• Kyungpook Mathematical Journal
• /
• v.54 no.4
• /
• pp.619-627
• /
• 2014

Let $\mathcal{M}(S)$ denote the set of all $m{\times}n$ matrices over a semiring S. For $A{\in}\mathcal{M}(S)$, zero-term rank of A is the minimal number of lines (rows or columns) needed to cover all zero entries in A. In [5], the authors obtained that a linear operator on $\mathcal{M}(S)$ preserves zero-term rank if and only if it preserves zero-term ranks 0 and 1. In this paper, we obtain new characterizations of linear operators on $\mathcal{M}(S)$ that preserve zero-term rank. Consequently we obtain that a linear operator on $\mathcal{M}(S)$ preserves zero-term rank if and only if it preserves two consecutive zero-term ranks k and k + 1, where $0{\leq}k{\leq}min\{m,n\}-1$ if and only if it strongly preserves zero-term rank h, where $1{\leq}h{\leq}min\{m,n\}$.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.6
• /
• pp.1851-1861
• /
• 2014

We introduce the concept of w-zero-divisor (w-ZD) rings and study its related rings. In particular it is shown that an integral domain R is an SM domain if and only if R is a w-locally Noetherian w-ZD ring and that a commutative ring R is w-Noetherian if and only if the polynomial ring in one indeterminate R[X] is a w-ZD ring. Finally we characterize universally zero divisor rings in terms of w-ZD modules.

• Kyungpook Mathematical Journal
• /
• v.51 no.1
• /
• pp.37-42
• /
• 2011

Let M be an R-module and S a semigroup. Our goal is to discuss zero-divisors of the semigroup module M[S]. Particularly we show that if M is an R-module and S a commutative, cancellative and torsion-free monoid, then the R[S]-module M[S] has few zero-divisors of size n if and only if the R-module M has few zero-divisors of size n and Property (A).

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.14 no.5
• /
• pp.472-478
• /
• 2003

In this paper, a near zero If mixer was designed in cascode structure by using two single-gate FETs. Since it is driven by the second order harmonic of LO signal, a sub-harmonic cascode FET mixer has good LO-RF port isolation characteristic. In order to solve DC offset of a homodyne system, near zero If is used instead of zero If and the mixer is driven by sub-harmonic of LO signal. As RF input power was -30 dBm and LO power was 6 dBm, the designed mixer had 6.7 dB conversion gain, 8.4 dB noise figure, 31.5 dB LO-RF port isolation, -1.9 dBm lIP3 and -2.8 dBm IIP2.

• Communications of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.197-207
• /
• 2021

The main purpose of this paper is to study the zero-divisor properties of the zero-symmetric near-ring of skew formal power series R₀[[x; α]], where R is a symmetric, α-compatible and right Noetherian ring. It is shown that if R is reduced, then the set of all zero-divisor elements of R₀[[x; α]] forms an ideal of R₀[[x; α]] if and only if Z(R) is an ideal of R. Also, if R is a non-reduced ring and annR(a - b) ∩ Nil(R) ≠ 0 for each a, b ∈ Z(R), then Z(R₀[[x; α]]) is an ideal of R₀[[x; α]]. Moreover, if R is a non-reduced right Noetherian ring and Z(R₀[[x; α]]) forms an ideal, then ann_R(a - b) ∩ Nil(R) ≠ 0 for each a, b ∈ Z(R). Also, it is proved that the only possible diameters of the zero-divisor graph of R₀[[x; α]] is 2 and 3.

• Kyungpook Mathematical Journal
• /
• v.62 no.3
• /
• pp.595-613
• /
• 2022

Let R be a commutative ring with identity and let I be a proper ideal of R. In this paper, we study the ideal based extended zero-divisor graph 𝚪'_I (R) and prove that 𝚪'_I (R) is connected with diameter at most two and if 𝚪'_I (R) contains a cycle, then girth is at most four girth at most four. Furthermore, we study affinity the connection between the ideal based extended zero-divisor graph 𝚪'_I (R) and the ideal-based zero-divisor graph 𝚪_I (R) associated with the ideal I of R. Among the other things, for a radical ideal of a ring R, we show that the ideal-based extended zero-divisor graph 𝚪'_I (R) is identical to the ideal-based zero-divisor graph 𝚪_I (R) if and only if R has exactly two minimal prime-ideals which contain I.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1629-1643
• /
• 2016

Let R be a ring with identity, X be the set of all nonzero, nonunits of R and G be the group of all units of R. A ring R is called unit-duo ring if $[x]_{\ell}=[x]_r$ for all $x{\in}X$ where $[x]_{\ell}=\{ux{\mid}u{\in}G\}$ (resp. $[x]_r=\{xu{\mid}u{\in}G\}$) which are equivalence classes on X. It is shown that for a semisimple unit-duo ring R (for example, a strongly regular ring), there exist a finite number of equivalence classes on X if and only if R is artinian. By considering the zero divisor graph (denoted ${\tilde{\Gamma}}(R)$) determined by equivalence classes of zero divisors of a unit-duo ring R, it is shown that for a unit-duo ring R such that ${\tilde{\Gamma}}(R)$ is a finite graph, R is local if and only if diam(${\tilde{\Gamma}}(R)$) = 2.

• Communications of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.163-168
• /
• 2011

In this paper we introduce the notion of the center ZBin(X) in the semigroup Bin(X) of all binary systems on a set X, and show that if (X,${\bullet}$) ${\in}$ ZBin(X), then x ${\neq}$ y implies {x,y}=${x{\bullet}y,y{\bullet}x}$. Moreover, we show that a groupoid (X,${\bullet}$) ${\in}$ ZBin(X) if and only if it is a locally-zero groupoid.

• Proceedings of the KIEE Conference
• /
• 2003.11c
• /
• pp.894-897
• /
• 2003

Recently, the rapid growth of mobile radio system has led to an increasing demand of low-cost high performance communication IC's. In this paper, we have designed RF front end for wireless LAN receiver employ zero-IF architecture. A low-noise amplifier (LNA) and double-balanced mixer is included in a front end. The zero-IF architecture is easy to integrate and good for low power consumption, so that is coincided to requirement of wireless LAN. But the zero-IF architecture has a serious problem of large offset. Image-reject mixer is a good structure to solve offset problem. Using offset compensation circuit is good structure, too. The front end is implemented in 0.25 ${\mu}m$ CMOS technology. The front end has a noise figure of 5.6 dB, a power consumption of 16 mW and total gain of 22 dB.

• Proceedings of the KIPE Conference
• /
• 2012.07a
• /
• pp.154-155
• /
• 2012

The dynamic voltage restorer (DVR) is an effective protection device for wind turbine generator based on doubly-fed induction generator (DFIG) operated under the unbalanced voltage dip conditions. The compensating voltages of DVR depend on the voltage dips and on the influence of the zero sequence components. If the $Y_0/{\Delta}$ step-up transformers are used, there are no zero sequence components on the DFIG side. However, if the $Y_0/Y_0$ step-up transformers are used, the zero sequence components will appear during faults. The zero sequence components result in the high insulation costs and the asymmetric of the terminal voltages. This paper proposes a method for controlling zero sequence components in DVR to protect DFIG under unbalanced voltage dips. Simulation results are presented to verify the effectiveness of the proposed control method.