• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.133-159
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• 2024

In a previous work we studied generalized Stirling numbers of the second kind S^{(a₂,b₂,p₂)}_a1,b1 (p₁, k), where a₁, a₂, b₁, b₂ are given complex numbers, a₁, a₂ ≠ 0, and p₁, p₂ are non-negative integers given. In this work we use these generalized Stirling numbers to define Bernoulli polynomials in two variables B_p1,p2 (x₁, x₂), and Euler polynomials in two variables E_p1p2 (x₁, x₂). By using results for S^{(1,x₂,p₂)}_1,x1 (p₁, k), we obtain generalizations, to the bivariate case, of some well-known properties from the standard case, as addition formulas, difference equations and sums of powers. We obtain some identities for bivariate Bernoulli and Euler polynomials, and some generalizations, to the bivariate case, of several known identities for Bernoulli and Euler numbers and polynomials of the standard case.

• 대한수학회지
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• 제59권1호
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• pp.71-85
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• 2022

In [4], the authors showed that if an h-vector (h₀, h₁, …, h_e) with h₁ = 4e - 4 and h_i ≤ h₁ is a Gorenstein sequence, then h₁ = h_i for every 1 ≤ i ≤ e - 1 and e ≥ 6. In th_is paper, we show that if an h-vector (h₀, h₁, …, h_e) with h₁ = 4e - 4, h₂ = 4e - 3, and h_i ≤ h₂ is a Gorenstein sequence, then h₂ = h_i for every 2 ≤ i ≤ e - 2 and e ≥ 7. We also propose an open question that if an h-vector (h₀, h₁, …, h_e) with h₁ = 4e - 4, 4e - 3 < h₂ ≤ (h₁)₍₁₎|⁺¹₊₁, and h₂ ≤ h_i is a Gorenstein sequence, then h₂ = h_i for every 2 ≤ i ≤ e - 2 and e ≥ 6.

• 마이크로전자및패키징학회지
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• 제30권4호
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• pp.79-85
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• 2023

(1-4x)Bi_1.5Zn_1.0Nb_1.5O₇-3xBi₂Zn_2/3Nb_4/3O₇-2xLiZnNbO₄(x=0.03-0.21) 조성의 새로운 저온 동시 소성 세라믹(LTCC) 유전체는 Bi_1.5Zn_1.0Nb_1.5O₇-xLi₂CO₃(x=0.03-0.21) 혼합물을 850℃~920℃에서 4 시간 반응성 액상소결(reactive liquid phase sintering)을 하여 제조하였다. 소결이 진행되는 동안 Li₂CO₃는 Bi_1.5Zn_1.0Nb_1.5O₇과 반응하여 Bi₂Zn_2/3Nb_4/3O₇과 LiZnNbO₄를 생성하였고 얻어진 소결체의 상대 소결밀도는 이론 밀도의 96% 이상이었다. 초기 Li₂CO₃ 함량(x)을 조절하여 최종 소결체내에 존재하는 Bi_1.5Zn_1.0Nb_1.5O₇, Bi₂Zn_2/3Nb_4/3O₇ 및 LiZnNbO₄ 상의 상대적인 함량을 제어함으로써 높은 유전율(ε_r), 낮은 유전손실(tan δ) 및 NP0 특성(TCε ≤ ±30 ppm/℃)의 유전율 온도계수(TCε)를 갖는 유전체를 개발할 수 있었다. Li₂CO₃의 첨가가 x=0.03 mol에서 x=0.15 mol로 증가함에 따라 얻어진 복합체 내의 Bi₂Zn_2/3Nb_4/3O₇와 LiZnNbO₄의 부피 분율은 증가하였고, Bi_1.5Zn_1.0Nb_1.5O₇의 부피 분율은 감소하였다. 그 결과 복합체의 유전율(ε_r)은 148.38에서 126.99로 유전손실(tan δ)은 5.29×10^-4에서 3.31×10^-4로 그리고 유전율 온도계수(TCε)는 -340.35 ppm/℃에서 299.67 ppm/℃로 변화되었다. NP0 특성을 갖는 유전체는 Li₂CO₃의 함량이 x=0.09일 때 얻을 수 있었고, 이 때의 유전율(ε_r)은 143.06, 유전손실(tan δ)값은 4.31×10^-4, 그리고 유전율 온도계수(TCε)값은 -9.98 ppm/℃ 이었다. Ag전극과의 화학적 호환성 실험은 개발된 복합 재료는 Ag 전극과 동시 소성 과정에서 전극과 반응이 없음을 보여주었다.

