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Hypoxia-inducible factor-1α/β-catenin axis:A conserved regulatory hub for enhancing stem cell function in tissue regeneration 认领 引用
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作者 Hui-Fang Wang Peng-Yu Yan +2 位作者 Shoaib Muhammad Yu-Xiang Liu Chun Liu 《World Journal of Stem Cells》 SCIE 2026年第5期1-8,共8页
This article provides an in-depth commentary on the study by Wang et al,which elucidates that the hypoxia-inducible factor-1α(HIF-1α)/β-catenin axis serves as a core hub regulating the function of peripheral blood ... This article provides an in-depth commentary on the study by Wang et al,which elucidates that the hypoxia-inducible factor-1α(HIF-1α)/β-catenin axis serves as a core hub regulating the function of peripheral blood mesenchymal stem cells(PBMSCs)under hypoxic conditions.The research confirms that in a hypoxic environment,HIF-1αacts as an upstream regulator by directly binding to and activating the transcription ofβ-catenin,a relationship that is unidirectional and irreversible.This axis enhances the therapeutic potential of PBMSCs through a dual mechanism:On one hand,it regulates anti-apoptotic proteins while inhibiting pro-apoptotic molecules,significantly improving cell survival and self-renewal capacity;on the other hand,it promotes the secretion of factors such as vascular endothelial growth factor,thereby enhancing angiogenic activity.In a rat myocardial infarction model,PBMSCs overexpressing HIF-1αshowed significantly improved retention in the infarcted area,reduced infarct size,and promoted neovascularization-effects that were abolished upon knockdown ofβ-catenin.This discovery provides a key target for optimizing stem cell therapy for myocardial infarction.By pre-activating this axis in vitro(e.g.,via lentiviral vectors or small-molecule regulators),it is possible to standardize and enhance the survival and reparative capacity of PBMSCs in ischemic tissues,holding important translational medical value. 展开更多
关键词 Hypoxia-inducible factor-1α β-catenin Stem cell Tissue regeneration Conserved regulatory hub
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The lawc gene emerged de novo from conserved genomic elements and acquired a broad expression pattern in Drosophila 认领 引用
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作者 Roman O.Cherezov Julia E.Vorontsova +3 位作者 Elena E.Kuvaeva Angelina A.Akishina Ekaterina L.Zavoloka Olga B.Simonova 《Journal of Genetics and Genomics》 SCIE CAS CSCD 2025年第7期901-914,共14页
It has recently become evident that the de novo emergence of genes is widespread and documented for a variety of organisms.De novo genes frequently emerge in proximity to existing genes,forming gene overlaps.Here,we p... It has recently become evident that the de novo emergence of genes is widespread and documented for a variety of organisms.De novo genes frequently emerge in proximity to existing genes,forming gene overlaps.Here,we present an analysis of the evolutionary history of a putative de novo gene,lawc,which overlaps with the conserved Trf2 gene,which encodes a general transcription factor in Drosophila melanogaster.We demonstrate that lawc emerged approximately 68 million years ago in the 5'-untranslated region(UTR)of Trf2 and displays an extensive spatiotemporal expression pattern.One of the most remarkable features of the lawc evolutionary history is that its emergence was facilitated by the engagement of Drosophilidae-specific short,highly conserved regions located in Trf2 introns.This represents a unique example of putative de novo gene birth involving conserved DNA regions localized in introns of conserved genes.The observed lawc expression pattern may be due to the overlap of lawc with the 5'-UTR of Trf2.This study not only enriches our understanding of gene evolution but also highlights the complex interplay between genetic conservation and innovation. 展开更多
关键词 De novo gene Overlapping genes Conserved regulatory element Expression pattern Drosophila
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Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems 认领 引用 被引量：6
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作者 张明江 方建会 +2 位作者 路凯 张克军 李燕 《Chinese Physics B》 SCIE EI CAS 2009年第11期4650-4656,共7页
This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non- conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conf... This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non- conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conformal invariance of the system are presented. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition that conformal invaxiance of the system would have Lie symmetry under single-parameter infinitesimal transformations is obtained. The corresponding conserved quantity of conformal invariance is derived with the aid of a structure equation. Lastly, an example is given to illustrate the application of the results. 展开更多
