• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.257-267
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• 2016

We find examples of Ideals in a tridiagonal algebra ALGL_∞ and study some properties of Ideals in ALGL_∞. We prove the following theorems: Let k and j be fixed natural numbers. Let A be a subalgebra of ALGL_∞ and let A_2,{k} ⊂ A ⊂ {T ∈ ALGL_∞ | T_(2k-1,2k) = 0}. Then A is an ideal of ALGL_∞ if and only if A = A_2,{k} where A_2,{k} = {T ∈ ALGL_∞ | T_(2k-1,2k) = 0, T_(2k-1,2k-1) = T_(2k,2k) = 0}. Let B be a subalgebra of ALGL_∞ such that B_2,{j} ⊂ B ⊂ {T ∈ ALGL_∞ | T_(2j+1,2j) = 0}. Then B is an ideal of ALGL_∞ if and only if B = B_2,{j}, where B_2,{j} = {T ∈ ALGL_∞ | T_(2j+1,2j) = 0, T_(2j,2j) = T_(2j+1,2j+1) = 0}.

• Journal of the Korean Chemical Society
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• v.67 no.4
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• pp.236-240
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• 2023

Non-concentration quenching EuGa₂S₄ and Eu₂Ga₂S₅ phosphors, in which the concentration of Eu²⁺ activator ion is 100%, were synthesized by a solid state reaction at temperature range from 800 to 1050 ℃. The wavelength of maximum intensity (λ_max) of EuGa₂S₄ and Eu₂Ga₂S₅ phosphors are 546 and 581 nm, respectively. An examination of the X-ray diffraction patterns and photoluminescent properties of EuGa₂S₄ and Eu₂Ga₂S₅ phosphors revealed that EuGa₂S₄ and Eu₂Ga₂S₅ phosphors were formed at lower temperature range (800~900 ℃) and higher temperature range (1000~1050 ℃), respectively.

• 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.

• 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.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.30 no.2
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• pp.47-54
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• 2020

To develop the bright-vivid red- and yellow-inorganic fluorescent pigments with high luminescence properties, A₃V₅O₁₄ (A = K and Rb) and Cs₂V₄O₁₁ inorganic pigments were synthesized by a water assisted solid state reaction (WASSR) method and a conventional solid state reaction method. Although impurity peaks corresponding to the AVO₃ and AV₃O₈ (A = K, Rb, and Cs) were observed in all samples prepared, the trigonal structure A₃V₅O₁₄ (A = K and Rb) and orthorhombic structure Cs₂V₄O₁₁ were successfully obtained as a main phase. These inorganic pigments showed the broad absorption band (under 550 nm) originated from CT transitions of VO₄ polyhedron, and the strong broad red- and green-emission bands due to ³T₂ → ¹A₁ and ³T₁ → ¹A₁ transitions of the [VO₄]^3- group. The A₃V₅O₁₄ (A = K and Rb) and Cs₂V₄O₁₁ pigments showed a bright-vivid red- and yellow-body color, where the a* values of the A₃V₅O₁₄ (A = K and Rb) were +35.5 and +45.9, respectively, and b* value of Cs₂V₄O₁₁ pigments was +50.3. The L* values of the A₃V₅O₁₄ (A = K and Rb) and Cs₂V₄O₁₁ inorganic pigments were over +45. These results indicate that the A₃V₅O₁₄ (A = K and Rb) and Cs₂V₄O₁₁ inorganic pigments could be an attractive candidate as a bright-vivid red- and yellow inorganic pigments.

• The Journal of the Convergence on Culture Technology
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• v.8 no.6
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• pp.927-933
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• 2022

We synthesized (C₁₀H₈N₂H)₂Cr₂O₇, The structure of the product was characterized with FT-IR(infrared) and elemental analysis. The oxidation of benzyl alcohol by (C₁₀H₈N₂H)₂Cr₂O₇ in organic solvents showed that the reactivity increased with the increase of the dielectric constant. The oxidation of alcohols was examined by (C₁₀H₈N₂H)₂Cr₂O₇ in DMF, acetone. As a resuit, (C₁₀H₈N₂H)₂Cr₂O₇ was found as efficicent oxidizing agent that converted benzyl alcohol, allyl alcohol, primary alcohol and secondary alcohols to the corresponding aldehydes or ketones(65%~95%). The selective oxidation of alcohols was also examined by (C₁₀H₈N₂H)₂Cr₂O₇ in DMF, acetone. (C₁₀H₈N₂H)₂Cr₂O₇ was selective oxidizing agent(15%~95%) of benzyl alcohol, allyl alcohol and primary alcohol in the presence of secondary ones. In the presence of DMF solvent with acidic catalyst such as H₂SO₄. (C₁₀H₈N₂H)₂Cr₂O₇ oxidized benzyl alcohol(H) and its derivatives. The Hammett reaction constant(ρ) was -0.69(308K). The observed experimental data were used to rationalize the hydride ion transfer in the rate determining step.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.31 no.6
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• pp.270-275
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• 2021

ZnO was synthesized according to the transformation behavior and crystallization conditions of Zn-intermediate obtained by zinc sulfate as a precursor and NaOH, Na₂CO₃ as a alkali agents. For ZnO crystallization, Zn₄(OH)₆SO₄·H₂O and Zn₅(OH)₆(CO₃)₂·H₂O as a Zn-intermediate were calcined at 400℃ and 800℃ for 1 h, respectively, based on decomposition temperature from TGA. Zn₄(OH)₆SO₄·H₂O was confirmed to have mixed Zn₄(OH)₆SO₄·H₂O and ZnO at 400℃, and was completely thermally decomposed at 800℃ to form ZnO phase. The prepared Zn₅(OH)₆(CO₃)₂·H₂O as a Zn-intermediate by the reaction with Na₂CO₃ was transformed to a complete ZnO crystallization over 400℃. Nano-sized ZnO can be synthesized at a relatively lower calcination temperature through the reaction with Na₂CO₃.

