• Journal of the Korean Magnetic Resonance Society
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• v.20 no.1
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• pp.1-6
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• 2016

The proton NMR line widths and spin-lattice relaxation rates, $T_1^{-1}$, of ferroelectric $LiH_3(SeO_3)_2$, $Li_2SO_4{\cdot}H_2O$, and $LiN_2H_5SO_4$ single crystals were measured as a function of temperature. The line width measurements reveal rigid lattice behavior of all the crystals at low temperatures and line narrowing due to molecular motion at higher temperatures. The temperature dependences of the proton $T_1^{-1}$ for these crystals exhibit maxima, which are attributed to the effects of molecular motion by the Bloembergen - Purcell - Pound theory. The activation energies for the molecular motions of $^1H$ in these crystals were obtained. From these analysis, $^1H$ in $LiH_3(SeO_3)_2$ undergoes molecular motion more easily than $^1H$ in $LiN_2H_5SO_4$ and $Li_2SO_4{\cdot}H_2O$ crystals.

• Membrane Journal
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• v.33 no.3
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• pp.94-109
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• 2023

1,3-Dioxolane is an exciting material that has attracted widespread interest in the chemical, paint, and pharmaceutical industries as a solvent, electrolyte, and reagent because 1,3-dioxolane is not toxic, carcinogenic, explosive, auto-flammable, and multifunctional, and due to their excellent miscibility in most organic and aqueous solvent conditions. Recently, this material has received increasing attention as a CO₂-selective polymer precursor to separating CO₂ from flue gas and natural gas mixtures. Poly(1,3-dioxolane) (PDXL) possesses higher ether oxygen content than polyethylene oxide (PEO), which demonstrates superior membrane CO₂/N₂ separation properties owing to their polar ether oxygen groups exhibiting strong affinity toward CO₂. Thus, PDXL-based membranes displayed an outstanding CO₂ solubility selectivity over non-polar (N₂, H₂, and CH₄) gases. However, the polar groups of PDXL, like PEO, promote chain packing efficiency and cause polymer crystallization, thereby reducing its gas permeability, which should be improved. In this short review, we discuss the recent advancement and limitations of PDXL membranes in gas separation applications. To conclude, we provide future perspectives for inhibiting the limits of 1,3-dioxolane-based polymers in the CO₂ separation process.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.371-399
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• 2020

Let P_s := 𝔽₂[x₁, x₂, …, x_s] = ⊕_n⩾0(P_s)_n be the polynomial algebra viewed as a graded left module over the mod 2 Steenrod algebra, ${\mathfrak{A}}$. The grading is by the degree of the homogeneous terms (P_s)_n of degree n in the variables x₁, x₂, …, x_s of grading 1. We are interested in the hit problem, set up by F. P. Peterson, of finding a minimal system of generators for ${\mathfrak{A}}$-module P_s. Equivalently, we want to find a basis for the 𝔽₂-graded vector space ${\mathbb{F}}_2{\otimes}_{\mathfrak{A}}$ P_s. In this paper, we study the hit problem in the case s = 5 and the degree n = 5(2^t - 1) + 6 · 2^t with t an arbitrary positive integer.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.407-417
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• 2020

Let (R, m) be a d-dimensional Cohen-Macaulay local ring with infinite residue field. Let I be an ideal of R that has analytic spread ℓ(I) = d, satisfies the G_d condition, the weak Artin-Nagata property AN^-_d-2 and m is not an associated prime of R/I. In this paper, we show that if j₁(I) = λ(I/J) + λ[R/(J_d-1 :_RI+(J_d-2 :_RI+I):_R m^∞)] + 1, then I has almost minimal j-multiplicity, G(I) is Cohen-Macaulay and r_J(I) is at most 2, where J = (x₁, _…, x_d) is a general minimal reduction of I and J_i = (x₁, _…, x_i). In addition, the last theorem is in the spirit of a result of Sally who has studied the depth of associated graded rings and minimal reductions for m-primary ideals.

• Communications of the Korean Mathematical Society
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• v.23 no.1
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• pp.61-65
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• 2008

In this paper we prove that every positive solution of the third order rational difference equation $$x_{n+1}\;=\;\frac{{\beta}x_n\;+\;x_{n-2}}{A\;+\;Bx_n\;+\;x_{n-2}}$ converges to the positive equilibrium point $$\bar{x}\;=\;\frac{{\beta}\;+\;1\;-\;A}{B\;+\;1}$, where $0\;<\;{\beta}\;{\leq}\;B$, $1\;<\;A\;<\;{\beta}\;+\;1$

• Transactions on Electrical and Electronic Materials
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• v.16 no.3
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• pp.130-134
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• 2015

This research proposes the use of a composition modulated (ZrO₂)_x(Al₂O₃)_1-x film as a charge trapping layer for charge trap flash memory; this is possible when the Zr (Al) atomic percent is controlled to form a variable bandgap as identified by the valence band offsets and electron energy loss spectrum measurements. Compared to memory devices with uniform compositional (ZrO₂)_0.1(Al₂O₃)_0.9 or a (ZrO₂)_0.92(Al₂O₃)_0.08 trapping layer, the memory device using the composition modulated (ZrO₂)_x(Al₂O₃)_1-x as the charge trapping layer exhibits a larger memory window (6.0 V) at the gate sweeping voltage of ±8 V, improved data retention, and significantly faster program/erase speed. Improvements of the memory characteristics are attributed to the special energy band alignments resulting from non-uniform distribution of elemental composition. These results indicate that the composition modulated (ZrO₂)_x(Al₂O₃)_1-x film is a promising candidate for future nonvolatile memory device applications.

