• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.869-881
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• 2011

The main goal in the present paper is to obtain a necessary and sufficient condition for a new connection with zero torsion vector to be an Einstein's connection and derive some useful representation of the vector defining the Einstein's connection in even-dimensional UFT $X_n$.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.735-744
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• 2024

In this note, we shed new light on Krull domains from the point view of Gorenstein homological algebra. By using the so-called w-operation, we show that an integral domain R is Krull if and only if for any nonzero proper w-ideal I, the Gorenstein global dimension of the w-factor ring (R/I)_w is zero. Further, we obtain that an integral domain R is Dedekind if and only if for any nonzero proper ideal I, the Gorenstein global dimension of the factor ring R/I is zero.

• Proceedings of the Korean Institute of Surface Engineering Conference
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• 2012.05a
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• pp.148-149
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• 2012

As one of zero-expansion coefficient materials $Al_2TiO_5$ ceramics was prepared and the thermal shock-resistance was investigated by using DV-X analysis. In this report the mechanism of thermal shock-resistance and low mechanical strength.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.929-949
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• 2022

Given an ACM set 𝕏 of points in a multiprojective space ℙ^m×ℙⁿ over a field of characteristic zero, we are interested in studying the Kähler different and the Cayley-Bacharach property for 𝕏. In ℙ¹×ℙ¹, the Cayley-Bacharach property agrees with the complete intersection property and it is characterized by using the Kähler different. However, this result fails to hold in ℙ^m×ℙⁿ for n > 1 or m > 1. In this paper we start an investigation of the Kähler different and its Hilbert function and then prove that 𝕏 is a complete intersection of type (d₁, …, d_m, d'₁, …, d'_n) if and only if it has the Cayley-Bacharach property and the Kähler different is non-zero at a certain degree. We characterize the Cayley-Bacharach property of 𝕏 under certain assumptions.

• Korean Journal of Materials Research
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• v.32 no.2
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• pp.66-71
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• 2022

In this article, Pb₂Ba_1.7Sr_0.3Ca₂Cu₃O_10+δ superconductor material was synthesized using conventional solid-state reaction method. X-ray diffraction (XRD) analysis demonstrated one dominant phase 2223 and some impurities in the product powder. The strongest peaks in the XRD pattern were successfully indexed assuming a pseudo-tetragonal cell with lattice constants of a = 3.732, b = 3.733 and c = 14.75 Å for a Pb-Based compound. The crystallite size and lattice strain between the layers of the studied compound were estimated using several methods, namely the Scherrer, Williamson-Hall (W.H), size-strain plot (SSP) and Halder Wagner (H.W) approach. The values of crystallite size, calculated by Scherrer, W.H, SSP and H.W methods, were 89.4540774, 86.658638, 87.7555823 and 85.470086 Å, respectively. Moreover, the lattice strain values obtained by W.H, SSP and H.W methods were 0.0063240, 0.006325 and 0.006, respectively. It was noted that all crystallite size results are consistent; however, the best method is the size-strain plot because it gave a value of R² approaching one. Furthermore, degree of crystallites was calculated and found to be 59.003321%. Resistivity analysis suggests zero-resistance, which is typical of superconducting materials at critical temperature. Four-probe technique was utilized to measure the critical temperature at onset T_c(onset), zero resistivity T_{c(off set)}, and transition (width ΔT), corresponding to temperatures of 128 K, 116 K, and 12 K, respectively.

• Journal of the Korean Chemical Society
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• v.55 no.6
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• pp.905-911
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• 2011

The possible minimum structures of $C_{60}(CH_2)_nOH$ (n=0~2) and $C_{60}(OH)_2$have been optimized using density functional theory (DFT) with the 6-311G (d,f) basis set. The harmonic vibrational frequencies and IR intensities are also determined to confirm that all the optimized geometries are true minima. Also zero-point vibrational energies (ZPVE) have been considered to predict the binding energies. The predicted binding energy of $C_{60}CH_2OH$ is about 10 kcal/mol more stable than the binding energy of $C_{60}OH$.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.621-634
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• 2022

