In this article the main theorem establishes the necessity and sufficiency of the Poincaré-Hopf inequalities in order for the Morse inequalities to hold. The convex hull of the collection of all Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data determines a Morse polytope defined on the nonnegative orthant. Using results from network flow theory, a scheme is provided for constructing all possible Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data. Geometrical properties of this polytope are described.
We give a surprisingly short proof that in any planar arrangement of n curves where each pair intersects at most a fixed number (s) of
times, the k-level has subquadratic (O(n2-1/2s) complexity. This answers one of the main open problems from the author’s previous paper [DCG 29, 375-393 (2003)],
which provided a weaker upper bound for a
restricted class of curves only (graphs of degree-s polynomials).
When combined with existing tools (cutting curves, sampling, etc.),
the new idea generates a slew of improved k-level results for
most of the curve families studied earlier, including a
near-O(n3/2 bound for parabolas. 相似文献
The first stage in a multi-attribute value analysis is the development of a hierarchical structure of the attributes of the problem. This paper reports the process of developing such a structure for the problem of choosing a suitable mode of transport for radioactive waste. The initial hierarchy of attributes went through several stages of development as new insights emerged about the nature of the problem. Some of the reasons behind this restructuring are discussed, and several important questions about the structuring process are formulated. 相似文献
Methods for obtaining alkylindoles, excluding the Fischer synthesis and direct alkylation, developed during the last 15 years are correlated.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1155–1172, September, 1987. 相似文献
The shortest-paths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one vertex to another often gives the best way to route a message between the vertices. This paper presents anO(n2) time sequential algorithm and anO(n2/p+logn) time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circular-arc graphs, wherep andn represent respectively the number of processors and the number of vertices of the circular-arc graph. 相似文献
The influence of the substrate temperature Tsub (20–360°C) and the oxygen pressure P(O2) (5 × 10−3−0.13 Pa) in an evaporation chamber on the structure and phase composition of films prepared through laser sputtering of a vanadium target is investigated by electron diffraction and in situ transmission electron microscopy (with the use of the bend extinction contour technique for determining the bending of the crystal lattice). It is demonstrated that the oxygen content in the films increases with an increase in the oxygen pressure P(O2) at a fixed substrate temperature Tsub and decreases with an increase in the substrate temperature Tsub at a fixed oxygen pressure P(O2). The conditions responsible for the formation and composition of the crystalline (VO0.9) and amorphous (V2O3) phases in the films are determined. It is established that the phase composition of the film depends on the angle of condensation of the vapor-plasma flow. The crystallization of the V2O3 amorphous phase is accompanied by an increase in the density by 9.2%. It is revealed that the V2O3 spherulites growing in the amorphous film have a bent crystal lattice. The bending of the crystal lattice can be as large as ∼42 deg/μm.
Data on methods for the production of isatin and indole aldoximes, ketoximes, and amidoximes and their reactions are reviewed. Individual syntheses of new heterocycles from indole and isatin oximes are discussed. The principal results from investigation of the biological activity of derivatives of the oximes are also presented. 相似文献
Furocoumarins modified by amino acids were prepared by condensation of the N-hydroxysuccinimide ester of 3-(2,3,5-trimethyl-7-oxofuro[3,2-g]chromen-6-yl)propanoic acid with amino acids. 相似文献