• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.73-82
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• 2022

Let K be a field of characteristic zero. We first show that images of the linear derivations and the linear 𝓔-derivations of the polynomial algebra K[x] = K[x₁, x₂, …, x_n] are ideals if the products of any power of eigenvalues of the matrices according to the linear derivations and the linear 𝓔-derivations are not unity. In addition, we prove that the images of D and 𝛿 are Mathieu-Zhao spaces of the polynomial algebra K[x] if D = ∑ⁿ_i=1 (a_ix_i + b_i)∂_i and 𝛿 = I - 𝜙, 𝜙(x_i) = λ_ix_i + 𝜇_i for a_i, b_i, λ_i, 𝜇_i ∈ K for 1 ≤ i ≤ n. Finally, we prove that the image of an affine 𝓔-derivation of the polynomial algebra K[x₁, x₂] is a Mathieu-Zhao space of the polynomial algebra K[x₁, x₂]. Hence we give an affirmative answer to the LFED Conjecture for the affine 𝓔-derivations of the polynomial algebra K[x₁, x₂].

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.18 no.3
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• pp.383-393
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• 2020

The corrosion behavior of Hastelloy C-276 was investigated to identify its applicability for carbon-anode-based oxide reduction (OR), in which Cl₂ and O₂ are simultaneously evolved at the anode. Under a 30 mL·min^-1 Cl₂ + 170 mL·min^-1 Ar flow, the corrosion rate was less than 1 g·m^-2·h^-1 up to 500℃, whereas the rate increased exponentially from 500 to 700℃. The effects of the Cl₂-O₂ composition on the corrosion rate at flow rates of 30 mL·min^-1 Cl₂, 20 mL·min^-1 Cl₂ + 10 mL·min^-1 O₂, and 10 mL·min^-1 Cl₂ + 20 mL·min^-1 O₂ with a constant 170 mL·min^-1 Ar flow rate at 600℃ was analyzed. Based on the data from an 8 h reaction, the fastest corrosion rate was observed for the 20 mL·min^-1 Cl₂ + 10 mL·min^-1 O₂ case, followed by 30 mL·min^-1 Cl₂ and 10 mL·min^-1 Cl₂ + 20 mL·min^-1 O₂. The effects of the chlorine flow rate on the corrosion rate were negligible within the 5-30 mL·min^-1 range. A surface morphology analysis revealed the formation of vertical scratches in specimens that reacted under the Cl₂-O₂ mixed gas condition.

• The Pure and Applied Mathematics
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• v.27 no.1
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• pp.25-33
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• 2020

In this paper, we consider the following quadratic (ρ₁, ρ₂)-functional equation (0, 1) $$N(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y)-{\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y))-{\rho}_2(4f({\frac{x+y}{2}})+f(x-y)-f(x)-f(y)),t){\geq}{\frac{t}{t+{\varphi}(x,y)}}$$, where ρ₂ are fixed nonzero real numbers with ρ₂ ≠ 1 and 2ρ₁ + 2ρ₂≠ 1, in fuzzy normed spaces. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (ρ₁, ρ₂)-functional equation (0.1) in fuzzy Banach spaces.

• Journal of the Korean Electrochemical Society
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• v.24 no.3
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• pp.52-64
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• 2021

The effect of Fe and BO₃ doping on structure, thermal, and electrical properties of Li_1+xFe_xTi_2-x(PO₄)_3-y(BO₃)_y (x = 0.2, 0.5)-based glass and glass ceramics was investigated. In addition, their crystallization behavior during sintering and ionic conductivity were also investigated in terms of sintering temperature. FT-IR and XPS results indicated that Fe²⁺ and Fe³⁺ ions in Li_1+xFe_xTi_2-x(PO₄)_3-y(BO₃)_y glass worked as a network modifier (FeO₆ octahedra) and also as a network former (FeO₄ tetrahedra). In the case of the glass with low substitution of BO₃, boron formed (PB)O₄ network structure, while boron preferred BO₃ triangles or B₃O₃ boroxol rings with increasing the BO₃ content owing to boic oxide anomaly, which can result in an increased non-bridging oxygen. The glass transition temperature (GTT) and crystallization temperature (CT) was lowered as the BO₃ substitution was increased, while Fe²⁺ lowered the GTT and raised the CT. The ionic conductivity of Li_1+xFe_xTi_2-x(PO₄)_3-y(BO₃)_y glass ceramics were 8.85×10^-4 and 1.38×10^-4S/cm for x = 0.2 and 0.5, respectively. The oxidation state of doped Fe and boric oxide anomaly were due to the enhanced lithium ion conductivity of glass ceramics.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.679-710
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• 2021

