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Self-evident Automated Proving Based on Point Geometry from the Perspective of Wu's Method Identity

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Journal of Systems Science & Complexity 2019年第1期32卷 78-94页

作者： zhang jingzhong PENG Xicheng CHEN Mao National Engineering Research Center for E-Learning Central China Normal University Institute of Computational Science and Technology Guangzhou University Chongqing Institute of Green and Intelligent Technology Chinese Academy of Sciences

The algebraic methods represented by Wu's method have made signi?cant breakthroughs in the ?eld of geometric theorem proving. Algebraic proofs usually involve large amounts of calculations, thus making it diffcult to understand intuitively. However, if the authors look at Wu's method from the perspective of identity, Wu's method can be understood easily and can be used to generate new geometric propositions. To make geometric reasoning simpler, more expressive, and richer in geometric meaning, the authors establish a geometric algebraic system(point geometry built on nearly 20 basic properties/formulas about operations on points) while maintaining the advantages of the coordinate method, vector method, and particle geometry method and avoiding their disadvantages. Geometric relations in the propositions and conclusions of a geometric problem are expressed as identical equations of vector polynomials according to point geometry. Thereafter, a proof method that maintains the essence of Wu's method is introduced to ?nd the relationships between these equations. A test on more than 400 geometry statements shows that the proposed proof method, which is based on identical equations of vector polynomials, is simple and e?ective. Furthermore, when solving the original problem, this proof method can also help the authors recognize the relationship between the propositions of the problem and help the authors generate new geometric propositions.

关键词： Geometry algebra point geometry proof method based on identical equations vector geometry Wu's method

Exact Bivariate Polynomial Factorization over Q by Approximation of Roots

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Journal of Systems Science & Complexity 2015年第1期28卷 243-260页

作者： FENG Yong WU Wenyuan zhang jingzhong CHEN Jingwei Chongqing Key Lab of Automated Reasoning and Cognition Chongqing Institute of Green and Intelligent Technology(CIGIT)Chinese Academy of Sciences

Factorization of polynomials is one of the foundations of symbolic *** applications arise in numerous branches of mathematics and other ***,the present advanced programming languages such as C++ and J++,do not support symbolic computation ***,it leads to difficulties in applying factorization in engineering *** this paper,the authors present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational *** proposed method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision *** addition,the numerical computation part often only requires double precision and is easily parallelizable.

关键词： Factorization of multivariate polynomials interpolation methods minimal polynomial numerical continuation.

OBTAINING EXACT INTERPOLATION MULTIVARIATE POLYNOMIAL BY APPROXIMATION

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Journal of Systems Science & Complexity 2011年第4期24卷 803-815页

作者： Yong FENG Xiaolin QIN jingzhong zhang Xun YUAN Laboratory of Computer Reasoning and Trustworthy Computation University of Electronic b'cience and 'l~ech-nology of China Chengdu 611731 China. Laboratory for Automated Reasoning and Programming Chengdu Institute of Computer Applications ChineseAcademy of Sciences Chengdu 610041 China Graduate University of Chinese Academy of Sciences Beijing100049 China. Laborutory of Computer Reasoning and 7Yustworthy Computation University of Electronic Science and Tech-nology of China Chengdu 611731 China. Laboratory for Automated Reasoning and Programming Chengdu Institute of Computer Applications ChineseAcademy of Sciences Chengdu 610041 China.

In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing, etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In order to improve the situation, exact interpolating methods are often proposed for the exact results and approximate interpolating methods for the ap- proximate ones. In this paper, the authors study how to obtain exact interpolation polynomial with rational coefficients by approximate interpolating methods.

关键词： Continued fraction multivariate interpolation numerical approximate computation symbolic-numerical computation Vandermonde determinant.

An advanced operating environment for mathematics education resources

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Science China(Information Sciences) 2018年第9期61卷 270-281页

作者： Yongsheng RAO jingzhong zhang Yu ZOU Yanchun SUN Xiangping CHEN Songhua XU School of Data and Computer Science Sun Yat-Sen University Academy for Intelligent Software Guangzhou University Institute of Mathematics and Computer Science Guizhou Normal College School of Electronics Engineering and Computer Science Peking University Key Laboratory of High Confidence Software Technologies Ministry of Education Beijing College of Computer Sciences New Jersey Institute of Technology

The potential of information technology(IT)in education modernization has been widely *** the broad efforts for advancing education IT,digital education resources continue to receive a high level of attention,with the... 详细信息

关键词： SSP OA An advanced operating environment for mathematics education resources OER Figure

Development of a portable reflectance confocal microscope and its application in the noninvasive in vivo evaluation of mesenchymal stem cell-promoted cutaneous wound healing

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Bio-Design and Manufacturing 2023年第3期6卷 268-283页

