• Korean Journal of Mathematics
• /
• 제26권4호
• /
• pp.675-681
• /
• 2018

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify three families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind and establish a new family of nonlinear ordinary differential equations in terms of the Stirling numbers of the second kind.

• 충청수학회지
• /
• 제36권2호
• /
• pp.65-76
• /
• 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.

• 대한수학회논문집
• /
• 제33권1호
• /
• pp.13-36
• /
• 2018

In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several quadratic and cubic Euler sums through zeta values and linear sums. Furthermore, some relationships between harmonic numbers and Stirling numbers of the first kind are established.

• 충청수학회지
• /
• 제26권3호
• /
• pp.591-599
• /
• 2013

A large number of sequences of polynomials and numbers have arisen in mathematics. Some of them, for example, Bernoulli polynomials and numbers, have been investigated deeply and widely. Here we aim at presenting certain interesting and (potentially) useful identities involving mainly in the second-order Eulerian numbers and Stirling polynomials, which seem to have not been given so much attention.

• Journal of Biosystems Engineering
• /
• 제32권6호
• /
• pp.389-394
• /
• 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
• /
• 제33권1호
• /
• pp.1-6
• /
• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제13권4호
• /
• pp.311-318
• /
• 2006

In this paper we establish some new identities involving Stirling numbers of both kinds. These identities are obtained via Riodan arrays with a variable x. Some well-known identities are obtained as special cases of the new identities for the specific number x.

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

• 대한수학회보
• /
• 제55권6호
• /
• pp.1909-1920
• /
• 2018

In the paper, the authors find a common solution to three series of differential equations related to the generating function of the Bernoulli numbers of the second kind and present a recurrence relation, an explicit formula in terms of the Stirling numbers of the first kind, and a determinantal expression for the Bernoulli numbers of the second kind.

• 대한기계학회논문집B
• /
• 제20권4호
• /
• pp.1426-1436
• /
• 1996

The effectiveness of the regenerator pertaining to Stirling cycle machines is studied by analyzing the heat transfer characteristics of the oscillating flow in a tube, and a new consistent definition of the regenerator effectiveness can be expressed by the ratio of the heat transfer in axial direction (Q$\_$axial/) to that in transverse direction (Q/su w/), and its approximate form is obtained as a function of Nusselt number for practical utility. Since an approximate value of the ratio Q$\_$axial//Qsub w/ can be expressed in terms of the time-averaged rather than transient temperatures, this expression is useful to estimate the heat transfer coefficient in the Stirling machine regenerator experimentally.