• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.677-685
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• 2023

For n ≥ 2 and a real Banach space E, 𝓛(ⁿE : E) denotes the space of all continuous n-linear mappings from E to itself. Let Π (E) = {[x^*, (x₁, . . . , x_n)] : x^*(x_j) = ||x^*|| = ||x_j|| = 1 for j = 1, . . . , n }. An element [x^*, (x₁, . . . , x_n)] ∈ Π(E) is called a numerical radius point of T ∈ 𝓛(ⁿE : E) if |x^*(T(x₁, . . . , x_n))| = v(T), where the numerical radius v(T) = sup_{[y^*,y1,...,yn]∈Π(E)}|y^*(T(y₁, . . . , y_n))|. For T ∈ 𝓛(ⁿE : E), we define Nradius(T) = {[x^*, (x₁, . . . , x_n)] ∈ Π(E) : [x^*, (x₁, . . . , x_n)] is a numerical radius point of T}. T is called a numerical radius peak n-linear mapping if there is a unique [x^*, (x₁, . . . , x_n)] ∈ Π(E) such that Nradius(T) = {±[x^*, (x₁, . . . , x_n)]}. In this paper we present explicit formulae for the numerical radius of T for every T ∈ 𝓛(ⁿE : E) for E = c₀ or l_∞. Using these formulae we show that there are no numerical radius peak mappings of 𝓛(ⁿc₀ : c₀).

• Journal of The Geomorphological Association of Korea
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• v.26 no.4
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• pp.81-96
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• 2019

The Yeongdeok 53m marine terrace (Y₅₃mT), Y₄₃mT, Y₃₃mT, Y₂₄mT, Y₁₉mT and Y₁₁mT distributed along the Yeongdeok coast, southeastern Korean Peninsula are well compared with the thalassostatic terraces of the high terrace 1 (ℓHT₁ ; 51m of the relative heights from the river floor), high terrace 2 (ℓHT₂ ; 43m), middle terrace 1 (ℓMT₁ ; 32m), middle terrace 2 (ℓMT₂ ; 25m), lower terrace 1 (ℓLT₁ ; 18m) and lower terrace 2 (ℓLT₂ ; 10m) respectively, developed along the lower reaches of the Chucksan-cheon and Obo-cheon rivers, judging from the comparison of paleosols (red soils) between the above marine and thalassostatic terraces. Using the Y₁₉mT of the MIS 5e as the key surface, we propose that the terraces of the Y₅₃mT and ℓHT₁, Y₄₃mT and ℓHT₂, T₃₃mT and ℓMT₁, Y₂₄mT and ℓMT₂, Y₁₉mT and ℓLT₁, and Y₁₁mT and ℓLT₂ have been formed at the MIS 11, 9, 7e and 7a (or 7a), 5e and 5a respectively. The red soils have been developed at the Y₁₉mT and ℓLT₁ and above them, but not on the Y₁₁mT and ℓLT₂ surfaces.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.795-814
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• 2021

In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: fⁿ + P(f) = R(z)e^α(z) and fⁿ + P_*(f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z) in the complex plane, where P(f) and P_*(f) are differential polynomials in f of degree n - 1 with coefficients being small functions and rational functions respectively, R is a non-vanishing small function of f, α is a nonconstant entire function, p₁, p₂ are non-vanishing rational functions, and α₁, α₂ are nonconstant polynomials. Particularly, we consider the solutions of the second equation when p₁, p₂ are nonzero constants, and deg α₁ = deg α₂ = 1. Our results are improvements and complements of Liao ([9]), and Rong-Xu ([11]), etc., which partially answer a question proposed by Li ([7]).

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1069-1078
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• 2021

Let R be a commutative ring with identity. A proper ideal I of R is called 1-absorbing primary ([4]) if for all nonunit a, b, c ∈ R such that abc ∈ I, then either ab ∈ I or c ∈ ${\sqrt{1}}$. The concept of 1-absorbing primary ideals in a polynomial ring, in a PID and in idealization of a module is studied. Moreover, we introduce weakly 1-absorbing primary ideals which are generalization of weakly prime ideals and 1-absorbing primary ideals. A proper ideal I of R is called weakly 1-absorbing primary if for all nonunit a, b, c ∈ R such that 0 ≠ abc ∈ I, then either ab ∈ I or c ∈ ${\sqrt{1}}$. Some properties of weakly 1-absorbing primary ideals are investigated. For instance, weakly 1-absorbing primary ideals in decomposable rings are characterized. Among other things, it is proved that if I is a weakly 1-absorbing primary ideal of a ring R and 0 ≠ I₁I₂I₃ ⊆ I for some ideals I₁, I₂, I₃ of R such that I is free triple-zero with respect to I₁I₂I₃, then I₁I₂ ⊆ I or I₃ ⊆ I.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.32-47
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• 1995

