• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.849-866
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• 2024

In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not metric, we are directly able to perform multiplicative differential-geometric concepts to investigate such curves. By several characterizations, we completely classify the multiplicative rectifying curves by means of the multiplicative spherical curves.

• Structural Engineering and Mechanics
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• v.28 no.4
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• pp.373-386
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• 2008

In this study stochastic analysis of non-linear dynamical systems under ${\alpha}$-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of ${\alpha}$-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with ${\alpha}/2$- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function of the system under Gaussian white noise and the probability density function of the ${\alpha}/2$-stable random parameter. Some numerical applications have been reported assessing the reliability of the proposed formulation. Moreover a proper way to perform digital simulation of the sub-Gaussian ${\alpha}$-stable random process preventing dynamical systems from numerical overflows has been reported and discussed in detail.

• Korean Journal of Weed Science
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• v.12 no.2
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• pp.144-157
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• 1992

The study was conducted to compare the interprete methods and examine the feasibility of mixture use of oxyfluorfen and bensulfuron in controlling principal Paddy weeds, annuals and perennials. Application ratio of both chemicals were obtained from the combinations of 5 levels(0, 5, 10, 15, 20 g ai/ha) of each chemicals, respectively. All the treatments were applied at 5 days after transplanting and water was maintained at 3.0cm in depth. Shoot fresh-weight of weeds was assessed at 35 days after treatments. Data obtained was analysed by Colby, Isobole, Calculus, Regression and EQM method, respectively. The results from the analysis of variance on the principal weeds treated with oxyfluorfen and bensulfuron showed significant interactions at 1% level on both Echinochloa crus-galli and Eleocharis Kuroguwai, and total species at 0.5% level on both Potamogeton distinctus and Cyperus serotinus, but non significant on Scirpus juncoides and Sagittaria pygmaea. Thereafter, the results of the models applied to Echinochloa crus-galli, Eleocharis kuroguwai and total species were as follows ; 1. The Colby method gave values nearly identical to regression estimate method (both multiplicative models) as provided by Akobundu et al. The Colby method and Regression method indicated synergistic toward Echinochloa curs-galli, and total species, but antagonistic toward Eleocharis kuroguwai. 2. The Isobole method shows synergism on Echinochloa crus-galli at $ID_{50}$, and total species at $ID_{60}$ on Eleochari kuroguwai. 3. The Calculus method gave positive signs for the first differentiation and negative signs for the second differentiation except for some rates on Echinochloa crus-galli and total species, but reverse on Eleocharis kuroguwai. These result does not agree with the observed values. 4. ${\theta}$ value from the EQM method was greater than one at all combinations. This result was quite different from those of other methods. 5. The various models did not show the same results, but mixture of oxyfluorfen and bensulfuron tend to have synergistic effect. Weeding effect also was high. Treatment in terms of two chemical combination was expected to reduce rates, and to enhence weeding efficacy compared with single treatment.