• Honam Mathematical Journal
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• v.38 no.1
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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.

• Honam Mathematical Journal
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• v.27 no.2
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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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• v.24 no.5
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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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• v.25 no.1
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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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• v.26 no.1_2
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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.

• Journal of KIISE:Information Networking
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• v.29 no.2
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• pp.147-155
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• 2002

Seamless connection can be a good solution to reduce processing delays in interworking points, a possible big burden to the data transmission in Internet. This paper, therefore, will present several interworking methods which can minimize the delays through seamless connections in interworking between MPOA networks, usually ATM-LANs, and MPLS networks, mainly Internet backbones. We compare characteristics of those networks, propose requirements for interworking, and describe three Interworking methods. Proposed Interworking methods reduce end-to-end transmission delay for seamless connection between ATM VC and LSP, as decreases the number of IP lookup processing in LER. We describe detailed process and characteristic of each interworking method, And we analyze and compare end-to-end delay, using Jackson's network theorem, of proposed interworking methods.