• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2003.05a
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• pp.824-827
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• 2003

With a rapid development of Information Telecommunication technique, network communication environment has been greatly improved. People come to feel more convinient to purchase products through Internet. Accordingly, various kinds of electronic payment systems have been developed and used. In this paper, we propose an algorithm which not only can associate the broker system with an electronic cash user, but also regenerate all amount of money previously paid using technique such as Meta-Message recovery and a RSA Blind Signature based on discrete logarithm problem.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1137-1146
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• 2011

Let {$X_i$, $i{\geq}1$} be a sequence of i.i.d. nondegenerate random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Denote $S_n={\sum}_{i=1}^n\;X_i$, $M_n=max_{1{\leq}i{\leq}n}\;{\mid}S_i{\mid}$ and $V_n^2={\sum}_{i=1}^n\;X_i^2$. Then for d > -1, we showed that under some regularity conditions, $$\lim_{{\varepsilon}{\searrow}0}{\varepsilon}^2^{d+1}\sum_{n=1}^{\infty}\frac{(loglogn)^d}{nlogn}I\{M_n/V_n{\geq}\sqrt{2loglogn}({\varepsilon}+{\alpha}_n)\}=\frac{2}{\sqrt{\pi}(1+d)}{\Gamma}(d+3/2)\sum_{k=0}^{\infty}\frac{(-1)^k}{(2k+1)^{2d+2}}\;a.s.$$ holds in this paper, where If g denotes the indicator function.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.291-301
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• 2010

This paper consists of two main parts. Firstly, we introduce an evolving binomial process from a binomial stock model and consider various types of limiting behavior of the logarithm of the evolving binomial process. Among others we find that the logarithm of the binomial process converges weakly to a Gaussian process. Secondly, we provide new approaches for proving the limit theorems for an integral process motivated by the evolving binomial process. We provide a new proof for the uniform strong LLN for the integral process. We also provide a simple proof of the functional CLT by using a restriction of Bernstein inequality and a restricted chaining argument. We apply the functional CLT to derive the LIL for the IID random variables from that for Gaussian.

• Food Science and Biotechnology
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• v.14 no.2
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• pp.249-254
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• 2005

The relationship between Sigumjang gas chromatographic patterns precisely analyzed with capillary column and ranked order in sensory analysis was investigated by stepwise multiple regression analysis. Highly predictable multiple regression models were obtained in the analysis. Ninety percent of the Sigumjang aroma was explained by the regression models at step 15 in four transformation except for absolute value transformed with root square and relative value transformed with logarithm. The aroma of Sigumjang was most affected by 2,3-dimethylpyrazine at absolute value and absolute value transformed with logarithm and by 2-furancarboxaldehyde in other transformation. The quality of sigumjang was highly affected by ${\beta}$-phallendrenal, methylpyrazine, tetramethylpyrazine, 5-methyl-2-furancarboxaldehyde, unknown 2, octanoic acid, 4-ethylphenol, methyl 10,13-octadecanoate and ethyl linoleate.

• Journal of Pharmaceutical Investigation
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• v.12 no.4
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• pp.101-111
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• 1982

The effect of salt addition to MO-CTB mixed micelle was studied. The logarithm of cmcs obtained from above experiment is a linear function of the logarithm of the sum of the cmc and the concentration of added salt. In order to investigate the relation of the color change and the structure, the measurement of conductance to the mixed micelle has been carried out. To see the color change and conductance data obtained in the present study, structure A is more probable one to the micelles having the ${\lambda}_{max}$ 376nm.

• Water Engineering Research
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• v.1 no.3
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• pp.171-185
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• 2000

A mathematical model to adequately predict complex mixing characteristics of sorptive polluants in natural streams with pools-and-riffes has been developed. In this model, sorption of pollutants onto the bed sediment as well as mass storage and exchange in the storage zones were incorporated into one-dimensional mass balance equatins. The geometric and hydraulic characteristics of the pool-riffle sequences were properly conceptualized. Simulations with parameters of pool-and-riffle streams better fit the measured data in overall shape and peak concentration than simulations with parameters for uniform channels. The analyses on the characteristics of the storage zone model parameters reveal that a linear relationship between the logrithm of the storage zone volume ratio and a function of the friction factor exists. A linear relatiohship might also be tenatively assumed between the logarithm of the dimensionless mass exchange coefficient and the logarithm of the aspect ratio of the storage zone if some of the high values of the dimensionless mass exchange coefficient collected on the successive bed forms are excluded.

• Fibers and Polymers
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• v.6 no.2
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• pp.139-145
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• 2005

The paper reports the physical and mechanical properties of hand-woven carpets, which have been put under static force. Two groups of wool fibres, from two parts of Iran, were prepared to spin pile yams for the carpets. Each group of the fibres included both conventional and tanned wool. Then two yam counts, $N_m$ = 4/2 and 6/2, were spun for two different knot densities. After weaving the carpets, they were put under static force and their thickness variations were measured and plotted against time, in logarithm scale. The resiliency of the carpets piles after eliminating the static force, were measured and plotted against time, in logarithm scale, too. The results were compared to each other and analysed with respect to parameters such as the type and quality of the wool fibres as well as knot density of the carpets.

• Archives of Pharmacal Research
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• v.2 no.1
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• pp.1-8
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• 1979

The flow rate of various sand through circular orifice can be measured from a knowledge of a few easily measurable properties of the system. These are the orifice column and particle diameters, the angle of inclination of the orifice with the horizontal and an angle of repose of the granular sand material. Straight lines were obtained when the logarithm of the flow rate was plotted versus the logarithm of orfice diameter. No influence of excessive compaction and bed height was observed and the flow rate increased with decrease of particle diameter. The profile of flow developed the edge of the aperture in a way independent of its size. Linear relationship was observed between the angle of inclination of the orifice and the flow rate.

• Journal of IKEEE
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• v.14 no.2
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• pp.64-68
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• 2010

This paper proposes efficient log and exponent calculation methods using a dual phase instruction set without additional ALU unit for a mobile enviroment. Using the Dual Phase Instruction set, it extracts exponent and mantissa from expression of floating point and calculates 24bit single precision floating point of log approximation using the Taylor series expansion algorithm. And with dual phase instruction set, it reduces instruction excution cycles. The proposed Dual Phase architecture reduces the performance degradation and maintain smaller size.

• Journal of Communications and Networks
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• v.18 no.1
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• pp.1-7
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• 2016

Most of the previous proxy re-encryption schemes rely on the average-case hardness problems such as the integer factorization problems and the discrete logarithm problems. Therefore, they cannot guarantee its security under quantum analysis, since there exist quantum algorithms efficiently solving the factorization and logarithm problems. In the paper, we propose the first proxy re-encryption scheme based on the hard worst-case lattice problems. Our scheme has many useful properties as follows: Unidirectional, collusion-resistant, noninteractive, proxy invisible, key optimal, and nontransitive.We also provided the formal security proof of the proposed scheme in the random oracle model.