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

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1047-1065
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• 2022

For two dimensional lattices, a Gaussian basis achieves all two successive minima. For dimension larger than two, constructing a pairwise Gaussian basis is useful to compute short vectors of the lattice. For three dimensional lattices, Semaev showed that one can convert a pairwise Gaussian basis to a basis achieving all three successive minima by one simple reduction. A pairwise Gaussian basis can be obtained from a given basis by executing Gauss algorithm for each pair of basis vectors repeatedly until it returns a pairwise Gaussian basis. In this article, we prove a necessary and sufficient condition for a pairwise Gaussian basis to achieve the first k successive minima for three dimensional lattices for each k ∈ {1, 2, 3} by modifying Semaev's condition. Our condition directly checks whether a pairwise Gaussian basis contains the first k shortest independent vectors for three dimensional lattices. LLL is the most basic lattice basis reduction algorithm and we study how to use LLL to compute a pairwise Gaussian basis. For δ ≥ 0.9, we prove that LLL(δ) with an additional simple reduction turns any basis for a three dimensional lattice into a pairwise SV-reduced basis. By using this, we convert an LLL reduced basis to a pairwise Gaussian basis in a few simple reductions. Our result suggests that the LLL algorithm is quite effective to compute a basis with all three successive minima for three dimensional lattices.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.6
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• pp.3316-3332
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• 2019

In a transitive signature scheme, a signer wants to authenticate edges in a dynamically growing and transitively closed graph. Using transitive signature schemes it is possible to authenticate an edge (i, k), if the signer has already authenticated two edges (i, j) and (j, k). That is, it is possible to make a signature on (i, k) using two signatures on (i, j) and (j, k). We propose the first transitive signature schemes for undirected graphs from lattices. Our first scheme is provably secure in the random oracle model and our second scheme is provably secure in the standard model.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.511-519
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• 2000

If G is a strict generalized orthomodular lattice and H={I｜I=[0, $\chi$, $\chi$$\in$G}, then H is prime ideal of the Janowitz's hull J(G) of G. If f is the janowitz's embedding, then the set of all commutatiors of f(G) equals the set of all commutators of the Janowitz's hull J(G) of G. Let L be an OML. Then L J(G) for a strict GOML G if and only if ther exists a proper nonprincipal prime ideal G in L.

• Current Applied Physics
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• v.18 no.11
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• pp.1294-1299
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• 2018

In this paper, we demonstrate the feasibility of constructing DNA nanostructures (i.e. DNA rings and double-crossover (DX) DNA lattices) with appropriate doxorubicin hydrochloride (DOX) concentration and reveal significant characteristics for specific applications, especially in the fields of biophysics, biochemistry and medicine. DOX-intercalated DNA rings and DX DNA lattices are fabricated on a given substrate using the substrateassisted growth method. For both DNA rings and DX DNA lattices, phase transitions from crystalline to amorphous, observed using atomic force microscopy (AFM) occurred above a certain concentration of DOX (at a critical concentration of DOX, $30{\mu}M$ of $[DOX]_C$) at a fixed DNA concentration. Additionally, the coverage percentage of DNA nanostructures on a given substrate is discussed in order to understand the crystal growth mechanism during the course of annealing. Lastly, we address the significance of optical absorption and photoluminescence characteristics for determining the appropriate DOX binding to DNA molecules and the energy transfer between DOX and DNA, respectively. Both measurements provide evidence of DOX doping and $[DOX]_C$ in DNA nanostructures.

