• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.545-551
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• 2008

Necessary and sufficient conditions for a radical class of rings to satisfy the polynomial equation $\rho$(R[x]) = ($\rho$(R))[x] have been investigated. The interrelationsh of polynomial equation, Amitsur property and polynomial extensibility is given. It has been shown that complete analogy of R.E. Propes result for radicals of matrix rings is not possible for polynomial rings.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.117-124
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• 2021

We obtain a new matrix generalization result dealing with weighted mean summability of infinite series by using a new general class of power increasing sequences obtained by Sulaiman [9]. This theorem also includes some new and known results dealing with some basic summability methods.

• Journal of the Korean Society for Heat Treatment
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• v.7 no.1
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• pp.17-24
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• 1994

The evaluation and analysis of diffusivity of lithium for coarsening and coarsening kinetics of ${\delta}^{\prime}$ precipitate in Al-Li-Cu-Mg-Zr alloy aged at $170^{\circ}C$ have been investigated by transmission electron microscopy. With ageing time, ${\delta}^{\prime}$ precipitate coaesened to followed $\bar{\gamma}{\propto}t^{1/3}$ and coarsening kinetics was found to be obeyed to the Lifshitz-Slyozov-Wagner(LSW) theory and diffusivity of lithium for coarsening of ${\delta}^{\prime}$ precipitate in Al-Li-Cu-Mg-Zr alloy was obtained to be $5.85{\times}10^{-17}{\sim}1.53{\times}10^{-16}$ by experimental coarsening rate constant and various coarsening kinetic theory. Diffusivity of lithium measured by using various model but MLSW and Tsumuraya (VI) et al. model in Al-Li-Cu-Mg-Zr alloy is similar to that calculated by the Costas's diffusivity equation. It was, therefore, suggested that additing to the Cu, Mg and Zr element in Al-Li system have no great effect on diiffusivity of lithium for coarsening of ${\delta}^{\prime}$ This suggest that in matrix.

• Journal of Korea Foundry Society
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• v.36 no.5
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• pp.167-173
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• 2016

The effect of various types of heat-treatment on the mechanical properties of cast Alloy 718 has been investigated. Cast Alloy 718 bars were subjected to 'standard heat-treatment'_(SHT), 'HIP (Hot Isostatic Pressing) heat-treatment'_(HHT), and 'HIP-simulated heat-treatment'_(HS). In the absence of long time high temperature heat-treatment, a small amount of Laves phase remained in the 'SHT' specimen, and needle shaped ${\delta}$ precipitated in the vicinity of the Laves phase. Due to the formation of the Laves and ${\delta}$ phases in the 'SHT' specimen, it exhibited lower tensile properties than those of the others_specimens. On the other hand, the Laves phase was completely dissolved into the matrix after 'HHT' and 'HS' treatments. It is known that isostatic pressure reduces the self-diffusion coefficient, because of the lower self-diffusivity under HIP conditions in the interdendritic region, Nb segregation and the high amount of ${\gamma}^{{\prime}{\prime}}$ precipitation that occurs. Due to the higher fraction of coarse ${\gamma}^{{\prime}{\prime}}$ phases, the 'HHT' treated Alloy 718 showed excellent tensile strength.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.829-841
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• 2000

We classify complete intersections I of grade 3 in a regular local ring (R, M) by the number of minimal generators of a minimal prime ideal P over I. Here P is either a complete intersection or a Gorenstein ideal which is not a compete intersection.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.873-884
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• 2009

We characterize QB-ideals of exchange rings by means of quasi-invertible elements and annihilators. Further, we prove that every $2\times2$ matrix over such ideals of a regular ring admits a diagonal reduction by quasi-inverse matrices. Prime exchange QB-rings are studied as well.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.475-486
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• 2001

In this paper we give a relationship among the Minkowski units, for all odd prime number including $\infty$, of 2-periodic knot is $S^3$, its factor knot, and the 2-component link consisting of the factor knot and the set of fixed points of the periodic action.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.285-295
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• 2014

In the setting of semidenite linear complementarity problems on $S^n$, we focus on the Stein Transformation $S_A(X)\;:=X-AXA^T$, and show that $S_A$ is (strictly) monotone if and only if ${\nu}_r(UAU^T{\circ}\;UAU^T)$(<)${\leq}1$, for all orthogonal matrices U where ${\circ}$ is the Hadamard product and ${\nu}_r$ is the real numerical radius. In particular, we show that if ${\rho}(A)$ < 1 and ${\nu}_r(UAU^T{\circ}\;UAU^T){\leq}1$, then SDLCP($S_A$, Q) has a unique solution for all $Q{\in}S^n$. In an attempt to characterize the GUS-property of a nonmonotone $S_A$, we give an instance of a nonnormal $2{\times}2$ matrix A such that SDLCP($S_A$, Q) has a unique solution for Q either a diagonal or a symmetric positive or negative semidenite matrix. We show that this particular $S_A$ has the $P^{\prime}_2$-property.

• Journal of Advanced Navigation Technology
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• v.20 no.4
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• pp.367-373
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• 2016

We propose an improved direction of arrival (DoA) estimation algorithm based on co-prime array and propagator method. The propagator method with co-prime array does not require singular value decomposition (SVD) requiring much less computational complexity but exhibiting somewhat worse performance in comparison with MUSIC based on co-prime array. We notice that one cause of the performance degradation was in the avoidance of the usage of the diagonal elements of the signal autocorrelation matrix that contains the noise power spectral density. So we propose an algorithm with the diagonal elements of the signal autocorrelation matrix based on the fact that the noise power spectral density can be estimated using noise observation over a long period of time. We observe, through simulations, that the proposed scheme in this paper improves the performance, with 4 times more computational requirement, by signal-to-noise ratio of 1.5dB and by DoA resolution of $0.7^{\circ}$ at the detection probability of 95% compared with the previously introduced co-prime array propagator scheme, resulting in performance much closer to that of co-prime array-based MUSIC scheme.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.139-144
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• 2000

The generalized noncommutative torus $T_{\rho}^d$ of rank m was defined in [2]. Assume that for the completely irrational noncommutative subtorus $A_{\rho}$ of rank m of $T_{\rho}^d$ there is no integer q > 1 such that $tr(K_0(A_{\rho}))=\frac{1}{q}{\cdot}tr(K_0(A_{\rho^{\prime}}))$ for $A_{\rho^{\prime}}$ a completely irrational noncommutative torus of rank m. All $C^*$-algebras ${\Gamma}({\eta})$ of sections of locally trivial $C^*$-algebra bundles ${\eta}$ over $M=\prod_{i=1}^{e}S^{2k_i}{\times}\prod_{i=1}^{s}S^{2n_i+1}$, $\prod_{i=1}^{s}\mathbb{PR}_{2n_i}$, or $\prod_{i=1}^{s}L_{k_i}(n_i)$ with fibres $T_{\rho}^d{\otimes}M_c(\mathbb{C})$ were constructed in [6, 7, 8]. We prove that ${\Gamma}({\eta}){\otimes}M_{p^{\infty}}$ is isomorphic to $C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C}){\otimes}M_{p^{\infty}}$ if and only if the set of prime factors of cd is a subset of the set of prime factors of p, that $\mathcal{O}_{2u}{\otimes}{\Gamma}({\eta})$ is isomorphic to $\mathcal{O}_{2u}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if and only if cd and 2u - 1 are relatively prime, and that $\mathcal{O}_{\infty}{\otimes}{\Gamma}({\eta})$ is not isomorphic to $\mathcal{O}_{\infty}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if cd > 1 when no non-trivial matrix algebra can be ${\Gamma}({\eta})$.