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1.
Gorenstein flatness and injectivity over Gorenstein rings   总被引:1,自引:0,他引:1  
Let R be a Gorenstein ring.We prove that if I is an ideal of R such that R/I is a semi-simple ring,then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein injective dimension of R/I as a left R-module are identical.In addition,we prove that if R→S is a homomorphism of rings and SE is an injective cogenerator for the category of left S-modules,then the Gorenstein flat dimension of S as a right R-module and the Gorenstein injective dimension of E as a left R-module are identical.We also give some applications of these results.  相似文献   

2.
We study the structure of a metric n-Lie algebra G over the complex field C. Let G = SR be the Levi decomposition, where R is the radical of G and S is a strong semisimple subalgebra of G. Denote by m(G) the number of all minimal ideals of an indecomposable metric n-Lie algebra and R ⊥ the orthogonal complement of R. We obtain the following results. As S-modules, R ⊥ is isomorphic to the dual module of G/R. The dimension of the vector space spanned by all nondegenerate invariant symmetric bilinear forms on G is equal to that of the vector space of certain linear transformations on G; this dimension is greater than or equal to m(G) + 1. The centralizer of R in G is equal to the sum of all minimal ideals; it is the direct sum of R ⊥ and the center of G. Finally, G has no strong semisimple ideals if and only if R⊥■R.  相似文献   

3.
In this paper, some test statistics Of Kolmogorov type and Cramervon Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis. The asymptotic properties of Bootstrap approximation are investigated and the tail behaviors of the statistics are studied.  相似文献   

4.
TESTS OF COVARIANCE MATRIX BY USING PROJECTION PURSUIT AND BOOTSTRAP METHOD   总被引:1,自引:0,他引:1  
Testing equality of covariance matrix has long been an interesting issue in statistics inference, To overcome the sparseness of data points in high-dimensional space and deal with the general cases, the author suggests several projection pursuit type statistics. Some results on the limiting distidbutions of the statistics are obtained. Some properties of bootstrap approximation are investigated. Furthermore, for computational reasons an approximation for the statistics based on number-theoretic roethod is applied. Several simulation experiments are performed.  相似文献   

5.
SOME COMPARISONS BETWEEN GENERALIZED ORDER STATISTICS   总被引:1,自引:0,他引:1  
Some stochastic comparisons of generalized order statistics under the right spread order,the location independent riskier order and the total time transform order are investigated in this paper.The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics.  相似文献   

6.
In this paper we obtain the Plancherel formula for the spaces of L~2-sections of the line bundles over the pseudo-Riemannian symmetric space G/H where G = SL(n + 1, R)and H = S(GL(1, R) × GL(n, R)). The Plancherel formula is given in an explicit form by means of spherical distributions associated with the character χ——λof the subgroup H. We follow the method of Faraut, Kosters and van Dijk.  相似文献   

7.
We identify R7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit sphere S6. It is known that a cone over a surface M in S6 is an associative submanifold of R7 if and only if M is almost complex in S6. In this paper, we show that the Gauss-Codazzi equation for almost complex curves in S6 are the equation for primitive maps associated to the 6-symmetric space G2/T2, and use this to explain some of the known results. Moreover, the equation for S1-symmetric almost complex curves in S6 is the periodic Toda lattice, and a discussion of periodic solutions is given.  相似文献   

8.
In this paper,we consider the problem of testing for an autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Lévy processes.For a test,we propose a class of test statistics constructed by an iterated cumulative sums of squares of the difference between two adjacent observations.It is shown that each of the test statistics weakly converges to the supremum of the square of a Brownian bridge.The test statistics are evaluated by some empirical results.  相似文献   

9.
Let R → S be a ring homomorphism and X be a complex of R-modules. Then the complex of S-modules S?_R~L X in the derived category D(S) is constructed in the natural way. This paper is devoted to dealing with the relationships of the Gorenstein projective dimension of an R-complex X(possibly unbounded) with those of the S-complex S?_R~L X.It is shown that if R is a Noetherian ring of finite Krull dimension and φ : R → S is a faithfully flat ring homomorphism, then for any homologically degree-wise finite complex X, there is an equality Gpd_RX = GpdS(S?_R~L X). Similar result is obtained for Ding projective dimension of the S-complex S?_R~L X.  相似文献   

