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31.
Sauer, Shelah, Vapnik and Chervonenkis proved that if a set system on n vertices contains many sets, then the set system has full trace on a large set. Although the restriction on the size of the
groundset cannot be lifted, Frankl and Pach found a trace structure that is guaranteed to occur in uniform set systems even
if we do not bound the size of the groundset. In this note we shall give three sequences of structures such that every set
system consisting of sufficiently many sets contains at least one of these structures with many sets. 相似文献
32.
Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras (Sym(N))N≥1, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N=1 and N=2). We compute their Hilbert series, introduce and study several combinatorial bases, and establish various algebraic identities
related to the multisection of formal power series with noncommutative coefficients.
Received November 19, 2004 相似文献
33.
The graph-theoretic operation of rooted subtree prune and regraft is increasingly being used as a tool for understanding and modelling reticulation events in evolutionary biology. In this paper, we show that computing the rooted subtree prune and regraft distance between two rooted binary phylogenetic trees on the same label set is NP-hard. This resolves a longstanding open problem. Furthermore, we show that this distance is fixed parameter tractable when parameterised by the distance between the two trees.Received March 16, 2004 相似文献
34.
Admissible slopes for monotone and convex interpolation 总被引:1,自引:0,他引:1
Summary In many applications, interpolation of experimental data exhibiting some geometric property such as nonnegativity, monotonicity or convexity is unacceptable unless the interpolant reflects these characteristics. This paper identifies admissible slopes at data points of variousC
1 interpolants which ensure a desirable shape. We discuss this question, in turn for the following function classes commonly used for shape preserving interpolations: monotone polynomials,C
1 monotone piecewise polynomials, convex polynomials, parametric cubic curves and rational functions. 相似文献
35.
36.
Paulo D. Cordaro 《Advances in Mathematics》2004,184(1):89-118
Taking as a start point the recent article of Meziani [7], we present several results concerning the normalization of a class of complex vector fields in the plane which degenerate along a real curve. We mainly deal with operators with finite regularity and analyze both the local situation as well as the case of normalization near a circle. Some related questions (e.g., on semi-global solvability and on the normalization of a class of generalized Mizohata operators) are also discussed. 相似文献
37.
Reduced rank regression assumes that the coefficient matrix in a multivariate regression model is not of full rank. The unknown rank is traditionally estimated under the assumption of normal responses. We derive an asymptotic test for the rank that only requires the response vector have finite second moments. The test is extended to the nonconstant covariance case. Linear combinations of the components of the predictor vector that are estimated to be significant for modelling the responses are obtained. 相似文献
38.
Abstract. We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem
resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore
these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature. 相似文献
39.
M Gubinelli 《Journal of Functional Analysis》2004,216(1):86-140
We formulate indefinite integration with respect to an irregular function as an algebraic problem which has a unique solution under some analytic constraints. This allows us to define a good notion of integral with respect to irregular paths with Hölder exponent greater than 1/3 (e.g. samples of Brownian motion) and study the problem of the existence, uniqueness and continuity of solution of differential equations driven by such paths. We recover Young's theory of integration and the main results of Lyons’ theory of rough paths in Hölder topology. 相似文献
40.