作者： Lixing zhang Xin Miao Meijia Wang Aihua Shi Jingwen Wang Zhonglin Ma Yunhai zhang jingzhong zhang Shuang Yu Suzhou Institute of Biomedical Engineering and Technology(SIBET) Chinese Academy of SciencesSuzhou 215163China Department of Biomedical Engineering School of Medical ImagingXuzhou Medical UniversityXuzhou 221004China Zhengzhou Zhongke Institute of Biomedical Engineering and Technology Affiliated with SIBET Zhengzhou 450001China School of Biomedical Engineering(Suzhou) Division of Life Sciences and MedicineUniversity of Science and Technology of ChinaHefei 230026China School of Radiation Medicine and Protection Soochow UniversitySuzhou 215123China

The process of wound healing is routinely evaluated by histological evaluation in the clinic,which may cause scarring and secondary *** confocal microscopy(RCM)represents a noninvasive,real-time imaging technique that allows in vivo evaluation of the *** RCM was wide-probe-based,which limited its application on uneven and covered *** this study,we report the development of a portable reflectance confocal microscope(PRCM)in which all components were assembled in a handheld *** the size and weight of the PRCM were reduced based on the use of a microelectromechanical system,the resolution was kept at 0.91μm,and the field of view of the system was 343μm×532μ*** used in vivo,the PRCM was able to visualize cellular and nuclear morphology for both mouse and human *** evaluations were then performed on wounds after topically applied mesenchymal stem cells(MSCs)or saline *** PRCM allowed visualization of the formation of collagen bundles,re-epithelization from the wound edge to the wound bed,and hair follicle regeneration,which were consistent with histological ***,we offer new insights into monitoring the effects of topically applied MSCs on the process of wound healing by using *** study illustrates that the newly developed PRCM represents a promising device for real-time,noninvasive monitoring of the dynamic process of wound healing,which demonstrates its potential to diagnose,monitor,or predict disease in clinical wound therapy.

关键词： Portable reflectance confocal microscope Wound healing Noninvasive optical imaging Real-time in vivo visualization

Neurotoxic mechanism of 1-methyl-4-phenyl-1,2,3,6-tetradropyridine

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Neural Regeneration Research 2006年第4期1卷 328-330页

作者： Xiulan Yang jingzhong zhang Qunyuan xu Beijing Institute for Neuroscience Beijing Center for Neural Regeneration and RepairCapital Medical University Beijing 100054 China

BACKGROUND ： To summarize the metabolic pathway of 1-methyl-4-phenyl-1,2,3,6-tetradropyridine （MPTP） and its mechanism in inducing Parkinson disease. DATA SOURCES： A computer-based online search of Medline database was undertaken to identify articles about the metabolic pathway of MPTP and its mechanism in inducing Parkinson disease published in English between January 1996 and August 2004, the keywords were ＂MPTP, Parkinson disease＂. Meanwhile, Chinese relevant articles published between January 2000 and August 2004 were searched in Wanfang database with the keywords of ＂MPTP, Parkinson disease＂. STUDY SELECTION： More than 300 relevant literatures were retrieved, and the full-texts were further searched, those about the establishment of animal models, molecular mechanism of MPTP neurotoxicity and the metabolism were selected, and the obviously repetitive ones, case report and reviews were excluded, finally 18 of them were selected for summarization. DATA EXTRACTION： The 18 literatures were categorized according to MPTP induced animal models of Parkinson disease, mechanism of MPTP in inducing apoptosis in models of Parkinson disease, role of dopamine in the neurotoxic mechanism of MPTP, the role of reactive oxygen species and nitric oxide in the neurotoxicity of MPTP. DATA SYNTHESIS： Animal models of Parkinson disease induced by MPTP can not only produce the clinical characters of Parkinson disease, also duplicate the main biochemical and pathological changes of Parkinson disease. The metabolic pathway of MPTP and its mechanism in inducing Parkinson disease included producing free oxygen and nitric oxide, damaging mitochondrial respiratory chain, and inducing apoptosis, etc. which could all lead to the degeneration and loss of dopaminergic neurons. CONCLUSION ： Although some aspects of the models of Parkinson disease are different from that in human beings, we can still know the neurodegeneration of Parkinson disease through studying the molecular mechanis

关键词： MPTP Neurotoxic mechanism of 1-methyl-4-phenyl-1,2,3,6-tetradropyridine

Novel pneumatically assisted atomization device for living cell delivery:application of sprayed mesenchymal stem cells for skin regeneration

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Bio-Design and Manufacturing 2022年第1期5卷 220-232页