关键词 conformal invariance conserved quantity third-order Lagrange equation non-conserved mechanical system
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Lie symmetries and conserved quantities for generalized Birkhoff system 认领 引用 被引量：2
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作者 梅凤翔 崔金超 《Journal of Beijing Institute of Technology》 EI CAS 2011年第3期285-288,共4页
To study Lie symmetry and the conserved quantity of a generalized Birkhoff system with additional terms, the determining equations of the Lie symmetry of the system is derived. A con- served quantity of Hojman＇ s typ... To study Lie symmetry and the conserved quantity of a generalized Birkhoff system with additional terms, the determining equations of the Lie symmetry of the system is derived. A con- served quantity of Hojman＇ s type and a Noether＇ s conserved quantity are deduced by the Lie symme- try under some conditions. One example is given to illustrate the application of the result. 展开更多
关键词 generalized Birkhoff system Lie symmetry Noether conserved quantity conservedquantity of Hojman＇ s type
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Biogenesis of flavor-related linalool is diverged and genetically conserved in tree peony(Paeonia×suffruticosa) 认领 引用 被引量：19
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作者 Shanshan Li Ling Zhang +4 位作者 Miao Sun Mengwen Lv Yong Yang Wenzhong Xu Liangsheng Wang 《Horticulture Research》 SCIE CSCD 2023年第2期15-27,共13页
Floral scent is an important and genetically complex trait in horticultural plants.Tree peony(Paeonia×suffruticosa)originates in the Pan-Himalaya and has nine wild species divided into two subsections,Delavayanae... Floral scent is an important and genetically complex trait in horticultural plants.Tree peony(Paeonia×suffruticosa)originates in the Pan-Himalaya and has nine wild species divided into two subsections,Delavayanae and Vaginatae.Their f lowers are beloved worldwide for their sweet f loral fragrance,yet the f lavor-related volatiles and underlying biosynthetic pathways remain unknown.Here,we characterized the volatile blends of all wild tree peony species and found that the flavor-related volatiles were highly divergent,but linalool was a unique monoterpene in subsect.Delavayanae.Further detection of volatiles in 97 cultivars with various genetic backgrounds showed that linalool was also the characteristic aroma component in Paeonia delavayi hybrid progenies,suggesting that linalool was conserved and dominant within subsect.Delavayanae and its hybrids,instead of species and cultivars from subsect.Vaginatae.Global transcriptome analysis of all wild tree peony species and 60 cultivars revealed five candidate genes that may be involved in key steps of linalool biosynthesis;especially the expressions of three TPS genes,PdTPS1,PdTPS2,and PdTPS4,were significantly positively correlated with linalool emissions across tree peony cultivars.Further biochemical evidence demonstrated that PdTPS1 and PdTPS4were the pivotal genes determining the species-specific and cultivar-specific emission of linalool.This study revealed a new insight into floral scent divergence in tree peony and would greatly facilitate our understanding of the phylogeny and evolution of Paeonia. 展开更多
关键词 conserved tree steps
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Detection of hyper-conserved regions in hepatitis B virus X gene potentially useful for gene therapy 认领 引用 被引量：10
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作者 Carolina González David Tabernero +12 位作者 Maria Francesca Cortese Josep Gregori Rosario Casillas Mar Riveiro-Barciela Cristina Godoy Sara Sopena Ariadna Rando Marcal Yll Rosa Lopez-Martinez Josep Quer Rafael Esteban Maria Buti Francisco Rodríguez-Frías 《World Journal of Gastroenterology》 SCIE CAS 2018年第19期2095-2107,共13页
AIM To detect hyper-conserved regions in the hepatitis B virus(HBV) X gene(HBX) 5' region that could be candidates for gene therapy.METHODS The study included 27 chronic hepatitis B treatmentnaive patients in vari... AIM To detect hyper-conserved regions in the hepatitis B virus(HBV) X gene(HBX) 5' region that could be candidates for gene therapy.METHODS The study included 27 chronic hepatitis B treatmentnaive patients in various clinical stages(from chronic infection to cirrhosis and hepatocellular carcinoma, both HBeA g-negative and HBeA g-positive), and infected with HBV genotypes A-F and H. In a serum sample from each patient with viremia > 3.5 log IU/m L, the HBX 5' end region [nucleotide(nt) 1255-1611] was PCRamplified and submitted to next-generation sequencing(NGS). We assessed genotype variants by phylogenetic analysis, and evaluated conservation of this region by calculating the information content of each