• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.661-669
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• 2021

For a simple, undirected graph G = (V, E), a perfect Roman dominating function (PRDF) f : V → {0, 1, 2} has the property that, every vertex u with f(u) = 0 is adjacent to exactly one vertex v for which f(v) = 2. The weight of a PRDF is the sum f(V) = ∑_v∈V f(v). The minimum weight of a PRDF is called the perfect Roman domination number, denoted by γ_R^P(G). Given a graph G and a positive integer k, the PRDF problem is to check whether G has a perfect Roman dominating function of weight at most k. In this paper, we first investigate the complexity of PRDF problem for some subclasses of bipartite graphs namely, star convex bipartite graphs and comb convex bipartite graphs. Then we show that PRDF problem is linear time solvable for bounded tree-width graphs, chain graphs and threshold graphs, a subclass of split graphs.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.625-634
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• 2024

The thrust of this paper is to extend the notion of Plithogenic vertex domination to the basic operations in Plithogenic product fuzzy graphs (PPFGs). When the graph is a complete PPFG, Plithogenic vertex domination numbers (PVDNs) of its Plithogenic complement and perfect Plithogenic complement are the same, since the connectivities are the same in both the graphs. Since extra edges are added to the graph in the case of perfect Plithogenic complement, the PVDN of perfect Plithogenic complement is always less than or equal to that of Plithogenic complement, when the graph under consideration is an incomplete PPFG. The maximum and minimum values of the PVDN of the intersection or the union of PPFGs depend upon the attribute values given to P-vertices, the number of attribute values and the connectivities in the corresponding PPFGs. The novelty in this study is the investigation of the variations and the relations between PVDNs in the operations of Plithogenic complement, perfect Plithogenic complement, union and intersection of PPFGs.

• Journal of Advanced Navigation Technology
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• v.22 no.5
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• pp.429-435
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• 2018

In radar systems, FFT (fast Fourier transform) operation is necessary to obtain the range and velocity of target, and the design of an FFT processor which operates at high speed is required for real-time implementation. The perfect shuffle network is suitable for high-speed FFT processor. In particular, twice perfect shuffle network based on radix-4 is preferred for very high-speed FFT processor. Moreover, radar systems that requires various velocity resolution should support scalable FFT points. In this paper, we propose a 8~1024-point scalable FFT processor based on twice perfect shuffle network algorithm and present hardware design and implementation results. The proposed FFT processor was designed using hardware description language (HDL) and synthesized to gate-level circuits using $0.65{\mu}m$ CMOS process. It is confirmed that the proposed processor includes logic gates of 3,293K.

• Journal of KSNVE
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• v.8 no.6
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• pp.1093-1102
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• 1998

The success of controllability of smart structures depends on the quality of the bonding along the interface between the main structure and the attached sensing and acuating elements. Generally, the analysis procedures neglect the effect of the interfacial bond layer or assume that this bond layer behaves like viscoelastic material. Three different bond layers. two modified epoxy adhesives, and one isocyanate adhesive were prepared for their toughness and moduli. Bond layer of the chosen adhesive provides an almost perfect bonding condition between the composite structure and the PZT while bended significantly like arrow-shape. The perfect bonding condition is tested by considering various material properties of the bond layers. and based on this perfect bonding condition, the effects of the interfacial bond layer on the dynamic behavior and controllability of the test structure is experimentally studied. Once the perfect bonding condition is achieved. dynamic effects of the bond layer itself on the dynamic characteristics of the main structure is negligible. but the contribution of the attached PZT elements on the stiffness of the multi-layered structure becomes significant when the thickness of the bond layer increased.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.679-687
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• 2005

In this paper we shall give a new definition for a quasi-power module P(M) and discuss some properties for P(M). The quasi-power module P(M) is a direct sum of invertible quasi-submodules C(H)'s of P(M) and then the quasi-submodule C(H) is also a direct sum of strongly cyclic quasi-submodules of C(H). When M is a quasi-perfect right R-module, we shall see that the quasi-power module P(M) is invertible.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.487-497
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• 2008

Buchsbaum and Eisenbud showed that every Gorenstein ideal of grade 3 is generated by the submaximal order pfaffians of an alternating matrix. In this paper, we describe a method for constructing a class of type 3, grade 3, perfect ideals which are not Gorenstein. We also prove that they are algebraically linked to an even type grade 3 almost complete intersection.

• Journal of the Korean Statistical Society
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• v.28 no.3
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• pp.389-398
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• 1999

We consider an imperfect repair model under which either a perfect repair or a minimal repair can be performed at each failure of a unit. Some stochastic properties of the number of perfect repairs and the number of minimal repairs under the imperfect repair model are investigated. We also derive the expressions for evaluating the expected numbers of perfect and minimal repairs in general and apply these formulas for certain parametric families of life distributions.

• Honam Mathematical Journal
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• v.32 no.2
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• pp.227-237
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• 2010

For a discrete group G, the kernel of a homomorphism from bounded cohomology $\hat{H}^*(G)$ of G to the ordinary cohomology $H^*(G)$ of G is called the singular part of $\hat{H}^*(G)$. We give some results on the space of the singular part of the second bounded cohomology of G. Also some results on the second bounded cohomology of a uniformly perfect group are given.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.435-442
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• 2001

Bayes estimators and generalized ML estimators for reliability of a k-unit hot standby system with the perfect switch based upon a complete sample of failure times observed from an exponential distribution using noninformative, generalized uniform, and gamma priors for the failure rate are proposed, and MSE's of proposed several estimators for the standby system reliability are compared numerically each other through the Monte Carlo simulation.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.685-693
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• 2005

An aperiodic perfect map(APM) is an array with the property that every array of certain size, called a window, arises exactly once as a contiguous subarray in the array. In this article, we deal with the generalization of APM in higher dimensional arrays. First, we reframe all known definitions onto the generalized n-dimensional arrays. Next, some elementary known results on arrays are generalized to propositions on n-dimensional arrays. Finally, with some devised integer representations, two constructions of infinite family of n-dimensional APMs are generalized from known 2-dimensional constructions in [7].