• Honam Mathematical Journal
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• v.36 no.1
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• pp.147-155
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• 2014

Let D be a square-free positive integer and let $K_D=\mathbb{Q}(\sqrt{-D})$ be the imaginary quadratic field. And let $h_D$ be the class number of the number field $K_D$. In this paper, we show the following: If D=l or 4l, where l is a prime number with $l{\equiv}3$ (mod 4), then $h_D$ is odd.

• Journal of Energy Engineering
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• v.11 no.3
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• pp.262-268
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• 2002

The present paper investigated the effect of ultrasonic vibrations on the melting process of phase-change materials (PCM). Furthermore, the present study considered constant heat-flux boundary condition, whereas many of the previous researches had adopted constant wall-temperature condition. The results of the present study revealed that ultrasonic vibrations accompanied the effects like acoustic streaming, cavitation, and thermally-oscillating flow. Such effects are a prime mechanism in the overall melting process when ultrasonic vibrations are applied. They speed up the melting process as much as 2.5 times, compared with the result of natural melting. Also, energy can be saved by applying ultrasonic vibrations to the natural melting. In addition, temperature and Nusselt numbers over time provided a conclusive evidence of the important role of ultrasonic vibrations on the melting phenomena.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.39-44
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• 1996

Throughout this paper $Z^p, Q_p$ and C_p$ will denote the ring of p-adic rational integers, the field of p-adic rational numbers and the completion of the algebraic closure of $Q_p$, respectively. Let $v_p$ be the normalized exponential valuation of $C_p$ with $$\mid$p$\mid$_p = p^{-v_p (p)} = p^{-1}$. We set $p^* = p$ for any prime p > 2 $p^* = 4 for p = 2$.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.111-131
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• 2006

The goal of this paper is to define p-adic Hardy sums and p-adic q-higher-order Hardy-type sums. By using these sums and p-adic q-higher-order Dedekind sums, we construct p-adic continuous functions for an odd prime. These functions contain padic q-analogue of higher-order Hardy-type sums. By using an invariant p-adic q-integral on $\mathbb{Z}_p$, we give fundamental properties of these sums. We also establish relations between p-adic Hardy sums, Bernoulli functions, trigonometric functions and Lambert series.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.251-263
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• 2004

In this paper, algorithms for computing the minimal polynomial and the common minimal polynomial of resultant matrices over any field are presented by means of the approach for the Grobner basis of the ideal in the polynomial ring, respectively, and two algorithms for finding the inverses of such matrices are also presented. Finally, an algorithm for the inverse of partitioned matrix with resultant blocks over any field is given, which can be realized by CoCoA 4.0, an algebraic system over the field of rational numbers or the field of residue classes of modulo prime number. We get examples showing the effectiveness of the algorithms.

• Journal for History of Mathematics
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• v.27 no.2
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• pp.111-125
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• 2014

Jisuguimundo is an inimitable magic hexagon devised by Choi Seok-Jeong, who was the author of GuSuRyak as well as a prime minister in Joseon dynasty. Jisuguimundo, recorded in GuSuRyak, is also known as Hexagonal Tortoise Problem (HTP) because its nine hexagons resemble a tortoise shell. We call the sum of numbers in a hexagon in Jisuguimundo a magic sum, and show that the magic sum of hexagonal tortoise problem of order 2 varies 40 through 62 exactly and that of hexagonal tortoise problem of order 3 varies 77 through 109 exactly. We also find all of the possible solutions for hexagonal tortoise problem of oder 2.

• ETRI Journal
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• v.35 no.2
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• pp.234-244
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• 2013

Internet protocol television (IPTV) service depends on the network quality of service (QoS) and bandwidth of the broadband service provider. IEEE 802.16j mobile multihop relay Worldwide Interoperability for Microwave Access networks have the opportunity to offer high bandwidth capacity by introducing relay stations. However, to actually satisfy QoS requirements for offering IPTV services (HDTV, SDTV, Web TV, and mobile TV) for heterogeneous users' requests, providers must use a video server for each IPTV service type, which increases the network load, especially bandwidth consumption and forwarding time. In this paper, we present a solution for forwarding IPTV video streaming to diverse subscribers via an 802.16j broadband wireless access network. In particular, we propose a new multicast tree construction and aggregation mechanism based on the unique property of prime numbers. Performance evaluation results show that the proposed scheme reduces both bandwidth consumption and forwarding time.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.819-829
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• 2016

In this paper, we study the order of growth of solutions to the non-homogeneous linear differential equation $$f^{(k)}+A_{k-1}e^{az}f^{(k-1)}+{\cdots}+A_1e^{az}f^{\prime}+A_0e^{az}f=F_1e^{az}+F_2e^{bz}$$, where $A_j(z)$ (${\not\equiv}0$) ($j=0,1,{\cdots},k-1$), $F_j(z)$ (${\not\equiv}0$) (j = 1, 2) are entire functions and a, b are complex numbers such that $ab(a-b){\neq}0$.

• Journal of the Korean Institute of Telematics and Electronics
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• v.12 no.5
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• pp.6-11
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• 1975

반복형 그래이 부호 중 14진 및 16진 부호용 디지트 절차(digit sequence 또는 DS)의 여러가지 특성에 관하여 논하였으며 그것들을 통일적으로 기적할 수 있는 PDS는 각각 31종 및 11종이 있다는 것을 명백히 하였다. 그리고 이 PDS들에 회전변환과 순렬변환을 실시하여 얻을 수 있는 DS의 총수와 각종 특수 DS의 성질에 관하여도 논하였으며 대칭형 DS를 이용한 14진 및 16진 GC Counter를 설계하여 그것들의 동작을 실험에 의하여 확인하였다. Investigations on some characteristics of Tetra-Decimal and Hexa-Decimal recycling Gray co de (GC)-digit sequence(DS) are carried out, and, 31 and 11 kinds of prime digit sequence(PDS) are proposed respectively. From these PDS, by means of rotational conversion and permutational conversion, the numbers of all DS are obtained, and also the characteristics of some special DS are studied. Tetra Decimal and Hexa-decimal GC counters are designed using symmetrical DS, and, their operations are experimentally verified.

• Journal of Korea Multimedia Society
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• v.25 no.5
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• pp.670-675
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• 2022

This study proposes an improved binarization method to improve image recognition rate. The research goal is to minimize the information loss that occurs during the binarization process, and to transform the object of the original image that cannot be determined through the transformation process into an image that can be judged. The proposed method uses a stepwise segmentation method of an image and divides blocks using prime numbers. Also, within one block, a trapezoidal type of fuzzy is applied. The fuzzy trapezoid is binarized by dividing the brightness histogram area into three parts according to the degree of membership. As a result of the experiment, information loss was minimized in general images. In addition, it was found that the converted binarized image expressed the object better than the original image in the special image in which the brightness region was tilted to one side.