• Journal of the Korean Mathematical Society
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• v.51 no.1
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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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• v.34 no.5_6
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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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• v.27 no.5_6
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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.

• Journal of Internet Computing and Services
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• v.19 no.1
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• pp.11-17
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• 2018

In this paper, we propose a novel frequency reuse method using the fractional frequency reuse (FFR) for enterprise femtocell networks (EFNs) in which a lot of femtocell base stations (fBSs) are deployed in a buinding, e.g., business companies, department stores, etc, and evaluate the system performance for the downlink of EFNs. First, we introduce the concept of the split reuse method to allocate the frequency bandwidth with considering the interference between the macrocell and femtocell. Then, we propose the resource allocation with the FFR for fBSs of EFNs to reduce the interference and increase the system capacity. Through simulations, we show that the proposed FFR method outperforms a traditional resource allocation method with frequency reuse factor 4 in terms of the mean fUE capacity, total EFN capacity, and outage probability.

• Computers and Concrete
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• v.8 no.2
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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.

• Journal of Korean Society for Quality Management
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• v.44 no.4
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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.