• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.315-326
• /
• 2021

Korobov type polynomials are introduced and extensively investigated many mathematicians ([1, 8-10, 12-14]). In this work, we define unified Apostol Korobov type polynomials and give some recurrences relations for these polynomials. Further, we consider the q-poly Korobov polynomials and the q-poly-Korobov type Changhee polynomials. We give some explicit relations and identities above mentioned functions.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.4
• /
• pp.733-747
• /
• 2021

Recently, Kim-Kim introduced Lah-Bell polynomials and numbers, and investigated some properties and identities of these polynomials and numbers. Kim studied Lah-Bell polynomials and numbers of degenerate version. In this paper, we study degenerate Lah-Bell polynomials arising from differential equations. Moreover, we investigate the phenomenon of scattering of the zeros of these polynomials.

• Journal of Applied and Pure Mathematics
• /
• v.5 no.5_6
• /
• pp.375-387
• /
• 2023

In this paper, we construct a fully modified q-poly-Euler numbers and polynomials of the second type and give some properties. Finally, we investigate the zeros of the fully modified q-poly-Euler numbers and polynomials of the second type by using computer.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.1
• /
• pp.99-111
• /
• 2024

In this paper, a new seven-parameter Mittag-Leffler function of a single complex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.

• Progress in Superconductivity and Cryogenics
• /
• v.5 no.1
• /
• pp.111-117
• /
• 2003

In the design of the split type free displacer Stilting cryocooler the motion of the displacer is very important to decide the cooling capacity, which depends upon the working gas pressure, the swept volume in the compression space and the expansion space, operating frequency, the phase shift between piston and displacer, etc. In this study, Stirling cryocooler actuated by the electric farce of the dual linear motor is designed and manufactured. Cool down characteristics of the cold end with laser displacement sensor in the expander of the Stilting cryocooler is evaluated. The charging pressure was 15kg$_{f}$/$\textrm{cm}^2$ and operating frequency was 50Hz. Input power and the lowest temperature were about 32W and 67K, respectively. And, displacement of the piston is measured by LVDTs (Linear Variable Differential Transformers), displacement of thedisplacer is measured by laser optic method, and phase shift between piston and displacer is discussed. As the peak-to-peak pressure of the compressor was increased, peak-to-peak displacement of the displacer was increased. The peak-to-peak displacement of the displacer increases in the range of 0 - 64.5Hz(resonant frequency of the displacer), but decreases steeply when the operating frequency is bigger than the resonant frequency. Finally when the phase shift between displacements of the Piston and displacer is 45。, operating frequency is optimum and is decided by resonant frequency of the expander, mass and cross section area of the displacer and constant by friction and flow resistance.e.

• Journal of Astronomy and Space Sciences
• /
• v.23 no.2
• /
• pp.153-160
• /
• 2006

A Protomodel Space Infrared Cryogenic System (PSICS) cooled by a stirling cry-ocooler has been designed. The PSICS has an IR sensor inside the cold box which is cooled by a stirling cryocooler with refrigeration capacity of 500mW at 80K in a vacuum vessel. It is important to minimize the heat load so that the background thermal noise can be reduced. In order to design the cryogenic system with low heat load and to reduce the remained heat load, we have performed numerical analyses. In this paper, we present the design factors and the results obtained by the thermal analysis of the PSICS.

• Journal of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1207-1220
• /
• 2018

The generalized hyperharmonic numbers $h^{(m)}_n(k)$ are defined by means of the multiple harmonic numbers. We show that the hyperharmonic numbers $h^{(m)}_n(k)$ satisfy certain recurrence relation which allow us to write them in terms of classical harmonic numbers. Moreover, we prove that the Euler-type sums with hyperharmonic numbers: $$S(k,m;p):=\sum\limits_{n=1}^{{\infty}}\frac{h^{(m)}_n(k)}{n^p}(p{\geq}m+1,\;k=1,2,3)$$ can be expressed as a rational linear combination of products of Riemann zeta values and harmonic numbers. This is an extension of the results of Dil [10] and $Mez{\ddot{o}}$ [19]. Some interesting new consequences and illustrative examples are considered.

• Proceedings of the Korea Institute of Applied Superconductivity and Cryogenics Conference
• /
• 2002.02a
• /
• pp.358-361
• /
• 2002

The millirneterwave high-T$_{c}$ superconducting(HTS) down-converter sub-system with the HTS/III-V integrated mixer as the central device is demonstrated first. The constituent components of HTS down-converter sub-system such as a single balanced type integrated mixer with rat-race coupler, a cavity type bandpass filter (26 GHz), and a HTS planar lowpass filter(1 GHz), semiconductor LNA and IF-power amplifier, a driving electronic module for A/D converter, and a Stirling type mini-cooler module were combined into an International stand- and rack of 19-inch. From the RF(-61 dBm, 26.5GHz)and LO signal(-1 dBm, 25.6 GHz), IF signal(0dBm, 0.9 GHz) agreed with simulated results is obtained.d.

• Journal of the Korean Society for Precision Engineering
• /
• v.19 no.11
• /
• pp.18-23
• /
• 2002

고품질의 극저온 환경의 생성 및 유지는 고품질 대용량 정보통신, 의료진단, 초전도 및 고집적반도체 제조공정 등의 차세대 유망 산업 분야에서 필수적인 요소로 자리 잡고 있으며, cryopump, 민수용 및 군수용의 적외선 검지기 및 초전도 RF 필터의 효과적 냉각을 위해 보다 높은 신뢰성과 수명, 고효율의 극저온 냉동기에 대한 수요는 점차 증대될 것으로 기대된다. 스터링 냉동기 및 맥동관 냉동기는 짧은 역사에도 불구하고, 다양한 분야에서 기존의 한제 및 극저온 냉동기를 대치하여 활용될 수 있을 것으로 전망된다.

• Communications of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.21-41
• /
• 2020

In this paper, we establish an explicit formula for r-Dowling numbers in terms of r-Whitney Lah and r-Whitney numbers of the second kind. This is a generalization of the Qi formula for Bell numbers in terms of Lah and Stirling numbers of the second kind. Moreover, we define the q, r-Dowling numbers, q, r-Whitney Lah numbers and q, r-Whitney numbers of the first kind and obtain several fundamental properties of these numbers such as orthogonality and inverse relations, recurrence relations, and generating functions. Hence, we derive an analogous Qi formula for q, r-Dowling numbers expressed in terms of q, r-Whitney Lah numbers and q, r-Whitney numbers of the second kind.