• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.409-431
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• 2022

In this paper, we deal with the existence of solutions of the following system of nonlinear rational difference equations with order five $x_{n+1}=\frac{y_{n-3}x_{n-4}}{y_n(a+by_{n-3}x_{n-4})}$, $y_{n+1}=\frac{x_{n-3}y_{n-4}}{x_n(c+dx_{n-3}y_{n-4})}$, n = 0, 1, ⋯, where parameters a, b, c and d are not executed at the same time and initial conditions x_-4, x_-3, x_-2, x_-1, x₀, y_-4, y_-3, y_-2, y_-1 and y₀ are non zero real numbers.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.381-403
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• 2021

Consider the three-dimensional system of difference equations $x_{n+1}=\frac{{\prod_{j=0}^{k}}z_n-3j}{{\prod_{j=1}^{k}}x_n-(3j-1)\;\(a_n+b_n{\prod_{j=0}^{k}}z_n-3j\)}$, $y_{n+1}=\frac{{\prod_{j=0}^{k}}x_n-3j}{{\prod_{j=1}^{k}}y_n-(3j-1)\;\(c_n+d_n{\prod_{j=0}^{k}}x_n-3j\)}$, $z_{n+1}=\frac{{\prod_{j=0}^{k}}y_n-3j}{{\prod_{j=1}^{k}}z_n-(3j-1)\;\(e_n+f_n{\prod_{j=0}^{k}}y_n-3j\)}$, n ∈ ℕ₀, where k ∈ ℕ₀, the sequences $(a_n)_{n{\in}{\mathbb{N}}_0$, $(b_n)_{n{\in}{\mathbb{N}}_0$, $(c_n)_{n{\in}{\mathbb{N}}_0$, $(d_n)_{n{\in}{\mathbb{N}}_0$, $(e_n)_{n{\in}{\mathbb{N}}_0$, $(f_n)_{n{\in}{\mathbb{N}}_0$ and the initial values x_-3k, x_-3k+1, …, x₀, y_-3k, y_-3k+1, …, y₀, z_-3k, z_-3k+1, …, z₀ are real numbers. In this work, we give explicit formulas for the well defined solutions of the above system. Also, the forbidden set of solution of the system is found. For the constant case, a result on the existence of periodic solutions is provided and the asymptotic behavior of the solutions is investigated in detail.

• 한국분말재료학회지
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• 제6권1호
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• pp.18-35
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• 1999

Phase equilibria in the system Si3N4-TiC-TiCxN1-x-C-N were determined by thermodynamic calculations (CALPHAD-method). The reaction peaction paths for Si3N4-TiC and SiC-TiC composites in the Ti-Si-C-n system were simulated at I bar N2-pressure and varying terpreatures. At a temperature of 1923 K two tie-triangles (TiC0.34N0.66+SiC+C and TiC0.13N0.87+SiC+Si3N4) and two 2-phase fieds (TiCxN1-x+SiC; 0.13

• 한국분말야금학회:학술대회논문집
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• 한국분말야금학회 2006년도 Extended Abstracts of 2006 POWDER METALLURGY World Congress Part2
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• pp.959-960
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• 2006

Li reacts with $N_2$ at room temperature. In order to activate Li, the mechanical milling of Li with stable metal oxide, namely, $Al_2O_3$ and MgO, using a high energy vibrating ball mill was performed. In the case of Li-MgO system, it reacts with $N_2$, but hardly reacts with $O_2$. The reaction with $N_2$ generally produces $Li_3N$, while for some vigorous reactions the $Mg_3N_2$ is produced as the major phases. In the case of $Li-Al_2O_3$ system, reactivities with both $N_2$ and $O_2$ are high. The difference is explained in terms of the reaction mechanism and the Li state.

• Journal of Electrical Engineering and Technology
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• 제13권2호
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• pp.943-952
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• 2018

This paper presents a new type of absolute rotary encoder system based on the affine n-digit N-ary gray code. A brief comparison of the existing encoder systems is carried out in terms of resolution, encoding and decoding principles and number of sensor heads needed. Using the proposed method, two different types of encoder disks are designed, namely, color-coded disk and grayscale coded disk. The designed coded disk pattern is used to manufacture 3 digit 3 ary and 2 digit 5 ary grayscale coded disks respectively. The manufactured disk is used with the light emitter and photodetector assembly to design the entire encode system. Experimental analysis is done on the designed prototype with LabVIEW platform for data acquisition. A comparison of the designed system is done with the traditional binary gray code encoder system in terms of resolution, disk diameter, number of tracks and data acquisition system. The resolution of the manufactured system is 3 times higher than the conventional system. Also, for a 5 digit 5 ary coded encoder system, a resolution approximately 100 times better than the conventional binary system can be achieved. In general, the proposed encoder system gives $(N/2)^n$ times better resolution compared with the traditional gray coded disk. The miniaturization in diameter of the coded disk can be achieved compared to the conventional binary systems.

