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101.
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
102.
Ultrasonic motors are suitable for a micro-actuator because of a direct drive, no brake and their simple construction. In order to fabricate micro-ultrasonic motors, a piezoelectric thin film is essential. In this study, a hydrothermal method was adopted to deposit a PZT thin film. The dimensions of the stator transducer were: outer diameter, 1.4 mm; inner diameter, 1.2 mm; and length, 5.0 mm. The resonance frequency of the stator transducer was 227 kHz, and the vibration amplitude was 58 nmp-p at an input voltage of 4.0 Vp-p. The maximum revolution speed was 680 rpm, and the maximum starting torque was 0.67 microNm. The experimental conditions were 20 Vp-p and 5.3 mN pre-load. The motor property versus scale was investigated using an equivalent circuit. The calculated results indicated that the output torque of the 100 microns diameter motor was 27 nNm. 相似文献
103.
We give a sufficient condition for admissibility of generalized Bayes estimators of the location vector of spherically symmetric distribution under squared error loss. Compared to the known results for the multivariate normal case, our sufficient condition is very tight and is close to being a necessary condition. In particular, we establish the admissibility of generalized Bayes estimators with respect to the harmonic prior and priors with slightly heavier tail than the harmonic prior. We use the theory of regularly varying functions to construct a sequence of smooth proper priors approaching an improper prior fast enough for establishing the admissibility. We also discuss conditions of minimaxity of the generalized Bayes estimator with respect to the harmonic prior. 相似文献
104.
105.
Mikio Morita 《Tetrahedron》2008,64(8):1753-1758
The reaction of trimethylsilyldiazomethane with thiobenzoyl isocyanates, in situ generated from thiazole-4,5-diones, yielded diazoketones, which were converted into 2-azaazulenes by the intramolecular Buchner reaction. 相似文献
106.
We propose a perturbation method for determining the (largest) group of invariance of a toric ideal defined in [S. Aoki, A. Takemura, The largest group of invariance for Markov bases and toric ideals, J. Symbolic Comput. 43 (5) (2008) 342–358]. In the perturbation method, we investigate how a generic element in the row space of the configuration defining a toric ideal is mapped by a permutation of the indeterminates. Compared to the proof by Aoki and Takemura which was based on stabilizers of a subset of indeterminates, the perturbation method gives a much simpler proof of the group of invariance. In particular, we determine the group of invariance for a general hierarchical model of contingency tables in statistics, under the assumption that the numbers of the levels of the factors are generic. We prove that it is a wreath product indexed by a poset related to the intersection poset of the maximal interaction effects of the model. 相似文献
107.
108.
Summary An existing commercial refractive index detector was modified for use with microbore column LC systems. The detector utilizes the Fresnel method. The effect of band dispersion and dilution at the detector side is of extreme importance in connection with the miniaturized LC system. In the modified model the original heat-exchanger tube was removed and a stainless steel capillary was used for heat-exchanging. Gaskets having different cell volumes were also examined with respect to band broadening and sensitivity. The detection limit was 10ng for di-n-pentyl phthalate. The examples include the detection of phthalates, alcohols, n-paraffins, and kerosine. 相似文献
109.
An existing commercial refractive index detector was modified for use with slurry-packed capillary column LC systems. The cell gasket of the original detector cell was replaced by a micro cell gasket giving a volume of 0.8 μL. The relationship between detector response and the amount of sample injected was examined. The limit of detection was 2-3 ng for di-n-pentyl phthalate. 相似文献
110.
R. Nishi I. Houda K. Kitano Y. Sugawara S. Morita 《Applied Physics A: Materials Science & Processing》2001,72(7):S93-S95
Noncontact imaging was successfully performed with the quartz resonator in air by using the FM detection method. A constant frequency shift mode was used. The frequency shift was about -30 mHz, which was induced by the attractive force gradient. A noncontact image of the Si(111) atomic step was obtained with vertical and lateral resolutions of 0.8 Å and 60 Å. 相似文献