We study the tensor product algebra P_k(x₁) ⊗ P_k(x₂) ⊗ ⋯ ⊗ P_k(x_m), where P_k(x) is the partition algebra defined by Jones and Martin. We discuss the centralizer of this algebra and corresponding Schur-Weyl dualities and also index the inequivalent irreducible representations of the algebra P_k(x₁) ⊗ P_k(x₂) ⊗ ⋯ ⊗ P_k(x_m) and compute their dimensions in the semisimple case. In addition, we describe the Bratteli diagrams and branching rules. Along with that, we have also constructed the RS correspondence for the tensor product of m-partition algebras which gives the bijection between the set of tensor product of m-partition diagram of P_k(n₁) ⊗ P_k(n₂) ⊗ ⋯ ⊗ P_k(n_m) and the pairs of m-vacillating tableaux of shape [λ] ∈ Γ_k^m, Γ_k^m = {[λ] = (λ₁, λ₂, …, λ_m)|λ_i ∈ Γ_k, i ∈ {1, 2, …, m}} where Γ_k = {λ_i ⊢ t|0 ≤ t ≤ k}. Also, we provide proof of the identity $(n_1n_2{\cdots}n_m)^k={\sum}_{[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ f^[λ]m_k^[λ] where m_k^[λ] is the multiplicity of the irreducible representation of $S{_{n_1}}{\times}S{_{n_2}}{\times}....{\times}S{_{n_m}}$ module indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$, where f^[λ] is the degree of the corresponding representation indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ and ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}=\{[{\lambda}]=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_m){\mid}{\lambda}_i{\in}{\Lambda}^k_{n_i},i{\in}\{1,2,{\ldots},m\}\}$ where ${\Lambda}^k_{n_i}=\{{\mu}=({\mu}_1,{\mu}_2,{\ldots},{\mu}_t){\vdash}n_i{\mid}n_i-{\mu}_1{\leq}k\}$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.709-737
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• 2020

Let R be a prime ring of characteristic different from 2. Suppose that F, G, H and T are generalized derivations of R. Let U be the Utumi quotient ring of R and C be the center of U, called the extended centroid of R and let f(x₁, …, x_n) be a non central multilinear polynomial over C. If F(f(r₁, …, r_n))G(f(r₁, …, r_n)) - f(r₁, …, r_n)T(f(r₁, …, r_n)) = H(f(r₁, …, r_n)²) for all r₁, …, r_n ∈ R, then we describe all possible forms of F, G, H and T.

• Journal of the Korean Electrochemical Society
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• v.23 no.1
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• pp.11-17
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• 2020

The Prussian blue analogues of Fe₂(CN)₆ and Na_xFe₂(CN)₆ are prepared by precipitation method and evaluated the electrochemical characteristics as positive electrode materials for lithium-ion batteries (LIBs) because of their low cost. Fe₂(CN)₆ shows a low reversible capacity of 34.6 mAh g^-1, whereas sodium-containing Na_xFe₂(CN)₆ exhibits a reversible capacity of 107.5 mAh g^-1 when the discharge process proceeds first. When charging is first carried out to remove sodium in the structure, the reversible capacity of 114.1 mAh g^-1 is achieved and the cycle performance is further improved. In addition, Na_x-Fe₂(CN)₆ is synthesized at 0℃, room temperature (RT), and 60℃, respectively. Regardless of the synthesis temperature, Na_xFe₂(CN)₆ shows similar initial reversible capacity, but the crystallite size is formed smaller and improved cycle performance when synthetic temperature is lower. The sample synthesized at 0℃ shows a reversible capacity of 86.4 mAh g^-1 at the 120^th cycle and maintains 76.8% of the initial capacity.