The scaled inverse of a nonzero element a(x) ∈ ℤ[x]/f(x), where f(x) is an irreducible polynomial over ℤ, is the element b(x) ∈ ℤ[x]/f(x) such that a(x)b(x) = c (mod f(x)) for the smallest possible positive integer scale c. In this paper, we investigate the scaled inverse of (xⁱ - x^j) modulo cyclotomic polynomial of the form Φ_p^s (x) or Φ_p^sq^t (x), where p, q are primes with p < q and s, t are positive integers. Our main results are that the coefficient size of the scaled inverse of (xⁱ - x^j) is bounded by p - 1 with the scale p modulo Φ_p^s (x), and is bounded by q - 1 with the scale not greater than q modulo Φ_p^sq^t (x). Previously, the analogous result on cyclotomic polynomials of the form Φ_2ⁿ (x) gave rise to many lattice-based cryptosystems, especially, zero-knowledge proofs. Our result provides more flexible choice of cyclotomic polynomials in such cryptosystems. Along the way of proving the theorems, we also prove several properties of {x^k}_k∈ℤ in ℤ[x]/Φ_pq(x) which might be of independent interest.

• International Journal of Naval Architecture and Ocean Engineering
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• v.10 no.6
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• pp.670-682
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• 2018

This paper presents the experimental and numerical investigation results of the response of low-temperature steel (LT-FH32 grade steel) beams under repeated impacts at room temperature and a single impact at a sub-zero temperature. After conducting tensile tests at room and sub-zero, repeated impact tests were conducted on two clamped single-beam models at room temperature, and single-impact tests of two other clamped single-beam models were conducted at $-50^{\circ}C$. The single and repeated impact tests were conducted by releasing a knife-edge striker using a drop testing machine. The permanent deflection of the model measured after each impact gradually increased with increasing number of impacts. Under the reduced temperature, the permanent deflection of the models slightly decreased. The numerical analyses were also performed to predict the damage response of the tested single-beam models. A comparison of the numerical prediction with those of experiments showed quite reasonable agreement.

• Journal of the Korean Chemical Society
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• v.54 no.6
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• pp.671-679
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• 2010

The geometrical parameters and binding energies of the benzene ion-water complex [$C_6H_6^+-(H_2O)_n$(n=1-5)] have been investigated using ab initio (MP2) and density functional theory (DFT) with large basis sets. The harmonic vibrational frequencies and IR intensities are also determined to confirm that all the optimized geometries are true minima. Also zero-point vibrational energies have been considered to predict the binding energies. The predicted binding energy of 8.6 kcal/mol for $C_6H_6^+-(H_2O)$ at the MP2/aug-cc-pVTZ level of theory is in excellent agreement with recent experimental result of $8.5{\pm}1$ kcal/mol.

• Korean Journal of Materials Research
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• v.23 no.6
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• pp.329-333
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• 2013

The structural phase transformations of $0.7Pb(Mg_{1/3}Nb_{2/3})O_3-0.3PbTiO_3$ (PMN-0.3PT) were studied using high resolution x-ray diffraction (HRXRD) as a function of temperature and electric field. A phase transformational sequence of cubic (C)${\rightarrow}$tetragonal (T)${\rightarrow}$rhombohedral (R) phase was observed in zero-field-cooled conditions; and a $C{\rightarrow}T{\rightarrow}$monoclinic $(M_C){\rightarrow}$ monoclinic ($M_A$) phase was observed in the field-cooled conditions. The transformation of T to $M_A$ phase was realized through an intermediate $M_C$ phase. The results also represent conclusive and direct evidence of a $M_C$ to $M_A$ phase transformation in field-cooled conditions. Beginning from the zero-field-cooled condition, a $R{\rightarrow}M_A{\rightarrow}M_C{\rightarrow}T$ phase transformational sequence was found with an increasing electric field at a fixed temperature. Upon removal of the field, the $M_A$ phase was stable at room temperature. With increasing the field, the transformation temperature from T to $M_C$ and from $M_C$ to $M_A$ phase decreased, and the phase stability ranges of both T and $M_C$ phases increased. Upon removal of the field, the phase transformation from R to $M_A$ phase was irreversible, but from $M_A$ to $M_C$ was reversible, which means that $M_A$ is the dominant phase under the electric field. In the M phase region, the results confirmed that lattice parameters and tilt angles were weakly temperature dependent over the range of investigated temperatures.