• Journal for History of Mathematics
• /
• v.19 no.4
• /
• pp.97-106
• /
• 2006

The lattice originated from logic, not mathematics. Around 1880, Peirce thought that all the lattices were distributives, however $Schr{\"{o}}der$ corrected the error around 1890. In 1993, Birkhoff used the term lattice for the first time that had a different meaning from today's lattice. This paper introduces Peirce, and studies correlation among atomic lattices, atomistic lattices, J-lattices, strong lattices and distributive lattices.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.15 no.1
• /
• pp.72-78
• /
• 2015

Alexandrov topologies are the topologies induced by relations. This paper addresses the properties of Alexandrov topologies as the extensions of strong topologies and strong cotopologies in complete residuated lattices. With the concepts of Zhang's completeness, the notions are discussed as extensions of interior and closure operators in a sense as Pawlak's the rough set theory. It is shown that interior operators are meet preserving maps and closure operators are join preserving maps in the perspective of Zhang's definition.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.7 no.12
• /
• pp.3261-3273
• /
• 2013

In the paper, we propose a novel adaptively secure hierarchical identity-based signature scheme from lattices. The size of signatures in our scheme is shortest among the existing hierarchical identity-based signature schemes from lattices. Our scheme is motivated by Gentry et al.'s signature scheme and Agrawal et al.'s hierarchical identity-based encryption scheme.

• Journal of the Chungcheong Mathematical Society
• /
• v.11 no.1
• /
• pp.27-34
• /
• 1998

We introduce ${\delta}$-frames, strong ${\delta}$-frames and completely distributive lattices, and investigate some relationships among those frames.

• Journal of applied mathematics & informatics
• /
• v.37 no.1_2
• /
• pp.65-71
• /
• 2019

In this paper we give some properties related to fuzzy functions on complete residuated lattices.

• 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.

• Communications of the Korean Mathematical Society
• /
• v.30 no.3
• /
• pp.155-168
• /
• 2015

Strong uni-soft filters and divisible uni-soft filters in residuated lattices are introduced, and several properties are investigated. Characterizations of a strong and divisible uni-soft filter are discussed. Conditions for a uni-soft filter to be divisible are established. Relations between a divisible uni-soft filter and a strong uni-soft filter are considered.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.23 no.1
• /
• pp.45-56
• /
• 2013

When a signer signs a message, strong designated verifier signature allows the signer to designate a verifier. Only the designated verifier can make sure that the signature is generated by the signer. In addition, no one except the designated verifier can know the signature generated by some signer. In this paper, we propose an identity-based strong designated verifier signature scheme where users' public keys are identities. Our proposed scheme is the first identity-based strong designated verifier scheme from lattices. Naturally, our proposed scheme is secure against quantum computing attacks and has low computational complexity.

• Bulletin of the Korean Chemical Society
• /
• v.34 no.3
• /
• pp.912-916
• /
• 2013

The electronic structure of LaFeAsO was analyzed by tight-binding band calculation based upon the normal and shrunk lattices. A strong Fermi surface nesting was found in the normal LaFeAsO, while most of the nesting area was disappeared in the shrunk LaFeAsO. It was found, therefore, high pressure atmosphere is required to become a superconductor for LaFeAsO by suppressing the SDW (spin density wave) state through the disappearance of the Fermi surface nesting.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2002.07a
• /
• pp.43-49
• /
• 2002

Gray-colored materials were synthesized from ball-milled ZnO powders under a thermal annealing at 1380$^{\circ}C$ with an argon carrier gas for 3 hours. The synthesized materials were identified to be wurtzitic hexagonal structured ZnO nanowires by X-ray diffraction and scanning electron microscopy. The ZnO nanowires have the long cylinder-like shape of which cross-section is a circle, and these nanowires are in the range 15∼40 nm width and 10-70 $\mu\textrm{m}$ length, respectively. Transmission electron microscopy revealed that these nanowires are single-crystalline and grow along [110] direction. The optical properties of the ZnO nanowires were investigated with photoluminescence. The analytic results revealed that ZnO nanowires have the singly ionized oxygen vacancies in the surface lattices, as they emit strong green light in room temperature PL. In addition, the growth mechanism of the ZnO nanowires can be described by the vapor-solid procedures.