• Korean Journal of Mathematics
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• v.30 no.2
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• pp.297-304
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• 2022

Fixed point theory has many useful applications in applied sciences. The object of this paper is to obtain fixed point for continuous self mappings in Hilbert C^*-module with rational conditions.

• Journal of the Korean Chemical Society
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• v.59 no.1
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• pp.9-17
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• 2015

The density functional theory (DFT) calculations on $(H_2O)_n@C_{60}$, (n=1-10) complexes have been performed to elucidate hydrogen interaction between fullerene and water clusters. The optimized geometries, harmonic vibrational frequencies, and binding energies are predicted at various levels of theory. The harmonic vibrational frequencies for the molecules considered in this study show all real numbers implying true minima. We also compare the H-bond interaction between $(H_2O)_n$ and $(H_2O)_n@C_{60}$, (n=1-10) clusters.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.33 no.2
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• pp.23-32
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• 2010

In this paper, we proposed the modified method of Metcalfe's law that is "Modfied law" in evaluating the network power for the measurement of combat effectiveness in C4I system. It is applied to JFOS-K (Joint Fire Operating System-Korea) C4I system that can connect KJCCS (Korea Joint Command and Control System) of Korea armed forces with JADOCS (Joint Automated Deep Operations Coordination System) of U.S. armed forces and achieve sensor to shooter system in real time in JCS (Joint Chiefs of Staff) level. The result of combat effectiveness using Modified law is compared to the one by C2 theory and found that both is similar. This study is meaningful because we improved the description level of reality in calculation of combat effectiveness in C4I system.

• Bulletin of the Korean Chemical Society
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• v.13 no.3
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• pp.296-306
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• 1992

$^{13}C$ spin-lattice relaxation times were measured for n-alkanes of moderate chain length, ranging from n-octane to n-dodecane, under the condition of proton broad-band decoupling within the temperature range of 248-318 K in order to gain some insight into basic features of segmental motions occurring in long chain ploymeric molecules. The NOE data showed that except for methyl carbon-13 dipole-dipole interactions between $^{13}C$ and directly bonded $^1H$ provide the major relaxation pathway, and we have analyzed the observed $T_1data$ on the basis of the internal rotational diffusion theory by Wallach and the conformational jump theory by London and Avitabile. The results show that the internal rotational diffusion constants about C-C bonds in the alkane backbone are all within the range of $10^9\;-10^10\;sec^{-1}$ in magnitude while the mean lifetimes for rotational isomers are all of the order of $10^{-11}\;-10^{-10}$ sec. Analysis by the L-A theory predicts that activation energies for conformational interconversion between gauche and trans form gradually increase as we move from the chain end toward the central C-C bond and they are within the range of 2-4 kcal/mol for all the compounds investigated.

• Advances in materials Research
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• v.11 no.1
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• pp.59-73
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• 2022

In the construction industry, thin-walled frame elements with very slender open cross-sections and low torsional stiffness are often subjected to a complex loading condition where axial, bending, shear and torsional stresses are present simultaneously. Hence, these often fail in instability even before the yield capacity is reached. One of the most common instability conditions associated with thin-walled structures is Lateral Torsional Buckling (LTB). In this study, a first order Generalized Beam Theory (GBT) formulation and numerical analysis of cold-formed steel lipped channel beams (C80×40×10×1, C90×40×10×1, C100×40×10×1, C80×40×10×1.6, C90×40×10×1.6 and C100×40×10×1.6) subjected to uniform moment is carried out to predict pure Lateral Torsional Buckling (LTB). These results are compared with the Finite Element Analysis of the beams modelled with shell elements using ABAQUS and analytical results based on Euler's buckling formula. The mode wise deformed shape and modal participation factors are obtained for comparison of the responses along with the effect of varying the length of the beam from 2.5 m to 10 m. The deformed shapes of the beam for different modes and GBTUL plots are analyzed for comparative conclusions.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.991-1018
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• 2006

Hypermaps are cellular embeddings of hypergraphs in compact and connected surfaces, and are a generalisation of maps, that is, 2-cellular decompositions of closed surfaces. There is a well known correspondence between hypermaps and co-compact subgroups of the free product $\Delta=C_2*C_2*C_2$. In this correspondence, hypermaps correspond to conjugacy classes of subgroups of $\Delta$, and hypermap coverings to subgroup inclusions. Towards the end of [9] the authors studied regular hypermaps with extra symmetries, namely, G-symmetric regular hypermaps for any subgroup G of the outer automorphism Out$(\Delta)$ of the triangle group $\Delta$. This can be viewed as an extension of the theory of regularity. In this paper we move in the opposite direction and restrict regularity to normal subgroups $\Theta$ of $\Delta$ of finite index. This generalises the notion of regularity to some non-regular objects.

