• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.739-748
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• 2015

The notion of quasi-lattice implication algebras is a generalization of lattice implication algebras. In this paper, we give an optimized definition of quasi-lattice implication algebra and show that this algebra is a distributive lattice and that this algebra is a lattice implication algebra. Also, we define a congruence relation Φ_F induced by a filter F and show that every congruence relation on a quasi-lattice implication algebra is a congruence relation Φ_F induced by a filter F.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.401-409
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• 2007

This paper is sequel to [3]. In this paper, we discuss some properties of an algebraic meet-continuous lattice and study a complete lattice which can be embedded into an algebraic meet-continuous lattice.

• International Journal of Railway
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• v.6 no.4
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• pp.160-168
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• 2013

A spiral lattice girder-reinforced Bi-block sleeper which has enhanced durability against increasingly growing impact force and vibration by wheel load and improved structural performance while train runs at 350km/h high speed is hereby proposed. The section of a spiral lattice girder has stable and superior structural performance thanks to its confinement effect. To compare and analyze the structural performance of spiral lattice girder-reinforced bi-block sleeper, strain and stress distribution were evaluated after applying same load condition as existing triangular lattice girder-reinforced biblock sleeper, and to compare the structural performance of triangular lattice girder and spiral lattice girder, structural analysis of lattice girder was performed separately. As a result, a spiral lattice girder proved to have had superior structural characteristics to bi-block sleeper, and furthermore as a result of evaluating the fastener interface and constructibility with shape-improved lattice girder, no interference with existing railroad structure was found and in terms of cost efficiency, a spiral lattice girder appeared to be superior to existing lattice girder.

• Journal of the Optical Society of Korea
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• v.18 no.3
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• pp.207-216
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• 2014

In this work, we report detailed numerical analysis of the near-elliptic core index-guiding triangular-lattice and square-lattice photonic crystal fiber (PCFs); where we numerically characterize the birefringence, single mode, cut-off behavior and group velocity dispersion and effective area properties. By varying geometry and examining the modal field profile we find that for the same relative values of $d/{\Lambda}$, triangular-lattice PCFs show higher birefringence whereas the square-lattice PCFs show a wider range of single-mode operation. Square-lattice PCF was found to be endlessly single-mode for higher air-filling fraction ($d/{\Lambda}$). Dispersion comparison between the two structures reveal that we need smaller lengths of triangular-lattice PCF for dispersion compensation whereas PCFs with square-lattice with nearer relative dispersion slope (RDS) can better compensate the broadband dispersion. Square-lattice PCFs show zero dispersion wavelength (ZDW) red-shifted, making it preferable for mid-IR supercontinuum generation (SCG) with highly non-linear chalcogenide material. Square-lattice PCFs show higher dispersion slope that leads to compression of the broadband, thus accumulating more power in the pulse. On the other hand, triangular-lattice PCF with flat dispersion profile can generate broader SCG. Square-lattice PCF with low Group Velocity Dispersion (GVD) at the anomalous dispersion corresponds to higher dispersion length ($L_D$) and higher degree of solitonic interaction. The effective area of square-lattice PCF is always greater than its triangular-lattice counterpart making it better suited for high power applications. We have also performed a comparison of the dispersion properties of between the symmetric-core and asymmetric-core triangular-lattice PCF. While we need smaller length of symmetric-core PCF for dispersion compensation, broadband dispersion compensation can be performed with asymmetric-core PCF. Mid-Infrared (IR) SCG can be better performed with asymmetric core PCF with compressed and high power pulse, while wider range of SCG can be performed with symmetric core PCF. Thus, this study will be extremely useful for designing/realizing fiber towards a custom application around these characteristics.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.613-626
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• 1996

This paper is a contribution to the study of the properties of the lattice of all lattice varieties. Among the properties, that of finite base is investigated here. The question whether the join of two finitely based modular lattice varieties is finitely based is investigated under certain conditions.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.1
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• pp.47-57
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• 2004

