Trace Equivalence in SU(2, 1)

In this paper it is shown that one can choose an arbitrarily large number of inconjugate elements of the group Z/2Z*Z/2Z*Z/2Z which have the property that, under all representations of the group in SU(2,1) as a discrete complex hyperbolic ideal triangle group, the elements are hyperbolic and correspond to closed geodesics of equal length on the associated complex hyperbolic surface. This is an analogue of the geometric fact that the multiplicity of the length spectrum of a Riemann surface is never bounded or the equivalent algebraic phenomenon that an arbitrarily large number of conjugacy classes in a free group can have the same trace under all representations in SL(2,R ).     

The Maximal Closed Classes of Unary Functions in p-Valued Logic

In many-valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many-valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many-valued logic functions, respectively. The first two problems have been completely solved ([1], [2], [8]), and the solution to the third problem boils down to determining all maximal subgroups in the k-degree symmetric group S_k, which is an open problem in the finite group theory. In this paper, all maximal closed sets in the set of unary p-valued logic functions are determined, where p is a prime. Mathematics Subject Classification: 03B50, 20B35.     

Image guide couplers with dielectric coupling elements and radiation reduction

Directional couplers in image guide technique for millimeter-wave circuits are discussed, and steps to improve their properties are demonstrated. The simple two-line-9 dB coupler with periodical coupling is compared to a design with an intermediate dielectric coupling element to reduce the frequency dependence. Radiation from the waveguide bends can be reduced significantly by inserting absorber materials at critical points. Experimental results for a-3 dB coupler are also given.     

New generalized computations of quasi-planar waveguides characteristics

An efficient hybrid field solution to the general multilayer substrates transmission line problems with full shielded and half open cross-sectional geometry is presented by using the waveguide modes coupling and decoupling procedure in the spectral domain. Modal transverse transmission lines corresponding to the LSE and LSM modes are taken into account so that the Green's elements for the edge conditions can be derived by a simple iterative method. In this paper, we analyze not only the propagation constants and characteristic impedances but also the available transmission power capacity and power distribution of most commonly used structures. Normalized eigenmode power levels characterizing the propagation features are computed.     

Transient flow towards a well in an aquifer including the effect of fluid inertia

Transient propagation of weak pressure perturbations in a homogeneous, isotropic, fluid saturated aquifer has been studied. A damped wave equation for the pressure in the aquifer is derived using the macroscopic, volume averaged, mass conservation and momentum equations. The equation is applied to the case of a well in a closed aquifer and analytical solutions are obtained to two different flow cases. It is shown that the radius of influence propagates with a finite velocity. The results show that the effect of fluid inertia could be of importance where transient flow in porous media is studied.List of symbols b Thickness of the aquifer, m - c ₀ Wave velocity, m/s - k Permeability of the porous medium, m² - n Porosity of the porous medium - p( ,t) Pressure, N/m² - Q Volume flux, m³/s - r Radial coordinate, m - r _w Radius of the well, m - s Transform variable - S Storativity of the aquifer - S _d(r, t) Drawdown, m - t Time, s - T Transmissivity of the aquifer, m²/s - ( ,t) Velocity of the fluid, m/s - Coordinate vector, m - z Vertical coordinate, m - Coefficient of compressibility, m²/N - Coefficient of fluid compressibility, m²/N - Relaxation time, s - (r, t) Hydraulic potential, m - Dynamic viscosity of the fluid, Ns/m² - Dimensionless radius - Density of the fluid, Ns²/m⁴ - (, ) Dimensionless drawdown - Dimensionless time - , x Dummy variables - ₀, ₁ Auxilary functions     

THE ESTABLISHMENT OF TWO SETS OF ALIEN ADDITION LINES OF WHEATWHEATGRASS

The procedure and method for the transfer of two sets of 14 pairs of wheatgrass (Agropyron interrnedium) chromosomes into common wheat to establish two sets of wheat-wheatgrass alien addition lines are reported. Meanwhile, observations and analyses have been made on the phenotypicaI characters of all the 14 alien addition lines established. It is determined that wheatgrass chromosomes in some of the established addition lines carry the rustresistant genes. In addition, questions concerning the location and distribution of certain agriculturally important genes of wheatgrass chromosomes have been discussed.     

New far infrared laser lines obtained by optically pumping13CD3OD

We have obtained laser action on 34 far infrared lines for the first time in fully deuterated methyl alcohol with the¹³C isotope (¹³CD₃OD), and we have measured the frequency of 13 lines. The molecule was pumped by a cw CO₂ laser. We have measured the wavelength, the relative polarization, the relative intensity of most lines, the frequency, and the CO₂ pump frequency offset of the strongest lines. The new lines are distributed in the wavelength region from 75.27 m to 464.7 m.Supported in part by a joint grant with the U.S. National Science Foundation grant # INT 80-19014 and the Brazilian Conselho Nacional de Pesquisas (CNPq).     

Radiometric observations of the 752.033-GHz rotational absorption line of H2O from a laboratory jet

The intensity and lineshape of the Doppler-broadened 752.033-GHz (2₁₁ 2₀₂) rotational transition of H₂O has been studied passively using a high-resolution two-stage heterodyne radiometer with single-sideband system noise temperature of 45,000 K. The purpose of the experiments was to demonstrate the observability at submillimeter wavelengths of a high-altitude rocket plume simulated by a laboratory H₂O jet in a vacuum chamber. First-stage mixing was accomplished by means of a GaAs Schottky diode with first local-oscillator power supplied by a CO₂-laser pumped formic-acid laser (761.61 GHz), generating and X-band IF signal. Second localoscillator power was provided by a tunable C-band source. One-MHz resolution capability was obtained by means of a 3-GHz waveguide cavity filter with only 9-dB insertion loss. In the H₂O jet experiments, the center frequency of the line was determined to within 1 MHz of the previously reported value. A rotational temperature 75 K, a linewidth 5 MHz, and a Doppler shift 3 MHz (from a 45-degree rotation of the flow direction) were measured with the line-of-sight intersecting the jet axis at a distance downstream of 30 nozzle diameters. These absorption data were ogtained against continuum background radiation sources at temperatures of 1175 and 300 K.     

Hypersurfaces of prescribed mean curvature enclosing a given body

Given a smooth domain Ω in ℝ ^m+1 with compact closure and a smooth integrable functionh: ℝ ^m+1→ℝ satisfyingh(x)≥H _∂Ω (x) on ∂Ω whereH _∂ω denotes the mean curvature of ∂Ω calculated w.r.t. the interior unit normal we show that there is a setA⊂ℝ ^m+1 with the properties andH _∂A=h on ∂A.     

Acoustooptic extension of the frequency tunability of CW CO2 lasers: New FIR lasers emissions from CH3OH and13CH3OH

We have increased the frequency tunability of our CW waveguide CO₂ lasers by means of an acoustooptic amplitude modulator, operating at the fixed frequency of 90 MHz. The up-shifted, or down-shifted, laser optical sideband can be generated independently by adjusting the orientation of the modulator. The efficiency is larger than 50%. The frequency tunability of the CO₂ laser around each laser line is thus increased by 180 MHz. To demonstrate the possibilities of this method, a source composed of the above modulator and of a CW, 300 MHz tunable waveguide CO₂ laser has been used for the search of new large offset FIR laser lines from optically pumped CH₃OH and¹³CH₃OH molecules. As a result 15 and 10 new large offset laser lines were discovered respectively. New assignments of some laser lines are also proposed. We have also measured the Stark effect, the offset, and the polarization of other already known lines. In particular a Stark effect frequency tuning of about 1 GHz is demonstrated for a laser line at 208.399 m.