• Journal of the Korean Society of Industry Convergence
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• v.25 no.5
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• pp.791-797
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• 2022

Using the fatigue limit (△σ_unsm) and residual stress (σ_r) of the UNSM smooth specimen, the harmless maximum crack depth (α_hml) according to the crack aspect ratio (As) was evaluated. α_hml evaluated the reliability in the relationship between the minimum crack depth (α_NDI1, α_NDI2) detectable by nondestructive inspection(NDI) and the crack depth (α₂₅, α₅₀) that reduces the fatigue limit by 25% and 50%. All α_hml was determined by the crack depth. The α_hml of 80N UNSM with high σ_r and high △σ_unsm was found to be large. σ_r in the depth direction had a much effect on α_hml. Since α_hml>α₅₀(As=0.6-0.1) and α_hml>α₂₅, α₂₅ and α₅₀(some range) can secure the safety and reliability. Since α_hml<α₅₀ (As=1. 0-0. 6), it cannot be made harmless by UNSM. So safety and reliability cannot be secured. α_NDI1 and α_NDI2 are larger than α₂₅, α₂₅ cannot be detected by NDI. α_NDI1 and α_NDI2 are smaller than α₅₀, α₂₅ can detected by NDI.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.429-441
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• 2020

Let M(X, Y) denote the space of multipliers from X to Y, where X and Y are analytic function spaces. As we known, for Dirichlet-type spaces 𝓓_α^p, M(𝓓_p-1^p, 𝓓_q-1^q) = {0}, if p ≠ q, 0 < p, q < ∞. If 0 < p, q < ∞, p ≠ q, 0 < s < 1 such that p + s, q + s > 1, then M(𝓓_p-2+s^p, 𝓓_q-2+s^q) = {0}. However, X ∩ 𝓓_p-1^p ⊆ X ∩ 𝓓_q-1^q and X ∩ 𝓓_p-2+s^p ⊆ X ∩ 𝓓_q-2+s^p whenever X is a subspace of the Bloch space 𝓑 and 0 < p ≤ q < ∞. This says that the set of multipliers M(X ∩ 𝓓 _p-2+s^p, X∩𝓓_q-2+s^q) is nontrivial. In this paper, we study the multipliers M(X ∩ 𝓓_p-2+s^p, X ∩ 𝓓_q-2+s^q) for distinct classical subspaces X of the Bloch space 𝓑, where X = 𝓑, BMOA or 𝓗^∞.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.571-595
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• 2021

In this paper we study the algebraic structure of ℤ_pℤ_p[u]/k>-cyclic codes, where u^k = 0 and p is a prime. A ℤ_pℤ_p[u]/k>-linear code of length (r + s) is an R_k-submodule of ℤ^r_p × R^s_k with respect to a suitable scalar multiplication, where R_k = ℤ_p[u]/k>. Such a code can also be viewed as an R_k-submodule of ℤ_p[x]/r - 1> × R_k[x]/s - 1>. A new Gray map has been defined on ℤ_p[u]/k>. We have considered two cases for studying the algebraic structure of ℤ_pℤ_p[u]/k>-cyclic codes, and determined the generator polynomials and minimal spanning sets of these codes in both the cases. In the first case, we have considered (r, p) = 1 and (s, p) ≠ 1, and in the second case we consider (r, p) = 1 and (s, p) = 1. We have established the MacWilliams identity for complete weight enumerators of ℤ_pℤ_p[u]/k>-linear codes. Examples have been given to construct ℤ_pℤ_p[u]/k>-cyclic codes, through which we get codes over ℤ_p using the Gray map. Some optimal p-ary codes have been obtained in this way. An example has also been given to illustrate the use of MacWilliams identity.

• Journal of Electrochemical Science and Technology
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• v.13 no.2
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• pp.292-307
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• 2022

The study presents kinetics of degradation and mineralization of an anti-epileptic drug Lamotrigine (LAM) in the aqueous matrix by electrochemical advanced oxidation process (EAOP) on Ti/DSA (Ta₂O₅-Ir₂O₅) and Stainless Steel (SS) anodes using sodium sulphate as supporting electrolyte. On both the anodes, kinetic behaviour was pseudo-first-order for degradation as well as mineralization of LAM. On Ti/DSA anode, maximum LAM degradation of 75.42% was observed at an associated specific charge of 3.1 (Ah/litre) at a current density of 1.38 mA/cm² and 100 ppm Na₂SO₄ concentration. Maximum mineralization attained was 44.83% at an associated specific charge of 3.1 (Ah/litre) at a current density of 1.38 mA/cm² and 50 ppm concentration of Na₂SO₄ with energy consumption of 2942.71 kWh/kgTOC. Under identical conditions on SS anode, a maximum of 98.92% LAM degradation was marked after a specific charge (Q) of 3.1 (Ah/litre) at a current density of 1.38 mA/cm² and 100 ppm concentration of Na₂SO₄. Maximum LAM mineralization on SS anode was 98.53%, marked at a specific charge of 3.1 (Ah/litre) at a current density of 1.38 mA/cm² and 75 ppm concentration of Na₂SO₄, with energy consumption of 1312.17 kWh/kgTOC. Higher Mineralization Current Efficiency (MCE) values were attained for EAOP on SS anode for both degradation and mineralization due to occurrence of combined electro-oxidation and electro-coagulation process in comparison to EAOP on Ti/DSA anode due to occurrence of lone electro-oxidation process.