共查询到20条相似文献,搜索用时 31 毫秒
1.
《中学生数学》2002,(13)
We find a formula for the sum of the first n squares:Sn = 12 22 32 42 … n2.We haveS1 = 1, S2 = 12 22 = 5, S3 = l2 22 32 = 14,S4 = 30, S5 = 55, S6 = 91.and so on. To make things a little simpler, we will also use the sum of the squares of the first zero terms , S0 = 02 = 0. Arranging these values in a table,we find thatSince the third differenes △3Sn are constant,these data values must follow a cubic pattern;that is, the formula for the sum of the squares of the first n integers is a cubic function, 相似文献
2.
3.
On the Growth of Components of Meromorphic Solutions of Systems of Complex Differential Equations 总被引:3,自引:0,他引:3
Ling-yun Gao 《应用数学学报(英文版)》2005,21(3):499-504
This paper investigates the problem of the growth of the components of meromorphic solutions of a class of a system of complex algebraic differential equations, and generalized some of N. Toda's results concerning the growth of differential equations to the case of systems of differential equations. The paper considers the existence of admissible solutions of the system of differential equations. 相似文献
4.
James P. Cossey 《代数通讯》2013,41(11):3972-3979
If G is a group of odd order and χ ∈ Irr(G) lifts an irreducible Brauer character ?, then we associate to χ a canonical pair (Q, δ) up to G-conjugacy, where Q is a vertex of ? and δ ∈ Irr(Q) is a linear character of Q. We show that (Q, δ) is a Navarro vertex for χ. We also discuss examples. 相似文献
5.
Qi-kang Ran Ai-nong FangDepartment of Applied Mathematics Shanghai University of Finance Economics Shanghai ChinaDepartment of Applied Mathematics Shanghai Jiaotong University Shanghai China 《应用数学学报(英文版)》2002,18(3):461-470
In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equationsin space W(θ,p)(Ω), which is bigger than W1,p(Ω). Next, using revise reverse Holder inequality we prove that if ωc is uniformly p-think, then there exists a neighborhood U of p, such that for all t ∈U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p. 相似文献
6.
R. A. Lasuriya 《Ukrainian Mathematical Journal》2004,56(4):547-559
We establish upper bounds for a group of *-deviations of Faber sums on the classes of -integrals in a complex plane introduced by Stepanets.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 4, pp. 451–461, April, 2004. 相似文献
7.
DynamicsofPolynomialAutomorphismsofC~N¥ZhangWenjun(HenanUniversity,Kaifeng,P.R.Chian,475001)Abstract:Thispaperisassignedtodis?.. 相似文献
8.
9.
《中国科学A辑(英文版)》2008,(7)
We compute the n-level correlation of normalized nontrivial zeros of a product of L-functions:L(s,π1)···L(s,πk), where πj, j=1,...,k, are automorphic cuspidal representations of GLmj(QA). Here the sizes of the groups GLmj(QA) are not necessarily the same. When these L(s,πj) are distinct, we prove that their nontrivial zeros are uncorrelated, as predicted by random matrix theory and verified numerically. When L(s,πj) are not necessarily distinct, our results will lead to a proof that the n-level correlation of normalized nontrivial zeros of the product L-function follows the superposition of Gaussian Unitary Ensemble (GUE) models of individual L-functions and products of lower rank GUEs. The results are unconditional when m1,...,mk 4,but are under Hypothesis H in other cases. 相似文献
10.
《数学研究与评论》1989,(1)
1. Introduction A theorem of Carleson,as generalized by Duren characterizes those positive measure μ on the unit disc U={z∈C:|z|<1} for which the H~p norm domiates the L~q(μ) norm of elements of H~p. Later on, Hasting proved an analogous results with H~p replaced by A~p, the Bergman space of fuctions f 相似文献
11.
The purpose of this paper is to describe the complexity of models by theirdegrees of unsolvability,J.Richter defined the degree of a structure to be deg ()=sup{deg(),deg(R_i),i=1,…,n},Where is a model for afinite language L={R_i,i=1,…,n}and the universe of is a subset of ω. Shepointed out that, according to her definition, there can be models which areisomorphic but their degrees are different.Also,her discussions are restricted tofinite languages and models whose universes are subsets of ω. 相似文献
12.
13.
Hao ZHAO Wen Huai SHEN 《数学学报(英文版)》2007,23(12):2145-2154
In general category, the group of self-equivalences of sum object can decompose as the product of its two subgroups under certain conditions and also several split short exact sequences are obtained. Subsequently, we apply the above results to the category of space under a space and get some results which are dual to those in fibrewise category. 相似文献
14.
