A function can be represented in many ways. A representation O of a function f is called 'obscure' if O is different from the representation D used as the definition of f and if it is (or, seems to be) computationally infeasible to get D from O. Such an obscure representation is useful for cryptographic techniques so that it is important to estimate its descriptive and executive complexity. We present a complexity-estimation method for certain functions used to constructing asymmetric cryptosystems. Let m be a positive integer and let K, K^m, and L denote the field {0, 1}, the set of all m-tuples over K, and an extention field or order m over K, respectively. The objective function is a composit g:K^m K^m of three functions s, e, and t, where s:K^m L and t:L K^m are affine and e:L L is defined by a univariate polynomial e over L. The obscure representation of g is an m-tuple g of m-variate polynomials over K. The complexity respect to g is well measured by its degree. So we give a theorem for estimating the degree of g in terms of a characteristic quantity of the polynomial e.

Three-wave interactions in a linear, active, and lossless system are investigated. The stability properties of the coupled-waves describing the interaction are discussed at length by taking into consideration possible combinations of parities and directions of group velocities of the component waves. Several schematic dispersion diagrams are presented for the classification of existing instabilities in this system. The power gains of traveling-wave amplification in the three-wave interaction are also analyzed. It is shown that when one passive-wave couples to other two active-waves propagating in the same direction, a power gain considerably larger than that of corresponding two-wave interaction can be obtained.

The quadratic Liénard equation, that is, the Liénard differential equation in which the coefficients of and x are polynomials of degree two in x is studied with respect to its periodic solutions of small amplitude. The equation can represent a hard or a soft oscillation depending on parameter values. The existence of periodic solutions is proved and a simple formula for amplitude is given.

This paper presents a rigorous Wiener-Hopf solution to the electromagnetic wave exitation by a waveguide mode, concerning a two-dimensional tunnel which might be the most simplified model of a rectangular tunnel. Surface impedance boundaries are assumed on the walls of tunnels surrounded by lossy dielectric materials, such as concrete, rock and others. A microwave simulation is also performed to determine whether the assumption used in the theory is good or not. From comparison of experimental results with theoretical ones, it is shown that the surface impedance model is an excellent approximation especially for tunnels of which dimensions are not so large compared with the wave length in the free space.

A 1.544 MHz timing-extraction ceramic filter is examined. This filter has been successfully introduced into a PCM carrier system. Second-order Gaussian approximated effective-parameter theory with gentle frequency-phase inclination characteristics is applied in the circuit design. A ladder transformer filter construction, employing two resonator units and a coupling capacitor, is adopted. A resonator unit, comprising a trapped-energy piezoelectric ceramic strip resonator operating in the width-shear vibration mode and a ceramic capacitor connected in series with the resonator, fulfils the function for easy frequency adjustment and temperature compensation of the resonant frequency. Filter input and output terminating resistances are 30 Ω and 1500 Ω, respectively. The 3 dB fractional bandwidth is 1.07% and the insertion loss at center frequency f₀ is -4.8 dB. The frequency deviation of f₀ is within 200 ppm over a -20 to 60 temperature range and the aging rate of f₀ is about 0.01%/decade. The frequency deviation over the operating temperature range is less than one-third and the aging rate is about one-half of the conventional LC filter used for this application. The filter size is reduced to one-fifth that of the LC filter.

The thickness dependence of structure, magnetic properties and read-write characteristics has been studied for sputtered iron oxide thin films prepared by RF reactive sputtering. For sputter-deposited Fe₃O₄ films, [111] preferential orientation perpendicular to film surface is improved and crystal size increases with an increase in thickness (δ). Magnetic properties for Fe₃O₄ films are affected by thickness. In particular, saturation magnetization rapidly decreases at thicknesses less than about 0.07 µm. From this perspective, it is concluded that a thickness larger than about 0.07 µm is available for practical use. For oxidation-annealed γ- Fe₂O₃ media, signal-output and media transition length are proportional to δ^0.7 and δ^0.5, respectively. A γ-(Co_0.025Cu_0.03Fe_0.945)₂O₃ medium with a 0.071 µm thickness shows 0.51 mV of E_pp, 2000 frpm of D_{-6 dB}, -35 dB of O/W and 38 dB of SNR.

Intensity noise reduction effects by superimposed pulse modulation are theoretically analyzed for LD inherent noise, feedback light noise, and modal noise. It is shown that noise spectrum spreading effects due to LD mode partition noise are very effective to reduce mode hopping noise and modal noise, that a short pulse width completely suppress beat noise and mode hopping noise based on submode structures constructed by feedback light, and that modal noise is effectively reduced by LD longitudinal mode linewidth broadening effect as long as a fiber bandwidth is sufficiently narrow compared with the broadened LD linewidth. It is also shown that LD quantum intensity noise increases for LD multimode operation, and that feedback light noise based on injection locking effect can not be suppressed without system parameter adjustment.

This paper describes on optical transmission system for a Time Compression Multiplexing (TCM) High Definition TV (HDTV) signal with a bandwidth of 20 MHz. Negative feedback is being employed to improve some of the shortcomings of the laser diode. In this paper the stability of the negative feedback circuit and its effect on reducing harmonic distortion and noise in the laser diode are examined. A laser diode module used in this experiment consists of a TJS-LD operating at a wavelength of 0.89 µm and a photo diode. In the final system, a method that superimposes high frequency pulses is employed for reducing modal noise. The signal-to-noise ratio (SNR) of the optical sender is achieved at 49 dB and harmonic distortion at about 44 dB, where the optical output level is 6.0 dBm and modulation depth is 0.5.