nucleotide position in a multiple alignment of all unique sequences(haplotypes) obtained by NGS. Conservation at the HBx protein amino acid(aa) level was also analyzed.RESULTS NGS yielded 1333069 sequences from the 27 samples, with a median of 4578 sequences/sample(2487-9279, IQR 2817). In 14/27 patients(51.8%), phylogenetic analysis of viral nucleotide haplotypes showed a complex mixture of genotypic variants. Analysis of the information content in the haplotype multiple alignments detected 2 hyper-conserved nucleotide regions, one in the HBX upstream non-coding region(nt 1255-1286) and the other in the 5' end coding region(nt 1519-1603). This last region coded for a conserved amino acid region(aa 63-76) that partially overlaps a Kunitz-like domain.CONCLUSION Two hyper-conserved regions detected in the HBX 5' end may be of value for targeted gene therapy, regardless of the patients' clinical stage or HBV genotype. 展开更多
关键词 Hepatitis B virus Hepatitis B X gene Hepatitis B X protein Gene therapy Next-generation sequencing HBV conserved regions Small interference RNA
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Conformal invariance and conserved quantity of Hamilton systems 认领 引用 被引量：29
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作者 蔡建乐 罗绍凯 梅凤翔 《Chinese Physics B》 SCIE EI CAS 2008年第9期3170-3174,共5页
This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the c... This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration. 展开更多
关键词 Hamilton system conformal invariance determining equation conserved quantity
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Dissecting conserved cis-regulatory modules of Glu-1 promoters which confer the highly active endosperm-specific expression via stable wheat transformation 认领 引用 被引量：8
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作者 Jihu Li Ke Wang +7 位作者 Genying Li Yulian Li Yong Zhang Zhiyong Liu Xingguo Ye Xianchun Xia Zhonghu He Shuanghe Cao 《The Crop Journal》 SCIE CSCD 2019年第1期8-18,共11页
Wheat high-molecular-weight glutenin subunits(HMW-GS) determine dough elasticity and play an essential role in processing quality. HMW-GS are encoded by Glu-1 genes and controlled primarily at transcriptional level, i... Wheat high-molecular-weight glutenin subunits(HMW-GS) determine dough elasticity and play an essential role in processing quality. HMW-GS are encoded by Glu-1 genes and controlled primarily at transcriptional level, implemented through the interactions between cis-acting elements and trans-acting factors. However, transcriptional mechanism of Glu-1 genes remains elusive. Here we made a comprehensive analysis of cis-regulatory elements within 1-kb upstream of the Glu-1 start codon(-1000 to-1) and identified 30 conserved motifs. Based on motif distribution pattern, three conserved cis-regulatory modules(CCRMs), CCRM1(-300 to-101), CCRM2(-650 to-400), and CCRM3(-950 to-750), were defined, and their functions were characterized in wheat stable transgenic lines transformed with progressive 5′ deletion promoter::GUS fusion constructs. GUS staining, qP CR and enzyme activity assays indicated that CCRM2 and CCRM3 could enhance the expression level of Glu-1, whereas the 300-bp promoter(-300 to-1), spanning CCRM1 and core region(-100 to-1), was enough to ensure accurate Glu-1 initiation at 7 days after flowering(DAF) and shape its spatiotemporal expression pattern during seed development. Further transgenic assays demonstrated that CCRM1-2(-300 to-209) containing Complete HMW Enhancer(-246 to-209) was important for expression level but had no effect on expression specificity in the endosperm. In contrast, CCRM1-1(-208 to-101) was critical for both expression specificity and level of Glu-1. Our findings not only provide new insights to uncover Glu-1 transcription regulatory machinery but also lay foundations for modifying Glu-1 expression. 展开更多
关键词 Conserved cis-regulatory modules Glu-1 Transcriptional regulation Transgenic wheat Triticum aestivum
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Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style 认领 引用 被引量：27
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作者 贾利群 解加芳 罗绍凯 《Chinese Physics B》 SCIE EI CAS 2008年第5期1560-1564,共5页
This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The defini... This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results. 展开更多
关键词 Nielsen style unilateral nonholonomic constrained system Mei symmetry Mei conserved quantity
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Structure equation and Mei conserved quantity for Mei symmetry of Appell equation 认领 引用 被引量：23
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作者 贾利群 解加芳 郑世旺 《Chinese Physics B》 SCIE EI CAS 2008年第1期17-22,共6页
