Tail probabilities of the limiting null distributions of the Anderson–Stephens statistics

For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) z_i, i=1,…,n, Anderson and Stephens (Biometrika 59 (1972) 613–621) proposed testing procedures based on the statistics S_max=max_u S(u) and S_min=min_u S(u), where u is a unit vector and nS(u) is the sum of squares of u′z_i's. In this paper, we also consider another test statistic S_range=S_max−S_min. We provide formulas for the P-values of S_max, S_min, S_range by approximating tail probabilities of the limiting null distributions by means of the tube method, an integral-geometric approach for evaluating tail probability of the maximum of a Gaussian random field. Monte Carlo simulations for examining the accuracy of the approximation and for the power comparison of the statistics are given.     

Applications of an automated apparatus for two-dimensional electrophoresis, Model TEP-1, for microsequence analyses of proteins.

Two-dimensional electrophoresis has become a rapid and powerful separation method for the preparation of samples for sequence analysis depending on the development of automated microsequencers accompanied by a blotting technique. We have constructed an automated apparatus for two-dimensional electrophoresis, Model TEP-1, which allows precise analytical runs under computer-control with a fully automated transfer from the first- to the second-dimensional gel. In the present paper we describe several applications of TEP-1 followed by blotting and sequencing to reveal the primary structure of proteins in a complex mixture. Several known and unknown proteins were analyzed. Enzymatic digests of proteins could be directly applied onto the TEP-1, in which a gel of lower molecular weight proteins was used as the second dimension. Subsequent blotting and sequencing provided internal sequence information. The use of TEP-1, followed by blotting, provides spots containing ca. 10-100 pmol protein. These figures permitted the identification of 10-40 amino acid residues from the N-terminus. The TEP-1 provides a simple and rapid separation of complex mixtures obtained from natural sources and chemical, biological or genetic products.     

Analysis of phenothiazines in human body fluids using disk solid-phase extraction and liquid chromatography

Seven phenothiazine derivatives, perazine, perphenazine, prochlorperazine, propericiazine, thioproperazine, trifluoperazine, and flupentixol, have been found to be extractable from human plasma and urine samples using disk solid-phase extraction (SPE) with an Empore C18 cartridge. Human plasma and urine (1 mL each) containing the 7 phenothiazine derivatives were mixed with 2 mL of 0.1M NaOH and 7 mL distilled water and then poured into the disk SPE cartridges. The drugs were eluted with 1 mL chloroform- acetonitrile (8 + 2) and determined by liquid chromatography with ammonium formate/formic acid-acetonitrile gradient elution. The detection was performed by ultraviolet absorption at 250 nm. The separation of the 7 phenothiazine derivatives from each other and from impurities was generally satisfactory using a SymmetryShield RP8 column (150 x 2.1 mm id, 3.5 microm particle size). The recoveries of the 7 phenothiazine derivatives spiked into plasma and urine samples were 64.0-89.9% and 65.1-92.1%, respectively. Regression equations for the 7 phenothiazine derivatives showed excellent linearity, with detection limits of 0.021-0.30 microg/mL for plasma and 0.017-0.30 microg/mL for urine. The within-day and day-to-day coefficients of variation for both samples were commonly below 9.0 and 14.9%, respectively.     

Short Radiative Lifetime and Non-Triplet Sensitization in Near-Infrared-Luminescent Yb(III) Complex with Tripodal Schiff Base

We prepared Ln(III) (Ln=Eu, Gd, and Yb) complexes with a tripodal Schiff base, tris[2-(5-methylsalicylideneimino)ethyl]amine (H₃L) and studied their photophysical properties. Upon ligand excitation, YbL showed Yb(III)-centered luminescence in the near-infrared region. While the overall quantum yield (0.60(1)%) of YbL in acetonitrile was moderate among the reported values for Yb(III) complexes, its radiative lifetime (0.33(2) ms) was significantly shorter than those reported previously. We propose that the ligand-to-metal charge-transfer (LMCT) state mediated the sensitization in YbL. The emission and excitation spectra of EuL indicated the participation of the LMCT state in the sensitization. The radiative lifetime (0.84(7) ms) for EuL in the solid state was rather short compared to those of reported Eu(III) complexes. Our results show that the Yb(III) complex with the Schiff base ligand has two features: the short radiative lifetime and the non-triplet sensitization path.     

Extremely low vertical-emittance beam in the accelerator test facility at KEK

Electron beams with the lowest, normalized transverse emittance recorded so far were produced and confirmed in single-bunch-mode operation of the Accelerator Test Facility at KEK. We established a tuning method of the damping ring which achieves a small vertical dispersion and small x-y orbit coupling. The vertical emittance was less than 1% of the horizontal emittance. At the zero-intensity limit, the vertical normalized emittance was less than 2.8 x 10(-8) rad m at beam energy 1.3 GeV. At high intensity, strong effects of intrabeam scattering were observed, which had been expected in view of the extremely high particle density due to the small transverse emittance.     

Some Geometry of the Cone of Nonnegative Definite Matrices and Weights of Associated X2 Distribution

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).