• Journal of the Korean Mathematical Society
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• v.56 no.1
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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].

• Journal for History of Mathematics
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• v.20 no.3
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• pp.1-16
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• 2007

In order to generalize theory of series in Iksan(翼算), we introduce a concept of double sequence of partial sums and elementary double sequence of partial sums, which play a dominant role in the study of double sequences of partial sums. We introduce a concept of finitely generated double sequence of partial sums and find a necessary and sufficient condition for those double sequences. Finally we prove a multiplication theorem for tetrahedral numbers and for 4 dimensional tetrahedral numbers.

• Proceedings of the KIEE Conference
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• 2006.04b
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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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• v.20 no.1_2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.4
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• pp.445-450
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• 2008

In order to analyze the reliabilities of the fuzzy systems, the reliabilities of the components in the fuzzy systems are represented by real values between zero and one, fuzzy numbers, intervals of confidence, vague sets, interval valued fuzzy sets, etc in the conventional researches. In this paper, we propose a method to represent and analyze the reliabilities of the fuzzy systems based on the interval valued vague sets defined in the universe of discourse [0, 1]. In the interval valued vague sets, the upper bounds and the lower bounds of the conventional vague sets[12, 14] are represented as the intervals. Therefore, it can allow the reliabilities of a fuzzy system to represent and analyze in a more flexible manner. Because the proposed method uses the simplified arithmetic operations of the fuzzy triangular numbers rather than the complicated of the fuzzy trapezoidal numbers mentioned by Kumar[14], the execution of the proposed method is faster than the one.

• Korean Journal of Construction Engineering and Management
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• v.5 no.5 s.21
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• pp.143-150
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• 2004

Nowaday, The tendency of complexity and extension of construction fields increase the need for efficient works managements like a construction management. Consequently, by the introduction of Decision-Making Theories, researches for improving construction field's efficiencies are actively performed. Fuzzy Analytical Hierarchy Process method is invented, so that describes a decision maker's ambiguous linguistic judgment with fuzzy numbers. but most of researches on Fuzzy-AHP use symmetric triangular fuzzy function for estimating each evaluation item with the consequence that exact judgments are impossible. those limits are caused by the point that employed fuzzy ranking methods can not support dissymmetric fuzzy numbers. In this research, we aims to overcome this problem with R.P.R(Relative Preference Ratio) method and suggest improved Fuzzy-AHP method which can use dissymmetric fuzzy triangular numbers.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.10
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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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.7 s.262
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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.

• Journal of the Korea Institute of Military Science and Technology
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• v.12 no.6
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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.