Locating subsets of a normed space

Within the framework of Bishop's constructive mathematics, we give conditions under which a bounded convex subset of a uniformly smooth normed space over is located, extending results presented recently by F. Richman and H. Ishihara for subsets of a Hilbert space.

     

The microwave spectrum of 1-phosphabut-3-ene-1-yne, CH2=CHCP

The new molecule 1-phosphabut-3-ene-1-yne, CH₂=CHCP, produced by pyrolyzing prop-1-ene-3-phosphorus dichloride, CH₂=CHCH₂PCl₂, was detected by microwave spectroscopy. The analysis of the rotational transitions indicates that the molecule is planar with constants: A₀ = 46 694(24), B₀ = 2807.7100(21), and C₀ = 2645.8356(21) MHz. These rotational constants indicate that the structure of the vinyl group is essentially the same as that in CH₂=CHCN and CH₂=CHCCH; r(C---C) = 1.432 Å and (C=C---C) = 123.9°. The dipole moment parameters are μ_A = 1.181(2), μ_B = 0.074(1), and μ = 1.183(2) D. The vibrational satellite spectra for the C---CP bending modes indicate that ν₁₁(a′) = 184 ± 30 cm⁻¹ and ν₁₅(a″) = 263 ± 30 cm⁻¹.     

The microwave spectrum,structure, and dipole moment of the unstable molecule phosphaethene,CH2PH

A detailed rotational analysis of the microwave spectrum between 26.5 and 40 GHz of phosphaethene, CH₂PH, has been carried out. This molecule is the simplest member of a new class of unstable molecules—the phosphaalkenes. The species can be produced by pyrolysis of (CH₃)₂PH, CH₃PH₂ and also somewhat more efficiently from Si(CH₃)₃CH₂PH₂. Full first-order centrifugal distortion analyses have been carried out for both ¹²CH₂³¹PH and ¹²CH₂³¹PD yielding: A₀ = 138 503.20(21), B₀ = 16 418.105(26), and C₀ = 14 649.084(28) MHz for ¹²CH₂³¹PH. The 1₀₁-0₀₀μ_A lines have also been detected for ¹³CH₂PH, cis-CDHPH and trans-CHDPH. These data have enabled an accurate structure determination to be carried out which indicates: $\text{r(}\text{H}{}_{\mathrm{c}}\text{C}\text{) = 1.09 ± 0.015}\text{A}\text{?}\text{, ∠(}\text{H}{}_{\mathrm{c}}\text{CP}\text{) = 124.4 ± 0.8°; r(}\text{H}{}_{\mathrm{t}}\text{C}\text{) = 1.09 ± 0.015}\text{A}\text{?}\text{, ∠(}\text{H}{}_{\mathrm{t}}\text{CP}\text{) = 118.4 ± 1.2°; r(}\text{CP}\text{) = 1.673 ± 0.002}\text{A}\text{?}\text{, ∠(}\text{HCH}\text{) = 117.2 ± 1.2°; r(}\text{PH}\text{) = 1.420 ± 0.006}\text{A}\text{?}\text{, ∠(}\text{CPH}\text{) = 97.4 ± 0.4°}$. The dipole moment components have been determined as μ_A = 0.731 (2), μ_B = 0.470 (3), μ = 0.869 (3) D for CH₂PH; μ_A = 0.710 (2), μ_B = 0.509 (10), μ = 0.874 (7) D for CH₂PD.     

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.     

Normal coordinate calculations of benzenoid hydrocarbons: Classification and characterization of Aromatic planar vibrations in polyacenes

Classification methods for aromatic planar vibrations are presented. These methods involve the potential energy distribution analysis and a ring motion analysis, which makes it possible to classify collective motions of CC bonds in these systems into certain typical patterns. The planar vibrations of benzene and polyacenes up to pentacene are classified in this way, and the characteristic vibrations of these molecules are so described and analyzed. Normal coordinate calculations of naphthacene and pentacene have been carried out to illustrate the classification, and results were found to be very satisfactory.     

Theoretical study of the optical manipulation of semiconductor nanoparticles under an excitonic resonance condition

We theoretically study the mechanical interaction between radiation and a semiconductor nanoparticle, based on a microscopic model of confined excitons. The exerted force is calculated by using the Maxwell stress tensor expressed in terms of the microscopic response field. The numerical demonstrations clarify the following: (1) The enhancement of the force by using electronic resonance is remarkable for a particle with a radius of less than 100 nm for semiconductor materials. (2) The spectral peak position of the exerted force is considerably sensitive to nanoscale-size changes which would be useful for highly accurate size-selective manipulation.     

Internal tissue displacement measurement based on ultrasonic wave Doppler signal digital detection and its application to fetal movement monitoring

We have developed a fetal movement monitoring system based on small displacement measurement of internal tissues. When ultrasonic pulses are transmitted to the fetus, the reflected ultrasonic waves which have a Doppler frequency shift due to the fetal movements are detected by using an ultrasonic pulsed Doppler technique. In this paper, we propose a displacement measurement method for internal tissues which is based on the Doppler signal digital detection technique. In the method, the received ultrasonic RF signals are sampled with a sampling frequency of four times higher than the centre frequency of the ultrasonic waves; the Doppler frequency shift signals are derived using digital signal processing. From the detected signals, the internal displacements are estimated using the arc-tangent method. The basic algorithm of the detection method has already been used in the area of blood flow sensing, however, we apply the algorithm to the displacement measurement of internal tissues. The comparison between the proposed method and the conventional method is presented. The fetal movement quantitative monitoring system based on the method which has been constructed is shown.     

Angle and speed distributions of hydrogen desorbing thermally from metal surfaces

On the basis of the theory developed in a previous paper (Part I), the angle and speed distributions of D₂ molecules desorbing thermally from the Ni(111) surface are numerically calculated in the present paper (Part II). The dynamical motion of the activated complex of the recombinative desorption process is calculated by using a model potential surface, which involves a few parameters introduced to describe the necessary features of the potential surface at the transition state. Numerical calculations are carried out, and the results show that the present dynamical theory reproduces very well a variety of the characteristic features of the experimental results, e.g., sharply focused angular distribution, mean translational energy lower than 2k _B T at grazing angle, and the non-Maxwellian profile of the TOF distribution.