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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.
( Fang Liang ),( Kui Du ),( Xiaobin Wen ),( Liming Luo ),( Yahong Geng ),( Yeguang Li ) 한국미생물 · 생명공학회 2015 Journal of microbiology and biotechnology Vol.25 No.12
To understand the effects of physicochemical factors on nitrite transformation by microalgae, a lipid-rich Chlorella with high nitrite tolerance was cultured with 8 mmol/l sodium nitrite as sole nitrogen source under different conditions. The results showed that nitrite transformation was mainly dependent on the metabolic activities of algal cells rather than oxidation of nitrite by dissolved oxygen. Light intensity, temperature, pH, NaHCO3 concentrations, and initial cell densities had significant effects on the rate of nitrite transformation. Single-factor experiments revealed that the optimum conditions for nitrite transformation were light intensity: 300 μmol/㎡/s; temperature: 30℃; pH: 7-8; NaHCO3 concentration: 2.0 g/l; and initial cell density: 0.15 g/l; and the highest nitrite transformation rate of 1.36 mmol/l/d was achieved. There was a positive correlation between nitrite transformation rate and the growth of Chlorella. The relationship between nitrite transformation rate (mg/l/d) and biomass productivity (g/l/d) could be described by the regression equation y = 61.3x (R(2) = 0.9665), meaning that 61.3 mg N element was assimilated by 1.0 g dry biomass on average, which indicated that the nitrite transformation is a process of consuming nitrite as nitrogen source by Chlorella. The results demonstrated that the Chlorella suspension was able to assimilate nitrite efficiently, which implied the feasibility of using flue gas for mass production of Chlorella without preliminary removal of NOX.
Angelica dahurica attenuates melanogenesis in B16F0 cells by repressing Wnt/β-catenin signaling
Fang Chien-Liang,Goswami Debakshee,Kuo Chia-Hua,Day Cecilia Hsuan,Lin Mei-Yi,Ho Tsung-Jung,Yang Liang-Yo,Hsieh Dennis Jine-Yuan,Lin Tzu-Kai,Huang Chih-Yang 대한독성 유전단백체 학회 2023 Molecular & cellular toxicology Vol.19 No.1
Background Melanogenesis is a complex process which is tightly regulated by several enzymes. However, abnormal melanogenesis can cause severe dermatological problems. Roots of Angelica dahurica have been used for skin care as a part of traditional Chinese medicine for many generations. However, the role of A. dahurica in melanogenesis remains unclear. Objective Previous in vitro and in vivo studies have demonstrated that NK-1R exerts positive effects in melanogenesis via the Wnt/βcatenin signaling pathway. In this study, we investigated the effects of A. dahurica ethanol extract (ADE) on NK-1R and Wnt/β-catenin signaling, and evaluated the effect of NK-1R on melanogenesis in B16F0 cells. Results Angelica dahurica ethanol extract efficiently downregulated Neurokinin-1 receptor and Wnt/β-catenin signaling by decreasing the expression of β-catenin, MITF, LEF-1, TYR, TRP1, and TRP2 and increasing the expression of GSK3β, which resulted from the weakened expression of the Neurokinin-1 receptor inhibitor [Sar9,Met(O2 )11]-Substance P (SMSP). Furthermore, the intracellular melanin assay and cellular tyrosinase activity confirmed these findings. Conclusion This study suggests that ADE has potential to downregulate Neurokinin-1 receptor in SMSP-induced B16F0 cells, thereby repressing the Wnt/β-catenin signaling and reduces melanin production.
PICARD VALUES AND NORMALITY CRITERION
Fang, Ming-Liang Korean Mathematical Society 2001 대한수학회보 Vol.38 No.2
In this paper, we study the value distribution of meromorphic functions and prove the following theorem: Let f(z) be a transcendental meromorphic function. If f and f'have the same zeros, then f'(z) takes any non-zero value b infinitely many times.
Water temperature and salinity tolerance of embryos and spat of the mussel, Musculista senhousia
Liang, Zhuo Liang,Kim, Young-Hun,Zhang, Zhi Fang,Lim, Sang-Min,Kang, Kyoung-Ho The Malacological Society of Korea 2009 The Korean Journal of Malacology Vol.25 No.3
The effects of water temperature and salinity on embryonic development and spat survival of mussel Musculista senhousia were investigated. Embryos were incubated in water ranging from 0 to $35^{\circ}C$ and with salinity from 5‰ to 40‰. Mussel spat were tested in water from 0 to $40^{\circ}C$ and with salinity from 0‰ to 100‰. The optimal conditions for mussel embryos were $20-25^{\circ}C$ and salinity from 25‰ to 35‰, based on Within this temperature range, higher temperatures correponded to a shorter duration of the embryonic period. Optimisation of mussel spat survival was at $25-35^{\circ}C$ and salinity from 30‰ to 40‰; both values are higher than those for embryo, which hinted M. senhousia embryos are more vulnerable than spat. Temperatures below $15^{\circ}C$ were lethal for embryos, making temperature a feasible method with which to control the large population of M. senhousia in ark-shell farm during its spawning period.
( Fang Liang ),( Xiao Bin Wen ),( Yahong Geng ),( Zheng Rong Ouyang ),( Li Ming Luo ),( Ye Guang Li ) 한국미생물 · 생명공학회 2013 Journal of microbiology and biotechnology Vol.23 No.4
The effects of culture depth (2-10 cm) and cell density on the growth rate and biomass productivity of Chlorella sp. XQ-200419 were investigated through the use of a selfdesigned open circular pond photobioreactor-imitation system. With increases in culture depths from 2 to 10 cm, the growth rate decreased significantly from 1.08 /d to 0.39 /d. However, the biomass productivity only increased slightly from 8.41 to 11.22 g/m2/d. The biomass productivity (11.08 g/m2/d) achieved in 4 cm culture with an initial OD540 of 0.95 was similar to that achieved in 10 cm culture with an initial OD540 of 0.5. In addition, the duration of maximal areal productivity at a 4 cm depth was prolonged from 1 to 4 days, a finding that was also similar to that of the culture at a 10 cm depth. In both cases, the initial areal biomass densities were identical. Based on these results and previous studies, it can be concluded that the influence of culture depth and cell density on areal biomass productivity is actually due to different areal biomass densities. Under suitable conditions, there are a range of optimal biomass densities, and areal biomass productivity reaches its maximum when the biomass density is within these optimal ranges. Otherwise, biomass productivity will decrease. Therefore, a key factor for high biomass productivity is to maintain an optimal biomass density.
Novel Double-Barrier Rotor Designs in Interior-PM Motor for Reducing Torque Pulsation
Fang, Liang,Kim, Sung-Il,Kwon, Soon-O.,Hong, Jung-Pyo IEEE 2010 IEEE transactions on magnetics Vol.46 No.6
<P> This paper presents various flux-barrier designs in an interior permanent magnet synchronous motor (IPMSM) for reducing torque pulsation. A conventional single-layer IPMSM model, a popular double-layer IPMSM model and two novel double-barrier IPMSM models featuring as a double pairs of flux-barrier flexibly coupled with the simplest single-layer PM, are built and compared together. The geometries of flux-barrier structure in each IPMSM model are optimized by performing response surface methodology (RSM) for minimizing torque ripple and cogging torque. The presented IPMSM models are analyzed by using finite element analysis (FEA), and the validity is confirmed by experiment. Finally, the beneficial attributes of the proposed novel double-barrier IPM designs compared with the single-layer and double-layer IPM designs are emphasized. </P>