• Journal of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.797-808
• /
• 2018

In [1], the authors generalize the concept of the class group of an integral domain $D(Cl_t(D))$ by introducing the notion of the S-class group of an integral domain where S is a multiplicative subset of D. The S-class group of D, $S-Cl_t(D)$, is the group of fractional t-invertible t-ideals of D under the t-multiplication modulo its subgroup of S-principal t-invertible t-ideals of D. In this paper we study when $S-Cl_t(D){\simeq}S-Cl_t(D_T)$, where T is a multiplicative subset generated by prime elements of D. We show that if D is a Mori domain, T a multiplicative subset generated by prime elements of D and S a multiplicative subset of D, then the natural homomorphism $S-Cl_t(D){\rightarrow}S-Cl_t(D_T)$ is an isomorphism. In particular, we give an S-version of Nagata's Theorem [13]: Let D be a Krull domain, T a multiplicative subset generated by prime elements of D and S another multiplicative subset of D. If $D_T$ is an S-factorial domain, then D is an S-factorial domain.

• Honam Mathematical Journal
• /
• v.27 no.1
• /
• pp.115-129
• /
• 2005

In this paper, we give a digital graph-theoretical approach of the study of digital images with relation to a simplicial complex. Thus, a digital graph $G_k$ with some k-adjacency in ${\mathbb{Z}}^n$ can be recognized by the simplicial complex spanned by $G_k$. Moreover, we demonstrate that a graphically $(k_0,\;k_1)$-continuous map $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}}^{n_1}$ can be converted into the simplicial map $S(f):S(G_{k_0}){\rightarrow}S(G_{k_1})$ with relation to combinatorial topology. Finally, if $G_{k_0}$ is not $(k_0,\;3^{n_0}-1)$-homotopy equivalent to $SC^{n_0,4}_{3^{n_0}-1}$, a graphically $(k_0,\;k_1)$-continuous map (respectively a graphically $(k_0,\;k_1)$-isomorphisim) $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}^{n_1}$ induces the group homomorphism (respectively the group isomorphisim) $S(f)_*:{\pi}_1(S(G_{k_0}),\;v_0){\rightarrow}{\pi}_1(S(G_{k_1}),\;f(v_0))$ in algebraic topology.

• The KIPS Transactions:PartD
• /
• v.9D no.6
• /
• pp.991-998
• /
• 2002

With the advent of XML and database languages armed with the object-oriented concept and deductive logic, the problem of efficient query processing for them has become a major issue. We describe a way of processing semi-structured XML data through an implementation of a Deductive and Object-oriented Database (DOODB) language with the explanation of query processing. We have shown how to convert an XML data model to a DOODB data model. We have then presented an efficient query processing method based on Connection Graph Resolution. We also present a knowledge-based query processing method that uses the homomorphism of objects in the database and the associative rule of substitutions.

• Kyungpook Mathematical Journal
• /
• v.51 no.1
• /
• pp.93-108
• /
• 2011

A ring R is called left weakly np- injective if for each non-nilpotent element a of R, there exists a positive integer n such that any left R- homomorphism from $Ra^n$ to R is right multiplication by an element of R. In this paper various properties of these rings are first developed, many extending known results such as every left or right module over a left weakly np- injective ring is divisible; R is left seft-injective if and only if R is left weakly np-injective and $_RR$ is weakly injective; R is strongly regular if and only if R is abelian left pp and left weakly np- injective. We next introduce the concepts of left weakly pp rings and left weakly C2 rings. In terms of these rings, we give some characterizations of (von Neumann) regular rings such as R is regular if and only if R is n- regular, left weakly pp and left weakly C2. Finally, the relations among left C2 rings, left weakly C2 rings and left GC2 rings are given.

• The Mathematical Education
• /
• v.12 no.2
• /
• pp.5-12
• /
• 1974

단위원을 가지는 하환환에 있어서의 Prime Spectrum에 관하여 다음 세가지 사실을 증명하였다. 1. X를 환 R의 prime spectrum, C(X)를 X에서 정의되는 실연적함수의 환, X를 C(X)의 maximal spectrum이라 하면 X는 C(X)의 prime spectrum의 부분공간으로서의 한 T-space로 된다. N을 환 R의 nilradical이라 하면, R/N이 regula 이면 X와 X는 위상동형이다. 2. f: R$\longrightarrow$R'을 ring homomorphism, P를 R의 한 Prime ideal, $R_{p}$, R'$_{p}$를 각각 S=R-P 및 f(S)에 관한 분수환(ring of fraction)이라 하고, k(P)를 local ring $R_{p}$의 residue' field라 할 때, R'의 prime spectrum의 부분공간인 $f^{*-1}$(P)는 k(P)(equation omitted)$_{R}$R'의 prime spectrum과 위상동형이다. 단 f*는 f*(Q)=$f^{-1}$(Q)로서 정의되는 함수 s*:Spec(R')$\longrightarrow$Spec(R)이다. 3. X를 환 S의 prime spectrum, N을 R의 nilradical이라 할 때, 다음 네가지 사실은 동치이다. (1) R/N 은 regular 이다. (2) X는 Zarski topology에 관하여 Hausdorff 공간이다. (3) X에서의 Zarski topology와 constructible topology와는 일치한다. (4) R의 임의의 원소 f에 대하여 f를 포함하지 않는 R의 prime ideal 전체의 집합 $X_{f}$는 Zarski topology에 관하여 개집합인 동시에 폐집합이다.폐집합이다....

