• Kyungpook Mathematical Journal
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• v.64 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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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.

• Journal of the Microelectronics and Packaging Society
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• v.30 no.4
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• pp.79-85
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• 2023

A novel low-temperature co-fired ceramic (LTCC) dielectric, composed of (1-4x)Bi_1.5Zn_1.0Nb_1.5O₇-3xBi₂Zn_2/3Nb_4/3O₇-2xLiZnNbO₄ (x=0.03-0.21), was synthesized through reactive liquid phase sintering of Bi_1.5Zn_1.0Nb_1.5O₇-xLi₂CO₃ ceramic at temperatures ranging from 850℃ to 920℃ for 4 hours. During sintering, Li₂CO₃ reacted with Bi_1.5Zn_1.0Nb_1.5O₇, resulting in the formation of Bi₂Zn_2/3Nb_4/3O₇, and LiZnNbO₄. The resulting sintered body exhibited a relative sintering density exceeding 96% of the theoretical density. By altering the initial Li₂CO₃ content (x) and consequently modulating the volume fraction of Bi_1.5Zn_1.0Nb_1.5O₇, Bi₂Zn_2/3Nb_4/3O₇, and LiZnNbO₄ in the final sintered body, a sample with high dielectric constant (ε_r), low dielectric loss (tan δ), and the temperature coefficient of dielectric constant (TCε) characterized by NP0 specification (TCε ≤ ±30 ppm/℃) was achieved. As the Li₂CO₃ content increased from x=0.03 mol to x=0.15 mol, the volume fraction of Bi₂Zn_2/3Nb_4/3O₇ and LiZnNbO₄ in the composite increased, while the volume fraction of Bi_1.5Zn_1.0Nb_1.5O₇ decreased. Consequently, the dielectric constant (εr) of the composite materials varied from 148.38 to 126.99, the dielectric loss (tan δ) shifted from 5.29×10^-4 to 3.31×10^-4, and the temperature coefficient of dielectric constant (TCε) transitioned from -340.35 ppm/℃ to 299.67 ppm/℃. A dielectric exhibiting NP0 characteristics was achieved at x=0.09 for Li₂CO₃, with a dielectric constant (ε_r) of 143.06, a dielectric loss (tan δ) value of 4.31×10^-4, and a temperature coefficient of dielectric constant (TCε) value of -9.98 ppm/℃. Chemical compatibility experiment with Ag electrode revealed that the developed composite material exhibited no reactivity with the Ag electrode during the co-firing process.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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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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• v.27 no.4
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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.

• Korean Journal of Materials Research
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• v.31 no.12
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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.

• Korean Journal of Materials Research
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• v.34 no.4
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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.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.31 no.5
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• pp.197-202
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• 2021

Synthesis of Z-type hexaferrite Ba₃Co₂Fe₂₄O₄₁ (Ba₃Z) and Ba_1.5La_1.5Co₂Fe₂₄O₄₁ (Ba_1.5La_1.5Z) powders were tried using molten salt synthesis after primary calcination. Ba₃Z calcined at 1000℃ was formed with both M-type and Y-type hexaferrite, and then Z-type was obtained when sintered with molten salt at 1150℃ and 1200℃. In the case of Ba_1.5La_1.5Z calcined at 1000℃, however, M-type hexaferrite, CoFe₂O₄ (Spinel phase), and LaFeO₃ were synthesized. As a result, Z-type hexaferrite was not synthesized after sintering with molten salt. In addition, the aspect ratio of the particles decreased as the sintering temperature increased with molten salt synthesis. To obtain a single-phase Ba_1.5La_1.5Z with a high aspect ratio, it is expected the raw materials have to calcine below the temperature of a spinel phase formation before sintering with molten salt.

• Korean Journal of Environmental Agriculture
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• v.42 no.4
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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 ).

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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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.