• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.467-485
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• 2005

Let p and q be odd primes with p=2q+1. We study the number of solutions of congruence equations $ax^i\;+\;by^j\;{\equiv}\;c$ (mod p) and a$ax^i\;+\;by^j\;+\;dz^t\;{\equiv}\;c(modp)$

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.729-743
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• 2019

In this paper, we introduce strongly quasi primary ideals which is an intermediate class of primary ideals and quasi primary ideals. Let R be a commutative ring with nonzero identity and Q a proper ideal of R. Then Q is called strongly quasi primary if $ab{\in}Q$ for $a,b{\in}R$ implies either $a^2{\in}Q$ or $b^n{\in}Q$ ($a^n{\in}Q$ or $b^2{\in}Q$) for some $n{\in}{\mathbb{N}}$. We give many properties of strongly quasi primary ideals and investigate the relations between strongly quasi primary ideals and other classical ideals such as primary, 2-prime and quasi primary ideals. Among other results, we give a characterization of divided rings in terms of strongly quasi primary ideals. Also, we construct a subgraph of ideal based zero divisor graph ${\Gamma}_I(R)$ and denote it by ${\Gamma}^*_I(R)$, where I is an ideal of R. We investigate the relations between ${\Gamma}^*_I(R)$ and ${\Gamma}_I(R)$. Further, we use strongly quasi primary ideals and ${\Gamma}^*_I(R)$ to characterize von Neumann regular rings.

• East Asian mathematical journal
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• v.31 no.1
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• pp.1-18
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• 2015

In this paper we characterize different classes of hemirings by the properties of their (${\in},{\in}{\vee}q$)-fuzzy ideals, (${\in},{\in}{\vee}q$)-fuzzy quasi-ideals and (${\in},{\in}{\vee}q$)-fuzzy bi-ideals.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.365-372
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• 2010

In this paper, we show that the mapping ${\varphi}(x)\;=\;0*x$ is an endomorphism of a Q-algebra X, which induces a congruence relation "~" such that X/$\varphi$ is a medial Q-algebra. We also study some decompositions of ideals in Q-algebras and obtain equivalent conditions for closed ideals. Moreover, we show that if I is an ideal of a Q-algebra X, then $I^g$ is an ignorable ideal of X.

• 한국지구물리탐사학회:학술대회논문집
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• 2008.10a
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• pp.97-100
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• 2008

Mount Fuji is the focus of intense study because of its potential hazard signaled by seismic, geologic and historical activity. Based on extensive seismic data recorded in the vicinity of Mt. Fuji, coda quality factor ($Q_c^{-1}$) using a single scattering model hypothesis, and intrinsic and scattering quality factor $(Q_i^{-1}$ and $Q_s^{-1})$ using the Multiple Lapse Time Window Analysis (MLTW) method was measured. To focus the study on the magmatic structure below Mt. Fuji, to the data were separated into two groups: a near-Fuji region of rays traversing an area with radius 5 km around the summit (R < 5 km), and a far-Fuji region of rays beyond a radius of 20 km around the summit (R > 20 km). The results of the study have a small error range due to the large data sample, showing that all $Q^{-1}$ values in near-Fuji area are greater than those of far-Fuji area, and $Q_i^{-1}$ for both the near and far-Fuji area is higher than $Q_s^{-1}$ at high frequencies. The $Q_i^{-1}$ values of the near-Fuji area are lower than those of the other volcanic areas considered, while values of $Q_s^{-1}$ are not. The low $Q_i^{-1}$ for the volcanic region of near-Fuji suggests that the magmatic activity, or percent of partial melt, at Mt. Fuji is not as active as hot spot volcanoes such as Kilauea, Hawaii.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.41 no.6 s.324
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• pp.1-7
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• 2004

The development of direct receiver techniques is expected to be a solution for future wideband or multi-band wireless systems based on software defined radio. In this Paper, we study the regeneration of I and Q signals for the SDR based direct conversion receiver, so that we can handle a wide bandwidth and maintain maximal flexibility in system utilization. After modeling the basic system considering the real wireless communication environment, and studying the impact of imperfect phase imbalance on the performance of a direct conversion receiver, we propose a suboptimal I and Q signal regeneration algorithm for the system. The proposed algerian regenerates I and Q signals using a real time early-late compensator which effectively estimates phase imbalances and gives feedback in a directreceiver. The proposed algorithm is shown to mitigate the impact of AWGN and improves performance especially at low SNR channel condition. According to the computer simulation, the BER performance of the proposed system is at least about 4 dB better than conventional systems under $45{\~}55$ degrees random phase errors.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.375-384
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• 2008

Let $k={\mathbb{F}}_q(T)$ and ${\mathbb{A}}={\mathbb{F}}_q[T]$. Fix a prime divisor ${\ell}$ q-1. In this paper, we consider a ${\ell}$-cyclic real function field $k(\sqrt[{\ell}]P)$ as a subfield of the imaginary bicyclic function field K = $k(\sqrt[{\ell}]P,\;(\sqrt[{\ell}]{-Q})$, which is a composite field of $k(\sqrt[{\ell}]P)$ wit a ${\ell}$-cyclic totally imaginary function field $k(\sqrt[{\ell}]{-Q})$ of class number one. und give various conditions for the class number of $k(\sqrt[{\ell}]{P})$ to be one by using invariants of the relatively cyclic unramified extensions $K/F_i$ over ${\ell}$-cyclic totally imaginary function field $F_i=k(\sqrt[{\ell}]{-P^iQ})$ for $1{\leq}i{\leq}{\ell}-1$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1513-1521
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• 2013

In this paper we will study cyclic codes over some special rings: $\mathbb{F}_q[u]/(u^i)$, $\mathbb{F}_q[u_1,{\ldots},u_i]/(u^2_1,u^2_2,{\ldots},u^2_i,u_1u_2-u_2u_1,{\ldots},u_ku_j-u_ju_k,{\ldots})$, and $\mathbb{F}_q[u,v]/(u^i,v^j,uv-vu)$, where $\mathbb{F}_q$ is a field with $q$ elements $q=p^r$ for some prime number $p$ and $r{\in}\mathbb{N}-\{0\}$.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.147-156
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• 2020

The functional equation related to a distance measure f(pr, qs) + f(ps, qr) = M(r, s)f(p, q) + M(p, q)f(r, s) can be generalized a sum form functional equation as follows $${\frac{1}{n}}{\sum\limits_{i=0}^{n-1}}f(P{\cdot}{\sigma}_i(Q))=M(Q)f(P)+M(P)f(Q)$$ where f, g is information measures, P and Q are the set of n-array discrete measure, and σ_i is a permutation for each i = 0, 1, ⋯, n-1. In this paper, we obtain the hyperstability of the above type functional equation.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2001-2011
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• 2013

Cho and Kim [4] have introduced the concept of the competition index of a digraph. Similarly, the competition index of an $n{\times}n$ Boolean matrix A is the smallest positive integer q such that $A^{q+i}(A^T)^{q+i}=A^{q+r+i}(A^T)^{q+r+i}$ for some positive integer r and every nonnegative integer i, where $A^T$ denotes the transpose of A. In this paper, we study the upper bound of the competition index of a Boolean matrix. Using the concept of Boolean rank, we determine the upper bound of the competition index of a nearly reducible Boolean matrix.