• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.19-29
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• 1995

In this paper, we investigate the asymptotic distributions of maximum queue length for M/G/1 and GI/M/1 systems which are positive recurrent. It is well knwon that for any positive recurrent queueing systems, the distributions of their maxima linearly normalized do not have non-degenerate limits. We show, however, that by concerning an array of queueing processes limiting behaviors of these maximum queue lengths can be established under certain conditions.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.25-35
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• 2001

In this paper we consider an age dependent branching process whose particles move according to a Markov process with continuous state space. The Markov process is assumed to the stationary with independent increments and positive recurrent. We find some sufficient conditions for he Markov motion process such that the empirical distribution of the positions converges to the limiting distribution of the motion process.

• East Asian mathematical journal
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• v.26 no.3
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• pp.351-363
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• 2010

We introduce a special class of real recurrent polynomials $f_m$$($m{\geq}1$) of degree m+1, with positive roots $s_m$, which are decreasing as m increases. The first root $s_1$, as well as the last one denoted by $s_{\infty}$ are expressed in closed form, and enclose all $s_m$ (m > 1). This technique is also used to find weaker than before [6] sufficient convergence conditions for some popular iterative processes converging to solutions of equations.

• BMB Reports
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• v.53 no.4
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• pp.234-239
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• 2020

Epilepsy is a chronic neurological disease characterized by spontaneous recurrent seizures and caused by various factors and mechanisms. Malfunction of the olfactory bulb is frequently observed in patients with epilepsy. However, the morphological changes in the olfactory bulb during epilepsy-induced neuropathology have not been elucidated. Therefore, in the present study, we investigated the expression of parvalbumin (PV), one of the calcium-binding proteins, and morphological changes in the rat main olfactory bulb (MOB) following pilo-carpine-induced status epilepticus (SE). Pilocarpine-induced SE resulted in neuronal degeneration in the external plexiform layer (EPL) and glomerular layer (GL) of the MOB. PV immunoreactivity was observed in the neuronal somas and processes in the EPL and GL of the control group. However, six hours after pilocarpine administration, PV expression was remarkably decreased in the neuronal processes compared to the somas and the average number of PV-positive interneurons was significantly decreased. Three months after pilocarpine treatment, the number of PV-positive interneurons was also significantly decreased compared to the 6 hour group in both layers. In addition, the number of NeuN-positive neurons was also significantly decreased in the EPL and GL following pilocarpine treatment. In double immunofluorescence staining for PV and MAP2, the immunoreactivity for MAP2 around the PV-positive neurons was significantly decreased three months after pilocarpine treatment. Therefore, the present findings suggest that decreases in PV-positive GABAergic interneurons and dendritic density in the MOB induced impaired calcium buffering and reciprocal synaptic transmission. Thus, these alterations may be considered key factors aggravating olfactory function in patients with epilepsy.

• Journal of Distribution Science
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• v.9 no.2
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• pp.49-59
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• 2011

A franchise can be said to be the main method of distribution and marketing. It appears to be the future of the retail industry and is one of the world's fastest growing businesses sectors, as many policy reports and research results have acknowledged. Korea's franchise industry began in the 1970s, spread out into many areas (including food services, retail, and the service industry), and has grown by over 10% each year ever since. The industry's influence on the national economy becomes ever greater. Although the size of the franchise industry is expected to grow as it spreads and as the government expands its support, it has not yet attracted much academic interest. Research has so far been very fragmented. The main interest has been the relationship and conflicts between the head offices and the affiliates. No study has yet occurred on whether the concepts of satisfaction and intent to conclude a contract directly affect the success or failure of the affiliates. Few studies have empirically inquired into the demographic characteristics and abilities of the affiliates that significantly affect their results. Domestic franchise industries must prepare to leap from quantitative to qualitative growth. Most important is the need for affiliate headquarters and affiliates to build confidence between them. A friendly and reliable relationship between affiliate headquarters and affiliates will eliminate distrust from the franchise and maintain a healthy franchise system. This study suggests that current and prospective heads of affiliation should concentrate not on attracting affiliates but on investment and techniques of affiliate support. They should work on the reinforcement of brand power, the appropriate affiliate business environment, systematic education/training, taking burdens off the affiliate business persons, consolidating the relationship with the affiliate business persons, marketing mix factors (e.g. products, price conditions, logistics and shipping services, promotion, supervising and supervisor, operation procedures/processes, and material evidence); these all greatly affect the success or failure of the affiliate business. Supporting the affiliates is an important factor that enhances their results and satisfaction and consequently increases the positive recommendations to others and the ratio of recurrent conclusions of contracts, which ultimately generate the growth of the franchises. In addition, it is suggested that prospective franchise founders should make every effort to choose a good head office since the characteristics of the head office greatly influence the success of the affiliates. This study is significant in that it grasps the characteristics of the head office of affiliation and of the affiliates that influence affiliate results in ways not yet academically attempted.