• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권3호
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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.

• 대한수학회보
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• 제52권3호
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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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• 제15권2호
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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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• 제4권3호
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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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• 제15권1호
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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.

• 대한수학회지
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• 제40권3호
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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.

• 한국정밀공학회지
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• 제31권12호
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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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• 제26권1호
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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.

• 한국군사과학기술학회지
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• 제16권6호
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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.

• 한국도로학회논문집
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• 제7권4호
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• pp.41-47
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• 2005

교통량, 속도, 차종 등으로 대표되는 교통자료는 도로를 계획하고 설계하는데 있어 매우 중요한 기초자료로 활용된다. 교통자료를 기준으로 해당 도로의 장래 서비스수준을 예측하며, 신설 및 확장될 도로의 기하구조가 결정되기 때문이다. 1985년 이후부터 건설교통부에서는 일반국도에 대해서 수시 교통량 조사와 상시 교통량 조사를 병행하고 있다. 이러한 교통조사는 일반국도와 일반국도 또는 일반국도와 고속국도가 만나는 네트웍 상의 노드를 중심으로 교통조사 구간을 설정하고, 이들 교통조사 구간에 대해서 교통량 조사를 수행하고 있다. 이러한 교통조사구간 설정 방법은 주요 도로가 만나는 결절점 사이의 구간에서는 교통량 변화패턴이 유사하다는 것을 전제로 하고 있다. 최근 우회도로의 신설, 중앙분리대 설치 등의 도로 기하구조 및 교통 시설물의 설치로 인하여 기존 구간의 특성이 변화되었다. 따라서 전국 일반국도를 대상으로 교통조사 구간의 유사성을 평가하여 국도의 동질성 구간에 대한 분석을 수행하였다. 유사성 평가를 위해서는 유전자 알고리즘을 적용한 모형을 구축하고, 모형의 적용을 통해 교통조사 구간을 정의하였다.