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The Hall effect has been investigated in the very low-temperature limit in bismuth, when the lattice scattering is dominant in solids. The energy band structure of bismuth carriers is assumed to follow the modified nonellipsoidal, nonparabolic (MNENP) model. Results show that the Hall coefficient and Hall angle oscillate with the dc magnetic field, and the period and amplitude of the oscillations increase with the dc magnetic field. We also compare our numerical results with those found using other types of energy bands.

A parallel algorithm for generating all combinations ofm (m fixed) items out of anyn given items in lexicographic order is presented. The computational model is a linear systolic array consisting ofm identical processing elements. This algorithm requires {ie23-1} time-steps for the {ie23-2} combinations, that is, one output at each time-step. Since all processing elements perform the same program, it is suitable for VLSI implementation. Based on mathematical induction, such an algorithm is proved to be correct.

A systolic algorithm for solving the 0/1-knapsack problems with n items is presented. The computational model used is a tree structure which consists of 2" identical processing elements (PEs). Each PE executes the same program at any time step. The time complexity varies from n to 3n - 2 steps which includes all the input/output data communication time. The design process and the correctness verification of this algorithm are considered indetail.

In this article, we show how the multiplication of polynomials can be performed in a pipelined fashion on a systolic array in linear time steps. The computational model consists of two linear systolic arrays with 2(n+1) processing elements used and (m+2n+2) running time steps needed, where m, n are the degrees of the two given polynomials, respectively. Since the same types of processing elements execute the same program, it is suitable for VLSI implementation. This algorithm is also proved to be correct.

Using time-independent perturbation theory, we solve the energy eigenvalue equation for a free-electron gas in bismuth with the McClure-Choi modified nonellipsoidal nonparabolic (MNENP) model in the presence of a uniform dc magnetic fieldB. We investigate the effect of the dc magnetic field on the electron density at very low temperatures and compare the numerical results for this new band model with those for the Cohen nonellipsoidal nonparabolic (NENP), Lax ellipsoidal nonparabolic (ENP), and ellipsoidal parabolic (EP) models. The results show that the quantum oscillations of the electron density for the MNENP model show up much more notably than in the NENP, ENP, and EP models. The MNENP model seems better suited than the other models for describing physical phenomena associated with the magnetic field effect in bismuth at very low temperatures.

The magnetoresistance effect in bismuth has been studied at the very low temperature limit when the lattice scattering is dominant in solids. Results show that the magnetoresistance oscillates with the dc magnetic field and displays sharp, cusplike discontinuities due to the nonlinear and singular properties of the energy band structure of bismuth for the modified nonellipsoidal, nonparabolic (MNENP) model.

Given n items, a parallel algorithm for generating all the n! permutations is presented. The computational model used is a linear array which consists of n identical processing elements with a simple structure. One permutation is produced at each other time step. The elapsed time to produce a permutation is independent of the integer n. The basic idea used is the iterative method and the exchange of two consecutive components in an existing permutation. The design procedures of this algorithm are considered in detail. The ranking and unranking functions of the required permutations are also discussed.

For arbitrary n×n matrix A and n×m matrix B, a systolic algorithm to solve the linear systems AX=B is presented. The cmputational model used consists of n(n+1) PEs. The number of PEs used is independent of m. This algorithm requires 4n+m-2 time steps to solve the linear systems. Since the structure of PE is simple and the PE with same type executes the identical program, it is very suitable for VLSI implementation. Moreover, if m is a singular matrix, it can be detected during the execution of the systolic algorithm.

The free-carrier absorption has been studied for quantum well structures fabricated from III–V semiconductors such as n-type InSb films when the acoustic phonon scattering is dominant. The energy band of carriers in semiconductors is assumed to be nonparabolic. The scattering mechanisms of phonons with carriers in semiconductors are considered for the deformation-potential coupling and the piezoelectric coupling separately. Results show that the free-carrier absorption coefficient in n-type InSb films depend upon the polarization of the radiation field relative to the direction normal to the quantum well structures, the photon frequency, the film thickness and the temperature. It is also found that the free-carrier absorption coefficient could be complex due to the interaction of the radiation field and the photon field with carriers in semiconductors. Thus, the index of refraction of semiconducting films could be change due to this carrier-phonon-photon interaction.