This paper investigates structure equation and Mei conserved quantity of Mei symmetry of Appell equations for non-Chetaev nonholonomic systems. Appell equations and differential equations of motion for non-Chetaev non... This paper investigates structure equation and Mei conserved quantity of Mei symmetry of Appell equations for non-Chetaev nonholonomic systems. Appell equations and differential equations of motion for non-Chetaev nonholonomic mechanical systems are established. A new expression of the total derivative of the function with respect to time t along the trajectory of a curve of the system is obtained, the definition and the criterion of Mei symmetry of Appell equations under the infinitesimal transformations of groups are also given. The expressions of the structure equation and the Mei conserved quantity of Mei symmetry in the Appell function are obtained. An example is given to illustrate the application of the results. 展开更多
关键词 Appell equation Mei conserved quantity Mei symmetry non-Chetaev nonholonomic system
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Mei Symmetry and Conserved Ouantity of Tzénoff Equations for Nonholonomic Systems of Non-Chetaev's Type 认领 引用 被引量：18
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作者 ZHENG Shi-Wang XIE Jia-Fang LI Yan-Min 《Communications in Theoretical Physics》 SCIE CAS 2008年第4期851-854,共4页
Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Suf... Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzenoff equations for the systems through Lie symmetry in the condition of special Mei symmetry is obtained. 展开更多
关键词 nonholonomic system Tzenoff equations Mei symmetry conserved quantity
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Conformal invariance and Hojman conserved quantities of first order Lagrange systems 认领 引用 被引量：19
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作者 陈向炜 刘畅 梅凤翔 《Chinese Physics B》 SCIE EI CAS 2008年第9期3180-3184,共5页
In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultan... In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given. Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results. 展开更多
关键词 first order Lagrange systems infinitesimal transformation conformal invariance Hojman conserved quantities
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A type of new conserved quantity deduced from Mei symmetry for Appell equations in a holonomic system with unilateral constraints 认领 引用 被引量：9
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作者 贾利群 解银丽 +1 位作者 张耀宇 杨新芳 《Chinese Physics B》 SCIE EI CAS 2010年第11期48-52,共5页
A type of new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints is investigated. The expressions of new structural equation and new conserved quantity ... A type of new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints is investigated. The expressions of new structural equation and new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results. 展开更多
关键词 unilateral constraint Appell equation Mei symmetry conserved quantity
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Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems 认领 引用 被引量：18
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作者 姜文安 李状君 罗绍凯 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第3期14-20,共7页
This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of m... This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation, the determining equations, the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed. The criterions of Mei symmetries, weak Mei symmetries and strong Mei symmetries of the system are given. New types of conserved quantities, i.e. the Mei symmetrical conserved quantities, the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system, are obtained. Then, a deduction of the first-order nonholonomic system is discussed. Finally, two examples are given to illustrate the application of the method and then the results. 展开更多
关键词 higher-order nonholonomic system Mei symmetry Mei conserved quantity
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Symmetry and Hojman Conserved Quantity of Tznoff Equations for Unilateral Holonomic System 认领 引用 被引量：16
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作者 ZHENG Shi-Wang XIE Jia-Fang JIA Li-Qun 《Communications in Theoretical Physics》 SCIE CAS 2007年第7期43-47,共5页
Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformationsof groups is investigated.Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tz... Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformationsof groups is investigated.Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tzénoffequations are given.Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given.Hojman conserved quantity of Tzénoff equations for the system above through special Lie symmetry and Lie symmetryin the condition of special Mei symmetry respectively is obtained. 展开更多
关键词 unilateral constraint Tzénoff equations symmetry Hojman conserved quantity
