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21.
Jesús de la Cal Javier Cárcamo 《Journal of Mathematical Analysis and Applications》2007,334(2):1106-1115
As a consequence of Jensen's inequality, centered operators of probabilistic type (also called Bernstein-type operators) approximate convex functions from above. Starting from this fact, we consider several pairs of classical operators and determine, in each case, which one is better to approximate convex functions. In almost all the discussed examples, the conclusion follows from a simple argument concerning composition of operators. However, when comparing Szász-Mirakyan operators with Bernstein operators over the positive semi-axis, the result is derived from the convex ordering of the involved probability distributions. Analogous results for non-centered operators are also considered. 相似文献
22.
In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows a classical idea of Cullen, but we use a more geometric formulation to show that it is possible to build a rather complete theory. Our theory allows us to extend some important results for polynomials in the quaternionic variable to the case of power series. 相似文献
23.
W. W. Bein P. Brucker M. F. M. Stallmann 《Mathematical Methods of Operations Research》1991,35(4):267-272
Meggido [1974] showed that the maximum flow through sets of sources in a multiple sink flow network is a polymatroidal function. Recently, Federgruen and Groenevelt [1985], [1986] have considered polymatroids that can be represented by a multiple source flow network and have improved the runnung time of an important scheduling application.We give a characterization of network representability and relate representable polymatroids to the theory of gammoids.
Zusammenfassung Meggido [1974] hat gezeigt, daß ein maximaler Fluß durch ein Netzwerk mit mehrfachen Senken eine polymatroidale Funktion beschreibt. Federgruen und Groenvelt [1985], [1986] haben kürzlich solche Polymatroide betrachtet, die durch Flüsse in derartigen Netzwerken repräsentiert werden können und haben so die Laufzeit einer wichtigen Schedulinganwendung verbessern können.Wir geben eine Charakterisierung von Funktionen, die durch derartige Netzflußnetzwerke realisierbar sind. Dabei stellen wir eine Verbindung her zwischen Repräsentierbarkeit und Gammoidtheorie.相似文献
24.
凸集的广义Reuleaux三角形 总被引:1,自引:1,他引:0
常宽凸集的面积最小者为Reulaux三角形,而非常宽凸集的面积最小者为何呢?它就是本文将给出的广义Reuleaux三角形△R。 相似文献
25.
本文研究了混合范数空间H(p,q,a)中解析函数f的Taylor系数,对0<p≤2,0<q<∞,a>0和2≤p<∞,0<q<∞,a>0两种情形,分别给出了f属于H(p,q,a)的必要条件和充分条件。用上述结果我们还得到了几个关于混合范数空间的乘子定理,这些结果也推广了Hardy和Littlewood关于H^p空间的相应结论。 相似文献
26.
The peeling of a d-dimensional set of points is usually performed with successive calls to a convex hull algorithm; the optimal worst-case convex hull algorithm, known to have an O(n˙ Log (n)) execution time, may give an O(n˙n˙ Log (n)) to peel all the set; an O(n˙n) convex hull algorithm, m being the number of extremal points, is shown to peel every set with an O(n-n) time, and proved to be optimal; an implementation of this algorithm is given for planar sets and spatial sets, but the latter give only an approximate O(n˙n) performance. 相似文献
27.
为了消除凸规划问题中极大熵方法所导致的数值病态,该文应用Lagrange乘子法及赋范原理,给出一类凸规划问题的极大熵函数序列,并证明该序列一致收敛于凸规划的最优解。 相似文献
28.
A program to compute many functions dependent on the electron density ρ(r) from the results of ab initio molecular calculations is presented. The program allows the generation of different one-, two-, and three-dimensional grids for further graphical representation or numerical analysis. Other options like extracting separate atom contributions to the function computed or locating maximum and minimum values are also implemented. A number of illustrative applications regarding different ρ(r)-dependent functions are presented and the performance and portability of the program is discussed. 相似文献
29.
In this paper we construct the linear support vector machine (SVM) based on the nonlinear rescaling (NR) methodology (see
[Polyak in Math Program 54:177–222, 1992; Polyak in Math Program Ser A 92:197–235, 2002; Polyak and Teboulle in Math Program
76:265–284, 1997] and references therein). The formulation of the linear SVM based on the NR method leads to an algorithm
which reduces the number of support vectors without compromising the classification performance compared to the linear soft-margin
SVM formulation. The NR algorithm computes both the primal and the dual approximation at each step. The dual variables associated
with the given data-set provide important information about each data point and play the key role in selecting the set of
support vectors. Experimental results on ten benchmark classification problems show that the NR formulation is feasible. The
quality of discrimination, in most instances, is comparable to the linear soft-margin SVM while the number of support vectors
in several instances were substantially reduced. 相似文献
30.
Alexander Koldobsky 《Advances in Applied Mathematics》2004,33(4):728-732
The Busemann–Petty problem asks whether origin-symmetric convex bodies in Rn with smaller areas of all central hyperplane sections necessarily have smaller n-dimensional volume. The solution was completed in the end of the 1990s, and the answer is affirmative if n4 and negative if n5. Since the answer is negative in most dimensions, it is natural to ask what information about the volumes of central sections of two bodies does allow to compare the n-dimensional volumes of these bodies in all dimensions. In this article we give an answer to this question in terms of certain powers of the Laplace operator applied to the section function of the body. 相似文献