A method is presented for analyzing the scalar wave scattering from a conducting target of arbitrary shape in random media for both the Dirichlet and Neumann problems. The current generators on the target are introduced and expressed generally by the Yasuura method. When using the current generators, the scattering problem is reduced to the wave propagation problem in random media.

A chordal ring network is a processor network on which n processors are arranged to a ring with additional chords. We study a distributed leader election algorithm on chordal ring networks and present trade-offs between the message complexity and the number of chords at each processor and between the message complexity and the length of chords as follows:For every d(1dlog* n1) there exists a chordal ring network with d chords at each processor on which the message complexity for leader election is O(n(log(d1)nlog* n)).For every d(1dlog* n1) there exists a chordal ring network with log(d1)nd1 chords at each processor on which the message complexity for leader election is O(dn).For every m(2mn/2) there exists a chordal ring network whose chords have at most length m such that the message complexity for leader election is O((n/m)log n).

There have been several studies related to a reduction of the amount of computational resources used by Turing machines. As consequences, Linear speed-up theorem", tape compression theorem" and reversal reduction theorem" have been obtained. In this paper, we discuss a leaf reduction theorem on alternating Turing machines. Recently, the result that one can reduce the number of leaves by a constant factor without increasing the space complexity was shown for space- and leaf-bounded alternating Turing machines. We show that for time- and leaf-bounded alternating Turing machines, the number of leaves can be reduced by a constant factor without increasing time used by the machine. Therefore, our result says that a constant factor on the leaf complexity does not affect the power of time- and leaf-bounded alternating Turing machines.