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.9 no.12
• /
• pp.5189-5208
• /
• 2015

To address the contradiction between data aggregation and data security in wireless sensor networks, a Recoverable Privacy-preserving Integrity-assured Data Aggregation (RPIDA) scheme is proposed based on privacy homomorphism and aggregate message authentication code. The proposed scheme provides both end-to-end privacy and data integrity for data aggregation in WSNs. In our scheme, the base station can recover each sensing data collected by all sensors even if these data have been aggregated by aggregators, thus can verify the integrity of all sensing data. Besides, with these individual sensing data, base station is able to perform any further operations on them, which means RPIDA is not limited in types of aggregation functions. The security analysis indicates that our proposal is resilient against typical security attacks; besides, it can detect and locate the malicious nodes in a certain range. The performance analysis shows that the proposed scheme has remarkable advantage over other asymmetric schemes in terms of computation and communication overhead. In order to evaluate the performance and the feasibility of our proposal, the prototype implementation is presented based on the TinyOS platform. The experiment results demonstrate that RPIDA is feasible and efficient for resource-constrained sensor nodes.

• The Journal of the Acoustical Society of Korea
• /
• v.15 no.1
• /
• pp.54-60
• /
• 1996

In most pattern recognition and image understanding applications, images are degraded by noise and other distortions. Therefore, it is more relevant to decide how similar two objects are rather than to decide whether the two are exactly the same. In this paper, we propose a method for recognizing degraded symbols using a distance measure between two graphs representing the symbols. a symbol is represented as a graph consisting of nodes and edges based on the run graph concept. The graph is then transformed into a reference model graph with production rule containing the embedding transform. The symbols are recognized by using the distance measure which is estimated by using the number of production rules used and the structural homomorphism between a transformed graph and a model graph. the proposed approach is applies to the recognition of non-note musical symbols and the result are given.

• Journal of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.643-702
• /
• 2021

Fix ℤ/2 is the prime field of two elements and write 𝒜₂ for the mod 2 Steenrod algebra. Denote by GL_d := GL(d, ℤ/2) the general linear group of rank d over ℤ/2 and by ${\mathfrak{P}}_d$ the polynomial algebra ℤ/2[x₁, x₂, …, x_d] as a connected unstable 𝒜₂-module on d generators of degree one. We study the Peterson "hit problem" of finding the minimal set of 𝒜₂-generators for ${\mathfrak{P}}_d$. Equivalently, we need to determine a basis for the ℤ/2-vector space $$Q{\mathfrak{P}}_d:={\mathbb{Z}}/2{\otimes}_{\mathcal{A}_2}\;{\mathfrak{P}}_d{\sim_=}{\mathfrak{P}}_d/{\mathcal{A}}^+_2{\mathfrak{P}}_d$$ in each degree n ≥ 1. Note that this space is a representation of GL_d over ℤ/2. The problem for d = 5 is not yet completely solved, and unknown in general. In this work, we give an explicit solution to the hit problem of five variables in the generic degree n = r(2^t - 1) + 2^ts with r = d = 5, s = 8 and t an arbitrary non-negative integer. An application of this study to the cases t = 0 and t = 1 shows that the Singer algebraic transfer of rank 5 is an isomorphism in the bidegrees (5, 5 + (13.2⁰ - 5)) and (5, 5 + (13.2¹ - 5)). Moreover, the result when t ≥ 2 was also discussed. Here, the Singer transfer of rank d is a ℤ/2-algebra homomorphism from GL_d-coinvariants of certain subspaces of $Q{\mathfrak{P}}_d$ to the cohomology groups of the Steenrod algebra, $Ext^{d,d+*}_{\mathcal{A}_2}$ (ℤ/2, ℤ/2). It is one of the useful tools for studying these mysterious Ext groups.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.11 no.3
• /
• pp.1510-1532
• /
• 2017

In smart grid, privacy implications to individuals and their families are an important issue because of the fine-grained usage data collection. Wireless communications are utilized by many utility companies to obtain information. Network coding is exploited in smart grids, to enhance network performance in terms of throughput, delay, robustness, and energy consumption. However, random linear network coding introduces a new challenge for privacy preserving due to the encoding of data and updating of coefficients in forwarder nodes. We propose a distributed privacy preserving scheme for random linear network coding in smart grid that considers the converged flows character of the smart grid and exploits a homomorphic encryption function to decrease the complexities in the forwarder node. It offers a data confidentiality privacy preserving feature, which can efficiently thwart traffic analysis. The data of the packet is encrypted and the tag of the packet is encrypted by a homomorphic encryption function. The forwarder node random linearly codes the encrypted data and directly processes the cryptotext tags based on the homomorphism feature. Extensive security analysis and performance evaluations demonstrate the validity and efficiency of the proposed scheme.

• Convergence Security Journal
• /
• v.14 no.2
• /
• pp.51-56
• /
• 2014

Be expressed in network-centric warfare, mainly battlefield environment of the future. The purpose of the system for the war of the future, is to recognize the enemy before the enemy, and rapid decision-making, to hit accurately. For this reason, it is during the construction of the integrated system of C4ISR+PGM. In such an integrated system, it is necessary to further enhance the security aspects of the information. In particular, strengthening of security leads to a decrease of efficiency. Therefore, security and efficiency should be considered together. In this study, we provide a homomorphic encryption system that can be safely managed information environment on the battlefield of the future. The proposed method uses encryption technology of homomorphic that can be the arithmetic operations on encrypted state. It has changed from the state of the encryption. Therefore, the attacker can not know a decent information.