• 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.

• Progress in Superconductivity
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• v.1 no.1
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• pp.9-13
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• 1999

The influence of quenching temperature and annealing time on superconducting characteristics has been investigated for a $(Pb_{0.6}V_{0.4})Sr_2(Ca_{0.65}Er_{0.35})Cu_2O_z$ compound. From the resistivity measurements for samples annealed at $400^{\circ}C$ to $860^{\circ}C$ in oxygen and subsequently quenched, it is observed that $T_c$(zero) of the sample decreases with the increase of annealing temperature up to $600^{\circ}C$ and increases again beyond $700^{\circ}C$. Annealings of the sample at $860^{\circ}C$ show that $T_c$(zero) goes through a maximum of 62K with the increase of the annealing time. It is also found that $T_c$(zero) of the sample quenched from high temperature decreases when the sample is subjected to low temperature annealing below. $600^{\circ}C$ in oxygen. The experimental results indicate that the as-prepared samples contain excessive oxygen and removal of this excessive oxygen in as-prepared samples is a key factor in controlling the superconducting properties of the samples and are discussed in connection with thermal gravimetric measurements.

• Korean Journal of Optics and Photonics
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• v.4 no.3
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• pp.252-259
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• 1993

A holosymmetric four-mirror system with unit magnification is designed for use in the micro-lithography using a deep ultraviolet wavelength of $0.248 {\mu}m$(KrF excimer laser line). In the holosymmetric system all orders of coma and distortion are zero. By applying this principle to the 4-spherical mirror system, we have obtained only one exact solution for the unit magnification holosymmetric four-spherical mirror system with all zero third order aberrations. For correction of the residual higher order aberrations of the system, aspherization is introduced keeping the holosymmetric properties. We have obtained near diffraction-limited performance for the wavelength of 0.248 pm within N.A. of 0.33 and image field diameter of 7.6 mm.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.11A
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• pp.1244-1252
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• 2004

In this paper, we derive some properties of linear detectors (zero forcing or minimum mean square error) at spatial multiplexing systems with alamouti's space-time block code. Based on the derived properies, this paper proposes low-complexity receivers. Implementing MMSE detector adaptively, the number of weight vectors to be calculated and updated is greatly reduced with the derived properties compared to the conventional methods. In the case of recursive least square algorithm, with the proposed approach computational complexity is reduced to less than the half. We also identify that sorted QR decomposition detector, which reduces the complexity of V-Blast detector, has the same properties for unitary matrix Q and upper triangular matrix R. A complexity reduction of about 50%, for sorted QR decomposition detector, can be achieved by using those properties without the loss of performance.

• The KIPS Transactions:PartC
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• v.9C no.3
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• pp.307-312
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• 2002

Among the various zero suppression (ZS) algorithms used in a for synchronous stream cipher system, a ZS-2 exhibits certain good properties, including the omission of the block synchronization, easy implementation, etc., yet also a weakness in channel error propagation. Accordingly, This paper proposes a new method by minimizing the bit-wide substitution in the substitution blocks of ZS-2 to improve the degenerated error property in a noisy channel. As a result, the proposed ZS-3 algorithm can decrease the mean error propagation by about 18.7% over that of ZS-2 at n=8.

• Current Optics and Photonics
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• v.2 no.6
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• pp.525-531
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• 2018

The effect of eccentricity on dispersion and nonlinear properties of a photonic crystal fiber having elliptical air holes is investigated using a fully vectorial effective index method. It is found that the effective refractive index increases with increase of eccentricity. The dependence of dispersion and nonlinear properties of the PCF on the eccentricity of the air hole is investigated. It is revealed that eccentricity of the air hole affects the zero dispersion wavelength. Further, the nonlinear properties such as mode field area, nonlinear coefficient and self phase modulation of the Photonic crystal fibers are analyzed. The mode field area increases and the nonlinear coefficient decreases with increase in eccentricity. The variation of the self phase modulation with elliptical air hole is also discussed.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.301-309
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• 2011

Let R = $Mat_2(F)$ be the ring of all 2 by 2 matrices over a finite field F, X the set of all nonzero, nonunits of R and G the group of all units of R. After investigating some properties of orbits under the left (and right) regular action on X by G, we show that the graph automorphisms group of $\Gamma(R)$ (the zero-divisor graph of R) is isomorphic to the symmetric group $S_{|F|+1}$ of degree |F|+1.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1017-1031
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• 2016

Let R be a commutative ring with the non-zero identity and n be a natural number. ${\Gamma}^n_R$ is a simple graph with $R^n{\setminus}\{0\}$ as the vertex set and two distinct vertices X and Y in $R^n$ are adjacent if and only if there exists an $n{\times}n$ lower triangular matrix A over R whose entries on the main diagonal are non-zero such that $AX^t=Y^t$ or $AY^t=X^t$, where, for a matrix B, $B^t$ is the matrix transpose of B. ${\Gamma}^n_R$ is a generalization of Cayley graph. Let $T_n(R)$ denote the $n{\times}n$ upper triangular matrix ring over R. In this paper, for an arbitrary ring R, we investigate the properties of the graph ${\Gamma}^n_{T_n(R)}$.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.723-729
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• 2020

Let ℤ_n be the ring of integers modulo n and let ℤ_n[X]] be either ℤ_n[X] or ℤ_n[[X]]. Let 𝚪(Z_n[X]]) be the zero-divisor graph of ℤ_n[X]]. In this paper, we study some properties of 𝚪(ℤ_n[X]]). More precisely, we completely characterize the diameter and the girth of 𝚪(ℤ_n[X]]). We also calculate the chromatic number of 𝚪(ℤ_n[X]]).

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.89-93
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• 1985

One of the most important problems in automatic continuity theory is to solve the question of continuity of an algebra homomorphism from a Banach algebra into a semisimple Banach algebra with dense range. Many results on this subject are obtained imposing some conditions on the domains or the ranges of homomorphisms. For most recent results and references in automatic continuity theory one may refer to [1], [4] and [5]. In this note we study some properties of homomorphisms from $C^{*}$-algebras into Banach algebras. It is shown that the range of an isomorphism from a $C^{*}$-algebra into a Banach algebra contains no non zero element of the radical of B. Using this result we show that the same holds for a continuous homomorphism, hence a Banach algebra which is the image of a $C^{*}$-algebra under a continuous homomorphism is necessarily semisimple. Thus if there is a homomorphism from a $C^{*}$-algebra onto a non-semisimple Banach algebra it must be discontinuous. Also it follows that every non zero homomorphism from a $C^{*}$-algebra into a radical algebra is discontinuous. Then we make a brief observation on the behavior of quasinilpotent element of noncommutative $C^{*}$-algebras in relation with continuous homomorphisms.momorphisms.