Probability distributions in fuzzy logic II

Probability distributions associated with several ‘iff’ ply operators are discussed. These exact distributions are compared with relevant normal approximants. Two possible applications are noted.     

High resolution three-dimensional microwave imaging of antennas

A procedure for imaging antenna currents that uses a relationship between the radiated far-field hemisphere and the Fourier transform domain of the source current density distribution is presented. The technique is applied to an array of two orthogonal waveguides, a slotted waveguide array and a reflector antenna. In each case the radiated far-field hemisphere is inverted to produce a high-resolution volumetric image of the antenna currents. Polarization discrimination is demonstrated as is the ability of the technique to `see behind' blockages by defocusing the foreground. It is shown that accurate distribution is available from the reconstructed image. Selective editing of the Fourier domain of the current distribution is performed to suppress unwanted artifacts in the reconstruction     

Opposite-polarity voltage generator by hole impact ionization in asilicon bipolar transistor

A single n-p-n transistor was used to generate a negative voltage at the collector terminal when a positive voltage was applied to the emitter relative to its grounded base. It is believed that this effect was a result of hole impact ionization at field E≃0 at the band-edge energy maximum in the base-collector junction, and some of the electrons so created diffused and drifted to the collector, thus accounting for the otherwise unexpected negative collector potential. Possible applications of this effect are given     

Effect of heat treatment on the electrical resistivity of near-eutectic Sn-Ag-Cu Pb-Free solder alloys

The electrical resistivity of solder joints prepared from Sn-Ag, Sn-Ag-Cu, and Sn-Ag-Cu-X alloys (where X = Co, Fe, or Bi) was characterized by a four-point probe technique and interpreted in terms of microstructure and composition. The resistivity is also reported of drawn solid wires of these alloys. The solder-joint samples were prepared by hand soldering to copper substrates and were electrically characterized over a temperature range from 293–423 K, covering the anticipated range of elevated-temperature operation for Pb-free solders. Selected joint specimens were measured before and after a 72-h heat treatment at 423 K. Metallographic inspection of the solder joints was performed to characterize coarsening effects and to determine the degree to which these changes affected electrical conduction.     

A note on character sums

Let $\text{S(k) = Σ}{}_{\mathrm{n=1}}{}^{\mathrm{p?1}}\text{(}\text{n}\text{p}\text{)n}{}^{\mathrm{k}}$ where p is a prime ≡ 3 mod 4 and k is an integer ≥ 3. Then S(k) frequently takes large values of each sign.     

Phosphoric acid solutions. I: Molecular association in a 57.8 molal aqueous solution

A 57.8 molal solution of orthophosphoric acid (85% w/w) has been studied by the wide angle X-ray scattering method. Both the ARDF and the intensity curve are consistent with a hydrogen-bonded ring structure for the dimeric (H₃PO₄)₂.     

Quasi-Peak-to-RMS Voltage Conversion

A technique is presented by which the conversion between quasi-peak and rms voltage levels may be made for any noise process for which the relative amplitude probability distribution is known. The technique is not exact, since it requires that the time waveform of the quasi-peak voltage be constant. However, the resulting error seems to be smail for many cases. Several results obtained using the techniques are given and compared with measurements. An analysis is also presented of the effect of the constant quasi-peak voltage requirement on the error.     

Characteristics of linewidth-narrowed distributed Bragg reflectorlasers with a fiber external cavity formed with the vertical gratingemission

Linewidth reduction has been observed in a distributed Bragg reflector (DBR) laser with a second-order grating when an external cavity is formed with the vertical emission. The external cavity consists of a length of optical fiber which is brought close to the top of the laser. Displayed linewidths as low as 26 kHz have been measured. To the authors' knowledge, this is the first report of linewidth reduction via vertical emission from a laser diode