• 대한수학회논문집
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• 제38권1호
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• pp.39-46
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• 2023

Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :_R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q₁ ∩ ⋯ ∩ Q_n with r(Q_i :_R M) = 𝖕_i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕_k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists m_j ∈ M such that 𝖕_j = (N :_R m_j). (iii) For each i, j = 1, . . . , n either 𝖕_i ⊆ 𝖕_j or 𝖕_j ⊆ 𝖕_i. Let Γ_E(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q₁∩ ⋯ ∩Q_n-1, Q₁∩ ⋯ ∩Q_n-2, . . . , Q₁} is an independent subset of V (Γ_E(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q₁ ∩ ⋯ ∩ Q_n = 0 is its minimal primary decomposition. Furthermore, it is proved that Γ_E(M)[(0 :_R M)], the induced subgraph of Γ_E(M) by (0 :_R M), is complete.

• The Korean Journal of Physiology and Pharmacology
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• 제27권4호
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• pp.325-331
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• 2023

α₁-adrenoceptors link via the G-protein Gq/G₁₁ to both Ca²⁺ entry and release from stores, but may also activate Rho kinase, which causes calcium sensitization. This study aimed to identify the subtype(s) of α₁-adrenoceptor involved in Rho kinase-mediated responses in both rat aorta and mouse spleen, tissues in which contractions involve multiple subtypes of α₁-adrenoceptor. Tissues were contracted with cumulative concentrations of noradrenaline (NA) in 0.5 log unit increments, before and in the presence of an antagonist or vehicle. Contractions produced by NA in rat aorta are entirely α₁-adrenoceptor mediated as they are competitively blocked by prazosin. The α_1A-adrenoceptor antagonist RS100329 had low potency in rat aorta. The α_1D-adrenoceptor antagonist BMY7378 antagonized contractions in rat aorta in a biphasic manner: low concentrations blocking α_1D-adrenoceptors and high concentrations blocking α_1B-adrenoceptors. The Rho kinase inhibitor fasudil (10 µM) significantly reduced aortic contractions in terms of maximum response, suggesting inhibition of α_1B-adrenoceptor mediated responses. In the mouse spleen, a tissue in which all 3 subtypes of α₁-adrenoceptor are involved in contractions to NA, fasudil (3 µM) significantly reduced both early and late components to the NA contraction, the early component involving α_1B- and α_1D-adrenoceptors, and the late component involving α_1B- and α_1A-adrenoceptors. This suggests that fasudil inhibits α_1B-adrenoceptor mediated responses. It is concluded that α_1D- and α_1B-adrenoceptors interact in rat aorta and α_1D-, α_1A- and α_1B-adrenoceptors interact in the mouse spleen to produce contractions and these interactions suggest that one of the receptors preferentially activates Rho kinase, most likely the α_1B-adrenoceptor.

• 한국재료학회지
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• 제31권12호
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• pp.682-689
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• 2021

NbC, HfC, TaC, and their solid solution ceramics have been identified as the best materials for ultrahigh-temperature ceramics. However, their structural stability and elastic properties are mostly unclear. Thus, we investigated structure and elastic properties of (Nb_1-xTa_x)C and (Nb_1-xHf_x)C solid solutions via ab initio calculations. Our calculated results show that the stability of (Nb_1-xTa_x)C and (Nb_1-xHf_x)C increases with the increase of Hf and Ta content, and (Nb_1-xHf_x)C is more stable than (Nb_1-xTa_x)C at the same content of Hf and Ta. The lattice constants decrease with increasing of Hf and Ta content. (Nb_1-xTa_x)C and (Nb_1-xHf_x)C carbides are mechanically stable and brittle. Bulk modulus of (Nb_1-xTa_x)C increases with increasing Ta content. In contrast, bulk modulus of (Nb_1-xHf_x)C decreases with increasing Hf content. Hardness of solid solutions shows the highest values at the (Nb_0.25Ta_0.75)C and (Nb_0.75Hf_0.25)C. In particular, (Nb_0.75Hf_0.25)C shows the highest hardness for the current system. The results indicate that the overall mechanical properties of (Nb_1-xHf_x)C solid solutions are superior to those of (Nb_1-xTa_x)C solid solutions. Therefore, controlling the Hf and Ta element and content of the (Nb_1-xTa_x)C and (Nb_1-xHf_x)C Solid solution is crucial for optimizing the material properties.

