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FSI-IDEALS AND FSC-IDEALS OF BCI-ALGEBRAS
Liu, Yong-Lin,Liu, San-Yang,Meng, Jie Korean Mathematical Society 2004 대한수학회보 Vol.41 No.1
The notions of FSI-ideals and FSC-ideals in BCI-algebras are introduced. The characterization properties of FSI-ideals and FSC-ideals are obtained. We investigate the relations between FSI-ideals (resp. FSC-ideals) and other fuzzy ideals, between FSI-ideals (resp. FSC-ideals) and BCI-algebras, and show that a fuzzy subset of a BCI-algebra is an FSI-ideal if and only if it is both an FSC-ideal and a fuzzy BCI-positive implicative ideal.
$FSI$-ideals and $FSC$-ideals of BCI-algebras
Yong Lin Liu,San Yang Liu,Jie Meng 대한수학회 2004 대한수학회보 Vol.41 No.1
The notions of FSI-ideals and FSC-ideals in BCI-algebras areintroduced. The characterization properties of FSI-ideals andFSC-ideals are obtained. We investigate the relations betweenFSI-ideals (resp. FSC-ideals) and other fuzzy ideals, betweenFSI-ideals (resp. FSC-ideals) and BCI-algebras, and show thata fuzzy subset of a BCI-algebra is an FSI-ideal if and only ifit is both an FSC-ideal and a fuzzy BCI-positive implicativeideal.
Lei Wang,Liu Yang,Xiao-San Zhou,Tao-Hong Li,Chao-Liang Liu 한국응용곤충학회 2018 Journal of Asia-Pacific Entomology Vol.21 No.3
Clip domain serine proteases (Clips) mediate various biological processes, especially in insect immune responses such as prophenoloxidase (proPO) activation and Toll pathway initiation. In the present study, we cloned and studied the functions of a clip domain serine protease from Antheraea pernyi (ApSnake). ApSnake contains a typical clip domain and a trypsin-like serine protease domain. It shares high similarity with serine protease snake in Bombyx mori, and groups into the CLIPC family. ApSnake mRNA expressions were detected in all tested tissues, particularly high in the hemocytes. Challenged with four different microorganisms (Escherichia coli, Beauveria bassiana, Micrococcus luteus or Nuclear polyhedrosis virus), the expressions of ApSnake mRNA were induced significantly compared with control, particularly challenged by B. bassiana and M. luteus. Recombinant ApSnake protein stimulated melanization reaction and prophenoloxidase activation in A. pernyi hemolymph, but had no effect on phenoloxidase activity. Injection of recombinant ApSnake into A. pernyi larvae increased the transcript levels of proPO and antimicrobial peptides (AMPs) in hemocytes significantly. Our results suggested that ApSnake might be a modulating protein that both stimulate the melanization activation process and AMPs synthesis, and plays an important role in the innate immunity of A. pernyi.
ON POSITIVE DEFINITE SOLUTIONS OF A CLASS OF NONLINEAR MATRIX EQUATION
Fang, Liang,Liu, San-Yang,Yin, Xiao-Yan Korean Mathematical Society 2018 대한수학회보 Vol.55 No.2
This paper is concerned with the positive definite solutions of the nonlinear matrix equation $X-A^*{\bar{X}}^{-1}A=Q$, where A, Q are given complex matrices with Q positive definite. We show that such a matrix equation always has a unique positive definite solution and if A is nonsingular, it also has a unique negative definite solution. Moreover, based on Sherman-Morrison-Woodbury formula, we derive elegant relationships between solutions of $X-A^*{\bar{X}}^{-1}A=I$ and the well-studied standard nonlinear matrix equation $Y+B^*Y^{-1}B=Q$, where B, Q are uniquely determined by A. Then several effective numerical algorithms for the unique positive definite solution of $X-A^*{\bar{X}}^{-1}A=Q$ with linear or quadratic convergence rate such as inverse-free fixed-point iteration, structure-preserving doubling algorithm, Newton algorithm are proposed. Numerical examples are presented to illustrate the effectiveness of all the theoretical results and the behavior of the considered algorithms.
On positive definite solutions of a class of nonlinear matrix equation
Liang Fang,San-Yang Liu,Xiaoyan Yin 대한수학회 2018 대한수학회보 Vol.55 No.2
This paper is concerned with the positive definite solutions of the nonlinear matrix equation $X-A^{*}\bar{X}^{-1}A=Q$, where $A, Q$ are given complex matrices with $Q$ positive definite. We show that such a matrix equation always has a unique positive definite solution and if $A$ is nonsingular, it also has a unique negative definite solution. Moreover, based on Sherman-Morrison-Woodbury formula, we derive elegant relationships between solutions of $X-A^{*}\bar{X}^{-1}A=I$ and the well-studied standard nonlinear matrix equation $Y+B^{*}Y^{-1}B=Q$, where $B, Q$ are uniquely determined by $A$. Then several effective numerical algorithms for the unique positive definite solution of $X-A^{*}\bar{X}^{-1}A=Q$ with linear or quadratic convergence rate such as inverse-free fixed-point iteration, structure-preserving doubling algorithm, Newton algorithm are proposed. Numerical examples are presented to illustrate the effectiveness of all the theoretical results and the behavior of the considered algorithms.
