• 호남수학학술지
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• 제38권1호
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• pp.25-37
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• 2016

In 1972, Andrews derived the basic analogue of Gauss's second summation theorem and Bailey's theorem by implementing basic analogue of Kummer's theorem into identity due to Jackson. Recently Lavoie et.al. derived many results closely related to Kummer's theorem, Gauss's second summation theorem and Bailey's theorem and also Rakha et. al. derive the basic analogues of results closely related Kummer's theorem. The aim of this paper is to derive basic analogues of results closely related Gauss's second summation theorem and Bailey's theorem. Some applications and limiting cases are also considered.

• 호남수학학술지
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• 제27권2호
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• pp.225-232
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• 2005

We obtain the approximation order to a smooth function on a compact subset of $\mathbb{R}$ by generalized translation networks. In our study, the activation function is infinitely many times continuously differentiable function but it does not have special properties around ${\infty}$ and $-{\infty}$ like a sigmoidal activation function. Using the Jackson's Theorem, we get the approximation order. Especially, we obtain the approximation order by a neural network with a fixed threshold.

• ETRI Journal
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• 제24권5호
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• pp.381-390
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• 2002

We analyze the performance of a telecommunications management network (TMN) system using models of networks of queues, Jackson's theorem, and simulation. TMN systems for managing public asynchronous transfer mode (ATM) networks generally have a four-level hierarchical structure consisting of a network management system, a few element management systems (EMSs), and several pairs of agents and ATM switches. We construct a Jackson's queuing network and present formulae to calculate its performance measures: distributions of queue lengths and waiting times, mean message response time, and maximum throughput. We perform a numerical analysis and a simulation analysis and compare the results.

• ETRI Journal
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• 제25권1호
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• pp.34-40
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• 2003

This paper considers a TMN-based management system for the management of public ATM switching networks using a four-level hierarchical structure consisting of one network management system, several element management systems, and several agent-ATM switch pairs. Using Jackson's queuing model, we analyze the effects of one TMN command on the performance of the component ATM switch in processing local calls. The TMN command considered is the permanent virtual call connection. We analyze four performance measures of ATM switches- utilization, mean queue length and mean waiting time for the processor directly interfacing with the subscriber lines and trunks, and the call setup delay of the ATM switch- and compare the results with those from Jackson's queuing model.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.317-324
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• 2008

This paper shows the degree of simultaneous neural network approximation for a target function in $C^r$[-1, 1] and its first derivative. We use the Jackson's theorem for differentiable functions to get a degree of approximation to a target function by algebraic polynomials and trigonometric polynomials. We also make use of the de La Vall$\grave{e}$e Poussin sum to get an approximation order by algebraic polynomials to the derivative of a target function. By showing that the divided difference with a generalized translation network can be arbitrarily closed to algebraic polynomials on [-1, 1], we obtain the degree of simultaneous approximation.

• 한국정보과학회논문지:정보통신
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• 제29권2호
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• pp.147-155
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• 2002

인터넷을 통해 사용자 정보가 여러 망을 거치는 동안 연동지점에서의 처리 지연은 고속 전송에 큰 부담이 되며 종단간의 심리스 연결이 가능하다면 좋은 해결책이 될 것이다. 이 논문에서는 ATM-LAN에 유력한 MPOA 망과 백본 기술로 적용이 검토되고 있는 MPLS 망을 심리스 연결하기 위한 방안을 제시한다. 두 망의 특징을 비교하고, 연동에 필요한 요구사항을 제시하며, 적용 가능한 세가지 연동 방안을 기술한다. 제시된 연동방안은 LER에서 ATM VC와 LSP를 심리스 연결함으로써 IP 룩업에 소요되는 처리 지연을 최소화하고 종단간 전송 지연을 줄인다. 각 연동 방안들의 세부 동작 절차와 특징을 기술하고, 잭슨망 이론을 이용하여 제시된 연동 방안들의 종단간 전송지연을 분석하고 그 결과를 비교한다.