• 한국재료학회지
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• 제34권4호
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• pp.185-193
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• 2024

In this study, NASICON-type Li_1+XGa_XTi_2-X(PO₄)₃ (x = 0.1, 0.3 and 0.4) solid-state electrolytes for all-solid-state batteries were synthesized through the sol-gel method. In addition, the influence on the ion conductivity of solid-state electrolytes when partially substituted for Ti⁴⁺ (0.61Å) site to Ga³⁺ (0.62Å) of trivalent cations was investigated. The obtained precursor was heat treated at 450 ℃, and a single crystalline phase of Li_1+XGa_XTi_2-X(PO₄)₃ systems was obtained at a calcination temperature above 650 ℃. Additionally, the calcinated powders were pelletized and sintered at temperatures from 800 ℃ to 1,000 ℃ at 100 ℃ intervals. The synthesized powder and sintered bodies of Li_1+XGa_XTi_2-X(PO₄)₃ were characterized using TG-DTA, XRD, XPS and FE-SEM. The ionic conduction properties as solid-state electrolytes were investigated by AC impedance. As a result, Li_1+XGa_XTi_2-X(PO₄)₃ was successfully produced in all cases. However, a GaPO₄ impurity was formed due to the high sintering temperatures and high Ga content. The crystallinity of Li_1+XGa_XTi_2-X(PO₄)₃ increased with the sintering temperature as evidenced by FE-SEM observations, which demonstrated that the edges of the larger cube-shaped grains become sharper with increases in the sintering temperature. In samples with high sintering temperatures at 1,000 ℃ and high Ga content above 0.3, coarsening of grains occurred. This resulted in the formation of many grain boundaries, leading to low sinterability. These two factors, the impurity and grain boundary, have an enormous impact on the properties of Li_1+XGa_XTi_2-X(PO₄)₃. The Li_1.3Ga_0.3Ti_1.7(PO₄)₃ pellet sintered at 900 ℃ was denser than those sintered at other conditions, showing the highest total ion conductivity of 7.66 × 10^-5 S/cm at room temperature. The total activation energy of Li-ion transport for the Li_1.3Ga_0.3Ti_1.7(PO₄)₃ solid-state electrolyte was estimated to be as low as 0.36 eV. Although the Li_1+XGa_XTi_2-X(PO₄)₃ sintered at 1,000 ℃ had a relatively high apparent density, it had less total ionic conductivity due to an increase in the grain-boundary resistance with coarse grains.

• 한국결정성장학회지
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• 제31권5호
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• pp.197-202
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• 2021

Z형 육방정 페라이트인 Ba₃Co₂Fe₂₄O₄₁(Ba₃Z)와 Ba_1.5La_1.5Co₂Fe₂₄O₄₁(Ba_1.5La_1.5Z) 분말을 1차 하소 후 용융염 합성법을 통해 합성하였다. Ba₃Z의 경우, 1000℃에서 하소한 결과 M형 육방정 페라이트와 Y형 육방정 페라이트가 합성되었으며, 이후 1150℃와 1200℃에서 소결했을 때 Z형 육방정 페라이트를 얻을 수 있었다. 하지만 Ba_1.5La_1.5Z의 경우 1000℃에서 하소하였을 때 M형 육방정 페라이트와 CoFe₂O₄(Spinel 상) 그리고 LaFeO₃으로 합성되었으며, Z형 육방정 페라이트는 용융염 합성 과정에서 합성되지 않았다. 또한 입자 형상의 종횡비는 용융염 합성 시 소결온도가 증가함에 따라 감소하는 경향을 보였다. 따라서 높은 종횡비를 갖는 단상의 Ba_1.5La_1.5Z를 합성하기 위해서는 용융염 합성 전 1차 하소 온도가 Spinel 상이 형성되는 온도보다 낮아야 될 것으로 판단된다.

