• East Asian mathematical journal
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• v.28 no.3
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• pp.333-337
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• 2012

Finiteness of regular normal binary Hermitian lattices are known in several articles. In this article, we point out that there are infinitely many imaginary quadratic fields that admit a regular subnormal binary Hermitian lattice.

• Kyungpook Mathematical Journal
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• v.45 no.1
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• pp.21-31
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• 2005

We introduce the notions of nilpotent element, quasi-regular element in a semiring which is a distributive lattice of rings. The concept of Jacobson radical is introduced for this kind of semirings.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.87-95
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• 2019

The homothety classes of lattices in a two dimensional vector space over a nonarchimedean local field form a regular tree ${\mathcal{T}}$ of degree q + 1 on which the projective linear group acts naturally where q is the order of the residue field. We show that for any finite regular combinatorial graph of even degree q + 1, there exists a torsion free discrete subgroup ${\Gamma}$ of the projective linear group such that ${\mathcal{T}}/{\Gamma}$ is isomorphic to the graph.

• Kyungpook Mathematical Journal
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• v.57 no.1
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• pp.85-97
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• 2017

The notions of regular uni-soft filters, uni-soft MV -filters and Boolean uni-soft filters are introduced, and related properties are investigated. Characterizations of regular uni-soft filters, uni-soft MV -filters and Boolean uni-soft filters are discussed.Relations between regular uni-soft filters and uni-soft MV -filters are considered. It is shown that the notion of a uni-soft MV -filter coincides with the notion of a regular uni-soft filter in BL-algebras.

• Journal of Ocean Engineering and Technology
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• v.2 no.2
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• pp.130-137
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• 1988

This thesis introduced that character of a treatment technique for a mading synthetic resin Hifiow-Ring. The material system of packings make an experiment air$NH_{3}$/air$H_{2}SO_{4}$, $SO_{2}$-air/NaOH, $NH_{3}$-air/$/H_{2}SO_{4}$ under general conditions. Lattices packing compared with conventional packings was proved low pressure loss and high separation efficiency for high loading per trans unit. And an inflow materal tested for absorption and rectification, it made an experiment under a range regular temperature, low energy and small amount of money. That made possible in simple equation, volume material tranfer coefficient$\beta_{L}$ . a by absorption or $\beta_{V}$ .a calculated in all range loading. The peculiarity pressure loss $\Delta\;P/NUT_{ov}$ for Hiflow-ring contributed to a fall cost of energy, a grade number of a vacuum rectification and absorption calculation.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2000.11a
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• pp.69-73
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• 2000

We systematically analyze the influence of fracture junction, solute transfer characteristics on transport patterns in discrete, two-dimensional fracture network models. Regular lattices and random fracture networks with power-law length distributions are considered in conjunction with particle tracking methods. Solute transfer probabilities at fracture junctions are determined from analytical considerations and from simple complete mixing and streamline routing models. For regular fracture networks, mixing conditions at fracture junctions are always dominated by either complete mixing or streamline routing end member cases. Moreover bulk transport properties such as the spreading and the dilution of solute are highly sensitive to the mixing rule. However in power-law length networks there is no significant difference in bulk transport properties, as calculated by assuming either of the two extreme mixing rules. This apparent discrepancy between the effects of mixing properties at fracture junctions in regular and random fracture networks is explained by the statistics of the coordination number and of the flow conditions at fracture intersections. We suggest that the influence of mixing rules on bulk solute transport could be important in systematic orthogonal fracture networks but insignificant in random networks.

• Journal of KIISE
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• v.44 no.11
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• pp.1178-1193
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• 2017

It is very important to understand system behaviors in collective pattern for each knowledge domain. However, there are structural limitations to represent collective behaviors because of the size of system components and the complexity of their interactions, causing the state explosion problem. Further composition with other systems is mostly impractical because of exponential growth of their size and complexity. This paper presents a practical method to model the collective behaviors, based on a new concept of domain engineering: behavior ontology. Firstly, the ontology defines each collective behavior of a system from active ontology. Secondly, the behaviors are formed in a quantifiably abstract lattice, called common regular expression. Thirdly, a lattice can be composed with other lattices based on quantifiably common elements. The method can be one of the most innovative approaches in representing system behaviors in collective pattern, as well as in minimization of system states to reduce system complexity. For implementation, a prototype tool, called PRISM, has been developed on ADOxx Meta-Modelling Platform.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.49 no.2
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• pp.18-27
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• 2012

Optimal quantizers in conducting the entropy-constrained quantization for high bit rates have the lattice structure. The quantization process is simple due to the regular structure and various quantization algorithms are proposed depending on the lattice. In this paper, such a lattice vector quantization is implemented by using the sample-adaptive product quantizer (SAPQ). It is shown that several important lattices can be implemented by SAPQ and the lattice vector quantization can be performed by using a simple integer-transform function of scalar values within SAPQ. The performance of the proposed lattice SAPQ is compared to the entropy-constrained scalar quantizer and the entropy-constrained SAPQ (ECSAPQ) at a similar encoding complexity. Even though ECSAPQ shows a good performance at low bit-rates, lattice SAPQ shows better performance than the ECSAPQ case for a wide range of bit rates.