Alternating copolymerization of ethylene oxide and sulfur dioxide

Copolymerization of ethylene oxide (EO) and sulfur dioxide (SO₂) was conducted by using a variety of amines as catalyst. Aromatic tertiary amines such as quinoline and pyridine were found to show the best catalytic property of the various amines, and copolymerization was carried out in the temperature range between 0 and 80°C with the use of quinoline. The copolymerization rate was approximately first-order in quinoline, EO, and also SO₂. The copolymer, was always composed of the two monomers: 1:1 ratio, independent of the initial concentration of the monomers. The copolymer obtained was a transparent viscous material which decomposed at 218°C to afford a considerable amount of ethylene sulfite. Spectroscopic analysis of the copolymer combined with the results of elemental analysis indicates the copolymer to have the structure The polymerizability of ethylene sulfite, which might be considered an intermediate compound in the copolymerization, was also examined at 60°C for 4 hr in the presence of quinoline, and it was found that ethylene sulfite could not be polymerized under these conditions.     

Photoluminescence of cis- and trans-polyacetylene

The emission intensity in cis-(CH)_χ increases a little and the emission peak shifts a little to shorter wavelength with increasing temperature, which can be interpreted by the distribution of several emission centers in energy. Photoluminescence is also observed in trans-(CH)_χ at around 1.03 μm for the first time.     

Transcendence of the values of infinite products in several variables

The aim of this paper is to prove the transcendence of certain infinite products. As applications, we get necessary and sufficient conditions for transcendence of the value of $\Pi_{k=0}^{\infty}(1+a_{k}^{(1)}{z_{1}r^{k}}+\cdot\cdot\cdot+a_{k}^{(m)}{z_{m}r^{k}})$ at appropriate algebraic points, where r ≥ 2 is an integer and {a_n ⁽ⁱ⁾}_{n≥ 0} (1 ≤ i ≤ m) are suitable sequences of algebraic numbers.     

A finite size scaling test of an SU(2) gauge-spin system

We calculate the correlation functions in the SU(2) gauge-spin system with spin in the fundamental representation. We analyze the result making use of finite size scaling. There is a possibility that there are no second order phase transition lines in this model, contrary to previous assertions.     

Measurement of flow-birefringence using a circularly polarized laser beam

A method of measuring flow-birefringence is reported. In this method, a circularly polarized light wave is transmitted through the flow-birefringent medium. The transmitted elliptically polarized wave is compensated by a Babinet-Soleil plate to convert it back into a circularly polarized wave. The state of circular polarization is confirmed using the rotating-analyser method. Measurements can be carried out with a sample having a fixed azimuth. The minimum detectable optical retardation angle was 5 × 10^-3 degree. This corresponds to a birefringence of Δn = 1 × 10^-10, when the optical path length of the sample cell is 100 mm.     

Laser beam transmission of catv signals using a 400 MHz bandwidth electro-optic light modulator

The optimum configuration of a total-internal-reflection type laser light modulator with surface interdigital electrodes has been obtained. The final specifications of the modulator were an effective half wavelenght voltage of 11.5 V, a capacitance between electrodes of 9.1 pF, and a modulation bandwidth of 400 MHz at 50 Ω load impedance. This corresponds to a remarkable safety factor of 1.7. Some effective means of eliminating harmful resonances due to acoustic waves excited in the electro-optic crystals by the interdigital electrodes were found. A practical optical communication system for transmitting catv signals in the open-air has been built and tested in the field using the modulator. In the system cross modulation and intermodulation between channels were found to be sufficiently small.     

Improvements in Carrier-to-Noise-Ratio (CNR) of Lightwave Amplitude Modulated Vestigial-Sideband (AM-VSB) Transmission Systems by the Use of Optical Isolators

In lightwave community antena television (CATV) systems as well as other optical fiber communication networks, a transmitted optical signal is known to be degraded by an intensity noise produced within the fiber due to the interference between the signal and doubly reflected light. We report on the improvements to the signal degradation due to the double Rayleigh backscattering by inserting optical isolators in the trunk lines of the systems. A carrier-to-noise ratio (CNR) has been calculated as a function of the number and the insertion loss of the isolators. The calculated results indicate that there is an optimum number of isolators, and if the insertion loss is less than 0.3 dB, the CNR degradation can be restored by more than 60%. To test the calculated results, we conducted experiments for the specific case of employing one isolator, and obtained good agreements between the two.     

Infinitely many solutions for a nonlinear Schrödinger equation with general nonlinearity

We prove the existence of infinitely many solutions for

$$\begin{aligned} - \Delta u + V(x) u = f(u) \quad \text { in } \mathbb {R}^N, \quad u \in H^1(\mathbb {R}^N), \end{aligned}$$

where V(x) satisfies \(\lim _{|x| \rightarrow \infty } V(x) = V_\infty >0\) and some conditions. We require conditions on f(u) only around 0 and at \(\infty \).

     

Generalized Contour Dynamics: A Review

Contour dynamics is a computational technique to solve for the motion of vortices in incompressible inviscid flow. It is a Lagrangian technique in which the motion of contours is followed, and the velocity field moving the contours can be computed as integrals along the contours. Its best-known examples are in two dimensions, for which the vorticity between contours is taken to be constant and the vortices are vortex patches, and in axisymmetric flow for which the vorticity varies linearly with distance from the axis of symmetry. This review discusses generalizations that incorporate additional physics, in particular, buoyancy effects and magnetic fields, that take specific forms inside the vortices and preserve the contour dynamics structure. The extra physics can lead to time-dependent vortex sheets on the boundaries, whose evolution must be computed as part of the problem. The non-Boussinesq case, in which density differences can be important, leads to a coupled system for the evolution of both mean interfacial velocity and vortex sheet strength. Helical geometry is also discussed, in which two quantities are materially conserved and whose evolution governs the flow.     

Synthesis of spirocyclic C-arylribosides via cyclotrimerization

[reaction: see text] Spirocyclic C-arylribosides were synthesized from the known gamma-ribonolactone derivative. Lithium acetylide addition followed by glycosylation with 3-(trimethylsilyl)propargyl alcohol converted the ribonolactone to silylated diynes. After desilylation or iodination, subsequent ruthenium-catalyzed cycloaddition of resultant diynes with alkynes or chloroacetonitrile gave spirocyclic C-arylribosides.