• Journal of Electrical Engineering and Technology
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• v.7 no.2
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• pp.151-156
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• 2012

The current study presents a zero-one integer programming approach to determine the minimum break point set for the coordination of directional relays. First, the network is reduced if there are any parallel lines or three-end nodes. Second, all the directed loops are enumerated to reduce the iteration. Finally, the problem is formulated as a set-covering problem, and the break point set is determined using the zero-one integer programming technique. Arbitrary starting relay locations and the arbitrary consideration of relay sequence to set and coordinate relays result in navigating the loops many times and futile attempts to achieve system-wide relay coordination. These algorithms are compared with the existing methods, and the results are presented. The problem is formulated as a setcovering problem solved by the zero-one integer programming approach using LINGO 12, an optimization modeling software.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.7 no.6
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• pp.1421-1424
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• 2006

By extending the Mandelbrot set for the complex polynomial $$M={c\in C\;:\; _{k\rightarrow\infty}^{lim}P_c^k(0)\;{\neq}\;{\infty}$$ we define the degree-n bifurcation set. In this paper, we formulate the boundary equation of a period-2 component on the main component in the degree-9 bifurcation set by parameterizing its image. We establish an algorithm constructing a period-2 component in the degree-9 bifurcation set and the typical implementations show the satisfactory result with Mathematica codes grounded on the analysis.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.193-204
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• 2022

A subset S of V(G), where G is a simple undirected graph, is a hop dominating set if for each v ∈ V(G)＼S, there exists w ∈ S such that d_G(v, w) = 2 and it is a locating-hop set if N_G(v, 2) ∩ S ≠ N_G(v, 2) ∩ S for any two distinct vertices u, v ∈ V(G)＼S. A set S ⊆ V(G) is a locating-hop dominating set if it is both a locating-hop and a hop dominating set of G. The minimum cardinality of a locating-hop dominating set of G, denoted by 𝛄_lh(G), is called the locating-hop domination number of G. In this paper, we investigate some properties of this newly defined parameter. In particular, we characterize the locating-hop dominating sets in graphs under some binary operations.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.575-590
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• 2017

A new class of functions called $R_{\theta}$-supercontinuous functions is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity, which already exist in the literature, is elaborated. The class of $R_{\theta}$-supercontinuous functions properly contains the class of $R_z$-supercontinuous functions [39] which in turn properly contains the class of $R_{cl}$-supercontinuous functions [43] and so includes all cl-supercontinuous (clopen continuous) functions ([38], [34]) and is properly contained in the class of $R_{\delta}$-supercontinuous functions [24].

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.5-10
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• 2002

In this paper, we investigate the prefilter base on a fuzzy set and fuzzy net ${\varphi}$ on the fuzzy topological space (X,${\delta}$). And we show that the prefilter base $\mathcal{B}({\varphi})$ determines by the fuzzy net ${\varphi}$ converge to a fuzzy point $p$ iff the fuzzy net ${\varphi}$ converge to a fuzzy point $p$. Also we prove that if the prefilter base $\mathcal{B}$ converge to a fuzzy point $p$, then the $\mathcal{B}$ has the cluster point $p$.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.127-144
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• 2009

Let f be a diffeomorphism of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper we introduce the notion of $C^1$-stable inverse shadowing for a closed f-invariant set, and prove that (i) the chain recurrent set $\cal{R}(f)$ of f has $C^1$-stable inverse shadowing property if and only if f satisfies both Axiom A and no-cycle condition, (ii) $C^1$-generically, the chain component $C_f(p)$ of f associated to p is hyperbolic if and only if $C_f(p)$ has the $C^1$-stable inverse shadowing property.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.1-12
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• 2009

Motivated by XTR cryptosystem which is based on an irreducible polynomial $x^3-cx^2+c^px-1$ over $F_{p^2}$, we study polynomials of the form $F(c,x)=x^3-cx^2+c^qx-1$ over $F_{p^2}$ with $q=p^m$. In this paper, we establish a one to one correspondence between the set of such polynomials and a certain set of cubic polynomials over $F_q$. Our approach is rather theoretical and provides an efficient method to generate irreducible polynomials over $F_{p^2}$.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.759-764
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• 1998

We define the rational lens algebra (equation omitted)(n) as the crossed product by an action of Z on C( $S^{2n＋l}$). Assume the fibres are $M_{ k}$/(C). We prove that (equation omitted)(n) $M_{p}$ (C) is not isomorphic to C(Prim((equation omitted)(n))) $M_{kp}$ /(C) if k > 1, and that (equation omitted)(n) $M_{p{\infty}}$ is isomorphic to C(Prim((equation omitted)(n))) $M_{k}$ /(C) $M_{p{\infty}}$ if and only if the set of prime factors of k is a subset of the set of prime factors of p. It is moreover shown that if k > 1 then (equation omitted)(n) is not stably isomorphic to C(Prim(equation omitted)(n))) $M_{k}$ (c).

• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.251-260
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• 2019

It has been little known when an Artinian (point) quotient has the strong Lefschetz property. In this paper, we find the Artinian complete intersection quotient having the SLP. More precisely, we prove that if ${\mathbb{X}}$ is a complete intersection in ${\mathbb{P}}^2$ of type (2, 2) and ${\mathbb{Y}}$ is a finite set of points in ${\mathbb{P}}^2$ such that ${\mathbb{X}}{\cup}{\mathbb{Y}}$ is a basic configuration of type (2, a) with $a{\geq}3$ or (3, a) with a = 3, 4, 5, 6, then $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ has the SLP. We also show that if ${\mathbb{X}}$ is a complete intersection in ${\mathbb{P}}^2$ of type (3, 2) and ${\mathbb{Y}}$ is a finite set of points in ${\mathbb{P}}^2$ such that ${\mathbb{X}}{\cup}{\mathbb{Y}}$ is a basic configuration of type (3, 3) or (3, 4), then $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ has the SLP.

• Annals of Fuzzy Mathematics and Informatics
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• v.16 no.3
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• pp.333-336
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• 2018

One of the well known results in general topology says that every compact subset of a Hausdorff space is closed. This result in soft topology is not true in general as demonstrated throughout this note. We begin this investigation by showing that [Theorem 3.34, p.p.23] which proposed by Varol and $Ayg{\ddot{u}}n$ [7] is invalid in general, by giving a counterexample. Then we derive under what condition this result can be generalized in soft topology. Finally, we evidence that [Example 3.22, p.p. 20] which introduced in [7] is false, and we make a correction for this example to satisfy a condition of soft Hausdorffness.