• Journal of KIISE:Databases
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• v.36 no.3
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• pp.180-188
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• 2009

Recently, the needs for an efficient and secure access control method of dynamic XML data in a ubiquitous data streams environment have become an active research area. In this paper, we proposed an improved role-based prime number labeling scheme for an efficient and secure access control labeling method in dynamic XML data streams. And we point out the limitations of existing access control and labeling schemes for XML data assuming that documents are frequently updated. The improved labeling method where labels are encoded ancestor-descendant and sibling relationships between nodes but need not to be regenerated when the document is updated. Our improved role-based prime number labeling scheme supports an infinite number of updates and guarantees the arbitrary nodes insertion at arbitrary position of the XML tree without label collisions. Also we implemented an efficient access control using a role-based prime number labeling. Finally, we have shown that our approach is an efficient and secure through experiments.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.245-258
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• 2005

In this paper we prove that the alternating groups A_n, for n = p, p+1, p+2 and symmetric groups $S_n$, for n = p, p+1, where p$\ge$3 is a prime number, can be uniquely determined by their order components. As one of the important consequence of this characterization we show that the simple groups An, where n = p, p+1, P+2 and p$\ge$3 is prime, satisfy in Thompson's conjecture and Shi's conjecture.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.143-155
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• 2008

Let p be a prime number. It is known that the order o(r) of a root r of the irreducible polynomial $x^p-x-l$ over $\mathbb{F}_p$ divides $g(p)=\frac{p^p-1}{p-1}$. Samuel Wagstaff recently conjectured that o(r) = g(p) for any prime p. The main object of the paper is to give some subsets S of {1,...,g(p)} that do not contain o(r).

• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.1109-1112
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• 2002

A non-coherent synchronous all-optical code-division multiple-access (CDMA) network is proposed. In this network, symmetric codes derived from prime sequence codes are used. We present the construction of symmetric codes and show that the pseudo-orthogonality of the new codes is the same as that of the original prime-sequence codes while the cardinality of the new codes is larger than that of the prime sequence codes and the modified prime codes in the same field GF(p). Therefore, an optical CDMA LAN using symmetric codes can have a larger number of potential subscribers. The new codes allow designing fully programmable serial all-optical transmitter and receiver suitable for low-loss, high-capacity, optical CDMA LANs. It is also shown that compared to systems using modified prime codes the proposed system can achieve better BER performance for low received chip optical power.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.149-156
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• 2019

Let G be a (p, q) graph. Let $f:V(G){\rightarrow}\{1,2,{\ldots},k\}$ be a map where $k{\in}{\mathbb{N}}$ and k > 1. For each edge uv, assign the label gcd(f(u), f(v)). f is called k-Total prime cordial labeling of G if ${\mid}t_f(i)-t_f(j){\mid}{\leq}1$, $i,j{\in}\{1,2,{\ldots},k\}$ where $t_f$(x) denotes the total number of vertices and the edges labelled with x. A graph with a k-total prime cordial labeling is called k-total prime cordial graph. In this paper we investigate the 4-total prime cordial labeling of some graphs.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2000.04a
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• pp.475-478
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• 2000

Recently encryption algorithms based on difficulties of factorization have been used with popularization. Prime number factorizations are progressed rapidly. In this paper, characteristics of elliptic curve are analyzed and generation of elliptic curves suitable for prime number factorization is discussed.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.543-549
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• 2001

We show that R[X] is a Krull (Resp. factorial) ring if and only if R is a normal Krull (resp, factorial) ring with a finite number of minimal prime ideals if and only if R is a Krull (resp. factorial) ring with a finite number of minimal prime ideals and R(sub)M is an integral domain for every maximal ideal M of R. As a corollary, we have that if R[X] is a Krull (resp. factorial) ring and if D is a Krull (resp. factorial) overring of R, then D[X] is a Krull (resp. factorial) ring.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.593-602
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• 2021

We use a kind of modified Hurwitz class numbers to express the number of representing a positive integer by some ternary quadratic forms such as the sum of three squares, and the Fourier coefficients of weight 2 modular forms of prime level with trivial character.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.815-827
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• 2019

It is well known that the denominator of the Dedekind sum s(c, d) divides 2 gcd(d, 3)d and that no smaller denominator independent of c can be expected. In contrast, here we prove that we usually get a smaller denominator in S(H, d), the sum of the s(c, d)'s over all the c's in a subgroup H of order n > 1 in the multiplicative group $(\mathbb{Z}/d\mathbb{Z})^*$. First, we prove that for p > 3 a prime, the sum 2S(H, p) is a rational integer of the same parity as (p-1)/2. We give an application of this result to upper bounds on relative class numbers of imaginary abelian number fields of prime conductor. Finally, we give a general result on the denominator of S(H, d) for non necessarily prime d's. We show that its denominator is a divisor of some explicit divisor of 2d gcd(d, 3).

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.611-619
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• 2024

For a finite group G, let 𝜓(G) denote the sum of element orders of G. If ${\psi}^{{\prime}{\prime}}(G)\,=\,{\frac{\psi(G)}{{\mid}G{\mid}^2}}$, we show here that the image of 𝜓'' on the class of all Dihedral groups whose order is twice a composite number greater than 4 is dense in $[0,\,{\frac{1}{4}}]$. We also derive some properties of 𝜓'' on the class of all dihedral groups whose order is twice a prime number.