• Journal of the Korean Applied Science and Technology
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• v.39 no.6
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• pp.916-923
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• 2022

Water samples were collected from three spots(Namcheon, Changwoncheon and Cheongwoonji) in Changwon and genomic DNA was isolated from them. Quantitative PCR was performed with the isolated DNA as template and primers targeting five different class A extended-spectrum beta-lactamase(ESBL) genes(bla_OXA-1, bla_SHV, bla_TEM, bla_CTX-M-1, bla_CTX-M-9). The number of total ESBL genes from each sample showed large variations between each sample. Thirty nanograms of DNA from Namcheon contained 1.93×10⁶ copies of ESBL genes whereas the same amount of DNA from Changwoncheon contained 1.47×10⁵ copies of ESBL genes. However, the same amount of DNA from Cheongwoonji pond contained only 9.5×10³ copies of ESBL genes. The ratio of each ESBL genes showed little difference between Namcheon river and Changwoncheon river, but DNA from Cheongwoonji pond showed a large difference from the rest. bla_OXA-1 gene was present at 65.3%, and bla_CTX-M-1 gene 33.6% for Namcheon comprising together almost 99%. bla_OXA-1 gene was present at 64.1%, and bla_CTX-M-1 gene 19.1% for Changwoncheon comprising together over 83%. bla_CTX-M-1 gene was present at 87.5% and bla_CTX-M-9 genes 9.8% for Cheongwoonji, a pond which is a closed and isolated environment.

• Korean Journal of Materials Research
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• v.33 no.8
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• pp.330-336
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• 2023

The effects of Ni²⁺ substitution for Mg²⁺-sites on the microwave dielectric properties of (Mg_1-xNi_x)(Ti_0.95(Mg_1/3Ta_2/3)_0.05)O₃ (0.01 ≤ x ≤ 0.05) (MNTMT) ceramics were investigated. MNTMT ceramics were prepared by conventional solid-state reaction. When the MgO / TiO₂ ratio was changed from 1.00 to 1.02, MgTi₂O₅ was detected as a secondary phase along with the MgTiO₃ main phase in the MNTMT specimens sintered at 1,400 ℃ for 4h. For the MNTMT specimens with MgO / TiO₂ = 1.07 sintered at 1,400 ℃ for 4h, a single phase of MgTiO₃ with an ilmenite structure was obtained from the entire range of compositions. The relative density of all the specimens sintered at 1,400 ℃ for 4h was higher than 95 %. The quality factor (Qf) of the sintered specimens depended strongly on the degree of covalency of the specimens, and the sintered specimens with x = 0.01 showed the maximum Qf value of 489,400 GHz. The dielectric constant (K) decreased with increasing Ni²⁺ content because Ni²⁺ had a lower dielectric polarizability (1.23ų) than Mg²⁺ (1.32ų). As Ni²⁺ content increased, the temperature coefficient of resonant frequency (TCF) improved, from -55.56 to -21.85 ppm/℃, due to the increase in tolerance factor (t) and the lower dielectric constant (K).

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1387-1400
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• 2021

Suppose that $T=\(\array{A&0\\U&B}\)$ is a formal triangular matrix ring, where A and B are rings and U is a (B, A)-bimodule. Let ℭ₁ and ℭ₂ be two classes of left A-modules, 𝔇₁ and 𝔇₂ be two classes of left B-modules. We prove that (ℭ₁, ℭ₂) and (𝔇₁, 𝔇₂) are admissible balanced pairs if and only if (p(ℭ₁, 𝔇₁), h(ℭ₂, 𝔇₂) is an admissible balanced pair in T-Mod. Furthermore, we describe when ($P^{C_1}_{D_1}$, $I^{C_2}_{D_2}$) is an admissible balanced pair in T-Mod. As a consequence, we characterize when T is a left virtually Gorenstein ring.