• The KIPS Transactions:PartC
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• v.8C no.1
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• pp.12-15
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• 2001

A summation generator creates sequence from addition with carry of LFSR (Linear Feedback Shift Register) sequences. Similarly, it is possible to generate keystream by bitwise exclusive-oring on two FCSR sequences. In this paper, we described the cryptographic properties of a sequence generated by the FCSRs.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.493-506
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• 2009

By using the improved Euler-Maclaurin summation formula and estimating the weight coefficients in this paper, a new dual Hardy-Hilbert's inequality and its reverse form are obtained, which are all with two pairs of conjugate exponents (p, q); (r, s) and a independent parameter ${\lambda}$. In addition, some equivalent forms of the inequalities are considered. We also prove that the constant factors in the new inequalities are all the best possible. As a particular case of our results, we obtain the reverse form of a famous Hardy-Hilbert's inequality.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.191-200
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• 2015

Generating functions play an important role in the investigation of various useful properties of the sequences which they generate. Exton [13] presented a very general double generating relation involving products of two Laguerre polynomials. Motivated essentially by Exton's derivation [13], the authors aim to show how one can obtain nineteen new generating relations associated with products of two Laguerre polynomials in the form of a single result. We also consider some interesting and potentially useful special cases of our main findings.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.605-618
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• 2018

The main goal of this paper is to study an extension of random summations of independent and identically distributed random variables when the number of summands in random summation is a partial sum of n independent, identically distributed, non-negative integer-valued random variables. Some characterizations of random summations are considered. The central limit theorems and weak law of large numbers for extended random summations are established. Some weak limit theorems related to geometric random sums, binomial random sums and negative-binomial random sums are also investigated as asymptotic behaviors of extended random summations.

• Proceedings of the KIPE Conference
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• 2004.07a
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• pp.155-158
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• 2004

This paper describes a lane following control of vision based mobile robot that follows guidline. Summation of binarization conversion and image data of vertical axis was used in image processing. As an extraction of specific parameters of lane image, the raw image was converted to the binary data, and the binary data was summerized to the specific data vertically. The specific parameters were made to the inputs of neural network. Summation of image data was used for input of the net, and optimized value of turn angles of learned mobile robot was output. By using neural network algorithm, possibility of mobile robot moving to the target point and following the guidlines quickly and effectively was proved.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.1C
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• pp.80-86
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• 2006

In this paper, we propose the PingPong-128(PP-128) keystream generator, based on summation generator. Proposed PingPong-128, a specific cipher of the PingPong Family, takes 128 bits key and 128 bit initial vector, has 258 bit internal state, and achieves a security level of 128 bits. The security analysis of PingPong-128 is presented, including the resistence to known attacks against the summation generator and other clock-controlled generators.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.217-231
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• 2017

In this paper, we introduce a generating function for a Legendre-based poly-Bernoulli polynomials and give some identities of these polynomials related to the Stirling numbers of the second kind. By making use of the generating function method and some functional equations mentioned in the paper, we conduct a further investigation in order to obtain some implicit summation formulae for the Legendre-based poly-Bernoulli numbers and polynomials.

• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.1188-1191
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• 2002

A number of studies have recently been published concerning neuron models and asynchronous neural networks. In the case of large-scale neural networks having neuron models, the neural network should be constructed using analog hardware, rather than by computer simulation via software, because of the limitation of the computational power, In this paper, we discuss the circuit structure of a synaptic section model having the spatio-temporal summation of inputs and utilizing CMOS processing.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.61-73
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• 2018

The main aim of this research paper is to evaluate the general integral of the form $${\int_{0}^{1}}x^{c-1}(1-x)^{c+{\ell}}[1+{\alpha}x+{\beta}(1-x)]^{-2c-{\ell}-1}\atop {\times}_3F_2\left\[ {a,\;b,\;2c+{\ell}+1} \\ {\frac{1}{2}(a+b+i+1),\;2c+j\;;\frac{(1+{\alpha})x}{1+{\alpha}x+{\beta}(1-x)} }\right]dx$$ in the most general form for any ${\ell}{\in}\mathbb{Z}$; and $i, j=0,{\pm}1,{\pm}2$. The results are established with the help of generalized Watson's summation theorem due to Lavoie, et al. Fifty interesting general integrals have also been obtained as special cases of our main findings.

• Journal of Korean Society on Water Environment
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• v.21 no.4
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• pp.393-397
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• 2005

In this study, flow in a porous medium is analyzed using a computer-extended perturbation series solution. The flow is modelled as a creeping flow in a periodically constricted channel. The channel walls have a sinusoidally varying width and the flow is analyzed in terms of its vorticity and stream functions in the Stokes flow regime. The perturbation series in terms of a small parameter, average width to length ratio, is extended with a computer resulting in purely asymptotic series and Pade summation is used to obtain final results. Resulting flow shows flow separations in the widening section and immobile zones in the widest section of the flow regime with reattachment in the narrowing section. Analysis of the flow separation phenomena resulted in a correlation between the two geometric parameters of the channel walls to predict the onset of flow separation in the Stokes flow regime.