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Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints 认领 引用 被引量：10
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作者 JIA Li-Qun ZHANG Yao-Yu +1 位作者 CUI Jin-Chao LUO Shao-Kai 《Communications in Theoretical Physics》 SCIE CAS 2009年第10期572-576,共5页
Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomi... Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomie mechanic systems with unilateral constraints axe established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups axe also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results. 展开更多
关键词 holonomic system with unilateral constraints Appell equation structural equation of Mei symmetry Mei conserved quantity
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A new type of conserved quantity of Mei symmetry for the motion of mechanico electrical coupling dynamical systems 认领 引用 被引量：16
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作者 赵丽 傅景礼 陈本永 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第4期1-4,共4页
We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico--electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-elec... We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico--electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico-electrical coupling dynamical systems is obtained. Finally, an example is given to illustrate the application of the results. 展开更多
关键词 new conserved quantity Mei symmetry mechanico-electrical coupling systems
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Mei Symmetry and New Conserved Quantities of Tzénoff Equations for the Variable Mass Higher-Order Nonholonomic System 认领 引用 被引量：6
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作者 ZHENG Shi-Wang WANG Jian-Bo +1 位作者 CHEN Xiang-Wei XIE Jia-Fang 《Chinese Physics Letters》 SCIE EI CAS CSCD 2012年第2期1-4,共4页
Operational systems of spacecraft are general variable mass mechanics systems,and their symmetries and conserved quantities imply profound physical rules of the space system.We study the Mei symmetry of Tzénoff e... Operational systems of spacecraft are general variable mass mechanics systems,and their symmetries and conserved quantities imply profound physical rules of the space system.We study the Mei symmetry of Tzénoff equations for a variable mass nonholonomic system and the new conserved quantities derived.The function expression of the new conserved quantities and the criterion equation which deduces these conserved quantities are presented.This result has some theoretical values in further research of conservation laws obeyed by the variable mass system. 展开更多
关键词 quantities conserved symmetry
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Conformal Invariance and a New Type of Conserved Quantities of Mechanical Systems with Variable Mass in Phase Space 认领 引用 被引量：5
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作者 ZHANG Ming-Jiang FANG Jian-Hui +2 位作者 LIN Peng LU Kai PANG Ting 《Communications in Theoretical Physics》 SCIE CAS 2009年第10期561-564,共4页
Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied.Firstly,the definition and determining equation of conformal invariance are presented.The... Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied.Firstly,the definition and determining equation of conformal invariance are presented.The relationship between the conformal invariance and the Lie symmetry is given,and the necessary and sufficient condition that the conformal invarianee would be the Lie symmetry under the infinitesimal transformations is provided.Secondly,a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system.Lastly,an example is given to illustrate the application of the results. 展开更多
关键词 conformal invariance conserved quantity variable mass system phhse space
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The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems 认领 引用 被引量：11
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作者 施沈阳 傅景礼 陈立群 《Chinese Physics B》 SCIE EI CAS 2008年第2期385-389,共5页
This paper investigates the Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems. The variational principle of discrete mechanics, from which discrete motion equations of sys... This paper investigates the Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems. The variational principle of discrete mechanics, from which discrete motion equations of systems are deduced, is generalized to the case of including the time variational. The requirement for an invariant group transformation is defined to be the Lie symmetry and the criterion when the Noether conserved quantities may be obtained from Lie symmetries is also presented. An example is discussed for applications of the results. 展开更多
关键词 discrete mechanics total variational principle Lie symmetry discrete conserved quantity
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