Principal points of a multivariate mixture distribution

A set of n-principal points of a distribution is defined as a set of n points that optimally represent the distribution in terms of mean squared distance. It provides an optimal n-point-approximation of the distribution. However, it is in general difficult to find a set of principal points of a multivariate distribution. Tarpey et al. [T. Tarpey, L. Li, B. Flury, Principal points and self-consistent points of elliptical distributions, Ann. Statist. 23 (1995) 103-112] established a theorem which states that any set of n-principal points of an elliptically symmetric distribution is in the linear subspace spanned by some principal eigenvectors of the covariance matrix. This theorem, called a “principal subspace theorem”, is a strong tool for the calculation of principal points. In practice, we often come across distributions consisting of several subgroups. Hence it is of interest to know whether the principal subspace theorem remains valid even under such complex distributions. In this paper, we define a multivariate location mixture model. A theorem is established that clarifies a linear subspace in which n-principal points exist.     

Synthesis and pharmacological evaluation of 1-isopropyl-1,2,3,4-tetrahydroisoquinoline derivatives as novel antihypertensive agents

A series of 1-isopropyl-1,2,3,4-tetrahydroisoquinoline derivatives were synthesized and their bradycardic activities were evaluated in isolated guinea pig right atria. Structure-activity relationship studies revealed that the introduction of an appropriate substituent and its position on the 1,2,3,4-tetrahydroisoquinoline ring are essential for potent in vitro activity. Furthermore, the tether between the piperidyl moiety and the terminal aromatic ring is important for potent antihypertensive activity. Oral administration of 6-fluoro-1-isopropyl-2-{[1-(2-phenylethyl)piperidin-4-yl]carbonyl}-1,2,3,4-tetrahydroisoquinoline (3b) to spontaneously hypertensive rats (SHR) elicited antihypertensive effects without inducing reflex tachycardia, which is often caused by traditional L-type Ca2? channel blockers.     

Synthesis and pharmacological evaluation of 1-alkyl-N-[(1R)-1-(4-fluorophenyl)-2-methylpropyl]piperidine-4-carboxamide derivatives as novel antihypertensive agents

We synthesized and evaluated inhibitory activity against T-type Ca(2+) channels for a series of 1-alkyl-N-[(1R)-1-(4-fluorophenyl)-2-methylpropyl]piperidine-4-carboxamide derivatives. Structure-activity relationship studies have revealed that the isopropyl substituent at the benzylic position plays an important role in exerting potent inhibitory activity, and the absolute configuration of the benzylic position was found to be opposite that of mibefradil, which was first launched as a new class of T-type Ca(2+) channel blocker. Oral administration of N-[(1R)-1-(4-fluorophenyl)-2-methylpropyl]-1-[2-(3-methoxyphenyl)ethyl]piperidine-4-carboxamide (17f) lowered blood pressure in spontaneously hypertensive rats without inducing reflex tachycardia, an adverse effect often caused by traditional L-type Ca(2+) channel blockers.     

Dynamical spin susceptibility of the d–p model in the over doping region

Dynamical spin susceptibility χ^s(q,ω) of the d–p model in the over doping region is investigated by using the auxiliary boson technique. It includes higher order terms of the 1/N-expansion within the random phase approximation (RPA) of the local vertex, where frequency dependence of the quasi-particle interaction is taken into account. The incommensurate spin fluctuation is obtained due to the nesting effect in the low energy region (ωω^*), whereas the commensurate one in the high energy region (ωω^*), the characteristic energy ω^* is estimated to be about 30 meV. Both of the spin–lattice relaxation rate 1/T₁ and the spin–spin relaxation rate 1/T_g monotonically increase as T decreases, while the spin Knight shift K is almost independent of T.     

Infrared spectra of 1-phosphapropyne,CH3CP,and its perdeuteride,CD3CP

The infrared spectra of 1-phosphapropyne, CH₃CP, and its perdeuteride, CD₃CP, have been measured in the gaseous and solid states. The Q_K branches of perpendicular bands have been analyzed in terms of the usual quadratic expression in K. Fermi resonances were identified for the ν₁, ν₂ + ν₃, 2ν₃, 2ν₆⁰; and ν₅, 2ν₃ + ν₈ band systems of CH₃CP and the ν₁, 2ν₃, 2ν₆⁰; ν₆, ν₇ + ν₈; and ν₇, 3ν₈¹ band systems of CD₃CP. The xy Coriolis interaction was also identified between the ν₃ and ν₆ bands of the two species. All the fundamentals were assigned and the normal coordinate treatment was carried out along with the Coriolis constants, ζ^z.