• 대한수학회지
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• 제56권1호
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• pp.67-80
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• 2019

For positive integers a, b, c, and an integer n, the number of integer solutions $(x,y,z){\in}{\mathbb{Z}}^3$ of $a{\frac{x(x-1)}{2}}+b{\frac{y(y-1)}{2}}+c{\frac{z(z-1)}{2}}=n$ is denoted by t(a, b, c; n). In this article, we prove some relations between t(a, b, c; n) and the numbers of representations of integers by some ternary quadratic forms. In particular, we prove various conjectures given by Z. H. Sun in [6].

• 한국수학사학회지
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• 제20권3호
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• pp.1-16
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• 2007

이상혁(李尙爀)(익산(翼算))의 퇴타술중 삼각타, 사각타 계열에 관한 부분을 조사하고, 익산(翼算)의 결과를 부분합 복수열의 성질로 재해석한다. 유한생성 부분합 복수열의 개념을 도입하고 삼각타, 사각타 계열에 의한 부분합 복수열이 유한생성 부분합 복수열임을 보인다. 단위 부분합 복수열이 부분합 복수열의 연구에 핵심적 역할을 함을 보인다. 또한, 부분합 복수열이 유한생성이 되기 위한 필요충분조건을 구한다. 그리고, 교초적에 대한 곱셈법칙에 대응하는 삼각타적, 삼각낙일적(三角落一積)에 대한 곱셈법칙을 구한다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2006년도 춘계학술대회 논문집 전기기기 및 에너지변환시스템부문
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• pp.270-274
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• 2006

This paper proposes a Chaos Pulse Width Modulation(CPWM) technique. For generating the chaotic numbers by chaos phenomenon, chaos area $\lambda$=0.99 in bifurcation tree of the proposed double tent mapping is used. A micro-controller is used for the generation of chaos numbers and triangular carrier with chaotic frequency is obtained through the process of frequency modulation according to the generated chaos numbers. The experiments are executed with the 1.5kw induction motor coupled with a 2.5A load. The experimental results show that the voltage / current spectra are spread to a chaotic range, and the switching noise of motor is reduced by the proposed method compared to the fixed frequency PWM method.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.345-354
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• 2006

In this paper first, we find a canonical symmetrical trapezoidal(triangular) for the solution of the fuzzy linear system $A\tilde{x}=\tilde{b}$, where the elements in A and $\tilde{b}$ are crisp and arbitrary fuzzy numbers, respectively. Then, a model for fuzzy linear programming problem with fuzzy variables (FLPFV), in which, the right hand side of constraints are arbitrary numbers, and coefficients of the objective function and constraint matrix are regarded as crisp numbers, is discussed. A numerical procedure for calculating a canonical symmetrical trapezoidal representation for the solution of fuzzy linear system and the optimal solution of FLPFV, (if there exist) is proposed. Several examples illustrate these ideas.

• 충청수학회지
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• 제31권4호
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• pp.379-386
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• 2018

We generalized the quadratic fuzzy numbers on ${\mathbb{R}}$ to ${\mathbb{R}}_2$. By defining parametric operations between two regions valued ${\alpha}-cuts$, we got the parametric operations for two triangular fuzzy numbers defined on ${\mathbb{R}}_2$. The results for the parametric operations are the generalization of Zadeh's extended algebraic operations. We generalize the 2-dimensional quadratic fuzzy numbers on ${\mathbb{R}}_2$ that may have maximum value h < 1. We calculate the algebraic operations for two generalized 2-dimensional quadratic fuzzy sets.

• 한국지능시스템학회논문지
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• 제18권4호
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• pp.445-450
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• 2008

퍼지시스템의 신뢰도를 분석하기 위해서 기존의 연구에서는 퍼지시스템의 구성요소의 신뢰도를 0과 1사이의 실수, 퍼지숫자, 신용구간, 모호집합, 구간값 퍼지집합 등으로 표현하였다. 본 논문에서 우리는 전체집합 [0, 1]에서 정의되는 구간값 모호집합을 기반으로 퍼지시스템의 신뢰도를 표현하고 분석하는 방법을 제안한다. 구간값 모호집합에서는 기존 모호집합[12, 14]의 상한과 하한을 각각 구간으로 표현한다. 그러므로 퍼지시스템의 신뢰도를 더 유연한 방법으로 표현하고 분석하는 것을 가능하게 한다. 제안한 방법은 Kumar[14]가 언급한 복잡한 퍼지 사다리꼴숫자 연간보다는 퍼지 삼각숫자의 간단한 산술연산을 사용하기 때문에 제안된 방법의 실행속도는 기존의 방법보다 실행이 더 빠르다.

