1,454 research outputs found

    Linear operators that strongly preserve regularity of fuzzy matrices

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    An ntimesnntimes n fuzzy matrix AA is called {regular} if there is an ntimesnntimes n fuzzy matrix GG such that AGA=AAGA=A. We study the problem of characterizing those linear operators TT on the fuzzy matrices such that T(X)T(X) is regular if and only if XX is. Consequently, we obtain that TT strongly preserves regularity of fuzzy matrices if and only if there are permutation matrices PP and QQ such that it has the form T(X)=PXQT(X)=PXQ or T(X)=PXtQT(X)=PX^tQ for all fuzzy matrices XX

    Linear preservers of term ranks of matrices over semirings

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    AbstractThe term rank of a matrix A over a semiring S is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we study linear operators that preserve term ranks of matrices over S. In particular, we show that a linear operator T on matrix space over S preserves term rank if and only if T preserves term ranks 1 and α(≥2) if and only if T preserves two consecutive term ranks in a restricted condition. Other characterizations of term-rank preservers are also given

    Linear Operators That Preserve Two Genera of a Graph

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    If a graph can be embedded in a smooth orientable surface of genus g without edge crossings and can not be embedded on one of genus g − 1 without edge crossings, then we say that the graph has genus g. We consider a mapping on the set of graphs with m vertices into itself. The mapping is called a linear operator if it preserves a union of graphs and it also preserves the empty graph. On the set of graphs with m vertices, we consider and investigate those linear operators which map graphs of genus g to graphs of genus g and graphs of genus g + j to graphs of genus g + j for j ≤ g and m sufficiently large. We show that such linear operators are necessarily vertex permutations

    A Study on the Healthy Housing Quality of Multi-family Attached House According to Dwelling Unit Age

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    AbstractThe purpose of this study is to understand the healthy housing quality of four different multi-family attached house complexes that the constructions were finished at different years. In order to evaluate their healthy housing quality, the evaluation indicators of healthy housing, that have already existed, were used and the four complexes with different dwelling unit ages, located in Busan of Korea, were evaluated. For this, this study carry out residents’ evaluations of healthy housing quality through surveys on their satisfaction, and the study mainly identified characteristic according to dwelling unit age. According to the study, the health housing quality of multi-family attached house, of which the dwelling unit age is 10, begins to decrease in terms of managerial aspect. The healthy housing quality of social and managerial aspects is important for dwellers. The evaluation results can then be utilized to develop guidelines to manage and maintain healthy housing environments for apartments

    Multi-Color Luminescence Transition of Upconversion Nanocrystals via Crystal Phase Control with SiO2 for High Temperature Thermal Labels

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    Upconversion nanocrystals (UCNs)-embedded microarchitectures with luminescence color transition capability and enhanced luminescence intensity under extreme conditions are suitable for developing a robust labeling system in a high-temperature thermal industrial process. However, most UCNs based labeling systems are limited by the loss of luminescence owing to the destruction of the crystalline phase or by a predetermined luminescence color without color transition capability. Herein, an unusual crystal phase transition of UCNs to a hexagonal apatite phase in the presence of SiO2 nanoparticles is reported with the enhancements of 130-fold green luminescence and 52-fold luminance as compared to that of the SiO2-free counterpart. By rationally combining this strategy with an additive color mixing method using a mask-less flow lithography technique, single to multiple luminescence color transition, scalable labeling systems with hidden letters-, and multi-luminescence colored microparticles are demonstrated for a UCNs luminescence color change-based high temperature labeling system
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