• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.513-519
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• 1997

We show that each orthomodular lattice containing only atomic nonpath-connected blocks is a full subalgebra of an irreducible path-connected orthomodular lattice and there is a path-connected orthomodualr lattice L containing a weakly path-connected full subalgebra C(x) for some element x in L.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.845-856
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• 2009

A block of an orthomodular lattice L is a maximal Boolean subalgebra of L. A site is a subalgebra of an orthomodular lattice L of the form S = A $\cap$ B, where A and B are distinct blocks of L. An orthomodular lattice L is called with finite sites if |A $\cap$ B| < $\infty$ for all distinct blocks A, B of L. We prove that there exists a weakly path-connected orthomodular lattice with finite sites which is not path-connected and if L is an orthomodular lattice such that the height of the join-semilattice [ComL]$\vee$ generated by the commutators of L is finite, then L is pathconnected.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.197-204
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• 2004

Every orthomodular lattice satisfying the loop lemma is the direct product of a Boolean algebra and an irreducible path-connected orthomodular lattice.

• Korean Journal of Materials Research
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• v.25 no.5
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• pp.221-225
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• 2015

In-situ neutron diffraction has been employed to examine the effect of strain path on lattice strain evolution during monotonic and cyclic tension in an extruded Mg-8.5wt.%Al alloy. In the cyclic tension test, the maximum applied stress increased with cycle number. Lattice strain data were acquired for three grain orientations, characterized by the plane normal to the stress axis. The lattice strain in the hard {10.0} orientation, which is unfavorably oriented for both basal slip and {10.2} extension twinning, evolved linearly throughout both tests during loading and unloading. The {00.2} orientation exhibited significant relaxation associated with {10.2} extension twinning. Coupled with a linear lattice strain unloading behavior, this relaxation led to increasingly compressive residual strains in the {00.2} orientation with increasing cycle number. The {10.1} orientation is favorably oriented for basal slip, and thus showed a soft grain behavior. Microyielding occurred in the monotonic tension test and in all cycles of the cyclic test at an applied stress of ~50 MPa, indicating that strain hardening in this orientation was not completely stable from one cycle to the next. The lattice strain unloading behavior was linear in the {10.1} orientation, leading to a compressive residual strain after every cycle, which, however, did not increase systematically from one cycle to the next as in the {00.2} orientation.

• Korean Journal of Mathematics
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• v.15 no.2
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• pp.177-183
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• 2007

In this paper, we study the Riordan matrices with the A-sequence (1,1,...,1,0,...) where 1's appear in m times. As a result, we obtain new Riordan matrices and give their lattice path interpretations.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.217-225
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• 1996

An orthomodular lattice (abbreviated by OML) is an ortholattice L which satisfies the orthomodular law: if x $\leq$ y, then $y = x \vee (x' \wedge y)$ [5]. A Boolean algebra B is an ortholattice satisfying the distributive law : $x \vee (g \wedge z) = (x \vee y) \wedge (x \vee z) \forall x, y, z \in B$.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.285-292
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• 1995

Some nonpath-connected orthomodular lattices are given : Every infinite direct product of othomodular lattices containing infinitely many non-Boolean factors is a nonpath-connected orthomodular lattice. The orthomodular lattice of all closed subspaces of an infinite dimensional Hilbert space is a nonpath-connected orthomodular lattice.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.181-193
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• 1997

The enumeration of various classes of paths in the real plane has an important implications in the area of combinatorics wit statistical applications. In 1887, D. Andre [3, pp. 21] first solved the famous ballot problem, formulated by Berttand [2], by using the well-known reflection principle which contributed tremendously to resolve the problems of enumeration of various classes of lattice paths in the plane. First, it is necessary to state the definition of NSEW-paths in the palne which will be employed throughout the paper. From [3, 10, 11], we can find results concerning many of the basics discussed in section 1 and 2.

• Journal of KIISE:Software and Applications
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• v.41 no.7
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• pp.523-532
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• 2014

In this paper, we propose a lattice-based discriminative approach for Korean morphological analysis and POS tagging. In our approach, for an input sentence, a morpheme lattice is first created from a lexicon where each node corresponds to a morpheme in the lexicon and each edge is formed between two consecutive morphemes. A candidate result of morphological analysis is then represented as a path in the morpheme lattice which is defined as the sequence of edges, starting in the initial state and ending with the final state. In this setting, the morphological analysis is simply considered as the process of finding the best path among all possible paths. Experiment results show that the proposed lattice-based method outperforms the first-order linear-chain CRF.

• Steel and Composite Structures
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• v.49 no.4
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• pp.393-405
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• 2023

In this paper, the energy absorption capability of a novel cruciform composite lattice structure was evaluated through the simulation of compression tests. For this purpose, several test samples of Polylactic acid cellular reinforced with continuous glass fibers were prepared for compression testing using the additive manufacturing method of material extrusion. Using a conventional path design for material extrusion, multiple debonding is probable to be occurred at the joint regions of adjacent cells. Therefore, an innovative printing path design was proposed for the cruciform lattice structure. Afterwards, quasistatic compression tests were performed to evaluate the energy absorption behaviour of this structure. A finite element model based on local material property degradation was then developed to verify the experimental test and extend the virtual test method. Accordingly, different combinations of unit cells' dimensions using the design of the experiment were numerically proposed to obtain the optimal configuration in terms of the total absorbed energy. Having brilliant energy absorption properties, the studied cruciform lattice with its optimized unit cell dimensions can be used as an energy absorber in crashworthiness applications. Finally, a cellular structure will be suitable with optimal behavior in crush load efficiency and high energy absorption.