Scientiae Mathematicae Japonicae

DEFORMATIONS OF THE CHEBYSHEV HYPERGROUPS

Tatsuya Tsurii

2017 Volume 80 Issue 3 Pages 209-218
Published: 2017
Released on J-STAGE: May 10, 2019

DOIhttps://doi.org/10.32219/isms.80.3_209

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A ROUTE OPTIMIZATION PROBLEM IN ELECTRICAL PCB INSPECTIONS WITH ALIGNMENT OPERATIONS

Hideki Katagiri, Hongwei Wu, Yosuke Kakiuchi, Hiroshi Hamori, Kosuke K ...

2017 Volume 80 Issue 3 Pages 219-232
Published: 2017
Released on J-STAGE: May 10, 2019

DOIhttps://doi.org/10.32219/isms.80.3_219

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This paper considers a route optimization problem in advanced electrical PCB inspections. By considering the constraint that “camera-based alignment of position” needs to be conducted before electrical tests, the PCB inspection route optimization problem (PCBIRP) is modeled as a precedence-constrained traveling salesman problem (PCTSP), especially, as a pickup and delivery traveling salesman problem (PDTSP). Two of mixed 0-1 integer programming problem formulations are proposed. The computational times for the proposed formulations are compared by solving benchmark instances using some of well-known mathematical programming solvers.

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CONTRA-γ-IRRESOLUTE MAPPINGS AND RELATED GROUPS

H. Maki, A.I. EL-Maghrabi

2017 Volume 80 Issue 3 Pages 233-245
Published: 2017
Released on J-STAGE: May 10, 2019

DOIhttps://doi.org/10.32219/isms.80.3_233

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The aim of the present paper is devoted to discuss some more properties of γ-irresolute mappings and contra-γ-irresolute mappings. Also, we introduce and study two new weak homeomorphisms such as contra-γr-homeomorphisms and contra- γ-homeomorphisms. Further, we investigate some groups related to the mappings above and some examples of them on digital lines.

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EXISTENCE OF UNBOUNDED SOLUTIONS TO A ONE DIMENSIONAL ISENTROPIC PERIODIC FLOW OF A COMPRESSIBLE VISCOUS FLUID WITH SELF-GRAVITATION

Masahiro Sawada, Yoshitaka Yamamoto

2017 Volume 80 Issue 3 Pages 247-268
Published: 2017
Released on J-STAGE: May 10, 2019

DOIhttps://doi.org/10.32219/isms.80.3_247

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We consider a one dimensional isentropic periodic flow of a compressible viscous fluid driven by a self-gravitation of the fluid. We show the existence of an unbounded solution of a system describing the flow. A sufficient condition for the unboundedness is given in terms of the initial values of an energy form.

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SOME INTEGRALS BETWEEN THE LEBESGUE INTEGRAL AND THE DENJOY INTEGRAL

Toshiharu Kawasaki

2017 Volume 80 Issue 3 Pages 269-293
Published: 2017
Released on J-STAGE: May 10, 2019

DOIhttps://doi.org/10.32219/isms.80.3_269

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LEFT REGULAR AND INTRA-REGULAR ORDERED HYPERSEMIGROUPS IN TERMS OF SEMIPRIME AND FUZZY SEMIPRIME SUBSETS

NIOVI KEHAYOPULU

2017 Volume 80 Issue 3 Pages 295-305
Published: 2017
Released on J-STAGE: May 10, 2019

DOIhttps://doi.org/10.32219/isms.80.3_295

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We prove that an ordered hypersemigroup H is left (resp. right) regular if and only if every left (resp. right) ideal of H is semiprime and it is intra-regular if and only if every ideal of H is semiprime. Then we prove that an ordered hypersemigroup H is left (resp. right) regular if and only if every fuzzy left (resp. right) ideal of H is fuzzy semiprime and it is intra-regular if and only if every fuzzy ideal of H is fuzzy semiprime.

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FUZZY SETS IN ≤–HYPERGROUPOIDS

NIOVI KEHAYOPULU

2017 Volume 80 Issue 3 Pages 307-314
Published: 2017
Released on J-STAGE: May 10, 2019

DOIhttps://doi.org/10.32219/isms.80.3_307

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This paper serves as an example to show the way we pass from ordered groupoids (ordered semigroups) to ordered hypergroupoids (ordered hypersemigroups), from groupoids (semigroups) to hypergroupoids (hypersemigroups). The results on semigroups (or on ordered semigroups) can be transferred to hypersemigroups (or to ordered hypersemigroups) in the way indicated in the present paper.

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