• Journal of applied mathematics & informatics
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• v.40 no.3_4
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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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• v.39 no.3_4
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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.

• Journal of Powder Materials
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• v.6 no.1
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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

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09b
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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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• v.13 no.2
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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.

• Journal of the Korean Ceramic Society
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• v.41 no.3
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• pp.235-242
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• 2004

Si, NH$_4$Cl, NaN$_3$, NaCl, $N_2$ were used as raw materials for preparation of $\alpha$-Si$_3$N$_4$ powder. NH$_4$Cl and NaN$_3$ were used as additives, and NaCl was used as a diluent. Initial $N_2$ gas pressure in the SHS reactor was 60 atm. In preparation of $\alpha$-Si$_3$N$_4$, the reactivity and the properties of the products were examined with the various kinds of additives and the content of diluent. At first, the optimum reaction system for the preparation of $\alpha$-Si$_3$N$_4$ is examined and then the optimum composition was examined in the optimum reaction system. The optimum reaction system was Si-$N_2$-additive(NH$_4$Cl+NaN$_3$)-diluent(NaCl) and the optimum composition was 38 wt%Si+50 wt%(NH$_4$Cl+NaN$_3$)+12 wt%NaCl. The maximum fraction of $\alpha$-phase of Si$_3$N$_4$ produced in this condition was 96.5 wt% and the shape of the $\alpha$-Si$_3$N$_4$ produced in this condition was an irregular fiber with a length of 10 ${\mu}{\textrm}{m}$ and a diameter of 1 ${\mu}{\textrm}{m}$.

• Journal of the Korean Ceramic Society
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• v.24 no.1
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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.

• Fire Science and Engineering
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• v.24 no.2
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• pp.139-144
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• 2010

An experimental study has been carried out to investigate the possibilities of an industrial $N_2$ generator that it replace Halon series as a natural extinguishing system. And this study comparison design standard of gas series extinguishing system with natural extinguishing system. We manufactured simple protected enclosure for analyzing fire-extinguishing performance of the $N_2$ generator. As a $N_2$ gas is exhausted on protected enclosure, a various of Oxygen concentration is measured to analyze fireextinguishing performance experimentally. The results, in case of $100m^3$ protected enclosure and $5m^3$/min $N_2$ flow rate, the Oxygen concentration is decreased below 15% within 3 minutes. And so, the $N_2$ generator make full use of an suffocating extinguishing system.

• Journal of Environmental Science International
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• v.12 no.4
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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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• v.5 no.2
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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.