We study two machine shop type scheduling problem in this paper. At shop type scheduling, one job is handled by plural machines. And it generally divided two types of problem. Flowshop type have been determined the order of operation at each machine. And it is not decided on Openshop type. In this paper, considering a problem with two machines and flexible jobs which have no strict order of machines, but have desirably order. The super shop problem which is mixed with flow shop and open shop is considered by Strusevich and suggests a solution method that based on 13 cases. In this paper, we extend this result and give more detailed condition on one case which include preemptive job. We also propose a solution to this problem by extending this result to flexible flowshop.

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Directional statistics have received a great deal of interest in recent years, and a variety of distributions on the circle have been proposed. In this paper, we propose circular distributions of a moving average model of order p type which includes the cardioid distribution, and discuss estimation of trigonometric moments based on binary series. We give an explicit form of the root n consistent estimator based on clipped series, which enables us to construct an efficient estimator by the Newton– Raphson iterative method. We also show a robustness of the proposed estimator when the probability density function is contaminated with a noise term.

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In BCK-algebras, it is well known that a commutative BCKalgebra is as a lower semilattice with respect to the operation ∧. In this paper, we show that a new class in BCK-algebras which is a proper large class than the class of the commutative BCK-algebras exists, and this class is as a lower semilattice with respect to the new operation ×.

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