• 대한수학회지
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• 제57권4호
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• pp.845-871
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• 2020

We consider generalized Dedekind sums in dimension n, defined as sum of products of values of periodic Bernoulli functions. For the generalized Dedekind sums, we associate a Laurent polynomial. Using this, we associate an exponential sum of a Laurent polynomial to the generalized Dedekind sums and show that this exponential sum has a nontrivial bound that is sufficient to fulfill the equidistribution criterion of Weyl and thus the fractional part of the generalized Dedekind sums are equidistributed in ℝ/ℤ.

• 비파괴검사학회지
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• 제29권6호
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• pp.557-562
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• 2009

Abrupt change of cross-section in mechanical parts is one of significant causes of structural fracture. In this paper, a hybrid method is employed to analyze the stress distribution of a discontinuous plate. The plate with an inclined crack is utilized in our experiment and the stress field in the vicinity of crack tip is calculated through isochromatic fringe order of given points. This calculation can be made handy through least-squares method integrated with complex power series representation(Laurent series) implemented on a computer program for high-speed processing. In order to accurately compare calculated results with experimental ones, both of actual and regenerated photoelastic fringe patterns are doubled and sharpened by digital image processing. The experiment results show that regenerated patterns obtained by hybrid method are quite comparable to actual patterns.

• Korean Journal of Mathematics
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• 제31권4호
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• pp.405-417
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• 2023

The RIP of rings was introduced by Kwak and Lee as a generalization of the one-sided idempotent-reflexivity property. In this study, we focus on rings in which all one-sided semicentral idempotents are central, and we refer to them as quasi-Abelian rings, extending the concept introduced by RIP. We establish that quasi-Abelianity extends to various types of rings, including polynomial rings, power series rings, Laurent series rings, matrices, and certain subrings of triangular matrix rings. Furthermore, we provide comprehensive proofs for several results that hold for RIP and are also satisfied by the quasi-Abelian property. Additionally, we investigate the structural properties of minimal non-Abelian quasi-Abelian rings.

• 한국안전학회지
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• 제12권4호
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• pp.27-38
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• 1997

The effect of geometry factors on the combined mode stress intensity factor behaviors of a slant crack in a non-uniform thickness material was analysed by 2-dimensional theoretical analysis. The analysis is based on the Laurent's series expansions of complex potentials where the complex coefficients of the series are determined from the compatibility and the equilibrium conditions of the thickness interface and the stress free conditions of the crack surface. In numerical calculations the perturbation technique is employed. The expressions for the crack tip stress intensity factor are given in the form of power series of dimensionless crack length $\lamda$, and the function of crack slant angle $\alpha$ and thickness ratio $\beta$. The results of numerical calculations for each problems are represented as the correction factors F($\lamda$, $\alpha$, $\beta$). The results clearly show the following characteristics : The correction factors of the combined mode stress intensity factors for a non-uniform thickness material can be defined in the form of F($\lamda$, $\alpha$, $\beta$). The stress intensity factor values for a given crack length are decreased with increase of thickness ratio $\beta$.

• 대한수학회지
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• 제55권1호
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• pp.101-129
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• 2018

From an analytical perspective, we introduce a sequence of Cartier operators that act on the field of formal Laurent series in one variable with coefficients in a field of positive characteristic p. In this work, we discover the binomial inversion formula between Hasse derivatives and Cartier operators, implying that Cartier operators can play a prominent role in various objects of study in function field arithmetic, as a suitable substitute for higher derivatives. For an applicable object, the Wronskian criteria associated with Cartier operators are introduced. These results stem from a careful study of two types of Cartier operators on the power series ring ${\mathbf{F}}_q$[[T]] in one variable T over a finite field ${\mathbf{F}}_q$ of q elements. Accordingly, we show that two sequences of Cartier operators are an orthonormal basis of the space of continuous ${\mathbf{F}}_q$-linear functions on ${\mathbf{F}}_q$[[T]]. According to the digit principle, every continuous function on ${\mathbf{F}}_q$[[T]] is uniquely written in terms of a q-adic extension of Cartier operators, with a closed-form of expansion coefficients for each of the two cases. Moreover, the p-adic analogues of Cartier operators are discussed as orthonormal bases for the space of continuous functions on ${\mathbf{Z}}_p$.

• 대한기계학회논문집
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• 제11권1호
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• pp.132-144
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• 1987

본 논문에서는 Isida의 이론해석 방법을 참고로 하여 유한한한 폭을 갖는 두 께가 변화하는 판재에서의 응력확대계수를 2차원 이론해석한 것이다.

• 자연과학논문집
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• 제7권
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• pp.121-131
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• 1995

오리엔탈리즘은 20세기 초에 스타일의 변화에서 시작되었다. 현대성은 역사적 개념이전의 거대한 변화의 흐름을 통해 이해될 수 있다. 서양에 있어 스타일의 변화는 동양적, 이국적 취미를 가진 예술가에 의해 시작되었다. 이것은 외형적으로 일본, 모로코, 북아프리카에 대한 외형의 재현이었다. 20세기 양식의 흐름은 표현주의, 큐비즘, 쉬르 뤼얼리즘, 팝아트로 이어진다. 그러나 오리엔탈리즘은 후에 원시주의로 보여지는 에그조티즘 이후 20세기 변화의 원천이 되었다. 현대복식에서는 신체의식을 변화시킨 뽈 뿌와레의 작품과 관련지어 본다. 그는 이브 생 로랑, 샤넬, 발렌시아가와 같은 이미지 창조자였다. 당시 러시아 발레, 야수파, 생생한 색상은 일련의 현대복식의 배경이 되었다. 부드럽고 유연한 신체, 비치는 스타킹, 미나레 튜닉, 터번 등은 오리엔탈 이미지의 시작이었다. 현대복식과 현대 조형은 역사적 개념이전에 미적 기초의 변화에서 비롯된 것이다.