• 한국환경농학회지
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• 제42권4호
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• pp.389-395
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• 2023

This study evaluated the effects of gibberellic acid (GA₃) on the growth and quality of creeping bentgrass (Agrostis palustris Huds.). Experimental treatments included a No application of fertilizer and GA₃ (NFG) Control [3 N active ingredient (a.i.) g/m²], 0.3GA₃ (GA₃ 0.3 a.i. mg/m²/200 mL), 0.6GA₃ (GA₃ 0.6 a.i. mg/m²/200 mL), 1.2GA₃ (GA₃ 1.2 a.i. mg/m²/200 mL), and 2.4GA₃ (GA₃ 2.4 a.i. mg/m²/200 mL). Additionally, the study included a 1.5N+GA₃ experiment with similar GA₃ treatments combined with 1.5N a.i. g/m² : NFG, Control (3N a.i. g/m²), 1.5N+ 0.3GA₃ (1.5N a.i. g/m²+GA₃ 0.3 a.i. mg/m²/200 mL), 1.5N+0.6GA₃ (1.5N a.i. g/m²+GA₃ 0.6 a.i. mg/m²/200 mL), 1.5N+1.2GA₃ (1.5N a.i. g/m²+GA₃ 1.2 a.i. mg/m²/ 200 mL), and 1.5N+2.4GA₃ (1.5N a.i. g/m²+GA₃ 2.4 a.i. mg/m²/200 mL). Compared to the NFG, turf color index chlorophyll content was not significantly different (p< 0.05). However, shoot length in 1.2GA₃, 2.4GA₃, 1.5N+0.3GA₃, 1.5N+0.6GA₃, 1.5N+1.2GA₃, and 1.5N+2.4GA₃ treatments increased by 0.8%, 10.6%, 5.15%, 8.3%, 13.5 %, and 21.6%, respectively, compared to the control. As compared to the control, clipping yield in 1.5N+1.2GA₃ and 1.5N+2.4GA₃ treatments increased by 7.1% and 14.3 %, respectively. These results indicated that GA₃ application increased shoot length, with the 1.2GA₃ treatment showing shoot length similar to the control (3N a.i. g /m² ).

• 대한수학회보
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• 제60권6호
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• pp.1651-1672
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• 2023

In 2010, Li-Ye [13, Theorem 0.1] proved that P(ζ(z), ζ'(z), . . . , ζ^(m)(z), Γ(z), Γ'(z), Γ"(z)) ≢ 0 in ℂ, where m is a non-negative integer, and P(u₀, u₁, . . . , u_m, v₀, v₁, v₂) is any non-trivial polynomial in its arguments with coefficients in the field ℂ. Later on, Li-Ye [15, Theorem 1] proved that P(z, Γ(z), Γ'(z), . . . , Γ⁽ⁿ⁾(z), ζ(z)) ≢ 0 in z ∈ ℂ for any non-trivial distinguished polynomial P(z, u₀, u₁, . . ., u_n, v) with coefficients in a set L_δ of the zero function and a class of nonzero functions f from ℂ to ℂ ∪ {∞} (cf. [15, Definition 1]). In this paper, we prove that P(z, ζ(z), ζ'(z), . . . , ζ^(m)(z), Γ(z), Γ'(z), . . . , Γ⁽ⁿ⁾(z)) ≢ 0 in z ∈ ℂ, where m and n are two non-negative integers, and P(z, u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n) is any non-trivial polynomial in the m + n + 2 variables u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n with coefficients being meromorphic functions of order less than one, and the polynomial P(z, u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n) is a distinguished polynomial in the n + 1 variables v₀, v₁, . . . , v_n. The question studied in this paper is concerning the conjecture of Markus from [16]. The main results obtained in this paper also extend the corresponding results from Li-Ye [12] and improve the corresponding results from Chen-Wang [5] and Wang-Li-Liu-Li [23], respectively.