• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.411-423
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• 2010

In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• Korean Institute of Interior Design Journal
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• no.31
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• pp.12-18
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• 2002

This study was performed to construct the spatial systems and shape grammars in architecture based on Froebel's educational idea and building gifts. Especially, it studies on the geometrical principles of Froebel's building gifts and it's types, and then illustrates applied examples about design vocabularies, spatial relations and shape rules of the spatial systems and shape grammars in architecture. The conclusions of this study that starts these purpose are as follows. First, Froebel's educational theory is based on principles and rules which are perceived through the observation of nature, and Froebel's kindergarten method consists of geometrical building gifts and categories of geometrical forms. Second, the characteristics of Froebel's building gifts are mathematical size, proportion, symmetry and the rules of spatial relation. Third, the development to the construction of spatial systems and shape grammars in architecture focus on the vocabularies of architectural elements, and Froebel's building gifts are used for illustration of examples in these formula.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2001.10a
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• pp.119-122
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• 2001

Annual demand of a precast concrete bench flume used in the irrigation canal of arable land readjustment has continuously increased units recently. The average life time of the precast concrete bench flume was estimated $8{\sim}10$ years, which is too shorter than the life time of in-site placed concrete structures. In order to increase the compressive strength of the precast concrete bench flumes, the highest temperature of being lower than $95^{\circ}C$ was suggested in this study, Through analyzing the relation between the compressive strength and the amount of chloride penetration into concrete specimens, a new formula early estimating durability of the concrete structure was suggested.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.1045-1073
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• 2014

The study of the identities of symmetry for the Bernoulli polynomials arises from the study of Gauss's multiplication formula for the gamma function. There are many works in this direction. In the sense of p-adic analysis, the q-Bernoulli polynomials are natural extensions of the Bernoulli and Apostol-Bernoulli polynomials (see the introduction of this paper). By using the N-fold iterated Volkenborn integral, we derive serval identities of symmetry related to the q-extension power sums and the higher order q-Bernoulli polynomials. Many previous results are special cases of the results presented in this paper, including Tuenter's classical results on the symmetry relation between the power sum polynomials and the Bernoulli numbers in [A symmetry of power sum polynomials and Bernoulli numbers, Amer. Math. Monthly 108 (2001), no. 3, 258-261] and D. S. Kim's eight basic identities of symmetry in three variables related to the q-analogue power sums and the q-Bernoulli polynomials in [Identities of symmetry for q-Bernoulli polynomials, Comput. Math. Appl. 60 (2010), no. 8, 2350-2359].

• Honam Mathematical Journal
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• v.36 no.3
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• pp.531-542
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• 2014

Recently, Srivastava et al. [18] introduced the incomplete Pochhammer symbol and studied some fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. Here we introduce the incomplete Lauricella function ${\gamma}_D^{(n)}$ and ${\Gamma}_D^{(n)}$ of n variables, and investigate certain properties of the incomplete Lauricella functions, for example, their various integral representations, differential formula and recurrence relation, in a rather systematic manner. Some interesting special cases of our main results are also considered.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.33A no.10
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• pp.61-70
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• 1996

In this paper, we find the values of near-end crosstalk coefficient in striplines of a FR-4 multilayer PCB by an analytic method and a HSPICE simulation method, and define calcualtion errors in an analytic method and define the application range, and simualte near-end crosstalk coefficients of the FCT (fast CMOS TTL) in complicated striplines by HSPICE and analyze near-en crosstalk coefficients in relation to dielectric thickness and trace spaces of striplines. As a result, we analyze coupling structure of the near-end crosstalk in the coplicated sstriplines that are impedance matched and define a coupling formula of near-end crosstalk coefficients in general complicated striplines. Especially, it is approximated in the layout grade rule.

• Korean Journal of Crystallography
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• v.12 no.1
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• pp.37-54
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• 2001

1960년대까지는 단결정 구조를 해석할 때 주로 Patterson 방법으로 중원자(heavy atom)를 찾고 이 중원자에 의한 위상에 기초하여 구조를 해석해 왔다. 회절점의 위상을 수학적으로 결정하는 직접법(direct method)은 1948년 Harker와 Kasper에 의해서 최초의 논문이 발표된 이후, 50∼60년 대에 이론적 기초가 구축되었으며, 70년대부터 컴퓨터 프로그램화되어 실용되기 시작하였다. 본 해설문에서는 직접법에 사용되는 정규화된 구조 인자(normalized structure factor)와 unitary 구조 인자의 정의를 소개한 후, 직접법의 기본식인 Sayre 방정식으로부터 유도되는 반전적 혹은 대칭중심적(centric)인 경우에서 성립하는 부호 관계(sign relationship) 및 ∑₂-관계(∑₂-relation)와 비반전적(acentric)경우에서 성립하는 탄젠트 공식(tangent formula)의 유도 과정을 설명하였고, 부호 관계와 탄젠트 공식이 필요로 하는 처음 몇 개의 회절점의 위상을 정하는 과정도 보였다.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.11a
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• pp.737-744
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• 2000

This paper resorts to rock mass rating and rock mass quality to draw value based on the evaluation of rock and to draw interrelation formula in relation to rock mass quality, A comparative analysis was given of survey values reported in the existing documents. This paper has tried to find out the relationship between RMR and Q System for the sake of choosing rational reinforcing patterns and of the safety of tunnels. The results run as follow: RMR=8.251n(Q)+43.83. This paper has also tried to find out the relationship between RMR and Q System by using Fuzzy Approximate Reasoning Concept. We suggest that those in charge should not depend on a single system only after evaluating the classification of rocks, and compare one result with another for the good of keeping track of the condition of base rocks in a better way.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1273-1287
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• 2008

In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.11 no.3
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• pp.98-103
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• 2012

One of the problems in the grinding process using the machining center(MC) with a small diametric wheels is machining error due to decrease of the quill diameter. In this thesis, side-cut grinding is performed with a vitrified bonded CBN wheel on the machining center to establish the basis of the grinding using MC. The grinding force and machining error are investigated experimentally for the change of the machining condition. It is possible to estimate the machining performance by the ratio of the setting depth of cut and actual depth of cut. In addition, the relation between normal grinding force and machining error is presented by the experimental formula.