• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.3
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• pp.7-20
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• 2007

We examined the steady state solution for a strongly exothermic mixtures in some class A geometries subjected to different boundary conditions under Arrhenius, Bimolecular and Sensitised reactions. The solution of the governing nonlinear reaction diffusion equation was obtained using the variational method formulation executed in Mathematica package. The paper elucidates the influence of geometry, boundary conditions and types of reaction on the thermal ignition of the reactive mixture. Apart from validating known results in literature, the solution gave further insight into the influence of material properties and conditions on the occurrence of thermal ignition.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.955-962
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• 2015

It has been established that the role played by complete graphs in graph theory is similar to the role Dowling group geometries and Projective geometries play in matroid theory. In this paper, we introduce a notion of H-tree, a class of representable matroids which play a similar role to trees in graph theory. Then we give some properties of H-trees such that when q = 0, then the results reduce to the known properties of trees in graph theory. Finally we give explicit expressions of the characteristic polynomials of H-trees, H-cycles, H-fans and H-wheels.

• Journal of Communications and Networks
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• v.15 no.2
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• pp.217-221
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• 2013

Quantum low-density parity-check (LDPC) codes based on the Calderbank-Shor-Steane construction have low encoding and decoding complexity. The sum-product algorithm(SPA) can be used to decode quantum LDPC codes; however, the decoding performance may be significantly decreased by the many four-cycles required by this type of quantum codes. All four-cycles can be eliminated using the entanglement-assisted formalism with maximally entangled states (ebits). The proposed entanglement-assisted quantum error-correcting code based on Euclidean geometry outperform differently structured quantum codes. However, the large number of ebits required to construct the entanglement-assisted formalism is a substantial obstacle to practical application. In this paper, we propose a novel class of entanglement-assisted quantum LDPC codes constructed using classical Euclidean geometry LDPC codes. Notably, the new codes require one copy of the ebit. Furthermore, we propose a construction scheme for a corresponding zigzag matrix and show that the algebraic structure of the codes could easily be expanded. A large class of quantum codes with various code lengths and code rates can be constructed. Our methods significantly improve the possibility of practical implementation of quantum error-correcting codes. Simulation results show that the entanglement-assisted quantum LDPC codes described in this study perform very well over a depolarizing channel with iterative decoding based on the SPA and that these codes outperform other quantum codes based on Euclidean geometries.

• Advances in aircraft and spacecraft science
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• v.4 no.3
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• pp.219-235
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• 2017

The large container ships and fast patrol boats are complex marine structures. Therefore, their global mechanical behaviour has long been modeled mostly by refined beam theories. Important issues of cross section warping and bending-torsion coupling have been addressed by introducing special functions in these theories with inherent assumptions and thus compromising their robustness. The 3D solid Finite Element (FE) models, on the other hand, are accurate enough but pose high computational cost. In this work, different marine vessel structures have been analysed using the well-known Carrera Unified Formulation (CUF). According to CUF, the governing equations (and consequently the finite element arrays) are written in terms of fundamental nuclei that do not depend on the problem characteristics and the approximation order. Thus, refined models can be developed in an automatic manner. In the present work, a particular class of 1D CUF models that was initially devised for the analysis of aircraft structures has been employed for the analysis of marine structures. This class, which was called Component-Wise (CW), allows one to model complex 3D features, such as inclined hull walls, floors and girders in the form of components. Realistic ship geometries were used to demonstrate the efficacy of the CUF approach. With the same level of accuracy achieved, 1D CUF beam elements require far less number of Degrees of Freedom (DoFs) compared to a 3D solid FE solution.

• Journal of Communications and Networks
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• v.15 no.1
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• pp.71-76
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• 2013

A new class of quantum low-density parity-check (LDPC) codes whose parity-check matrices are dual-containing matrices constructed based on lines of Euclidean geometries (EGs) is presented. The parity-check matrices of our quantum codes contain one and only one 4-cycle in every two rows and have better distance properties. However, the classical parity-check matrix constructed from EGs does not satisfy the condition of dual-containing. In some parameter conditions, parts of the rows in the matrix maybe have not any nonzero element in common. Notably, we propose four families of fascinating structure according to changes in all the parameters, and the parity-check matrices are adopted to satisfy the requirement of dual-containing. Series of matrix properties are proved. Construction methods of the parity-check matrices with dual-containing property are given. The simulation results show that the quantum LDPC codes constructed by this method perform very well over the depolarizing channel when decoded with iterative decoding based on the sum-product algorithm. Also, the quantum codes constructed in this paper outperform other quantum codes based on EGs.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.461-486
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• 2003

It is known that the CR geometries of Levi non-degen-erate hypersurfaces in $\C^n$ and of the elliptic or hyperbolic CR submanifolds of codimension two in $\C^4$ share many common features. In this paper, a special class of normalized coordinates is introduced for any CR manifold M which is one of the above three kinds and it is shown that the explicit expression in these coordinates of an isotropy automorphism $f{\in}Aut(M)_o {\subset}Aut(M),\;o{\in}M$, is equal to the expression of a corresponding element of the automorphism group of the homogeneous model. As an application of this property, an extension theorem for CR maps is obtained.

