• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.235-254
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• 2022

Let ℍⁿ be the Heisenberg group and Q = 2n + 2 be its homogeneous dimension. Let 𝓛 = -∆_ℍⁿ + V be the Schrödinger operator on ℍⁿ, where ∆_ℍⁿ is the sub-Laplacian and the nonnegative potential V belongs to the reverse Hölder class $B_{q_1}$ for q₁ ≥ Q/2. Let H^p_𝓛(ℍⁿ) be the Hardy space associated with the Schrödinger operator 𝓛 for Q/(Q+𝛿₀) < p ≤ 1, where 𝛿₀ = min{1, 2 - Q/q₁}. In this paper, we consider the Hardy type estimates for the operator T_𝛼 = V^𝛼(-∆_ℍⁿ + V )^-𝛼, and the commutator [b, T_𝛼], where 0 < 𝛼 < Q/2. We prove that T_𝛼 is bounded from H^p_𝓛(ℍⁿ) into L^p(ℍⁿ). Suppose that b ∈ BMO^𝜃_𝓛(ℍⁿ), which is larger than BMO(ℍⁿ). We show that the commutator [b, T_𝛼] is bounded from H¹_𝓛(ℍⁿ) into weak L¹(ℍⁿ).

• Korean Journal of Mineralogy and Petrology
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• v.33 no.3
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• pp.251-258
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• 2020

Single crystal of fully dehydrated and partially Ca²⁺-exchanged zeolites A (|Ca₄Na₄|[Si₁₂Al₁₂O₄₈]-LTA) was brought into contact with Se in fine pyrex capillary at 523 K for 5 days. Crystal structure of Se-sorbed |Ca₄Na₄|[Si₁₂Al₁₂O₄₈]-LTA has been determined by single-crystal X-ray diffraction techniques at 294 K in the cubic space group $Pm{\bar{3}}m$ (a = 12.2787(13) Å). The crystal structure of yellow |Ca₄Na₄Se₄|[Si₁₂Al₁₂O₄₈]-LTA has been refined to the final error indices of R₁/wR₂ = 0.0960/0.3483 with 327 reflections for which F_o > 4s(F_o). In this structure, 4 Na⁺ and 4 Ca²⁺ ions fill every 6-ring site: These ions are all found at three crystallographic positions, on 3-fold axes equipoints of opposite 6-rings. Selenium atoms are found at three crystallographically distinct positions: 2 Se atoms per unit cell at Se(1) are located opposite 6-rings in the sodalite cavity (Se(1)-Na(1) = 2.53(5) Å) and 1 at Se(2) opposite 4-rings (Se(2)-O(1) = 2.76(10) Å) and 1 at Se(3) opposite 6-rings in the large cavity (Se(3)-Na(1) = 2.48(5) Å). Two molecular of Se₂ (Se(1)-Se(1) = 2.37(7) or 2.90(8) Å and Se(2)-Se(3) = 2.91(5) ) Å) are found in all sodalite cavity and large cavity. Other clusters such as Se₄ and Se₈ could be existed in large cavity. The inter-selenium distances turned out to be longer that of gases Se₂ molecule.

• The Pure and Applied Mathematics
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• v.30 no.3
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• pp.337-345
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• 2023

Different versions of the boundary Schwarz lemma for the 𝒩 (𝜌) class are discussed in this study. Also, for the function g(z) = z+b₂z²+b₃z³+... defined in the unit disc D such that g ∈ 𝒩 (𝜌), we estimate a modulus of the angular derivative of g(z) function at the boundary point 1 ∈ 𝜕D with g'(1) = 1 + 𝜎 (1 - 𝜌), where ${\rho}={\frac{1}{n}}{\sum\limits_{i=1}^{n}}g(c_i)={\frac{g^{\prime}(c_1)+g^{\prime}(c_2)+{\ldots}+g^{\prime}(c_n)}{n}}{\in}g^{\prime}(D)$ and 𝜌≠1, 𝜎 > 1 and c₁, c₂, ..., c_n ∈ 𝜕D. That is, we shall give an estimate below |g"(1)| according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and z ≠ 0. Estimating is made by using the arithmetic average of n different derivatives g'(c₁), g'(c₂), ..., g'(c_n).

