• 대한수학회보
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• 제59권2호
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• pp.481-506
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• 2022

This paper is concerned with the study of various notions of shadowing of dynamical systems induced by a sequence of maps, so-called time varying maps, on a metric space. We define and study the shadowing, h-shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties of these dynamical systems. We show that h-shadowing, limit shadowing and s-limit shadowing properties are conjugacy invariant. Also, we investigate the relationships between these notions of shadowing for time varying maps and examine the role that expansivity plays in shadowing properties of such dynamical systems. Specially, we prove some results linking s-limit shadowing property to limit shadowing property, and h-shadowing property to s-limit shadowing and limit shadowing properties. Moreover, under the assumption of expansivity, we show that the shadowing property implies the h-shadowing, s-limit shadowing and limit shadowing properties. Finally, it is proved that the uniformly contracting and uniformly expanding time varying maps exhibit the shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties.

• 대한수학회논문집
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• 제39권2호
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• pp.313-329
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• 2024

An (additive) commutative monoid is called atomic if every given non-invertible element can be written as a sum of atoms (i.e., irreducible elements), in which case, such a sum is called a factorization of the given element. The number of atoms (counting repetitions) in the corresponding sum is called the length of the factorization. Following Geroldinger and Zhong, we say that an atomic monoid M is a length-finite factorization monoid if each b ∈ M has only finitely many factorizations of any prescribed length. An additive submonoid of ℝ_≥0 is called a positive monoid. Factorizations in positive monoids have been actively studied in recent years. The main purpose of this paper is to give a better understanding of the non-unique factorization phenomenon in positive monoids through the lens of the length-finite factorization property. To do so, we identify a large class of positive monoids which satisfy the length-finite factorization property. Then we compare the length-finite factorization property to the bounded and the finite factorization properties, which are two properties that have been systematically investigated for more than thirty years.

• 한국세라믹학회지
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• 제55권2호
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• pp.135-139
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• 2018

The glass structure and antibacterial properties of $(65-x)ZnO-xB_2O_3-35P_2O_5$ glasses were investigated. Zinc borophosphate glasses were prepared using a conventional melt-quenching technique at $1000^{\circ}C$. Glass transition temperature and CTE were studied and the structure of zinc borophosphate glasses was evaluated by FTIR. The $Zn^{2+}$ state increase with increasing ZnO content was investigated by XPS and a single sharp Zn $2P_{3/2}$ peak was confirmed, showing that Zn $2P_{3/2}$ exists as $Zn^{2+}$. In order to to evaluate the antimicrobial activity, Escherichia coli (E. coli) was used following the Japanese Industrial Standard JIS Z 2801; the E. coli death rate was found to increase with increasing $Zn^{2+}$ content of glasses.

• 한국세라믹학회지
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• 제39권5호
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• pp.490-497
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• 2002

$CaO-SiO_2-B_2O_3$계의 결정화유리의 소결 특성 및 기계적 특성, 생체활성을 알아보았다. 이 조성의 결정화유리는 750-830${\circ}$ 사이에서 소결 되었으며 치밀한 미세구조를 보였다. 이 결정화 유리는 단사정계 월라스토나이트(monoclinic wollastonite), 칼슘보레이트(Calcium borate, $CaB_2O_4$) 결정상과 보로실리케이트(borosilicate) 유리 기지상(matrix)의 3상으로 구성되었다. 기계적 강도는 지금까지 알려진 다른 생체활성 세라믹스보다 우수하였으며 특히 압축강도(2813 MPa), 파괴인성($3.12 MPa{\cdot}m^{1/2}$)이 높았다. 생체활성은 결정화유리 중 calcium borate와 보로실리케이트 유리의 양에 의존하였는데, 용해도가 높은 calcium borate는 의사체액(SBF)의 칼슘이온의 과포화도를 상승시키고 borosilicate 유리는 탄산아파타이트 핵생성에 필요한Si-OH기를 형성시켜 탄산아파타이트 층이 빨리 생성되기 때문으로 판단된다. 따라서 $CaB_2O_4$와 borosilicate 유리가 많을수록 결정화유리의 생체활성이 뛰어난 것으로 생각된다.

