• 대한수학회지
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• 제51권1호
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• pp.55-65
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• 2014

A graph G is called a fractional (g, f, n)-critical graph if any n vertices are removed from G, then the resulting graph admits a fractional (g, f)-factor. In this paper, we determine the new toughness condition for fractional (g, f, n)-critical graphs. It is proved that G is fractional (g, f, n)-critical if $t(G){\geq}\frac{b^2-1+bn}{a}$. This bound is sharp in some sense. Furthermore, the best toughness condition for fractional (a, b, n)-critical graphs is given.

• Journal of applied mathematics & informatics
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• 제34권5_6호
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• pp.435-441
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• 2016

Let G be a graph, and let g, f be two nonnegative integer-valued functions defined on V (G) with g(x) ≤ f(x) for each x ∈ V (G). A graph G is called a fractional (g, f, n)-critical graph if after deleting any n vertices of G the remaining graph of G admits a fractional (g, f)-factor. In this paper, we obtain a binding number condition for a graph to be a fractional (g, f, n)-critical graph, which is an extension of Zhou and Shen's previous result (S. Zhou, Q. Shen, On fractional (f, n)-critical graphs, Inform. Process. Lett. 109(2009)811-815). Furthermore, it is shown that the lower bound on the binding number condition is sharp.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1157-1163
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• 2009

Let G be a graph with vertex set V(G) and let f be a nonnegative integer-valued function defined on V(G). A spanning subgraph F of G is called a fractional f-factor if $d^h_G$(x)=f(x) for all x $\in$ for all x $\in$ V (G), where $d^h_G$ (x) = ${\Sigma}_{e{\in}E_x}$ h(e) is the fractional degree of x $\in$ V(F) with $E_x$ = {e : e = xy $\in$ E|G|}. In this paper it is proved that if ${\delta}(G){\geq}{\frac{b^2(k-1)}{a}},\;n>\frac{(a+b)(k(a+b)-2)}{a}$ and $|N_G(x_1){\cup}N_G(x_2){\cup}{\cdots}{\cup}N_G(x_k)|{\geq}\frac{bn}{a+b}$ for any independent subset ${x_1,x_2,...,x_k}$ of V(G), then G has a fractional f-factor. Where k $\geq$ 2 be a positive integer not larger than the independence number of G, a and b are integers such that 1 $\leq$ a $\leq$ f(x) $\leq$ b for every x $\in$ V(G). Furthermore, we show that the result is best possible in some sense.

• 인터넷정보학회논문지
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• 제19권1호
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• pp.11-17
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• 2018

본 논문에서는 회사 또는 백화점 등과 같은 고층 건물에 다수의 펨토셀 기지국들(Femtocell base stations, fBSs)이 밀집되어 배치되는 기업형 펨토셀 네트워크(Enterprise femtocell network, EFN) 환경에서 부분 주파수 재사용 (Fractional frequency reuse, FFR) 자원할당 방법을 이용하여 하향링크에 대한 시스템 성능을 분석한다. 이를 위해, 먼저 매크로셀과 펨토셀 사이의 주파수 간섭을 완화시키는 Split reuse 주파수 할당 방법에 대해 소개하고, 이후 EFN의 fBS들에게 주파수 간섭 완화 및 주파수 효율을 극대화할 수 있는 FFR을 이용한 자원할당 방법을 제안한다. 마지막으로 시뮬레이션을 통해 제안하는 FFR 자원할당 방법의 시스템 성능을 분석하고, EFN 환경에서 주파수 재사용 계수(Frequency reuse factor: FRF)를 4로 사용하는 전형적인 FRF 4 방법보다 제안하는 FFR 자원할당 방법이 평균 fUE 용량, 전체 EFN 용량, 그리고 Outage probability 측면에서 우수한 성능임을 보인다.

• Computers and Concrete
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• 제8권2호
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• pp.229-241
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• 2011

In this work, cement paste samples with 1% (by cement mass) of a conductive carbon fiber admixture have been studied under uniaxial compression. Three different arrangements were used to measure the resistivity of the samples. According to the results obtained, the resistance should be measured using the four wire method in order to obtain good sensitivity and repeatability. The effect of the load value and the load rate on the fractional change of the volume resistivity has been determined. It has been observed that the gage factor (fractional change in resistance respect to strain) increases when the maximum load is increased, and the loading rate does not affect significantly this parameter. The effect of the sample ambient humidity on the material piezoresistivity has also been studied, showing that the response of the composite is highly affected by this parameter.

• 품질경영학회지
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• 제44권4호
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• pp.799-811
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• 2016

Purpose: The conjoint analyst in marketing are interested in detecting whether there exist synergy or antagonistic effects between two attributes. In the cases where attributes have two or three levels, we research on the design of survey questionnaire to estimate all the main effect and as many two factor interaction effects as possible. Methods: We consider the balanced incomplete block (BIB) mixed level factorial design $2^f{\times}3^g$ or fractional factorial design. To reduce the number of questions in a questionnaire, we propose the balanced incomplete block mixed level design with minimum aberration which is generated by implementing proc factex in SAS. Also, we propose using two or three level BIB factorial design instead of mixed level designs by transforming three level attributes into two attributes of two levels and two level attribute into three level attribute by using dummy level technique. Results: We propose three methods for designing survey questionnaire where the block and design generators are found with practical number of questions in a questionnaire. By analyzing all the respondents survey data generated by the simulation study, we find the proper model and do the concepts optimization. Conclusion: The proposed methods of designing survey questionnaires seem to perform well in the sense that the proper model, and then the optimal concept is found in a case study where all the respondents survey data are generated by the simulation study.