• Journal of Korean Institute of Industrial Engineers
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• v.25 no.1
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• pp.125-129
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• 1999

The Little's formula, $L={\lambda}W$, expresses a fundamental principle of queueing theory: Under very general conditions, the average queue length is equal to the product of the arrival rate and the average waiting time. This useful formula is now well known and frequently applied. In this paper, we demonstrate that the Little's formula has much more power than was previously realized when it is properly decomposed into what we call the microscopic Little's formula. We use the M/G/1 queue with server vacations as an example model to which we apply the microscopic Little's formula. As a result, we obtain a transform-free expression for the queue length distribution. Also, we briefly summarize some previous efforts in the literature to increase the power of the Little's formula.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.465-474
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• 2014

Many mathematicians have studied various relations beween Euler number $E_n$, Bernoulli number $B_n$ and Genocchi number $G_n$ (see [1-18]). They have found numerous important applications in number theory. Howard, T.Agoh, S.-H.Rim have studied Genocchi numbers, Bernoulli numbers, Euler numbers and polynomials of these numbers [1,5,9,15]. T.Kim, M.Cenkci, C.S.Ryoo, L. Jang have studied the q-extension of Euler and Genocchi numbers and polynomials [6,8,10,11,14,17]. In this paper, our aim is introducing and investigating an extension term of generalized Euler polynomials. We also obtain some identities and relations involving the Euler numbers and the Euler polynomials, the Genocchi numbers and Genocchi polynomials.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.1
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• pp.6-9
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• 2006

A generalized net is used to construct a model which describes the process of evaluation of the problems solved by students. The model utilizes the theory of intuitionistic fuzzy sets. The model can be used to simulate some processes, related to estimation of students' background.

• Structural Engineering and Mechanics
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• v.6 no.4
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• pp.395-409
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• 1998

This paper concerns the development and implementation of an orthotropic, stress resultant elasto-plastic finite element model for the collapse load analysis of reinforced concrete plates. The model implements yield line plasticity theory for reinforced concrete. The behaviour of the yield functions are studied, and modifications introduced to ensure a robust finite element model of cases involving bending and twisting stress resultants ($M_x$, $M_y$, $M_{xy}$). Onset of plasticity is always governed by the general yield-line-model (YLM), but in some cases a switch to the stress resultant form of the von Mises function is used to ensure the proper evolution of plastic strains. Case studies are presented, involving isotropic and orthotropic plates, to assess the behaviour of the yield line approach. The YLM function is shown to perform extremely well, in predicting both the collapse loads and failure mechanisms.

• The Pure and Applied Mathematics
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• v.21 no.3
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• pp.147-163
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• 2014

In this paper, we study the existence of positive solutions for singular impulsive differential equations with integral boundary conditions $$\{u^{{\prime}{\prime}}(t)+q(t)f(t,u(t),u^{\prime}(t))=0,\;t{\in}\mathbb{J}^{\prime},\\{\Delta}u(t_k)=I_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\{\Delta}u^{\prime}(t_k)=-L_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\u=(0)={\int}_{0}^{1}g(t)u(t)dt,\;u^{\prime}=0,$$) where the nonlinearity f(t, u, v) may be singular at v = 0. The proof is based on the theory of Leray-Schauder degree, together with a truncation technique. Some recent results in the literature are generalized and improved.

• Journal of Industrial and Engineering Chemistry
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• v.67
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• pp.236-243
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• 2018

A series of $Er^{3+}/Yb^{3+}$ co-doped fluorophosphate glasses with varying $YbF_3$ concentration were prepared by a high temperature melt quenching technique. Absorption and emission cross-sections were determined by using the McCumber theory. The larger emission cross-section ($9.86{\times}10^{-21}cm^2$) and longer fluorescence lifetime (12.37 ms) were obtained for the $^4I_{13/2}{\rightarrow}^4I_{15/2}$ transition of ABS3Er4Yb glass. The sensitivity and temperature of the maximum sensitivity were evaluated by the fluorescence intensity ratio method from the measured upconversion spectra. The results were discussed and compared to the other reported glasses.

