨,在黎曼（Riemann）可积条件下,给出有限维赋范线性空间上的曲线弧长计算公式．     

On Some Families of Smooth Affine Spherical Varieties of Full Rank

Let G be a complex connected reductive group. Losev has shown that a smooth affine spherical G-variety X is uniquely determined by its weight monoid, which is the set of irreducible representations of G that occur in the coordinate ring of X. In this paper we use a combinatorial characterization of the weight monoids of smooth affine spherical varieties to classify:(a) all such varieties for G = SL(2) × C~×and(b) all such varieties for G simple which have a G-saturated weight monoid of full rank. We also use the characterization and Knop's classification theorem for multiplicity free Hamiltonian manifolds to give a new proof of Woodward's result that every reflective Delzant polytope is the moment polytope of such a manifold.     

On some spaces which can be partitioned by the rational line

Extending the Main Theorem of [8], we consider in this paper some topological spaces (not necessarily metrizable) which can be partitioned by the rational line. Based on W. Sierpiski's theorem (Lemma 1) the following results are obtained. Theorem. A regular, first countable, self-dense and hereditarily paracompact space can be partitioned by the rational line. Theorem. A hereditarily paracompact orderable space can be partitioned by the rational line iff it is self-dense and first countable. Some important non-metrizable spaces satisfying the hypotheses of the above theorems, as examples, are enumerated. We take orderable _µ-metric spaces (u>0) as example to illustrate the fact: there exist spaces which are hereditarily paracompact, orderable but can't be partitioned by the rational line.     

A Factorization Problem on a Smooth Two-Dimensional Surface

Mathematical Notes - Given a continuous complex-valued function $$a$$ and nonnegative functions $$\rho_1$$ and $$\rho_2$$ on a two-dimensional smooth connected closed surface such that...     

防范经理事后隐藏信息的模型研究

首先,指出了经理隐匿信息的道德风险行为对所有者的危害性.其次,构造了一个防范经理在签约后隐匿信息的报酬契约.再次,在委托代理框架下给出了契约的最优解.最后,分析了最优契约的特征与性质.文章得到的一些结论对经理选任聘任机制和报酬激励机制的设计有一定的参考价值.     

On the Affine Schur Algebra of Type A II

By studying certain centralizer subalgebras of the affine Schur algebra we show that is Noetherian and we determine its center. Assuming n ≥ r, we show that is Morita equivalent to , and the Schur functor is an equivalence under certain conditions. The author acknowledges support by National Natural Science Foundation of China No.10131010.     

Infinite Patterns that can be Avoided by Measure

A set A of real numbers is called universal (in measure) ifevery measurable set of positive measure necessarily containsan affine copy of A. All finite sets are universal, but no infiniteuniversal sets are known. Here we prove some results relatedto a conjecture of Erds that there is no infinite universalset. For every infinite set A, there is a set E of positivemeasure such that (x + tA)E fails for almost all (Lebesgue)pairs (x, t). Also, the exceptional set of pairs (x, t) (forwhich (x + tA)E) can be taken to project to a null set on thet-axis. Finally, if the set A contains large subsets whose minimumgap is large (in a scale-invariant way), then there is ER ofpositive measure which contains no affine copy of A. 1991 MathematicsSubject Classification 28A12.     

On the Topology of Singularities of the Set of Supporting Hyperplanes of a Smooth Submanifold in an Affine Space

Many new universal relations are obtained between the Eulernumbers of manifolds of singular supporting hyperplanes of anarbitrary generic smooth closed k-dimensional submanifold inRⁿ where n 7 or k = 1. These relations are applied to Barner-convexcurves in an odd-dimensional space Rⁿ. A universal (nontrivial)linear relation is established between the numbers of singularsupporting hyperplanes of various types but of the same totalmultiplicity n of tangency with a given generic smooth closedconnected Barner-convex curve in Rⁿ. The coefficients of thisrelation are defined by Catalan numbers.     

On the Extent to Which Certain Fixed-Charge Depot Location Problems can be Solved by LP

This paper considers a class of feasible set fixed-charge depot location problems which have been formulated as mixed-integer programmes. Computational results are reported to show that linear programming often produces integer solutions to uncapacitated problems as required. It is suggested that this represents a practical solution approach. Computational evidence suggests this convenient property does not extend to capacitated problems.Discussion of reducing infinite set problems to such feasible set problems is included.     

A characterization of graphs which can be approximated in area by smooth graphs

For vector valued maps, convergence in W ^1,1 and of all minors of the Jacobian matrix in L ¹ is equivalent to convergence weakly in the sense of currents and in area for graphs. We show that maps defined on domains of dimension n≥ 3 can be approximated strongly in this sense by smooth maps if and only if the same property holds for the restriction to a.e. 2-dimensional plane intersecting the domain. Received April 29, 1999 / final version received July 21, 2000?Published online September 25, 2000     

On graphs that can be oriented as diagrams of ordered sets

We study some equivalent and necessary conditions for a finite graph to be the covering graph of a (partially) ordered set. For each 1, M. Aigner and G. Prins have introduced a notion of a vertex colouring, here called -good colouring, such that a 1-good colouring is the usual concept and graphs that have a 2-good colouring are precisely covering graphs. We present some inequalities for the corresponding chromatic numbers , especially for x ₂. There exist graphs that satisfy these inequalities for =2 but are not covering graphs. We show also that x ₂ cannot be bounded by a function of x=x ₁. A construction of Neetil and Rödl is used to show that x ₂ is not bounded by a function of the girth.