• East Asian mathematical journal
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• 제39권5호
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• pp.523-528
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• 2023

Let S_n = [S(i, j)]_1≤i,j≤n and S^*_n = [S(i + j, j)]_1≤i,j≤n where S(i, j) is the Stirling number of the second kind. Choi and Jo [On the determinants of the square-type Stirling matrix and Bell matrix, Int. J. Math. Math. Sci. 2021] obtained the diagonal entries of matrix U in the LU-factorization of S^*_n for calculating the determinant of S^*_n, where L = S_n. In this paper, we compute the all entries of U in the LU-factorization of matrix S^*_n. This implies the identities related to Stirling numbers of both kinds.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.133-159
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• 2024

In a previous work we studied generalized Stirling numbers of the second kind S^{(a₂,b₂,p₂)}_a1,b1 (p₁, k), where a₁, a₂, b₁, b₂ are given complex numbers, a₁, a₂ ≠ 0, and p₁, p₂ are non-negative integers given. In this work we use these generalized Stirling numbers to define Bernoulli polynomials in two variables B_p1,p2 (x₁, x₂), and Euler polynomials in two variables E_p1p2 (x₁, x₂). By using results for S^{(1,x₂,p₂)}_1,x1 (p₁, k), we obtain generalizations, to the bivariate case, of some well-known properties from the standard case, as addition formulas, difference equations and sums of powers. We obtain some identities for bivariate Bernoulli and Euler polynomials, and some generalizations, to the bivariate case, of several known identities for Bernoulli and Euler numbers and polynomials of the standard case.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.465-474
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• 2014

Many mathematicians have studied various relations beween Euler number $E_n$, Bernoulli number $B_n$ and Genocchi number $G_n$ (see [1-18]). They have found numerous important applications in number theory. Howard, T.Agoh, S.-H.Rim have studied Genocchi numbers, Bernoulli numbers, Euler numbers and polynomials of these numbers [1,5,9,15]. T.Kim, M.Cenkci, C.S.Ryoo, L. Jang have studied the q-extension of Euler and Genocchi numbers and polynomials [6,8,10,11,14,17]. In this paper, our aim is introducing and investigating an extension term of generalized Euler polynomials. We also obtain some identities and relations involving the Euler numbers and the Euler polynomials, the Genocchi numbers and Genocchi polynomials.

• Journal of Biosystems Engineering
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• 제20권3호
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• pp.205-216
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• 1995

A fast and inexpensive approximate analysis method to predict power output characteristics of the Stilting engines in a preliminary design stage was investigated. In basic equations proposed by Walker, typical temperatures of working fluids in expansion and compression spaces were treated as those of working fluids in heater and cooler respectively. While the temperature of working fluid in the expansion space was actually lower than that of working fluid in the heater, the temperature of working fluid in the compression space was higher than that of working fluids in the cooler. In this paper, the working fluid temperature of expansion space was treated as lower than the heater temperature and that of compression space was treated as higher than the cooler temperature. Also, according to them, the power output characteristics of the Stirling engine were evaluated with respect to the GPU-3 and 4-215 Stilting engines. The following conclusions were drawn from the analysis. 1. Using the available experimental data from the GPU-3 Stirling engine, it was shown that the approximate analysis predicts the brake power with a maximum error of 19 percent at 1, 000rpm and with a minimum error of 3 percent at 2, 000rpm. 2. The approximate analysis data which for the GPU-3 Stirling engine were much closer to the experimental data than those of adiabatic 2nd order and 3rd order analysis within 1, 500rpm to 2, 500rpm. 3. The approximate analysis data which for the GPU-3 and 4-215 Stilting engines were much closer to the experimental data than those of the Beal number analysis.

• 한국전산유체공학회지
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• 제16권2호
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• pp.56-61
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• 2011

Numerical study is conducted to design the high temperature heat exchanger of Stirling engine by using the commercial CFD solver, FLUENT. The Fin-tube type of heat exchanger is designed as a reference model by considering the type of engine which is ${\beta}$-configuration. To find the optimal design of heat exchanger in heat transfer capacity numerical calculation is conducted by changing the shape, the number, and material of reference model in three-dimensional combustion field. Adjusted one-way constant velocity of working fluid that is helium is considered as the representative velocity of oscillating flow. The optimal design of heat exchanger considering the heat transfer capability is suggested by using the calculation results.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2010년 춘계학술대회논문집
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• pp.163-166
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• 2010

Numerical analysis is conducted to design the high temperature heat exchanger of Stirling engine by using the commercial CFD solver FLUENT. The fin-tube type of heat exchanger numerical calculation is conducted by changing the shape, number and material of fin shape of working fluid channel, etc in three-dimensional combustion field. Adjusted one-way constant velocity is used as the representative velocity of oscillating flow. The optimum design of heat exchanger considering the heat trasfer capability is suggested by using the calculation results.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.435-446
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• 2018

Using the theory of combinatoric convolution sums, we establish some arithmetic identities involving Liouville functions and restricted divisor functions. We also prove some relations involving restricted divisor functions and Stirling numbers of the first kind for divisor functions.

• 에너지공학
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• 제25권1호
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• pp.9-14
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• 2016

본 연구는 주위의 온도보다 약 $20{\sim}30^{\circ}C$ 밖에 높지 않은 저온폐열을 활용하기 위한 TM(Thermal to Mechanical) 발전변환기의 개발을 위하여 저온도차 스털링엔진의 하나인 MM-7에 대한 성능실측 연구를 수행하였다. 스털링엔진의 흡열부와 방열부의 온도차에 대한 토크 및 분당회전수를 측정하고 이를 바탕으로 MM-7 엔진의 출력을 산출하였으며, 이를 통하여 효율적인 TM발전변환기의 개발 방안을 모색하였다.

• Nuclear Engineering and Technology
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• 제53권7호
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• pp.2184-2194
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• 2021

The Free-Piston Stirling engine (FPSE) is of interest for many research in aerospace due to its advantages of long operating life, higher efficiency, and zero maintenance. In this study, a 1-kW FPSE was proposed by analyzing the requirements of Space Reactor Power Systems (SRPS), of which performance was evaluated by developing a code through the Simple Analysis Method. The results of SAM showed that the critical parameters of FPSE could satisfy the designed requirements. The heater of the FPSE was designed with the copper rectangular fins to enhance heat transfer, and the parametric study of the heater was performed with Computational Fluid Dynamics (CFD) software STAR-CCM⁺. The Performance Evaluation Criteria (PEC) was used to evaluate the heat transfer enhancement of the fins in the heater. The numerical results of the CFD program showed that pressure drop and Nusselt number ratio had a linear growth with the height of fins, and PEC number decreased as the height of fins increased, and the optimum height of the fin was set as 4 mm according to the minimum heat exchange surface area. This paper can provide theoretical supports for the design and numerical analysis of an FPSE for SRPSs.

• 대한수학회지
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• 제44권2호
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• pp.487-498
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• 2007

In this paper, we obtain important combinatorial identities of generalized harmonic numbers using symmetric polynomials. We also obtain the matrix representation for the generalized harmonic numbers whose inverse matrix can be computed recursively.