• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1051-1066
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• 2013

By utilizing known characterizations of ${\omega}$-Noetherian rings in terms of injective modules, we give more characterizations of ${\omega}$-Noetherian rings. More precisely, we show that a commutative ring R is ${\omega}$-Noetherian if and only if the direct limit of GV -torsion-free injective R-modules is injective; if and only if every R-module has a GV -torsion-free injective (pre)cover; if and only if the direct sum of injective envelopes of ${\omega}$-simple R-modules is injective; if and only if the essential extension of the direct sum of GV -torsion-free injective R-modules is the direct sum of GV -torsion-free injective R-modules; if and only if every $\mathfrak{F}_{w,f}(R)$-injective ${\omega}$-module is injective; if and only if every GV-torsion-free R-module admits an $i$-decomposition.

• Textile Coloration and Finishing
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• v.8 no.1
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• pp.15-25
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• 1996

Wool fabric and merino wool top were dyed with two dyes, C.I. Acid Red 13 and C.I. Direct Blue 1 in presence of hydrogen peroxide/glyoxal redox system at various conditions such as dyeing time, temperature and redox concentration. The pH of dye bath was 4.5 in buffer solution of $KH_{2}PO_{4}$ (0.1mol/1)/$Na_{2}HPO_{4}$ (0.1mol/1). Also dyeing of cotton fabric was carried out with C.I. Direct Blue 1 in absence or presence of redox system. The color depth(K/S) increased with redox concentration and dyeing temperature. The increases in dyeing rate and equilibrium dye exhaustion of Acid Acid 13 and Direct Blue 1 on wool fiber and fabric in the present of hydrogen peroxide/glyoxal have been caused by decreasing in pH value during dyeing process which due to the decomposition of hydrogen ion in glyoxal with the assistance of hydrogen peroxide. But the decreases in exhaustion of Direct Blue 1 on cotton may be attributed to repulsive interac ion between salt and salt.

• Korean Chemical Engineering Research
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• v.61 no.2
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• pp.175-188
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• 2023

Global interest in hydrogen energy is increasing as an eco-friendly future energy that can replace fossil fuels. Accordingly, a next-generation hydrogen production technology using microorganisms, nuclear power, etc. is being developed, while a lot of time and effort are still required to overcome the cost of hydrogen production based on fossil fuels. As a way to minimize greenhouse gas emissions in the hydrocarbon-based hydrogen production process, methane direct decomposition technology has recently attracted attention. In order to improve the economic feasibility of the process, the simultaneous production of value-added carbon materials with hydrogen can be one of the most essential aspects. For that purpose, various studies on catalysis related to the quality and yield of high-value carbon materials such as carbon nanotubes (CNTs). In terms of process technology, a number of the research and development of fluidized-bed reactors capable of continuous production and improved gas-solid contact efficiency has been attempted. Recently, methane direct decomposition technology using a fluidized bed has been developed to the extent that it can produce 270 kg/day of hydrogen and 1000 kg/day of carbon. Plus, with the development of catalyst regeneration, separation and recirculation technologies, the process efficiency can be further improved. This review paper investigates the recent development of catalysts and fluidized bed reactor for methane direct pyrolysis to identify the key challenges and opportunities.

• Applied Chemistry for Engineering
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• v.20 no.4
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• pp.453-458
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• 2009

Iron-containing TNU-9 zeolites were prepared by aqueous ion exchange in the range of Fe contents 0.6~3.3 wt%. Direct decomposition of $N_2O$ was performed varying $N_2O$ concentrations and reaction temperatures. Fe-TNU-9 zeolites used were characterized using XRD, $N_2$ sorption, SEM/EDX. A 2.7 wt% Fe-TNU-9 zeolite showed high activities and above this contents of Fe the effect of catalytic activity was little dominated. Fe-TNU-9 zeolites after ion exchange conserved their TNU-9 structure although the degree of crystallinity was decreased until ca. 60% in 3.1 wt% Fe-TNU-9 zeolite after ion exchange in 0.01 M Fe solution. The decrease in the degree of crystallinity could be correlated with the decrease of surface area and pore volume. The partial reaction order of $N_2O$ in the decomposition of $N_2O$ was dependent on the reaction temperature from 0.69 at $420^{\circ}C$ to 0.97 at $494^{\circ}C$. The activation energy of $N_2O$ was also dependent on the $N_2O$ concentration and its value is ranged to 34~43 kcal/mol.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.77-85
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• 2001

If an Azumaya algebra A is a homomorphic image of a finite group ring RG where G is a direct product of subgroups then A can be decomposed into subalgebras A(sub)i which are homomorphic images of subgroup rings of RG. This result is extended to projective Schur algebras, and in this case behaviors of 2-cocycles will play major role. Moreover considering the situation that A is represented by Azumaya group ring RG, we study relationships between the representing groups for A and A(sub)i.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.475-491
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• 2009

In [2], we identified the group of units of finite local rings $\mathbb{Z}_4[X]$/($X^k+2X^a$, $2X^r$) with certain restrictions on a. In this paper we find direct sum decomposition of the group of units of such rings without restrictions on a into cyclic subgroups by finding their generators. And further generalization is considered.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.295-311
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• 2009

The purpose of this paper is to identify the group of units of finite local rings of the types ${\mathbb{F}}_2[X]/(X^k)$ and ${\mathbb{Z}}_4[X]/I$, where I is an ideal. It turns out that they are 2-groups and we give explicit direct sum decomposition into cyclic subgroups of 2-power order and their generators.

• Journal of the Chungcheong Mathematical Society
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• v.1 no.1
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• pp.43-53
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• 1988

The main result of this paper is a characterization of almost projective modules over art in algebras by means of irreducible maps and almost split sequences. A module X is an almost projective module if and only if it has a presentation $0{\longrightarrow}L{\longrightarrow^{\alpha}}P{\longrightarrow}X{\longrightarrow}0$ with projective module P and irreducible maps ${\alpha}$. Let X be an injective almost projective non simple module and $0{\rightarrow}Dtr(x){\rightarrow}E{\rightarrow}X{\rightarrow}0$ be an almost split sequence. If $E=E_1{\oplus}E_2$ is a direct decomposition of indecomposable modules then ${\ell}(X)=3$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1501-1509
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• 2020

We discuss the decomposition of degree two basic cohomology for codimension four taut Riemannian foliation according to the holonomy invariant transversal almost complex structure J, and show that J is C^∞ pure and full. In addition, we obtain an estimate of the dimension of basic J-anti-invariant subgroup. These are the foliated version for the corresponding results of T. Draghici et al. [3].

• Proceedings of the KIEE Conference
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• 2006.07d
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• pp.1832-1833
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• 2006

This paper presents a design method of the wavelet neural network(WNN) controller based on a direct adaptive control scheme for the intelligent control of Autonomous Underwater Vehicle(AUV) steering systems. The neural network is constructed by the wavelet orthogonal decomposition to form a wavelet neural network that can overcome nonlinearities and uncertainty. In our control method, the control signals are directly obtained by minimizing the difference between the reference track and original signal of AUV model that is controlled through a wavelet neural network. The control process is a dynamic on-line process that uses the wavelet neural network trained by gradient-descent method. Through computer simulations, we demonstrate the effectiveness of the proposed control method.