• Korean Journal of Mathematics
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• 제32권2호
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• pp.195-211
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• 2024

In this paper, we introduce the concept of a fuzzy lattice ordered group, which is based on a fuzzy lattice that Chon developed in his paper "Fuzzy Partial Order Relations and Fuzzy Lattice". We will also discuss fuzzy lattice-ordered groups in detail, provide several results that are analogous to the classical theory of lattice-ordered groups, and characterize the relationship between a fuzzy lattice-ordered group using its level set and support. Moreover, we define the concepts of fl-subgroups, quotients, and cosets of fl-groups and obtain some fundamental results for these fuzzy algebraic structures.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.45-48
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• 2008

Periodic lattice structures such as the large space lattice structures and carbon nanotubes may take the extension-transverse shear-bending coupled vibrations, which can be well represented by the extended Timoshenko beam theory. In this paper, the spectrally formulated finite element model (simply, spectral element model) has been developed for extended Timoshenko beams and applied to some typical periodic lattice structures such as the armchair carbon nanotube, the periodic plane truss, and the periodic space lattice beam.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2008년도 추계학술대회 논문집
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• pp.1403-1406
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• 2008

Periodic lattice structures such as the large space lattice structures and carbon nanotubes may take the extension-transverse shear-bending coupled vibrations, which can be well represented by the extended Timoshenko beam theory. In this paper, the spectrally formulated finite element model (simply, spectral element model) has been developed for extended Timoshenko beams and applied to some typical periodic lattice structures such as the armchair carbon nanotube, the periodic plane truss, and the periodic space lattice beam.

• Progress in Superconductivity
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• 제6권1호
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• pp.52-55
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• 2004

The inductive coupling theory in serially stacked $Bi_2$$Sr_2$$CaCu_2$$O_{8+x}$ intrinsic Josephson junctions predicts that the lattice structure of the Josephson vortices along the c axis gradually changes from the triangular to the rectangular lattice with increasing the vortex velocity. This lattice transition appears as voltage jumps or sub-branch splitting in the Josephson vortex-flow region of current-voltage characteristics (IVC). We report the IVC in external magnetic fields from 2 to 4 T. The stack, with the lateral size of 1.4${\times}$15 $u\m^2$, was fabricated by using the double-side cleaving technique. The sub-branches in the Josephson vortex-flow region, corresponding to a plasma propagation mode in serially coupled intrinsic Josephson junctions, were also observed in the range of 2∼4T. Switching from one branch to another in Josephson vortex-flow region suggests the structural transition of the moving Josephson vortex lattice.

• 대한화학회지
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• 제15권4호
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• pp.165-169
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• 1971

A general method of calculating the frequency shift due to lattice defects is developed for a one dimensional lattice with an arbitrary number of lattice points. The method is based on the Fourier transform of the equation of motion. It is shown that the frequency spectrum is determined by the roots of 5${\times}$5 secular equation, the coefficients of which depend on defects in the mass and the force constant as well as the number of the lattice points. For the limiting case of infinite lattice, the dimension of the secular equation reduces to three and the result agrees with that of Montroll and Potts.

• 대한수학회논문집
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• 제19권1호
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• pp.11-21
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• 2004

We discuss the n-fold implicative/fantastic filters in lattice implication algebras, which are extended notions of implicative/fantastic filters. Characterizations of n-fold implicative/fantastic filters are given. Conditions for a filter to be n-fold implicative are provided. Extension property for an n-fold fantastic filter is established.

• 대한수학회지
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• 제36권3호
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• pp.621-631
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• 1999

In this paper we briefly describe the geometry of the Cayley hyperbolic plane and we show that every uniform lattice in quaternionic space cannot be deformed in the Cayley hyperbolic 2-plane. We also describe the nongeometric bending deformation by developing the theory of the Cartan angular invariant for quaternionic hyperbolic space.

• Steel and Composite Structures
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• 제24권2호
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• pp.249-264
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• 2017

In this paper free linear vibration of lattice composite conical shells will be investigated. Lattice composite conical shell consists of composite helical ribs and thin outer skin. A smeared method is employed to obtain the variable coefficients of stiffness of conical shell. The ribs are modeled as a beam and in addition to the axial loads, endure shear loads and bending moments. Therefore, theoretical formulations are based on first-order shear deformation theory of shell. For verification of the obtained results, comparison is made with those available in open literature. Also, using FEM software the 3D finite element model of composite lattice conical shell is built and analyzed. Comparing results of analytical and numerical analyses show a good agreement between them. Some special cases as variation of geometric parameters of lattice part, effect of the boundary conditions and influence of the circumferential wave numbers on the natural frequencies of the conical shell are studied. It is concluded, when mass and the geometrical ratio of the composite lattice conical shell do not change, increment the semi vertex angle of cone leads to increase the natural frequencies. Moreover for shell thicknesses greater than a specific value, the presence of the lattice structure has not significant effect on the natural frequencies. The obtained results have novelty and can be used for further and future researches.

• 대한화학회지
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• 제44권6호
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• pp.587-591
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• 2000

고분자액체의 상태방정식을 구하기 위하여 많은 이론들이 제안되어 왔다. 이론들의 대부분은 cell, hole, free volume 또는 lattice 등의 개념에 근거를 두고 있다. 가장 성공적인 이론중의 하나로 평가받고 있는 것이 free volume의 개념을 근거로 한 Flory의 상태방정식 이론이다. 본 연구에서는 Flory 이론에서 사용한 van der Waals 포텐셜을 수정하여 새로운 상태방정식을 만들었다. 계산결과 새로운 상태방정식은 Flory 이론보다 PVT 실험값과 더 잘 일치함을 알 수 있었다.

• 대한화학회지
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• 제31권6호
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• pp.481-485
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• 1987

확장된 Flory-Huggins의 격자이론에 의해 예측될 수 있는 액체 이성분계의 여러 부분혼화도를 제시하였으며, 각 경우에 있어서의 수학적 조건를 구하였다. 그리고, 그 이론을 사용하여 물-2-부탄올계에서 나타나는 비정상적인 부분혼화도가 존재할 수 있음을 보였다.