作者： Lixing zhang Xintao Yan Li An Meijia Wang Xi Xu Zhonglin Ma Mengting Nie Fangzhou Du jingzhong zhang Shuang Yu Suzhou Institute of Biomedical Engineering and Technology Chinese Academy of SciencesSuzhou 215163China Zhengzhou Institute of Engineering and Technology Affiliated with SIBET Zhengzhou 450001China Xuzhou Medical University Xuzhou 221004China Academy for Engineering and Technology Fudan UniversityShanghai 200433China

Large cutaneous wounds pose a severe medical problem and may be deadly in cases when regeneration is ***,topical stem cell therapy has been realized as a promising strategy for wound healing and skin ***,stem cells must be administrated uniformly to the wound area,otherwise treatment will be ineffective,which has been a limitation of current administration ***,the delivery pressure and nozzle features of most clinical cell spray devices are unknown,which may significantly affect the viability of sprayed cells and their capacity for ***,we developed a novel pneumatically assisted atomization device(PAAD)in which cell suspensions were uniformly atomized at a low delivery *** optimized the applied fluidic pressure and air pressure to maximize cell survival and function for the application of multiple cell types,while ensuring uniform dispersal across the wound ***,we found that the application of sprayed umbilical cord-derived mesenchymal stem cells to wound sites significantly accelerated wound healing and promoted appendage regeneration on an excisional cutaneous wound ***,the novel PAAD system delivered living cells uniformly and maintained the viability and differentiation of sprayed cells,strongly suggesting its potential for application in clinical cell therapy,especially for large,irregular,and severe skin wounds.

关键词： Cell delivery Skin wound Wound healing Spray application Cell-spray autografting Stem cell therapy

Active shim coils design for Halbach magnet based on inverse boundary element method

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Magnetic Resonance Letters 2022年第3期2卷 159-169页

作者： Yajie Xu Feng Wang Ya Wang Peng Yu jingzhong zhang Xiaodong Yang Suzhou Institute of Biomedical Engineering and Technology Chinese Academy of SciencesSuzhou215163China School of Electronics and Information Engineering Changchun University of Science and TechnologyChangchun130022China School of Biomedical Engineering(Suzhou) Division of Life Sciences and MedicineUniversity of Science and Technology of ChinaHefei230026China Jinan Guoke Medical Technology Development Co. LtdJinan250101China

With advantages of small volume,high field strength,and compact stray field,the Halbach array magnet is of great potential in desktop NMR ***,field inhomogeneity poses a main obstacle to its *** shimming is necessary for improving the field *** active shim coil design method for cylindrical Halbach magnet based on inverse boundary element method(iBEM)is introduced in this *** coils targeting 1st~3rd and Z4/Z5/Z6 spherical harmonic(SH)terms were designed with constraints of field accuracy,resistance,inductance,and current *** loops and symmetric property influence were discussed to further improve the performance of high-order shim ***,with the prototype of the shim coils constructed,field pattern and SH transformation proved that the coils designed could fit the target SH distribution,though contamination from low-order components existed in highorder terms.A practical shimming experiment on the Halbach magnet has improved the homogeneity from 40.3 ppm to 3.8 ppm in radius 2.5 mm,height 5 mm cylindrical sample space,verifying the coils'compensation *** work provides a flexible inverse coil design method for cylindrical Halbach magnet and discusses the high-order shim coil design and implementation,which is potential in nuclear magnetic resonance applications based on Halbach magnet arrays.

关键词： Active shimming iBEM Halbach Magnetic resonance

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基于复数法的几何定理可读机器证明

计算机研究与发展 2013年第9期50卷 1963-1969页

作者：李涛张景中广州大学数学与信息科学学院广州510006 广州大学计算机科学与教育软件学院广州510006

已有的机器证明方法在处理一些涉及大规模符号运算的几何问题时,常因算法复杂度过高或机器能力的限制,有时并不能在合理时间内实现可读机器证明.故提出了复数法这一新的几何定理机器证明算法,并选用符号计算功能较为强大的软件Mathemat... 详细信息

已有的机器证明方法在处理一些涉及大规模符号运算的几何问题时,常因算法复杂度过高或机器能力的限制,有时并不能在合理时间内实现可读机器证明.故提出了复数法这一新的几何定理机器证明算法,并选用符号计算功能较为强大的软件Mathematica创建了新证明器CNMP(complex number method prover).新提出的复数法能有效地解决构造型几何命题,对用于测试与评价几何定理证明器性能的综合性平台TGTP(thousands of geometric problems for geometric theorem provers)上的180个几何问题的实验结果表明,CNMP的解题能力与运行效率均令人满意.尤其是对于一些具有相当难度的几何定理,如五圆定理、Morley定理、Lemoine圆定理、Thebault定理、Brocard圆定理等,CNMP均能在短时间内给出可读机器证明.

关键词：复数法 CNMP 可读机器证明 TGTP 五圆定理