• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.271-276
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• 2020

Let R be a commutative ring with identity, R[X] the polynomial ring over R, ∗ a radical operation on R and ⋆ a radical operation of finite character on R[X]. In this paper, we give Hilbert basis theorem for rings with ∗-Noetherian spectrum. More precisely, we show that if (I^∗R[X])^⋆ = (IR[X])^⋆ and (I^∗R[X])^⋆ ∩ R = I^∗ for all ideals I of R, then R has ∗-Noetherian spectrum if and only if R[X] has ⋆-Noetherian spectrum. This is a generalization of a well-known fact that R has Noetherian spectrum if and only if R[X] has Noetherian spectrum.

• Journal of the Korean Statistical Society
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• v.17 no.1
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• pp.30-45
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• 1988

Let ${X(t) : 0 \leq t < \infty}$ be a real-valued process with stationary independent increments. In this paper, we obtain necesary and sufficint condition for there to exist a positive, nondecreasing function $\beta(t)$ so that $0 < lim sup $\mid$X(t)$\mid$/\beta(t) < \infty$ a.s. both as t tends to zero and infinity. When no such $\beta(t)$ exists we give a simple integral test for whether $lim sup $\mid$X(t)$\mid$/\beta(t)$ is zero or infinity for a given $\beta(t)$.

• Journal of dental hygiene science
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• v.21 no.3
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• pp.178-184
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• 2021

Background: As the importance of the esthetic function of teeth increases, the use of esthetic restoration materials and whitening treatment are increasing. The purpose of this study was to investigate the color change of esthetic restoration materials upon using staining and whitening toothpaste. Methods: Light curing (LC) packable composite resin, LC flowable resin, LC glass ionomer (GI), and self-curing GI specimens were colored in coffee or curry for three hours a day for seven days. After that, regular toothpaste, whitening toothpaste containing hydrogen peroxide, and whitening toothpaste containing activated charcoal were applied for three minutes three times a day for two weeks. Luminosity (L), chromaticity a (a), and chromaticity b (b) were measured using a spectrophotometer once a week. Results: In the coffee-colored group, the change in L^2*a^2*b² (E²) with time was significant (p=0.004), there was no difference for different toothpaste types (p=0.646), and there was significant difference (p<0.001) for different esthetic restorative materials. The change of E² in the curry-colored group was significant only for different esthetic restorative materials (p<0.001). In the coffee-colored group, the L, a, and b values of the light-curing GI showed greater change than other materials after staining and one week after whitening, turning dark, red, and yellow. In the curry-colored group, L did not differ for different materials and times, and a and b showed the greatest difference in light-curing GI after staining and one and two weeks after whitening. Conclusion: The use of whitening toothpaste for two weeks was not different from the use of general toothpaste in the removal of staining or whitening. Since light-curing GI is the most vulnerable to coloration, it is recommended that coloring by food chromogen should be explained in advance, before using light-curing GI for teeth restoration.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.379-386
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• 2015

The original geometric mean of two positive definite operators A and B is given by A#B = A^1/2(A^-1/2BA^-1/2)^1/2A^1/2. In this article we provide a new proof to construct from the two-variable geometric mean to the multivariable mean via symmetrization introduced by Lawson and Lim [5]. Finally we provide an algorithm to find three-variable geometric mean via symmetrization, which plays an important role to construct higher-order geometric means.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.305-311
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• 2023

We exhibit some properties of the weighted Berezin transform T_αf on L^∞(B_n) and on L¹(B_n). As the main result, we prove that if f ∈ L^∞(B_n) with lim_k→∞ T^k_αf exists, then there exist unique M-harmonic function g and $h{\in}{\bar{(I-T_{\alpha})L^{\infty}(B_n)}}$ such that f = g + h. We also show that of the norm of weighted Berezin operator T_α on L¹(B_n, ν) converges to 1 as α tends to infinity, where ν is an ordinary Lebesgue measure.

• Bulletin of the Korean Chemical Society
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• v.33 no.8
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• pp.2785-2788
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• 2012

• Bulletin of the Korean Chemical Society
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• v.31 no.8
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• pp.2379-2382
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• 2010

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.803-813
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• 2020

Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ : M⨂_R M^∗ → Hom_R(Hom_R(M, M), R) is a surjective homomorphism. Particularly, if G-gldim(R) ⩽ ∞ and Extⁱ_R(M, M) = 0 (i ⩾ 1), then M is projective.

• Proceedings of the Korean Magnestics Society Conference
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• 2014.11a
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• pp.137-137
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• 2014

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.259-266
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• 2021

Let R be a commutative ring with identity and let S be a nonempty subset of R. We define S to be an almost multiplicative subset of R if for each a, b ∈ S, there exist integers m, n ≥ 1 such that a^mbⁿ ∈ S. In this article, we study some utilization of almost multiplicative subsets.