Heat load prediction in district heating and cooling (DHC) systems is one of the key technologies for economical and safe operations of DHC systems. The heat load prediction method using a three-layered neural network proposed by the authors has been used in an actual DHC plant on a trial basis. However, there exists a drawback that its prediction becomes less accurate in periods when the heat load is nonstationary. In this paper, we improve the heat load prediction method through the introduction of a recurrent neural network for adapting the dynamical variation of heat load together with a new kind of input data in consideration of the characteristics of heat load data. In order to show the efficiency of the proposed method, we carry out several numerical experiments using actual heat load data.

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In this paper, the concept of a left fixed map in an BE-algebra is discussed and some fundamental properties to BE-algebras are discussed.

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In this paper, we introduced the concept of f-derivation which is a generalization of derivation in subtraction algebra, and some related properties are investigated.

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In this paper, by considering the notion of a ∧-closed set in BCK-algebras, we construct the fractions of BCK-algebras and prove some related results. Moreover, we study the notion of a BCK-module and prove that any BCK-algebra is a BCK-module on itself. Finally, we construct the fractions of BCK-modules.

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In this paper we prove an extension of Ekeland’s variational principle in the setting of locally complete spaces. We also present an Equilibrium version of the Ekeland-type variational principle, a Caristi-Kirk type fixed point theorem for multivalued maps and a Takahashi minimization theorem, we then prove that they are equivalent.

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We bridge between submanifold theory and contact geometry. We give a geometric meaning of some fundamental notions such as Sasakian, nearly Sasakian, Kcontact from the viewpoint of the result in [3] (Theorem 1). Moreover, motivated by the notion of totally η-umbilic hypersurfaces in a nonflat complex space form, we give a new notion in contact geometry (Theorem 2).

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This paper presents three kinds of balanced fractional 3m factorial designs such that the general mean and all the main effects are estimable, and furthermore (A) the linear by linear components of the two-factor interaction are estimable, and the factorial effects of the quadratic by quadratic and linear by quadratic ones of the two-factor interaction are confounded with each other, (B) the quadratic by quadratic ones of the two-factor interaction are estimable, and the effects of the linear by linear and linear by quadratic ones of the two-factor interaction are confounded with each other, and (C) the linear by quadratic ones of the two-factor interaction are estimable, and the effects of the linear by linear and quadratic by quadratic ones of the two-factor interaction are confounded with each other, where the three-factor and higher-order interactions are assumed to be negligible and the number of assemblies is less than the number of non-negligible factorial effects. These designs are concretely given by the indices of a balanced array of full strength, which is called a simple array.

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As an effective use of the CAS (computer algebra system) in the mathematics education, we can perform mathematics experiment and can do heuristic learning. One of the roles expected to use of CAS in mathematics learning is to be able to carry out experimental mathematics to make heuristically by myself. We introduce a trial (mathematical search) to practice such an activity in university mathematics. We can obtain degeneracy conditions of singularities by using Gr¨obner basis. In classification of singularities, the defining equations of certain types are polynomials with parametric coefficients. In general, the Gr¨obner basis generated by such polynomials depends on the values of the parameters, and those calculations are not easy. A structure of zero set defined by polynomials with parameters changes by the values of the parameters. This is the learning problem that is important in the university mathematics. As one of such teaching materials, the defining equation of singularity with parameters is suitable. We show various examples of the calculations to students and teach these calculations. When students learn those calculations as algorithm, an interesting subject is preferable, mathematically. The singularity on the algebraic curve can arouse the interest of the students. We can make the learning of the algebraic curve with parameters more interesting in university mathematics. This trial is significant to show utility of the mathematics by using computer and to clarify the pleasure of the calculations to students. Then, the calculation based on Gr¨obner basis theory is necessary. If they calculate thoughtlessly, they will not obtain significant results. The mathematical result to show in this paper is still an experiment stage on the way. We show these search activities as the material of the experiment in university mathematics in this paper.

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