Scientiae Mathematicae Japonicae

A COMMON IMPROVEMENT OF FUZZY TOPOLOGICAL SPACES AND FUZZY (QUASI) UNIFORM SPACES

Gerhard Preuss

2009 年 69 巻 2 号 p. 153-168
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_153

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Using fuzzy filters in the sense of P. Eklund and W. Gähler [2], it turns out that fuzzy preuniform convergence spaces introduced in [11] form a strong topological universe in which fuzzy topological spaces as well as fuzzy (quasi) uniform spaces can be studied. Thus, better tools such as the existence of natural function spaces, the existence of one-point extensions (and consequently, the hereditariness of quotient maps), and the productivity of quotient maps are available.

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INTERVAL HAUSDORFFNESS AND INITIALITY

S. N. Hosseini

2009 年 69 巻 2 号 p. 169-174
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_169

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BIPOLAR FUZZY IMPLICATIVE HYPER BCK-IDEALS IN HYPER BCK-ALGEBRAS

Young Jun, Min Su Kang, Hee Sik Kim

2009 年 69 巻 2 号 p. 175-186
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_175

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Bipolar-valued fuzzification of the notion of implicative hyper BCK-ideals is considered. Using the concepts of positive and negative lever sets, a characterization of a bipolar fuzzy implicative hyper BCK-ideal is provided. A relation between a bipolar fuzzy hyper BCK-ideal and a bipolar fuzzy implicative hyper BCK-ideal is established. A condition for a bipolar fuzzy hyper BCK-ideal to be a bipolar fuzzy implicative hyper BCK-ideal is given. By using a collection of implicative hyper BCK-ideals, a bipolar fuzzy implicative hyper BCK-ideal is established.

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A CONSTRUCTIVE THEORY OF APARTNESS ON LATTICES

D.S. Bridges, L.S. Vîţa

2009 年 69 巻 2 号 p. 187-206
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_187

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The theory of apartness spaces is lifted to the more abstract context of complemented frames with habitation, thereby providing another point-free constructive approach to topology.

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STABLE RANK OF THE C∗-ALGEBRAS OF ALMOST COMMUTING OPERATORS

Takahiro Sudo

2009 年 69 巻 2 号 p. 207-210
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_207

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We estimate the stable rank of the soft tori of Exel and their isometric versions. Especially, it is found that there exists a connection between stable rank and no continuity of C∗-algebra fields.

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THE BEST CONSTANT OF SOBOLEV INEQUALITY WHICH CORRESPONDS TO SCHRÖDINGER OPERATOR WITH DIRAC DELTA POTENTIAL

Yoshinori Kametaka, Hiroyuki Yamagishi, Kohtaro Watanabe, Atsushi Naga ...

2009 年 69 巻 2 号 p. 211-225
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_211

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We consider boundary value problems for the one-dimensional Schrödinger operator with Dirac delta potential. Green functions G(x, y) are constructed by using the symmetric orthogonalization method, and their aspects as reproducing kernel are also investigated. As an application, the best constants of the corresponding Sobolev inequalities is expressed as the maximum of the diagonal value G(y, y).

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STRONG CONVERGENCE THEOREMS BY A HYBRID STEEPEST DESCENT METHOD FOR COUNTABLE NONEXPANSIVE MAPPINGS IN HILBERT SPACES

SHIGERU IEMOTO, WATARU TAKAHASHI

2009 年 69 巻 2 号 p. 227-240
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_227

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In this paper, we introduce a new iterative procedure for finding a solution of the variational inequality problem over the intersection of fixed point sets of infinite nonexpansive mappings in a Hilbert space and then discuss the strong convergence of the iterative procedure.

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THE SHANNON FIELD OF NON-NEGATIVE INFORMATION FUNCTIONS

E. GSELMANN, GY. MAKSA

2009 年 69 巻 2 号 p. 241-248
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_241

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Motivating the known result that there are non-negative information functions different from the Shannon information function, we investigate how large the set is on which every non-negative information function coincides with the Shannon’s one. The structure of this set is also discussed.

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OPERATOR INEQUALITIES OF ANDO-HIAI TYPE AND THEIR APPLICATIONS

MASATOSHI FUJI, EIZABURO KAMEI

2009 年 69 巻 2 号 p. 249-255
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_249

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ON THE OPERATOR EQUATION AB = zBA

Muneo Cho, Jun Ik Lee, Takeaki Yamazaki

2009 年 69 巻 2 号 p. 257-263
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_257

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In this paper, we study the operator equation AB = zBA for bounded operators A,B on a complex Hilbert space. In [10], J. Yang and H.-K. Du proved that if A and B are normal operators, then |z| = 1 by using the Fuglede-Putnam Theorem. In this paper, we give an elementary proof of this result without using the Fuglede-Putnam Theorem and some examples. Then we shall relax normality in the result by Yang and Du. A quasinormality of an operator is given by using Aluthge transformation and the operator equality.

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A KANTOROVICH TYPE INEQUALITY WITH A NEGATIVE PARAMETER

Jun Ichi Fujii, Young Ok Kim

2009 年 69 巻 2 号 p. 265-270
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_265

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A SELECTING METHOD OF REASONABLE NON-DOMINATED SCHEDULES ON OPEN SHOP

Sangsu Han

2009 年 69 巻 2 号 p. 271-276
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_271

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In this research, a selection method of non-dominated schedules is investigated on m machines open shop scheduling problem with maximum completion times for each of machines as multiobjective. In formulation of the problem, we introduce a concept of schedule vector and lexicographic ordering based on burdened machine. For this problem, the aim is to find a preemptive schedule that lexicographically minimizes the maximum completion times Cmaxi, i = 1, 2, · · · ,m on m machines Mi, respectively. We propose a flexible algorithm and discuss its validity and computational complexity.

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A NOTE ON COOK’S INEQUALITY FOR SIMPLE CLOSED CURVES

K.T. Hallenbeck

2009 年 69 巻 2 号 p. 277-279
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_277

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The question of Howard Cook: “Do there exist, in the plane, two simple closed curves Y and X, such that X is in the bounded complementary domain of Y, and the span of X is greater than the span of Y ?”is answered, in the negative, for several types of simple closed curve pairs.

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ON COMMUTATIVE BE-ALGEBRAS

ANDRZEJ WALENDZIAK

2009 年 69 巻 2 号 p. 281-284
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_281

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In this paper we investigate the relationship between BE-algebras, implicative algebras, and J-algebras. Moreover, we define commutative BE-algebras and state that these algebras are equivalent to the commutative dual BCK-algebras.

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A RANK-BASED SELECTION WITH CARDINAL PAYOFFS AND A COST OF CHOICE.

Krzysztof Szajowski

2009 年 69 巻 2 号 p. 285-293
発行日: 2009年
公開日: 2020/03/06

DOIhttps://doi.org/10.32219/isms.69.2_285

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A version of the secretary problem is considered. The ranks of items, whose values are independent, identically distributed random variables X1,X2, . . . ,Xn from a uniform distribution on [0; 1], are observed sequentially by the grader. He has to select exactly one item, when it appears, and receives a payoff which is a function of the unobserved realization of random variable assigned to the item diminished by some cost. The methods of analysis are based on the existence of an embedded Markov chain and use the technique of backward induction. The result is a generalization of the selection model considered by Bearden [2]. The asymptotic behaviour of the solution is also investigated.

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