Xiu-Shi Yang,Li-Li Wang,Xian-Rong Zhou,Shaomin Shuang,Zhi-Hua Zhu,Nan Li,Yan Li,Fang Liu,San-Cai Liu,Ping Lu,Guixing Ren,Chuan Dong 한국식품과학회 2013 Food Science and Biotechnology Vol.22 No.6
Quantitative detection of protein, fat, starch,and amino acids in foxtail millet using Fourier transformnear-infrared spectroscopy (NIRS) was investigated. Foxtail millet samples (n=259) were analyzed using NIRS. Spectral data were linearized with data from chemicalanalyses. Calibration models were established using apartial least-squares (PLS) algorithm with cross-validation. Optimized models were tested using external validation setsamples with coefficients of determination in the externalvalidation (R2val) of >0.90. Residual predictive deviation(RPD) values were nearly equal to or >2.5 for crudeprotein, alanine, aspartic acid, glutamic acid, isoleucine,leucine, and serine. However, for glycine, histidine,phenylalanine, proline, threonine, tyrosine, and valine, theR2val values were >0.83 and RPD values were nearly equalto or >2.0. For crude fat, total starch, arginine, and lysine,the R2val values were >0.70 and RPD values were >1.5. NIRS is a rapid determination tool for foxtail milletbreeding, and for quality control.
Ju, Jyh-Cherng,Yang, Jyh-Shyu,Liu, Chien-Tsung,Chen, Chien-Hong,Tseng, Jung-Kai,Chou, Po-Chien,Cheng, San-Pao Asian Australasian Association of Animal Productio 2003 Animal Bioscience Vol.16 No.1
Experiments were conducted to evaluate the effect of blastomere diameters and cell cycle stages on the subsequent development of nuclear transplant rabbit embryos (NT-embryos) using nuclei derived from the 16- or 32-cell stage embryos. All blastomeres and NT-embryos were cultured individually in modified Ham's F-10 medium supplemented with 10% rabbit serum (RS) at $38^{\circ}C$ and 5% $CO_2$ in air. The diameter of blastomeres from 16-cell stage embryos was found twice of those from 32-cell stage (51 vs 27 ${\mu}m$). Significant differences were observed in cleavage rates ($\geq$3 divisions) in the isolated single blastomeres (54 vs 48 for 16-cell; 28 vs 14 for 32-cell, p<0.05), but the fusion rates of oocytes with transferred nuclei were similar between small and large single blastomeres derived from either 16-cell or 32-cell stage embryos. When 16-cell stage blastomeres were used as nuclear donors, cleavage rates ($\geq$3 divisions) of the NT-embryos were greater in the small nuclear donors than in the large donors (73 vs 55%, p<0.05). On the contrary, significantly higher cleavage (43 vs 6%, p<0.05) and developmental rates (14 vs 0%, p<0.05) were observed in the large blastomere nuclear donor group of the 32-cell stage embryos. When the cell cycle stages were controlled by a microtubule polymerization inhibitor (Demicolcine, DEM) or the combined treatment of DEM and Aphidicolin (APH), a DNA polymerase inhibitor, fusion rates were 88-96% for the 16-cell donor group (without DEM treatment), which were greater than the 32-cell donor group (54-58%). Cleavage rates were also greater in the transplants derived from G1 nuclear donor group (93-95%) than those from the DEM and APH combined treatment (73%) for the 16-cell donor group (p<0.05). No significant difference was detected in the morula/blastocyst rates in either donor cell stage (p>0.05). In conclusion, it appeared that no difference in the developmental competence between large and small isolated blastomeres was observed. When smaller 16-cell stage blastomeres were used as nuclear donor, the cleavage rate or development of NT-embryos was improved and was compromised when 32-cell stage blastomeres were used. Therefore, control nuclear stage of the donor cell at $G_1$ phase in preactivated nuclear recipients seemed to be beneficial for the cleavage rate of the reconstructed embryo in the 16-cell transplant, but not for subsequent morula or blastocyst development.
Jiang, Zhao-Lin,Liu, San-Yang 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.14 No.1
The level-m scaled circulant factor matrix over the complex number field is introduced. Its diagonalization and spectral decomposition and representation are discussed. An explicit formula for the entries of the inverse of a level-m scaled circulant factor matrix is presented. Finally, an algorithm for finding the inverse of such matrices over the quaternion division algebra is given.