The aim of the present paper is to introduce and study the concept of operation-α-open sets, operation-semi-open sets and some operation-closures by using operations from SO(X, τ) into P(X). We obtain some operation-closure formulas. As corollaries, well known formulas on α-closures and semi-closures are obtained.

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It is known that for a semigroup S and any two idempotent elements e, f of S, the following assertions are satisfied: (1) Reg(eSf) = Reg(eS) ∩ Reg(Sf); (2) Gr(eSf) = gr(eSf) = Gr(eS) ∩ Gr(Sf); (3) E(eSf) = E(eS) ∩ E(Sf); (4) Gr(Se) = gr(Se) and Gr(eS) = gr(eS). Also that for a semigroup S and an idempotent element e of S, the following conditions are equivalent: (i) Reg(eSe) = Reg(Se); (ii) Reg(Se) ⊆ Reg(eS); (iii) E(eSe) = E(Se); (iv) E(Se) ⊆ E(eS). We extend these results in ordered semigroups. As an application of the result of the present paper, the above mentioned results hold for any elements a, b of a semigroup S and not only for idempotent elements of S. Some additional information are also obtained.

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In this paper, we continue our study that began in recent papers [2] and [3] concerning a simple yet effective Taylor series expansion method to approximate a solution of integral equations. The method is applied to Volterra integral equation of the second kind as well as to systems of Volterra equations. The results obtained in this paper improve significantly the results reported in recent papers, [7] and [8]. An error analysis is also provided.

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In this paper, we first obtain a weak mean convergence theorem of Baillon’s type for generalized hybrid mappings in a Hilbert space. Further, using an idea of mean convergence, we prove a strong convergence theorem of Halpern’s type for generalized hybrid mappings in a Hilbert space.

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Evolutionarily stable strategies(ESSs) of asymmetric animal contests are formulated by using Bayesian games. A criterion which is a generalization of that of Abakukus([1]) and a strengthened Selten’s theorem([9]) are given. As an example, a Hawk-Dove game with roles, in which the animals having the same role may possibly meet each other, is investigated and all possible Nash equilibria and ESSs are obtained for given parameters.

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In previous studies on operation planning of urban district heating and cooling plants, plans for operating the instruments are formed on one hour basis. However, it is important to consider operation planning by the smaller unit of time since the load on the plants rapidly increases in the morning. On the other hand, if the unit of time for planning is too small, the computational time for obtaining operation plans becomes huge due to the increase of the number of input data for prediction and the combinatorial number of plans available. Furthermore, it is needed to take account of the cost and time of switching instruments in order to derive more practical operation plans. In this paper, we propose a heat load forecasting method in which the number of input data does not explosively increase even when more detailed plans are made. And we propose several operation planning models based on various criteria and examine the efficiency of the proposed models through the comparison of the experimental results using actual data.

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We introduce the notion of operator Q-class function. Every non-negative operator convex function is of operator Q-class, but the converse is not true in general. Some inequalities for the operator Q-class functions are presented. In particular, we consider some conditions under which the operator Q-class functions have the operator monotonicity property.

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Various generalizations of Hardy’s theorem and Morgan’s theorem, which assert that a function on and its Fourier transform cannot both be very small, are known. We give two theorems which improve various generalizations known so far.

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The first part of this paper derives the asymptotic distribution of the ordinary least squares estimator in a linear regression model with deterministic regressors when the variance of the innovations is a function of an integrated time series. In the second part of this paper we study the impact of heteroscedasticity on the standard t-test for the slope coefficient in a linear trend model.

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