• Nuclear Engineering and Technology
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• v.53 no.5
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• pp.1464-1478
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• 2021

Selective Production of Exotic Species is an innovative plant for advanced nuclear physic studies. A radioactive beam, generated by using an UCx target-ion source system, is ionized, selected and accelerated for experimental objects. Very high vacuum conditions and appropriate safety systems to storage exhaust gases are required to avoid radiological risk for operators and people. In this paper, Failure Mode, Effects, and Criticality Analysis of a preliminary design of high activity gas recovery system is performed by using a modified Fuzzy Risk Priority Number to rank the most critical components in terms of failures and human errors. Comparisons between fuzzy approach and classic application allow to show that Fuzzy Risk Priority Number is able to enhance the focus of risk assessments and to improve the safety of complex and innovative systems such as those under consideration.

• Structural Engineering and Mechanics
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• v.62 no.4
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• pp.507-517
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• 2017

Due to the discontinuous nature of uncertainty quantification in conventional evidence theory(ET), the computational cost of reliability analysis based on ET model is very high. A novel ET model based on fuzzy distribution and the corresponding combination rule to synthesize the judgments of experts are put forward in this paper. The intersection and union of membership functions are defined as belief and plausible membership function respectively, and the Murfhy's average combination rule is adopted to combine the basic probability assignment for focal elements. Then the combined membership functions are transformed to the equivalent probability density function by a normalizing factor. Finally, a reliability analysis procedure for structures with the mixture of epistemic and aleatory uncertainties is presented, in which the equivalent normalization method is adopted to solve the upper and lower bound of reliability. The effectiveness of the procedure is demonstrated by a numerical example and an engineering example. The results also show that the reliability interval calculated by the suggested method is almost identical to that solved by conventional method. Moreover, the results indicate that the computational cost of the suggested procedure is much less than that of conventional method. The suggested ET model provides a new way to flexibly represent epistemic uncertainty, and provides an efficiency method to estimate the reliability of structures with the mixture of epistemic and aleatory uncertainties.

• (The)Study of the Eastern Classic
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• no.72
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• pp.365-400
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• 2018