• Journal of Electrochemical Science and Technology
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• v.11 no.2
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• pp.187-194
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• 2020

Two types of sodium cobalt pyrophosphates, triclinic Na_3.12Co_2.44(P₂O₇)₂ and orthorhombic Na₂CoP₂O₇, are compared as high-voltage cathode materials for Na-ion batteries. Na₂CoP₂O₇ shows no electrochemical activity, delivering negligible capacity. In contrast, Na_3.12Co_2.44(P₂O₇)₂ exhibits good electrochemical performance, such as high redox potential at ca. 4.3 V (vs. Na/Na⁺) and stable capacity retention over 50 cycles, although Na_3.12Co_2.44(P₂O₇)₂ delivered approximately 40 mA h g^-1. This is attributed to the fact that Na₂CoP₂O₇ (~3.1 Å) has smaller diffusion channel size than Na_3.12Co_2.44(P₂O₇)₂ (~4.2 Å). Moreover, the electrochemical performance of Na_3.12Co_2.44(P₂O₇)₂ is examined using Na cells and Li cells. The overpotential of Na cells is smaller than that of Li cells. This is due to the fact that Na_3.12Co_2.44(P₂O₇)₂ has a smaller charge transfer resistance and higher diffusivity for Na⁺ ions than Li⁺ ions. This implies that the large channel size of Na_3.12Co_2.44(P₂O₇)₂ is more appropriate for Na⁺ ions than Li⁺ ions. Therefore, Na_3.12Co_2.44(P₂O₇)₂ is considered a promising high-voltage cathode material for Na-ion batteries, if new electrolytes, which are stable above 4.5 V vs. Na/Na⁺, are introduced.

• Korean Journal of Mineralogy and Petrology
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• v.34 no.2
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• pp.107-120
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• 2021

The Komdok Pb-Zn deposit, which is the largest Pb-Zn deposit in Korea, is located at the Hyesan-Riwon metallogenic zone in Jiao Liao Ji belt included Paleoproterozoic Macheolryeong group. The geology of this deposit consists of Paleoproterozoic metasedimentary rocks, Jurassic Mantapsan intrusive rocks and Cenozoic basalt. The Komdok deposit which is a SEDEX type deposit occurs as layer ore and vein ore in the Paleoproterozoic metasedimentary rocks. Based on mineral petrography and paragenesis, dolomites from this deposit are classified four types (1. dolomite (D₀) as hostrock, 2. early dolomite (D₁) associated with tremolite, actinolite, diopside, sphalerite and galena from amphibolite facies, 3. late dolomite (D₂) associated with talc, calcite, quartz, sphalerite and galena from amphibolite facies, 4. dolomite (D₃) associated with white mica, chlorite, sphalerite and galena from quartz vein). The structural formulars of dolomites are determined to be Ca_1.00-1.20Mg_0.80-0.99Fe_0.00-0.01Zn_0.00-0.02(CO₃)₂(D₀), Ca_1.00-1.02M_0.97-0.99Fe_0.00-0.01Zn_0.00-0.02(CO₃)₂(D₁), Ca_0.99-1.03Mg_0.93-0.98Fe_0.01-0.05Mn_0.00-0.01As_0.00-0.01(CO₃)₂(D₂) and Ca_0.95-1.04Mg_0.59-0.68Fe_0.30-0.36Mn_0.00-0.01 (CO₃)₂(D₃), respectively. It means that dolomites from Komdok deposit have higher content of trace elements (FeO, MnO, HfO₂, ZnO, PbO, Sb₂O₅ and As₂O₅) compared to the theoretical composition of dolomite. These trace elements (FeO, MnO, ZnO, Sb₂O₅ and As₂O₅) show increase and decrease trend according to paragenetic sequence, but HfO₂ and PbO elements no show increase and decrease trend according to paragenetic sequence. Dolomites correspond to Ferroan dolomite (D₀, D₁ and D₂), and Ferroan dolomite and ankerite (D₃), respectively. Therefore, 1) dolomite (D₀) as hostrock was formed by subsequent diagenesis after sedimentation of Paleoproterozoic (2012~1700 Ma) silica-bearing dolomite in the marine evaporative environment. 2) Early dolomite (D₁) was formed by hydrothermal metasomatism origined metamorphism (amphibolite facies) associated with intrusion (1890~1680 Ma) of Paleoproterozoic Riwon complex. 3) Late dolomte (D₂) was formed from residual fluid by a decrease of temperature and pressure. and dolomite (D₃) in quartz vein was formed by intrusion (213~181 Ma) of Jurassic Mantapsan intrusive rocks.

• 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.