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1025-1039
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• 2022

For given non-negative real numbers 𝛼_k with ∑^m_k=1 𝛼_k = 1 and normalized analytic functions f_k, k = 1, …, m, defined on the open unit disc, let the functions F and Fn be defined by F(z) := ∑^m_k=1 𝛼_kf_k(z), and F_n(z) := n^-1 ∑^n-1_j=0 e^-2j𝜋i/nF(e^2j𝜋i/nz). This paper studies the functions f_k satisfying the subordination zf'_k(z)/F_n(z) ≺ h(z), where the function h is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

• Bulletin of the Korean Chemical Society
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• v.26 no.1
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• pp.146-150
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• 2005

Two new barium vanadium borophosphate compounds, $(NH_4)_2(C_2H_{10}N_2)_6[Ba(H_2O)_5]_2[V_2P_2BO_{12}]_6{\cdot}8H_2O$, Ba- VBPO1 and $(NH_4)_8(C_3H_{12}N_2)_4[Ba(H_2O)_7][V_2P_2BO_{12}]_6{\cdot}17H_2O$, Ba-VBPO2 have been synthesized by interdiffusion methods in the presence of diprotonated ethylenediamine and 1,3-diaminopropane. Compound Ba-VBPO1 has an infinite chain anion (${[BaH_2O)_5]_2[V_2P_2BO_{12}]_6}$$^{14-}$, whereas Ba-VBPO2 has a discrete cluster anion {[$Ba(H_2O)_7][V_2P_2BO_{12}]_6$}$^{16-}$. Crystal Data: $(NH_4)_2(C_2H_{10}N_2)_6[Ba(H_2O)_5]_2[V_2P_2BO_{12}]_6{\cdot}8H_2O$, triclinic, space group P$\overline{1}$ (no. 2), a = 13.7252(7) $\AA$, b = 15.7548(8) $\AA$, c = 15.8609(8) $\AA$, α = 63.278(1)$^{\circ}$, $\beta$ = 75.707(1)$^{\circ}$, $\gamma$ = 65.881(1)$^{\circ}$, Z = 1; $(NH_4)_8(C_3H_{12}N_2)_4[Ba(H_2O)_7][V_2P_2BO_{12}]_6{\cdot}17H_2O$, monoclinic, space group C2/c (no. 15), a = 31.347(2) $\AA$, b = 17.1221(9) $\AA$, c = 22.3058(1) $\AA$, $\beta$ = 99.303(1)$^{\circ}$, Z = 4.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.9-17
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• 2016

In this paper, it has been shown that the hairy cycle C_n ⊙ rK₁, n ≡ 3(mod4), the graph obtained by adding pendant edge to each pendant vertex of hairy cycle C_n ⊙ 1K₁, n ≡ 0(mod4), double graph of path P_n and double graph of comb P_n ⊙ 1K₁ are k-graceful.

• Korean Journal of Clinical Laboratory Science
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• v.54 no.3
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• pp.179-191
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• 2022

