• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.465-486
• /
• 2005

We study the relationship between intuitionistic fuzzy ideals and intuitionistic fuzzy congruences on a distributive lattice. And we prove that the lattice of intuitionistic fuzzy ideals is isomorphic to the lattice of intuitionistic fuzzy congruences on a generalized Boolean algebra.

• Bulletin of the Korean Chemical Society
• /
• v.23 no.5
• /
• pp.727-735
• /
• 2002

Proton coupled carbon-13 relaxation experiment was performed to investigate the effect of vicinal protons on spin-lattice relaxation of methylene carbon-13 in n-undecane. A BIRD type pulse sequence was employed as a way to check the validity of describing the 13CH2 moiety as an isolated AX2 spin system. The results show that the presence of vicinal protons exerts substantial influence on the relaxation of methylene carbon-13, indicating that it is not a very good approximation to treat a methylene moiety as an isolated AX2 spin system.

• Journal for History of Mathematics
• /
• v.23 no.2
• /
• pp.101-121
• /
• 2010

This article includes an introduction, a history of Pick's theorem on lattice polyhedron and its proof, Reeve's theorem on 3-dimensional lattice polyhedrons extended from the Pick's theorem and Ehrhart polynomial generalized as an n-dimensional lattice polyhedron, and then shows the relationship between the volume of 3-dimensional polyhedron and the number of its lattice points by means of Reeve's theorem. It is aimed to apply the relationship to the visualization of sums in sequences.

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.385-392
• /
• 2003

Using a fuzzy filter, a new congruence relation induced by the fuzzy filter is given in lattice implication algebras, and some of their properties are investigated.

• Journal of the Korean Crystal Growth and Crystal Technology
• /
• v.8 no.3
• /
• pp.377-382
• /
• 1998

GaN epilayers having good adhesion and quality were obtained directly on the sapphire {1120} substrates by the OMVPE method without introducing a buffer layer at the lower temperature. The preferred orientations of epilayers turned out to be <0002> and at least 4 kinds of epilayers were competitively grown. Slight distortions of lattices caused by lattice mismatches between sapphire and GaN were observed at the lattices within 2~3 nm region from the interface. Accordingly, TEM investigation revealed that GaN epilayers could be grown on sapphire {1120} planes without a buffer layer.

• Journal of the Korean institute of surface engineering
• /
• v.36 no.2
• /
• pp.135-140
• /
• 2003

The difference in lattice parameter and thermal expansion coefficient between GaN and Si which results in many defects into the grown GaN is larger than that between GaN and sapphire. In order to obtain high quality GaN films on Si substrate, it is essential to understand growth characteristics of GaN. In this study, GaN layers were grown on Si(111) substrates by MOCVD at three different GaN growth temperatures ($900^{\circ}C$, $1,000^{\circ}C$ and $1,100^{\circ}C$), using AlN and LT-GaN buffer layers. Using TEM, we carried out the comparative investigation of growth characteristics of GaN by characterizing lattice coherency, crystallinity, orientation relationship and defects formed (transition region, stacking fault, dislocation, etc). The localized region with high defect density was formed due to the lattice mismatch between AlN buffer layer and GaN. As the growth temperature of GaN increases, the defect density and surface roughness of GaN are decreased. In the case of GaN grown at $1,100^{\circ}$, growth thickness is decreased, and columns with out-plane misorientation are formed.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.32 no.5
• /
• pp.765-777
• /
• 2022

The SABER algorithm, a PKE/KEM algorithm presented in NIST PQC Standardization Round 3, is an algorithm based on the Module-LWR problem among lattice-based problems and has a Meta-PKE structure. At this time, the secret information used in the encryption process is called a ephemeral key, and in this paper, the ephemeral key reuse attack using the Meta-PKE structure is described. For each parameter satisfying the security strengths required by NIST, we present a detailed analysis of the previous studies attacked using 4, 6, and 6 queries, and improve them, using only 3, 4, and 4 queries. In addition, we introduce how to reduce the computational complexity of recovering ephemeral keys with a single query from the brute-force complexity on the n-dimension lattice, 2^7.91×n, 2^10.51×n, 2^12.22×n to 2^4.91×n, 2^6.5×n, 2^6.22×n, for each parameter, and present the results and limitations.

• Journal of the Semiconductor & Display Technology
• /
• v.5 no.2 s.15
• /
• pp.1-5
• /
• 2006

The GaN thin film on the 8 periods InGaN/GaN multi-quantum well structure was grown on the sapphire substrate using metal-organic chemical vapor deposition. The nano-scaled triangular-lattice holes with the diameter of 150 nm were patterned on a polymethylmethacrylate blocking film using an electron beam nano-lithography system. The thin slab and two-dimensional photonic crystals with the thickness of 28 nm were fabricated on the GaN layer for the blue light diffraction sources. The photonic crystal with the lattice parameter of 460 nm enhances spectral intensity of photoluminescence indicating that the photonic crystals provides the source of nano-diffraction for the blue light of the 450-nm wavelength.

• Kyungpook Mathematical Journal
• /
• v.50 no.2
• /
• pp.195-211
• /
• 2010

Let A be a locally finite total algebra of finite type such that $k^A(a_1,\cdots,a_n)\;{\neq}\;a_i$ ai for every operation $k^A$, elements $a_1,\cdots,a_n$ an and $1\;\leq\;i\;\leq\;n$. We show that the weak subalgebra lattice of A uniquely determines its (strong) subalgebra lattice. More precisely, for any algebra B of the same finite type, if the weak subalgebra lattices of A and B are isomorphic, then their subalgebra lattices are also isomorphic. Moreover, B is also total and locally finite.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.35 no.6C
• /
• pp.523-529
• /
• 2010

We propose a very low complexity lattice reduction (LR) algorithm for MIMO detection in time varying channels. The proposed scheme reduces the complexity by performing LR in a block-wise manner. The proposed scheme takes advantage of the temporal correlation of the channel matrices in a block and its impact on the unimodular matrices during LR process. From this, the proposed scheme can skip a number of redundant LR processes for consecutive channel matrices and performs a single LR in a block. The simulation results investigated in this letter reveal that the proposed detection scheme requires only 43.4% multiplications and 17.3% divisions of LLL-LR and only 50.2% multiplications and 68.2% divisions of the conventional adaptive LR with almost no performance degradation.