The signs of $G{\bar{a}}nzh{\bar{i}}$(干支: the sexagesimal calendar system) almanac, which marked each year, month, day and time with 60 ordinal number marks made by combining 10 $Ti{\bar{a}}ng{\bar{a}}ns$(天干: the decimal notation to mark date) and 12 $D{\grave{i}}zh{\bar{i}}s$(地支 : the duodecimal notation to mark date), were used not only as the sign of the factors affecting the occurrence of a disease and treatment in the area of traditional oriental medicine, but also as the indicator of prejudging fortunes in different areas of future prediction techniques.(for instance, astrology, the theory of divination based on topography, four pillars of destiny and etc.) While theories of many future predictive technologies with this $G{\bar{a}}nzh{\bar{i}}$(干支) almanac signs as the standard had been established in many ways by Han dynasty, it is difficult to find almanac discussion later on the fundamental theory of 'how it works like that'. As for the method to mark the era of $Ti{\bar{a}}nt{\check{i}}l{\grave{i}}$(天體曆: a calendar made with the sidereal period of Jupiter and the Sun), which determines the name of a year depending on where $Su{\grave{i}}x{\bar{i}}ng$(歲星: Jupiter) is among the '12 positions of zodiac', there are three main ways of $$Su{\grave{i}}x{\bar{i}}ng-J{\grave{i}}ni{\acute{a}}nf{\check{a}}$$(歲星紀年法: the way to mark an era by the location of Jupiter on the celestial sphere), $$T{\grave{a}}isu{\grave{i}}-J{\grave{i}}ni{\acute{a}}nf{\check{a}}$$ (太歲紀年法: the way to mark an era by the location facing the location of Jupiter on the celestial sphere) and $$G{\bar{a}}nzh{\bar{i}}-J{\grave{i}}ni{\acute{a}}nf{\check{a}}$$(干支紀年法: the way to mark an era with Ganzhi marks). Regarding $$G{\bar{a}}nzh{\bar{i}}-J{\grave{i}}ni{\acute{a}}nf{\check{a}}$$(干支紀年法), which is actually the same way to mark an era as $$T{\grave{a}}isu{\grave{i}}-J{\grave{i}}ni{\acute{a}}nf{\check{a}}$$(太歲紀年法) with the only difference in the name, there are more than three ways, and one of them has continued to be used in China, Korea and so on since Han dynasty. The name of year of $G{\bar{a}}nzh{\bar{i}}$(干支) this year, 2018, has become $W{\grave{u}}-X{\bar{u}}$(戊戌) just by 'accident'. Therefore, in this discussion, the need to realize this situation was emphasized in different areas of traditional techniques of future prediction in which distinct theories have been established with the $G{\bar{a}}nzh{\bar{i}}$(干支) mark of year, month, day and time. Because of the 1 sidereal period of Jupiter, which is a little bit shorter than 12 years, once about one thousand years, 'the location of Jupiter on the zodiac' and 'the name of a year of 12 $D{\grave{i}}zh{\bar{i}}s$(地支) marks' accord with each other just for about 85 years, and it has been verified that recent dozens of years are the very period. In addition, appropriate methods of observing the the twenty-eight lunar mansions were elucidated. As $G{\bar{a}}nzh{\bar{i}}$(干支) almanac is related to the theoretical foundation of traditional medical practice as well as various techniques of future prediction, in-depth study on the fundamental theory of ancient $Ti{\bar{a}}nt{\check{i}}l{\grave{i}}$(天體曆) cannot be neglected for the succession and development of traditional oriental study and culture, too.

• Cross-Cultural Studies
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• v.48
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• pp.289-323
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• 2017

L'Espoir, a novel by Andre Malraux, contains traits of the genre of literacy reportage that depicts the full account of the Spanish Civil War as non-fiction based on his personal experience of participating in war; the novel has been dramatized into a semi-documentary film that corresponds to reportage literature. A semi-documentary film is the genre of film that pursues realistic illustration of social incidents or phenomenon. Despite difference in types of genre of the novel and the film L'Espoir, such creative activities deserve close relevance and considerable narrative connectivity. Therefore, $G{\acute{e}}rard$ Genette's narrative discourse of novel and film based on narrative theory carries value of research. Every kind of story, in a narrative message, has duplicate times in which story time and discourse time are different. This is because, in a narrative message, one event may occur before or later than another, told lengthily or concisely, and aroused once or repeatedly. Accordingly, analyzing differing timeliness of the actual event occurring and of recording that event is in terms of order, duration, and frequency. Since timeliness of order, duration, and frequency indicates dramatic pace that controls the passage of a story, it appears as an editorial notion in the novel and the film L'Espoir. It is an aesthetic discourse raising curiosity and shock, the correspondence of time in arranging, summarizing, deleting the story. In addition, Genette mentions notions of speech and voice to clearly distinguish position and focalization of a narrator or a speaker in text. The necessity to discriminate 'who speaks' and 'who sees' comes from difference in views of the narrator of text and the text. The matter of 'who speaks' is about who portrays narrator of the story. However, 'who sees' is related to from whose stance the story is being narrated. In the novel L'Espoir, change of focalization was ushered through zero focalization and internal focalization, and pertains to the multicamera in the film. Also, the frame story was commonly taken as metadiegetic type of voice in both film and novel of L'Espoir. In sum, narrative discourse in the novel and the film L'Espoir is the dimension of story communication among text, the narrator, and recipient.