• 한국건설관리학회논문집
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• 제5권5호
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• pp.143-150
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• 2004

본 연구는 다기준의사결정문제인 건설 프로젝트의 공법선정문제에 있어서 퍼지계층분석법 및 그 결과 생성되는 각 공법별 퍼지 점수의 상대평가를 위해 퍼지 선호도 함수를 적용하여 상대평가를 하고자 하였다. 지금까지의 건설 공법 선정에 대한 퍼지계층분석법에 대한 연구는 대부분 최종적인 공법선정을 위해서 각 공법별로 도출된 퍼지 점수의 순위결정기법으로 절대평가를 수행하였다. 그러나 이러한 기법은 비교 대상공법에 대한 일관적인 순위결과를 산출해 내지 못하므로 결과적으로 공법선정과정의 전반적인 타당성을 저해하는 문제점을 지니고 있었다. 따라서 본 연구에서는 건설 분야의 MCDM(Multiple Criteria Decision Making)에 관한 기존의 연구들을 바탕으로 순위 결정기법에 R.P.R(Relative Preference Ratio)기법을 도입하여 각 공법에 대한 퍼지 점수를 상대 평가함으로써 체계적이고 효율적인 건설 공법선정기법을 제시하였고, 이를 창호공법의 선정문제에 적용하여 그 타당성을 살펴보았다.

• 대한기계학회논문집B
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• 제28권10호
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• pp.1139-1146
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• 2004

The effect of triangular tabs attached at the perimeter of jet nozzle on heat transfer enhancement was investigated experimentally. The modified flow structure was visualized using a smoke-wire method. Four different types of jet nozzle having 0, 4, 6 and 8 tabs were tested at jet Reynolds number Re=15,000 to investigate the effect of tabs on the variation of heat transfer rate. The local and average Nusselt numbers are increased with increasing the number of tabs. At nozzle-to-plate distance of L/D=4, the average Nusselt number was increased about 9.9% at Re=15,000 in the impingement region for the case of 8 tabs attachment. As the nozzle-to-plate distance increases, however, the heat transfer enhancement effect of triangular tabs is reduced. For the case of 4 tabs, the heat transfer enhancement is not so distinctive at L/D=8. As the protrusion depth of tabs into the jet flow increases, the heat transfer rate is also enhanced when the nozzle-to-plate distance is smaller than L/D=6.

• 대한기계학회논문집B
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• 제31권7호
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• pp.628-634
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• 2007

The present study investigated the heat/mass transfer characteristics in an equilateral triangular channel simulating the leading edge cooling passage in gas turbine blade. Using naphthalene sublimation method and pressure measurement experiments, local mass (heat) transfer and pressure coefficients were obtained. The experiments were conducted with three rotating numbers between 0.0 and 0.1; two channel orientations of $0^{\circ}$ (model A) and $30^{\circ}$ (model B); the fixed Reynolds number of 10,000. The results showed that the channel rotation caused the heat transfer discrepancy between suction and pressure sides. Due to the secondary flow induced by Coriolis force, the high heat transfer appeared on the pressure side. When the channel orientation was $30^{\circ}$ (model B), the secondary flow caused the more uniform heat transfer distribution among leading edge and inner wall on pressure side than that of the model A.

• 한국군사과학기술학회지
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• 제12권6호
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• pp.808-814
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• 2009

Numerical flow-filed computations have been conducted around a projectile with a triangular ballute at Mach numbers of 0.3 ~ 0.9 and angles of attack of $0^{\circ}\;{\sim}\;30^{\circ}$. The expansion shape of a triangular ballute has been determined from both the manufacturing dimensions and the wind tunnel test results. It has been assumed that the shape does not alter after the ballute has been expanded completely. The computed results showed a good agreement with the wind tunnel test results. A sensitivity analysis on the aerodynamic coefficients has been performed to evaluate the quantitative effects on the flight performance. Trajectory simulation results were also in good agreement with the flight test results.