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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.
The stiffness-degradation law of base metal after fatigue cracking in steel bridge deck
Liang Fang,Zhongqiu Fu,Bohai Ji,Xincheng Li 국제구조공학회 2023 Steel and Composite Structures, An International J Vol.47 No.2
The stiffness evaluation of cracked base metal is of great guidance to fatigue crack reinforcement. By carrying out fatigue tests and numerical simulation of typical cracking details in steel box girder, the strain-degradation law of cracked base metal was analyzed and the relationship between base metal stress and its displacement (stiffness) was explored. The feasibility of evaluating the stress of cracked base metal based on the stress field at the crack tip was verified. The results demonstrate that the stiffness of cracked base metal shows the fast-to-slow degradation trend with fatigue cracking and the base metal at 50mm or more behind the crack tip basically lose its bearing capacity. Drilling will further accelerate stiffness degradation with the increase of hole diameters. The base metal stress has a negative linear relation with its displacement (stiffness), The stress of cracked base metal is also related to stress intensity factor and its relative position (distance, included angle) to the crack tip, through which the local stiffness can be effectively evaluated. Since the stiffness is not uniformly distributed along the cracked base metal, the reinforcement patch is suggested to be designed according to the stiffness to avoid excessive reinforcement for the areas incompletely unloaded.
Co-Delivery of Hydrophobic and Hydrophilic Drugs from Nanoparticle–Aptamer Bioconjugates
Zhang, Liangfang,Radovic-Moreno, Aleksandar F.,Alexis, Frank,Gu, Frank X.,Basto, Pamela A.,Bagalkot, Vaishali,Jon, Sangyong,Langer, Robert S.,Farokhzad, Omid C. WILEY-VCH Verlag 2007 ChemMedChem Vol.2 No.9
<B>Graphic Abstract</B> <P>Herein we report a novel targeted drug delivery system consisting of nanoparticle–aptamer bioconjugates, which can carry both hydrophobic and hydrophilic chemotherapeutic drugs simultaneously, and deliver them selectively in a targeted and temporally distinct manner. This work provides a robust platform for targeted co-delivery of chemotherapeutic agents with the hope of both leveraging the synergistic effects of multiple drugs and also potentially suppressing the likelihood of drug resistance by the treated tissues. <img src='wiley_img/18607179-2007-2-9-CMDC200700121-content.gif' alt='wiley_img/18607179-2007-2-9-CMDC200700121-content'> </P>
Zhao, Jiagang,Sun, Woong,Cho, Hyo Min,Ouyang, Hong,Li, Wenlin,Lin, Ying,Do, Jiun,Zhang, Liangfang,Ding, Sheng,Liu, Yizhi,Lu, Paul,Zhang, Kang American Society for Biochemistry and Molecular Bi 2013 The Journal of biological chemistry Vol.288 No.1
<P>Spinal cord injury (SCI) results in devastating motor and sensory deficits secondary to disrupted neuronal circuits and poor regenerative potential. Efforts to promote regeneration through cell extrinsic and intrinsic manipulations have met with limited success. Stem cells represent an as yet unrealized therapy in SCI. Recently, we identified novel culture methods to induce and maintain primitive neural stem cells (pNSCs) from human embryonic stem cells. We tested whether transplanted human pNSCs can integrate into the CNS of the developing chick neural tube and injured adult rat spinal cord. Following injection of pNSCs into the developing chick CNS, pNSCs integrated into the dorsal aspects of the neural tube, forming cell clusters that spontaneously differentiated into neurons. Furthermore, following transplantation of pNSCs into the lesioned rat spinal cord, grafted pNSCs survived, differentiated into neurons, and extended long distance axons through the scar tissue at the graft-host interface and into the host spinal cord to form terminal-like structures near host spinal neurons. Together, these findings suggest that pNSCs derived from human embryonic stem cells differentiate into neuronal cell types with the potential to extend axons that associate with circuits of the CNS and, more importantly, provide new insights into CNS integration and axonal regeneration, offering hope for repair in SCI.</P>
( Chao Hsuan Chen ),( Yan Han Wang ),( Teruaki Nakatsuji ),( Yu Tsueng Liu ),( Christos C. Zouboulis ),( Richard L. Gallo ),( Liangfang Zhang ),( Ming Fa Hsieh ),( Chun Ming Huang ) 한국미생물 · 생명공학회 2011 Journal of microbiology and biotechnology Vol.21 No.4
Free fatty acids (FFAs) are known to have bacteriocidal activity and are important components of the innateimmune system. Many FFAs are naturally present in human and animal skin, breast milk, and in the bloodstream. Here, the therapeutic potential of FFAs against methicillin-resistant Staphylococcus aureus (MRSA) is demonstrated in cultures and in mice. Among a series of FFAs, only oleic acid (OA) (C18:1, cis-9) can effectively eliminate Staphylococcus aureus (S. aureus) through cell wall disruption. Lauric acid (LA, C12:0) and palmitic acid (PA, C16:0) do not have this ability. OA can inhibit growth of a number of Gram-positive bacteria, including hospital and community-associated MRSA at a dose that did not show any toxicity to human sebocytes. The bacteriocidal activities of FFAs were also demonstrated in vivo through injection of OA into mouse skin lesions previously infected with a strain of MRSA. In conclusion, our results suggest a promising therapeutic approach against MRSA through boosting the bacteriocidal activities of native FFAs, which may have been co-evolved during the interactions between microbes and their hosts.