• Journal of the Korean Society for Precision Engineering
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• v.31 no.12
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• pp.1127-1132
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• 2014

Fast tool servo (FTS) is an enabling technology to fabricate various shapes of functional surface geometries in a precise and controllable manner. FTS can be also employed as a straightforward and efficient surface treatment way of making such products more durable. In this work, process characteristics using high-precision FTS-based surface texturing were qualitatively and quantitatively investigated to provide a class of surface design rule. The morphologies of surfaces processed with different conditions were first examined by observing the resultant 2D/3D surface profiles. In addition, the effects of the surface treatment using FTS on hardness and wear properties were characterized and compared to those without treatment.

• Bulletin of the Korean Chemical Society
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• v.26 no.1
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• pp.63-71
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• 2005

Equilibrium geometries, electronic structures, and energies of borocarbon clusters (binary compounds of carbon and boron), an unexplored class of molecules with highly unusual characteristics and potential for further development, have been investigated by means of B3LYP/6-311+G$^*$ density functional theory computations. A large number of B$_7$C${_1}^{1-}$, B$_6C_2$, and B$_5C_{3}\,^{1+}$ clusters with planar and non-planar monocyclic and polycyclic rings, as well as cage structures, have been systematically studied. Unexpectedly, planar forms are predicted not only to be the most stable structures, but also, in many cases, to have unprecedented planar heptacoordinate boron (p-heptaB) and planar heptacoordinate carbon (p-heptaC) arrangements. All these pheptaB and p-heptaC have 6π electrons and are aromatic according to the nucleus independent chemical shift (NICS). This novel bonding pattern is analyzed in terms of natural bond orbital (NBO) analysis. For virtually all possible B$_7$C${_1}^{1-}$, B$_6C_2$, and B$_5C_{3}\,^{1+}$ combinations, the p-heptaB arrangements are the more stable than other type structures.

• Journal of the Korea Institute of Military Science and Technology
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• v.16 no.6
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• pp.847-856
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• 2013

In this study, thermal performance of recuperators with plain and offset strip fins is investigated to enhance the thermal efficiency of a micro gas turbine. Thermal cycle analysis is conducted to determine major design parameters of a single-pass counterflow recuperator. In order to evaluate the performance of the recuperator, the effectiveness and the pressure drop in the recuperators are chosen as the objective function and the design constraint, respectively. The optimized geometries for internal structure of the recuperators with plain and offset strip fins are obtained with varying the fin spacing and height. From the result, the recuperator with offset strip fins has better thermal performance when the fin spacing, s, is smaller than 1.45mm and the thermal performance of the recuperator with plain rectangular fins is higher than that with offset strip fins in the region of $s{\geq}1.45mm$. In addition, it is found that the entrance region effect and the longitudinal wall heat conduction effect should be taken into account for accurately predicting the thermal performance of the recuperators with both plain and offset strip fins.

• International Journal of Highway Engineering
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• v.7 no.4 s.26
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• pp.41-47
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• 2005

Traffic data such as traffic volume, speed, and vehicle Class are very important basic data for the plan and design of highway. Based on traffic data, the future service level of a specific highway and geometry of newly constructed or expended road is predicted and determined. The Ministry of Construction & Transportation has simultaneously surveyed coverage count and permanent count at highways since 1985. Traffic volume survey sections were determined at jointed nodes of highways and jointed nodes of highways and other roads such as freeway and local highway. Volume survey was performed at these sections. The premise to decide these sections is assumed that links between jointed nodes of main highways exhibit similar traffic characteristics. Recently, due to the change of highway geometries such as construction of detour road and installations of traffic facilities such as installation of media, traffic characteristics of the existing traffic volume survey sections was changed. To reflect these changes, traffic characteristics at homogeneous road sections was widely evaluated and analyzed. Using Genetic Algorithms, a model was developed for the evaluation of traffic characteristics at homogeneous road sections. Traffic volume survey sections were then determined through the application of the developed model for current traffic system.