• Proceedings of the KIPE Conference
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• 2005.07a
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• pp.687-689
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• 2005

Francis turbine of commercial small hydro -power plants under 10kw which is investigate a flow characterist and an efficiency in the research which it sees, the problem and an improvement is investigate. In the research which it is simply model with casing, guide-vane, runner, draft tube for simulation numerical analysis of small-sized Francis turbine. model uses the Gambit and it composes with approximately 800,000 nonuniform lattices. Solutions are investigate the hydraulic characteristics against an outward angle of guide vane, the number of guide vane, head(inlet velocity) by using FLUENT which is a commercial business code.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.1-20
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• 2020

A simple but elegant result of Rival states that every sublattice L of a finite distributive lattice 𝒫 can be constructed from 𝒫 by removing a particular family 𝒥_L of its irreducible intervals. Applying this in the case that 𝒫 is a product of a finite set 𝒞 of chains, we get a one-to-one correspondence L ↦ 𝒟_𝒫(L) between the sublattices of 𝒫 and the preorders spanned by a canonical sublattice 𝒞^⋄ of 𝒫. We then show that L is a tight sublattice of the product of chains 𝒫 if and only if 𝒟_𝒫(L) is asymmetric. This yields a one-to-one correspondence between the tight sublattices of 𝒫 and the posets spanned by its poset J(𝒫) of non-zero join-irreducible elements. With this we recover and extend, among other classical results, the correspondence derived from results of Birkhoff and Dilworth, between the tight embeddings of a finite distributive lattice L into products of chains, and the chain decompositions of its poset J(L) of non-zero join-irreducible elements.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.31 no.3
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• pp.509-516
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• 2021

The transitive signature scheme is a technique that can be very useful when authenticating edges in a graph that is transitively closed. In other words, when there is an authentication value for an edge (i, j) and an authentication value for an edge (j, k), the authentication value for the edge (i, k) can also be calculated immediately without any separate authentication procedure through a transitive signature. In this paper, we propose the first identity-based transitive signature scheme. Our scheme is based on the lattice problem.

• Nuclear Engineering and Technology
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• v.52 no.6
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• pp.1120-1130
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• 2020

The CREOLE experiment performed In the EOLE critical facility located In the Nuclear Center of CADARACHE - CEA have allowed us to get interesting and complete experimental information on the temperature effects in the light water reactor lattices. To analyze these experiments with accuracy an elaborate calculation scheme using the Monte Carlo method implemented in the MCNP6.1 code and the ENDF/B-VII.1 cross section library has been developed. We have used the ENDF/B-VII.1 data provided with the MCNP6.1.1 version in ACE format and the Makxsf utility to handle the data in the specific temperatures not available in the MCNP6.1.1 original library. The main purpose of this analysis is the qualification of the ENDF/B-VII.1 nuclear data for the prediction of the Reactivity Temperature Coefficient while ensuring the ability of the MCNP6.1 system to model such a complex experiment as CREOLE. We have analyzed the case of UO₂ lattice with 1166 ppm of boron in ordinary water moderator in specified temperatures. A detailed comparison of the calculated effective multiplication factors with the reference ones [1] in room temperature presented in this work shows a good agreement demonstrating the validation of our 3D calculation model. The discrepancies between calculations and the differential measurements of the Reactivity Temperature Coefficient for the analyzed configuration are relatively small: the maximum discrepancy doesn't exceed 1,1 pcm/℃. In addition to the analysis of direct differential measurements of the reactivity temperature coefficient performed in the poisoned UO₂ lattice configuration, we have also analyzed integral measurements in UO₂ clean lattice configuration using equivalency of the integral temperature reactivity worth with the driver core fuel reactivity worth and soluble boron reactivity worth. In this case both of the ENDF/B-VII.1 and JENDL.4 libraries were used in our analysis and the obtained results are very similar.

• Korean Journal of Computational Design and Engineering
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• v.12 no.1
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• pp.58-73
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• 2007

This paper described a method for the construction of a surface through a set of nonuniform scattered points. When the shift vectors of some points as constraints on the original surface are given, those of the other points should be computed to make the new surface. To keep up the look-see and smoothness with the original surfaces, the proper relationship should be formulated between the shifts of the constraint points and those of the other points. Vector fields for 3 dimensional shift of a point on the surface are made based in the constraint shifts. Vector fields for 3 dimensional shift of a point on the surface are made based on the constraint shifts. Multilevel B-spline approximation technique was used to construct the vector field. The technique uses coarse-to-fine hierarchy of control lattices. The developed method was applied to shoe sole design system especially for grading. Using this system, a shoe sole can be modified effectively.