• Kyungpook Mathematical Journal
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• 제45권1호
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• pp.45-53
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• 2005

A basis of the cycle space C (G) is d-fold if each edge occurs in at most d cycles of C(G). The basis number, b(G), of a graph G is defined to be the least integer d such that G has a d-fold basis for its cycle space. MacLane proved that a graph G is planar if and only if $b(G)\;{\leq}\;2$. Schmeichel showed that for $n\;{\geq}\;5,\;b(K_{n}\;{\bullet}\;P_{2})\;{\leq}\;1\;+\;b(K_n)$. Ali proved that for n, $m\;{\geq}\;5,\;b(K_n\;{\bullet}\;K_m)\;{\leq}\;3\;+\;b(K_n)\;+\;b(K_m)$. In this paper, we give an upper bound for the basis number of the semi-strong product of a bipartite graph with a cycle.

• Bulletin of the Korean Chemical Society
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• 제16권11호
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• pp.1089-1093
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• 1995

The p-xylyl radical has been produced in a jet from the precursor p-xylene with a corona excited supersonic expansion. Rotationally cooled vibronic emission spectra in the transition of 12A2→12B2 of the p-xylyl radical have been recorded using a Fourier transform spectrometer. The spectra were analyzed on the basis of the known vibrational frequencies and the bandshapes given by the rotational selection rules.

• 대한수학회지
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• 제41권2호
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• pp.345-368
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• 2004

A preconditioning algorithm is developed in this paper for the iterative solution of the linear system of equations resulting from the p-version boundary element approximation of the three dimensional integral equation with hypersingular operators. The preconditioner is derived by first making the nodal and side basis functions locally orthogonal to the element internal bases, and then by decoupling the nodal and side bases from the internal bases. Its implementation consists of solving a global problem on the wire-basket and a series of local problems defined on a single element. Moreover, the condition number of the preconditioned system is shown to be of order $O((1＋ln/p)^{7})$. This technique can be applied to discretization with triangular elements and with general basis functions.

• 대한수학회보
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• 제38권1호
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• pp.65-69
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• 2001

For any closed subspace X of $\ell_p, \; 1<\kappa<\infty$, K(X) is proximinal in L(X), and if X is a Banach space with an unconditional shrinking basis, then K(X, c$_0$) is proximinal in L(X,$ \ell_\infty$).

• 제어로봇시스템학회논문지
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• 제12권12호
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• pp.1178-1183
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• 2006

This paper is concerned with the modeling and identification of pH neutralization process as nonlinear chemical system. The pH control has been applied to various chemical processes such as wastewater treatment, chemical, and biochemical industries. But the control of the pH is very difficult due to its highly nonlinear nature which is the titration curve with the steepest slope at the neutralization point. We apply SVM which have become an increasingly popular tool for machine teaming tasks such as classification, regression or detection to model pH process which has strong nonlinearities. Linear and radial basis function kernels are employed and each result has been compared. So SVH based on kernel method have been found to work well. Simulations have shown that the SVM based on the kernel substitution including linear and radial basis function kernel provides a promising alternative to model strong nonlinearities of the pH neutralization but also to control the system.

• Korean Journal of Mathematics
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• 제26권1호
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• pp.23-41
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• 2018

The main aim of this paper is to prove some results related to the growth rates of composite entire and meromorphic functions on the basis of their relative (p, q)-th order, relative (p, q)-th lower order, relative (p, q)-th type and relative (p, q)-th weak type where p and q are any two positive integers.

• Korean Journal of Mathematics
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• 제27권1호
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• pp.93-117
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• 2019

In this paper we wish to study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of (p, q)-th relative Ritt order, (p, q)-th relative Ritt type and (p, q)-th relative Ritt weak type where p and q are integers such that $p{\geq}0$ and $q{\geq}0$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권4호
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• pp.297-336
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• 2018

In this paper we wish to establish some basic properties of entire functions represented by a vector valued Dirichlet series on the basis of (p, q)-th relative Ritt order, (p, q)-th relative Ritt type and (p, q)-th relative Ritt weak type where p and q are integers such that $p{\geq}0$ and $q{\geq}0$.

• Asian-Australasian Journal of Animal Sciences
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• 제16권6호
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• pp.843-851
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• 2003

An experiment was conducted to investigate the effects of pre-wilting Bana grass (Pennisetum purpureum x P. americanum) herbage under sunny conditions for 0, 6, 18, 24, 32 and 48 h and ensiling it with maize meal. Four levels of maize meal(viz., 0, 5, 10 and 15% on fresh weight (Fw) basis) were tested. The experiment had a split-plot design. Wilting increased the concentration of water soluble carbohydrates (WSC) significantly (p<0.001) on a Fw basis, although there were no significant changes on DM basis. Unwilted grass contained $36.1g{\cdot}WSC{\cdot}kg^{-1}{\cdot}Fw$ ($127.6g{\cdot}kg^{-1}{\cdot}DM$) and this increased to $64.1g{\cdot}WSC{\cdot}kg^{-1}{\cdot}Fw$ ($116.7g{\cdot}kg^{-1}{\cdot}DM$) after 48 h of pre-wilting. Wilting also increased the DM content of herbage significantly (p>0.001) from 250 to $620g{\cdot}kg^{-1}$, between 0 and 48 h respectively. The concentration of fermentation end-products decreased (except butyric acid) and pH increased when the period of wilting increased, indicating that fermentation was restricted. In particular, lactic acid content declined from 50.8 to $26.2g{\cdot}kg^{-1}{\cdot}DM$ (p<0.01) and the residual WSC contents of silage increased from 2.7 with fresh herbage to $18.1g{\cdot}kg^{-1}{\cdot}DM$ with 48 h of wilting (p<0.001). Rapid wilting for 24 h, to a DM of $450g{\cdot}kg^{-1}$ was optimum since important increases in pH, residual WSC and DMD occurred at this level of wilting. Acetic acid, butyric acid and ammoniacal-N contents were lowest with 24 h of wilting. There were no significant interactions between length of wilting and the incorporation of maize meal. Wilting had a greater influence on fermentation than the incorporation of maize meal. Addition of maize meal facilitated fermentation by increasing forage DM content and reducing effluent production. In addition, the maize meal increased DMD. It was concluded that maize meal should generally be incorporated at a level of 5% on fresh weight basis.

• 대한화학회지
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• 제22권5호
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• pp.295-303
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• 1978

정팔면체[Co(III)-$O_3N_3$], 정사면체[M(II)-$O_2N_2$] 및 정사각형형[M(II)-$O_2N_2$]형태 착물의 쌍극자모멘트를 중심이온의 valence basis sets와 리간드의 single basis 궤도함수($2p_z$)를 사용하여 spherical harmonics의 전개방법에 의하여 계산하였다. 이들 착물에 대하여 계산한 쌍극자모멘트의 값이 실험치와 일치하였다.