• Transactions of Materials Processing
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• v.19 no.2
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• pp.88-94
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• 2010

The next generation of diesel engine can operate at high injection pressure up to 1,800bar. The common rail pipe must have higher internal strength because it is directly influenced by the high-pressure fuel. Folding defects in the Common rail pipe can not ensure the structural safety. Therefore, Preform design and fatigue-life analysis are very important for preventing the head of the common rail pipe from folding in the heading process and for predicting fatigue life according to the amount of folding. In this study, a closed form equation to predict fatigue life was suggested by Goodman theory and pressure vessels theory in ASME Code in order to develop an optimization technique of the heading process and verified its reliability through fatigue-structural coupled field analysis. The results calculated by the theory were in good agreement with those obtained by the finite element analysis.

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.89-93
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• 1985

One of the most important problems in automatic continuity theory is to solve the question of continuity of an algebra homomorphism from a Banach algebra into a semisimple Banach algebra with dense range. Many results on this subject are obtained imposing some conditions on the domains or the ranges of homomorphisms. For most recent results and references in automatic continuity theory one may refer to [1], [4] and [5]. In this note we study some properties of homomorphisms from $C^{*}$-algebras into Banach algebras. It is shown that the range of an isomorphism from a $C^{*}$-algebra into a Banach algebra contains no non zero element of the radical of B. Using this result we show that the same holds for a continuous homomorphism, hence a Banach algebra which is the image of a $C^{*}$-algebra under a continuous homomorphism is necessarily semisimple. Thus if there is a homomorphism from a $C^{*}$-algebra onto a non-semisimple Banach algebra it must be discontinuous. Also it follows that every non zero homomorphism from a $C^{*}$-algebra into a radical algebra is discontinuous. Then we make a brief observation on the behavior of quasinilpotent element of noncommutative $C^{*}$-algebras in relation with continuous homomorphisms.momorphisms.

• Journal of information and communication convergence engineering
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• v.20 no.3
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• pp.153-159
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• 2022

Plain radiographic analysis is the initial imaging modality for suspected small bowel obstruction. Among the many features that affect the diagnosis of small bowel obstruction (SBO), the presence of gas-filled or fluid-filled small bowel loops is the most salient feature that can be automatized by computer vision algorithms. In this study, we compare three frequently applied pixel-clustering algorithms for extracting gas-filled areas without human intervention. In a comparison involving 40 suspected SBO cases, the Possibilistic C-Means and Fuzzy C-Means algorithms exhibited initialization-sensitivity problems and difficulties coping with low intensity contrast, achieving low 72.5% and 85% success rates in extraction. The Adaptive Resonance Theory 2 algorithm is the most suitable algorithm for gas-filled region detection, achieving a 100% success rate on 40 tested images, largely owing to its dynamic control of the number of clusters.

• Bulletin of the Korean Chemical Society
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• v.30 no.12
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• pp.2973-2978
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• 2009

The decomposition reaction mechanism of $CH_3CF_2O$ radical formed from hydroflurocarbon, $CH_3CHF_2$ (HFC-152a) in the atmosphere has been investigated using ab-initio quantum mechanical methods. The geometries of the reactant, products and transition states involved in the decomposition pathways have been optimized and characterized at DFT-B3LYP and MP2 levels of theories using 6-311++G(d,p) basis set. Calculations have been carried out to observe the effect of basis sets on the optimized geometries of species involved. Single point energy calculations have been performed at QCISD(T) and CCSD(T) level of theories. Out of the two prominent decomposition channels considered viz., C-C bond scission and F-elimination, C-C bond scission is found to be the dominant path involving a barrier height of 12.3 kcal/mol whereas the F-elimination path involves that of a 28.0 kcal/mol. Using transition-state theory, rate constant for the most dominant decomposition pathway viz., C-C bond scission is calculated at 298 K and found to be 1.3 ${\times}$ 10$^4s{-1}$. Transition states are searched on the potential energy surfaces involving both decomposition channels and each of the transition states are characterized. The existence of transition states on the corresponding potential energy surface are ascertained by performing Intrinsic Reaction Coordinate (IRC) calculation.