• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.907-915
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• 2024

Let f be an integral quadratic form in k variables, F the Gram matrix corresponding to a ℤ-basis of ℤ^k. For r ∈ F^-1ℤ^k, a rational number n with f(r) ≡ n mod ℤ and a positive integer c, set N_f(n, r; c) := #{x ∈ ℤ^k/cℤ^k : f(x + r) ≡ n mod c}. Siegel showed that for each prime p, there is a number w depending on r and n such that N_f(n, r; p^ν+1) = p^k-1N_f(n, r; p^ν) holds for every integer ν > w and gave a rough estimation on the upper bound for such w. In this short note, we give a more explicit estimation on this bound than Siegel's.

• East Asian mathematical journal
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• v.32 no.1
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• pp.93-100
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• 2016

The generalized Gaussian image of a spacelike surface in $L^n$ lies in the indefinite positive quadric ${\mathbb{Q}}_+^{n-2}$ in the open submanifold ${\mathbb{C}}P_+^{n-1}$ of the complex projective space ${\mathbb{C}}P^{n-1}$. The purpose of this paper is to find out detailed information about ${\mathbb{Q}}_+^{n-2}{\subset}{\mathbb{C}}P_+^{n-1}$.

• Journal of the Korean Chemical Society
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• v.31 no.3
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• pp.207-214
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• 1987

Rates of solvblysis of benzyl chloride in ethanol-water mixtures have been measured at 30 and $40^{\circ}C$ under various pressures up 1.6 kbar. The plots of 1n k as a function of pressure are fitted to a second order function in p, and values of ${\Delta}V^{\neq}$and ${\Delta}{\beta}^{\neq}$ are obtained from the results. Also the values of various pseudo thermodynamic quantities were evaluated from the rate constants. The relationships of the 1n k to $Q_w$ or 1n $C_w$ indicate that the reaction proceeds through $S_N1$ mechanism. A comparison between the present and the previous results gives that the increasing order of ${\mid}{{\Delta}V_0}^{\neq}{\mid}$ and n-values are $p-Cl>p-H>p-CH_3$ and $p-CH_3>p-H.p-Cl$, respectively. From these results, it is believed substituent such as the $p-CH_3$group favors the $S_N1(1)$ character, while the p-Cl group leads to the $S_N1(2)$ character.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.53 no.10
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• pp.495-499
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• 2004

Characteristics of ohmic Ni/Si/Ni contacts to n-type 4H-SiC are investigated systematically. The ohmic contacts were formed by annealing Ni/Si/Ni sputtered sequentially The annealings were performed at 950℃ using RTP in vacuum ambient and N₂ ambient, respectively. The specific contact resistivity(p/sub c/), sheet resistance(R/sub s/), contact resistance (R/sub c/) transfer length(L/sub T/) were calculated from resistance(R/sub T/) versus contact spacing(d) measurements obtained from TLM(transmission line method) structure. While the resulting measurement values of sample annealed at vacuum ambient were p/sub c/ = 3.8×10/sup -5/Ω㎠, R/sub c/ = 4.9 Ω and R/sub T/ = 9.8 Ω, those of sample annealed at N₂ ambient were p/sub c/ = 2.29×10/sup -4/Ω㎠, R/sub c/ = 12.9 Ω and R/sub T/ = 25.8 Ω. The physical properties of contacts were examined using XRD 3nd AES. The results showed that nickel silicide was formed on SiC and Ni was migrated into SiC. This result indicates that Ni/Si/Ni ohmic contact would be useful in high performance electronic devices.

• Journal of Ginseng Research
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• v.20 no.3
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• pp.291-298
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• 1996

Free amino acid (FAA) compositions in the central part (pith-xylem : P-X) and the outer part (phloem-cortex : P-C) of root were investigated for P ginseng (P.g), p. quinque-folium (P.q) an, B P nutoginsen (P.n) by an amino acid analyzer. Total free amlno acids content (TFAA) was highest in p.맥 and lowest in p.n. The TFAA of P-Xs were higher than those of P-Cs in these Panax species except p.n. The higher the TFAA in P-X, the higher the ratio of TFAA in P-X to that in P-C. Seven- teen free amino acids and ammonia were identified, and four unknown peaks appeared before the usual amino acids eluted. The total aspartic acid equivalent of these unknown peaks was corresponded to 77% of known TFAA in P-C of p.n, 17% in P. n, and 7% in p.q. The pattern of unknown peaks of p.g was different from p.q and similar to P.n. In all samples six major amino acids and ammonia accounted for 90~95% of TFAA. Arginine was comprised from 29% (P.n) to 43% (P.g) by amole as amino acid and from 50 to 71% by amole as nitrogen (N amole) in TFAA. Ammonia was the second abundant one by amole and the third by Npmole. Histidine was the second by Npmole. Praline was one of major FAA in p.q. Pattern similarity of FAA composition (excluding Arg and Am) by simple correlation was closer between P-C of p.g and P-X of p.q than between both P-Xs and quite different between the P-X of p.g and that of p.n. The pattern similarities of major FAA percent abundance excluding Arg and Am were significant only between P-X and P-C of the same species. Arginine content (amole) had positive correlation (r=0.859, p=0.05) with Arg/Am among species. Ammonia content was higher than arginine in p.n. Tryptophan content was greatest in p.n among species and higher than lysine only in p.n. The ratios of TFAA to N(W/W) were in the range of 3.89~4.14 for TFAA and 3.61~3.92 for TFAA plus ammonia.