Carbapenem-resistant Enterobacteriaceae (CRE) poses an increasing public health threat and has limited treatment options with high associated mortality. Genotypes of carbapenemase that threaten public health (bla_KPC, bla_NDM, bla_IMP, and bla_VIM) and bla_OXA-48-like genes were detected by phenotypic and molecular diagnosis, and related gene distribution patterns were investigated. Phenotypic testing using the modified Hodge test confirmed positivity in all 41 strains examined, and carbapenemase inhibitory testing using meropenem+phenyl boronic acid or meropenem+EDTA confirmed positivity in 18 and 8 strains, respectively. Polymerase chain reaction revealed the presence of amplification products in 28 strains of bla_KPC, 25 strains of bla_NDM, 5 strains of bla_IMP, 1 strain of bla_VIM, and 13 bla_OXA-48-like strains. In addition, 7 strains of bla_KPC+bla_NDM, 1 strain of bla_KPC+bla_IMP, 1 strain of bla_NDM+bla_OXA-48-like, 1 strain of bla_NDM+bla_VIM, 4 strains of bla_KPC+bla_NDM+bla_IMP, and 4 strains of bla_KPC+bla_NDM+bla_OXA-48-like were identified. Melting curve analysis using real-time PCR was wholly consistent with PCR results. The study shows genetic identification of highly specific CRE by real-time PCR could be used to provide early diagnoses and infection control, improve surveillance, and prevent the transmission of CRE.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.29 no.6
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• pp.342-347
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• 2016

We investigated the effect of $Bi_{1/2}(Na_{0.82}K_{0.18})_{1/2}TiO_3$ (BNKT) modification on the ferroelectric and electric-field-induced strain (EFIS) properties of lead-free $0.97Bi_{1/2}(Na_{0.82}K_{0.18})_{1/2}TiO_3-0.03LaFeO_3$ (BNKTLF) ceramics as a function of BNKT content (x= 0, 0.1, 0.2, 0.3, 0.5, and 1). BNKT-modified BNKTLF powders were synthesized using a conventional solid-state reaction method. As the BNKT content x increased from 0 to 1 the normalized electric-field-induced strain ($S_{max}/E_{max}$) was observed to increase at relatively low fields, i.e., below the poling field. Moreover, BNKTLF-30BNKT showed about 460 pm/V as low as at 3 kV/mm, which is a considerably high value among the lead-free systems reported so far. Consequently, it was confirmed that ceramic-ceramic composite, a mixture of an ergodic relaxor matrix and embedded ferroelectric seeds, is a salient way to make lead-free piezoelectrics practical with enhanced EFIS at low field as well as less hysterical.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.401-415
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• 2020

It is well-known that if char𝕜 = 0, then an Artinian monomial complete intersection quotient 𝕜[x₁, …, x_n]/(x₁^a₁, …, x_n^a_n) has the strong Lefschetz property in the narrow sense, and it is decomposed by the direct sum of irreducible 𝖘𝖑₂-modules. For an Artinian ring A = 𝕜[x₁, x₂, x₃]/(x₁⁶, x₂⁶, x₃⁶), by the Schur-Weyl duality theorem, there exist 56 trivial representations, 70 standard representations, and 20 sign representations inside A. In this paper we find an explicit basis for A, which is compatible with the S₃-module structure.

• Journal of Sensor Science and Technology
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• v.17 no.6
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• pp.418-424
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• 2008

The PZT based piezoelectric thick films prepared by screen printing method have been mainly used as a functional material for MEMS applications due to their compatibility of MEMS process. However the screen printed thick films generally reveal poor electrical and mechanical properties because of their porous microstructure. To improve microstructure we mixed attrition milled powder with ball milled powder of 0.01Pb$(Mg_{1/2}W_{1/2})O_3$-0.41Pb$(Ni_{1/3}Nb_{2/3})O_3$-$0.35PbTiO_3$-$0.23PbZrO_3$+0.1 wt% ${Y_2}{O_3}$+1.5 wt% ZnO composition. By mixing 25 % of attrition milled powder and 75 % of ball milled powder, the broadest particle size distribution was obtained, leading to a dense thick film with crack-free microstructure and improved dielectric properties. The X-ray diffraction analysis revealed that the film was in wellcrystallized perovskite phase. The remanent polarization was increased from $13.7{\mu}C/cm^2$ to $23.3{\mu}C/cm^2$ at the addition of 25 % attrition milled powder.