《数学研究与评论》1989,(3)
Two new kinds of direct product of matrices are defined. Their properties are investigated. Direct products of matrix and set of continuous functions are also defined. Many complete sets of orthogonal functions, such as those sets given by Walsh [2], Paley [3], Chrestenson[4], and Watari [5], may be generated by these newkinds of direct product. Direct products are also applicable to the generation of sets of piecewise orthogonal functions. 相似文献
15.
In this paper, we study the orthogonality graphs (see Definition 1.2) of ortholattices. We provide a graph theoretic condition for an ortholattice to be orthomodular. We prove that, the orthogonality graphs of two orthomodular lattices are isomorphic if and only if the lattices are isomorphic. As an application, it is proved that the zero-divisor graph of a Rickart ?-ring is obtained by successively duplicating the vertices of the orthogonality graph of the lattice of projections in the ring. We characterize the finite Rickart ?-rings for which the orthogonality graph of projections is connected. 相似文献
16.
Søren Asmussen José Blanchet Sandeep Juneja Leonardo Rojas-Nandayapa 《Annals of Operations Research》2011,189(1):5-23
We consider the problem of efficient estimation of tail probabilities of sums of correlated lognormals via simulation. This
problem is motivated by the tail analysis of portfolios of assets driven by correlated Black-Scholes models. We propose two
estimators that can be rigorously shown to be efficient as the tail probability of interest decreases to zero. The first estimator,
based on importance sampling, involves a scaling of the whole covariance matrix and can be shown to be asymptotically optimal.
A further study, based on the Cross-Entropy algorithm, is also performed in order to adaptively optimize the scaling parameter
of the covariance. The second estimator decomposes the probability of interest in two contributions and takes advantage of
the fact that large deviations for a sum of correlated lognormals are (asymptotically) caused by the largest increment. Importance
sampling is then applied to each of these contributions to obtain a combined estimator with asymptotically vanishing relative
error. 相似文献
17.
Rahul Pandharipande 《Acta Mathematica》2012,208(2):335-388
The subalgebra of the tautological ring of the moduli of curves of compact type generated by the κ classes is studied in all genera. Relations, constructed via the virtual geometry of the moduli of stable quotients, are used to obtain minimal sets of generators. Bases and Betti numbers of the κ rings are computed. A universality property relating the higher genus κ rings to the genus 0 rings is proven using the virtual geometry of the moduli space of stable maps. The λg-formula for Hodge integrals arises as the simplest consequence. 相似文献
18.
LetR
S (resp.R
A) be the radius of convergence of the Poincaré series of a loop space (S) (resp. of the Betti-Poincaré series of a noetherian connected graded commutative algebraA over a field
of characteristic zero).IfS is a finite 1-connected CW-complex, the rational homotopy Lie algebra ofS is finite dimensional if and only ifR
S-1. OtherwiseR
S<1.There is an easily computable upper bound (usually less than 1) forR
S ifS is formal or coformal.On the other handR
A=+ if and only ifA is a polynomial algebra andR
A=1 if and only ifA is a complete intersection (Golod and Gulliksen conjecture). OtherwiseR
A<1 and the sequence dim Tor
p
H
grows exponentially withp. 相似文献
19.
Jackson Chan 《Geometric And Functional Analysis》2008,17(5):1416-1478
We study the one-dimensional discrete quasi-periodic Schr?dinger equation
. We introduce the notion of variations of potential and use it to define typical potential. We show that for typical
C
3 potential V, if the coupling constant λ is large, then for most frequencies ω, the Lyapunov exponent is positive for all energies E.
Received: December 2005, Accepted: March 2006 相似文献
20.
Students’ views of themselves as learners of mathematics are a decisive parameter for their engagement and success in school. We are interested in students’ experiences with mathematics encompassing cognitive, emotional and motivational aspects. In particular, we focus on capturing the structural properties of affect related to mathematics. Participants in our study were 1,436 randomized chosen students of secondary schools from overall Finland. In the Finnish upper secondary school, there are two different syllabi for mathematics: the general and the advanced one. Schools were invited to organize the survey by one of their year 2 general syllabus courses and one of their year 2 advanced syllabus courses in grade 11. By means of factor analysis, we obtained seven dimensions in which students’ hold beliefs and emotions about mathematics partly intertwined with their motivational orientations. These dimensions are described by reliable scales, which allow outlining an average image of Finnish students’ views of themselves as learners of mathematics. Moreover, we analyzed relations between the seven dimensions and what kind of structure they generate. Thereby, a core of three high correlating dimensions could be identified, yielding different accentuations with regard to course choice. 相似文献