The Goldreich-Goldwasser-Halevi(GGH)'s signature scheme from Crypto '97 is cryptanalyzed, which is based on the well-blown lattice problem. We mount a chosen message attack on the signature scheme, and show the signature scheme is vulnerable to the attack. We collects n lattice points that are linearly independent each other, and constructs a new basis that generates a sub-lattice of the original lattice. The sub-lattice is shown to be sufficient to generate a valid signature. Empirical results are presented to show the effectiveness of the attack Finally, we show that the cube-like parameter used for the private-key generation is harmful to the security of the scheme.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.1
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• pp.26-33
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• 1992

This paper presents lattice structure of bilinear filter and the conversion equations from lattice parameters to direct-form parameters. Billnear models are attractive for adaptive filtering applications because they can approximate a large class of nonlinear systems adequately, and usually with considerable parsimony in the number of coefficients required. The lattice filter formulation transforms the nonlinear filtering problem into an equivalent multichannel linear filtering problem and then uses multichannel lattice filtering algorithms to solve the nonlinear filtering problem. The lattice filters perform a Gram-Schmidt orthogonalization of the input data and have very good easily extended to more general nonlinear output feedback structures.

• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.1-8
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• 2023

This study is on a Boolean B or Boolean lattice L in abstract algebra with closed binary operation *, complement and distributive properties. Both Binary operations and logic properties dominate this set. A lattice sheds light on binary operations and other algebraic structures. In particular, the construction of the elements of this L set from idempotent elements, our definition of k-order idempotent has led to the expanded definition of the definition of the lattice theory. In addition, a lattice offers clever solutions to vital problems in life with the concept of logic. The restriction on a lattice is clearly also limit such applications. The flexibility of logical theories adds even more vitality to practices. This is the main theme of the study. Therefore, the properties of the set elements resulting from the binary operation force the logic theory. According to the new definition given, some properties, lemmas and theorems of the lattice theory are examined. Examples of different situations are given.

• Journal of Korean Tunnelling and Underground Space Association
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• v.15 no.3
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• pp.201-214
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• 2013

Lattice girders are widely used as a substitute for H-steel ribs at domestic tunnels. However, lattice girders have a weak point in terms of the support capacity compare to H-steel ribs because of the lower stiffness and the weakness of the welded parts. To improve the weakness of the lattice girder, reformed lattice girders are developed in Korea by adding one more spider and having flat welded surface. Laboratory tests and field measurements were performed for the original and the reformed lattice girders to evaluate the performance of the reformed lattice girders. According to the laboratory compression test, reformed lattice girders have 16% higher load bearing capacity than that of original lattice girders. Reformed lattice girders are more stable than original lattice girders because reformed lattice girders tend to bend less according to the field measurements.

• Journal of Korean Tunnelling and Underground Space Association
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• v.21 no.6
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• pp.897-908
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• 2019

The objective of this study is to evaluate the field support performance of highperformance lattice girder (BK-Lattice Girder) by using numerical analysis. Three types (50, 70, 95-type) of existing and high performance lattice girders were applied to the cross section of highway 2, 3, and 4 lane tunnels to compare the supporting performance. The numerical analysis was the finite element method and the lattice girder was modeled in three dimensions with an elasto-plastic frame. The ground was modeled as a spring receiving only compression. The load was applied as a concentrated load on the central ceiling of the tunnel section. The yield strengths of the lattice girders were determined from the numerical results to compare the supporting performance of lattice girder. In case of 50-type, the yield strengths of high-performance lattice girders were increased by 6.7~10.0% compared with those of the existing lattice girders. In the case of 70-type, the high-performance lattice girders increased yield strengths by 12.1~14.9% than the existing lattice girder. In the case of 95-type, the high-performance lattice girders increased yield strengths by 13.3~20.0% than the existing lattice girder. As a result of numerical analysis, it was considered that the high-performance lattice girder supported better than the existing lattice girder when only the lattice girders were constructed.