• 충청수학회지
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• 제36권2호
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• pp.65-76
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• 2023

With the Stirling matrix S of the second kind and the Pascal matrix T, we study recurrence rules and sequences of certain sums over the matrix ST^k. We find a matrix E satisfying ST = ES and interrelations of S and the Stirling matrix of the first kind.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제6권2호
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• pp.121-127
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• 1999

We can get the Pascal's matrix of order n by taking the first n rows of Pascal's triangle and filling in with 0's on the right. In this paper we obtain some well known combinatorial identities and a factorization of the Stirling matrix from the Pascal's matrix.

• 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.

• Journal of Biosystems Engineering
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• 제32권6호
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• pp.389-394
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• 2007

The power output of the stirling engine is influenced by the regenerator effectiveness. The regenerator effectiveness is influenced by heat transfer and flow friction loss of the regenerator matrix. In this paper, in order to provide basic data for the design of the regenerator matrix, characteristics of working fluid velocities were investigated by a packed method of matrix in the oscillating flow as the same condition of operation in a Stirling engine. As matrices, two different wire screens were used. The results are summarized as follows; 1. When a regenerator is not filled with any wire screen, working fluid velocity of the oscillating flow shows 1.3 times faster than that of one directional flow. 2. When a regenerator is filled with the wire screen of No.50, working fluid velocity of the oscillating flow reveals 2.5 times faster than that of one directional flow. 3. When a regenerator is filled with the wire screen of No. 100, working fluid velocity of the oscillating flow shows 2 times faster than that of one directional flow, regardless of the number of packed wire screens. 4. Working fluid velocity is decreased wire the increase in number of meshes and packed wire screens.

• Journal of Biosystems Engineering
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• 제33권1호
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• pp.1-6
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• 2008

The output of the Stirling engine is influenced by the regenerator effectiveness. The regenerator effectiveness is influenced by heat transfer and flow friction loss of the regenerator matrix. In this paper, in order to provide basic data for the design of regenerator matrix, characteristics of flow friction loss were investigated by a packed method of matrix in the oscillating flow as the same condition of operation in a Stirling engine. As matrices, two different wire screens were used. The results are summarized as follows; 1. With the wire screen of No. 50 as regenerator matrices, pressure drop of working fluid of the oscillating flow is shown as 3 times higher than that of one directional flow, not too much influenced by the number of packed meshes. 2. With the wire screen of No. 100 as regenerator matrices, pressure drop of working fluid of the oscillating flow is shown as 2.5 times on the average higher than that of one directional flow, not too much influenced by the number of packed meshes. 3. Under one directional flow which used regenerator matrices with both 200, 240, and 280 wire screens of No. 50 and 320, 370, and 420 wire screens of No. 100, the relationship between the friction factor and Reynold No. is shown as the following formula. $$f=\frac{0.00326639}{Re\iota}-1.29106{\times}10^{-4}$$ 4. Under oscillating flow which used regenerator matrices with both 200, 240, and 280 wire screens of No. 50 and 320, 370, and 420 wire screens of No. 100, the relationship between the friction factor and Reynold No. is shown as the following formula. $$f_r=\frac{0.000918567}{Re\iota}+1.86101{\times}10^{-5}$$ 5. The pressure drop is shown as high in proportion as the number of meshes has been higher, and the number of packed wire screens as matrices increases.

• Journal of Biosystems Engineering
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• 제30권4호
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• pp.202-209
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• 2005