The coefficient of determination R/sup 2/, as the proprtation of by explained by a set of independent variavles x/sub 1/, x/sub 2, .cdots., x/sub k/ through a linear regression model, is a very useful tool in linear regression analysis. Suppose R/sup 2//sub yx/ is the coefficient of determination when y is regressed only on x/sub i/ alone. If the independent variables are correlaated, the sum, R/sup 2//sub {yx/sub 1/}/ +R/sup 2//sub {yx/sub 2/}/+.cdots.R/sup 2//sub {yx/sub k/}/, is not equal to R/sup 2/sub {yx/sub 1/x/sub 2/.cots.x/sub k/}/, where R/sup 2//sub {yx/sub 1/x/sub 2/.cdots.x/sub k/}/ is the coefficient of determination when y is regressed simultaneously on x/sub 1/, x/sub 2/,.cdots., x/sub k/. In this paper it is discussed that under what conditions the sum is greater than, equal to, or less than R/sup 2//sub {yx/sub 1/x/sub 2/.cdots.x/sub k/}/, and then the proofs for these conditions are given. Also illustrated examples are provided. In addition, we will discuss about inequality between R/sup 2//sub {yx/sub 1/x/sub 2/.cdots.x/sub k/}/ and the sum, R/sup 2//sub {yx/sub 1/}/+R/sup 2//sub {yx/sub 2/}/+.cdots.+R/sup 2//sub {yx/sub k/}/.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.16 no.8
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• pp.676-680
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• 2003

In this study, to develop the low temperature sintering ceramics for piezoelectric transformer, PSN-PNN-PZT system ceramics were manufactured as a function of V$_2$O$_{5}$ addition, that is the low melting point oxide. Its dielectric and piezoelectric characteristics were investigated. With increasing the amount of V$_2$O$_{5}$ addition, electromechanical coupling factor(kp) and mechanical quality factor(Qm) were decreased. For piezoelectric transformer application, the 0.1wt% V$_2$O$_{5}$ added specimen sintered at 1,00$0^{\circ}C$ showed the proper value of $\varepsilon$r=1,590, kp=0.51 and Qm=748.m=748.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.17 no.7
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• pp.718-723
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• 2004

Crystal structure of $(Ba-{1-x}La_x)[Mg_\frac{1+x}{3}}Nb_\frac{{2-x}{3}}]O_3$ (BLMN) ceramics with 0\leq1x \geq was investigated using synchrotron X-ray powder diffraction (XRD) and high reso(B $a_{l-x}$L $a_{x}$)[M $g_{(1+x)}$3/N $b_{(2-x)/3}$］ $O_3$lution transmission electron microscopy (HRTEM). When the La content, x, is above 0.1, the 1:2 ordered hexagonal structure found in Ba($Mg_\frac{1}{3}Nb_\frac{2}{3}})O_3$(BMN) was transformed into 1:1 ordered cubic structure. The 1:1 ordered cubic structure was maintained up to x=0.7. When x exceeded 0.7, however, BLMN was transformed into 1:1 ordered structure which has cation displacement and in-phase and anti-phase tilt of octahedra.

• Progress in Superconductivity and Cryogenics
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• v.25 no.4
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• pp.14-18
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• 2023

We have investigated the behavior induced by Ga substitution in B-1212 system and observed an anomalous superconductor-like resistivity drop with an onset near 260 K and an offset at 248 K in the nominal (B_0.65Ga_0.35)(Ba_1.25Sr_0.75)(Er_0.5Ca_0.5)Cu₂O_z compound. However, this property degraded with repeated cycling. Systematic studies of the superconducting properties of the (B_1-xGa_x)(Ba_1.25Sr_0.75)(Er_0.5Ca_0.5)Cu₂O_z compounds are reported and discussed in the context of the anomalous resistivity transition.

• Journal of the Korean Chemical Society
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• v.65 no.3
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• pp.203-208
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• 2021

As part of our attempt to discover novel active compounds against multi-drug resistant pathogens, we hereby report two new complexes of iron(III) with formulae: [Fe(L₁)₂(H₂O)₂]Cl₃ and [Fe(L₁)₂(L₂)(H₂O)]Cl₂ where L₁ = 1,10-phenanthroline (C₁₂H₈N₂) and L₂ = guanide (C₅H₄N₅O^-). The synthesized complexes were characterized using spectroscopic analysis (ESI-MS, ICP-OES, FT-IR, and UV-Vis), cyclic voltammetry, CHN analysis, gravimetric chloride determination, melting point determination, and conductance measurement. Octahedral geometries are assigned to both complexes. In vitro antibacterial activity was tested on two Gram-positive (Staphylococcus aureus, Streptococcus epidermidis) and two Gram-negative (Escherichia coli and Klebsiella pneumoniae) bacteria using the disc diffusion method. The complexes demonstrated appreciable activity against these pathogens. Interestingly, the [Fe(L₁)₂(L₂)(H₂O)]Cl₂ complex manifested a higher degree of inhibition against the drug-resistant Gram-negative bacteria than the commercially available drug, namely erythromycin.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.598-609
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• 2023

The purpose of this article is to obtain the spectrum, fine spectrum, approximate point spectrum, defect spectrum and compression spectrum of the double band matrix U (a₀, a₁, a₂; b₀, b₁, b₂), b₀, b₁, b₂≠0 on the sequence space ℓ_p (1 < p < ∞).