• 한국세라믹학회지
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• 제41권3호
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• pp.235-242
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• 2004

원재료로서 Si, NH$_4$Cl, NaN$_3$, NaCl을 사용하고 SHS법을 이용하여 $\alpha$-Si$_3$N$_4$ 분말을 제조하였다. NH$_4$Cl과 NaN$_3$는 첨가제로서, NaCl은 희석제로서 사용되었고 반응기내 최초 $N_2$ 압력은 60 atm이었다. $\alpha$-Si$_3$N$_4$분말을 제조함에 있어, 첨가제의 종류와 조성, 희석제의 첨가량에 따른 반응성 및 생성물의 특성을 조사하였는데, 우선 $\alpha$-Si$_3$N$_4$ 분말의 제조를 위한 최적의 반응계를 조사하였고, 최적의 반응계에서 최적의 조성을 확립하였다. 최적의 반응계는 Si-$N_2$-additive(NH$_4$C+NaN$_3$)-diluent(NaCl)이었고, 이때 최적의 조성은 38wt%Si+22.5wt%NH$_4$Cl+27.5wt%NaN$_3$+l2wt%NaCl이었다. 이 조건에서 생성된 최고 $\alpha$-Si$_3$N$_4$의 분율은 96.5wt%이었으며 생성된 분말의 입형은 길이가 약 10 $mu extrm{m}$이고 직경이 약 1 $\mu\textrm{m}$인 일방향으로 길게 성장한 부정형의 fiber 형태였다.

• 한국세라믹학회지
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• 제24권1호
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• pp.23-32
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• 1987

Synthesis of high purity ultrafine Si3N4 and ${\beta}$-Sialon powders was investigated via the simultaneous reduction and nitriding of amorphous SiO2, SiO2-Al2O3 system prepaerd by hydrolysis of alkoxides, using carbonablack as a reducing agent. In Si(OC2H5)4-C2H5 OH-H2 O-NH4OH system, hydrolysis rate increased with increasing reaction temperature and pH. Pure ${\alpha}$-Si3N4 was formed at 1350$^{\circ}C$ for 5 hrs in N2 atmosphere. In Si(OC2H5)4-Al(OC3H7)3-C6H6-H2 O-NH4OH system, weight loss increased as Si/Al ratio decreased. Single phase ${\beta}$-Sialon consisted of Si/Al=2 was formed at 1350$^{\circ}C$ in N2 and minor phases of ${\alpha}$-Si3N4, AIN, and X-phase were existed besides theSialon phase at other Si/Al ratios. The Si3N4 and Sialon powders synthesized from alkoxides consisted of uniform find particles of 0.05-0.2$\mu\textrm{m}$ in diameter, respectively.

• 한국화재소방학회논문지
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• 제24권2호
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• pp.139-144
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• 2010

본 연구에서는 산업용으로 일반적으로 사용하고 있는 질소발생기를 사용하여 할론 계열의 소화약제를 대체할 청정소화설비로 적용할 수 있는지에 대한 소화성능 실험을 간단히 수행하였다. 산업용 질소발생기의 소화성능을 분석하기 위하여 간단한 방호구역을 제작하여 실제 질소발생기에서 발생하는 질소가스를방사하면서 방호구역 내의 산소농도 변화를 실험적으로 파악하였다. 실험결과, 현재 많이 사용하고 있는 질소발생기로 방호구역 $100m^3$에 대하여 질소가스를 $5m^3$/min로 방사하면 3분 이내에 방호구역 내의 산소 농도를 15% 이내로 낮추어 질식소화가 충분히 가능하다.

• 한국환경과학회지
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• 제12권4호
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• pp.427-437
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• 2003

An evaluation of the application of SBR and biofilm en small sewerage system was conducted. A newly developed small sewerage system, using SBR, was successfully applied to the nutrient treatment using municipal wastewater. The system was consisted of 6 compartments. Two systems, with SBR (A type) or without SBR (B type), were compared by several parameters (COD, SS, T-N, NH$_4$$\^$+/-N, NO$_3$$\^$-/-N, NO$_2$$\^$ -/-N, alkalinity, pH, DO) in all experimental periods. Also, the time variation of several parameters (DO, pH, NH$_4$$\^$+/-N, NO$_3$$\^$-/-N NO$_2$$\^$-/-N) was examined in a SBR applied sewerage system. T-N removal efficiency of B type Was higher than that Of A type by the effect of nitrification and denitrification even though the COD removal efficiencies were similar. In aeration stage, the pH was decreased from 6.4 to 6.3 within 1 h and increased to 6.65 at the end of aerobic stage, and pH was decreased to 6.2 in non-aeration stage, and these phenomena were explained. The effects of nitrification and denitrification were compared in A type and B type sewerage system, and the typical nitrification and denitrification were observed in B type sewerage system.

• Communications for Statistical Applications and Methods
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• 제5권2호
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• pp.353-359
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• 1998

Factorial designs with two-level factors represent the smallest factorial experiments. The system of notation and confounding and fractional factorial schemes developed for the $2^N$system are found in standard textbooks of experimental designs. Just as in the $2^N$ system, the general confounding and fractional factorial schemes are possible in $3^N,5^N$, .... , and $\rho^N$ where $\rho$ is a prime number. Hence, we have the $\rho^N$ system. In this article, the author proposes a new algorithm for constructing fractional factorial plans in the $\rho^N$ system.