• 대한수학회보
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• 제54권2호
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• pp.559-571
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• 2017

We investigate modules M having the injective property relative to nonsingular modules. Such modules are called "$\mathcal{N}$-injective modules". It is shown that M is an $\mathcal{N}$-injective R-module if and only if the annihilator of $Z_2(R_R)$ in M is equal to the annihilator of $Z_2(R_R)$ in E(M). Every $\mathcal{N}$-injective R-module is injective precisely when R is a right nonsingular ring. We prove that the endomorphism ring of an $\mathcal{N}$-injective module has a von Neumann regular factor ring. Every (finitely generated, cyclic, free) R-module is $\mathcal{N}$-injective, if and only if $R^{(\mathbb{N})}$ is $\mathcal{N}$-injective, if and only if R is right t-semisimple. The $\mathcal{N}$-injective property is characterized for right extending rings, semilocal rings and rings of finite reduced rank. Using the $\mathcal{N}$-injective property, we determine the rings whose all nonsingular cyclic modules are injective.

• Korean Journal of Mathematics
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• 제14권2호
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• pp.169-183
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• 2006

In this paper, we define and study the C-integral and the strong C-integral of functions mapping an interval [a,b] into a Banach space X. We prove that the C-integral and the strong C-integral are equivalent if and only if the Banach space is finite dimensional, We also consider the property of primitives corresponding to Banach-valued functions with respect to the C-integral and the strong C-integral.

• 대한수학회보
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• 제58권3호
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• pp.573-591
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• 2021

We study the equivariant Gromov-Witten theory of ℙ^r-1 for all r ≥ 2. We prove a polynomiality property in r of the Gromov-Witten classes of ℙ^r-1. Using this polynomiality property, we define a set of polynomial valued classes in $H^*({\bar{M}}_{g,n})$ which generalize the limit of Witten's s-spin classes studied by Pandharipande, Pixton and Zvonkine.

• 대한수학회보
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• 제59권2호
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• pp.419-429
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• 2022

An integral domain R is an RTP domain (or has the radical trace property) (resp. an LTP domain) if I(R : I) is a radical ideal for each nonzero noninvertible ideal I (resp. I(R : I)R_P = PR_P for each minimal prime P of I(R : I)). Clearly each RTP domain is an LTP domain, but whether the two are equivalent is open except in certain special cases. In this paper, we study the descent of these notions from particular overrings of R to R itself.

• 전자공학회논문지CI
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• 제42권6호
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• pp.101-108
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• 2005

본 논문에서는 UWB 멀티미디어 통신 시스템을 위한 새로운 펄스 생성과 검출 알고리즘을 제안한다. 현재 가우시안 펄스를 사용하고 있는 UWB 시스템은 주파수 대역의 한계와 주파수 시프트 등의 문제점을 가지고 있으며, 이러한 문제점을 해결하기 위하여 본 논문에서는 중심 주파수와 주파수대역을 제어할 수 있는 변조 방법을 적용하여 전송 신호의 검출 성능을 향상 시켰다. 그리고, 웨이블렛 합성 필터를 사용하여 여러개의 전송 채널을 합성시켜 1개의 전송 채널로 전송 시킬 수 있는 알고리즘을 제안하였다. 웨이블렛 필터의 perfect reconstruction 특성 때문에 접속자의 수에 따라 비트에러율(BER)이 변화하지 않고 채널의 전송 특성에 따라 전송 데이터의 BER 특성이 변화한다. 본 논문에서 AWGN 채널 상에서 2dB부터 8dB까지 2dB씩 변화시켜 가며 실험한 결과, AWGN 채널의 SNR이 4dB일 때 BER는 $3.9063{\times}10-4$ 을 가짐을 확인할 수 있었다.

• JSTS:Journal of Semiconductor Technology and Science
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• 제11권4호
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• pp.336-343
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• 2011

This paper introduces a simple variable gain amplifier (VGA) structure that shows an inherently dB-linear gain control property. Requiring no additional components for dB-linear control, the structure is compact and power efficient. The designed two-stage VGA shows a gain control range of 60dB with the gain error in the range of ${\pm}0.4$ dB. The power consumption including the output buffer is 20.4 mW from 1.2 V supply voltage with bandwidth of 630 MHz. The prototype was fabricated in a 0.13 ${\mu}m$ CMOS process and the VGA core occupies 0.06 $mm^2$.