• Korean Journal of Mathematics
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• v.7 no.2
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• pp.215-218
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• 1999

We investigate characterizations of rings whose simple singular right R-modules are GP-injective. It is proved that if R is a semiprime ring whose simple singular right R-modules are GP-injective, then the center $Z(R)$ of R is a von Neumann regular ring. We consider the condition ($^*$): R satisfies $l(a){\subseteq}r(a)$ for any $a{\in}R$. Also it is shown that if R satisfies ($^*$) and every simple singular right R-module is GP-injective, then R is a reduced weakly regular ring.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.525-537
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• 2005

We introduce the notions of regular preopen sets and $p^{\ast}-closed$ spaces and investigate some of these properties. Also we give a characterization of p-closed spaces.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.551-558
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• 2004

We shall discuss some properties of quasi-homomorphisms associated with automata. We shall give some characterizations in terms of characteristic semigroups for regular and invertible attomata.

• East Asian mathematical journal
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• v.31 no.1
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• pp.127-134
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• 2015

We give a rth conic regular functions with conic quaternion variables in $\mathbb{C}^2$ and obtain a hyper-conjugate harmonic function of conic regular function in conic quaternions in the sense of Clifford analysis.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.991-1018
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• 2006

Hypermaps are cellular embeddings of hypergraphs in compact and connected surfaces, and are a generalisation of maps, that is, 2-cellular decompositions of closed surfaces. There is a well known correspondence between hypermaps and co-compact subgroups of the free product $\Delta=C_2*C_2*C_2$. In this correspondence, hypermaps correspond to conjugacy classes of subgroups of $\Delta$, and hypermap coverings to subgroup inclusions. Towards the end of [9] the authors studied regular hypermaps with extra symmetries, namely, G-symmetric regular hypermaps for any subgroup G of the outer automorphism Out$(\Delta)$ of the triangle group $\Delta$. This can be viewed as an extension of the theory of regularity. In this paper we move in the opposite direction and restrict regularity to normal subgroups $\Theta$ of $\Delta$ of finite index. This generalises the notion of regularity to some non-regular objects.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.389-394
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• 1999

A v-path of an arc xy in a multipartite tournament T is an oriented oath in T-y which starts at x such that y does not dominate and end vertex of the path. We show that if T is a regular n-partite (n$\geq$7) tournament, then every arc of T has a v-path of length m for all m satisfying 2$\leq$m$\leq$n-2. Our result extends the corresponding result for regular tournaments, due to Alspach, Reid and Roselle [2] in 1974, to regular multipartite tournaments.

• East Asian mathematical journal
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• v.25 no.4
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• pp.441-447
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• 2009

Jat and Choudhari defined a near-ring R with left bipotent or right bipotent condition in 1979. Also, we can dene a near-ring R as subcommutative if aR = Ra for all a in R. From these above two concepts it is natural to investigate the near-ring R with the properties aR = $Ra^2$ (resp. $a^2R$ = Ra) for each a in R. We will say that such is a near-ring with (1,2)-potent condition (resp. a near-ring with (2,1)-potent condition). Thus, we can extend a general concept of a near-ring R with (m,n)-potent condition, that is, $a^mR\;=\;Ra^n$ for each a in R, where m, n are positive integers. We will derive properties of near-ring with (1,n) and (n,1)-potent conditions where n is a positive integer, any homomorphic image of (m,n)-potent near-ring is also (m,n)-potent, and we will obtain some characterization of regular near-rings with (m,n)-potent conditions.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.2
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• pp.147-155
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• 2002

In this paper, the regular rotational gaits of the quadruped crawling robot are studied. It is assumed that the proposed regular rotational gaits starts from one of six support patterns in a translational gaits and end up with one of six support patterns in a translational gaits. Noting that six support patterns in a regular translational gait belong to two different groups with respect to regular rotational gait, the static stability margin and the maximum rotational displacement during one rotational stride period for the two representative support patterns are investigated. It is expected that the proposed regular rotational gaits will enhance the omni-directional characteristics of the quadruped crawling robot.

• Textile Coloration and Finishing
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• v.14 no.6
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• pp.319-327
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• 2002

Nylon 6 ultramicrofiber(UMF, monodenier 0.074d) and regular staple fiber(monodenier 2.05d) were dyed with acid and disperse dyes to investigate the effect of the difference of the fiber fineness. Also X-ray diffraction pattern, birefringence, DSC thermogram, moisture regain and water absorption of these fibers are measured. The dyeing rate of nylon UMF with acid dyes is increased compared with that of regular fiber, but not increased for disperse dyes. Also the saturation dye uptake of UMF with acid dyes is higher than that of regular fiber, while it is unchanged for disperse dyes. The moisture regain of UMF is similar to the regular fiber, whereas the water absorption of UMF is two times th그n that of the regular fiber. The crystallinity percentage of UMF is higher than that of regular fiber.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.507-519
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• 2017

We present an upper bound on the Cheeger constant of a distance-regular graph. Recently, the authors found an upper bound on the Cheeger constant of distance-regular graph under a certain restriction in their previous work. Our new bound in the current paper is much better than the previous bound, and it is a general bound with no restriction. We point out that our bound is explicitly computable by using the valencies and the intersection matrix of a distance-regular graph. As a major tool, we use the discrete Green's function, which is defined as the inverse of ${\beta}$-Laplacian for some positive real number ${\beta}$. We present some examples of distance-regular graphs, where we compute our upper bound on their Cheeger constants.