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1.
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.
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   

3.
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   

4.
Existence of nonzero positive solutions  of systems of second order elliptic boundary value problems under sublinear conditions is obtained. The methodology is to establish a new result on existence of nonzero positive solutions of a fixed point equation in real Banach spaces by using the well-known theory of fixed point index for compact maps defined on cones, where the fixed point equation involves composition of a compact linear operator and a continuous nonlinear map. The conditions imposed on the nonlinear maps involve the spectral radii of the compact linear operators. Moreover, the nonlinear maps are not required to be increasing in  ordered Banach spaces.  相似文献   

5.
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   

6.
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   

7.
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   

8.
DynamicsofPolynomialAutomorphismsofC~N¥ZhangWenjun(HenanUniversity,Kaifeng,P.R.Chian,475001)Abstract:Thispaperisassignedtodis?..  相似文献   

9.
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   

10.
A matching M of a graph G is an induced matching if no two edges in M arejoined by an edge of G.Let iz(G) denote the total number of induced matchings of G,named iz-index.It is well known that the Hosoya index of a graph is the total number of matchings and the Hosoya index of a path can be calculated by the Fibonacci sequence.In this paper,we investigate the iz-index of graphs by using the Fibonacci-Narayana sequence and characterize some types of graphs with minimum and maximum iz-index,respectively.  相似文献   

11.
1.IntroductionPeoplehavepaidmoreattentiontolathcevaluedlogicsystem,whichwillbecomemuchbetterlogicalsystemforintelligentcomputer.InreferenceL1JXuYangpresentanalgebrastructure-latticeimplicationalgebrabycomblngthelatticewithimplicationalgebraastruevaluefieldoflatticevaluedlogicaIsystem.Afterthat,westudytheimplicationhomomor-phism,congruencerelationsandalgebraicstructureoflatticeimplicationalgebraanddiscussthefirstorderlogicalsystemFMbasedonlatticeimplicationalgebras,andobtainedseveralimpor-ta…  相似文献   

12.
Berezhnoi  E. I. 《Mathematical Notes》2003,74(3-4):316-325
In the first part of this paper, we give a complete answer to an old question of the geometric theory of Banach spaces; namely, we construct an infinite-dimensional closed subspace of Hölder space such that each function not identically zero is not smoother at each point than the nonsmoothest function in Hölder space. In the second part, using constructions from the first part, we show that the set of functions from Hölder space which are smoother on a set of positive measure than the nonsmoothest function is a set of first category in this space.  相似文献   

13.
Boris Youssin 《K-Theory》1997,11(4):373-395
We define the notion of cobordism of two objects in a trianulated category, and the Witt group of such category is defined as the Grothendieck group of cobordism classes of self-dual objects. We prove that the Witt group of a t-category is a free Abelian group generated by the classes of irreducible self-dual objects of its heart. In case of derived category of of complexes of sheaves on a stratified space with the middle-perversity t-structure, these irreducibles are local systems on the strata.  相似文献   

14.
We construct the topological Fukaya category of a surface with genus greater than one, making this model intrinsic to the topology of the surface. Instead of using the area form of the surface, we use an admissibility condition borrowed from Heegaard-Floer theory which ensures invariance under isotopy. In this paper we show finiteness of the moduli space using purely topological means and compute the Grothendieck group of the topological Fukaya category. We also show the faithfulness of MCG-action on the topological Fukaya category in this setup.  相似文献   

15.
孟晓青 《数学进展》1996,25(4):305-310
广义度量空间和偏序集都具有函数空间.而函数空间的存在为数学构造和计算提供了很大方便.本文还讨论了广义度量空间和偏序集之间的相互转化问题.  相似文献   

16.
首先引入了直觉Fuzzifying邻域系和直觉Fuzzifying邻域空间的概念,进而证明了直觉Puzzifying邻域空间范畴IFYNS同构于直觉Fuzzifying拓扑空间范畴IFYTOP.  相似文献   

17.
We investigate the category of cubical sets with some additional degeneracies called connections. We prove that the realisation of a cubical set with connections is independent, up to homotopy, of whether we collapse those extra degeneracies or not and that any cubical set which is Kan admits connections. Using this type of cubical sets we define the cubical classifying space of a category and prove that this is equivalent to the simplicial one.  相似文献   

18.
The dicoverings of a “well pointed” d-space are classified as quotients of the universal dicovering space under congruence relations. We prove that the subcategory of d-spaces generated by the subcategory of directed cubes is equal to the category generated by the interval and the directed interval. Similarly, the category of topological spaces generated by simplices may be generated by the interval.  相似文献   

19.
我们定义纯奇点范畴D_(psg)~b(R)为有界纯导出范畴D_(pur)~b(R)与纯投射模构成的有界同伦范畴K~b(■)的Verdier商,得到了纯奇点范畴D_(psg)~b(R)三角等价于相对纯投射模的Gorenstein范畴的稳定范畴■的一个充分必要条件.同时,还给出三角等价D_(psg)~b(R)≌D_(psg)~b(S)的充分条件,这里R和S都是环.  相似文献   

20.
In this note we prove that the coherent homotopy category over a fixed space B with morphisms represented by certain homotopy commutative squares (see [8]) is isomorphic to the category obtained by formally inverting those maps in the category TopB of topological spaces over B which are ordinary homotopy equivalences.  相似文献   

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