食饵种群具有常数收获率的捕食—食饵模型分析

本文研究食饵种群具有常数收获效的捕食－食饵模型：｛ｄｘ／ｄｔ＝ｂｘ＾２（１－ｘ／ｋ）－βｘｙ－ｈｄｙ／ｄｔ＝－ｃｙ＋ｄｘｙ讨论了极限环的存在性、唯一性和正平衡点的全局稳定性以及分界线环的存在性。     

带膨胀机的CO_2跨(超)临界逆循环的热力学分析

ＣＯ２是一种安全可靠的自然工质,可望在空调和热泵系统中得到应用。根据热力学第二定律,本文提出比较各类循环的统一方法一当量温度法。本文对带膨胀机的ＣＯ２跨临界循环及其系统进行分析和研究。结果显示该循环具有较高的用能效率,在技术上是可行的．     

平面多项式系统及其相伴系统

引进平面多项式系统的相伴系统的概念 ,分析了多项式系统与其相伴系统之间在极限环不存在性 ,唯一性 ,中心焦点的判定等问题上的相似之处和不同之处 ,提出了几个公开问题 .     

离心式冷水空调机组中CFC11替代工质的研究

对几种 HFCs、HFEs 类新工质和混合工质M1、M2进行了以在离心式冷水空调机组中替代 CFC11为目标的理论循环性能分析。结果表明,M1具有作为 CFC11 灌注式替代物的潜力;HFC143 循环性能优良,更适合应用于新设计的系统中。     

2-阶邻域连通无爪图的Hamilton性

设Ｇ是无爪图．对ｘ∈Ｖ（Ｇ），若Ｇ［Ｎ（ｘ）］不连通，则存在ｙｉ∈Ｖ（Ｇ）－｛ｘ｝（ｉ－１，２），使｜Ｎ（ｙｉ）∩Ｋｉ（ｘ）｜≥２，且｜Ｎ（ｙｉ）∩Ｎ（Ｋｉ＋１（ｘ））｛ｘ｝｜≥２（ｉ模２），那么称无爪图Ｇ是强２－阶邻域连通的，其中Ｋ１（ｘ），Ｋ２（ｘ）分别表示Ｇ［Ｎ（ｘ）］的两个分支．本文证明了：连通且强２－阶邻域连通的无爪图是Ｈａｍｉｌｔｏｎ图．     

Generalized Poincaré Classes and Cubic Equivalences

Let Y be a smooth projective algebraic surface over ?, and T(Y) the kernel of the Albanese map CH₀(Y)_deg0 → Alb(Y). It was first proven by D. Mumford that if the genus Pg(Y) > 0, then T(Y) is 'infinite dimensional'. One would like to have a better idea about the structure of T(Y). For example, if Y is dominated by a product of curves E₁ × E₂, such as an abelian or a Kummer surface, then one can easily construct an abelian variety B and a surjective 'regular' homomorphism B^?z2 → T(Y). A similar story holds for the case where Y is the Fano surface of lines on a smooth cubic hypersurface in P⁴. This implies a sort of boundedness result for T(Y). It is natural to ask if this is the case for any smooth projective algebraic surface Y ? Partial results have been attained in this direction by the author [Illinois. J. Math. 35 (2), 1991]. In this paper, we show that the answer to this question is in general no. Furthermore, we generalize this question to the case of the Chow group of k—cycles on any projective algebraic manifold X, and arrive at, from a conjectural standpoint, necessary and sufficient cohomological conditions on X for which the question can be answered affirmatively.     

THE VARIATION OF INVARIANT LINES AND LIMIT CYCLES FOR A QUADRATIC DIFFERENTIAL SYSTEM

１ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｒｅａｌｑｕａｄｒａｔｉｃｄｉｆｅｒｅｎｔｉａｌｓｙｓｔｅｍｘ＝－ｙ＋δｘ－４ｘ２＋３ｘｙ＋１３ｙ２ｙ＝ｘ（１－１３ｘ－ｙ）．（１）Ｆｉｒｓｔ，ｆｏｒｃｏｎｖｅｎｉｅｎｃｅ，ｗｅｄｅｎｏｔｅｔｈｅｔｗｏ...     

Sets of Type (a, b) From Subgroups of ΓL(1, pR)

In this paper k-sets of type (a, b) with respect to hyperplanes are constructed in finite projective spaces using powers of Singer cycles. These are then used to construct further examples of sets of type (a, b) using various disjoint sets. The parameters of the associated strongly regular graphs are also calculated. The construction technique is then related to work of Foulser and Kallaher classifying rank three subgroups of AL(1, p ^R). It is shown that the sets of type (a, b) arising from the Foulser and Kallaher construction in the case of projective spaces are isomorphic to some of those constructed in the present paper.     

Curvatures and Currents for Unions of Sets with Positive Reach, II

A class of subsets of ^d which can berepresented as locally finite unions of sets with positive reach isconsidered. It plays a role in PDE's on manifolds with singularities.For such a set, the unit normal cycle (determining the d – 1curvature measures) is introduced as a (d – 1)-currentsupported by the unit normal bundle and its properties are established.It is shown that, under mild additional assumptions, the unit normalcycle (and, hence, also the curvature measures) of such a set can beapproximated by that of a close parallel body or, alternatively, by themirror image of that of the closure of the complement of the parallelbody (which has positive reach). Finally, the mixed curvature measuresof two sets of this class are introduced and a translative integralgeometric formula for curvature measures is proved.