• Journal of the Korean Magnetics Society
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• v.5 no.5
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• pp.641-644
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• 1995

We have studied the effect of the nitrogen on the microstructure, thermomagnetic properties and corrosion resistance of Fe-Hf-C-N nanocrystalline thin films with high permeability and high saturation magnetization. These films were fabricated by reactive sputtering in $Ar+N_{2}$ plasma using an rf magnetron sputtering apparatus. As $P_{N2}$ increases, the microstructure changes from amorphous to crystalline $\alpha$-Fe phase and again returns to amorphous one. Spin wave stiffness constant increases with $P_{N2}$ until 5% $P_{N2}$, and then decreases with the further increase. This trend corresponds well with that of the microstructure with increasing $P_{N2}$. The Fe-Hf-C-N films with over 3% $P_{N2}$ show higher corrosion resistance than the N-free Fe-Hf-C films. The Fe-Hf-C-N films are considered to have high potentials for the head core materials suitable for high density recording systems, owing to their excellent soft magnetic properties and corrosion resistance.

• Korean Journal of Crystallography
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• v.12 no.3
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• pp.141-144
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• 2001

From the reaction of Na[Ga(N₃)₄] with PPh₃, an ionic compound [Ph₃P(OH)]/sup +/[N₃]/sup -/ (1) was isolated. Compound 1 was characterized by spectroscopy (¹H-NMR, /sup 13C{¹H}-NMR, and IR) and X-ray diffraction. Crystallographic data for 1 : orthorhombic space group P2₁2₁2₁, a = 10.491 (4) Å, b=11.603(5)Å, c=13.149(5)Å, Z=4, R(wR₂)=0.0547(0.0978).

• Journal of the Korean Institute of Telematics and Electronics
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• v.20 no.1
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• pp.22-26
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• 1983

P+N and P+NN+ solar cells with the area of 3.36 $\textrm{cm}^2$ were fabricated by thermal diffusion. Under the light intensity of 100 mW/$\textrm{cm}^2$, total area(active area) conversion efficiency was 13.4%(14.7%) for P+N cell fabricated by 15 min boron predeposition at 94$0^{\circ}C$ and 20 min annealing at 80$0^{\circ}C$, and 14.3%(15.6%) for P+NN+ cell processed by 15 min boron predeposition at 94$0^{\circ}C$ and 50 min annealing at 80$0^{\circ}C$ after 20 min back phosphorus diffusion at 1,05$0^{\circ}C$. The minority carrier lifetime in bulk of P+NN+ cells was increased about 2~3 times comparing with P+N cells because of guttering and BSF effect due to back phosphorus doping. The methods used for efficiency improvement were AR coating, Ag electroplating, back doping and fine grid pattern as well as the control of front doping profile.

• Journal of Energy Engineering
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• v.25 no.1
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• pp.48-55
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• 2016

The autoignition temperature (AIT) of a material is the lowest temperature at which the material will spontaneously ignite. The AIT is important index for the safe handling of flammable liquids which constitute the solvent mixtures. This study measured the AITs of n-hexanol+p-xylene system by using ASTM E659 apparatus. The AITs of n-hexanol and p-xylene system which constituted binary system were $275^{\circ}C$ and $557^{\circ}C$, respectively. The experimental AITs of n-hexanol+p-xylene system system were a good agreement with the calculated AITs by the proposed equations with a few A.A.D.(average absolute deviation).

• Journal of the Korean Institute of Gas
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• v.20 no.5
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• pp.1-8
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• 2016

The autoignition temperature (AIT) of a substance is the lowest temperature at which the vapor ignites spontaneously from the heat of the environment. The AIT is important index for the safe handling of flammable liquids which constitute the solvent mixtures in the process. This study measured the AITs of n-butanol+p-xylene mixture by using ASTM E659 apparatus. The AITs of n-butanol and p-xylene which constituted binary system were $340^{\circ}C$ and $557^{\circ}C$, respectively. The experimental AITs of n-butanol+p-xylene mixture were a good agreement with the calculated AITs by the proposed equations with a few A.A.D.(average absolute deviation).