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41.
Some Geometry of the Cone of Nonnegative Definite Matrices and Weights of Associated X2 Distribution
Satoshi Kuriki Akimichi Takemura 《Annals of the Institute of Statistical Mathematics》2000,52(1):1-14
Consider the test problem about matrix normal mean M with the null hypothesis M = O against the alternative that M is nonnegative definite. In our previous paper (Kuriki (1993, Ann. Statist., 21, 1379–1384)), the null distribution of the likelihood ratio statistic has been given in the form of a finite mixture of 2 distributions referred to as X2 distribution. In this paper, we investigate differential-geometric structure such as second fundamental form and volume element of the boundary of the cone formed by real nonnegative definite matrices, and give a geometric derivation of this null distribution by virtue of the general theory on the X2 distribution for piecewise smooth convex cone alternatives developed by Takemura and Kuriki (1997, Ann. Statist., 25, 2368–2387). 相似文献
42.
William J. Martin 《Designs, Codes and Cryptography》2000,21(1-3):181-187
A code C F
n is s-regular provided, forevery vertex x F
n, if x is atdistance at most s from C then thenumber of codewords y C at distance ifrom x depends only on i and the distancefrom x to C. If denotesthe covering radius of C and C is -regular,then C is said to be completely regular. SupposeC is a code with minimum distance d,strength t as an orthogonal array, and dual degrees
*. We prove that d 2t + 1 whenC is completely regular (with the exception of binaryrepetition codes). The same bound holds when C is(t + 1)-regular. For unrestricted codes, we show thatd s
* + t unless C is a binary repetitioncode. 相似文献
43.
If X is a Hausdorff space we construct a 2-groupoid G
2
X with the following properties. The underlying category of G
2
X is the `path groupoid" of X whose objects are the points of X and whose morphisms are equivalence classes f, g of paths f, g in X under a relation of thin relative homotopy. The groupoid of 2-morphisms of G
2
X is a quotient groupoid X / N X, where X is the groupoid whose objects are paths and whose morphisms are relative homotopy classes of homotopies between paths. N X is a normal subgroupoid of X determined by the thin relative homotopies. There is an isomorphism G
2
X(f,f) 2(X, f(0)) between the 2-endomorphism group of f and the second homotopy group of X based at the initial point of the path f. The 2-groupoids of function spaces yield a 2-groupoid enrichment of a (convenient) category of pointed spaces.We show how the 2-morphisms may be regarded as 2-tracks. We make precise how cubical diagrams inhabited by 2-tracks can be pasted. 相似文献
44.
本文给出了基于Lascenov多项式零点(0,2)-插值正则性的充要条件,并给出基多项式存在时的明显表达式。 相似文献
45.
I. G. Mamedov 《Computational Mathematics and Mathematical Physics》2009,49(1):93-104
The Cauchy problem for a fourth-order pseudoparabolic equation describing liquid filtration problems in fissured media, moisture transfer in soil, etc., is studied. Under certain summability and boundedness conditions imposed on the coefficients, the operator of this problem and its adjoint operator are proved to be homeomorphism between certain pairs of Banach spaces. Introduced under the same conditions, the concept of a θ-fundamental solution is introduced, which naturally generalizes the concept of the Riemann function to the equations with discontinuous coefficients; the new concept makes it possible to find an integral form of the solution to a nonhomogeneous problem. 相似文献
46.
Hélène Esnault 《Advances in Mathematics》2008,218(2):395-416
The goal of this article is to show a part of Grothendieck's section conjecture using the identification of sections with neutral fiber functors as defined in [H. Esnault, P.H. Hai, The fundamental groupoid scheme and applications, preprint, 2006, 34 pp.]. 相似文献
47.
在工业和工程领域中,广泛地应用圆柱形弹性薄壁贮液容器。在冲击或地震地面运动激励下,此种容器的变形,严格地说就遵循薄壳结构动力学规律。考虑到在水平地震作用下短圆柱形容器的变形,剪切效应起主导作用,因而可用剪切梁变形理论来近似地代替。对于盛有液体的贮液容器,因为激励引起的振动是耦联的,即液体中产生的液动压力与结构的变形有关,而结构的变形又受到液动压力的很大影响。欲寻求此种耦联体系的动力响应,必须对其动力特性进行分析。为此,本文根据Fischer“冲击质量”理论,提出了对圆柱形弹性贮液容器基频的近似计算方法。此方法概念清晰,计算简便,很便于工程上应用。 相似文献
48.
José Luis Palacios José Miguel Renom 《International journal of quantum chemistry》2010,110(9):1637-1641
Using probabilistic tools, we give tight upper and lower bounds for the Kirchhoff index of any d‐regular N‐vertex graph in terms of d, N, and the spectral gap of the transition probability matrix associated to the random walk on the graph. We then use bounds of the spectral gap of more specialized graphs, available in the literature, in order to obtain upper bounds for the Kirchhoff index of these specialized graphs. As a byproduct, we obtain a closed‐form formula for the Kirchhoff index of the d‐dimensional cube in terms of the first inverse moment of a positive binomial variable. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 相似文献
49.
50.
Baole Lu Haowei Chen Jiaxi Guo Renjian Zhang Zhaoyu Ren 《Optics Communications》2011,284(7):1941-1944
A dual-wavelength laser at 1064 nm and 1319 nm is obtained by a single Nd:YAG crystal rod. On the basis of 1064 nm and 1319 nm dual-wavelength laser installation, the second harmonic waves at 532 nm and 660 nm can be achieved by using non-linear frequency conversion technology. When 1064 nm and 1319 nm lasers oscillate simultaneously, the maximum output power is 30.5 W and 8.78 W, respectively. When the 1319 nm laser is restrained, we obtain a 35.6 W maximum output power at 1064 nm and by contrary 11.2 W at 1319 nm. The maximum output powers of 532 nm and 660 nm lasers are 5.34 W and 1.353 W when oscillating simultaneously. With one of them restrained, the maximum output power is 6.72 W at 532 nm and 1.90 W at 660 nm. The optimum repetition rate of the acousto-optic Q-switch is 10.5 KHz and 20.5 KHz for 532 nm and 660 nm lasers, respectively. The optical-to-optical conversion efficiency from the fundamental waves to the harmonic waves is 17.5% and 15.4%. The instability is less than 2%. 相似文献