The output of Stirling engine is influenced by the regenerator effectiveness. The regenerator effectiveness is influenced by heat transfer and flow friction loss of the regenerator matrix. In this paper, in order to provide a basic data for the design of regenerator matrix, characteristics of heat transfer and flow friction loss were investigated by a packed method of matrix in the oscillating flow as the same condition of operation in a Stirling engine. As matrices, 6 kinds of steel wires, 4 kinds of combined steel wires, 8 kinds of combined steel wires with screen meshes were used. The results are summarized as follows; Among 6 kinds of steel wires $({\phi}0.7\;mm,\;{\phi}0.9\;mm,\;{\phi}1.2\;mm,\;{\phi}\;1.6\;mm,\;{\phi}2.0\;mm,\;{\phi}2.7\;mm),$ the two steel wires $({\phi}0.7\;mm,\;{\phi}0.9\;mm)$ showed the highest in effectiveness. Among 4 kinds of combined steel wires $({\phi}l.6-{\phi}l.2\;mm,\;{\phi}1.2-{\phi}l.6\;mm,\;{\phi}0.9-{\phi}l.2\;mm,\;{\phi}l.2-{\phi}0.9\;mm),\;the\;{\phi}1.2-{\phi}0.9\;mm$ showed the highest in effectiveness. Among 8 kinds of combined steel wires with screen meshes $(150-{\phi}0.9\;mm,\;150-{\phi}l.2\;mm,\;{\phi}0.9\;mm-150,\;{\phi}1.2\;mm-150,\;150-{\phi}0.9\;mm-150,\;150-{\phi}1.2\;mm-150,\;150-{\phi}l.6\;mm-150,\;150-{\phi}2.0\;mm-150),\;the\;{\phi}l.2\;mm-150$ showed the highest in effectiveness.

• Journal of Biosystems Engineering
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• 제30권4호
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• pp.195-201
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• 2005

The output of Stirling engine is influenced by the regenerator effectiveness. The regenerator effectiveness is influenced by heat transfer and flow friction loss of the regenerator matrix. In this paper, in order to provide a basic data for the design of regenerator matrix, characteristics of heat transfer and flow friction loss were investigated by a packed method of matrix in the oscillating flow as the same condition of operation in a Stirling engine. As matrices, several kinds of combined wire screen meshes were used. The results are summarized as follows; The packed meshes with high mesh no. in the side of heater part of regenerator showed effective than the packed meshes with low mesh no. in the side of cooler part of regenerator. The temperature difference and pressure drop of the regenerator were not made by the specific surface area of wire screen meshes but by the minimum free-flow area to the total frontal area. Among the No. 150 single screen meshes, 200-60 combined meshes, the 200-150-100 combined meshes showed the highest in effectiveness.

• Journal of Biosystems Engineering
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• 제27권6호
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• pp.529-536
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• 2002

The performance of stilting engine, in particular, its energy conversion efficiencies are critically influenced by the regenerator characteristics. The regenerator characteristics are influenced by effectiveness, void fraction. heat transfer loss and fluid friction loss in the regenerator matrix. These factors were influenced by the surface geometry and material properties of the regenerator matrix. The regenerator design goals arc good heat transfer and low pressure drop of working Bas across the regenerator. Various data for designing a wire screen matrix have been given by Kays and London(1984). The mesh number of their experiment. however, was confined below the No. 60. which seems rather small for the Stirling engine applications. In this paper. in order to provide a basic data for the design of regenerator matrix, characteristics of heat transfer and flow friction loss were investigated by a packed mettled of matrix in oscillating flow as the same condition of operation in a Stirling engine. Seven kinds of sing1e wire screen meshes were used as the regenerator matrices. The results are summarized as follows; 1. While the working fluid flew slowly in the regenerator. the temperature difference was great at the both hot-blow(the working fluid flows from healer to cooler) and cold-blow(the working fluid flows from cooler to healer). On the other hand. while the working fluid flew fast. the temperature difference was not distinguished. 2. The No.150 wire screen used as the regenerator matrix showed excellent performance than tile others. 3. Phase angle variation and filling rate affected heat transfer or regenerator matrices. 4. Temperature difference between the inlet and outlet of the regenerator is very hish in degree of 120 phase angle.

• 대한수학회지
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• 제45권2호
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• pp.479-491
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• 2008

In [4], the authors studied the Pascal matrix and the Stirling matrices of the first kind and the second kind via the Fibonacci matrix. In this paper, we consider generalizations of Pascal matrix, Fibonacci matrix and Pell matrix. And, by using Riordan method, we have factorizations of them. We, also, consider some combinatorial identities.

• 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.