• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.1009-1020
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• 1999

The minimum permanent and the set of minimizing matrices over the face of the polytope n of all doubly stochastic matrices of order n determined by any staircase matrix was determined in [4] in terms of some parameter called frame. A staircase matrix can be described very simply as a Ferrers matrix by its row sum vector. In this paper, some simple exposition of the permanent minimization problem over the faces determined by Ferrers matrices of the polytope of n are presented in terms of row sum vectors along with simple proofs.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.267-278
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• 2024

In this paper, we continue to explore an idea presented in [3] and introduce a new class of matrix rings called staircase matrix rings which has applications in noncommutative ring theory. We show that these rings preserve the notions of reduced, symmetric, reversible, IFP, reflexive, abelian rings, etc.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.1732-1733
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• 2011

This paper presents observer-based controller design for interval type-2 fuzzy system with staircase membership approximation. In type-2 fuzzy case, membership function is itself fuzzy set itself. Thus, type-2 fuzzy system can deal with parametric uncertainties of nonlinear system by capturing the uncertainties in membership function. Likewise, stabilization condition of type-2 fuzzy system is derived from quadratic Lyapunov function, and it goes to linear matrix inequality. Furthermore, in this paper, to relax the conservativeness of stabilization condition, staircase membership function approximating method is applied. Observer-based control method is adopted to control system which has some unmeasurable states. To prove suitability of our proposed method, numerical example is presented.

• Journal of Korean Society for Quality Management
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• v.35 no.3
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• pp.107-117
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• 2007

The fatigue has been considered the most failure mode of metal, ceramic, and composite materials. In this paper, numerical experiments to asses the usefulness of two Dixon's methods(small and large samples) and 14 S-N methods on assumptions of lognormal fatigue limit distribution under RFL(Random Fatigue Limit) model are conducted for staircase(or up-and-down) test and compared by MSE(Mean Squared Error) and bias for estimates of mean log-fatigue limit. Also, guidelines for staircase test plans to choose initial stress level and step size are recommended from numerical experiments including sensitivity analyses. In addition, the parametric bootstrap method to construct a confidence interval for the mean of log-fatigue limit by the percentile method using a transition probability matrix of Markov chain is presented and illustrated with an example.

• Korean Journal of Construction Engineering and Management
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• v.20 no.5
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• pp.104-114
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• 2019

This study explored to analyze the winning determinants of the lawsuit cases on the urban and housing redevelopment project based on jurimetric methods. Based on affirm-rate and staircase matrix tables, 441 lawsuit judgments are analyzed. Research findings in affirm-rate analysis indicate that past legal relation, no own defect of accreditation, no ownership or association member status, lapse of period of litigation, and no legal interest are identified as higher rate in order for the reason for plea on the merit. And so are defect on calculation of consent rate, defect in relation with written consent, approval before zoning designation, defect in relation with general meeting, and defect on zoning designation for the issue on the merit. It is noteworthy from the staircase matrix table analysis that the criteria for affecting the lawsuit outcome is determined based on key forecasting variables such as past legal relation and no ownership or association member status. This study intends to provide the implication that the unnecessary disputes can be reduced in the urban and housing redevelopment project by the implementation of jurimetric quantitative analysis methodology from the perspective of empirical law.

• Proceedings of the KIEE Conference
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• 2000.07e
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• pp.136-141
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• 2000

This paper proposes the novel control of a static synchronous compensator (STATCOM). This STATCOM system consists of cascade multilevel inverter which employs H-bridge inverter(HBI) The STATCOM system is modeled in the d-q transform matrix. This model is used to design a controller. The selective harmonic elimination method(SHEM) allows to keep the total harmonic distortion (THD) low in the output voltage. The switching method produces the staircase type waveform in cascade multilevel inverter. To balance the DC voltages in HBIs capacitor, the rotated switching scheme is newly proposed in this paper. The proposed control scheme is verified in the simulated results.

• The Journal of the Petrological Society of Korea
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• v.9 no.4
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• pp.211-237
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• 2000

Major element zoning has been analyzed in garnet porphroblasts obtained from the Grt-St and Ky-Grt-St grade assemblages in Zones I on the northern flank of the Pelham Dome, north central Massachusetts. These porphyroblasts grew during multiple phases of deformation and meta-morphism revealed by the inclusion trail geometry plus the chemical zoning patterns within garnet porphyroblasts. Unusual zoning patterns, including zoning reversals and gradient changes in XMn, zlgzag patterns in Fe/(Fe +Mg) and staircase-shaped patterns in XCa, are coincident with textural truncations and other changes in microstructure within the garnet porphrublasts. Chemical variations in plagioclase, biotite, muscovite and staurolite combined with inclusion trail geometry and petrography reveal that the garnet zoning patterns are modified by combinations of the following. (1) Uni-and divariant reactions involving garnet consumption(Grt+ Chl+Ms=St+Bt+Qtz + $H_2$O) and production(St+Ms + Qtz= Bt+ Grt +A1$_2$$SiO_{5}$ + $H_2$O). (2) Deformation induced episudic ionit dissolution, preferential diffusion and re-distribution during foliation development. (3) P-T changes during growth of the porphyroblasts. The P-T paths combined with petrographic and inclusion trail morphology observations consist of two pattens; (1) heating/compression during NW-SE shortening; and (2) decompression with cooling during NNW-SSE shortening. Based on temperature-time(T-t) geochronological data and late-Paleozoic tectonic model, Alleghanian metamorphism, which is the result of heterogeneous shearing concentrated along the boundary between the Abalone Terrane(Pelham dome) and cover rocks(Bronson Hill Terrane), has produced Ky-St-Ms mineral assemblage during Pennsylvanian(290-300 Ma) in Shutesbury area. However, temperature of alleghanian metamorphism was not high enough to form garnet and staurolite in the Northfiled syncline area. Alleghanian metamorphism has affected only the matrix due to heterogeneous shearing in the study area.