10.
The authors construct PP type estimated Kolmogorov statistics by Projection Pursuittechnique to deal with simultaneously the sparseness of sample points in high-dimensionalspace and the case that distribution occupies the unknown location parameter and disper-sion matrix.Furthermore,the tali behavior of the limit of the statistics is investigated.  相似文献   

11.
Many problems of applied statistics, in particular, hypotheses testing, contain no information about true distributions of the statistics under consideration. Therefore, limit distributions of those statistics are used, which may give inadequate results in actual practice. Problems on the refinement of the distributions thus arise. In the present paper, we extend the results of H. Daniels, R. Lugannani, and S. Rice to the multidimensional case. We prefer to use the Lugannani-Rice method because it yields approximations which are as good as those of other forms and do not depend on variation of statistics. Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 195–202, Perm, 1993.  相似文献   

12.
13.
变换图的直径及Brualdi猜想   总被引:1,自引:0,他引:1  
钱建国 《数学学报》2002,45(2):411-416
设R=(r1,r2…rm)及 S=(S1,S2,…,Sn)为两个正整数向量,满足Σmi=1ri=Σnj=1sj= K.记G(R,S)为(0,1)-矩阵类 U(R,S)的变换图.Brualdi在文山中给出了 G(R,S)的直径厂(G(R,S))的一个上界:mn/2-1,并猜想D(G(R,S))≤mn/4.本文通过对有向图围长的研究得到了D(G(R,S))的一个新的上界:1/2mn-1/6t(t-1)(4t+1),其中T=  .  相似文献   

14.
称R∈Cm×m为k次轮换矩阵若 R的最小多项式为xk-1(k≥2).令μ∈{0,1,…,k-1}和ζ=e2πi/k.若R∈Cm×m和S∈Cn×n为k次轮换矩阵,则称A∈Cm×m为(R,S,μ)对称矩阵若RAS-1μA.本文研究了(R,S,μ) 对称矩阵的逆问题和最佳逼近问题,得到了解的表达式. 并讨论了最佳逼近解的扰动分析,得到了比较满意的理论结果, 最后通过数值算例验证了该理论结果的正确性.  相似文献   

15.
We introduce new estimates and tests of independence in copula models with unknown margins using ?-divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the parameter is an interior point or not. To cite this article: S. Bouzebda, A. Keziou, C. R. Acad. Sci. Paris, Ser. I 347 (2009).  相似文献   

16.
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   

17.

Some new statistics are proposed to test the uniformity of random samples in the multidimensional unit cube These statistics are derived from number-theoretic or quasi-Monte Carlo methods for measuring the discrepancy of points in . Under the null hypothesis that the samples are independent and identically distributed with a uniform distribution in , we obtain some asymptotic properties of the new statistics. By Monte Carlo simulation, it is found that the finite-sample distributions of the new statistics are well approximated by the standard normal distribution, , or the chi-squared distribution, . A power study is performed, and possible applications of the new statistics to testing general multivariate goodness-of-fit problems are discussed.

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18.
In this note we prove the following special case of Serre's conjecture on Intersection Multiplicity: Let be a regular local ring and let , be two prime ideals such that , and dimension of . Then ; here denotes the Hilbert-Samuel multiplicity for any finitely generated module with respect to .

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19.
S-内射模及S-内射包络   总被引:1,自引:0,他引:1  
设R是环.设S是一个左R-模簇,E是左R-模.若对任何N∈S,有Ext_R~1(N,E)=0,则E称为S-内射模.本文证明了若S是Baer模簇,则关于S-内射模的Baer准则成立;若S是完备模簇,则每个模有S-内射包络;若对任何单模N,Ext_R~1(N,E)=0,则E称为极大性内射模;若R是交换环,且对任何挠模N,Ext_R~1(N,E)=0,则E称为正则性内射模.作为应用,证明了每个模有极大性内射包络.也证明了交换环R是SM环当且仅当T/R的正则性内射包e(T/R)是∑-正则性内射模,其中T=T(R)表示R的完全分式环,当且仅当每一GV-无挠的正则性内射模是∑-正则性内射模.  相似文献   

20.
We say that a function is a Hamel function ( ) if , considered as a subset of , is a Hamel basis for . We prove that every function from into can be represented as a pointwise sum of two Hamel functions. The latter is equivalent to the statement: for all there is a such that . We show that this fails for infinitely many functions.

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