• Kyungpook Mathematical Journal
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• 제61권3호
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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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• 제42권3호
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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.

• 한국항행학회논문지
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• 제22권5호
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• pp.429-435
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• 2018

레이다 시스템의 경우, 타겟의 거리와 속도를 추출하기 위해 FFT (fast Fourier transform) 연산이 필수적으로 요구되며, 실시간 구현을 위해 고속으로 동작하는 FFT 프로세서의 설계가 필요하다. 고속 FFT 프로세서를 위한 하드웨어 구조로 완전 셔플 네트워크 (perfect shuffle network) 구조가 적합하며, 특히 초고속 연산을 위해 radix-4 기반의 이중 완전 셔플 네트워크 (twice perfect shuffle network) 구조가 가장 적절하고 볼 수 있다. 더불어, 다양한 속도 해상도를 요구하는 레이다 응용을 고려할 때, FFT 프로세서는 가변길이 FFT 연산을 지원할 필요가 있다. 이에 본 논문에서는 8~1024 포인트의 가변 길이 연산을 지원하는 이중 완전 셔플 네트워크 기반의 FFT 알고리즘을 제안하였으며, 이의 하드웨어 구조 설계 및 구현 결과를 제시한다. 제안된 FFT 프로세서는 HDL (hardware description language)을 활용하여 RTL (register transfer level) 설계가 수행되었으며, $0.65{\mu}m$ CMOS 공정을 활용하여 논리 합성한 결과, 총 3,293K개의 논리 게이트로 구현 가능함을 확인 할 수 있었다.

• 소음진동
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• 제8권6호
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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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• 제17권1_2_3호
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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.

• 대한수학회논문집
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• 제23권4호
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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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• 제28권3호
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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.

• 호남수학학술지
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• 제32권2호
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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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• 제8권2호
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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.

• 대한수학회논문집
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• 제20권4호
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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].