• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.505-510
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• 2011

We give a constructive proof that a (partial) evaluation of a multivariate algebraic function with algebraic numbers is again an algebraic function. Especially, we obtain a bound on the degree of an evaluation with the degrees of the original algebraic function and the algebraic numbers evaluated. Furthermore, we show that our bound is sharp with an example.

• Elastomers and Composites
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• v.14 no.2
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• pp.83-102
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• 1979

The purpose of this dissertation is to study some of the vulcanization characteristics of rubber-bound antioxidants such as G-1, [N-(3-methacryloyloxy-2-hydroxypropyl)-N'-phenyl-p-phenylene diamine] and acryl, acrylamide & acrylester substituted hindered phenols. The influence of these antioxidants upon vulcanization characteristics in NR and SBR compounds in the presence of vulcanizing accelerators such as MSA, TT, DM, M & D was evaluated by means of Oscillationg Disk Cure Meter. The comparison was also made between the influence of rubber-bound antioxidants and that of conventional non-reactive antioxidants such as N-alkyl substituted PADA series. Regarding the influence of reactive type antioxidant G-1 mixed with accelerator TT upon vulcanization characteristics, rapid onset of vulcanization and higher degree of cross-linking were discovered, whereas in the case of accelerator M and DM, the result was slow onset of vulcanization and lesser degree of cross-linking. The comparison of vulcanizing characteristics among acrylic substituted hindered phenols as antioxidants was made under several vulcanization accelerator systems. Under such systems, MSA-S combined accelerator caused the onset of vulcanization to slow down and lowered the degree of cross-linking. Finally in the case of hindered phenol derivatives containing longer substituent, the delayed onset of vulcanization and the lowered degree of cross-linking could be discerned.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.203-207
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• 2019

The commutativity degree of a finite group is the probability that two randomly chosen group elements commute. In this paper we give a sharp upper bound of commutativity degree of nonabelial groups in terms of their order.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.573-578
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• 1991

A stability analysis technique has been proposed for linear SISO system associated with fuzzy logic controller. An analysis technique using the concept of well-known sector bound nonlinearity and its graphical interpretation, i.e., the circle criterion, is presented. Thus the use of classical Nyquist locus and the BODE diagram is brought into the picture. The aim of this present note is to represent a graphical approach based on sector bound nonlinearity and circle criterion for assessing the performance(degree of stability) of the linear SISO system associated with fuzzy logic controller. The degree of stability of the system is defined in terms of its gain and phase margins as defined in Section 3.

• Proceedings of the Korean Information Science Society Conference
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• 2011.06b
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• pp.488-491
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• 2011

For given g ${\geq}$ 3, this paper provides an O(1) time and O(n) space complexity algorithm for generation of biconnected rooted colored outerplanar graphs with face size bound g, where the graphs generated contain at most n vertices. The vertices are colored in such a way that each color has a corresponding degree bound. There is also a face size bound for each inner face of the graph. No duplications or isomorphic copies of a same graph are generated.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.113-125
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• 2019

In this paper, we introduce the elimination ideal $I_D(G)$ associated to a simple finite graph G. We obtain the upper bound of Castelnuovo-Mumford regularity of elimination ideal for various classes of graphs.

• Analytical Science and Technology
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• v.12 no.2
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• pp.159-165
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• 1999

The adsorption and separation behaviors of transition metal ions using a merrifield resin bound 1,12-diaza-3,4:9,10-dibenzo-5,8-dioxacyclopentadecane (NTOE) and 1,12,15-triaza-3,4:9,10-dibenzo-5,8-dioxacycloheptadecane(NDOE) were investigated in aqueous solution. The orders of adsorption degree(E) and distribution ratio(D) of transition metal ions were Cu(II)$t_R$) of metal ions were affected by adsorption degree(E) and distribution ratio(D). This results showed good separation efficiency of Ag(I) from mixed metal solution.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.593-609
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• 2002

The order of speciality of an ample invertible Sheaf L on a curve is the least integer m so that $L^{ m}$ is nonspecial. There is a reasonable upper bound of the order of speciality for a simple invertible sheaf in terms of its degree and projective dimension. We study the case where it reaches the upper bound. Moreover we for mulate Castelnuovo's genus bound involving the order of speciality.ality.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.257-265
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• 2009

In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.461-473
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• 2016

Let C be a projective plane curve of degree d whose singularities are all isolated. Suppose C is not concurrent lines. P loski proved that the Milnor number of an isolated singlar point of C is less than or equal to $(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$. In this paper, we prove that the Milnor sum of C is also less than or equal to $(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$ and the equality holds if and only if C is a P loski curve. Furthermore, we find a bound for the Milnor sum of projective plane curves in terms of GIT.